Production and Transport of Oil and Gas- Part a- Flow Mechanics and Production

Developments in Petroleum Science, 18 APRODUCTION AND TRANSPORT OF OIL AND GAS Second completely revised edition PART A Flow mechanics and production by A. P. SZILAS Professor of Petroleum Engineering Petroleum Engineering Department Mi,skolc Technical Univer.sity,/or Heavy Industries, Hungary ELSEVIER Amsterdam-Oxford-New York-Tokyo 1985 Joint edit~onpublished by Elsevier Science Publishers, Amsterdam, The Netherlands and Akadkmiai Kiad6, the Publishing House of the Hungarian Academy of Sciences, Budapest. Hungary First English edition 1975 Translated by B. Balkay Second revised and enlarged edition 1985 Translated by B. Balkay and A. Kiss The distribution of this book is being handled by the following publishers for the U.S.A. and Canada Elsevier Science Publishing Co., Inc. 52'Vanderbilt Avenue, New York, New York 10017, U.S.A. for the East European Countries, Korean People's Republic, Cuba. People's Republic of Vietnam and Mongolia Kultura Hungarian Foreign Trading Co., P.O.Box 149, H-1389 Budapest, Hungary for all remaining areas Elsevier Science Publishers Molenwerf 1. P.O.Box 21 1, 1000 AE Amsterdam, The Netherlands Library of Congress Cat.logiog Data Szilas, A. PHI. Production and transport of oil and gas. (Developments in petroleum science; 18A-) Translation of KGolaj i s foldgbtermeles. 1. Petroleum engineering. 2. Petroleum-Pipe lines. 3. Gas, Natural-Pipe lines. I. Title. 11. Series. TN870.S9413 1984 62T.338 84-13527 ISBN W 9 9 5 9 8 - 6 (V. 1) ISBN w 9 9 5 6 4 - 1 (Series) 0Akadhniai Kiado, Budapest 1985 Printed in Hungary Preface TO THE SECOND EDITION The material of the first edition is considerably revised in this second two-volume edition. The changes can be ranged in three groups: I wished to take into account the latest developments in the world oil industry and incorporate the latest research of my Institute; I have modified some chapters to make it easier for readers to cope with the material; the field of trade, as indicated in the title is more consciously determined, and therefore the content and length of some chapters - primarily in the second volume - are changed. It would be a great pleasure if through this work I could contribute to the acceptance of the "production and transport of oil and gas" as a specific field of science and technology of oil and gas "mining". I should like to express my sincere gratitude to my co-workers who participated in the preparation of this work. First of all, I wish to emphasize the assistance of Mr. Gabor Takacs and his always helpful contributions. The high quality work on the figures was done by Mrs. ~ v Szota. a Ms. Piroska Polyinszky, the editor, took upon herselftheexacting task ofproof-reading the text. Last but not least I wish to express my special thanks to my wife, Mrs. Elisabeth Szilas. She showed patience and goodwill towards my having spent years on the rewriting of my book and she was my untiring helper in preparing the manuscript. The Author Preface TO THE FIRST EDITION Oil and gas production in the broad sense of the word can be subdivided into three more or less separate fields of science and technology, notably (1) production processes in the reservoir (reservoir engineering), (2) production of oil and gas from wells, and finally (3) surface gathering, separation and transportation. The present book deals with the second and the last of the three topics. Chapter 1 reviews those calculations concerning flow in pipelines a knowledge of which is essential to the understanding and designing of single-phase and multiphase flow in wells and in surface flow lines. In compiling Chapters 2-5, which deal with oil and gas wells and in the treatment of those subjects, I have followed the principle that the main task of the production engineer is to ensure the production of that amount of liquid and/or gas prescribed for each well in the field's production plan, at the lowest feasible cost of production. The technical aim outlined above can often be attained by several different methods of production, with several types of production equipment and, within a given type, with various design and size of equipment; in fact, using a given type of equipment, several methods of operation are possible. Of the technically feasible solutions, there will be one that will be the most economical; this, of course, will be the one chosen. I have attempted to cover the various subjects as fully as possible, but have nevertheless by-passed certain topics which are treated in other books, such as the dynamometry of sucker rod pumps and gas metering. A discussion of these topics in sufficient depth would have required too much space. Chapter 6 deals with the main items of surface equipment used in oil and gas fields. In this case, I have also aimed at conveying a body of information setting out the choice of the technically and economically optimal equipment. Equipment is not discussed in Chapters 7 and 8 which treat the flow of oil and gas in pipelines and pipeline systems. The reason for this is that comparatively short pipelines are encountered within the oil or gas field proper, and the relevant production equipment is discussed in Chapter 6; on the other hand, it seemed reasonable to emphasize the design conception which regards the series-connected hydraulic elements of wells, on-lease equipment and pipelines as a connected hydraulic system with an overall optimum that can be and must be determined. It 12 PREFACE should be emphasized, however, that this method of designing also requires a knowledge of rheology. Naturally, in the treatment of each subject I have attempted to expose not only the "hows" but also the "whys" and "wherefores" of the solutions outlined. It is a regrettable phenomenon, and one which I have often found during my own production experience and in my work at the University, that the logical consistency as well as the economy of the solution adopted will tend to suffer because the design or production engineer is just following "cookbook rules" without understanding what he is actually trying to do. An understanding of the subject is a necessary critical foundation, and this is a prime reason of textbooks and handbooks. In denoting physical quantities and in choosing physical units I have followed the SI nomenclature. In choosing the various suffixes to the symbols used in this book, the wide range of the subjects covered has necessitated some slight deviations from the principle of "one concept - one symbol". I sincerely hope that such compromises, adopted for the sake of simplicity, will not create any difficulties for the reader. In compiling the present volume and in its preparation for publication I have been assisted by many of my co-workers at the Petroleum Engineering Department of the Miskolc Technical University of Heavy Industries. I am deeply grateful for their cooperation, without which the present book, a compendium of three decades' production and teaching experience, could hardly have been realized. Among them I wish to give special credit to Ferenc Patsch, Jr., who played a substantial part in the writing of Chapter 8, to Gabor Takhcs and Tibor Thth, both of whom gave a great deal of help in the calculation and correction of the numerical examples in Chapters 1-7, and to Mrs. E. Szota for her painstaking work concerning the figures. The Author List of symbols and units for frequently used physical quantities acceleration temperature distribution factor weight reduction factor for sucker-rod string pipe diameter rate of shear in pipe Fanning friction factor acceleration of gravity height permeability length pumping speed exponent of "power law" or productivity equation pressure fluid flow rate radius polished rod stroke length time, time span temperature flow velocity well completion factor gas deviation factor cross-sectional area volume factor coefficient of gas well's productivity equation rate of shear modulus of elasticity force, load, weight unit weight of column head capacity productivity index of oil well Coberly factor LJST OF SYMBOLS length, depth torque molar mass mass factor dimensionless number power universal molar gas constant volumetric ratio of fluids dimensionless slippage velocity temperature volume work, energy angle of inclination, angular displacement specific weight cross-sectional fraction efficiency dynamic factor for sucker-rod pumping ratio of specific heats Weisbach friction factor thermal conductivity factor dynamic viscosity kinematic viscosity dimensionless pressure gradient density normal stress, strength geothermal gradient shear stress angular velocity, cycle frequency - W J/kmole K m3/m3 - K m J rad, " N/m mZ/m2 - FREQUENTLY USED SUBSCRIPTS Subscript Meaning allowable bubble-point critical opening, choke fluid friction flowing, producing gas inside Example allowable stress bubble point pressure critical pressure diameter of valve port fluid flow rate pressure drop to friction flowing bottom-hole pressure of well gas rate inside cross-sectional area of pipe LIST OF SYMBOLS k m m max min n a a opt P P r S S mixture UP motor Pm mass urn maximal Fmax minimal Fmin standard state P" outside do oil 40 optimal dopt plunger A, Pump LP rod A, polished rod Fs superficial (only for symbols v, first letter) us, slippage (only for symbol v,, second subscript) Bt multiphase well Lw water qw casing PC valve dome TD depth PL tubing PT surface, wellhead PTO 15 mixture flow velocity motor power mass flow velocity maximum load minimum load standard pressure outside diameter of pipe oil flow rate optimal pipe diameter plunger's cross-sectional area pump setting depth cross-sectional area of rod polished rod load superficial gas velocity gas slippage velocity multiphase volume factor well depth water rate casing pressure valve dome temperature pressure at depth L tubing pressure surface tubing pressure OTHER SYMBOLS A - difference (before symbol) average (above symbol) Ap P pressure difference average pressure CHAPTER 1 SELECTED TOPICS IN FLOW MECHANICS 1.1. Fundamentals of flow in pipes Pressure drop due to friction of an incompressible liquid flowing in a horizontal pipe is given by the Weisbach equation: v21p A p f = I-, 2di where v = q/A. If the Reynolds number is less than about 2000-2300, then flow is laminar, and its friction factor I is, after Hagen and Poiseuille, For turbulent flow in a smooth pipe, for NRe< lo5, the Blasius formula gives a fair approximation: Likewise for a smooth pipe and for Nu,> lo5, the explicit Nikuradse formula is satisfactory: A.=0-0032+0.221~R;0'~~~. 1.1 -5 The Prandtl-Karman formula is valid over the entire turbulent region but its implicit form makes it difficult to manipulate. In rough pipes, for the transition zone between the curve defined by Eq. 10 is that they do not provide a satisfactory accuracy beyond a NRe range broader than just two orders of magnitude.l .6 and the so-called boundary curve (cf. NRe by a formula which differs from Eq. 1.1 . to be calculated using Eq.. If we have an idea of the relative roughness to be expected.1 .8 provide results sufficiently accurate for any practical purpose. .3 and from 1. Consider e. The drawback of formulae of type 1.8 are illustrated in the Moody diagram shown as Fig. then we can characterize the relationship A v.1 . range is the Supino formula where A. Prandtl and Khrman give the relationship Although Eqs 1.g.12) the Colebrook formula gives Also for rough pipes.10 where a and b are constants characteristic of the actual value of relative roughness and of the NRerange involved. 1.1 .1. In the transition zone 1depends both on the relative roughness k/di and on N R e ..b.1 . The dashed curve in the diagram is the boundary curve that separates the transition zone from the region of full turbulence.6 to f . but for the zone beyond the boundary curve. in order to avoid the cumbersome implicit equations. The graphs of Eqs 1. Explicit formulae can be derived from the following consideration.5. the formula of this type of Drew and Genereaux (Gyulay 1942): Short sections of the graph of this function can be approximated fairly well by an exponential function A=aN.1 -6 only in its constants.1 -4 or 1.1 . A relationship that is somewhat more complicated but provides a fair approximation over a broader N.1.1..18 1. SELECTED TOPICS 1N FLOW MECHANICS 1.1 .1 . Eq. 1. other formulae are often used to determine the pressure drop of turbulent flow in rough pipes. is the friction factor of smooth pipe. 1. 1.7 and 1. At the temperature and pressure prevailing in the fluid. for which k/di=0. v=2.00017. Friction factor in pipes. v = 2-5 x m2/s.1 . Let us find the friction pressure drop of oil flowing in a horizontal pipeline I = 25 km long. di = 0. The equation of the boundary curve is Example 1.00017. FUNDAMENTALS OF FLOW I N PIPES 6810'12 3 4 6 8 0 ' 1 2 3 C 5 . The pipeline is made of seamless steel pipe.1. p=850 kg/m3.3 m. 3 0 ' 1 2 3 4 68KJ812 3 4 6 8 0 ' 1 2 3 4 N R ~ 19 6. k/di=0.000 m. q = 0. we have 1= 25. Converting the data of the problem to SI units.310~ Fig. Flow velocity is and 2* .075 m3/s. according to Moody whereas in the region of full turbulence it is a function of k/di alone.I.300 m.1 .5 cSt and p=850 kg/m3. q = 270 m3/h. 1 . 1.1. if di =0. I ) reveals that for k/di=0. substitute di by the equivalent pipe diameter. 1 ..1-5: Using in further computation the value 1=0. for the case in hand. = 2300.1 for the flowing pressure drop The pressure drop of flow in spaces of annular section can be determined as follows.. A=0.1. d. 1 .018 we get by Eq.1 -7 and the definitive value of 1 can be found using that equation. 1 .=4 x wetted cross section wetted circumference ' For an annular space. 1 . however. The Moody diagram (Fig. 1 .7 holds. 1 .1 thus modifies to . 1 . Let us calculate the friction factor also from Eq. SELECTED TOPICS I N FLOW MECHANICS Flow is turbulent because 1. and hence.27 x 10' is greater than the critical Reynolds number. Eq.. 1 . 1.flow is in the transition zone where Eq. The procedure is rather insensitive to the error of reading off the diagram. 1 . If a more accurate value is required (which is. In Eq.00017. the value of 1 thus read off the diagram may be put into the right-hand side of Eq. d. N. 1. In the case in hand. In a general way. usually rendered superfluous by the difficulty of accurately determining relative roughness). where d l is the ID of the outer pipe and d 2 is the OD of the inner pipe. 1 . It enables us to read off directly that.. then. using a A. 1.1 . furnished by Eq.20 I .1 1 .018. where For turbulent flow. but E.1 .~ ~ 1.1 . = 0 . . the friction factor is given t o a fair enough accuracy by (Knudsen and Katz 1958). however.5 and N R e =lo5.=0. According to Deyssler and Taylor. = 2 0 0 0 .15. for N. 3 0 4 ~ . the friction factor decreases with increasing eccentricity (Knudsen and Katz 1958). If for instance r2/rl = 3. no satisfactory result is to be expected except when the walls can be regarded as hydraulically smooth.... In that case. = 7 0 0 the actual friction factor will deviate from the value valid for laminar flow given by Eq. Quite often the inner pipe is eccentrical within the outer pipe. belonging to maximum velocity. then I=0. Let us define eccentricity as the ratio of the distance between pipe centres to the difference between radii: The decrease in friction factor may be appreciable.1. Full turbulence sets in at N.1. will develop gradually. The relationships derived by these authors imply.. starting according to Prengle and Rothfus (Knudsen and Katz 1958) at the point of maximum velocity. 0 '. The limit between laminar and turbulent flow is at approximately N R .16 NRe is to be computed using the hydraulic diameter (dl -d2). = 2200. 1.014 for e=1.019 for e=0. FUNDAMENTALS OF FLOW IN PIPES For laminar flow. the formula where Even at N R e . according to Knudsen and Katz (1958): 3.. . Turbulent flow. together with the boundary conditions p=p. we get This equation has a variety of solutions. Then dh = sin adl. Substituting the above expressions of p and v into Eq. Gas flow in pipes 1. the energy spent in accelerating the gas flow is relatively smaI1. the mean values in question are constant all along the pipeline. vdu = 0. Then Let the pipe include an angle a with the horizontal. SELECTED TOPICS IN FLOW MECHANlCS 1. The energy equation valid for steady flow will thus hold for infinitesimal lengths of pipe dl only when the pressure differential between the two ends of the infinitesimal section dl is dp.2.2.1. also z = Z and A = 2 i. The solutions of the equation will depend on the function used to describe the variation of z and A v. T= T. if 1=0 and h sina=-=const. or to have a constant mean temperature.2-2: . 1 leads to the following solution of Eq. 1. p and 7:In most formulae used to describe steady flow it is assumed in practice that.. 1.2.1.I .. in an approximation satisfactory for practical purposes. This assumption. it is therefore usual to assume that. Fundamentals The density and flow velocity of a gas flowing in a pipe will significantly vary along the pipeline as a result of temperature and pressure changes. The general gas law yields and Most often. The flow is in most cases assumed to be isothermal. and rearranging.e. in addition to T= T. 2. 1. we get Introducing the value of I given by Weymouth's Eq.2 .2-2 then yields for the horizontal pipeline. as in Eq. = 1. T= T.1 m.9 let us find the gas flow rate in a horizontal pipeline if T. GAS FLOW IN PIPES R is 8315. I = X and 1=0 if p =p . p. 1.1 bars. let g=9. One of the most widely used formulae was written up by Weymouth: It gives rather inaccurate results in most cases. : Substituting R=8315 and the numerical value of n/4. we get Example 1. =0. 1. p. assuming.013 bars. X is expressed in a variety of ways. the elevation difference h between the two ends of the pipeline can be neglected. Using Eq. Eq. Substituting this I for Xin 1.=288-2K. p2 = 2.2-5 we arrive at the widely used formula Solving for gas flow rate. = 44.2. T . z =2.2 -4.I . 1. then and hence.1.9 bars.2 -4 we get In a gas pipeline laid over terrain of gentle relief. d.8067. 1 x 105+2. The Reynolds number figuring in Eq. = 4. The gas flow rate sought. 1.1 .44 M Pa = 44. In the foregoing Example we have had p . let us first calculate by Eq.24 I.1 . and hence Consequently.1 bars.10 rather than from the Weymouth formula. 1 = 15 kms. In Eq. T.10 is where .= 207 K. In order to find i.90. p .7 bars. = 46. An input pressure higher by 0 3 bar is thus required to overcome the elevation difference of 150 m if the gas flow rate of 2. Using Eq. 1. Figure 8. Eqs 8.2 yields Z=0. 1. and the reduced parameters p.3 and 8. = 0-63 and T.9x lo5 According to Diagram 8-1.= I . M = 18.33 (cf. 44.1 p.1 .3. =44. SELECTED TOPICS I N FLOW MECHANICS = 275 K.4 bars . 1.2-6.2. Equation 1.383 m3/s is to be maintained. 1.26 an approximate mean pressure p in the pipeline: I (2.1 -4).9 x 105)~ =29-5 x 10' P a .2.2-7 becomes a more accurate tool of computation if ilis taken from Eq.2-2. find the input pressure in the pipeline of the foregoing Example provided the output end of the pipeline is situated higher by h= 150 m than its input end.82 kdkmole. Example 1.1 . 1 .10. where. For instance.qnM diT.1 .2. 1. = 1.2 .1 . obviously.2-7 we obtain the following general relationship for the calculation of q. we get N Re- 1 7c -R 4 p. range only.33.6 and 8.121 and b =0. Substituting the expressions for v.13 and the data of Example 1. Substitution into 1.7: p= Hence.10 and replacing the result into Eq. 1. GAS FLOW IN PIPES and-the general gas law yields - P= Mp and q=+. p q iT PZn T. . A given set of constants will yield friction factors of acceptable for a given N. the numerical values of the constants a and h depend on the pipe diameter. P and q into the fundamental equation and assuming that zn= 1 in a fair approximation.63 and T.2. a =0.3.2 . Find the gas flow rate in a horizontal pipeline using Eq. = 0.15. we read off Diagrams 8. 1 0 p Pas.ji Substituting this into Eq.11 yields Example 1.1 . For a given roughness..1. 1. Using the known values p.: The various formulae used in practice to express A are all of the form 1.1.2 . There are however.At high Reynolds numbers.T z and A along the string (Aziz 1962-1963).1 -6. The region of turbulent flow can be characterized by two types of equation. the calculation method of Cullender and Smith permits us to determine accurately the pressure drop of flow in a vertical string. bends. .1 -8) is to be used in any given case can be decided by finding the value of N.5 and 1 to be constant all along the flow string.. more abrupt than in the case of the curves illustrating the Colebrook Formula 1. The first of these is the modified 'smooth-pipe' Equation 1. The latter can be calculated to a satisfactory degree of accuracy using Eq. 1. and A. formulae that account also for changes of .1-7. SELECTED TOPICS I N FLOW MECHANICS The values furnished by the two formulae are seen to differ rather widely: &= 3. The temperature is estimated from operational data. The transition between them is appreciably shorter. Its main cause is the considerable flow resistance due to pipe fittings. bends and breaks and weld seams in actual pipelines. A careful consideration of the suitability of any formula selected for use is essential. which can be calculated for any given value of NR.26 I .7 percent 3-00 .. has a decisive influence on the friction factor. the relative roughness k / d . A useful basis for such considerations is a series of tests carried out at the Institute of Gas Technology (Uhl 1967a). breaks and weld seams per unit length of pipe. The question as to which of the two equations (1. which can be written to read .2-2. The calculation is based likewise on Eq.38 100 = 20. valid for relatively low Reynolds numbers: where 5 is a resistance factor accounting for the fittings. These tests have revealed a considerable difference between pipe in the laboratory and in the field.14 or 1. is the friction factor for smooth pipe.8. which tend to bring about a modification of the Moody diagram.2. 1. Approximate values are given in a diagram by Uhl (1967b). The two equations respectively characterize the transition and fully turbulent regions. Among them.00 . We have so far assumed the mean values T.. that satisfies both equations simultaneously: Determining the value of 5 requires in-plant or field tests.1 .2. by means of PI + P 2 . the tubing in a gas well) we get. .1. I. Then. is computed in a similar way.2-18. The accuracy of the procedure can be improved by correcting the value of p. Eqs 1. 1. 1.2-20 yield In a first approximation. To solve any practical problem it is usually sufficient to assume only one intermediate pressure p. at 2 . GAS FLOW IN PIPES 27 Integrating between the limits 1=0.1.g.2-20 PZ Computation proceeds as follows. formally PZ where The integral can be evaluated by a successive approximation.2. p=p2 characterizing the vertical string (e.which is used to improve I. . starting from p. one first computes the pressure for the half-length of the vertical string. and l = L . using Eq.2-17 and 1.P z ) ( ~ z + ~ ~ ) + @ I . . For the half-length of the string. In a general way. Starting from the surface (wellhead) pressure. 1.This value can be computed using Eq.p.P ~ ) ( ~ + ~ I ) ~ .2 . then i I dp= 1 [ ( P ~ . p = p . Eq. one then computes the bottom-hole pressure. The successive approximation is continued until pk 'returns' with a satisfactory accuracy.. the Simpson formula.2 -21 then yields a first approximation ofp.18. using the value of I. using this latter. . = I . T= 288 K.2 .2. Find the gas flow rate in a pipeline if di=0. 1.1. Substituting into 1.2-9 we get + A similar formula. 1. 1 =420 m Ap Pa. T. p.2-4.g. can be determined by the above formulae.= --28. Let p.3. 1.01 3 bars. Pressure drop of gas flow in high-pressure pipes The gas pressure at various sections of pipelines. A pressure traverse can thus be established.= 288. For the pipeline sections AB and BC in Fig.= 1.23.) x 2p. = 2943 and by Eq. f = I and ( p . e. is an arithmetic or logarithmic mean estimated from operational measurements.)=Ap. SELECTED TOPIC'S I N FLOW MECHANICS The friction factor may be computed from whichever formula is deemed most suitable. 1.28 I . by assuming that the mean value z = 5of the compressibility factor is constant all along the pipeline (Smirnov and Shirkovsky 1957).2-8. -p. 1.= 2-026 bars. it yields with coefficients expressed in M the SI system. is that of Pole (Stephens and Spencer 1950). ( p .2 -24. 1.2. approximately by Eq.2. By Eq. which was used in American practice as. Eq.early as the last century. An approximate pressure traverse can also be derived more simply. 1. M = 18-82 kg/kmole.0266 m.2 K. Pressure drop of gas flow in low-pressure pipes The pressure drop of low-pressure gas flow can be calculated by means of the formulae discussed above but there exist simpler formulae that are just as satisfactory in most cases.2.96 ' Example 1. and with y. T. located at arbitrary distances from the input end.2-9 yields . GAS FLOW IN PIPES P bors w = h 1 Fig. pxl = ((50x 10')' .25.3 etc. Pressure traverse of a horizontal high-pressure gas pipeline and respectively. Let p . The specific energy consumption of gas flow is thus lower at higher pressures.1.2-5.2. -(2 x 105)2]0.2-25 provided the pressures p . Then.2 . . 1. prevailing at the two ends of the pipeline are known.5 =41. The value of grad p is seen to be significantly higher at lower pressures.4 x 10' Pa .1. Example 1. These two equations imply and hence Pressure at a pipe section situated at a distance of x < 1 from the input end of the pipeline can be computed using Eq. Greater gas flow rates are thus revealed to be more economically feasible at higher pipeline pressures.8 x 10' Pa etc. The pressure line p=f(x) connecting the points thus computed is shown in Fig.1)0'5 =47.1. and p. 1. Establish the pressure traverse.2 . Let x.[(50 x px2 = ((50x 10')'-[(50 x 10')'-(2 x 105)2]0. =0-1.2. 1. x2 = 0. 1. by Eq. = 50 bars and p2 = 2 bars.3)0. 2 km.1541 m.1.2 K. (b) Time-dependent fluids.2. whose viscosity is constant at a given pressure and temperature. 1. 1= 36. and M = 17.2 . Substitution of the values thus found into Eq. SELECTED TOPICS IN FLOW MECHANICS 1. (a) Purely viscous or time-independent fluids. we obtain Example 1.6. Classification of fluids in rheology Fluids fall by their rheological properties into the following groups.= 288. p.I .2 K. T = 277. whose . T. as well as non-Newtonian fluids in the strict sense.013 bars. whose apparent viscosity is a function of shear stress.2-27 yields 1.1 -2.38 kg/kmole.3. Mean pressure in gas pipes The mean pressure in a gas pipeline is: 1 Substituting for px the approximate value given by Eq.2 . Assuming z.25 and solving for p. = 1. = 50 bars. 1. whose viscosity is independent of the duration of shear. 1. the mean pressure in the pipeline is From diagram 8. Find the volume. we read Y=089. The group includes Newtonian fluids.3. Flow of nowNewtonian fluids in pipes 1. in standard cubic metres of the gas contained in a pipeline if p. the combined gas law gives and By Eq.4. di= 0. p2 =25 bars.2-26. = 1. #O and n = I .3-2. Flow curves of the types of fluid listed above are shown in Fig. 1. in 1. Let us note that in the subsequent equations factor p' of Eq. 1. &ibiting several of the properties of groups (a). (b) and (c). Porst. For a laminar flow in a pipe This relation is the so-called power law of Ostwald and De Waele. The flow 'curve' of a Newtonian fluid is the straight line A.3. By non-Newtonian fluids in the broader sense one means all fluids except the Newtonian ones.1. denoted p.1. as dynamic viscosity. 1. = 0. and finally as plastic or differential viscosity. (c) Viscoelastic liquids. in Eq.3. If T. The more important formulae are shown in Table 1. denoted p". which can be used to characterize the behaviour of some pseudoplastic (1 > n > 0) and dilatant (n> 1) fluids.3 .3. (a) Purely viscous fluids To describe the flow curves of purely viscous fluids several mathematical models of phenomenological character may be used. The most widespread of them is the model created by Herschel].1. Flow curves illustrate the variation of shear stress v. in 1. this relationship simplifies to the equation in the case of Newtonian fluids. also called Bingham plastics. Flow properties are characterized by flow curves or sets of such.3. then This relationship is characteristic of plastic fluids.1 turns up as a flow factor. Beside the "power law" shown in Eq. starting from the origin of coordinates.3 . The oil industry most often has to deal with fluids of groups (a) and (b). T.3-2 other formulae are also used to model mathematically the flow curve of the pseudoplastic fluids. The significance of the different descriptions generally lies only in the fact that between the related points T and D of . denoted p'.3-1. 1. in 1. whose apparent-viscosity is a function of both the shear stress and the extent of deformation. If. FLOW OF NON-NEWTONIAN FLUIDS IN PIPES 31 apparent viscosity depends in addition to the shear stress also on the duration of the shear. then D is the absolute value of the rate of shear. At n = 1. Moskowitsch and Houwink. shear rate.4.3. (d) Complex rheological bodies. =ax Skelland (1967) Powell-Eyring Skelland (1967) Ellis Skelland (1967) Sisko Meter Sisko (1958) p=a+hxD'"-" p=pm + Po-/& ----1 +(T/T. D in Fig.3. likewise starts from the origin of coordinates. but its slope decreases as the deformation rate increases. in certain cases one curve.g0. is concave upward. The apparent viscosity thus increases as the shear rate increases. may be due to several causes. 1.5+h sinh1(. with their major axes in the direction of shear.valid at a given shear D rate. The flow curve of dilatant fluids.5=a Casson (1959) . 1. and even those few oils of this type have flow curves of insignificant curvature.3. . The term apparent Z viscosity (pa)means for any non-Newtonian fluid the ratio .3.3-1.. can be applied with the proper accuracy in a longer run. B in Fig. Dilatant behaviour is rare in crude oils. The characteristic behaviour ofpseudoplasticfluids. so the apparent viscosity of the system increases. The typical flow curve. Commonly used formulae for rheological models Author Herschell-Bulkley Casson Prandtl-Eyring Equation References Govier-Aziz (1973) 7-r. and in other cases the other curve.3-1. The best known is the Ostwald-de Waele formula. Dilatant behaviour is often encountered in wet sand whose properties were also studied by Reynolds himself. 1. shown in Eq.)("-" Meter-Bird (1964) Note: descriptions of the parameters used in the above equations can be found in the references cited.1. SELECTED TOPICS I N FLOW MECHANICS Table 1. One simple interpretation of this behaviour is that in a liquid phase (serving as a dispersing medium) a solid dispersed phase of asymmetric particles is contained and shear will impress upon these randomly orientated particles a preferred orientation. This preferred orientation will reduce the apparent viscosity. which is a "power law" formula and which will also be used in the present study to interpret the pseudoplastic flow curves.) . so that the error due to regarding them as Newtonian and their flow curves as linear when calculating pressure drops is also insignificant (Govier and Ritter 1963).=axDK r0. the given crudes.32 I. calculated by different methods.. Increase of shear results in a progressive volume increase (dilatation) of the dispersed system because some of the moving sand grains enter into direct contact without a lubricating liquid film between them. orfluids of structural viscosity. 3. called rheopectic. with paraffins of lower melting point depositing on crystal nuclei formed at higher temperatures. the flow curve of any D Fig.= r >O.H2.. Flow curves are difficult to establish at very low shear rates. These paraffins include normal straight-chain paraffins and branched isoparaffins of the general formula C. Little is said in literature about the causes of plastic behaviour. These causes are probably similar to those governing pseudoplastic flow. The thixotropic-pseudoplastic flow properties are brought about by dissolved paraffin molecules of very diversified composition found in oils at high temperature.. According to Metzner. monocyclical paraffins of the general formula C. A decrease in temperature will always result in the formation of mixed crystals. 1. iwery steep and very close to the shear-stress axis. (b) Time-dependent fluids The time-dependent fluids whose apparent viscosity under a constant shear stress decreases with stress duration are called thixotropic. .3.1.+. describing behaviour at low deformation rates. FLOW OF NON-NEWTONIAN FLUIDS IN PIPES 33 The flow curve of a plastic fluid or Bingham plastic is a straight line whose intercept on the shear-stress axis is z. It is debatable whether the observation that the flow curve intersects the shear-stress axis at a finite positive value is correct. (a yield stress) is required for flow to start at all.H. In oil-industry practice. and those of increasing viscosity are. plastic (C) and dilatant (D) fluids Bingham plastic can in fact be substituted by two intersecting straight lines.1. for instance. it is improbable that any real fluid should support a shear stress for an indefinite time without displacement (Longwell 1966). This means that a shear stress equal to 7 . the first type is of considerable importance. Presumably. pseudoplastic (B). which begin to separate out in solid state during cooling. thereby modifying . Flow curves of Newtonian (A). one of which. and polycyclical paraffins described by other formulae. as a number of crudes tend to exhibit thixotropicpseudoplastic behaviour. Rheological behaviour is significantly affected by those paraffins that constitute a solid or a colloidal dispersed phase in oil in the temperature range between 0 and 100 "C. they keep the asphaltenes in solution by their peptizing influence. Under the effect of differences in velocities of the laminar flow established in an annular or circular space. called shell-basis. breaks down as a result of shear effect under isothermal conditions but. The essence of this theory is as follows. link those having the same duration of shear (Fig. The shape "pattern" of the lattice in an annular cylinder shell with good approximation corresponds to the cylinder-section of the original spacelattice. During the latest research work of the author. Under the effectof friction. The macroscopic structure of the separated paraffins may vary appreciably also with the rates of cooling. Slow cooling gives rise to tabular. Along the generatrix of the annular cylinders. from among several values of shear stress obtained at a constant rate of shear. This is determined by the cross-sectional dimensions of paraffin-filaments. After time A t the realization frequency of bonds dividing and uniting under the effect of shear will be the same and apparent viscosity typical of flow properties is stabilized. The three-dimensional paraffin network may be significantly modified by. crude oil decays into coaxial cylinders of thickness Ar. Its essence is that the paraffin network.and second-order chemical reactions. the crystals in favoured places will try to unite. only tangentially to the normal cross-section. which could not be accounted for earlier. It is the gridshell theory that seems adequate to interpret these phenomena. shells no shear effect is produced.34 I . The phenomenon is well characterized by isochronous flow curves. whereas other solids affect it to lesser extent. Rapid cooling produces a multitude of small independent crystal grains. Some significant and explainable features are: . which rotates at a different rate. The system can resist shear effect best in an undisturbed condition with the resistance decreasing as the network breaks down. SELECTED TOPICS IN FLOW MECHANICS the crystal form of the original nucleus. which. they protrude from the shell-basis touching the neighbouring shell-basis. The shearing impact while cooling may contribute to the development of the network. The maltenes have two main rheological effects: on the one hand. thus affecting the initial form of the paraffin structure. This theory furnished a good basis for solving several problems of the project concerning stabilized and partly transient flow in the pipeline. simultaneously. Asphaltene particles may serve as nuclei for parafin crystals. Phenomena. It is also used in the following parts of this work. can be interpreted by the grid shell theory. especially hysteresis. acicular and ribbon-like crystals which may aggregate to form a threedimensional network. 1. and on the other. the other part bends on touching but remains linked to it. To the shell-basis paraffin filaments are connected temporarily or durably in such way that at least one of their end is loose. however. one part of the divergent particles loses contact with the shell-basis. it has become clear that this hypothesis cannot account for some flow occurrences. they may inhibit the formation of larger parafin crystals and thereby the formation of a coherent three-dimensional network by being adsorbed on paraffin crystals (Milley 1970).3-2).the asphaltene and maltene content of the oil. Among the interpretations for the phenomenon of crude oil thixotropy the best known is the kinetic consideration by Govier and Ritter (Govier and Aziz 1973) founded on the analogy of the first. having already formed. 1. Hungary Pas 0 I 50 100 200 150 D.1.3 . 11s Fig. shear rate in thixotropic-pseudoplasticcrude from AlgyB.3-2. 1. 1984). 1. Apparent viscosity is seen to decrease with time at any rate of shear. in the course of relaxation anisotropic parafin network develops.3-3. If the slightly curving part (the valuation is often arbitrary!) of a zero shear duration flow curve I 0 t . 1. Hungary . The variation of apparent viscosity v. Apparent viscosity v. Flow curves of a thixotropic crude from Algyo. the flowing properties of the oil are influenced by shearing history (Szilas 1982. rnin 1 Fig. FLOW OF NON-NEWTONIAN FLUIDS IN PIPES 35 the existence of stabilized hysteresis curve.3. the structural change of the oil and therefore the change of flowing behaviour due to shearing is irreversible under some circumstances. there is no (or only very limited) space lattice regeneration during motion.3-2. The oil is the same Algyo crude which was used for the determination of the curves on Fig.3. rate of shear for various durations of shear is shown in Fiy. the value of z: in that case. 1. but this type of rheological behaviour is characteristic of certain fluids used in strata fracturing. Any stress acting on such a fluid will engender a deformation that will increase at a rate decreasing in time. In oil production practice it is often necessary to move watery oil through a pipeline. in general.then the ordinate intersection. after GOVIEK and RITTEK(1963) Rheopectic fluids are much rarer than thixotropic ones.36 I . or asymptotically to a limiting value. -10 0 10 20 T. 1. They can essentially be regarded as dilatant fluids which need a non-negligible period of time for the development of steady-state particle arrangements. is little known as yet. SELECTED TOPICS I N FLOW MECHANICS ( F i g . nowNewtonian (Persoz 1960). called apparent yield stress zk. . then.3 -2 intersects the shearstress axis at z = 15 N/m2. the deformation decays gradually to zero. that is. 1.3-4. They are.is obtained. O c Fig. Viscoelasticity can most readily be recognized by the Weissenberg effect: a viscoelastic fluid will climb up a shaft rotating in it (Longwell 1966).Investigation into a watery emulsion of an Azerbaijan oil showed plastic flow behaviour (Abdurashitov and Avenesyan 1964). No viscoelastic oil has so far been encountered. in semilogarithmic co-ordinates (Govier and Ritter 1963). steady-state flow parameters. If the stress acting on the deformed system is reduced to zero. Apparent yield stress v. The rheological behaviour of these emulsions. 1. for various temperatures reveals the apparent yield stress increases exponentially as the temperature decreases. Determining the value 2. mostly of the water-in-oil type.3 -2) is extrapolated to D = 0. The two liquids will quite often form emulsions. (c) Viscoelastic fluids Viscoelastic fluids exhibit both viscous and elastic properties. The curve in question in Fig. temperature of Pembina crude. Water-in-oil-type emulsions of pseudoplastic behaviour were investigated too (Sherman 1963). Fig.3-4 illustrates this relationship for a Pembina oil. This is. p. Written up after a slight formal modification. = const. 377 (used with permission of McGraw-Hill Book Company) . It is clear that for a given oil ( z ..3-7. FLOW OF NON-NEWTONIAN FLUIDS I N PIPES 1.1966. the latter being that radius for which the shear stress z = z .3 .3-5 illustrates the variation of the relative velocity v / I . The flow velocity of plastic fluids is described by the equation For this equation to hold (indeed. . the plastic fluid flows as a solid plug. after LONGWELL. Within this radius.2. ri vrdr.3. at a velocity equal to the liquid velocity v . prevailing at the radius r. If zi <T. for flow to start at all). and inside radius r e . the greater the shear stress 0 1 2 0 1 2 0 I 2 Fig. 1. 0 In a plastic fluid.5. the mean velocity can be characterized by the Buckingham equation (Reher and Mylius 1967). (Longwell 1966): In a general way. 1. will be discussed in this section. the mean or bulk velocity is the mean height of the solid of rotation of radius r and 'height' v. pipe radius (Longwell 1966).) the diameter of the solid plug moving along in the flow string will be the smaller. The fluid filling out the pipe will not start flowing under a pressure gradient giving rise to zi. it is necessary that the shear stress T arising at a given radius r be equal to or greater than the yield stress z. Flow-velocity profiles of plastic fluids. which can be derived from Eq. then the oil will flow 'as a liquid' only in annular space with outside radius r i . then even the greatest shear stress arising in the pipe will be less than the static shear stress. that is. . the two types of fluid most frequently encountered in the oil industry. Velocity distribution in pipes Flow velocity distributions in plastic and pseudoplastic fluids.If til z .1.. this equation reads Figure 1.3. 6 shows flow-velocity distributions for four fluids (Longwell 1966). SELECTED TOPICS I N FLOW MECHANICS at the pipe wall. The graphs for these pseudoplastic fluids are determined in two ways: one. the velocity distribution will approximate that of a Newtonian fluid the better.g. whereas the n's are the power-law exponents 1. if not exactly the same. These permit us to establish velocity distributions in much the same way as above.3-6. is only very slightly different. Notice how the velocity distribution approaches that of plastic flow as n decreases. value characterizing it. O n the other hand.3 -2. Figure 1. 1. p. inside this annular region. the non-negligible influence on the result of the mathematical model chosen. The graphs of the Ellis formula and the power model coincide in sections (a) and (d). the way the velocity distribution is affected by various degrees of pseudoplasticity and. the parameters of flow in a pipe and hence also the velocity distributions are rather similar. Also in this case. (c) and (d) refer to pseudoplastic fluids. the greater the pressure gradient that keeps the fluid flowing.3-2 (dashed curves). The calculated velocity distribution will depend to some extent on the mathematical model used to characterize pseudoplastic flow. pipe radius. on the one hand. In the Figures. to the Ellis Longwell 1966. whereas they differ in sections (b) and (c). that is.sections (b).1966.3. The Figure reveals. we may likewise find a central plug that flows at a velocity which. using the power law 1. Flow-velocity profiles of pseudoplastic fluids. that is. similar relationships exist in characterizing flow velocity v. the 'less plastic' the fluid in flow. an annular space with a rather Fig. after LONGWELL. the less the 7. 383 (used with permission of McGraw-Hill Book Company) steeply varying velocity distribution may develop next to the pipe wall. As regards pseudoplasticfluids. . using the Ellis formula (given e. . on the other. at a given pressure gradient and . in . and two. refer formula. Because of the essential similarity between plastic and pseudoplastic flow. the parameters r i .ri engendered by it.38 I . ~ . full curves). section (a) shows the velocity distribution as a limiting case of a Newtonian fluid. The generalized Reynolds number Let the shear stress in a fluid flowing in a pipe exceed the true or apparent static shear stress even in the centre line of the pipe. had been derived by Rabinowitsch and Mooney. that is.3. in this case. The general relationships and are also valid. and putting v = 6.. Using these equations and Eqs 1. equal to the shear rate at the pipe wall.1 . a formula describing the relation between the terms 8614 and (-duldr).. 1.1 to 1. derived by Metzner and Reed (1955).1 -3 hold. 1.11 of pseudoplastic flow.3-2 we get where For laminar flow in a horizontal pipeline Eqs 1. provided NR. as . we may write up the generalized Reynolds number. FLOW OF NON-NEWTONIAN FLUIDS IN PIPES 1..3-7. and the bulk velocity of flow will be correctly characterized by the general Eq. For pseudoplastic fluids.3.1. in Newtonian fluids. the flow will have no 'solid core'.3 -2 and 1. = N.3. from this equation the Wilkinson equation can be derived (Reher and Mylius 1967): li It is verifiable that the expression on the left-hand side is.3. This formula was written by Metzner and Reed (1955) in the form Substituting the expression for (-dvldr) into Eq. The formula can. 1.1 -2. N o general equation has been derived so far. n is the slope of the tangent and k is the ordinate belonging to the value (Soldi)= 1.40 I. also on a number of other factors affected by the rheological properties of the fluid.. 86 di Substituting these expressions into Eq.3. 1. According to Eq.4.3 . NR. If the flow behaviour is characterized by a zi = f(86/di)curve. in addition to the Reynolds number... 1. read the .. Eq. 1. Replacing p' in Eq. can be derived even more simply by the following consideration (LeBaron Bowen 1961). or are known on the basis of a ri = f(8fi/di)curve.3.. 13.and p=vp. obviously..ri belonging to the (Soldi) value corresponding to the intended 6 and di off an experimentally established zi=f(85/di)curve and substitute the appropriate data into Eq. In this case it is sufficient to assume that Eq. Transition from laminar to turbulent flow The transition from laminar to turbulent flow in non-Newtonian fluids depends. we get This relationship is of a general validity for all non-Newtonian fluids including pseudoplastic fluids deviating from the power law (where. or by field tests on a pipeline. . The apparent viscosity at the inner pipe wall is Ti p = . 1.15 by the expression in Eq.13. then k and n are constants and their numerical values are known.3 .. SELECTED TOPICS I N FLOW MECHANICS By the above considerations.12 is the equation of the tangent to the ri = f(8E/di)curve plotted in an orthogonal bilogarithmic system of co-ordinates. then N. The tangent should touch the curve at the point whose abscissa (8C/di) corresponds to the actual values of q and d i . 1.12 if the fluid obeys the power law.).= N. To find the Reynolds number by this equation.18.3 . in which case p' and n are constant and are given numerically in the equation of the flow curve. we get This formula is used if the rheological properties of the fluid have been determined by means of a capillary viscosimeter.15 is valid for pseudoplastic fluids obeying a power law. 1.3. however. also be used if the fluid deviates from the power law. as well as on the specific weight difference between the dispersing medium and the dispersed phase. FLOW OF NON-NEWTONIAN FLUIDS I N PIPES 41 but individual research workers have published valuable partial results. As the mathematical criteria established till now are far from unequivocal.3-7. 1.. The set of Graphs B includes characteristic curves for turbulent flow in pipes of various diameters. 1. the critical Reynolds number of pseudoplastic fluids varies in the range 2100 to 2400. after I<FBAKONBOWEN(1961) Dodge and Metzner (1959)have found N. The less the diameter.=2100 in Newtonian fluids. Ryan and Johnson have introduced a stability parameter which has permitted them to write up the critical Reynolds number for pseudoplastic fluids obeying the power law as follows: where Assuming that NRe..38.3. (1969). the greater the abscissa (86/di) at which flow becomes turbulent. According to Mirzadzhanzade et al.3.1. Laminar and turbulent flows in pipelines. to fall more or less into the domain of transition of Newtonian fluids and to increase slightly as n decreases. depending on the exponent n of the power law (Longwell 1966). the development of turbulency depends to a significant extent on the particle size and concentration of the dispersed phase.. e. . Graph A characterizes laminar flow independently of pipe diameter.= 3100 at n=0.7 have been determined experimentally (LeBaron Bowen 1961).. Fig. The graphs in Fig. According to these authors. NRep. it is expedient in doubtful cases to determine experimentally the type of flow prevailing under the intended flow conditions.g. 4 ~ . 1. 1. 1. =0.3. 1. 86/di for a given oil is plotted 4 in Fig. the shear stress developing at the pipe wall in a fluid flowing in a pipe is. at given values of k and n.3-8 on the basis of pipeline experiments.I .3. For this value of the abscissa. = 2 = ----. when q =200 m3/h at the given flow parameters. 4X12. Calculation of friction loss (a) Laminar flow of pseudoplastic fluids By Eq.5 grad p.308 Fig. a function of 80/di only.3-8 gives and hence.12. the direct calculation of the friction losses for any other pipe diameter. This consideration permits.5. with the possession of experimental data obtained by means of a capillary extrusion viscosimeter of capillary diameter d. or in a flow test on a pipe.I .= 162 N/m3 = 1. . The variation of 7i = di grad 0. Fig.3. Example 1. di 0.3 -8.. Find the pressure gradient in a pipe of d.308 m.62 bar/km. SELECTED TOPICS I N FLOW MECHANICS 1. 3. The equation of the flow curve is that is.1 -3 and then the friction loss by Eq.338. 1.3 . then the constants p' and n of Eq.1 . established generally by means of the rotation viscosimeter. or sets of them. If theflow curve obeys the power law. it is often sufficient for the designer to know the parameters valid for steady-state flow. 1. On finding that flow is laminar.1.3. Flow behaviour is thus characterized by flow curves. we compute 1 by Eq.308 m if at the given parameters of flow q = 200 m3/h and p = 880 kg/m3. Substituting the figures obtained into Eq.746 m/s in agreement with the foregoing example.16. We compute N R e P p for the intended oil flow rate q.3 .3 .9 shows flow curves of Algyo oil (Hungary) for Fig. 1. FLOW OF NON-NEWTONIAN FLUIDS I N PIPES 43 If the fluid is a time-dependent.08 Pas and n=0. and impossible to determine by the extrusion viscosimeter. Then .ri=f(86/di). thixotropic. 1. pseudoplastic one. The practical use of this idea is hindered by the fact that the flow curves of thixotropic pseudoplastic fluids are difficult and expensive to establish by field tests.3-2 are known. we get . flow velocity 17and pipe diameter di using Eq. Pressure drop is then calculated in a way other than the above-outlined one. Example 1. Figure 1.9.1.3-2. Find the flowing pressure gradient in a pipeline of di =0. pf=4. and the flow curves permit us to find the pressure drop of steady-state flow in the pipe. 1.16. Steady-state flow curves of thixotropic-pseudoplastic crude from Algyo (Hungary) steady-state flow at various temperatures (Szilas 1971). I7 is 0. 1. 3 . or for rough pipes where. it is therefore justified to use Eq. at D = 1.208 0.1 -1.44 I . 1. Tomita (Govier and Aziz 1973). 1981). The formula can be interpreted as a generalized Colebrook formula and is valid for the turbulent transition zone.65 bar/km. the tangents to the flow curves plotted in orthogonal bilogarithmic co-ordinates. The desired value of n is given by their point of intersection. = 1 2di 2 x 0. To find the deformation rate for which p' and n hold at the intended velocity 17 and pipe diameter d i . (b) Turbulent flow of pseudoplastic fluids The former formulae to define the pressure drop of turbulent flows were obtained either for smooth pipe.7462 x 880 = 165 N/m3 = 1. e.1 -3.16 p' means the ordinate intercept.308 If the flow curve does not obey the power law.10' . using. we determine the value of n belonging to each. on the one hand. of the tangent to the flow curve plotted in an orthogonal bilogarithmic system of coordinates.g. but also the function of the relative roughness k/di (Szilas et al. and n means the slope of said tangent. Shaver and Merri11(1959). Eq. The BobokNavratil-Szilas equation (later BNS) was analytically derived and the friction factor is not only the function of the Reynolds number and the exponent of the power law. SELECTED TOPICS IN FLOW MECHANICS Flow is laminar.we may use Eq. on the other.11 and.11 by Reed and Metzner (Govier and Ritter 1963). however. A P / = i-v 2 p = 0. then in Eq. The two functions are then plotted in a diagram. which yields Now by Eq. 1. the roughness of the experimental pipes are "incorporated" in the constants in the formulae.3. p' is furnished by the ordinate intercept at D = 1 of the tangent to the flow curve valid for the deformation rate belonging to this particular value of n. 1. This latter possibility was chosen by Clapp (Govier and Aziz 1973). Calculation may proceed as follows: assuming several values of D. It was found that in the Reynolds number ranges of lo4. 1. Dodge and Metzner (1959).3 . grad p. 1. Its accuracy was tested by a series of experiments performed in a pipeline transporting pseudoplastic crude. 2 + 7Lg 2: [ N I-.3 m Oa20- 0.3.30n = 0.10.lO - 0. Dodge-Metzner 1 i 1.60 2 $= 000117 ~ s " l r n 9 = di = 820 kglm3 0. CLAPP 6.1. FLOW OF NON-NEWTONIAN FLUIDS IN PIPES L 4. 1 0 j 6-7 7. (1981) . Pressure gradients of pseudoplast~cfluid flow after Szlu\s et al. BNS.48 5. 0 - 7 100 200 300 9 [m3/h1 Fig.-1. k l d i = 3 . RePP -5 (+) ] + ~ ( s n 1 h = 0. 1.3. Shaver-Merrill j 2 1. It is clearly seen that the application of different equations leads to significantly differing values.1.One is a Reynolds number which involves the plastic viscosity p" in the place of the simple viscosity: .). the error due to use of the steady-state pressure gradient may be quite considerable. The boundaries of the fully turbulent region however will be different in cases of Newtonian and non-Newtonian crudes.5(a). a.1 percent. The same Figure shows pressure gradient-flow rate curves obtained with the BNS method for three different k/di relative roughness values of practical importance. x w and then Eq. In the possession of a flow curve characterizing the behaviour of the fluid.3.I0 shows several curves (Apf/Al)di= f(q. while the standard deviation. relatively short pipelines are to be designed for pressure drop. was 0. Fig. accuracy is little influenced by the fact that the pressure gradient is slightly higher in a short section near the input end than the steady-state value in the rest of the pipeline. 1. the following consideration. When.1 -8. The flow curve belonging to infinite shear duration is consequently suitable for determining the flow parametefs of steady-state flow. (c) Thixotropic pseudoplastic fluids Figure 1. provided the graph of the function zi= f(8z7/di) has been determined experimentally. In the fully turbulent region N R . In this region the friction factor is not influenced by the flow parameters of the fluid and thus by the non-Newtonian flow behaviour. (d) Plastic fluids By the considerations in Section 1. As an example. 1.81 percent. and hence also the friction loss. however. calculated by using well-known methods from the literature.3-2 shows that the flow curve belonging to any shear duration of a thixotropic-pseudoplastic oil looks like the flow curve of a time-independent pseudoplastic oil.3..3. SELECTED TOPICS I N FLOW MECHANICS the average absolute error was 4. in the way outlined in the previous paragraphs.0 and the temperature of the crude decreased from 43°C to 9°C. by means of an extrusion viscosimeter or by field tests. A procedure for computing pressure drops under transient structural and flow conditions has been developed by Ritter and Baticky (1967). the pressure drop can be calculated by.5 and 1. 1. In the experimental pipeline n varied between 0. In practice it is often found that after a shear duration in the order of 10 minutes the flow curve approximates quite closely the values to be expected at infinite duration of shear. It has been shown by Hedstrom that the friction coefficient of plastic fluids is a function of two dimensionless numbers (Hedstrom 1952). In designing relatively long pipelines for pressure drop. the pressure drop of a plastic fluid in laminar flow can also be determined in the way outlined in Example 1. Eq.46 I .3-21 is simplified to the Prandtl-Kannan formula. Friction factor of plastic fluids.12.3-3.8. Find the friction pressure gradient in the fluid characterized by flow curve in Fig.For flow Fig. 1. are known (API 1960). for instance at (. 1/e Example 1. Let us add that the curve for turbulent flow refers to a smooth pipe and therefore gives approximate results only..308 m and p = 880 kg/m3.11if N.6 =0.. and N.4 . di=0.140 Pa s .The flow curve yields .3. 1.6 Pa and.12. the rest hold for laminar flow.4 Pa.. the friction factor can be read from Fig.3. 30 D.11. Hence 1 1.re = 8. 1. 20 .3 . FLOW OF NON-NEWTONIAN FLUIDS IN PIPES The other dimensionless number is named the Hedstrom number This number accounts first and foremost for the fact that the 'soIid core' of the flow reduces the cross-section free for 'liquid' flow (LeFur and Martin 1967). 10 Fig. T = 1 1. .3 20 .dv/dr) = 20 l/s.1. if q = 200 m3/h.. 1.3. The curve marked Tholds for turbulent flow. according to HEDSTR~M (1952) in a pipeline. 3 . 3. grad p. The taking. In case of artificially made non-Newtonian fluids. (3) the flow behaviour characteristics can be significantly influenced by the temperature and shear history (Szilas 1971). 1. (a) Measurements with extrusion viscometers The extrusion viscometer is the type of capillary or discharge viscometer where the fluid to be measured flows in the measuring section not because of gravity but due to the pressure differential occurring at the two ends of the measuring pipe section. transport.3. by Eq.185.Through hole 4 the .3.185 0.1. Many types and models of extrusion viscometers are known.308 = 147 N/m3 = 1.g.24. 1. (2) the light hydrocarbon components are evaporating while storing. Figure 1. its inside diameter is 76 mm and it can be used with an allowed internal overpressure of 10 bars. e. = I = 0. Determining flow curves The basic condition of determining a representative flow curve is to ensure that the flow behaviour of the tested sample is the same as the fluid which will flow in the designed pipeline.2 mm. They are fixed to the bottom of the tank. The length of tank 1 of the extrusion viscosimeter shown on Fig. Three main difficulties must be considered: (I) the dispersed phase settles out in the dispersion medium. and by Eq. in the case of fluids applied for hydraulic formation fracturing.6.11 yields 1=0.746' x 880 2 x 0. 1.6 mm and 3.3 -23. The temperature is measured with three thermometers. Their IDS are 1.1 "C.47 bar/km . the preparation of the samples are prescribed by special rules (API 1960).1 . respectively. 1. 1. SELECTED TOPICS I N FLOW MECHANICS Now by Eq.3-13 is 610 mm. storage and preparation of thixotropic-pseudoplastic crude samples must be made with special care.I . each having a measuring accuracy of 0. Then. For the measurement of flow curves extrusion or rotary viscometers are generally applied. In the following section (after Le Baron Bowen 1961)we shall speak of a model suitable to measure pseudoplastic crudes. Two stainless steel measuring pipes of different lengths (2) are mounted in the tank. in the case of the instrument shown in Fig.13. FLOW OF NON-NEWTONIAN FLUIDS IN PIPES 49 crude in tank 1 is forced through the measuring section with the help of nitrogen gas. This. Extrusion viscometer Thus the principle of measurement is comparatively simple. of the fluid flowing in the instrument . Fig. p2 .3. As the result of the measurement several (@Idi) -(diApf/41)pairs of values are obtained. The measurement aims at determining the volume of the fluid flowing through the two measuring pipes at different pressure differentials during unit time periods.1. A-A and B-B.3 . The difference between the pressure.is ensured as the fluid to be measured surrounds the measuring pipe in the rank of the instrument. are linked with a continuous curve.. to keep errors at the lowest possible level. Let us record the energy balance for two sections. p. 1.13. 1. however.is not directly the same as the Apf pressure differential of the expression diApf/41. It is advisable to determine the IDSof the measuring pipes on the basis of filling up with mercury. and the atmospheric pressure measured at the ouflow. The tank is surrounded by jacket 5. measured above the fluid level. Great care must be taken. after being plotted on a diagram. which. It is important that the measured temperature is really that of the fluid flowing in the measuring pipe. which includes heat insulating asbestos cement.3. (b) Measurement with rotary viscometer Rotary viscometers are more complicated than capillary ones. It should be checked. Separate regulbtions are valid for the determination of single components (Van Wazer et al. to apply this type of viscometer for the determination of the flow curves of time dependent fluids.3. for the pseudoplastic thixotropic fluids. before the inflow into the measuring capillary within the tank. and h. e. that the flow in the measuring pipe is not turbulent (see Section 1. approximately equals zero. The extrusion viscometer is suitable to determine only the flow behaviour of purely viscous fluids. however. The flow velocity. however. . SELECTED TOPICS I N FLOW MECHANICS where h is the elevation difference of the variable A-A and that of the constant B-B sections. 6.g. behaviour of the measured fluid.!-!@ obtained by 41 the extrusion viscometer can be generalized only in the case of laminar flow. defined by the different di pipe diameters and by the average flow velocity. is the intake head loss. v . h. The main advantages are: 1. It is not possible. Let the measured pressure difference be Ap. advantageous for the measurement of the flow behaviour of non-Newtonian fluids.50 I. . is required of the stabilization of the structural. the shear stress belonging to the adjusted shear rate can be determined at different shearing times. its application is extremely advantageous because the expected pressure gradient ApJ/l can be directly calculated from the ordinate value ApJd. 1966). hi.. considering the expected shear rate in the pipe. -p2 and the flowing pressure drop ApJ-hfpg.4). is the frictional head loss. Their application is. which..characterizing the different flow rates. then the above equation can be modified as follows: The expression in parenthesis is the correction which is to be subtracted from the measured pressure drop in order to obtain the frictional pressure drop of the measuring capillary.=p./41 belonging to the 8C/di group. and thus the flow. therefore. first.. In this case. 2. The duration of the flow in the measuring pipe is generally much less than the period. is the outflow head loss. The relations di . the shear stress valid for steady state can be measured for different single shear rates. The velocities developing at different radii within the annular space ofthe viscometer are shown in Fig. the shear stress of the same sample can be determined at different shear rates. while the shear velocities are plotted by the family of curves B (Van Wazer et al.14. on the basis of Dinsdale's theory (Dinsdale and Moore 1962) we shall discuss the scheme and measurement principles of a rotary viscometer. The value of the measured shear stress is valid on the pipe wall. Cylinder 2 is rotated with an adjustable angular velocity. This cylinder is suspended on a torsional wire. with coaxial cylinder. 1. These structural elements are generally coaxial cylinders but there are measuring elements of other shapes as well.3. structural element. FLOW OF NON-NEWTONIAN FLUIDS IN PIPES 51 3. first. Theoretical schema of rotary viscometer In the next section.3.1. 3.3. respectively.and the developed torque is measured with the relative angular displacement of inside cylinder 1. or different. the shear rate of the fluid sample in the viscometer only varies slightly. 1. (In the case of the extrusion viscometer the shear rate and the shear stress vary considerably along the radius of the measuring pipe.) Several types of rotary viscometers are known. belonging to the second group. o. laminar. the end effect is negligible and no slippage occurs on the surface of the cylinders. They are generally classified into two groups on the basis that they measure the torque and the angular velocity on the same.15 by the family ofcurves A. Let us suppose that the flow between the two cylinders is stationary. The principal scheme of the instrument is shown on Fig. 1966). Thus due to the above features the instrument is suitable to determine the flow behaviour of time dependent fluids. Let the . 4. so it is possible to obtain the shear stress valid at the given shear rate.3. Fig.14. as compared to this radius. Since.15. on the first term on dr the right-hand side.3.i. In the case of rotary viscometers. contrary to the case of the flow in do pipelines. That is why dr the shear rate will be noted as D in the future. while it is independent of the absolute value of the angular velocity. it is obvious that the shear stress in the analyzed sample is essentially constant. . r -. the velocity gradient. differs from the shear rate. duldr. the annular space containing the fluid is very small. 1. To define the shear effect let us record the total differential of the equation u = r o : and heno5 dv=rdo+wdr do The rate of the shear depends only on the expression r -.e. Distribution of flow and shear velocities in rotary viscometers angular velocity in the fluid sample at a distance r from the shaft be w.52 I . SELECTED TOPICS I N FLOW MECHANICS (a) f l u ~ dat r e s t (b) Newtonian fluid ( c ) Plastic fluid ( d ) Pseudoplastic fluid (e) Dilatant fluid Fig. The torque exercised by the outer fluid mantle upon the fluid cylinder of radius r is where h is the height of the fluid cylinder and rr is the shear stress generated at radius r that is According to the equation the shear stress is inversely proportional to the square of the radius measured from the shaft. equals the angular velocity of the rotating cylinder. the mean shear stress is and f = pD. the angular velocity. which is . . the Haake type rotary viscometer discussed below.1. A measuring instrument of this type is. and thus by applying Eqs 1.27 and then We assume that no slippage occurs on the pipe walls. FLOW OF NON-NEWTONIAN FLUIDS IN PIPES For Newtonian fluids Z. 1.3 . If. = pD. These are the boundary conditions with which we solve the equation. and at r = r .26 and 1.e.3. In the first case. i. generally. however. and on the basis of Eqs 1. considering Eq. or if the rotated cylinder is also a structural element suspended on the torsional wire. The average shear rate and average shear stress can be determined either as an arithmetic or as a geometric mean. o .3 . if r = r . and the outer cylinder is suspended on a torsional wire. The above equations are valid. respectively. The equation is also valid if the internal cylinder is rotated with an angular velocity. for example. they can be applied for non-Newtonian fluids as well.28 and 1.3. only for the fluids of Newtonian behaviour. then w =O. the annular space between the two cylinders is small enough. w. from which the torque where C is an instrument constant depending on the geometrical parameters of the instrument.29 the arithmetic mean of the shear rate is The geometric mean values are * A and respectively.3-26.3. 3. Sch~ematicdiagram of rotary viscometers made by . and potentiometer 6. The flexible axis transmits the rotating movement to cylinder 1 through clock spring 4. Ten basic speeds can be adjusted on the instruments and these speeds can be reduced to one-tenth or onehundredth by applying a speed reducer.4 x lo6 Pas.16. Cylinder 1 is rotated by the flexible axis. at the prescribed speed.3 . The possible shear rates are between lo-'.54 1. 1. pseudoplastic crudes in large ranges. 2. The cylinder is vertically fixed with axis 3.lo4 I/s. SELECTED TOPICS IN FLOW MECHANICS suitable for the measurement of thixotropic. 1. the measurable shear stress is 1 x 105Pa. The instrument is shown schematically in Fig. 8 Fig. and the measurable apparent viscosity is in the range 5 x .16. The measurement of the torque proportional to the angular displacement of the spring is obtained by contact 5. Hence. The specific volume of oil will decrease slightly owing to the escape of gas and to the decrease in temperature and increase slightly owing to the decrease in pressure. In the course of upward flow. further complicated by the phenomenon of slippage. Now the total mass of the fluid filling 1 m of this pipe will be . we should be faced with much more of a problem than in the case of single-phase flow. to the escape of more and more dissolved gas from the flowing oil under the decreasing pressure. although research cannot be regarded as complete. Multiphase flow of liquids and gases 1. moreover. These formulae are based on various theoretical approaches.4. when the velocity of the elements of the rising liquid are exactly the same as that of the gas bubbles in it. The gas bubble entering the flow string at the tubing shoe will leave the liquid element entering with it far behind. MULTIPHASE FLOW OF LIQUIDS A N D GASES 1. Friction loss is an energy loss similar to that which arises in singlephase turbulent flows. The energy loss of flow is. owing to the decrease of the pressure acting on it. (b) slippage losses arise in addition to friction losses. which considerably affects friction is. however. This is due.1. to the expansion of the free gas entering at the tubing shoe and. on the one hand. significantly influenced by the flow pattern. The problems of flow will be discussed below with the main emphasis on wells producing a gaseous liquid. Numerous new theories have been published since. Let the cross-section of the pipe be " A . and. (A) The specific volume of gas gradually increases as it surges upwards. Both effects are mitigated by the decrease in temperature.1.4. (c) flow is affected by a great number of parameters and (d) liquid and gas may assume a variety of flow patterns. on the other. (B) Two-phase vertical flow involves two types of energy loss: friction loss and slippage loss. the friction factor may vary considerably because the relative gas content of the fluid in contact with the pipe well and the flow velocity both increase monotonously.4. even if the only loss to be reckoned with were due to friction. The velocity distribution over the cross-section of the flow string. and in solving various problems or explaining various phenomena encountered in oil and gas production the formula that is frequently changes. Slippage loss is due primarily to the great difference in specific weight between the gas and the liquid. The reasons why the relationships describing two-phase vertical flow so complicated are (a) that the specific volume of the flowing fluid varies appreciably as a function of pressure and temperature. however. Slippage loss can be considered zero. we are today in possession of formulae of satisfactory accuracy for the flow regions important in practice. Flow in vertical pipe strings (a) Introduction Research into the laws governing two-phase vertical flows has long been pursued. Versluys (1930) was the first to give a general theory. proportional to the slippage loss is. that fills the tubing. The average density of the mixed gas-liquid flow will then be described by Taking the figures of the above example and assuming that k is equal to 1.66 = 347 kg/m3. Let the liquid flow rate through section A of the flow string situated at a given depth be q. the density of the mixture will be p. and let the effective gas flow rate be q. =0. Let a fraction E. inclination of the tubing to the vertical. of the section be filled with liquid and the rest.2 the average density of the mixture will be that is.) and the liquid flow rate (q. ( 1 . of the gas is increased to k x v. Since it is quite obvious that such increase in velocity will necessarily result in a decrease of the gas-filled volume of the section from E. then ( C )The pressurz gradient of flow. relative roughness of pipe well.66)+ 10 x 0. p.) being kept constant. additional energy during production. . 1.E . also called the flow gradient. with both the gas-flow rate (4.. flow velocity. the phenomenon of slippage resulted in an increase of the density. When p. .66. Ros (1961)has listed 12 such factors ( I D of tubing.56 I . is affected by a host of independent variables. The flow velocity of the liquid is and that of the gas is The slippage velocity. Slippage loss is great in the case of relatively low gas-flow rates in relatively large diameter tubings. SELECTED TOPICS I N FLOW MECHANICS From this equation the average density of the liquid-gas mixture is: = pdl -&.E.= 10 kg/m3 and E. of course. by gas.1 Example. to ~ ~ / k . ) = E . = 1000 (1 -0. thus. also in an increase of the mass of the fluid column. = 1000 kg/m3.I + P. To lift this excess mass needs. density. and. Let us suppose now that the velocity v.4. 4. There is no full agreement in literature as to the classification of flow patterns. 1.1. (I) Frothflow. interface tension. whereas in froth flow in the strict sense of the term. Boundaries of flow patterns and the transition region after DUNSand Ros (1963) arrangements are called flow patterns. acceleration of gravity). The typical Fig. the bubbles are in turbulent motion. wetting angle.4-2. but the gas-oil ratio is usually less than in the other flow patterns.4 - Fig. may take a variety of forms. The number and size of gas bubbles may vary over a fairly wide range. (D) The spatial arrangement relative to each liquid and gas and the filling-out of space by the individual phases. the flow is called bubble flow. flow temperature. e. 1. MULTIPHASE FLOW OF LIQUIDS A N D GASES 57 viscosity of both liquid and gas. The continuous liquid phase contains dispersed gas bubbles. whose influence can at best be estimated.g. If the gas bubbles move more or less parallel to the centre line of the pipe. . There are further factors. The following classification seems to be the most natural. whereas in condensate-gas wells pattern (111) comes into its own. Here the gas is the continuous phase: it contains a finely dispersed mist of liquid. According to Orkiszewski the boundary of flow patterns I and I1 at various tubing string diameters can be read from Fig. may play an important role. dimensionless gas velocity on the ordinate axis (Duns and Ros 1963). Others state that in addition to the effective gas-oil ratio. (111) Mistflow. SELECTED TOPICS IN FLOW MECHANICS (11) Plugflow (slug flow). patterns (I) and (11) are of the greatest importance. and express the differential pressure drop as The first term on the right-hand side of the equation is proportional to the change ot the kinetic energy.58 I. Earlier GOR alone was held to be decisive in this context. for example. There are two boundaries -the upper one of Flow Region (11) and the lower one of Flow Region (111)-on this diagram with a pronounced transition zone between the two. It is difficult to accurately delimit the zones of the individual flow patterns. Gladkov. Plug flow takes place in a succession of gas and liquid plugs. stated the upper limit of froth flow to be at GOR 20 m3/m3* (Muravyev 1959). The differential velocity change of the fluid mixture can now . some of the coagulated gas bubbles fill out the entire pipe section at a certain height.4. In flowing and gas-lift wells. the velocity of the mixture can be assumed to be essentially equal to the velocity calculated on the gas flow rate alone..I. (b) Flow gradient When neglecting the Coriolis coefficient in the kinetic energy term. Let us now introduce vk instead of o and pk instead of p for the velocity and density of the mixed flow. Figure 1.4-2 (reproduced after Duns and Ros) shows a diagram calibrated in dimensionless liquid velocity on the abscissa axis v. That is: v. that is: Since it only gains importance in high GOR mist flow. The gas-oil ratio is very high. the stationary upward flow of a gas-liquid mixture in a pipe can be described by the extended Bernoulli-formula: dp PS - vdu ++dh+ 9 dpf PS -= O with the fourth term representing the energy loss due to friction. as well as that of the oil and the gas itself. respectively. the velocity of the mixed flow. 1. w o. An oil mist may be dispersed in the gas plugs and a gas froth dispersed in the oil plugs. The gas-oil ratio is higher. MULTIPHASE FLOW OF LIQUIDS A N D GASES be calculated from Boyle's law by total differentiation: d(pu.in to consideration also: This is essentially the ratio of acceleration pressure drop to total pressure drop along the differential dh length of tubing.4-8. taking Eq.dp=O and hence Based on this where or. and .4-8 into 1. Friction loss along the differential length of tubing can be calculated from the Weisbach formula (called the Fanning equation in the English-speaking world): where or taking Fanning's formula into account: Let us now substitute the terms of Eqs 1. When expressing C . 1. more exactly.4-7 and 1.)=pdv. in the difference form of Eq.1.4.4-5. Ah= Apf.+v. the signs will partly change as follows (Szilas 1980): Ap=C1Ap+pkgAh+C2dh. Now When developing the above equation into the difference form. 1. that is C .4-6. Krylov performed his experiments with water and air and corrected for the friction loss of the liquid by assuming the viscosity of oil to be five times that of water. 1.g by y.4. (slippage included) and Ap. Both ends of the pipes were fitted with quick-closing valves and pressure gauges.4. that is. Let us now substitute p.11 l= . (c) Production characteristics of the tubing string of Krylov's theory Krylov's theory (Muravyev and Krylov 1949)is based on laboratory experiments.. Krylov assumed that these lengths of pipe could be regarded as infinitesimal. although taking it into account. in Eq. =O. In these flow regions acceleration is negligible. SELECTED TOPICS I N FLOW MECHANICS substituting it into the above formula.11.+ 5 J . and we obtain: The expression on the left side stands for the dimensionless pressure-gradient while the second term on the right-hand side represents the dimensionless friction-loss gradient. in the same formula and divide both sides of the equation by 7. In addition to this there is also some disagreement concerning the role of acceleration. 1. He has worked out his theory for froth-flow and plug-flow.60 I . The direct aim of his experiments was to establish the constants of Eq. =O). use slightly different ways of approximation to estimate it. In the following we denote the former by 5 and the latter by 5. The essential difference between the formulae proposed by different authors lies in the method of calculating p. while others.4. the pressure gradient will be This is the equation from which all of the fundamental gradient formulae we discuss in the followings can be deduced. The experimental piping consisted of 18 to 20 m long standard-size tubing pipes. In the new notation Yk 1. some authors are of the opinion that it can be neglected (C.10 C.. 7 Based on laboratory experiments and theoretical considerations Krylov characterized yk as: and . 1. Fig. according to KRYLOV time. The gas flow rate is expressed in terms of standard cubic meters per unit of Fig. The conduit 3 delivers gas likewise at a pressure p . but at an arbitrarily variable rate to tubing 2. Liquid flows from a constant-level reservoir tank 1 to the lower end of tubing 2. 1. . If gas is delivered to the tubing string at a . Consider now the simplified model shown in Fig. 1.4. 1.)<. 1. however. Transport curve of vertical tubing string. succeed in giving a mathematical expression for it (Shaw 1939). MULTIPHASE FLOW OF LIQUIDS A N D GASES 61 Assuming 5 and di to be constant Eq.ifor tubing strings of field length is of a similar form. where its pressure is p ..11 may be used to construct a ql = f(q.4-4. The liquid rises in the flow string and flows out of the wellhead at a rate as high as can be carried by the gas flow. .4. A curve of this type had earlier been described by Shaw who did not. Since the pressures at the lower and upper end of the tubing string and the length of the tubing are constant.4-3. 1. the mean pressure gradient will also be constant and so the operation of the tubing string will be characterized as shown in Fig.4-3.4-4. diagram characteristic of the operation of an infinitesimal length of tubing ( F i g . 1.4 -3). The relationship ql=f(qg)5. the gas flow rate. q. The operating point belonging to this value is "the operating point of maximum liquid throughput". SELECTED TOPICS IN FLOW MECHANICS rate lower than qgl then the gas will turn the liquid column of original height h in the tubing into a froth and raise its level to. With increasing gas flow rates the well will be kicked off at q... A gas flow rate increased from qg2to q. The level will reach the tubing head when the gas flow rate attains q..62 I..... Meanwhile.. of the tubing is attained at a gas flow rate q. The slope of the position vector is greatest at q.. the specific gas consumption. 1.. .. at its lower and upper ends.. If the gas flow rate is increased above q.diagram of Fig.. liquid transport ceases.. will be determined by the gas flow rate q.. is called "the operating point of most economical gas lift". The shape of the q. At the gas flow rate q. of the tubing.. and the density of the liquid p.. =f(qg)<.4-5... This state is illustrated in Fig.. The inverse slope of the position vector to any point of the graph equals q./q. say. the energy consumption rate v. The maximum liquid throughput capacity q. that is. and p . The variation of the total energy with the gas flow rate is shown by line 1. showing P. = f(qg)t. hi.. the specific gas consumption of the gas lift gradually decreases. the respective pressures p .the entire energy of the gas delivered into the tubing will be consumed by slippage. The length of the flow string L. both the liquid flow rate and the economy of operation will decline.i diagram characterizing the liquid throughput capacity of the tubing string is determined by the relative magnitudes of the friction and slippage losses. Power consumption of vertical two-phase flow attains a value q. and liquid flow rate will gradually increase until the gas flow rate Fig. The operating point q. specific gas consumption is least at that point. The liquid flow ratc belonging to this operating point is optimal. but at the expense of an increased specific consumption. which renders operation less than optimally economical. are considered constant.4-5. 1. and the liquid flow rate q. entails an increased liquid flow rate. =O.. At gas flow rates below qgl. The operating point belonging to the gas flow rate q... "the operating point of kickoff'. Curve 3 is geometrically similar to the q.... 1. At a given q. m3/s Fig. according to KRYLOV Fig.4-7. the ordinate difference between line 1 and curve 2 represents friction loss. The Figure reveals the ratio of slippage loss to total energy consumption to be most important at comparatively low gas-oil ratios.4.4 qp . 1. Transport curves of tubing string for various flow gradients.4-3. according to KRYLOV . the ordinate difference between curves 2 and 3 represents slippage loss. MULTIPHASE FLOW OF LIQUIDS A N D GASES 63 1. According to Andriasov the friction loss gradient reaches it maximum at <=0. whereas friction loss becomes predominant at comparatively high GORs. showing the useful energy output. whereas the ordinate of curve 3 represents the useful energy consumption. 1. Transport curves of tubing strings for various tubing sizes.4-6. then the mean pressure gradient. consequently.4. and (f) the volume change of the gases can be characterized by the perfect gas laws. Equation 1. is constant. In Soviet oil production practice. 1. 1. (e) flow temperature equals the standard temperature. be brought to a form suitable for practical calclllations. the mean gas flow rate is Substituting the value of <as given by Eq. by certain rearrangements and simplifications. The ratio of friction loss to total energy consumption increases with decreasing 5 values (Razrabotka . 1972).4. and (c) the less . we obtain Krylov's formula for field lengths of tubing.1 1 we get. mean values valid for field lengths of tubing.=O. .4. 1. as referred to temperature and pressure. It can be seen that the greater the value of 5 (a) the less the gas flow rate at which the well is kicked off.4 .4. . as the kickoff criterion for an infinitesimal length of tubing. m3/s of standard state gas.4-6 presents several transportation curves computed using Eq.5.12 and the value of ggas given by 1.1 1 . expressed in metres of liquid column. Figure 1. the volume change of the gas is isothermal.4.in view of the slopes of the position vectors to the operating points . (b) the density of the liquid. SELECTED TOPICS I N FLOW MECHANICS with 16 percent as related to 5. In order to extend it to field lengths Krylov substituted for 5 and q. (d) the flow and.7 shows three graphs for standard tubing sizes at 5 =0. and also (b) the greater the liquid throughput capacity of the tubing at both the optimum and the maximum operating points of the curve. (c) gas solubility in the liquid equals zero. Putting this value into Eq.1 1 for constant values of 5 usually encountered in practice. It can be derived from the above assumptions that at the mean pressure prevailing in the tubing string. At the operating point of kickoffq. When forming the means he assumed that (a) the pressure traverse of the tubing string is linear.13 into Eq. 1. relations derived from the three critical operating points of the tubing string are preferred to this formula.1 1 is valid for infinitesimal lengths of tubing. It can be seen that the greater the tubing diameter d. (b) the greater both the optimal and the maximal liquid flow rate..4. however. .. is Let the gas flow rate through the tubing be q. (a) thegreater the gas flow rate required for kickoff.64 I. Figure 1. If the pressure traverse is linear. which can.the specific gas consumption of a given liquid flow rate. .16 can also be used t o derive the optimal and maximal liquid flow rates for field lengths of tubing if 5 is replaced by the mean value f given by Eq.4. of curves similar to the set in Fig.16 The gas flow rates required to assure liquid flow rates corresponding to these operating points are Equations 1.15 and 1.12 and 1. given by Eqs 1. In order to establish formulae for the operation points of optimum and maximum liquidflow rutes. respectively.4 .....4 . and wrote up his equations: 41 max = 55di 5 3 1.4 bars and p. according 1000 m long is 20 bars. 1.= 900 kg/m3.4. 1. MULTIPHASE FLOW OF LIQUIDS A N D GASES 65 Substituting into this equation the mean values % and q..4.. Kickoff characteristics of long tubing string.4. It is seen that if the pressure prevailing at the lower end of a tubing string Fig.12.4. .1. = 1. p. then the gas flow rate required for kickoff is at least qgn= 290 m3/h. Krylov connected the points q.4 . 1.8 illustrates this equation for d = 2 718 in.8.5 - 1.13 we see that the kickoff criterion for field lengths of tubing becomes Figure 1.4..4 -6 referring to various tubing sizes (see dashed lines 1 and 2). and q. is and R. In a similar manner.4-9. both sides are multiplied by the specific weight of the liquid y. Optimum and maximum flow rates in long tubing string... = 0-123 LY.9 shows the variation of q. the specific gas consumption. It is clear that in the range of practical significance e<0. however.12 to 1. d P " r ~ n lg ~ 1 1 '~ 2 Figure 1. for a tubing size of 2 7/8 in.. and q.4. respectively.66 1.5.17 and 1.18 it can be shown that the specific gas consumption of liquid production through field lengths of tubing at the optimum and maximum liquid flow rates. required to produce a unit volume or unit weight of liquid) is more suitable: Using Eqs 1. 3 Fig..4.4. according to K R Y ~ . SELECTED TOPICS I N FLOW MECHANICS Soviet practice is to operate with flow rates expressed in terms of weight rather than volume per unit of time. 1. R. the liquid throughput capacity increases at both operating points as the hydraulic gradient increases.... (the amount of gas. For practical purposes. a relationship for calculating the gas flow rates required for given liquid flow rates in field lengths of tubing can also be derived.. To adapt formulae to this viewpoint.. expressed in standard volume units.4. and a liquid density of 900 kg/m3.. = 1000 kg/m3.. 1.the specific gas consumption of liquid production decreases as the hydraulic gradient increases. p. and Apf = dp. had been the definition of the pressure gradient.g= y. Numerous problems connected with the planning and operation of a well can be solved by the knowledge of the pressure traverses. Optimum and maximum specific gas requirements in long tubing string.4-10 shows the variation of R. 9~0. .. and R.. the effect of acceleration is neglected. Differences proved to be highest at gradients of g> 0. assuming that the dynamic level.. obviously.5. MULTIPHASE FLOW OF LIQUIDS AND GASES 67 Figure 1. the aim of Poettmann and Carpenter. further.0 bar. C. the effective height of lift as measured from the wellhead. v.4. that is. in the range of practical significance. that is. and that pressure loss is essentially described by the .. =O. They also assume that all the pressure losses can be satisfactorily represented by Ap.. .4. flowing density of the fluid is interpreted without slippage of the gas and a Ap. is hd= L(1. with their fundamental equation. d = 2 718 in.. say between the lower and upper end of a tubing string. = 1.1. Fig. loss factor is used instead of the friction loss factor Ap. As well as Krylov.0 = 400 m and.He established that gas flow rates observed in field lengths of tubing are higher than those calculated using the Krylov formula.10 by assuming p.4. and p.4.10. The equation can be derived from Eq. The Poettmann-Carpenter theory The immediate aim of the theory and calculation method of Poettmann and Carpenter (1953)was to predict pressure traverses p = f(h) in vertical flow strings.. 1972). according to KRYLOV (d) Pressure traverses in vertical tubing strings. The accuracy of Krylov's theory was analysed by Andriasov (Razrabotka . 1. 68 I . stands for the total mass of gas..8/b for A p . 1. Consequently the fundamental relationship is as follows: When replacing the Fanning equation expressed by Eq. SELECTED TOPICS I N FLOW MECHANICS Fanning equation. To calculate the specific weight of the fluid they introduce the formula. where M. Energy loss factor in vertical two-phase flow. the mass factor. oil and water produced per cubic metre of stock-tank oil. the multiphase volume factor.4 . and B. according to POETTMANN and CARPENTER (1953) .11. indicates the volume of the same fluid mass at pressure p and temperature 7:Then Fig 1..4. MULTIPHASE FLOW OF LIQUIDS A N D GASES substitution of the expression for ykand v. 1. The f v.4.). the loss curve) based on data obtained from test wells and calculated using the above formulae.22 and the introduction of notation results in Poettmann and Carpenter determined values off for numerous flowing and gas-lift wells and plotted them v.27 go M. 1. . Expressing pk by yJg and replacing yk by Eq. a "viscosity-less Reynolds number". 1. is shown as Fig. (dipto.4.4-23 and uL by Eq.4-12. 1.11./di as the independent variable.24 we obtain 1. M. that is.qo/didiagram (that is.4 . into Eq. Since the 12 'C 11 10 9 8 7 6 5 4 3 2 1 lo-' 1 90 Mt kg/s 8 Fig.4 .69 1. 1. . pressure.M. must depend on the same quantities. Poettmann and Carpenter proposed constructing the pressure traverse by means of graphical integration. In order to calculate the pressure gradient Poettmann and Carpenter constructed sets of AplAh = @(q. When transposing their calculation procedure to SI units it seemed simpler to prepare only C = @(g'o MI). has to be computed.4. diagrams. Knowledge of the pressure either at the wellhead or at the lower end of the tubing Fig. for each of which the actual flowing specific weight yk = M.)and d.4-25.. 1. 1. calculated for the total length of tubing. 1.4-25 (see Fig.26. 1.. conversely. Graphical construction of pressure traverse curve string is a prerequisite of the calculations.4 . or. as defined by Eq. y.26 in the knowledge of C. the factor C.12)..).70 I .4 . SELECTED TOPICS I N FLOW MECHANICS loss factor f is the function of (qoM.4. Integrating graphically with respect tb p we obtain the variation of lift-height "h" v.13. With some slight modifications the procedure is as follows. 1. are plotted against pressure.4 . For the di tubing string size C can be read off at the abscissa point qoM. using Eq. nomograms on the basis of Eq. 1.g/B. When starting from a known bottom pressure we select a sequence of decreasing pressures.. and to calculate the pressure traverse using Eq.26 and the inverses of the values in differential form of dhldp. the pressure traverse of the . Then the pressure gradient Ap/Ah is calculated for each of the selected pressures using formula 1. can be established by means of diagrams based on laboratory experiments. The multiphase volume factor can be established using the following equation: Fig. P The variation of B.4 .1.14.15.4. 1. 1. . for various pressures.p. + n.4 . Fig. MULTIPHASE FLOW OF LIQUIDS A N D GASES 71 tubing string (see Fig..4-13). the amount of gas dissolved in a unit volume of oil against pressure at the mean flowing temperature. we have to know B.4. Deviations will not be significant except at low pressures. =R . 1. The curves B.15). R.14 and 1. The pressure traverse can also be constructed starting from a known wellhead pressure.4. the volume factor of oil. In order to determine y. and of gas solubility.. In the notations used in the graphs and R. = @(p)and Rs= @'(p) can often be substituted in a fair approximation by straight lines (Figs 1. .0 34.40 1.1 114 120 128 135 139 2.18 1.2 48.0 26.3 Remark: M.06 4 - pw z Bt Pk m3/m3 m3/m3 kg/m3 kg/m3 10-Zbar/m m/bar 1.= 10 m3/m3. = 164 m3/m3.981 bar and T.89 5.p. di=O-062m.99 0.72 I. 1150m.1. L.496 kgis.4-28 M i = 830+ 164 x 1.4.6 1 2.83 3.5 bars.55 0..76 7.52 1.3 65.50 3.77 5.496 kg/s. the flowing wellhead pressure will be 26.21 1-19 1. 3.875 0900 0.77 0.= 1000 kg/m3.1. m3/m3 m3/m3 0. n.40 1.=0~00m3/m3.14 m3/m3. The principal intermediate results of the calculation are listed in Table 1.52 C Pk d~ dh dh d~ 53 45 35 25 20 1.16 0.10 2.27 at the pressure values 53.45 x lo3.T.4. 1. Construct the pressure traverse if q.87 4.1.935 0.13 is the differential curve dhldp = q p ) .1 1 10.1 kg/m3.07 1.69 304 26 1 204 145 116 4. M t =4. n.9 15.= 1.1 50.26 33.74 5. The starting point of this graph is defined by the co-ordinates Land p.44 P "UP B0 bars 53 45 35 25 20 m3 m3 8.0 44.is calculated using Eq.d=2 718 in. T=324 K.4 . According to the diagram. - - ~RP m3/m3 Rs m3/m3 R-R. p.35 3.7 79.=830+ 164 x 1.4 .0 36.8 bars.45. R.=4. Graph I1 represents the function h = @(p) resulting from the graphical integration of Graph I. Table 1.17 3. valid at the lower end of the tubing string. Diagram 1. 1.45 x lo3 .4.47 x l o 3 (m3/m3)/bar.4 28. If the pressure required to transport the well fluids through the flow line is less than that.= 1..93 694 8.4. p.=45.35.66 3.32 3. =0.. pw.= 1. the well will flow.40 14 0 1.4 m3/d. SELECTED TOPICS I N FLOW MECHANICS The multiphase mass factor Example 1.=830 kg/m3. P bars T~.4 18. C = 1.0 38. By Eq.9 25.22 1.91 x x 1010=0.12 now yields C = 1.=232 K.75 (m3/m3)/bar.25 and 20 bars.1= 1010 kg/m3. 1. q .40 1.91 x x 1010=0.1 = 1010 kg/m3 and q0M.56 7.Rw.00 12. p0. =53 bars. p.. R. Graph I in Fig.950 40.855 0. Bo. = 42.= 288 K. =0.03 2.10 6. thus. therefore. The Gilbert procedure presupposes.4 m3/d..4-2. MULTIPHASE FLOW OF LIQUIDS A N D GASES 73 It was Poettmann and Carpenter (1953) who first emphasized the significance of pressure traverse and introduced the method of constructing pressure traverses by using the concept of pressure gradient. = 53 bars.i.I to A . as well as the actual ratio of liquid to gas and sometimes also the flow pattern. d = 2 718 in. In addition to the gradient curves. the gas-oil ratio R.. Remarkable deviations may arise. 1. and the bracketing q.. curves for various flow rates. This operation results in the h = @(p). (e) Gilbert's set of curves According to Gilbert (1955) it is superfluous to determine pressure traverses by calculation. The ordinate h' corresponding to a pressure p.. Figures A .10 in the Appendix show Gilbert's pressure gradient curves. both of which are traced ori the same sheet of tracing paper. then. = 42. curve shown in Fig. 1.1 by Gilbert's method. Deviations of the calculated pressure gadients from those observed in oil wells are considered to be the results of (a) the second term of the right-hand side of Eq.. the curve section between the points A and B is the actual pressure gradient curve. 1. the last five to tubing of 2 718 in. . diameter. is interpolated between the two gradient curves belonging to the two bracketing values of q. Example 1.. Gilbert has constructed sets of curves based on flow experiments in oil wells: it is sufficient to choose the flow curve suited to the problem in hand. Gilbert has also published similar sets of gradient curves for the standard tubing sizes of 1. Solve example 1.5 in. diameter.16..9 and 3.L= 1150 m. Experience shows. the curve should be constructed by interpolation on tracing paper placed on the sheet./Ah have been taken as proportional to the square of flow velocity). (b) The loss factor (f) is supposed to be constant for the total length of tubing. From the set of sheets corresponding to the tubing size d in question 1 selects the two sheets with the 9. These cases are..4.6.4. At a distance L from that point one finds the wellhead pressure p. He performed his experiments on wells producing oil of 825 -964 kg/m3 density. The required pressure gradient curve can be selected as follows. however. that the pressure gradient depends largely on the tubing diameter d.4 ..the "flowing loss" . The data of the problem are: p. and the pressure p. that specific volume of the fluid. may be subject to change along the tubing string and thus the loss factor cannot be constant either. in the problem. the flow rate q.9 corresponding to d = 2 718 in. in systems where slippage predominates over friction. inadequately characterized.. If the sheets show no gradient curve for the desired R value... (c) Flowing losses are assumed to be independent of viscosity and this necessarily leads to inaccuracies especially when the flowing viscosity of the oil is high. which are shown here in SI units. The first five Figures refer to tubing of 2 318 in. Select sheets A . but deemed his curves approximately suitable for liquids of other densities also. The gradient curve for the desired value of q.. Each sheet carries a set of h = @(p).4-22 . The curve with the least mean gradient is indicated by an arrow.'s bracketing the actual q.being described as of a purely frictional nature (Ap. at the lower end of the tubing is read from this curve. R = 164 m3/m3. q.8 and A .1.. reveal that to any liquid flow rate q.74 1. 1. tubing string of 2438 m length at a wellhead pressure of 1 bar for a variety of gas-oil ratios. there belongs a specific gas . is the only independent variable. The wellhead pressure is. interpolate curves for R = 164 between the curves for R = 150 and R = 200 on both sheets.)/Ly. is shown here as Fig.17. According to the co-ordinate system on the sheet which is visible through or can be transferred to the tracing paper. 17-6bars. =42-4 m3/d.. the curves p. and R. bars "I Fig. curves reveal that to any value of specific gas consumption there is a liquid flow rate q.7 and 63. SELECTED TOPICS IN FLOW MECHANICS equal to 31.4.16.. so that p.4. = @(q. =8'(R). consequently. read at 2100. On a sheet of tracing paper.).5 m3/d. The diagram thus essentially shows the relationship between p.1150=950 m. (or 8 will be greater than the minimum. since in the relationship F=(p. then interpolate between the two traces to obtained the pressure gradient curve carresponding to q. -p.0 and 17. It shows the liquid flow rates of a 2 7/8 in. The total energy loss increases above this minimum by the increase in friction loss at higher flow rates and by the increase in slippage loss at lower ones... The points p. 1.6 bars (see Fig. p. d and p2 kept constant. respectively. the h' value p. are connected by curve 1. q. Thinking back to Krylov's theory we may visualize the vertical co-ordinate axis calibrated in the pressure gradient rather than in p.= 53 p. The p . 1. at which the tubing-bottom pressure p. Flow in the tubing string will be characterized by the pressure traverse between 53. transposed into SI units. with L. On the other hand. It was on the basis of the pressure gradient curves that Gilbert prepared his diagram which.0 bars is 2100 m. (or the pressure gradient 8 is a minimum. Determining wellhead pressure using pressure traverse curves belonging to 53.16).4. . The total energy loss increases above this minimum owing to an increased slippage loss at lower. MULTIPHASE FLOW OF LIQUIDS A N D GASES 75 consumption R at which p .4.4. and to an increased friction loss at higher. Despite all these problems ease and rapidity are undeniable merits of Gilbert's method. relative gas concentrations.17. therefore.and gas-lift wells was previously permitted by this method only. There is. Characteristic surface of vertical two-phase flow after GILBERT (1955) tannot be established to a satisfactory accuracy unless the properties of the liquid and gas and the temperature conditions of the well in question closely resemble those studied by Gilbert (1955). which is. The points pi. Based on the Poettmann-Carpenter theory several sets ofcurves resembling those of Gilbert's . are connected by curve 2. 1. of remarkable practical significance. Gilbert's pressure gradient curves permit the rapid solution of numerous ~racticalproblems. Theoretical solution of a wide variety of problems connected to hoth flowing. (or 0 is least. the disadvantage that pressure changes Fig. however.1. . the smaller the pressure gradient. The greater the gas-oil ratio of the mixed fluid flow. the more so since computerized numerical methods are generally unsuited for didactic representation of theoretical interrelations. at least not in planning. USA) gas-oil ratio. Duns and Ros 1963). 1. The .18.5. 1. ps9 Fig. The diagram of the experimental apparatus is shown in Fig. . a curve of which is shown in Fig. The gas conduit on the right-hand side. delivers air to this same pipe. Pump 1 delivers liquid from tank 2 to the experimental pipe 3. Although today Gilbert's sets of curves have no practical significance. (Handbook . theoretically they are sound enough to be used hereinafter freely. For an example consider the diagrams of the Garrett Oil Co. Longview. indicated by an arrow. SELECTED TOPICS IN FLOW MECHANICS had been computed and constructed for oil and water of various physical properties.76 I.18 in the original American units. Texas. 1959. Family of pressure traverse curves.4-19. 1959). p. Inc. 1.4.. It clearly demonstrates the conceptual fault of the Poettmann-Carpenter theory: due to inappropriate description of slippage losses these curves do not exhibit an optimal L 0 feet loo0 2000 3000 Goo0 5000 6000 7000 m KX)8001200)6002000ZMO P. (f) Ros' and Duns' theory Ros' and Duns' theory is based on laboratory experiments (Ros 1961.4. 825 (by permission of Axelson. from US1 Handbook of Gas Lift.4 . 19. by as much as three times. flow temperature is measured by thermometer 13. separated in separator 6 is recirculated to tank 2.g results in The left-hand side now stands for the dimensionless pressure-gradient 5. Liquid throughput is measured by instrument 9.10 by p. A radioactive tracer is admixed to the liquid: the counter 14 serves to determine the radiation level in pipe section 4. MULTIPHASE FLOW OF LIQUIDS A N D GASES 77 experimental pipe consists of three sections: the inflow section 3. 1.1. ~ i v i s i o nof both sides of Eq. Ros' experimental set-up. the gradients in the measuring section. The pressure gradient is much greater in the initial section of an experimental pipe than higher up. from its reading. The liquid. respectively. after Ros (1961) Pressures in pipe section 4 are measured by manometer 1 1 and differential pressure gauge 12. the liquid-gas saturation affected by slippage can be calculated. Liquid level and pressure in the separator are regulated by devices 8 and 7. and the outflow section 5.4. He found pressure gradients in the inflow section exceeded. 1.4.4. t Fig. the air escapes in the direction of the upper arrow. Ros used an inflow section of 25 m in length before his measuring pipe section of 10 m length. gas throughput by instrument TO. the measuring section 4. Multiplication and division by Ah of the first term of the denominator on the righthand side results in ~k g d h P ~ s A ~ . 78 I. = ( ~ s I P I + ~ sPg ~ g ) ~ . as listed in Table 1. one can derive 10 dimensionless factors Table 1. According to Eq. 1. Ros has shown that the flowing pressure gradient is a function of twelve variables. we find that c.4-2. ~ q . 1'1 PS PI PS ML-' ML-3 ML-IT-' ML-'T-' Surface tension Wetting angle u Acceleration of gravity k Vsl LT-I LT-I M T .) !h P Apart from the somewhat different notation this is the so-called Ros' gradient formula.4-29 results in (= rm 1-( 4 1 P I + 4f 1.-~1 S Ah is the dimensionless friction gradient. by the approximate term us.4-2. Flow velocity of gas over entire cross-sectional area A. SELECTED TOPICS IN FLOW MECHANICS which represents the static pressure of the fluid mixture column Ah. Roughness of wall Deflection of hole from vertical di cp L L - Liquid density Gas density Liquid viscosity Gas viscosity Flow velocity of liquid over entire cross-sectional area A. When substituting this expression into the above equation and substituting o. D. 1.4-30 + csq P. Substitution of the deduced relations into Eq. I Designation Symbol I Dimension of variable (I) Pipe parameters (11) Liquid and gas parameters (111) Parameters of interaction between liquid and gas I. where ( q k p k ) is the mass-flow P rate OkPk = 4kPk 7= z 1 ( ~ l ~ I + ~ g ~ g ~ = ~ s l ~ l + ~ s . The expression is also called the dimensionless mass gradient tm. These variables do not include pressure and temperature.7/a C.4 . = -. Applying the rules of dimensional analysis.~ a LT-~ . because the gradient is to be established a t the actual values of these two parameters. expressed in liquid column height units as related to the pipe length. .4 .. i. a dynamic state.. Pressure changes due to energy consumption on acceleration within Flow Regions I and I1 are slight enough to be negligible in almost every practical application. Both are characterized by gas bubbles dispersed in the continuous liquid phase. have no physical meaning. 1. Vsl -4/m Ros' and Duns' proposed different way of computation of the pressure gradient are expressed by Eq.4 . In Region 111. = pdp. The pressure difference between the two ends of the pipe-string will then be Let us now rewrite this Equation using p. Of these only five play significant roles according to Ros. the flow is of the mist-flow type..1. =di J ~ l g I o N. liquid flow velocity number N.) and dividing both sides by p. The left-hand side will now stand for the dimensionless mass gradient: To calculate the mass gradient E. (01. The mass gradient 5. = v.. Introducing notations qg/A = v.1.that is there is a well-marked transition zone between the two. I1 and 111 in Fig. in-situ gas-oil ratio R 91 =!k Nd...=P~ N. gas-liquid density number N . has to be known.30.e. Transition from Region I1 to Region 111 is gradual . Three flow regions are distinguished.. MULTIPHASE FLOW OF LIQUIDS AND GASES 79 from the 12 variables.4-2.4. pipe diameter number N. that is C. to call it the mass gradient.4 can be rewritten in the form It should be noted that us. they can also be called . gas is the continuous phase containing fineiy dispersed drops of fluid. on the contrary..4. Let the bulk density of a liquid-gas mixture filling a pipe-string of Ah length be p. and qJA =us. because it is affected also by slippage losses which presuppose flow.Ros terms the static gradient. With some slight modifications these five factors are: N. replacing 6. Eq. I. in the present author's opinion. = 0 and thus the dimensionless pressure gradient <. Flow in Regions I and I1 is of the slug or foam type. 1. 1. and us. It is more appropriate. Rgl. . as expressed in Eq. 1. Interpretation of the mass gradient according to the above concept is as follows.. liquid-viscosity number N. by (1-E. .. 1. Consequently.32. ..). S= are parameters depending on w.4-22 L.. S in Flow Region 11 Flow here is of the slug or foam type.. Flow Region I1 extends from the upper boundary of Region 1 to the boundary Special attention should be paid to heading. depend.4-23 and 1.. that is. According to Ros and Duns the dimensionless form of the slippage velocity can be expressed as If S is known the v.. .4-33 and finally 5.4. can be calculated using Eq. + L z N .1 . S is a function of four dimensionless quantities..(g)3..N.between the gradients valid in Regions I and I1 in the way described in Section 1.35 should also be used here. ..N. . can be calculated by Eq. that is. . In the case of annular flow.4 ..4-2 Flow Region I is of the slug or foam type and By Figs 1. the properties of the liquid. N. . 1. The total pressure gradient is to be determined by interpolation . on the liquid properties. 1. I1 and I11 Ros and Duns proposed the following methods: S in Flow Region 1 By Fig.= L. as above.4-20 and 1.4. also. by Figs 1. N d depends on the wetted circumference: 7 Region I extends between R. .. Quantities F . In the case of annular flow.. = O and R. . N.. and L 2 both depend on N . SELECTED TOPICS I N FLOW MECHANICS the virtual or the superficial gas or liquid flow velocity. in this case.4-24. 1.80 I . 1. the dimensionless tubing diameter. S is. 1... .4-21 the quantities F.. To compute S for flow Regions I. next E. a function of the four dimensionless factors. by Eq.4. N .34. Eq.. R. By Fig. 4. 1. 1. MULTIPHASE FLOW OF LIQUIDS A N D GASES Fig. Fig. Fig. 1. u .4-21.4-22.4-20.1. I .4.=O. using Eq.4-23. S in Flow Region If1 In the case of mist flow. 1. SELECTED TOPICS I N FLOW MECHANICS Fig. the high-velocity gas entrains the small drops of oil so fast that there is practically no velocity difference between the phases. 1.4-32. v. Substitution into Eq.. i t is easy to calculate t. 1.. ..33 results in VSI Having determined E. that is. Let the volume of the oil be unity. and diby the appropriate dimensionless factors we find that Experiments have furnished the friction factor formula. A relationship suited for calculating this effect is the "Fanning form" of Eq. (p.p.8: GP.. and hence the total mass is ( p .and substituting u. 1. 1.=75+84N~.)..39 (f)2..4. The total fluid density in the tubing is. then. = 4f 2di 1. us.75..Friction loss in Flow Regions I and I1 is due to shear in the continuous liquid phase. Ah.1.p.4 .....4-40 we get Dividing both sides of this equation by the specific weight of the liquid phase. MULTIPHASE FLOW OF LIQUIDS A N D GASES 83 There is a zone of transition between Flow Regions I1 and 111. Ap. The mass of liquid in this length of tubing is p.4-40 The presence of gas results in accelerated flow of the liquid phase..).g). and that of the gas be R. 1.4. . + R. The lower boundary of Region 111 does not coincide with the upper boundary of Region 11: it is defined by the relationship Rg1Nl. . The bulk velocity through the cross-section AT is Let the volume of an infinitesimal length of tubing be (1 + R.. Substituting the above equations for vk and pk into Eq. The friction gradient t. that of the gas is R. because the mass of the gas is usually a negligible fraction of the total fluid mass. is another correction factor. 1. depends at a given tubing size primarily on the in-situ gas-liquid ratio and can be read off Fig.which can be read off a slightly modified Moody diagram as a function of the Reynolds number for the liquid (Fig. 0. SELECTED TOPICS IN FLOW MECHANICS Factor f depends largely on f.4-25). after DUNSand Ros (1963) Fig. 1.. whose value depends on the viscosity of .01 0.02 0..4-25 differsfrom the Moody diagram for single-phase flow in that the transitional zone between the laminar and turbulent regions is different..008 0.26.4 -25. Figure 1. Factor f.04 0... Factor f.006 0. Friction factor of vertical two-phase flow. Its value is close to unity at low values of R. but decreases appreciably at higher R. simpler.84 1.002 10 2 lo3 104 105 lo6 N uet 10' Fig. In the case of annular flow di is to be substituted by (dci+dTa)and fl 0.4.R. N i l 3 . 1.4 -26 as a function of the dimensionlessexpressionf.s. 1.001 0.03 . In mist flow the roughness of the pipe does not enter into direct play. the continuous phase is the gas.. on transition the roughness of the pipe. the ripple effect is weak but never less than x d i . it is "sensed" through the intermediary of a liquid film covering the pipe wall. 1.4. on the gas-liquid ratio R g I . Ah 2di and 5 --Apf *-A ~ P I ~ the friction gradient. This phenomenon can be characterized by the Weber number The value of N w . The relationship holds for Flow Regions I and 11. that is. due to friction between the gas and the pipe wall. = 50 36NI. PP2 In mist flow and at high values of v.. can be read from Fig.= 0 to R. N . and. In Region 111.. With this knowledge k can be calculated from Eq. . MULTIPHASE FLOW OF LIQUIDS A N D GASES 85 the liquid. being responsible for a major part of the friction loss.4-27 in the function of expression 2 2 . friction loss is. On the other hand.1. The intensity of this effect is a function of the roughness k. that is. about PgvsgC(l . therefore. and its value can be read from the Moody diagram at the Reynolds number referring to the gas. is and using dimensionless factors Factor f equalsf. expressed in terms of liquid column height. once again. Previously it was assumed that the liquid film was of constant thickness but we are aware today that the situation is much more complicated than that. from RgIN I . that is. 1. values currently in practice this factor has no particular significance except when liquid dynamic viscosity exceeds 50 mPas.4-52. Since + A p f = 4 f -V&P. The liquid ripples on the pipe wall are generated by the upward drag of the gas on the liquid film covering the wall.. This film can be strongly rippled and thus exert a considerable hydraulic resistance.It can be calculated from the equation At R. k). a small quantity ofdispersed oil ( < 1%) may remain in the water and make it opaline and milky. Even if the largest part of the oil and water separate spontaneously from each other.86 I . u. in slug-type flow the waviness of the film may be quite considerable. ( d i . di may be V. Practice suggests that the error of the definition is rather considerable and that is why the problem will not be discussed here. As a further refinement of the calculation method. then the following formula should be used: A strong rippling of the liquid adhering to the pipe wall may be an appreciable obstacle to gas flow. The calculation of flowing gradients in the transition flow regime is made according to Section g(3). (03. owing to the breaking of each ripple as it collides with the next ripple above. especially in the liquid film along the pipe wall.di2 substituted by ( d i . . 1. k / d i > 0. influencing the flowing gradient.05. differ from those of pure water and thus may cause great errors in computation. If k/di < 0.A significant quantity of specific energy used for accelerating the rising well stream in the tubing and thus a significant pressure drop can be expected first in case of mist flow and near the surface.4.kI2 Fig.4-30. Ros and Duns propose a solution for the calculation of the pressure drop of the mixed stream even for the case when the liquid contains water but the water content does not exceed 10%. .27. The parameters of this water.Z. k/di may then attain values up to 0. may be read from the Moody diagram. on the other hand. by ---. An important finding of the authors is that in joint occurrence of oil and water in the mist flow pattern (calculation tegion 111) emulsion can develop. If.05 thenf.5. 1.and k may be determined by iteration. SELECTED TOPICS IN FLOW MECHANICS to Region 11. The totalflowing gradient and its application. Consideration of this phenomenon is made possible by Eq. 20 3.398 2. n. k = 5 x Pas.353 4. p.57 1. pOn=830 d. R. B.65 0.376 2.93 0751 0. from the following equations. In order to obtain a clear understanding of the computing method the following example is solved by graphic integration.4-3.89 6.4 37.371 1 low pattern I 11 I1 11 11 I1 .. us. R. = 1.81 0. L=1150m.1985 0. in the same way as in the poettmann-Carpenter method (Secfion 1..3590 1 R 1.2220 717. however. p..05 1 N p L1 L2 10-2 - - 1.81 m/s2.. p.1903 1. 1 kg/m3.92 1.365 29.92 1.580 1 30.6 49. y = 9.1 .78 0. P PI Py bars kg/m3 kg/m3 53 45 35 25 20 10 1 Usr m/s Us# m/s 679.333 8..55 Nr" - RNrt - N.9360 709-0 2032 0.85 1 1-321 1 16.g. The basic factors of the variables of the equations depending on pressure p are p l . =42. MULTIPHASE FLOW OF LIQUIDS A N D GASES The pressure traverse curve.1880 1 2.4.383 2.6076 704. = 164 m3/m3. The pressure gradient is computed from Eq. These factors can be defined in more than one way. p.404 2.981 bar.72 2.741 10739 1 2.4 25. theoretically. p.341 1 686.55 01940 0. and o. e.= 10 m3/m3.340 6.3 (A).23 1. T.726 m3/(m3 bar). on the basis of the pressure gradients calculated for assumed pressures. all the other data being the same as in I.42 12.=53.5 1 11.4 m3/day. In everyday practice.547 29. p l = 5 x kg/m3. T = 3 2 4 K.76 1.= 232 K.30. Let us define the pressure traverse curve on the basis of Ros' theory if the production data are: (I) q..004 29.91 1..(d)).92 1.. due to the large labour requirements of the computation the pressure traverse curve is computed by applying numerical integration with the help of computers.04 1 0.1965 0. = 45. Example 1.1915 0. a =0.365 3.5 bar.748 0747 0.38 1.8 59.561 29.47 x 10-3 m3/(m3 bar).379 2.390 2.030 N/m. if the liquid is waterless oil: Table 1.= 1 .4.4. di=0. can be computed.i - 1.13 4.= 1-14 m3/m3. Tn= 288 K. (11) Rgl=400 m3/m3.92 1.236 29.4.062 m.0 bar.=0.87 1. 1.4323 695.. =0.744 0. n. 163 0.163 - F5 5.3376 0.163 0.345 2.62 6.4613 I33825 0.2415 - &I 3.0.782 10-'bar/m 6) 1673 - 1.768 4.64 6.63 6.5274 0.481 1.802 3.163 I3163 0.64 6.13 F6 6.506 1.0150 1.067 1.23 4.800 2.4 .Y m/s Ugs 0.0 - F4 0.312 1.3320 Table 1. F2 FI P 39. 0.66 5.2810 2.65 loZ F.071 1.977 16.5421 97074 1.388 - .641 I - f2 .502 1.415 3.31 202 - - - bars 53 45 35 25 20 10 F.100 8.131 0.243 1.932 7.030 0.57 4.41 lo-' N R ~ ~fl 10-2 1.5287 0. 2.3483 0.783 3.3 (B).79 4.885 0806 0.448 1.898 1. 4-28. .9 dp Remark: dh = i y .3.4.95 39.4. ($Irn Table 1.396 2.1 5. 1.20 53. dp dh dh - lo-* bar/m m/bar 3. . dp ‘-Ih f P bar/m bars 53 45 35 25 20 10 3.824 3.861 2. The variation of the inverse gradients in the function of pressure is shown on Fig.881 26. part D lists inverse gradients of (11) in Example 1.4-3.16 = [ m i l and ($)r dp = dh dp .837 3. 1. B.3 (C).45 34. MULTIPHASE FLOW OF LIQUIDS AND GASES Table 1.4.4-28. Parts A.1 7. Fig.06 26.1.15 29.551 1.1 6.0 9.3 (D).4. and C list intermediate results of (I). The curves h=f(p) obtained by graphic integration are also shown. Due to the graphical solution the gradients are shown as differentials. The main intermediate results of the computation can be seen from Table 1.5 4. /4..'75) .N.4 ..lNl"<(50+ 36NI") RglNl. principally the computation of the transition zone is also performed by applying this correlation with some formal changes. >(75 + 84NP. Let us substitute the expression for mass flow q.4-4.>(50+36Nl.. and.I . N. he also improved the computational relations. For description of the slug flow pattern the same correlation served as the basis but was improved. $ can be defined by the following equation: .4-4 Flow pattern Designation Physical nature Bubble Slug Continuous liquid phase with dispersed gas bubbles Liquid and gas slugs Transition Continuous liquid phase gradually ceases Mist Continuous gas phase with liquid mist Equations of pattern boundaries + 4./A instead of v. His analysis on the basis of the measured data of 148 wells (a large part of the data were taken from the literature) showed that no single correlation or calculation method existed which was accurate enough to be applied in practice for all cases. and then and the pressure gradient The boundaries of the flow and proper calculation regions can be calculated from the equations of Table 1. That is why he selected theories he considered the most suitable for the different flow patterns. he also wished to match the calculation regions with the flow patterns. To simulate the mist flow he applied the Ros-Duns correlation and. 1. < 49/41 > $ R.2 Table 1.. As an improvement. compared to the Duns-Ros theory. = pkvkAinto Eq.7/a and q. in order to increase the accuracy in certain cases. The flowing gradient can be derived on the basis of the following considerations...) R. SELECTED TOPICS IN FLOW MECHANICS (g) Orkiszewski's theory To elaborate his method Orkiszewski (1967)made use of several correlations. < ( 7 5 + 8 4 ~ : : " ) R. To describe the bubble or froth flow he applied the Griftith-Wallis correlation without any change. is considered to be constant by the author. Bubbleflow. respectively. compared to that of the fluid of greater density.4-2. calculution region 11. .4 . The size and material of slug g remains the same. 1. MULTIPHASE FLOW OF LIQUIDS A N D GASES 91 (g) 1.4.Liquid and gas slugs rise. the fluid of lower density. If. this latter will fall back relatively along the pipe wall and will increase the height of the slug below.g. . . -From equations 1.. P1 1. It suggests .) = q. Slugflow. 1.will clearly define the average density of the fluid rising in the tubing.while that of the fluid of lower density is q.cl)= E~ . The pressure gradient due to friction can be calculated from the Weisbach formula valid for liquid flow: where v. so that the top of slug g will penetrate into the bottom of slug I. the real liquid flow velocity. If the velocity of the two fluid streams is the same then during a longer period. proportionally. 1. above each other in the tubing string. when it reaches it. the number and total length of the 1 slugs present in the tubing at the same time will be smaller.) fluid stream rises to the surface and its flow velocity is (q.A steady (q.4. (ql + q. can be defined from Eq. however.4 .+q. the cross-sectional fraction of the gas phase can be derived: o.24m/s.4-62 (g) 2. With this knowledge 6. its value is 0. but their material changes. . The I slugs become shorter at the bottom at the same rate that they become longer at the top. e. from Eq.1 and 1. Let us suppose that slugs or column of two incompressible fluids of different density are rising in the tubing and following each other. It means that their total length remains the same./q. the ratio of the lengths of the fluid slugs rising in the tubing will match the ratio of the fluid volumes produced at the surface.4. The quasi-stationary flow rate of the fluid of greater density is q. the shorter the time required to raise the g slugs in the tubing and this means that. a density difference occurs between the two fluids. one day.4 and from (1 . from the Moody diagram at the actual Reynolds number: ~~diul N R e =-. g.60 and p. from Eq. The greater the rising velocity of the fluid of smaller density.1 can be directly determined. + q. The gas slippage and the increase in flowing density of the mixture columns can be interpreted in the following manner. . .)/A. the producing volume ratio. by the author.1. q.1 is read. the flow velocity will also differ. calculation region I . will attempt to break through the fluid slug of greater density. Knowing the densities of the two fluids. SELECTED TOPICS I N FLOW MECHANICS that the greater the slippage velocity of the fluid g.4-29. 1.4 .30 0. It can be clearly seen that no change occurs in the above conclusion if the fluid of greater density is real liquid.40 C3 0.29. 0. according to OKKISZEWSKI (1967) On the basis of former literary sources Griffith and Wallis assume that the actual rising velocity of the liquid slugs is while that of the gas slugs is These assumptions lead to the conclusion that the mixture density is According to Grifith and Wallis the gas slippage velocity is vgs=c3c4 JZ? where C3 can be read from Fig. and C4 from Fig. 1.20 0.4-30 in the function of Nitel= Pldivt PI . Factor C . while that of the smaller density is (compressible) gas.10 0 0 10 30 20 40 50 N~egs Fig. 1. . the greater the flowing pressure effecting the tubing shoe.92 1. 1.2 1.4-69 are not used in their derived form but they are reduced so that q. That is why he extended the formula of Eq. according to ORKISZEWSKI (1967) Orkiszewski (1967) found that in slug flow the Griffith-Wallis correlation is of sufficient accuracy only at low flow rates.: In addition to the diagrams for the determination of C. According to Orkiszewski the mixture density is To characterize T he derived a formula from the data published by Hagedorn and Brown (1965). = q.e. but also in the form of liquid film covering the pipe wall as well as in the form of mist dispersed in the gas phase. .4-30.i. 1. which if the liquid is water and if it is oil The values for ai and n can be found in Table 1. . v.4-5. v. T. 1.4 1. for a greater range of validity are given by the author. 1. the total fluid mass flow .0 0 1000 2000 3000 4000 5000 6000 N ~ e t Fig.3 1. and C..5 c.. Factor C .1..4-65 and 1. The pressure drop due to friction in Orkiszewski's opinion is It is remarkable that to determine pko Eqs 1.1 1.By this he wished to express that liquid flows not only in well distinguishable slugs from the gas. MULTIPHASE FLOW OF LIQUIDS AND GASES 93 The total flow velocity.65 and introduced the liquid distribution factor.4. is a fictitious physical quantity which is used by some authors for the approximate calculation of the mixture flow velocity.4. ) I k ( 1 O 3 ~ . +1) -./Ah valid for the transition zone Orkiszewski basically uses the weighted averages suggested by Ros and Duns. and Ap. SELECTED TOPICS IN FLOW MECHANICS Table 1. The formulae for calculation with dimensionless factors and similarly A p.63 Igd. ..+ %. The friction factor 1can be read in the function of N.4. Limit of applicability u.25.516+lg v.722+0.. 1 1 1 Ir> The continuous liquid phase is water 2. (g) 3.162 -0. 75 84Nf. 1. in the case ofmist flow.523 x lo-' -0.75-(50 + 36N.+ 0.N.547 x ~ is considered to be equal with the liquid mass flow. calculation region 1 1 1 . expressed with Eq. - Ah 75 + 84NP.428 0 r 2 -0. Transition and mistflow putterns. 1.'75.4-5. d!'s71 1. m/s <3 >3 n / 1 1-38 a3 a2 01 a.888 0 -*(I x 0.4 . t In Orkiszewski's opinion the value of the frictional gradient is more accurate in the transition zone if.Rg.. q.AT -:I) The continuous liquid phase is oil * a s = -(0.. a. the superficial gas velocity is calculated with the following equation: .T o detine the p.232 -0..782 0.) + [*I Ah .799 1 7 4 2 x 1 0 3 1 2 5 0.68 from Fig..1.213 0. Flowchart for calculating a Ahi=f(Api) increment for the determination of vertical twophase pressure drops .4 .58 and for each Ap. compared to the starting depth.1.86 -- di where ~.+ CAhi and the corresponding values pi .4. 1. is performed as described in Section 1. Ah is expressed from Eq. Determining pressure traverses. 10% of the given pi pressure value. with regard to liquid film wetting the pipe wall.~. the depth increment Ahi is calculated. .005 then k =34 - di and if N >0. then k 174. If the abscissa value N SO. r-l Estrmate ~ h . u Assume A p.4.27 he expressed the relative roughness kld. give the depth sequence Li=L.005. MULTIPHASE FLOW OF LIQUIDS AND GASES 95 The calculation of the friction pressure drop. -T o determine the pressure traverse curve starting from the wellhead or bottom-hole pressures p i .Li give the pressure traverse curve. 1. 1.. Orkiszewski has only introduced the following computative simplification: From the curve shown in Fig.4. 1 *] Colculofe in-situ Colculote Ah. The sum of the depth increments Ah.Zgdi 9 (g) 4.2.4-31. uslng Eq 1 4-58 iterative procedure I Compute a furt h e r step I Fig.1 -(f). pressure sequence is taken with Api steps. In order to secure proper accuracy the Api pressure step is selected to be ca.di ~g~. 1. (b) slug.4-31.4-32. SELECTED TOPICS I N FLOW MECHANICS Calculate NRegri NRI. . the next step can be calculated. finishing the iteration. If the assumed Ah: matches the Ahi value calculated from Eq.and (c) mist flow patterns The flow chart of the calculation of one step is shown in Fig. 1. is done by iteration.4.- I. & Determine l 5r Calculate & Determine Calculate C1 (c) Fig. Flowchart of mixture density and frictional pressure drop calculations by the Orkiszewski correlation for (a) bubble-. 1.58 with a prescribed accuracy then. Due to the effect of the temperature (which is a pre-determined function of depth) on the in situ flow parameters the determination of Ah. b. Accuracy tests show that the correlation or the computational method. a.4 -33 is valid for the fluids of oil field Algyo and shows a sheet of family curves defined by computer on the basis of the Orkiszewski theory. Figure 1. c also refers to the mist flow correlation treated by Ros. MULTIPHASE FLOW OF LiQUiDS A N D GASES The flow chart. Family of gradient curves for the Algyo (Hungary) oilfield. yield a relatively good results in water cut oil as well. bars Fig. serving as the basis of a computer program.4-33. 1.4. constructed by Orkiszewski method .4 -32.97 1. An optimal gasliquid ratio similar to the gradient curves of Gilbert type can also be seen here. Figure 32. c. can be seen in Fig. respectively. p. 1. i..3 5 ) . This expression. In addition to the above-described theories there are several others which can be rather accurate for certain cases.4-34.. They made their experiments in the La Paz field. the different ways of the application. and the gas-liquid mass flow rate-ratio. 1 b= eO. N.. . is the following: where a= Rm and 1+R. 7he improvement of the Poettmann-Carpenter method. and ( o )flowlines y.e. 1. . and 3 1/2 in. with producing wells using 2 7/8 in. at the same time.. Tek recognized one of the mistakes of the Poettmann-Carpenter theory. That is why he wanted to make the method more accurate by giving the loss factor curve on the basis of field measurement data in the function of a particular expression ( F i g . 1. and those of the liquid stream. R. N.4 .. Venezuela.Baxendell and Thomas attempted to extend the applicability of the Poettmann-Carpenter correlation by extending the "Jcurve" for larger mass flow rates (Fig. when determining the loss factor the gas and liquid fraction of the well stream is not taken into account (Tek 1961). containing the Reynolds numbers on the basis of the characteristics of the gas stream. which is why their application may be justified. after BAXENDELL and THOMAS (1961) (h) 1. 1. Experlrnents In ( 0 ) vertical annulus.g Fig. SELECTED TOPICS IN FLOW MECHANICS (h) Other correlations The theories described so far were selected to introduce the main stations of the development of the multiphase vertical flow theories. and. . Energy loss factor.4-34). ' .lR. In the following part these correlations will be discussed briefly.I . diameter tubing (Baxendell and Thomas 1961). after TEK(1961) 10' f 1o0 10' lo0 Fig.4. 1. Energy loss factor. NRe.)-0.O b lg ( NRe.l R.O 4. after FANCHERand BROWN .1. 10' lo2 10' 4vg [kglmsl Energy loss factor.O 6. 1. MULTIPHASE FLOW OF LIQUIDS A N D GASES 3.O a 5.4-36.4-35. Fig. 1.1.. Rearranging Eq. R. The curves were determined by measurements in a well ofca. that is + pk = p I ( l -cg) P.36). 1. The second theory of Hagedorn and Brown (1965). and $.).4-37.2M: vk= 7then . 2400 m depth with tubing of 2 3/8" nominal diameter (Fig. + The procedures applied by the different authors vary because of the different approaches they used to calculate E. Except for Patsch they use the Weisbach or Fanning equations (Eq. 1. pg(l . SELECTED TOPICS IN FLOW MECHANICS For the same reasons Fancher and Brown (1963) modified PoettmannCarpenter's f curve so that the expressio-n (di up) remained for the independent variable. 1. 1. respectively. 1. @. but moref curves were given for the different gas-oil ratios. Substituting it into Eq. To determine E. can be read from Fig. . di a Ah 1'23pkd? Let us interpret C. (h)2. More accurate methods to calculate pk . 4.4-8) with some modifications to determine the friction pressure drop.4.Other researchers tried to define pk of the basic Eq.1 is used.10 more accurately than Ros. and then pk = PIE. Duns and Orkiszewski. To calculate the pk mixture density we use Eq.7 / b .= -24.100 1. 1.4. from the difference form of Eq. No flow patterns and calculation regions are differentiated but a uniform calculation method is applied for bubble and slug flow patterns.10 we obtain the following relation Let us express Apl/Ah from Eq. respectively. froth and slug flow patterns. 1. E.4.4 . . 1.4. If we know factors @. The derived relations are valid for bubble.experiments were performed in surface experimental setups and relations were derived from these experiments. .E.4-78 we obtain the basic Hagedorn-Brown equation expressed in SI units.4.. can be calculated from equation as follows . To characterize the mixture density Eq. 1.E.4-8 interpreted as a difference-equation and let the mixture flow velocity qoM. 4.4. 1.4-39 where 1. . ----* ae fi'Q 0.4-38 as the function of N .6 0. 1.4 0. 1. from Fig. MULTIPHASE FLOW OF LIQUIDS AND GASES where C N . Fig.4-38.o ---. lo-( ro-' lo-2 . Factor +can be determined as the function of @.. 1.101 1.2 0 lo-' lo-= Fig. can be obtained from Fig.37. by numerical integration. SELECTED TOPICS IN FLOW MECHANICS 0 0. To determine the friction factor in Eq.1 1 can be expressed in the form Similarly to the "western methods" Patsch considered this basic equation as a difference equation.1. v.09 0. A = us. 1.01 0. 1.. the Moody-diagram is used so that the Reynolds number is NRe= -.04 0.e. 1.07 0.05 0. where ~ d i ~ k Pk and the average viscosity of the mixture can be determined from The kinetic term (the third member of the right-hand side of Eq. that is Av. differently to Krylov..03 0. .06 0. 1. which. is calculated from Eq.4 .o ? ~. us.4. Patsch (1969.102 I .4-8 of the friction pressure drop.g Eq. = u. 1971) extended Krylov's theory.: . i.~.10 02 Fig. flow velocities of the gas. A it follows that the cross-sectional fraction of the gas phase is equal to the ratio of the superficial.08 0. and actual. With the interpretation < = Ap/Ahp.4-78) is calculated on the basis of the velocities valid for the input and output cross-sections of the examined pipe section.4-39. From u. p. 1. can be solved in the same way as the basic gradient equations of other correlations.02 0. 2. that the viscosity of the oil for the given cases was 1 cPas.4 . The basic equation applied by Aziz-Gooier-Fogarasi (1972) in their calculation method is essentially the same as Eq. were calculated for different mixture flow velocities. To calculate the mixture density they use Eq. i. however.) + 0. These equations were taken from different studies by different authors. in the different flow patterns they tried to apply the vgs gas slippage velocity relations which characterize the best of the physical phenomena. The calculation method is performed for the first two flow patterns.4. MULTIPHASE FLOW OF LIQUIDS AND GASES 103 From measurement data obtained in flowing wells in the Algyo oilfield the values of and o.026 (us. Following Zuber and Findlay Eq. For bubble flow pattern and in Wallis' opinion for the slug flow pattern where Here the liquid viscosity number is .e. and annular-mist flow patterns are differentiated. 1.1. To calculate^.+vsq by applying the Ros-Duns method. slug.83 is generalized in the following form: where o. According to Zuber and Findlay for turbulent flow C = 1. less than 10 cP. v. It was found that for the bubble and slug flow patterns studied vq = 1. 1.. froth. An advantage of this method is that it is a good approach of the Ros-Duns method for the flow patterns mentioned and the required computer time is no more that 5 percent of the Ros-Duns process.+ us. On the basis of earlier studies of Govier-Radford and Duns a particular flow pattern map is also used. static liquid column. 1.=vs.4. is the rising velocity of the gas bubble in a stationary.4-78.. It should be noted.1. Here bubble.28 and that is why E. To determine the friction gradient Eq.35 25 It should also be noted that to determine E. in the latter flow pattern another calculation method. In the case of two or more models or calculation methods having the same accuracy the model or method requiring the least computer time should be selected. judged to be ofequal rank. and extrapolation of Eq. The columns of this table show that.4-6 gives a general picture of the main characteristics of the different vertical two-phase flow correlations.7 [also after Takacs's (1978) study (Tables 1 and 2)] shows the values and standard deviations of the average errors of the pressure drop predictions of ten flow correlations. Table 1. according to the number of evaluations how many . 1. (i) Concluding remarks Table 1. That is why before planning the production of a given oilfield . was also elaborated by the authors.40 and 1. From these data some conclusions can be drawn concerning the application ranges. Table 1. there are ways to establish an approximate evaluation.4-8 was made using the data of Table 1.4.4 -41 (after Takics 1978)show liquid and gas flow rates applied in the experiments of the authors of the different theories. From this summary it is clearly seen that no unanimous order of rank can be stated concerning the accuracy of the correlations examined.4 . > 250 18-250 < 18 then m 10 69 (N1. 1. Above this value the flow is turbulent and the friction factor is calculated from the Colebrook equation.it is always rational to select the most accurate pressure drop calculation model on the basis of a comparison with control measurements. For greater Reynolds numbers valid for higher mixture streams they suggest the application of Nicklin's results which can be well fitted to the original Griffith and Wallis curves.4-8 was used.7.4-66 for extended ranges to calculate bubble rise velocity is also erroneous.104 I . Chierici. so that the Reynolds number was calculated from The value of the critical Reynolds number is 2100. Ciucci and Slocchi (1974) start from the Orkiszewski method and find that in slug flow the Griffith-Wallis equations would not have had to be modified by the liquid distribution factor T .)-0. Though in view of the above-stated facts the establishment of an objective hierarchy of the theories is hardly possible. Figures 1. SELECTED TOPICS IN FLOW MECHANICS and the Eotvos number is if Ni.4. Even correlations considered to be the best it frequently occurs that the differences between the measured and computed values are significant. Progressing from the greatest number towards the smallest one we get an order of accuracy (column 9). its standard deviation the smallest{column 4) and the largest (column 5).measurement errors . the largest (column 2). In column 12 the products of the data of columns 9.non-realistic consideration of the temperature . In addition to this last reason we have to add that this error first occurs with wells.the non-Newtonian flow behaviour of the oil .inaccurate consideration of the physico-chemical and thermodynamical properties of the well stream .1. while in column 11 it is established according to the standard deviation. cannot be considered to be an order of rank of the full value and objectivity because the evaluations of the different authors examined here referred to wells of different numbers and parameters.paraffin or scale deposits . In column 10 order is established according to absolute values of the average errors.the impact of the water and emulsion contents of the well stream . there is a one-phase well stream at the tubing shoe and the gas begins to escape somewhere up the tubing. because a certain amount of time is required for equilibrium to develop. it also shows the arithmetic average error of the different theories (column 3) and their standard deviation (column 6). Considering the numbers in columns 1 and 4 to be positive and those in 2 and 5 to be negative we obtain summarized numbers in column 8. that is. . of course. Experiments show that gas begins to leave the solution during flow at a pressure less than the pressure measured as bubble point pressure in laboratory conditions for steady state. 10 and 11 can be seen and in column 13 these products are arranged according to magnitude.changes of the flow parameters of the non-Newtonian oils in the course of cooling . This evaluation.ignorance concerning the in the tubing string pipe wall roughness . Further research should be aimed at the elimination of errors and uncertainties due to the above factors. In two theories having the same score the one which was evaluated by more authors is ranked to be more accurate (column 7). where the tubing shoe pressure is greater than. From this we can see that the Orkiszewski theory seems to be the most accurate and the Poettmann-Carpenter theory the least. That is why even differences of 10 bars can occur between bubble point pressures measured in the laboratory and the starting pressures of the gas separation in tubing string conditions. In the opinion of the author the main reasons of this phenomenon are the following: .neglected tubing inclination .4. MULTIPHASE FLOW OF LIQUIDS A N D GASES 105 times was the average error of the correlation the smallest (column l). or equal to the bubble point pressure.the supersaturation of the liquid with gas. SELECTED TOPICS IN FLOW MECHANICS Table 1. slug bubble. 1. addition or modification Previous theories ineluded in "complete" methods Basic method for addition Essence of addition complete Poettmann Carpenter 1953 complete none none - - - - - - - PoettmannCarpenter "j curve" extended for larger rates PoettmannCarpenter "f curve" correlated with GLR Calculations depend on flow patterns Valid for flow patterns no no PoettmannCarpenter "f curve" correlated with Reynolds number no no no bubble. according . Liquid flow rate ranges of different vertical two-phase pressure drop correlations.6.I . slug bubble. slug bubble. [m31dl Fig.4. slug Yes no no no no 1959 Slippage and friction losses treated separately lo0 lo' 1961 lo2 10' 9. Authors References Krylov Muravyev PoettrnannCarpenter Tek BaxendellThomas Fancher Brown FancherBrown 1963 Tek 1961 BaxendellThomas addition addition addition "Complete" method.4-40. slug bubble. Gas-liquid ratio ranges ofdifferent vertical two-phase pressure drop correlations. 1972 1974 Orkiszewski HagedornBrown 1965 Orkiszewski 1963 complete complete complete modification complete modification none none - numerous correlations - - - GriffithWallis: Duns-Ros - - - no Yes bubble. bubble. slug bubble.Wilde 1967 Krylov - Orkiszewski pressure traverses constructed from flowing gradients - modified formulae for slug flow Yes no yes Yes bubble. MULTIPHASE FLOW OF LlQUlDS AND CASES Duns-Ros Duns-Ros HagedornBrown Patsch Aziz-GovierFogarasi Chierici-CiucciSlocchi Patsch 1971 Aziz rf al. 1. mist Yes - 1 I !!!!I!!! - ' Fig.4 -41. according to TAKACS(1978) . slug. Chierici et al. slug.107 1. slug. mist Yes bubble. slug mist Yes yes Moore . slug Yes yes bubble.4. 1972. the transport curve and the pressure traverse curve..9 44 -0.7 726 -42.2 35 d a Aziz et al.3 195.1.4 17 11.8 17 . Correlations PoettmannCarpenter BaxendellThomas 1 2 3 d a n d 6.6 223 17 -5. .3 261 726 .8 10.9 38 -2.4 50.6 38 2. 1974.0 4.2 22.9 10 4. 8 Takics 1975.3 9.5 6.5 10 ..5 361 726 .6 726 -9.4 76 1.15.6 17.7.4 7.17.3 195.1 726 .7 17. SELECTED TOPICS IN FLOW MECHANICS Table 1.1 44 16.7 726 .2 148 2. 4 McLeod et al.4 19.2 427 -8. 1974.4-7.8 47 3.9 17 -7.7 76 01 9.5.8 27.4 35 8 .2 17 -8.7 44 -2. 9 Vincze 1973.6 17 9 6.108.2 26.4 17.9 17.3 17 -12.8 25. 2 Espanol 1968.5 10 3.9 13.1 19.2 17 -9.5 10 References: 1 Orkiszewski 1967.1 19. The disadvantage is that for the determination of the transport curves only the Krylov gradient-equation is discussed in the literature and the accuracy of this equation has not been improved during the last three decades.9 35 -3.4 16.0 5. d u n Beggs-Brill d u n -4.3 4. 5 Lawson and Brill.4 76 u n FancherBrown d u n d HagedornBrown 11.5 4.8 19.9 17.7 726 -2.8 10 -3.3 17 -4.5.4 27-0 148 -0.8 10 -2.6.1 7.7 65 References 5 6 7 .1.61 21.8 6.9 17 .6 48 8. 6 Vohra et al..8 43-9 726 . With the help of the pressure gradient two relations of graphic type can be determined for the performance of tubing.6 35. 1972.6 21. The main advantage of the transport curve determined by Krylov is that by using simple equations derived from the curve the diameter of the tubing for the least specific gas requirement and the maximum flow rate can be easily calculated. .9 19. 7 Browne 1975. u Duns-Ros n d u n Orkiszewski d u n Patsch 4 07 24. 3 Aziz et al.0 12.107.8 148 17.9 21.I.2 34. n d a n Chierici et al. 10.9 17. Beggs-Brill Authors - 1 2 2 3 2 - - - 2 1 2 1 1 1 1 2 1 d max min -25.4 18.5 -7.2 -2.4-8. u max min Table 1.2 -2.6 72.3 -3.7 22.4 23. -4 0 1 -2 1 4 0 . 11 10 9 6 7 2 1 4 3 8 5 13 Final order .9 8.8 17-4 13.6 -37.9 26.1 -9. 1 1 2 1 1 2 - 2 - 1 3 1 2 - 57.5 4 3 2 6 6 8 2 5 3 3 7 6 5 4 1 of evaluations avg.PoettmannCarpenter Baxendell-Thomas Fancher-Brown Hagedorn-Brown I1 Duns-Ros Orkiszewski Patsch Aziz et al.4 -18.8 23. Chierici et al.8 -4.0 3 avg. 504 63 810 600 160 288 20 4 35 24 12 Product of cob 9.2 -3 2 8 Scores 9 I0 4 6 1 2 5 3 8 7 10 9 10 6 5 8 4 1 7 2 9 3 a Orders d-u 9 10 8 6 5 2 1 4 7 3 11 5 . and. A special problem is that the pipeline is not generally laid horizontally but follows the hilly terrain. too. Mandhane et al.1977. it consists of sections ofdifferent inclinations. as Mandhane's comparison of the values of the 10. since they are the most probable in character (Appendix. It is usually applied with the help of a "prefabricated" family of curves or "pressure lines" occasionally calculated numerically by computers. are described and applied. The results of the study were published by Lockhart and Martinelli in 1949. Pipe inclination has a great impact on pressure loss. This impact can be calculated mcrc or less accurately only on the basis of the more recent researches. This curve has several well known applications. In recent years several evaluations have been published concerning the accuracy of the more important theories and calculation methods (Brown 1977. deviated wells (Beggs-Brill). Since then several experts examined the flow phenomena. Figs 1 . The number of publications reflecting their achievements amounted to hundreds in certain years. In the literature the family of curves calculated by the Poettmann-Carpenter and the HagedornBrown method and determined by Gilbert's measurements are discussed (US1 1959.4.110 I.g.2 Flow in horizontal and inclined pipelines (a) Introduction The methodical study of the rules of the common flow of gas and liquid through horizontal pipelines began in 1939. In the present work Gilbert's family of curves. no unambiguous final conclusions concerning the accuracy of the theories can be drawn. As well as its relative accuracy the third one was selected because it makes it possible to consider the impact of hilly terrain.10). 1. or near-vertical. The second was selected because of relative accuracy was proven by several authors (Dukler 11). Winkler and Smith 1962.500 frictional pressure drops stored in the data bank in Calgary). Contrary to the other gradient curves cited they have an optimum gas-oil ratio. i.e. Brown 1967. 1. transcribed into SI units. the steepness of the pressure traverse curves continuously increase parallel to the increase of the specific gas volume (Fig.4-28). SFLECTED TOPICS IN FLOW MECHANICS The other type of curve characteristic of the performance of tubing is the pressure traverse curve. An advantage is that following the new theories the determination of a more accurate "basic curve" is possible. The first is of historical significance and was selected because of its simplicity (LockhartMartinelli). 1977). . The comparatively simple equations obtained on the basis of laboratory experiments prove to be sufficiently accurate for certain cases even today. and the gradient curve belonging to this optimum is the steepest.1980 and Gilbert 1955). it can be used for modelling the flow occurring in vertical. With regard to the above limitations we shall'discuss here only a few theories and calculation methods. what is more. In spite of the fact that results were calculated with a large number of measurement data (e. In the other published families of curves. to the Baker diagram (Fig. in our opinion. also increases the friction pressure drop.4-42..1. there is no optimum solution. for example. 1. we shall not go into detail concerning the various concepts of the different Froth p g q q Plug Annular Stratified Mist -- Dimtion of flow Wavy Fig. 1... In all sections of the pipeline the liquid level often changes during flow and these level changes consume energy. and these maps are different to some extent. Since. A similar situation concerns the flowing pressure loss of the gas phase. The reasons of this phenomenon follow. somewhat similar to the rough pipewall. The gas phase occupies a section of the pipe volume and thus reduces the cross-sectional area available to liquid flow. The abscissa is calibrated in the whereas the ordinate effective liquid-gas ratio in terms of the expression o.4 3 ) . wavy. according to Alves. after BAKEK(1954) authors but shall deal with the widespread Alves-Baker-Holmes theory.l..4-42). Two-phase flow patterns in horizontal pipelines.i$/v. . or mist type ( F i g . by which the base factors derived for the flow of water and air at atmospheric pressure and 20 "C temperature can be adapted to the prevailing conditions (Baker 1954). To predict the flow pattern prevailing under any given condition one may resort. slug.4 . annular. similar to those developing in vertical flow./. 1 . is calibrated in gas mass velocity. MULTIPHASE FLOW OF LIQUIDS A N D GASES 11 1 At common flow of gas and liquid in a horizontal pipeline the actual friction pressure drop is greater than the sum of the pressure drops calculated separately for the two different phases. are called flow patterns. In some gasliquid flow patterns the gas-liquid interface is not smooth but "rough". This interface. 1 and are pressure and temperature correction factors (after Holmes). given by the expression v.4. The friction pressure drop of the flowing liquid is inversely proportional to a more than the first power of the flow area. Several authors made flow pattern maps. (b) Flow patterns Gas and liquid flowing together in a horizontal pipe may assume a variety of geometrical arrangements and these arrangements. Alves states (Baker 1954) that the flow pattern can be of bubble. stratified. 67 cN/m. p. and p. is the surface tension of the liquid. 1 Example 1. the correction factors are and . is its viscosity.4-90 and 1.89 m3/s and p. By Eqs 1.4-91. =0.= 53. = 777 kg/m3 and a.722 kg/m3 under standard conditions. All factors are to be taken at the mean flowing pressure and at the temperature prevailing in the flow string or string section considered.8 x 10--4Pas.=3. is the flowing density of the gas. and p. where a. is the density of the liquid. q.0121 m3/s. = 5. p. if q.2 kg/m3. p. SELECTED TOPICS II*I FLOW MECHANICS where p.. =0..4-4. = 1.257 m. What is the prevailing flow pattern when oil and gas flow together in a horizontal pipeline of di=0. A( mean pipeline pressure and temperature. Fig.112 I . Ap.4-43 is.4. 1. then and the value of the abscissa is Plotting the calculated values in Fig. is the friction pressure drop.4-44. 1.44. MULTIPHASE FLOW OF LIQUIDS A N D GASES The value of the ordinate in the graph of Fig.and @.4 . (1970) after SCHLICH~NG To determine @. (c) The calculation method of Lockhardt and Martinelli The fundamental relationships obtained from the experimental data are and Ap. Lockhardt and Martinelli plotted the diagram shown on Fig.1. Also.92 and 1.4. Equations 1. 1. is the pressure drop if only liquid is flowing in the pipeline (Lockhardt and Martinelli 19491. Fig. Cha5acteristic factors of horizontal two-phase flow according to Lockhart and Martinelli.4 -93 may be freely chosen. assuming that only gas is flowing in the given pipeline. can be read as a function of . Depending on the choice @. 1.4-43 reveals the flow pattern under these conditions to be of the slug type. or @. These are to be chosen according to whether the flow of the gas and liquid. even with comparatively large. 1. first the pressure traverse along the pipe length and then the output pressure can be taken.. if the gas-liquid ratio involving the standard gas volume does not exceed 100. 80%. that the calculation gives fairly good approximate results. which. Subsequent investigations have shown. .4-43 by the area enclosed by the dashed line (Schlichting 1970).is determined for each section and. is laminar or turbulent. . but of these we shall only mention Schlichting's method. The pressure drop. .. No. The Reynolds number is to be calculated for each phase as if the other phase were not present. free water contents. No. The condition of turbulent flow is that these numbers be greater than 2000. has the advantage that it can be applied among rather wide ranges of liquid viscosity (10-60. the standard deviation does not exceed +20%. taken separately.000 cP). especially if the viscosity of the liquid is in the 5OcP range and if the liquid phase contains no free water (Schlichting 1970). . In his opinion. notwithstanding. The suggested application ranges of the theory are shown in Fig.114 I. according to the author. The basic equation of the calculation is where and The pressure drop of the pipe flow can be determined by dividing the total length. Several researchers have modified and improved the method of Lockhardt and Martinelli. 1. SELECTED TOPICS IN FLOW MECHANICS The Figure shows four graphs for each of @# and @.. 1 2 3 4 The condition of laminar flow for both the liquid and the gas is that the respective Reynolds numbers.. be less than 1000. into several sections of A1 length. Ap. No. The method of Lockhardt and Martinelli takes no account of the prevailing flow pattern.and N. The appropriate graph is then chosen as follows: Flow of liquid Flow of gas Laminar Turbulent Laminar Turbulent Laminar Laminar Turbulent Turbulent Graph to be taken No. from these. NR. = ------- di The velocity of the mixture flow. of which we shall now discuss the second (Dukler 1969). It gives uniform calculation scheme for the determination of the pressure drop in horizontal pipelines. is the liquid flow rate as compared to the total fluid rate i..1. MULTlPHASE FLOW OF LIQUIDS AND GASES (d) Dukler's correlation There are two correlation and calculation methods elaborated by Dukler. The average density of the flowing mixture is In this equation R. is characterized by the so-called total velocity.k Ap. The friction pressure drop valid for the pipe section of length 1is calculated on the basis of the Fanning equation: 2 f k ~ k 2 1 ~. v. .e. . regardless of the flow pattern.4. can be determined only by iteration. . that of the gas is 6. can be read from Fig.116 I .. .4-46.2 kg/m3. At the flowing pressure and temperature the density of the oil is p. 1. = 810 kg/m3. . in order to calculate pk of the Reynolds number. 1. and the Reynolds number related to the mixture from Fig.. is determined with an accuracy of 5% compared to the previous one.2 x lo-' m3/s oil and qg= 3. 2 ~lo-' Pas. Let us calculate the pressure drop for a horizontal pipeline of I = 1000 m length with a diameter of di=0.p. 1.0 x Pas and that of the gas is 1 .2 if at the average flow pressure and temperature there is a multiphase flow ofq.4-5. SELECTED TOPICS I N FLOW MECHANICS and el is the in situ liquid fraction.4-45 The mixture viscosity can be calculated from Since. can be accepted if the value E. The flow chart for computer calculation is shown in Fig. The friction factor of the basic equation can be calculated in the function of the Reynolds number from Factor C. Example 1.4 x m3/s gas. The value of p. the viscosity of the oil is 5. as a function of R. = 1.4-47. which can be read as a function of R. we need to know E. 4-47.97 The viscosity of the mixture by Eq. MULTIPHASE FLOW OF LIQUIDS A N D GASES By Eq. according to T A K(1978) ~ .= f(Api) increment for the determination of horizontal twophase pressure drop by the Dukler correlation. I c Assume t .101 is I s Set Ap.4. 1. Calculate qL N R ~ ~ i i Calculate Ati Fig. 1. 1 parameters at Pi. A s s u m AI.. 1.1.. Flowchart for calculating a A/.4.4. is ~. including the bubble and mist regions. The boundaries of the regions are shown in the following summarizing table: segregated or transitional intermittent or IV. <0. 1. 1.4 R.35 and then.4-46 C =2. 1.4 -45. <NFr< L3 L3 <NFr<L . and according to the data obtained above the Reynolds number from Eq.= 138. 2 0. 111.4--102 is Correspondingly. including the stratified. wavy and annular. . the flowing pressure drop is (e) The theory of Beggs and Brill Their experiments were performed on surface equipment of workshop scale.4.. distributed or R.100 is Knowing all this. according to Fig. 2 0. transitional.4 and and and and and and and NFr<Ll NFr<L2 L. 1.01 R. SELECTED TOPICS IN FLOW MECHANICS Let the assumed value of E. be 0.With somewhat different boundaries they also determined the Alves-type flow patterns. first approximation of the in situ liquid fraction. according to Eq. After several iteration steps its final value is 0. <0.8/b.0kg/m3 and NRek= 3-07x lo4. According to Fig. These regions are: I.The mixture density valid for this value is p. 1.417.. 11. with Eq. Brown 1977).. <0-4 R.4 R. and IV. including the plug and slug. segregated.01 R. L3 <NFr5 L4 NFr2 Ll NFr> L.4-98.4..01 5 R.410..=0.. 1. distributed. This facilitated the measurement of the parameters not only in horizontal pipe sections but in sections inclined upwards and downwards at different angles (Beggs and Brill 1973. 20-01 0.04 and so the friction factor from Eq. >= 0..118 I. intermittent. For calculation purposes they classified these patterns into three combined and one transitional regions. 4 . can be reduced to The gas slippage velocity and Eq. R.= P If the pipeline is horizontal and the energy loss on acceleration i.4. the acceleration pressure gradient.4-99 is 41R.108 while calculating the mixture density pkonly in the mass gradient term.4 . valid for vertical pipes.4 .. i.. MULTIPHASE FLOW OF LIQUIDS A N D GASES The flow parameters are the Froude number.108. 1. the flowing liquid content.4. pkg sin a.4-97 expressed by v. . generalized form of Eq. PkUkusg C. considering Eq.g sin a. 1. is small or negligible then Eq.7/a if vk = vt and v. = -41 + 49 and the uk mixture velocity.4.4-8 Weisbach equation and C1 according to Eq.e. . and by writing A1 sin a instead of Ah. 1.e. and in . 1. 1.10. is The equations of the boundaries: The basic equation of the calculation is the modified. 1..8. 1.4. which according to Eq. where a is the pipe axis angle with the horizontal. which according to Eq.1. 1. = v. where A1 is the axial length of the pipe and Ah is the elevation difference of the pipe ends. and obtained by s~bstitutingp~g of the right-hand side with p.1 is considered in Eq. So the pressure gradient along the pipe axis is AP *p/ pkg sin a + A1 where the friction gradient can be calculated according to the 1. its angle with the horizontal equals O": Depending on the flow patterns.4.e. = f(a). el.2 region and that is why it is calculated from The in situ liquid content of Eq. 1. factors a. should be calculated from where and The in situ gas content is significantly influenced by pipe inclination. The authors think that this is due to the density and viscosity of the liquid phase. In the transition flow pattern. 1. It can be clearly seen that at about +50° the curves have extremums. with Eq. but it is not considered with the friction gradient calculated from Eq.109.4.113 can be calculated from the following equation assuming that the pipeline is horizontal.4-9. 1. Figure 1. The friction factor for horizontal pipe flow is where and n is undefined in the 1 < m < 1. 1.4..100. In this latter case The viscosity is similarly calculated by Eq. i. 1.120 I .4 -48 shows curves E. b and c can be found in Table 1. When .101. The Reynolds number can be calculated according to Eq. determined by the experimental data of Beggs and Brill (1973). that is.4.4. SELECTED TOPICS IN FLOW MECHANICS calculating C.7/a.. ) In (dR. If the angle of inclination goes on increasing. the in situ liquid fraction valid for pipelines of a inclination can be calculated.119 . 1..1 0 0 10 Fig. 30 50 70 90 dO equation. In downhill pipelines the flow patterns are segregated in almost every Table 1. The greater the interface of the liquid and the pipewall. Ni. The inclination factor. On the basis of the curves shown in Fig. 1.4.4. 1.R..121 1. Ng.).4. Simultaneous with an increase in inclination the liquid flow velocity increases and the in situ liquid content decreases. Flow patterns Segregated Intermittent Distributed case. 1. the liquid may block the total cross section. and using the E.4-9.4-48. and C = (1 . With additional growth of the angle the flow pattern gradually becomes annular.4-48 the authors have determined a correction -90 -70 -50 -30 .. factor determined for horizontal pipelines. will increase. the flow velocity of the liquid decreases due to the gravitational force and for the same reason the gas slippage velocity and the in situ liquid contents increase. MULTIPHASE FLOW OF LIQUIDS AND GASES the inclination of the pipe from the horizontal increases. and this results in a decrease in the difference between the velocities of the liquid and gas and this reduces e l . With the help of this correction.117 h a = &lo d' . the smaller the flow velocity of the liquid and c. In a vertical pipeline or = 90" and Exumple 1.01 1 2. and R.99 and it also agrees with the value given in the former Example.5056 Factors d.4.4 and 0.305 3. 2 6 0 9 ~ " ~ ~ = 4 . i.5. according to Eq. = 316 x 0. 1.e.6 . it is 0. or downhill flow. 1. If we consider the constants of Table 1.2609<0.10.4 .4.5 x 0 .4-104-107 the boundaries of the flow patterns and calculation regions are L. 1.0978 (no correction) 4. e.4. and whether the pipe axis is inclined for uphill.e.e.614 0. the Froude number is In accordance with Eqs 1.4. According to Eq.110 the mixture density is . 1.2609°'302=210.= = 2.4-5. i. i..2x 7lo3 3 .70 1 -0.96 . mean line pressure p = 6 x lo5 Pa.2609.4-6.I . since 0.3.7031 < 1. it is intermittent.768 0. o. .4. a. is the same as it was in Example 1.103. 1.on the basis of Eq.f and g are shown in Table 1. It is clearly seen that in our case the flow takes place in flow region 111.4.N/m. Let us determine the flowing pressure drop of a horizontal pipeline and a pipeline of 30"uphill inclination if the diameter of the pipeline and the parameters of the flowing fluid are the same as in Example 1.01 < 0.3692 C=O I)= 0.6 =002550 L2=04009252 x 0.10. depending on the flow pattern.4473 .9.4-97.5 x 10. Flow patterns Segregated uphill Intermittent uphill Distributed uphill Downhill for all cases d e f 9 0.539 -0. SELECTED TOPICS IN FLOW MECHANICS Table 1.4.1244 I 1 el= f(a) -0. it is 1. According to Eq.1.464 m/s.2609-2'4684 L3=O~10~O~2609-1'4516=O~7031 L4=0.1 15 According to Eq.092< 2 10. 1.4.109.0306. 1.4.100 the Reynolds number is From Eqs 1.4.3.1 18 the inclination factor is $ = 1 + 0.1541 [sin (1. is Iko= [2 lg ( e0.1.4. is The C factor.10) It should be noted. according to Eq. 1. MULTIPHASE FLOW OF LIQUIDS A N D GASES By Eq. In a horizontal pipeline the flowing pressure drop.119. is . 1.097.815 x 1 O4 . in accordance with Eq.1 1 1.4-112 m and n are and The friction factor.3736 4.It means that the in situ liquid fraction.4.333 sin3 (1.4.4-113 and 1.4. for inclined uphill flow is (the constants can be read from Table 1.. 1. is and so According to Eq. according to Eq. however.5223 lg 4. that the dimensionless liquid velocity number was calculated from I where v.4.8 x 30) -0.815 x lo4 4.8 x 30)] = 1. from Eq.117. 1.8215 >I =0. . however.12. 1. respectively. These average values are not small and the parameters. h. . and at greatel velocities k =0.0303.1 13. Here it should also be considered that the inclination of the increment calculated by one length should be approximative constant. It underlines.9 0. n =0. The same parameters with the theory of Beggs and Brill are .7 x 1-464x 1 a08 + 368.7 x 9. From them the average percentage error of the friction factor with the Dukler method is -9.124 I. possible in certain cases.0303 Ap = . 1.282.81 sin 30 0. (f) Conclusion For the determination of the pressure drop of the horizontal two-phase flow Dukler's second correlation.2 1000= 1. The accuracy of the calculation of the pressure drop is less if the pipeline is designed to be laid on a hilly terrain. the accuracy of each calculation method significantly deteriorates.4. are the heights of terrain elevations interpreted in Fig. . . The following information concerning the expected accuracy was determined on the basis of data from 296 comparative experiments (Vohra et al. Calculation is to be done for incremental lengths. one of the characteristics in which the two-phase flow differs from the one-phase flow.38.84 x lo6 Pa. SELECTED TOPICS IN FLOW MECHANICS and taking it into consideration according to Eqs 1.4 and the standard deviation is 32. 368. are even greater. It is desirable that the pressure drops of the given increments should not exceed 1 bar. - Fig.3630 and 1. 1.5.108 is 1. k=0.4-49. h.4622x 215. The equation is approximate to a great extent. and. In Vohra's opinion. Formerly it was thought (Baker 1954)that in pipelines laid on hilly terrains the pressure drop caused by the terrain could be estimated from the following formula: where with a flow velocity of vk < 3 m/s.4.4.0 and 31.112 and 1 1 1 m = 1. discussed here. and the method of Beggs and Brill were found to be the most accurate.4. with a liquid content of under ten percent. 1975).4-49. =0. The pressure drop from Eq. however. Flow of compressible mediums through a choke (a) Flow of gases The velocity of gas flowing through a choke can be calculated using the wellknown de Saint Venant equation. assuming that the gas is perfect and the flow is frictionless and adiabatic (see e.4. introducing the discharge coefficient a. With the Beggs-Brill correlation. MULTIPHASE FLOW OF LIQUIDS AND GASES 125 especially. from the liquid flow: the hydrostatic pressure in the uphill and downhill pipe sections do not compensate each other. and solving for the gas flow rate through the choke assuming standard conditions. 4 . For an adiabatic change of state The mass of gas flowing through per unit of time is and the gas flow rate referred to the standard state is The combined gas law implies ?'I Pel =- M P" M and p. = RT.3. Binder 1958): . 1. ' R TI Substituting these expressions into Eq. Subscript 1 refers to the state on the upstream side of the choke and subscript 2 to the state on its downstream side.g. it can be calculated with a better approximation..4. 1. we get In SI units fl? = 101. In a rough estimate the hydrostatic pressure in the downhill pipe sections is negligible.121.1.3.4. 1.4.).4.123.11 gives (p. It is.4.4. 1.4.122 is limited by the critical pressure ratio (p2/p. it is necessary to replace it in Eqs 1.123. First.123.4-11.126 I . the flow rate. If the given pressure ratio is greater than that in Eq. 1. which can be expressed from Eq. and C values for some K values. .4. It is at this pressure ratio that the velocity (and the flow rate) of gas flowing through the choke isgreatest: For the purpose of calculating choke diameters.4. and is in direct proportion to it.122 and 1. Table 1.122.4..121 and 1.25. In that case at a given choke diameter qg/p. Tand a values) the qg/pl ratio depends only on the choke diameter. = k is constant. = kp.. If the given pressure ratio p2/p. therefore. at which the flow velocity attains the speed of sound./p. 1. depends only on the pressure upstream of the choke.). 1./pl for different d. in cases of less than critical pressure ratio. M. satisfactory in practice to calculate with the constant value K = 1. It can clearly be seen that with values smaller than that of the critical ratio (in given K. In Fig. the equation can be used without restriction. Let us add that the adiabatic gas exponent K is relatively insensitive to temperature variations as well as to molecular weight within the range subtended by the gaseous hydrocarbons.125 are used as follows.4.122 in the form where I Equations 1. 1. is shown as a function of p.125 by the critical ratio. SELECTED TOPICS I N FLOW MECHANICS The validity of Eqs 1.122 to 1. it is preferable to rewrite Eq.4-50 the expression qg/p. the critical pressure ratio is calculated by Eq.4.4. is less than that in Eq. According to the formula q. Table 1.4.. choke diameters. too. assuming standard conditions. T.4-123 Now in the case of (i) which is greater than the critical pressure ratio. 1.1. p . Find the gas flow rate.= 288 K. for gases with comparatively small liquid content. further. = 1. Hence by Eq. p. if M = 20 kg/kmole.25. Fig. = 35 bars.. _ p2 'PI By Eq. 1.122 .85.00 bar.4. = 10 mm. a = 0. TI = 333 K and. and (ii) p2 = 14 bars. through a choke of diameter d. with a good approximation.4-50.4.4. K = 1. Example 1.7. MULTIPHASE FLOW OF LIQUIDS A N D GASES 127 The above correlations are also valid. let (i) p2 = 28 bars. 1. which is less than the critical value 0. By the above considerations 288 q.4-8. ~ ~ ~ = 5. however. SELECTED TOPICS IN FLOW MECHANICS In the case of (ii). d.134x 10-3 x 1 1 5 0 .59 x lo4. likewise valid at below-critical pressure ratios: . o.= 101.. = 8 mm.59.Ol2 x 35 x lo5-----. 1.x 0. PI = 3.128 I .4. Find the upstream pressure by Eq.o(j81. and p2/pl =0. q.126 if q0=98 m3/d. The properties of the fluid flowing through the choke are taken into account to a more satisfactory degree by the Ros-Poettmann-Beck equation (Poettmann and Beck 1963).3 x 0.85 x 1 x 105 (b) Two-phase flow of gases and liquids The equation was developed by Gilbert (1955) primarily to derive the upstream pressure of a fluid flowing through a choke mounted in a wellhead assembly.89 The Gilbert equation is based on the tacit assumption that at the pressure and temperature prevailing on the upstream side.00 x 1O6 Pa = 50.0 bar. It is valid if Example 1.555. and R agree with the values. It further includes the assumption of a standard choke geometry whose discharge coefficient (in SI units) is incorporated in the constant 3. R = 115 m3/m3.59 x 104 x 1. assuming to standard conditions. BO1= 1. T.=0. Find the rate of oil flow through a choke of diameter d. = 303 K . is the oil fraction of the flowing mass. assuming to standard conditions.. ~and Factor R is the gas-oil ratio. .4. / V .9. By Eqs 1.0 bar. estimated to be 303 K by the authors.4-56 and 1. T. p... the above equation can be used in the simpler form ~ the substitution of Eqs 1.4.06 and z. R . MULTIPHASE FLOW OF LIQUIDS AND GASES 129 Since q k m = q 0 M .4.and the authors suggest the value of 0-5 for the dispersion coefficient fl and 1.55 815 P o l = 1.875.= 288 K.55. pon=815 kg/m3. = 8 mm. ~ . = V .03 for the discharge coefficient C.4-54 and 1... p.910 kg/m3. = 2 0 m3/m3. Po 1 Rm1 = Pol +RIP. Subscript 1 refers to the temperature on the upstream side of the choke.1.4 . p.54 and 1. can be calculated by means of formulae 1. The specific volume of oil upstream of the choke is Example 1.06 = 769 kg/m3 . p. = 1. = 0. R. if R = 115 m3/m3.4. pol and p. = 5 0 bars.4-57 results in Here. = 2-0 bars. the oil flow rate through the choke is.4-57. the standard deviation at the flow parameters investigated by them was 44. An empirical relationship for the two-phase flow of gas-water mixtures which gives more accurate values than the preceding theory.=815+115x0~910=920kg/m3. 1969).4%for the Gilbert method. calculated with Eq. especially in the case of smallbore chokes (1.The actual pressure ratio must not exceed 0.134 m3/s) value given in Example 1. is the density or mass ratio number: N P = -Pg 1 Pwl and N.4. 1..132.4-8.4. Substitution of the values thus obtained into Eq. 1. effective gas-liquid ratios exceeding unity and water flow rates less than 127 m3/d has been determined by Omana et al.126 has been used. In the pertinent experiments.15% for the method. and us. can be obtained from Eqs 1.546. according to the calculation method illustrated here.130 I . . and 1.4-28 M. proposed by them. 29.128 yields that is.. where Eq. the pressure upstream of the choke was varied over a range of 28 to 69 bars (Omana et al.4-56 and 1. The relationship is where Nqw is the liquid volume rate number: N .. 1. N .6 mm < dch< 5.4. the critical ratio. SELECTED TOPICS IN FLOW MECHAN~CS By Eq. 1. is the upstream pressure number R is the gas-liquid ratio where us.0%for the Ros method. by 20%higher than the 98 m3/d (1. (1969). is the diameter number: According to the authors.6 mm). the fluid will traverse a number of hydraulical systems of differing parameters: the reservoir. The reservoir and the well constitute a seriesconnected two-component hydraulical system. Flowing wells are by far the most economical. the choke and the flow line. that portion of the wellbore surface where the fluid enters the wellbore through pores and perforations. The production capacity of the well is characterized by the relationship between various steady-state .(1) The fluid entering the well from the reservoir is endowed with an energy content composed. of position. too. and. The production parameters of a well should therefore be ascertained even before completion. It is desirable that the tubing string. 2. Changing the tubing in a flowing well is a timeconsuming. If the available energy of the fluid is sufficient to lift it through the well to the surface.CHAPTER 2 PRODUCING OIL WELLS . pressure. the production maps of an already producing field. On the interface the pressures prevailing in the two components of the hydraulic system are equal. then the well will produce by flowing. be optimally dimensioned. The interface between the two components. in its passage to the stock tank. Well testing. Economy therefore demands the selection of well completion and production parameters that will ensure flowing production as long as possible. Relevant information may be gathered from geophysical well logs. this aim is achieved by a carefully designed combination of tubing size and wellhead pressure.1. inflow performance curves In steady-state flow the amount and composition of fluid entering and leaving the well per unit of time are identical. Any change of flow parameters in any one of these components will affect all the other flow parameters. the results of well testing operations. is called the sand surface. The interface is most often situated at the bottom of the wellbore. run in on completion of the well. In the case ofcontinuous-flow production. last but not least. costly operation. among others. This task looks simple enough but is complicated in reality by the fact that. the well. because the well production equipment required is cheap and simple and keeping up the flow requires no extraneous source of energy. kinetic and thermal energies. and if the oil is considered incompressible. h. PRODUCING OIL WELLS-41) flowing bottom-hole pressures ( B H P ) pwf and the corresponding oil production rates go. re and r .1 .1. The inflow performance curve corresponding to the productivity equation 2.1 . If k.. then.=pws. then In the course of production. which in a very good approximation equals the steady-state B H P of the shut-in well. the filtration rate is v = . p.1 . Inflow performance curve homogeneous isotropic formation permeability k. The .then the flow of oil from the reservoir into the wellbore of radius i. as shown in Fig. If the fluid flowing into the wellbore is pure oil.. flow can be described by Darcy's law.. that is. then pw. 2. the solution of Eq.1-1. in the laminar region of relatively low flow velocities. If the thickness h of the reservoir is very small as compared to the well's influence radius r e . are constant.90 A = kdp -- pdl ' where p is the viscosity of the oil at the flowingpressure and temperature.1 is Factor p. that is. is the pressure prevailing on the circumference of the area of influence of the well. For isothermal flow in a porous reservoir rock of Pws_ Pwf Fig. 2. 2. If qo=O. h -gre.132 2. In the case of a horizontal reservoir and of steady-state flow.3 is then a straight line. the static B H P . has a tendency to vary rather slowly so that it may be regarded as constant over relatively short spans of time (a few weeks or months). The graphical plot of this relationship is the inflow performance curve. will be plane-radial for all practical purposes. p. The pores of the formation will then contain some free gas as well as a liquid phase.3 and the graph in Fig. 2. because a decrease in pressure will liberate gas in the formation. however. If the reservoir is comparatively thick.1.2. 2.1-2. at p w f = O is the potential yield of the well.1. then its viscosity p.1 -2. The aggregate result of all these changes is a graph illustrating Eq. In this case the productivity equation and the inflow performance curve are of the same form as Eq. The production of the well is then characterized.1 . and decrease the permeability with respect to oil. 2. 2. 2.5. If the composition of the oil did not change. which more or less closely resembles the Graph f(p) of Fig. the flowing BHP is often less than the saturation pressure. WELL TESTING 133 theoretically attainable production rate q.1 . respectively. flow may closely approach the spherical-radial type.. according to Muskat and Everdingen. the liberation of gas will result in an increase of liquid viscosity. would decrease as the pressure decreases.1 . Plotting the inflow perfomance curve for a gaseous fluid In wells producing a two-phase gas-oil mixture. the . but increased by the volume increase of the oil. With the knowledge of this Graph. Fig. all other flow parameters being equal. k. 2. instead of Eq. is decreased by degassing. the oil formation volume factor B.1 -2. by the following equation (Frick 1962): Pw. On decrease of pressure. Pwr The integrand is a function of pressure. 1 . that is.g. 2.. then. and various final pressures pwri. along which pressure p. Fractured limestone reservoirs are described by relationships other than Eq. Eq. is at a given pressure difference (p. The static and flowing BHPs are usually measured by means of a down-hole.. varies at a given p. be concave from below. the expression remains constant and can be denoted by the constant J'.. e. Comparison of Areas 1 and 11 below the Graph f@)reveals the daily oil production to be less if the reservoir pressure p. Curves convex from below are bound to be the results of careless measurements. even if all other parameters are equal..1 . 2. If the casing annulus is not closed off at the tubing shoe and the flowing BHP is less than the saturation . The integral curve of Graph f(p) is determined by graphic integration for initial pressure p.1 -6 that is. 2..1-3. the inflow performance curve for a slightly compressible reservoir fluid becomes (Ban 1962) where a and b are formation constants... While testing a given well. then. In agreement with the notation used in Eq. 2. the variation of the daily production of the well will have a curvature much like the heavy curve in Fig. The inflow performance curves of wells are usually determined in practice by producing the wells against a variety of wellhead pressures by means of a number of production chokes of different sizes. 40 = J'F@. The integral curve defines Graph F(p). J1=J here. This decrease can be temporarily forestalled by increasing the drawdown (p. To each wellhead pressure a different BHP will correspond. The method itself belongs to the domain of reservoir engineering. The indicator curve of a well producing gaseous oil from the reservoir described above will. For instance. 2. In the case of sandstone reservoirs.1 -2.-p. After the wellhead pressure has stabilized. the flowing BHP and the oil production rate are measured. Tests are usually carried out at three to five operating points. This implies that.)pWs. or reservoir. PRODUCING OIL WELLS-<I) inflow performance trend for depletion type reservoirs can be established by the following consideration.-p. by decreasing the flowing BHP faster than the reservoir pressure decreases. if in the course of well testing the stabilization of the individual flow rates is not given sufficient time...4 is. the decrease of reservoir pressure during the life of the well will entail a gradually decreasing production rate even if the draw-down remains constant. The solution of Eq. 2.134 2. pressure gauge.) lower.7.).6 can be approximated well enough by the formula where n < l .1 . .00118LWM Pwf=Pco e =% * 2. R.2 . Characteristics derived from well-test results gas-oil ratio curve R.1 -3 shows characteristic curves plotted from well-testing results. (i) One cannot attain lower wellhead pressures than the input pressure of the flow line. putting h = L. WELL TESTING 135 pressure of the fluid produced./q.. it might be advantageous to calculate the pressure pw. A relationship suitable for calculation can be derived from Eqs 1..1. When changing chokes in the course of well testing.3 and 1. and q. and q. attention should be paid to the following. = q. The producing P4. at the tubing shoe from the casinghead pressure pc0.2. bars Fig. = 0.2 -4.. belonging to each individual flowing bottom-hole pressure. the restarting of . Then 0. because it is at this point that the amount of formation gas required to lift one m3 of oil is least.1 -3. steady-state gas production rates q. is seen to have a minimum in this particular case. Such minima do appear quite often. 2. (ii) If in the coyrse of well testing a choke is replaced with a smaller-size one. and the corresponding oil production rate q.. it may be expedient to operate it at R. If there is no prescription as to the flowing BHP at which to produce the well..1 -9 On well testing. has been plotted from pairs of q. referred to standard conditions are also determined at each individual bottom-hole pressure. Figure 2. This is a result of certain reservoir mechanical phenomena.. and pw. The higher the qo/qoma. which.10 .1. driving some of the oil from the above-mentioned liquid annulus into the tubing. by producing the well through some intermediate sizes of choke before introducing the small-bore one.. This latter being closed on top.--q. The tubing will thus receive significantly more liquid and less gas than under steady-state conditions. PRODUCING OIL WELLS { I ) production may trigger certain irregularities in wells with an open casing annulus. 2. in a fair approximation.. so that the fluid produced will have a much lower GOR. p. and the average reservoir pressure. When flow starts through the smaller-bore choke. Let us calculate (a) the potential production rate.. pWf=35. The annulus tends to fill up with gas duringsteady-stateproduction. Example 2.. provided the flowing bottom-hole pressure is less than the bubble-point pressure: A great advantage of this equation is that the inflow performance relationship (IPR) can be determined with the help of one related pair of values.0 bar. p. This type of trouble may often be prevented by gradually increasing the BHP.. Its gas content may be insufficient to ensure flowing production. q.0 bars.in the course of the well test.2 m3/d.Experience shows that the equation can be well applied for wells producing from reservoirs with drives other than the solution gas drive. paralleled with reservoir depletion. inflow performance relationship. the fluid coming from the reservoir will start to let off gas into the casing annulus. The measurement data obtained at the well test are: q0 = 20.136 2. with a liquid annulus developing above tubing bottom level. equals the static bottom-hole pressure. In Vogel's opinion the accuracy of the equation. may decrease. so that the well may die. the shoe pressure increases to a value pkL>pTL.= 71. Vogel (1968) has pointed out that for wells producing from reservoirs with solution gas drive the following equation describes the fluid inflow into the well. notably.0 bar. and (c) the expected production rate at pwf = 60. p.. of the fluid rising in the tubing string.1 .. but the error concerning well rate estimations may not exceed 20%. part of the fluid coming from the reservoir must flow into the annulus.. and compress the gas column in it.. where the stabilization of the different well flow rates takes longer. Substituting the given values in Eq. if multiphase flow in the reservoir exists. too. The pressureof the gas column at the level of the tubing shoe equals the shoe pressurep.For the casing-annulus pressure to attain this increased value at shoe level.. Subsequently.1 .. the more accurate the equation obtained. its gas pressure will increase. (b)the go=f(pWf).. The application is extremely promising for wells producing from low permeability rocks. 2. is the friction loss in the flow line and in the fittings of the tank station. Ap. p. The BHP is where A p f is friction loss in the tubing. is the pressure loss in the wideopen (chokeless) wellhead assembly.7. Ap.0. and Ap. Flowing wells producing gasless oil The GOR of an oil-well fluid may be so low that no gas is liberated during flow through the well: flow is then single-phase. is friction loss in the casing between the well bottom and the tubing shoe. p.. it is possible to determine (i) the optimum tubing size that will result in flowing production for the longest possible time. in an approximation satisfactory for practical purposes. and (iii) to predict several reservoir parameters affecting production.31 x 71x10~ x 1.2. 2. is the pressure loss in the choke..31 x (71~10~)~ '"'= The expected production rate at a flowing bottom-hole pressure of 60 bars is On the basis of the well test the characteristic curve of the well can be determined by applying Eqs 2.1 . is composed of the hydrostatic pressure of the fluid entering the flow line through the wellhead assembly. will mean the depth below the wellhead on the top of the sandface. (ii) the most favourable artificial lifting method for a rate which cannot be produced by self flowing.1 . Let us specify that well depth L. The resistance to flow of a chokeless wellhead assembly is usually negligible. The operating parameters of the well are comparatively simple to calculate (Szilas 1955).31 x 0.---- '"I- 0. 2.8 or 2..1 . plus the energy flow pressure drop in it where Ap. relying also on the results of other type of reservoir oriented well tests.8 x 3.10.2 x 3. is the hydrostatic pressure acting upon the wellhead. FLOWING WELLS PR3DIJCING GASLESS OIL and from here The inflow performance relationship (IPR): q. . Hence.=3. composed of the hydrostatic pressures of the oil in the flow line and in the tank. With this information.2. Graph I1 is the internal pressure-loss curve of the well. depending on the physical properties and saturation conditions of the formation. decreases as the production.138 2. resemble the graphs of a centrifugal pump lifting fluid through a vertical flow string.1 shows the variation of pressure as described by Eq. The inflow performance curve. the form of Graph I1 is considerably influenced by the fact that an increased production rate will increase the mean temperature of the oil flowing through the tubing. corresponds to the head capacity curve depending on structural and geometrical features of the centrifugal pump. thus reducing its mean gravity and viscosity..ld Fig.rate increases. based on operation parameters.the hydrostatic pressure of the liquid column in the well. PRODUCING OIL W E L L S ~ I ) Figure 2. v. 2. rate of production. This .2. representative of the interaction of reservoir and well.2-1. a plot of production rate v. whereas 179 178 177 100 200 qm1 330 t. Graph I is an inflow performance curve characteristic of the inflow of oil into the wellbore. In the case under consideration.2. provides some useful information concerning operation of the well: the intersection of Graphs I and 11. a plot of the hydrostatic pressure of the oil column flowing in the well plus the friction loss. These two Graphs. point A. and friction losses do not increase as rapidly with the production rate as should be expected in isothermal flow.2 applied to a well at Nagylengyel. flowing BHP. This is why Lwy.I . is the operating point of the maximum liquid production rate q. Pressure utilization curves of a well producing gasless crude. 2. pwf. Hungary. after SZILAS (1955) the internal pressure-loss graph of the well corresponds to the resistance curve of the riser fed by the pump.2 . Figure 2. is the thermal conductivity coeficient of the rock surrounding the well.-jfor the hydrostatic pressure of the fluid filling the well can be determined in a number of ways. valid at q.. The present author has therefore added a heat-transfer correction factor C to BoldizsLr's formula.. oil and cement. The diagram can often be used to predict performance at a future date. a given tank station is joined to the well by a given flow line. A. the productivity index J will often have a tendency to stay approximately constant. from a fractured. This means that Graph I will have an unchanged slope. with Ap. Its value can be determined by field tests. We have to know the mean temperature of the oil flowing in the well. A formula for calculating the temperature ofwater flowing in wells has been derived by Boldizshr (1958). for instance. etc. Most water wells have no tubing. = 0. one of which follows. on the other hand. and the water rises in the casing string. carbonic rock. The Figure reveals the increase in production rate that can be attained by minimizing the flow resistance of the surface equipment (increase of flowline diameter. If the pressure-loss curves are assumed to stay unchanged. where A T .2-2 for a given well at a number of different production rates. 2. in the following way.). and k is a dimensionless rock-heating coefficient. Boldizsar has assumed the hot water to lose heat to a thermally homogeneous surrounding.2. that is. whose value is furnished by the integral . is the temperature difference between the flowing fluid and the original temperature of the rock at a height h above the well bottom. Oil flowing in the tubing of oil wells is surrounded by a jacket of oil filling the casing annulus. The expression L. the maximum flow rate will be the lower value q. when the wellhead offers no resistance and oil flows from the tubing into the open through a wide-open valve. If the well produces. = 0.2. then est~mateswill be on the safe side because the mean fluid gravity belonging to a given flow rate will decline in time owing to the warming up of the rock surrounding the wellbore. it will merely shift to a smaller intercept p. heating or thermal insulation of flow line. Reservoir pressure will equal the p!.. sinking into the ground of tanks. =0. to account for the heat passing from the flowing fluid to the host rock through piping. with no choke in the wellhead assembly. that is. The corresponding operating point is B. then. Boldizsar's corrected formula is. If. The pressure-loss diagram can be constructed by calculating the factors in Eq. FLOWING WELLS PRODUCING GASLESS OIL 139 'wide-open' flow rate will be obtained at the gauge pressure p. The C factor of a given well is constant over a rather wide flow rate range... u is the integration variable. F can be assumed to be constant in a fair approximation. In that case. the higher the flow rate. the flowing temperature of the oil will increase even if the flow rate remains unchanged. Example 2. q. more specifically. a single test at a given production rate will directly furnish not only C but also the product Ck = k'. it is warmer. Production gives rise to a 'thermal jacket'. L. and (iii) the outflow temperature to be expected at a production rate q.2 -1..=2108m. 2. If production preceding a well test was much longer than the duration of testing. and F is the Fourier coefficient: where a is the theoretical thermal conductivity coefficient for liquid flowing through an uncased well. The reason for this is that some of the heat content of previously produced oil has already heated up some of the colder surroundings. Equation 2. both at the same production rate q. = 1. PRODUCING OIL W E L L S ~ I ) Joand Yo are zero-order Bessel functions of the first and second kind.5 are tabulated as a function of F in a paper by Jager and Clarke (1942).701 kgjs. di=62 mm. Values of the integral 2. the geometry of which in the case of a given well drilled in a given rock is at any instant a function of previous production history. t is the time elapsed between the start-up of production to the data of testing. q. find (i) the expression k'= Ck at the production rate q . = 1.2 -2.(ii) the change of temperature of the oil as it rises through the flow string and its mean flowing temperature.2-3 reveals that the oil entering the wellbore is at the height of the sand surface (h = 0) at precisely the same temperature as the rock surrounding the well..082 kgjs. but at any other elevation the flowing oil is warmer. Analysis of the formula makes it apparent that as production proceeds (as t increases). The tubing string reaches down to the well bottom. The outflow temperature is TTol= . .2 . respectively. r is the radius of the flow string through which flow takes place.140 2. Fig. Given the data of a test on a well producing gasless oil. p288= 929 kg/m3.3 and assuming that the mean specific heat is approximately the same also at other flow rates.2 . = 342. Ground temperature next to the wellhead equals the annual mean temperature. Whether this is necessary is to be decided individually in each case. k'=0. (i) The mean flowing temperature T= TT1required to determine the mean specific heat is estimated at 273..5 K .06 x 103 x 4.9 K Substitution of the values obtained into Eq.5418 x 1.1 . depth can be calculated in the knowledge of T . 0 6 ~ 1 0 ~ =67.24 x K/m.2 K . 2. If desired.141 2.4 .2 .838 X 2108 1 -e-(1.838 x 2 1 0 8 1.24 x K/m.701 ~ 2 .2 + 67.2.3 = 351.24 x k' 1.7 ~=p2s8-~T(?--288. we get A T .2-3 results in 1.24 x 0. Following Cargoe: + + The difference between the outflow temperature and the ground temperature next to the wellhead is AT.701 x 2.2 K .2.082~2.2 + 68.=95. 2.1 K at the production rate q .9 = 342.06x1 0 3 ) 57. FLOWING WELLS PRODUCING GASLESS OIL = 273.9 = I . the mean flowing temperature is established as T T . by means of an iteration procedure..06 x l o 3 x 4. the mean specific heat can be calculated more accurately.838 This resolves to k'l. Adding to this value the original rock temperature T.3 K .e . 2. 4 7 1.2 -2 is a plot v.2 = 57.838 W(mK). (iii) By Eq.. depth of the rock and oil temperatures thus determined. at various elevations h above the well bottom. 2. . The mean density can be calculated using Eq.7 erT and a.2 K . a.2 1 1) = 284.2 K and o.2. at any elevation we get the flowing temperature at the height h. Figure 2.= 4.1(1 .5418.2)+~pfi.= 1. (273. can be obtained from laboratory tests.838 1 -e- I 0. The outflow temperature of the oil is TTO2= 284. (ii) Substituting the above value of k' into Eq. = 4.. can also be determined from the shut-in data of the well (Szilas 1959).= 361.082 x 2.284. the outflow temperature difference at the flow rate 9 .3. 2. = 1. is AT. I.5418 x 1.2 88 = 361. 0.=284. By planimetering the surface under the curve TT= f(h). The variation of rock temperature v. The friction loss A p f can be determined either . The relationship will furnish the temperature differences AT. 2. Eqs 1. . r r .3 to hold. we obtain for pressure loss due to friction in the tubing the relationship If the tubing string is not run through to the well bottoni. the BHP will not change from the steady-state flowing value and the temperature of the oil in the well will likewise remain unchanged. the impulse content of the liquid column held by the flow string will give rise to a pressure surge in the bars I 4o . The wellhead tubing pressure will increase from the steady-state flowing pressure pTo to pTz and the casing head pressure from pco to pcz.1 -2 and 1.2-3. . . ' . and after the decay of the pressure surge.(Fig. if the flowing well is abruptly shut in. z f 30 r . Notably. Pressure build-up at a wellhead after sudden shut-off. Because of the abrupt shut-in. then. . ' ~ . . . . 2. 1.1 . then the above relationships can also be used to calculate Ap. which will normally decay in a span of time on the order of 10 s. . can be determined quite accurately by a relatively simple well testing procedure. before shut-in. A p f and Ap. ' s . ' . 10. We may. PRODUCING OIL WELL-I) by field tests or by calculation. .1 . s Fig. . write up that. . . that is. 20 s .142 2. ~ t.1. The letter is based on Eq. . after SZILAS(1959) wellhead.2 -3). di then denotes the ID of the production casing. . friction loss in the casing section between the well bottom and the tubing shoe. . Substituting and assuming the flow to be laminar. 2. 2. =951 kg/m3.0 bars. and 7. on the other hand. 2. q.4 bars.5 bars.9 results that is.505 kg/s. = 1.2 . Subtraction of Eq.2. the pressure surge in the tubing head equals the total pressure loss due to friction of oil flow in the well before shut-in.8 gives a friction loss The friction loss as calculated from wellhead pressures measured during the abrupt shut-in test (Eq. = 2016 m. in the tubing. the difference between the pressure differences in the tubing head and casing head equals that part of the friction loss of oil flow in the well before shut-in which is due to friction in the tubing string. the pressure surge in the casing head equals that part of the friction loss of oil flow in the well before shut-in which arises between the well bottom and the tubing shoe. Equation 2.2-2.10 x 10 .=9.7.m2/s.. and in the casing annulus.5 bars. pTo = 4.10 from Eq.062 m. Given L. a. = 7. we get that is. Example 2.2. Let us note that 7. FLOWING WELLS PRODUCING GASLESS OIL Subtracting the first equation from the second and rearranging. pa = 6. and after the decay of the pressure surge. pco = 6. =0. 2. p. Find the flowing pressure at the tubing shoe of a flowing well producing gasless oil. respectively denote the mean gravities of the oil in the casing between the well bottom and the bottom of the tubing string. F=4. pT. .384 x lo-' kg/mN. p is therefore to be determined by successive approximation.2.1 1 ) is The mean flowing density required to calculate the hydrostatic pressure of the liquid column flowing through the tubing depends by Eq.7 also on mean pressure. d. 2.2.58 kg/m3K. The pressure balance between the well bottom and the casing-head gives.2 .2 . Let us first assume that p=O. Subtraction of the first equation from the second gives that is. aT=0.2-7 gives the approximate mean density . T=367-0 K . Then Eq.. the corresponding wellhead pressure p. Replacing Ap. of course. The efficiencyof production of the well can be found by dividing the useful work W2expended in lifting one kg of oil from the well bottom to the surface by the total energy expenditure W.3 +9. and p.. however.834 x pwJ=2016 x 914. By the procedures outlined above.0x lo5= = 1. it would be most expedient to have wells untubed and to produce them through the casing. 4 x 105+4. by the following consideration.l ) . Figure 2. exploited the more efficiently. Tangents to the pressure utilization curves parallel . The more accurate mean pressure calculated using this BHP does not appreciably affect the final result any more.144 2. As established above. we obtain The specific energy available at the well bottom is. This last case may be justified e. Graph I1 and the inflow performance curve I. (ii) produces a corrosive fluid.52 x 106=914-7kg/m3. the ordinate difference between Graphs I and I1 equals at any production rate q. we get as the mean decsity x 9.2-4 shows pressure utilization graphs for a variety of tubing sizes.g.883 x lo7 P a = 188.2-8.2. .. the pressure-loss. then. 2.3 bars.. tubing plus the casing annulus. PRODUCING OIL WELLS+!) The approximate mean pressure is Using this value. We have assumed for simplicity that the tubing string reaches down to the well bottom. can be determined for a given well. can be calculated. 2.7 x9. By this consideration. The method is not. p=905.. that is. characterizing flow through the sand surface (Fig. (iii) the well is to be produced at a relatively low rate. by the expression in Eq. p. The pressures Ap. A further advantage of this solution is.81 f 3 . the greater the I D of the tubing string. One of the graphs refers to simultaneous production through a 2 718411. the saving due to dispensing with the tubing. applicable if (i) the well produces sandy oil which may lead to casing erosion. One and the same wellhead pressure p. also Fig. and q. qm2 - qm Fig. To remedy this.belonging to the point of tangency.. the prevention of water coning) may indeed demand a reduction of the production rate. 2.2. Insertion of a smaller-bore choke may then result in fluctuation or eventual dying of the well.2. Unstable operation interval of a well producing gasless crude. the well will permit also of a lower-rate production. Fig. (Cf.2-4. may belong to two different produc'tion rates q.. FLOWING WELLS PRODUCING GASLESS OIL 145 to the performance line define a set of operating points connected by the dashed line. through the tubing in question. Pressure utilization curves of a well producing gasless crude.2-4. that is. 2. pumping is often started.. 2. Understanding this phenomenon of well behaviour is of considerable practical importance because reservoir engineering considerations (e.=O and the qk .2-5. Running a smaller-size tubing will shift the upper limit of the unstable zone to the left in Fig.2-5. after SZILAS (1955) fluctuating. and the well may even die. on either side of the dashed line. after SZILAS (1955) 0 q. although by .) The well in question cannot be produced at rates between q.g. 2. Production will be unsteady.. and hence a slightly different L. v.1 . 2. Inflow curves from well tests .3. q. that is. a well with a relatively small-sjze tubing is to be produced above the operating point of maximum flow rate.) function should result for each tubing size. belonging to given values of p. qgn. Figure 2. .. provided the casing is not menaced by erosion and/or corrosion. In another possible case.3 .1. . -qgn by a curve calibrated in terms of flowing BHP. plotted in a q. and qgn. refrained from an accurate calculation of these. Figure 2.I is a plot of the oil production rate. however.1 . The relationship T=f(q.y= f'q.3-2 shows pairs of values q.2-4 has been plotted in a rather approximate fashion. for instance.3. q.14 and 1.-q. production-rate graph.) varies somewhat with the tubing size. Flowing wells producing gaseous fluids 2.. These curves resemble the qg.15.16 x m3/s and qg. Krylov joined the corresponding pairs q.-q.. 1. curves Fig.1. .as provided by a well test.At a flowing BHP of 55 bars.. The approximate curves have been calculated by extending also to other tubing sizes the temperature v. p.77 m3/s.146 2. The friction loss of production through the casing annulus can be calculated by means of Eq. the flowing BHP p. Krylov's general flow equation (Muravyev and Krylov 1949)for long tubing strings (not detailed in the present book) permits us to determine throughput curves for the tubing string. plotted in a coordinate system calibrated in q. The flowing cross-section can then be increased by bringing the casing annulus into play. plotted for the tubing size at which the well test has been carried out. = p. 2.=0. We have. This curve is then the characteristic performance curve for inflow from one formation. PRODUCING OIL WELLWI) the above considerations steady flow could be achieved simply by running in a smaller-size tubing. Interaction of well and formation (a) Krylov's theory Figure 2.and of the gas production rate referred to standard conditions.. In adapting the Figure we have used the approximation 1 at E 1 bar. coordinate system. go= 1.v.3. The tubing in the well in question has been run to the well bottom. 2. according to K K Y L ~ V Fig. FLOWING WELLS PRO1)UCING GASEOUS FLUIDS 147 referring to the throughput of infinitesimal lengths of tubing (cf.the only variable in its expression.3 -2. just equal the production rate which can be delivered to the surface through the given tubing.3 bars. at the given wellhead pressure and at the tubing shoe pressure of 49.. on the left-hand side of Fig. = 1.2. The set of curves in Fig. we use as a parameter p.. The flowing B H P decreases by a smaller amount than the wellhead pressure.4-3). Fig. Characteristics of well-formation interaction for various tubing sizes according to KRYLOV B H P . 2. The graphical solution of the set ofequations represented by the inflow performance curve and a throughput capacity curve of the flow string furnished that flowing Fig. d = 2 718 in. then to 10 bars by the insertion of larger-bore chokes. 1. because the . then the flowing B H P will decrease accordingly. Performing the construc. 2.3 bars.3. and the oil and gas flow rates will increase. 2.3.3-3. = I000 m. It is apparent that if the original wellhead pressure of 30 bars is decreased first to 20.. at which the inflow rates into the well. pWf =49. = const.=2-45 x m3/s for oil.we get the Graphs p. Characteristics of well-formation interaction for a given tubing size.3 .tion with L. Instead o f t .21 m3/s for gas and q..2 refers to the conditions L.3. and pTo = 2 bars. . q. and d unchanged but for various values of wellhead pressure pTo . can be constructed (Gilbert 1955). A different tubing size will have a different throughput capacity curve.7 bars for a wellhead pressure of 2 bars if the tubing size is changed to 4 1/2 in.3-4. This situation is restricted to very high-capacity wells. . Transferring the pressures p.. by the insertion of suitably dimensioned reduction orifices (chokes in common parlance).. using Eq. is a constant independent of the production rate. in place. = 10 bars). the curves in Fig. Let us consider various flow rates q.. a larger size tubing must be run in.3-4 is an inflow performance graph characterizing the inflow of fluid from the reservoir.and using Gilbert's pressure-gradient curves. production rate.148 2. respectively upstream and downstream of the choke. Joining these pairs results in Graph I1 of wellhead pressure v. Let us determine now the production rate with a given choke diameter d. . The system analysed was a series-connected twocomponent hydraulic system whose components had different flow characteristics. It is thus apparent that when using a 2 7/8-in.-q. This is due to the circumstance that. This relationship is illustrated by the straight-line. Starting from various tubing-shoe pressures p. Flowing production is seen to bc restricted to the interval between A and B. Such situations are fairly frequent especially in medium-capacity wells.. (b) Gilbert's theory Graph I in Fig.5 . illustrated by Fig. R.6 bars at p. are constant. as is well known.. b. and that the producing gas-oil ratio. 2.. belonging to each of these on the abscissa axis. 2. If the wellhead pressure is decreased to 2 bars.. 2. we get a set of corresponding pairs p. the increase in flowing pressure gradient entails an increase in B H P greater than the decrease in wellhead pressure. the flowing B H P will increase and the rate of production will decrease. thus obtained to Fig. as outlined above.. increasing the choke bore will not improve the production rate beyond a comparatively small increase (corresponding to p. we can calculate the upstream pressure e. the desired wellhead pressure is attained. If d. . slippage being relatively insignificant. 2. A method for establishing the common operating points of the threecomponent hydrodynamic system composed of the reservoir.2 -3. a. In the example above. Assuming that pressures p.g. PRODUCING OIL W E L L S ~ I ) increased mass flow rate.. the wellhead pressure varies directly as the production rate.. 2. = 47. the tubing and the choke was developed by Gilbert.. If a greater production is required.3-4. In production practice. each illustrating pressure v. in Fig. elevation in the tubing string at a given production rate. give a ratio less than critical.. and let us mark off the BHP's p. The intercept k O gives the wellhead pressure p. The actual choke graph is . = p. size tubing.126. Graph 111. b.3 -4. 1.. mean specific volume and flow velocity will increase the total flowing energy loss and hence the mean flowing pressure gradient. Let us assume that the length of the tubing string is L. to be expected at the production rate considered. and R. the flowing BHP will decrease to 35. most of whose energy loss in the tubing is due to friction even at the least production rates. So far we have studied the interaction of well and reservoir at certain constant values of wellhead pressure. and p . + Ap'.3.. the pressure upstream of the choke will increase by Eq. . Are both operating points feasible? Figure 2.. The higher wellhead pressure entails a higher B H P and hence a reduction of inflow..then a temporary increase of the flow rate will give rise to a pressure upstream of the choke that is insufficient to 'stabilize the flow. in accordance with the operating point at E".3-5 shows Graphs I1 and 111of the preceding Figure in somewhat more detail.) should stabilize itself at the wellhead.).. however. Fig.. .. 2. 1. then. the production rate decreases temporarily by a value Aqb'. after GILBERT (1955) for a wellhead pressure p. because after slight fluctuations of the production rate.. + AqbE). produce at a rate go. then the stability of flow requires that a pressure (p..126 to (p.5. E is thus revealed as a stable operating point. meaning that flow parameters will vary in time but their mean values will stay constant.. the pressure upstream of the choke will be less than the value needed to keep up flow at this reduced rate. on the other hand. The lower wellhead pressure entails a decrease in B H P and a consequent increase in inflow. the operating parameters will swing in spontaneously to their original values. These are in principle the operating points characterizing the reservoir-tubing-choke system. If the production rate increases temporarily from qoE to (go. In practice..2. Now if the well produces at the rate q.. . flow will not be quite steady but quasisteady. at the operating point E. Well-formation interaction. The decrease in wellhead pressure will reduce the B H P and .If. FLOWING WELLS PRODUCING GASEOUS FI.Ap. Graph 111 intersects Graph I1 at the points D and E. Let us assume that the well will. At this increased flow rate.UIDS 149 seen to deviate somewhat from a straight line near the origin of coordinates.3-4... .. The point in question is the common operating point of the formation-well-choke system. Operating point D is therefore unstable.then a process opposite to the one just described will become operative: flow will decrease to zero. Concentrating on the curve for R. Figure 2. . a given choke bore fixes one production rate at q0 qoo qo. forcing the system back to . Fig. 2. Stable and unstable operating points of a well producing'gaseous crude. corresponding to the stable operating point is attained. on the other hand. after GILBERT one stable operating point. 2.8-mm choke.3-6. e. determined for various values of R. =284 we find that a rather acute-angled intersection would develop. The restoring pressure differential. and various choke bores.150 2. the well will die.3-6 shows the operating points E. PRODUCING OIL WELLS X I ) increase the production rate until the value q. Let us now find out whether a stable production rate can be assigned to every choke size. regarded as stable. when using a 2.5.g. after GILBERT (1955) Fig. By the above considerations. then.3 .. If.. Influence of choke diameter upon the stability of operation of a well producing gaseous (1955) crude.. the flow rate decreases below the original q. . both simpler than the above procedure. Graph I1 joins several points plotted in the same manner. starting from the prescribed pressure pro. Figure 2. in the manner discussed in Section 1.3. . 2..3-5. belonging to q. This curve can be plotted also by selecting the pressure gradient curve belonging to a given triplet of d. FLOWING WELLS PRODUCING GASEOUS FLUIDS 151 the stable operating point is thus much less than in the case shown as Fig. is read off. In a general way.3 . the peak of every Graph I1 will define a least production rate feasible in agiven formation-plus-well system. .6 shows that the choke diameter required to ensure stable flow is the greater..3 -4.3 . Graph I1 is the pTo=f(qo) curve introduced in connection with Fig. the first step is likewise to find the pressure gradient curve belonging to the given triplet of d.the greater the rate at which a well can be produced through a given tubing size.7. and R..2.3.. The intersection with Graph 11 of a line parallel to the abscissa axis. Establishing well-formation interaction curve intersects the curves of formation plus well to the right of their respective peaks. provides the production rate q. The common operating point of formation plus well at a prescribed wellhead pressure pTo can be determined according to Nind in two ways. The production rate q. R. A plot of several pairs (q. Rgo and the production rate q..3 -4 (Nind 1964). The well will thus operate under the permanent risk of dying. the control process is sluggish and the flow rate will not yet have swung in to a stable value when it is deviated again by another fluctuation.finding the value of pT. and R..) yields Graph 111 (the function pTw=f'(q. By the above consideration. already outlined in connection with Fig. 2. If a lower production rate is desired.7. read off Graph I. The resorting force being weak. this value of pTo is plotted v. 2. q. . the restoring pressure differential will be insufficient unless the choke Fig. defined by the intersection of Graphs I and 111 is the same as that furnished by the foregoing procedure. the greater the producing GOR. p.Then. the greater the producing GOR. the assumed value of q.3-7. q. In Fig. 2.4.1 -(e). . 2.. and then determining the wellhead pressure pTo of the well of depth L. 2. . Graph I is the inflow performance curve. It is further apparent that. passing through the prescribed wellhead pressure pT. given pTo. 2. the tubing-shoe pressure to be expected at the depth L.3.. In the second procedure. looked for. .7.)) in Fig. a smaller-size tubing string will have to be run in. In Fig.. . 2. A principal draft of such a possible path is shown in Fig.. to be constant. 2. one can construct the curves p. we find that the least feasible wellhead pressure equals the least required pressure at the inflow end of the flow line. 2. (d) Flowing pressure drops from the reservoir to the separator The pressure of the well stream from the outer boundary of the drainage area to the separator is continuously decreasing while it flows through a "production spoke" made up of elements of different hydraulic characteristics connected in series. Interaction of well and flow line... If the flow line is laid over a level terrain. Line pipe sizes increase in the direction of the arrow. PRODUCING OIL W E L L S g I ) (c) Influence of the flow line Removing the wellhead choke and neglecting the pressure drop due to passage through the Christmas-tree assembly. The greater the diameter of the horizontal flow line.. one can plot the wellhead pressures of a well of given parameters v.R. The pressure . and the maximum production rate of a given well through a given flow line. the common operating point of the formation-well-flowline system.1. the less the wellhead pressure.7. 2. be determined as follows.4.3 . (1966).. for the corresponding size of line pipe. The set of curves characterizing the flow line may be determined in principle by any one of the calculation methods described in Section 1. 2. The resulting curve has likewise been marked Graph I1 in Fig. Using Brill's curves. and the greater the production rate that can be realized in the given setup.3-8. (1966) 1. Assuming R.8.. constructed or calculated. the production rate in the manner of Graph I1 in Fig. In possession of said curves.4. The and the intersection of Graphs I1 and IVe predicts the wellhead pressure production rate q.... Sets of curves of this type have been demonstrated by Brill et al. valid for flow lines of a given length and a variety of pipe diameters (Graphs IVa-e. The boundary of the drainage area (7) is indicated as is the well bottom (6). provided the method in question is deemed to be accurate enough. the pressure traverse of multiphase flow along the flow line can be characterized by gradient curve sets p =f(f).3-9. similar to those used to characterize flow in vertical strings in Section Fig.2. = f(q. can respectively.).3. after BRILL et al. .4.4. The flowing pressure drop for all three vertical pipe sections can be calculated as discussed in Section 1.10 shows the pressure drop of the previously described "production spoke" as a function of the liquid flow rate. A bottom hole choke is placed between 4/a and 4/b and a surface choke between points 3 and 2. Figure 2. Curve p . the producing bottom-hole pressure was calculated and is shown by curve p. while between points 5 -4/b and 4/a. Schema of "production spoke" calculated according to Section 1. The pressure loss occurring in these sections can be Fig. In the calculation of the pressure drop . R.3. The gas-liquid ratio.2.1. the construction starts from p . = q. The curve belonging to diameter dl3 is shown by the solid line. Practically. while the curves belonging to the other two diameters is shown by dashed lines. Due to didactic reasons the ordinate axis is positive in the downward direction. the flowing pressure drops of three flow lines of different diameters were added.1). .4. Between points 2 and 1 there is a flowline and the calculation of pressure loss of the wellstream is described in Section 1. starting from the reservoir pressure p . Though their flow resistance can also be calculated. Between points 6 and 5 the wellstream flows in the casing. FLOWING WELLS PRODUCING GASEOUS FLUIDS 153 loss between the two is characterized by the inflow performance relationship (see Section 2. Then. it flows in the tubing. respectively. which is independent of the flow rate. In the "production spoke" changes in direction and different fittings can also be found.3-9. Independent of the flow rate the pressure in the separator is a constant value.3.3. 2. and generally they are neglected. is obtained by plotting the pressure drop of the wellstream flowing vertically in the casing at different flow rates.2. To the separator pressure p .3. their relative magnitude is small. can be different for different values of q. . The highest possible oil rate that can be realized by the tubing and flow line of the given diameters is determined by the point of intersection of curves p. and highest if the diameters of the flow line and the tubing are d l . time of the total oil production Vo the producing gas-oil ratio R.10.2.154 2.In our case the maximum rate will be lowest if flow line d13 and tubing d... is represented Fig. .respectively (q. Reservoir engineering calculations permit us to determine the variation v. Brown et al. Time course of production parameters The need to procure lifting equipment at the correct time and to predict the power requirements of artificial lifting makes it important to predict the flowing life of a well.pressure reducing effect of it equals the desired A p 3 . 2. Three tubings of different diameters are assumed on the Figure. and p3(Ap3.)..3. pressure drop value for the given q. Pressure distribution in a "production spoke" by the solid line while the two others are by dashed lines.. Similar system analysis was elaborated by K. 2. can be produced by a surface choke of such diameter that the. (Proano 1979). PRODUCING OIL WELLS---(I) in the tubing the effect of bottom hole choke 4 is also taken into consideration.. In the previous Figure it can be seen that the pressure drop A p 3 .. and d T 3 . are applied. The curve corresponding to d. =0). values curve p3 is obtained. Subtracting the pressure drops from the p.3. and productivity index J . The common operating points are joined by the curve marked with xs. Figure 2. for further production planning for each well (key wells).).7 bars.3. For design and estimation it is essential to obtain the reservoir engineering design. equals the production GOR required to lift the fluid to the surface.. This graph can be plotted by assuming a number of gas-oil ratios occur sometime during the flowing life of the well. Keeping each R. Figure 2. characterizing the liquid throughput Fig. Graph I 1 illustrated the function pWf = f(q. Tracing the IP line corresponding to the end point and reading off its intercept at q.=O. this will be the flowing life of the well at the given tubing size. rates by means of pressure gradient curves (see Graph 111 in Fig.3-11 is diagram prepared in this fashion. gives data on how the quantity and composition of the wellstream lifted daily and the producing .11 shows this pressure will be attained approximately 251 days after start of production. 2.1 1 capacity of the tubing string.3-7)... as delivered by the reservoir to the flow string. 2.3. we get the reservoir pressure expected at the end of the flowing life.. FLOWING WELLS PRODUCING GASEOUS FLUIDS 155 of a well typical of a larger group of wells in a field. There is a more general solution for the determination of the flowing life of wells. Figure 2.3. as well as the time variation of the reservoir pressure p. 2..11.. The end point of this curve marks the end of the flowing life of the well.12 shows the inflow performance curves of the same well as the seven instants of time indicated in Fig. 146. which.2.3 . the flowing BHP is determined for various production constant and using pTOmi. The reservoir and the well will cooperate if the GOR.The IP curves are straight lines as we have assumed the exponent n of the performance equation to equal unity (Graph I).3 . 3. according to SZILAS (1979) . Because of the errors P bars 0 2 4 6 8 10 12 14 q. The intersections of curves A with line B show how long the well is able to yield the daily rate prescribed in the reservoir engineering design by flowing in tubings of different diameters. Each of them shows the change of the wellhead pressure. according to WOODWARD(GILBERT 1955) t . Determination of flowing life. Line B shows the expected pressure of the gathering system on the wellhead.12.g.3.156 2. for January 1 each year.3. assumed tubing diameter. e. 10-' 16 18 m3/s Fig. .13. 2. PRODUCING OIL WELLS-(I) bottom-hole pressure changed during the production life. From this information obtained at different intervals. 2.13 is obtained. 2. for a different. with time. yeors Fig. Determining the flowing life of wells. Joining these points the set of curves A on Fig. the producing wellhead pressure can be determined. 1964. Each curve marked with a capital letter corresponds to the line marked with the same lowercase letter.7 can be used to construct tubing throughput capacity curves ( A . The figures will also furnish . New York-Toronto-London) Table 2..7 46. 2.94 0 qo/qopo.. bars At a. used with permission of McGrawHill Book Company Inc.8 1 5.5 0 the right diameters must be applied and the chokes must be changed from time to time. Reservoir-engineering estimations. similar to those described in connection with Fig. The first procedure described in connection with Fig. 2.D 173 138 103 90 40 10-'m3/s 7.A At b. In order to produce the rates prescribed by the reservoir engineering design with the planned tubing at different periods of the production history.14. 2. FLOWING WELLS PRODUCING GASEOUS FLUIDS 157 that can be expected both in reservoir engineering planning and in the simulation of the well production separate estimation has to be made regarding the accuracy of this time point determination (Szilas 1979).7 35.7 mm at the time when reservoir pressure assumes the value defined by the IP curve. 142. p. The points of intersection of the corresponding curves indicate the production rate of the well through a choke of diameter d.B At c.15 2. = 12.3 .2. % 50.1.14.3 .C). In the next section the influence of an unchanged wellhead choke upon the production rate will be illustrated (Nind 1964).11 permit the tracing of the set of inflow performance curves plotted in Fig. Estimation of production rate (after NINI). Pw.3.3 .3. 2.3 . surface chokes of bars Fig. a -d.C At d. If the tubing were shorter. . now another definition may turn out to be most useful. the actual production rates q.3. The idea underlying each one of these interpretations is the choice of a tubing size that causes the least flowing pressure drop under the conditions envisaged. and the well-head pressure p. In the knowledge of that value. Depending on the circumstances. PRODUCING OIL WELLS--([) potential production rates at various values of reservoir pressure.. can be expressed as percentages of the potential production rates. and assures flowing production for the longest possible time. 270) the tubing size is optimal if it is large enough to let the start-up flow rate (which is usually maximal) pass. (iii) According to Nind (1964. It is apparent that a decline in reservoir pressure will entail a decrease in the ratio of feasible to potential production rates. once this or that interpretation of the term has been accepted. the choice of d and L is more critical. (iv) Tubing size is optimal if it ensures production at a minimum formation GOR. that the optimum tubing length equals the well depth L. 84). It would be a self-defeating attempt to try to uniformize the interpretation of optimum performance..158 2. because once production has been started up. This is why the tubing should be run invariably down to the well bottom (which. Of these. with the tubing shoe flush with the upper limit of the sandface. in a string of larger-than-optimum diameter. However. (ii) According to Krylov (Muravyev and Krylov 1949. The parameters in question include the diameter d and length L of the tubing. The relevant parameters are listed in Table 2. and the flowing pressure gradient would consequently be greater than optimal. the change thus involves considerable cost and downtime. Designing flowing wells for optimum performance parameters There is no consensus as to what the term optimum performance exactly means. questions as to optimal well structure or production can be unambiguously answered. without justification for the time being. Let us assume... p. because at a lower reservoir pressure the energy required to keep the fluid flowing through the tubing string is a greater fraction of the total pressure required to move the reservoir fluid from the periphery of the zone of influence to the wellhead (Nind 1964). In the following we shall therefore outline methods for finding optimum tubing sizes for each of the above-mentioned criteria. in practice. the tubing string can be changed only after shutting in the well.1.3.3 . We shall now concentrate on finding optimum tubing sizes under the following interpretations of the term optimum performance. the tubing size is optimal if it ensures a maximum flow rate out of the well at a given wellhead pressure p. p. now one. that is. the well fluid flow between the well bottom and the tubing shoe in the casing. means the top of the sandface). 2. (i) Tubing size is optimal if at a prescribed rate it delivers oil at a minimum producing GOR.. We shall give both 'East-European' and 'Western' solutions to each of the problems. Substitution of this size into Eq.15 provides the optimum tubing size: The standard tubing size closest to the calculated value. = 0. = 63. by Eq. = 1. and q.I .5 m3/d. no flowing production is feasible through either the calculated tubing or tubing of any other size.0 bar. 1. Rgo= 320 m3/m3.. L. Krylov's equations . is the GOR as determined after separation. let us find the tubing size which at the prescribed rate will produce at a minimum producing GOR.4-12. the minimum realizable wellhead pressure pTomin. p.ratiol.81 = 8142 N/m3.= 1400m. as suggested by its name 'gas-oil. provided that pressure in the string is a linear function of length: and R . (a) 1. Example2. R. too. and the well may produce also some water. .1 x m2/N.0 x l o 5 =0..0bars. and the gas must lift this water.3 . According to Krylov. to be produced at the prescribed BHP.the oil and gas flow rates q. If this is less than the effective GOR available.0 x l o 5 .4. Rs is the solution GOR in the tubing string at the mean pressure prevailing in it. of the tubing string. the well will produce by flowing. The notion of effective GOR has to be introduced because part of the gas flow measured downstream of the separator is still dissolved in the oil while it rises in the tubing string. 23. 1. the length L .. refers to oil. pTL=23. is to be chosen. Find (i) the tubing size requiring the least producing GOR and (ii) decide whether the well will flow if q.0 bars. -Since y = pg = 830 x 9. 1400x8142 '= The tubing size looked for is.19 yields the minimum producing GOR required for flowing production. referred to the temperature and pressure prevailing in the separator.3. pTomin=2. Ref. In the contrary case.4. the effective GOR is where R. and the physical properties of the liquid and gas.2.Equation 1.3. On the other hand. 2.. n -4.=pw.1 . = 830 kg/m3.184.2. the mean pressure gradient is. R . FLOWING WELLS PRODUCING GASEOUS FLUIDS (a) Dimensioning the tubing string for minimum GOR. is the water-oil ratio of the liquid produced.. by Eq. p. with time-invariant flow parameters Given a prescribed bottom-hole pressure pT. let us select that curve along which the pressure increase from p. (a) 2. 1. 2... The tubing size belonging to this R. PRODUCING 011. The well will consequently produce by flowing. Using Gilbert's pressure gradient curves find the tubing size giving the least producing GOR under the conditions stated in the previous example.> R. top. . Of the several GORs corresponding to the various tubing sizes.. The R. takes precisely the length L. by Eq.4 1 ) Table 2..3-2 (see later) shows the next standard tubing size to be 2 718 in. this is the tubing that will.160 2.3-2.3-2. by Eq.. by Eq. nominal with an ID of 0062 m..4 . . is optimal. The effective GOR is.Of the set of curves valid for a given standard tubing size and a given oil flow rate yo..19. Pressure-gradient curves. produce oil at the least producing GOR. 2.3. The least producing GOR required to keep the well flowing is. parameter of this curve furnishes the GOR at which the well will produce by flowing through the P ---+ w Fig.15. at the prescribed operation parameters.. one will be a minimum. The solution GOR at the mean tubing pressure is. R90 chosen size of tubing at the prescribed operation parameters. 2..3-3.WELLS. since Re. Example 2. though. Now we may calculate q.4 . but not reproduced in the Appendix to this book. The decline of the flowing B H P will entail an increase in producing GOR according to both Fig. size will permit flowing production at a producing GOR of a round 300 m3/m3. = 63. A . a tubing string of 2 718 in.6 and Section 2. as the optimum size.. Figure 1.16.4.2. 1.Let us substitute the initial G O R into Eq. Production efficiency will therefore be rather poor initially. The producing GOR of a well may vary in time according to a variety of functions.. The two parallels with define sections~of length Lion the individual curves L=f(p). the producing G O R of the well will at first increase rather sharply over a comparatively low initial value.3..15 shows one of the possible ways of choosing the suitable pressure-gradient curve...3. gives a specific gas consumption of a round 320 m3/m3.. In the case of a dissolved-gas drive.9 at d = 2 718 in Figure 2. According to Fig. to pick out d. 1. notwithstanding. ensuring a maximum liquid flow rate for a number of standard tubing sizes d. no particular disadvantage since a considerable specific-energy content remains available at the well bottom. . both procedures give the standard tubing of 2 718 in. Interpolation or the use of an auxiliary diagram will permit selection of the curve on which the prescribed pressure drop takes precisely a length L . Other flowing-life histories are also possible. using the chosen ds and the corresponding pressure gradients The tubing size to be c.4 . comparatively high production rate to flow through..20 and find the wellhead pressure p. also the flowing B H P . and so will. A . for instance. A curve for 3 112-in.3 . FLOWING WELLS PRODUCING GASEOUS FLUIDS 161 Figure A ..tubing published by Gilbert (1955). however. . equal to the given tubing length. The solution usually chosen is to run the least tubing size that still permits the initial. size.4 (see Appendix) holds for a flow rate of q. .7shows how a decrease in oil flow rate will at a given producing GOR permit flowing production through a smaller-size tubing.. and p..4 . Analysis based on the pressure gradient curves in Fig.5 m3/day and at d =2 318 in. The production will generally decline apart from certain fluctuations.9 (see Appendix). 1. and draw parallels to the ordinate axis through the prescribed pressure values p. by means of Eq. The procedure permits us. (b) Dimensioning the tubing string for minimum GOR. Let us place a sheet of tracing paper over the set of Gilbert curves. with time-variable flow parameters The composition of the fluid and the rate of production will vary over the flowing life of any well. This is.. most often. Comparison of the solutions found respectively in paragraphs (a) 1 and (a) 2 reveals that although the results concerning the producing G O R are rather far apart. The dense set of steep curves at low pressures allows a rather approximate estimation only. A -4 (see Appendix) -eveals that no flowing production is possible through a tubing string of 2 318 in. Krylov's equations. An interaction of the factors outlined above very often results in a situation where progressively smaller tubing diameters would be required in order to ensure a minimal producing GOR.2. however. (b)l. and the gradually decline below it. while Fig. pTo is 19. find the tubing size ensuring the longest flowing life of the well. tubing will ensure the longest flowing life of the well. since 1. to be expected with a tubing size of 2 3/8 in.5 .Let us find the pressure gradient curve valid for the given q. Pressure gradient curves.76 find fusing Eq. Appendix). .0409 0. the optimum tubing size is 2 3/8 in.3 m3/day (= 1.0409 m.55 2. the effective GOR is stated by Eq. by a set of Gilbert curves not reproduced in this book.=O.1 x mZ/N.9 m3/s 0.374 0..0 bar..9.12 and q.0 bars..062 m by successive approximations using Eq.0506 m. = 2.. 1.3-2 to be Let us first find p. A . but procedure (b)2 furnishes a higher wellhead pressure than procedure (b)1.LT = 1400 m. RgO=255m3/m3. A . no flowing production is possible through tubing of 1.9-in. n. using Eq. it is 17. =4.5 bars for 2 318 in. 1.4.0620 9. among the curve sets for various tubing sizes.. By Fig.0 bars. at the d values 0. Comparison of the two solutions shows that.3-4. or by means of an auxiliary diagram.5bars.3 .0506 m and 0. Given q0=95. Starting from the ordinate corresponding to the prescribed bottom-hole pressure p. in the case considered. = 830 kg/m3.=255.5 bars for the 2 718411. and then Table 2. 2. p.3-3.The least of these sizes is to be chosen.4. nominal whose ID is > 1-1x This is the least tubing size of throughput 0. The examination is to be extended to nominal tubing sizes of 1. and.3 -2. and R.2 318 and 2 718 in.361 0. Pro bars 0. let us measure along the curve in question the tubing length L T and read off the curve of the wellhead pressure pTo to be expected. Example 2. pTOmin R..162 2.. 0. (b)2.55 x capacity greater than the initial production rate envisaged..16. Example 2..8 10.10 x m3/s). size tubing (see Fig. results are more or less identical: there is agreement in that 2 318-in. -The tubing to be chosen is 2 318-in.0506 0. Since pTOmi. Solve the preceding example using Gilbert's pressure gradient curves. 1.= 51. p. . The results of the calculation are listed in Table 2. PROI>UCING OIL WELLS-+I) chosen is the least size of throughput capacity equal to or greater than the envisaged initial production rate.353 1.2. = 1.10 (see Appendix).is less than the wellhead pressure of pTo = 17.4 . size at a GOR of R. The well will produce by flowing through any size tubing for which p T O > p T o m i n . Assuming the mean wellhead pressure to be 10 bars.20.. 7.3. In such cases.= f(q.16. transformed into metric units. by reservoir-engineering considerations. Let us determine for each case examined the maximum flow rates attainable at a wellhead pressure corresponding topTOmln. that is. Pressure gradient curves. 2. p..3 . = pTOmin..16 shows the resultant curves. e. that tubing size is considered optimal which permits a maximum production rate. The result looked for is the common operating point of the formation and the tubing string at various tubing sizes and wellhead pressures. used with permission of McGraw-Hill Book Company Inc.1964. 2. 2. although the production rate through 2 318-in.. Krylov's equations.g. Quite often. FLOWING WELLS PRODUCING GASEOUS FLUIDS 163 (c) Dimensioning the tubing string for maximum liquid production rate..9 in. the production rate may be permitted to vary over a comparatively wide range of flowing BHPs. The optimal tubing size is that which permits a maximum production rate at a given p. size tubing is almost as high. (c)2.The problem can be solved in principle by the procedure given in connection with Fig. Fig. Figure 2. that the liquid production rate is limited. Finding the tubing size of maximum production capacity (after NIND. however. Let us establish for various tubing sizes the characteristic p. reproduced after Nind. . 129.3 -3.) curve of the interaction between reservoir and well by the procedure outlined in connection with Fig.3. with time-invariant parameters We have so far assumed that the flow rate to be attained is determined as a function of a prescribed flowing B H P .2. New York-Toronto-London) (c)l..3. The tubing size to be selected is that which ensures the . The optimum tubing size in the case in question is seen to be 1. Nind (1964) has solved the problem for a given well using Gilbert's sets ofcurves. . and the tubing string(s). so-called telescopic strings. The solution has. were often employed. on the other hand. introduction of down-the-hole instruments. considered to cause less flowing pressure loss. Note. etc. gradually increasing upward. We have so far assumed that the entire string is made up of tubing of constant size..3-17. As far as the present author is aware. in a selective completion. the casing-size requirement would depend on the maximum tubing size employed. The solution based on Krylov's general theory of the operation of a tubing string is rather cumbersome. it is therefore not discussed in the present book. This principle of dimensioning is of a more or less pure theoretical interest as the data available at the time of well completion do not usually provide the R. no telescopic tubing is employed anywhere today. a number of drawbacks: dewaxing. Its three main parts are the casing head(s) I . PRODUCING OILW E L L ~ I ) maximum production rate. Such strings were composed of standard sizes of tubing. 2. the tubing size run into the well is too large or too small. with time-invariant parameters We have stated in connection with Fig.3. The tubing is to be chosen so as to permit production at the operating point of R. 2. the operating point of Rmi.=f(q. which . Production at this operating point has the advantage of ensuring the most economical exploitation of the gas energy contained in the reservoir. on the one hand and the advantages to be expected of a tubing of different size on the other. (d) Dimensioning the tubing string for minimum formation GOR. It is the wellhead equipment that holds in place the casing strinds) reaching to the surface. The extrapolated data is rather unreliable. of course. (a) Wellhead equipment The fluid entering the well across the sandface and rising through the tubing to the surface passes through the wellhead equipment on its way to the flow line. shown in Fig. the tubing head 2 and the Christmas-tree assembly 3. Completions will be discussed only to such depth as is required for an understanding of production aspects.) function to the accuracy required by this mode of designing. In earlier production practice. Wen completions The actual techniques of well completion involving a drilling or well completion rig will not be described here.4.164 2. 2. If. will have to be established by extrapolation from a production test performed through a tubing unsuited for the purpose.. seldom exceed the drawbacks involved in exchanging the tubing string. the unloading of the well by swabbing become cumbersome if not impossible.1-3 that the curve describing the specific gas production of a well at different rates of total production possesses a minimum.. The tubing head is connected with the so-called Christmas-tree assembly which incorporates all the valves and other equipment required to shut off. Wellhead assembly of single completion .3. strength of 483 . 6A (11th Ed. This is. The lowermost casing head is screwed onto the male thread of the largest-size casing string (the surface pipe) and supports the next casing string. and incorporating two casing strings. it supports the third casing string. the so-called production casing. FLOWING WELLS PRODUCING GASEOUS FLUIDS 165 presents the wellhead equipment of a well producing a single zone. 1977) the wellhead assemblies must be manufactured from steel with a tensile.517 MPa. regulate and direct the flow of the well fluid. in the present case. It is within this last casing string that the tubing string is run. According to API Spec..3. October.17. Threaded connections may be applied only at those wellhead assemblies where the maximum working pressure does not Fig.690 MPa and a yield strength of 248 . The next casing head is connected with the lowermost casing head. 2.2. As already stated in connection with Fig. Casing heads. As a result. 2. the lowermost casing head is usually screwed onto the end of the outermost casing string. The annulus between the two casing strings can be packed off either by a resilient seal or by welding the casing top to the casing head. The above-mentioned API specification does not deal with wellheads whose maximum working pressures exceed 1380 bars.The weight of the casing string energises the oil-resistant rubber packing to provide the positive packoff required. lower slips 4 will also engage the casing automatically. A vertical bore is also drilled into RX and BX type gaskets for the purpose of allowing through the fluid jammed between the gaskets and the groove. and thus reducing the fluid . The second casing string is held in a tensioned state by the slips of the casing hanger. This solution with two sets of slips is preferable to the entire casing weight being supported by a single set. Clamp-on connections are also Fig. he studded types require less room and are more fire resistant.690. their advantages are that they require a comparatively small space and can be quickly mounted (Snyder and Suman 1978).29 of OCT Co. Ring gaskets corresponding to API Std 6A are shown in Fig.3. because casing deflection and deformation is less and the hanging capacity of the casing head is nevertheless higher.18.3 . The next casing head is fixed with nuts and bolts to the flange of the first casing head. 345. Figure2. The connections can be of flanged. wellheads of 2070 bars were already applied. The casing. The two casing heads are provided with a polished-in ring gasket usually of soft iron. slightly slackened after drawing.166 2. 2. The maximum working pressures of the standard flanged assemblies are 138. In the industry. studded or threaded types. OCT C-29 type casing head known. 1035 and 1380 bars. and the next casing string is hung in much the same way. . R and RX type gaskets are applied at comparatively lower pressures (345 and 690 bars). type C .1380 bars). 2.207.19. is caught by slips 2 slipping into conical bowl 1. (a)l. PRODUCING OIL WELLS+]) exceed 138 bars. while BX type gaskets are used for higher pressures (690.3-17.18shows a modern resilient-seal lowermost casing head. fitting into groove 5.3 . however. FLOWING WELLS PRODUCING GASEOUS FLUIDS 167 pressure in the groove. shown as Fig. (iii) the seating of tubing hangers for single or multiple completions. (ii)the size and geometry of the tubing head should permit the passage of tools of size corresponding to the ID of the producing casing string.3. Each . In choosing a tubing head.3 . Ring gaskets after RPI Std 6A (1977) (a)2. One type of latch-around hanger (the National H .345. ad (iii). Tubing heads. (iv) the mounting of such valves as correspond to the pressure rating of the tubing head. (vi) the permitted working pressure should be equal to or greater than the maximum shut-in pressure to be expected at the wellhead. possibly throughout the life of the well. No comment concerning (i). In the course of usage the ring gasket becomes deformed and that is why its reuse is not recommended. 2. Several types of tubing hanger are in use. The tubing head is fixed to the uppermost casing head.7).140. -The permissible working pressures according to API Std 6A of standard tubing heads are round 69. is composed of two hinged halves.19. Even slight knocks may lead to deformation which entails the escape of gas.2.3 -20. the following criteria should be observed according to Foster (Frick 1962):(i) the geometry and permissible working pressure of the lower flange should equal those of the casing-head flange with which it is to be connected. Fig. 2. The polishing of the ring gasket and the subsequent transportation and assembly require great care. (ii). (v) the top flange should ensure the required fit to the Christmas tree and should be provided by lock screws which ensure the sealing of the tubing hanger even with the Christmas tree not in place.207. (v) and (vi) above seems indicated.690 and 1035 bars. in which case the hanger will merely function as a blow-out preventer without having to support the tubing weight.168 2. Packoff is provided by two O-ring seals or a plastic seal between the tubing head and the bowl.6) emplaced in a tubing head is shown as Fig. One make of boll-weevil hanger of the stuffingbox type (National H . and by plastic seal 3 between the hanger and the .3 . as the mandrel 2 can be installed on disconnected tubing ends only. The advantage of the latch-around hanger is that if the well kicks off while the tubing is being run. 2. 2.3 -21). Once the hanger is seated in the tubinghead bowl. 2. PRODUCING OIL WELLHI) of the halves consists of one top and one bottom steel half-mandrel with a resilient half-ring seal sandwiched between the two. If the well kicks off.3 -21.20. the top mandrel will compress the sealing element so as to provide pack-off between tubing and tubing head. and secured in place by the tubing-head lock screws ( I in Fig. National H-7tubing hanger Fig. At comparatively low pressures. however. National H-6 tubing hanger tubing and seated in the bowl of the tubing head. it can be immediatly latched around the Fig.21.3 . with the top upset of the landed tubing compressing the hanger. 2. Circulation can then be started in the tubing. Bollweevil hangers are cheaper than latch-around ones. the Christmas tree (see p. After the well has quietened down and the entire tubing string has been run in. the tubing can even be stripped through the hanger between upsets. 147) can be attached to the top tubing thread. seating it is more complicated. that on the right is of the boll-weevil type. 2. Mandrel hangers. Several types are known. After seating. OCT dual tubing hanger and seat during the running or pulling of the tubing string. used on high-pressure wells. Each segment occupies its part of the bowl when landed. 2. such as gas-lift valves.3 . The orientated emplacement of hangers should be feasible.3 -22.3-23 shows an OCT make double hanger and seat of a combination type. This solution permits the use also of accessories jutting beyond the tubingjoint outline. FLOWING WELLS PRODUCING GASEOUS FLUIDS 169 tubing. The tubing string is hung from a mandrel attached to the top thread of the tubing string. It is fundamentally a split-packoff preventer which provides a seal towards the tubing and at the same time supports its upset. National H-1 tubing hanger Fig.3. The arrangement of the tubing strings is readily visible in Fig. The individual strings are run with separate guides. 2. are not required. this upset reaches up into the Christmas tree where another safety seal of the highpressure hydraulic grease-gun type is installed. The hanger on the left is of the mandrel type. This type of hanger is used in connection with 'quiet' wells.23. 2. It should not be necessary to remove the blowout preventer before all the tubing strings have been run. Selective completion of wells producing several formations raise the following additional requirements as to tubing hangers: the tubing-head bowl should permit the hanging not only of the maximum designed number of tubing strings. A safe construction. The hanger on the left has O-ring seals.2. The hanger is held in place by the lock-down screws I.3 . If the well kicks off Fig. Figure 2. there is a separate hanger of cylinder-segment shape for each tubing string. Packoff against the tubing-head bowl is ensured by two plastic O-ring seals (I). is the Cameron LD tubing head. even only one if that be required. seating requires a fairly long time. The National H . that on the right has resilient rings. but also of a smaller number. The tubing can be moved under pressure in the hanger between upsets.3-22. Other types of hanger used with comparatively low-pressure wells are also known. In the multiple-segment hanger.1 type mandrel hanger is shown as Fig. the mandrel is a cylindrical body with a separate bore for each tubing string. It functions as a blowout preventer during well completion and as a tubing head during production. In the multiple-bore mandrel hanger. This is the simplest and most easily installed hanger but has the drawback of being limited to applications where accessories jutting beyond the tubing-joint outline.The tubing cannot be moved after the seating of the mandrel. The valve is Fig. Orientated seating and fixation are ensured by the holes I and screws 2. 2. This pipe is fixed to the outlet of the valve. Cameron tubing-head flange and hangers for triple completion opened. Side outlets are provided with threads (for working pressures of usually up to 140 bars). and the changing tool and the leaky valve are both removed. 3 is a resilient seal disk. of which one only is shown although three are used (see also the Christmas-tree assembly). studs (usually above 207 bars) and extended flanges (for any. The leaky valve is closed and the changing tool is installed. Changing a valve is performed as follows. The change is feasible only if the opening device of the valve is not damaged. These outlets are to be provided with outlet valves. 4 is a back-pressure valve. Side outlets on tubing heads permit access to the annulus between the production casing and the tubing. The changing tool is fundamentally a length of pipe in whose interior a well-packed rod can be rotated. The plug is retrieved.41) -24. At the end of the rod there is a detachable male-threaded plug which fits into a female thread provided for this purpose in the side outlet. PRODUCING OIL WELLS. showing a Cameron type tubing head flange with tubing hangers for a triple completion. using a valve-changing tool.3 . The rod is then detached from the plug. 4 in Fig. but usually high. .3-21 shows a threaded outlet. Modern types of equipment use full-opening gate or plug valves. 2. The outlets are designed so as to permit the changing of leaky valves under pressure. ad (iv). and the rod is turned until the plug seats itself in the appropriate bore.24. pressures). the valve is closed and finally the changing tool is removed.170 2. A good valve is now installed with the changing tool mounted on it. Christmas-tree valves are also made of highstrength alloy steels. The master valve 311 in Fig. The bonnet shown in Fig. The element in direct contact with the tubing string is the flange or bonnet. For simplicity. All have the common trait of being sealed together with the tubing head by a metal ring gasket.3 -25.17 may be of the restricted-opening type. provided it does not significantly raise the flowing pressure drop of the fluid produced. of course. 1 is the master valve of one tubing string. Figure 2. 2 is its wing valve and 3 is its swabbing valve. These may be of the wedging or non-wedging types. Both have either flanged or threaded connections.3. O n high-pressure wells. much easier to install. Figure 2.2. .3-21 is of the male thread type. Numerous types are available.3. pressure gauges and lubricator flanges are of the stud type. monoblock-type Christmas trees incorporating the Fig. Gate valves are more widely used. The wing valve 312 in Fig. The main types differ in their connection with-the master valve. FLOWING WELLS PRODUCING GASEOUS FLUIDS 171 (a)3.17 should be of the full-opening type. we shall concentrate on gate valves in the following.3-25 shows a Cameron B type valve block for a dual completion. 2. or to the rated working pressure.3 -17 shows such an assembly. For master valves with a male lower thread. respectively. Such blocks are.g. with a clearance equal to or greater than the ID of the tubing.A Christmas tree is an assembly of valves. The two current types are gate and plug valves. fittings and other accessories with a purpose of regulating production. 5 and 6. . Christmas-tree valves are required to close safely even if the well fluid is gaseous or pure gas.3. Connections towards the flow lines. Christmas-tree assembly.2. Recently. which may be of the male or female thread or flange type. Cameron dual-completion solid block wellhead equipment functions of several valves and spools have become popular. two series-connected master valves are often used. an adapter may be inserted. The corresponding items for the other tubing string are numbered 4 . 2. according to the number of tubing strings used in the completion. with a nominal size somewhat less than that of the master valve. 2. Design differ e. PRODUCING OIL WELLWI) Christmas trees are sensitive to sand in the oil which may cause severe erosion especially in bends and deflections.28 is suited for working pressures of up to 690 bars. The Willis T-type shown as Fig. for sandy crudes (a)4. Chokes. The valve in question is shown as (b) in Fig. wing valves 3 are opened and the master valve 2 is closed. Figure 2. Soviet Christmas tree. If safety plug 2 is removed . The tubing can even be circulated. 2.3 -26. if the need arises. the other with a spring lock.3-17 shows the choke-carrying insert 313 with a choke mounted in a thread. 2.3-27.3 -27 shows a National B . through the back-pressure valve. while the eroded elements above valve 2 are changed. When the tree is eroded. When that operation is finished.-Back-pressure valve.3-26) is used in producing sandy fluid. When a change of choke is required. Christmas-treefittings.172 2.8M type bonnet whose top thread will accept a back-pressure valve of the first type. Part (b) of the Figure permits us to follow the path of the well fluid. Once the Christmas tree has been connected with the top end of the tubing and the tubing has been landed in the tubing head. type 1 AFT. The Soviet-type 1 -AFT Christmas tree (Fig. it is necessary either to shut in the well. (a) Fig. or to have another choked outlet. This is a check valve installed in the tubing hanger or in the wellhead bennet in order to seal the tubing bore while the blowout preventer is being removed and the Christmas tree is being mounted in place. one is fixed in place with a thread. The device functions at the same time as a wing valve. by means of a special tool.The choke mounted in insert 5 is a wear-resistant ceramic-lined type. Modern wellhead assemblies include chokes which can be changed without shutting-in the well. Flange 1is connected with the master valve. The normal outlet into the flow line is marked 1. production is switched back to wing 1.3 . 2. the back-pressure valve can be retrieved through the open master valve. There are several such designs. similar to the one shown in Fig. 2. Flow now continues in the direction marked 4.3 -26. Of the two current types of back-pressure valve. 2. even under pressure.2. 2. it is usually mounted between the wing valve and the choke. This device is mounted on the Christmas tree or in the flow line. It will close when pressure builds up above or drops below a predetermined level.2. A cylinder may incorporate five chokes and a blind plate.3 -27.3. When installed on the Christmas tree. FLOWING WELLS PRODUCING GASEOUS FLUIDS 173 and screw 3 loosened. (a 1 (b) Fig. then by rotating choke cylinder 5 about pin 4 it is possible to bring any choke in the cylinder flush with channel 6. National B-8M bonnet and backpressure valve Fig. Overpressure protection is necessary if an increase in pressure may damage the flow line or other surface equipment. Such overpressure may be . Willis T-type wellhead choke (b) Well safety equipment Surface safety valve. 2. Any one of these can be installed without interrupting production.3-28. If the pressure is between preset limits. forces the valve gate to close. too. and the pilot valve will move downward. The liquid or gas pressure prevailing in the valve body is communicated by power piston 1 through the manually operated piston valve 2 to the pilot valve 3. the pilot valve sinks to its previous position and the valve opens by a reverse of the above process. moreover. depressing it. to a hydrate plug or a closed valve in the flow line. that is. when the level in a tank rises above a permissible maximum. the pressure in the valve body 4 tends to force gate 5 and piston 1 upward into the open position. Safety valves are usually set so that the high-pressure limit is about 10 percent above normal flowing pressure and the low-pressure limit is from 10 to 15 percent below it. then the upward pressure of the fluid acting on pilot valve 3 will be less than the force of spring 8. Underpressure protection is necessary because a flow-line break. the closing of the valve at the output end of the flow line will entail a pressure surge in the line. the pressure will drop in the flow line and the safety valve will open. All can be . This solution may be favourable when producing a high-pressure intermittent well. A substantial advantage of this design is that the device can be installed on a standard Cameron valve body. the storm choke is open under normal operating conditions. because even when the well is shut-in. Now again channel 7 will deliver pressure to the top end of power piston 1which will thereupon close the gate. (ii) actuated by pressure within the valve body and controlled by pressure from an external source. then the pressure acting on the pilot valve 3 overcomes the spring force 6 and the pilot valve moves up.and. Safety valves may be arranged so as to be controlled by fluid levels and shut down e. Installed in the tubing string. The main types are: (i) actuated and controlled by pressure within the valve body. There are several current surface safety valve designs. (iv) actuated by pressure from an internal or external source and controlled by some electrical signal. They can also be used to cut the well off from the separator. Channel 7 delivers pressure to the top of power piston 1. Tubing safety valves (storm chokes). When the pressure drops again to the preset value. pressure in the flow line will be comparatively low and.g. Storm chokes were originally used on offshore and townsite locations. it will shut the well in when damage to the wellhead permits flow above a predetermined rate or the pressure in the tubing drops below a predetermined value. may deliver well fluid into the open and constitute a fire and explosion hazard. If the internal pressure exceeds a preset maximum. it will not be necessary to take the trouble of going out to the well to shut it down.3-29 belongs in type (i) above. The Cameron B-type automatic safety valve shown as Fig. In this latter arrangement. it is both actuated and controlled by pressure within the valve body. Opening is automatic once the pressure builds above the preset minimum. If the output-end valve is opened.g. The valve operates as follows. If the pressure in the valve drops below a preset minimum. 2. (iii) actuated and controlled by pressure from an external source. which will close the valve. but they are to be recommended in any situation where the wellhead is liable to be damaged. Several types of storm choke are known. PROIWCING OIL WELLS ( I ) due e.174 2. By moving handle 9 the automatic safety valve can be manually operated. for instance. Chamber 1 is charged with gas to a predetermined pressure prior to installation. Some can be seated on a special landing nipple. others can be landed on slips at any point of the tubing. The latter then obstructs the aperture of the valve. The above-described type of storm choke is called the direct-control type because it is the pressure or the pressure gradient of the immediate surroundings that . This type of storm choke can be used up to pressure differentials of 700 bars.3. This solution has the considerable advantage that the valve seat is not exposed to erosion because in the open state it is covered by the ball. Some types are triggered by a pressure differential in excess of a predetermined value. The latter type includes the OTIS-H type storm choke.3 .3-29. 2. 2. Cameron B-type automatic safety valve Fig. shown as Fig. FLOWING WELLS PRODUCING GASEOUS FLUIDS 175 run and retrieved by wire line. others by a pressure drop below a predetermined value.3-30. then cylinder 3 moves up and turns ball valve 4. OTIS-H type safety valve pressure in the chamber plus the force of spring 2.2. 2.30. If the pressure of the surrounding medium decreases below the Fig. or some failure of the surface system. The situation may require. The flapper type Camco B valve is a subsurface safety valve that is retrievable with wireline and can be hydraulically controlled from the surface. the rise of the pressure of the separator. of pneumatic drive. If the surface pump. . PRODUCING O I L WELLS-41) triggers closure.g. The surface Fig. This operation can be provoked by a too low or too high flow line pressure. The advantage of this solution is that the amount of well fluid that can escape into the atmosphere prior to closure is less than in the case of direct control. the use of a valve controlled by wellhead pressure. to a higher than allowed value. however. or that of the liquid level. e.176 2. transmitted to the safety valve by a pressure conduit outside the tubing. 2.3-31. Camco B flapper type subsurface safety valve in (a) closed and open positions (b) pressure is transmitted by the actuating fluid through a control line situated in the casing that leads to the seating nipple. A pressure drop in the control line closes the valve. operates at the prescribed working pressure the flapper valve is open. The wireline retrievable complete unit 2 is placed in a seating nipple of the right profile.3.32. Figure 2. If the control fluid on the surface is not under pressure the flapper valve is held closed by spring 4 and the well pressure.2. too. The alphabetic order of the (b) (c) (c? (dl (el Fig. The control line 3 is connected to this unit. Three types of subsurface safety valves are used by the AMOCO company in its gas wells on the North Sea: bypass. When there is sufficient control line pressure the hydraulic cylinder. offers a device of this type for the protection of underground gas storage facilities but similar devices are widely used in numerous oil and gas wells. particularly where the wellhead is liable to be damaged by acts of sabotage or violence. FLOWING WELLS PRODUCING GASEOUS FLUIDS I77 Figure 2. (c) Underground well equipment Modern principles of production do not permit the exploitation of several zones through one and the same well. A storm choke can be installed also in the casing annulus. with no communication between any two formations.3 -3 summarizes the typical features of each piece of equipment after Turner (1954).3-32 shows equipment permitting the separate production of two zones in a dual completion. The flapper type proved to be the most suitable.3-31 shows the subsurface safety valve of CAMCO-B type. 2. travels downward and with a snap-action the flapper opens without any intermediate longlasting throttling. for instance. ball and flapper. that is.3 . In (a) the flapper valve 1 can be seen in a closed state. after TURNER (1954) . In the fully open state (b) the flapper and the valve port are completely blocked from the wellstream. 5. Medley (1978) wrote about the results of 3472 checkings of this kind. Table 2. The results of the analysis are valid for application in oil wells as well. Safety valve (storm choke) installed in the casing annulus. The OTIS company. It is advisable to check the operation of the subsurface safety valves every month. Dual completions. except if a multiple completion permits to produce the individual formations selectively. Also. It can be exchanged for piece permitting the same production pattern as in (a). The feasibility or otherwise of using a solution is indicated by a plus or minus sign. and vice versa. This solution permits the unloading by pumping of the upper formation as well as its acidizing and fracturing. If flowing production from the upper zone ceases. it is possible to shut in one zone and produce the other through the casing. Plug 3 can be pulled by means of a wire-line tool.3 . When the tubing is pulled. The lower zone can be produced by means of a pump. lower pumped 4. If the flow of fluid through the casing annulus is shut in at the surface. the production of the lower formation through the casing annulus and the upper one through the tubing. Crossover piece I in part (a) of the Figure is shown in blow-up. flapper valve 4 closes. The fluid rising from the lower zone passes plug 3 in piece A.3. the fluid from the upper zone will enter the tubing through port 2 and rise to the surface through the tubing.2. the tubing shoe can be anchored to the long string.3 Downhole well testing 2. if the need arises.2 Formation treatment 2. the upper one refers to the upper formation.1 By liquid-column pressure 3. This flexibility is an advantage because the comparatively large cross-section of the casing annulus will permit flowing production of relatively . as contrary to case (a).178 2. Of the two signs in row 2. In order to improve the output of the pump.2 Upper formation flowing.2 By inhibitor 4 Applicability 4.1 Both formations flowing 4.1 Acidizing 2.3 Lower formation flowing.4 Dewaxing 3 Casing protection 3. Let us add a few explanatory details.4 Both formations pumped a b c d e f A C E B D F A C E B D F B B C - B E A D - T -f. Comparison of selectively producing dual well completions Well completion type 1 First cost 2 Maintenance cost 2. respectively.2. Crossover choke I in solution (d) permits. Solution (c')is a variant of type (c). The upper zone is produced through the casing annulus. ++ A B B A A B f f + - - - + - + + + B B A B B B C B A C B C - D D C A A - B C A B - + A F A + + drawings is the order of increasing drawbacks on a relative scale. upper pumped 4. The choke can be changed by means of wire-line tools.2 Fracturing 2. a pump can be built in. PRODUCING OIL WELLS-(1) Table 2.1 Running and pulling 2.4. too. A possible wellhead assembly for a midi well is shown as Fig. tubing pipe. At . Equipment for octuple completions is available today. this is why these were originally call 'tubing-less completions'. Still. Parafin removal is a problem in any casing annulus. after BONSALL - structure to various tasks of production increases in this same order. usually cased with 2 7/8-in. The term refers to very small-diameter wells. Christmas tree of midi (slim(1960) hole) complet~on. A dual completion usually costs from 66 to 83 percent of the cost of two single-completion wells producing the same two formations (Prutzman 1955). In the last decade. FLOWING WELLS PRODUCING GASEOUS FLlJIDS 179 high-capacity zones only.2. 2. equipment permitting the separate production of more and more formations has been designed and built. A zone must not be produced through the casing annulus if the well fluid is corrosive or if sand erosion is liable to occur.one.3 -33.A tubingless midi well is convenient provided the well fluid will not harm the casing. does not express the significant feature. Dual midi (1960) completion. Midi installations. This term. 2. Coaxial double tubing requires a larger cross-section and two parallel strings of tubing an even larger . The well diameter puts a restriction on production capacity.after BONSALL Fig. But the adaptability of the well Fig. the dual completion requiring the slimmest well is the one with a single string of tubing. often it can be performed only after pulling the tubing.3 -33 (Bonsall 1960). 2. The term midi as used here is an ~bbreviationfor minimum diameter.A greater saving is likely to be realized at greater depth.3. Quite often there is no separate tubing string.3 34. however. 87 6. It must protect the casing from corrosive and erosive well fluids and.3 73.180 2. Accordingly. The tubing has to provide the most favourable flowing cross-section to the fluid rising from the well bottom.2 48.4 42. tubing joints should have the least possible excess OD (flush joints).3-4/a. The structure shown as Fig.05 5.4 77.5 1.9 88.9 88.9 51. the tubing plays a prime role in a well completion.0 57. diameter tubing size cemented in.57 18.65 13.6 35.6 114. 2.315 1.3 60.9 88.18 12.9 101.0 88.0 46.( I ) the designing stage. also from excessive pressure. In the case considered by Bonsall. (d) Tubing From a production viewpoint. It is often required to stand pressure differentials of several hundred bars.76 18.60 8.68 2. a 1500m deep midi well has turned out to be cheaper by 28 percent than a conventional well of the same depth (Bonsall 1960). it is important to know the intended future production rates of the well and the periods over which these are supposed to be kept up.12 14.56 9.8 50. Because of the need to run several strings of tubing in a casing of the least possible diameter.3 21. Quality requirements have been raised significantly by the spread of multiple completions.050 1.9 76.38 4.29 13.7 33.23 . if a packer is used. and its threads must provide a hermetic metal-to-metal seal.6 47. SAC and 5AX) Nominal size OD ID Calculated mass per length in mm mm kg/m 1.57 1 1.0 74.1 40. with two strings of 2 718 in.9 90. PRODUCING OIL WELLS . Dual-completion midi wells are often used to advantage when two zones are to be produced selectively. this solution was cheaper by 18 percent than a conventional dual completion.1 100.3 60. In a given case. as well as the estimated variation with time of the BHP during the producing life of the well.3-34 after Bonsall is a well drilled to a diameter of 200 mm to total depth.0 73.50 3.3 60. This has led to the use of higher-strength steels and Table 2.660 1 900 2 3/8 2 318 2 318 2 7/8 2 718 3 1/2 3 112 3 112 3 1/2 4 4 1/2 26. Main dimensions of API plain tubing (after API Spec. quality requirements facing tubing pipe are fairly stringent.4 62.2 69. 5A. on the basis of the same standards.12 18. The strength requirements. FLOWING WELLS PRODUCING GASEOUS F L U I I X Table 2.50 3. Some standard and non standard joints. Main dimensions of A P I external upset tubing (after A P I Spec.38 4. external upset end and integral types. The risk of leaks and of breakdowns has been reduced by the use of integral joints to replace the coupling rings of the past. 5A.~~~~ass to the devising of threaded joints providing a higher thread strength and a better seal. most often as an anticorrosion measure. SAC and 5AX) Calculated mass per length Nominal size kg/m 1.4 and 5AX) Nominal size I OD 1 1 CaI~. 5. are shown in Table 2.4/c.23 Table 2. 5A. Main dimensions of API integral tubing (after API Spec. according to API Spec.58 18.68 2.57 13. 5AC and 5AX. Glass linings are most widespread in the Soviet Union . Since 1950.3-4/b.05 6.65 15. Table 2.60 8. 2.3-5. the latter with special threads.3 -4a.3 . b and c gives the main specifications of the tubings of non-upset end. are shown in Fig.56 9.2. It is worth adding that nominal tubing size prior to 1950 meant the approximate ID in inches..3.3-35.~. the API standard regards as the nominal diameter the precise OD in inches. Tubing is sometimes provided with an internal lining.1 8 12. 3-5.3 -35 is of this type. Strength of API tubing (after API Spec.3-35. Using this type of tubing it is necessary to ensure that the unlined thread at the joint be protected from contact with the well fluid. 552 759 932 I API API API API Spec. The (tentative) API Spec. 2. 5AC . SAC API Spec. The Dowsmith Company. The lower roughness of the pipe wall results in an increased liquid and gas throughput capacity. 5A Spec. The Hydril make tube shown in Fig.182 2. for instance. M P a 414 518 690 828 Tensile strength 1 I Remarks min. SAC and SAX) Steel grade Yield strength a. SAC API Spec.plastic is popular in the USA. 276 380 552 725 ( I max. This can be ensured by correct design or by the insertion of a plastic seal ring. 2. 5A Spec. 5AR lists 13 standard tubings Table 2. Little or no paraffin will settle on plastic. At relatively small depths and pressures tubings made entirely of plastics are also used. 5A Spec. PRODUCING OIL WELLS ( I ) API p l a ~ n H y d r ~ l'CS-CD' API external upset Groyloc - Alton Bedford Monnesmann Fig.or glass-lined tubing walls. 5A. Tubing joints (Zotov and Kand 1967). produces tubings of fiberglass reinforced epoxy resin. 5AX For corrosive well streams 656 725 518 62 1 API Spec. The swab sinks easily into the fluid. all have the aim of reducing the liquid column pressure acting on the well bottom to below the reservoir pressure. check valve 2 in the interior of the swab is open. FLOWING WELLS PRODUCING GASEOUS FLUIDS 183 within the nominal size ranges 1. While it is being pulled.5). The long term static pressure strength of the tubings made of CT-80 material is 55. The standard tubings must meet ten different strength requirements. The density of the applied plastics is 2008 kg/m3.e. escape from the annulus. gas lift. Volume and pressure of gas in the annulus will gradually increase. if unhampered. Unloading may be effected by swabbing. Producing a well (a) Starting up a well A new well after perforating a zone or an older well that has been shut in for some time. When the flow of air through the open valve into the annulus ceases. by exchanging the mud column in the well by a lower-gravity one. roughly equal to the ratio of the cross-sectional areas of the tubing and the annulus. will often fail to start flowing when switched to the tank battery.5. During this period. One of the widely used types of tubing swabs is the Guiberson type shown as Fig. and.2. Let us assume that there is no packer closing the annulus at the bottom.2. During operation the swab depends from a wire line wound onto the relatively high-rpm winch of a hoist.5 in. Most of the liquid column above the swab is delivered to the surface.3 . and this value is significantly lower than the value of tensile strength in standard steel tubings (see Table 2. in the proportion of their respective cross-sectional areas. the liquid accumulated earlier in the annulus will be pushed into the tubing. or to the tank battery. the casing annulus is open at the wellhead. usually into a temporary storage tank placed beside the wellhead. 23. At the beginning of swabbing. however. the impression of liquid and gas together. or. i. The fluid delivered by the reservoir would. because the OD of the wire-protected rubber cups 1 is less in the unloaded state than the ID of the tubing. The swab is lowered to a depth of 10.3-36. The annulus is then shut down. to a value equal to or temporarily less than the required BHP for continuous flowing production. The specification mentioned above deals with strength requirements as well. the weight of the fluid makes the sealing cups press against the tubing wall and closes the check valve.3. especially in new wells. Swabbing.2 MPa. The GOR of the fluid in the tubing will therefore be significantly less than the GOR of . The liquid column filling the well must then be unloaded by means of an external energy source. as a result.660-4. more precisely. as it is closed in on top. flow into both the tubing and the annulus. Several suitable procedure are known. it is hardly more than one-quarter the density of steel. whereas the liquid flow rate in the tubing will be greater than the flow rate out of the reservoir. Also. then. this means that the reservoir has started to deliver fluid to the well.100 m below the fluid surface and then pulled up. either. Gas cannot now. Further swabbing will gradually decrease the BHP. only a fraction of the gas delivered by the reservoir will enter the tubing. thereafter the well will produce at a uniform rate.. Once more. and an increase in flowing BHP.184 2.... and may go on repeating itself a few times at declining pressure amplitudes. p. PRODUCING O I L WELLS+I) the fluid delivered by the reservoir. . some gas will pass from Fig. This is when flowing production usually starts. The flowing pressure at tubing-shoe level. In this state. The entire process repeats itself at a lower intensity. the casing annulus will be filled with gas in its entire length. Guiberson tubing swab the annulus into the tubing via the tubing shoe.. of the gas column in the annulus. At the instant when all the liquid has been pushed out of the annulus. as a result. Now the tubing-shoe pressure in the tubing decreases and. 2. will equal the casing-head pressure p. however.. The liquid column will be rather short.. The decrease in BHP entails an increase in the rate offlow into the well. which in turn entails an increase in the gravity of the fluid in the tubing. The annulus 'blows down'. and the GOR in the tubing increases. The tubing-shoe pressure of the fluid column in the tubing is likewise p. and the tubing will produce a fluid composed of gas and liquid. this latter is occupied by a gas column whose pressure at tubing-shoe level is p. its pressure decreases. plus the static pressure p.36. All further fluid delivered by the reservoir enters the tubing in the original composition.3 . fluid composed of both liquid and gas will enter the casing annulus. as a result of the decline in reservoir energy and hydrocarbon reserves. Surging is caused by the fact that the wellhead choke alternatingly passes now a gas. Surging of the first type is a consequence of a slug pattern of flow. (b) Types and control of flowing wells There are three types of flowing well: those producing at a steady uniform rate. Most flowing wells do indeed belong in this group. (b)l. but the average pressure over several periods is approximately constant. however. gas will flow from the annulus into the tubing through the tubing shoe. at the casing head.and tubing-head pressures that appear to be constant in the short term. Surging wells. nor consequently. then there will be no inflow after perforating a productive zone. these pressures are also subject to slow changes. and will permit a further amount of gas to . FLOWING WELLS PRODUCING GASEOUS FLUIDS 185 For unloading a well by gas lift see Section 2. We have so far tacitly assumed all flowing wells to belong in the first group. in fact. In the slug flow pattern the flow is quasi-steady. whose tubing-head pressure fluctuates while the casing-head pressure stays constant. now a liquid slug. -These fall into two groups: one. say. Ofcourse. If such a well is filled at the time of completion with a mud of. Owing to the greater viscosity of the liquid. whose casinghead pressure fluctuates as well as their tubing-head pressure.Some wells will start to flow at this BHP. the resistance to liquid flow of the choke will be much greater than its resistance to gas flow. By the end of the procedure. This will entail a decrease in fluid gravity and tubing-shoe pressure. If. The pressure fluctuations observed at the tubing head generally do not reach deep. whose flow velocities through the tubing are nearly equal. when the specific energy content of the well fluid is still high. It is therefore indicated to choose an unloading method which decreases the B H P slowly and gradually. particularly in the first phases of their lives. those producing continuously but in surges and those producing intermittently. If the tubing-shoe pressure temporarily declines for some reason during production.2. Wells of the second type are comparatively low-capacity ones. pure gas is being pumped into the annulus. such as the following. that is. the mud is replaced by pure water. The liquid load in the well is thus replaced by a gaseous fluid of decreasing gravity. and two. tubing-head pressure fluctuates rather rapidly (at a period of a few minutes). The producing sandface may be sufficiently friable to cave in under a sudden decrease in BHP brought about by unloading processes. they cannot be perceived at the tubing shoe. the B H P will decrease to round Lwyw. however. This may cause the well to sand up. The formation pressure of oil and gas reservoirs often stands close to the hydrostatic pressure of a water column whose height equals well depth. then gas is added gradually to the liquid pumped in. This type of well is characterized by casing.4 where it is given full treatment. Wells with a somewhat lower reservoir pressure will start to flow it the water is replaced by oil. to produce a steady flow. The casing annulus is first filled full of oil by means of a surface pump. 1200 kg/m3 density.3. the rate of decrease can be regulated at will. 126 let . after NIND. d = 2 318 in.3 .0506 m).=f(qo) graphs describing the interaction of reservoir and well at Rgo=20 and Rg.3 -5.3-37. Using Eq.3. The process continues until the decrease in BHP and the consequent increase of liquid inflow rate into the well bring about an increase of fluid gravity in the tubing. The gas delivered by the reservoir into the Fig. During this process. however. respectively. Given L. Example 2.= 350 m3/m3. flow of fluid into the well is represented by the I P curve I in Fig. calculate the production rate of the well assuming. Using Gilbert's pressure gradient curves let us plot the p.. New York-Toronto-London) annulus cannot escape through the closed casing head. PRODUCING OIL WELLS+I) enter the tubing from the annulus.4. (di = 0. In this phase the well will produce a fluid of low C U R . 2. = 1220 m. The rates of change of the flow parameters are comparatively slow. the well produces fluid at a decreasing GOR. Find the rate of production of the well and the mean GOR.186 2.5 mm.. 1. the well produces through a choke of diameter d. a production cycle usually is of the order of some hours. its pressure increases until it can push out all the liquid in the annulus through the tubing. Hence. also. The pressure of the gas that has stayed behind in the annulus is less than the now increasing tubing-shoe pressure in the tubing wherefore a column of liquid will rise in the annulus. but the GOR is subject to appreciable fluctuations. 172 (used with permission of McGraw-Hill Book Company Inc. transposed into SI units). This second type of surging is harmful because the energy of gas delivered by the reservoir is utilized at a lower efficiency than in the case of continuous flow.37. =9. the production GOR of the well is Rgo=20 m3/m3 over 22 hours and then 350 m3/m3 over 2 hours. This state of facts is illuminated by the following example (after Nind. the well will continually produce both gas and oil. Specific gas demand of continuous and intermittent flowing production.. steady continuous flow through the same choke at the same daily gas consumption. 2.1964. p. applying the procedure described in Section 2. so as to reduce its output.. The reservoir delivers liquid and gas to a tubing which is open at the surface. although kept continually open.2. and the tubing-shoe pressure will decrease accordingly.. Intermittent production of a flowing well means that liquid flow out of the well will entirely cease periodically. The mean GOR of surging production is If the well produced steadily at this latter GOR. This type of intermittent flowing production is harmful because an appreciable part of the gas is able to escape the well without doing any useful work. (b)3. This gas will now be able to start liquid flow. in cases when the throughput capacity of the tubing is greater than the inflow capacity of the reservoir. so that all the gas delivered by the resevoir will enter the tubing.) graphs characterizing the operation of the choke at these same GOR s. The intersection of these two curves shows that the daily oil production of the well would then equal 5.Surging production of the fluctuating-casing-pressure type and 'natural' intermittent production are comparatively inefficient ways of using formation gas to drive a well. and the well will 'blow off. Just as in the case of unloading the well (cf. = f (9.8 x 350 = 2044 m3. The results of the construction are shown as Graphs I1 and 111 in Fig. This effect is enhanced by the flow of higher-pressure gas from the annulus into the tubing. then the rate of production-v.3 -37. That part of it which enters the tubing bubbles through the liquid column without doing any useful work. is incapable of delivering at a steady rate. or else the well. Intermittent wells. The intersections of the corresponding curves reveal flow rates of 4. Gas pressure in the casing annulus. Since the liquid flow rate from the formation into the well is very low gas pressure in the annulus is free to decrease abruptly.7 x 20 + 3.400=47 m3. Section 2. There are several known ways to improve this . Filling up the well with fluid then starts at a slow rate corresponding to the low productivity and low reservoir pressure of the well. Either the well is only periodically opened up to start with.5 m3 of oil at the given gas flow rate. PLOWING WELLS PROI>IJCING GASEOUS FLUIDS 187 us plot the p.3. (b)2. . increases the while. After a while the well will produce gas only.. This latter case is largely restricted to comparatively small-capacity wells producing from a low-pressure reservoir.44 x lop4x 86. Flow regulation. 2.27 x respective durations of the two modes of production.5-(a) the annulus at a given stage cannot hold more gas. Surging thus deprives the operator of a daily 47.5= 7. the daily oil production is and the daily gas production is V..= 350.39. until it is sufficient to push out the liquid accumulated in the annulus.3. the well 'is empty'.51 m3/s at R. Taking into account the x 1 0 m3/s at R. The gas present is insufficient to ensure flowing production.wellhead-pressure relationships would be represented by the graphs shown as dashed lines. = 35.. closed on top. = 20 and 5. 5 mm Fig. The continuous liquid throughput capacity of the well approaches. PRODUCING OIL WELLWI) efficiency. the rate of continuous inflow from the reservoir. and (iii) methods which. 2. We shall discuss some of the more important solutions below. will prevent the production of gas without liquid. Figure 2. Orifice meter charts of one well for two different size chokes . by periodical shut-in and unloading of the well. These fall into the following groups: (i) methods reducing the liquid throughput capacity of the well. The greater resistance to flow of the new choke will reduce the rate of flow of the well fluid.3-38.188 2. (i) The wellhead choke is replaced by a smaller-bore one. Production is seen to have steadied considerably owing to the replacement of a 15. (ii) methods preventing the abrupt entrance of large volumes of gas from the annulus into the tubing.8 mm choke by a 6.3-38 shows diagrams of the gas flow rates of a well at two different rates of liquid flow. or indeed attains. however. will kill the well.3 -39 shows the rather well-known OTIS-B type removable bottom-hole choke.6c. The work potential of the gas is increased further by the fact that at the lower mean flowing pressure more gas will escape from solution and hence the effective GOR will increase.2. It can be installed and retrieved under pressure. the ambient temperature is likely to be much higher.4 x 106/1. so that no hydrate will form.e.3. especially in highpressure gas wells. Of the latter. i. R p . The non-removable type is practically a pressure-reducing insert in the tubing that can be removed only by pulling the tubing. FLOWING WELLS PRODUCING GASEOUS FLUIDS 189 one. A lubricator is installed on the wellhead and the choke is lowered through it to the required depth by wire line with a suitable landing tool.24c. According to Soviet literature. Recovery is by a pulling tool . Let the prescribed flowing BHP be 44 bars and the minimum feasible wellhead pressure. it is expedient to install several bottomhole chokes one above another. Also.1x 106=0. others can be seated at any point of the tubing. the slips will grab the tubing wall and thus fix the choke in place. At the depth where the bottom-hole choke is installed. is brought about at the wellhead or at the tubing shoe. then wellhead pressure will increase to 2 + 9 = 11 bars. There are several types of removable bottom-hole choke that can be installed and retrieved by means of wire-line tools. irrespective of whether the choking. that is. on the other hand. and so to distribute the required expansion. The work potential of the gas is. which reduces the BHP from 44 bars to 35 bars at the lower end of the tubing. Let us assume that a pressure drop of 9 bars is required to squelch surging. then the well fluid will energise the resilient seal cups. the pressure drop at the wellhead choke reduces gas temperature below the hydrate point: gas hydrates will form and.5 x 106/2 x lo6= 1. we may bring about the required pressure drop at the tubing shoe. In pTL/pT0. the damping effect upon surging will be much the same. Wellhead pressure will then be 2 bars and no further choke will be required in the wellhead. The isothermal work expended by the gas in the tubing will then equal c lg 4. For instance. some have seals energised by a pressure differential in the tubing. If cooling due to expansion is still too great. this may be expressed as c Ig pTL/pT0 if the GOR is constant. Using a bottom-hole choke. The drawback of reducing the choke bore is that it entails a higher wellhead pressure and a consequent lower work potential of the gas. let the useful energy output per m3 of stock tank oil of gas in a flowing well approximately equal isothermal work. others provide packoff if triggered mechanically. The landing tool is then recovered by means of the wire line. then. The work potential of the gas will be much greater. on the other hand. pTOmin= 2 bars. c Ig 3. A further advantage of a bottom-hole choke is that it reduces the pressure acting during production upon the wellhead assembly. Also. Its operation is cumbersome and therefore not recommended. Some have to be seated in a special landing nipple. the pressure drop. it might kill the well if the GOR is small. The risk of killing the well is considerably reduced if the choke is installed at the tubing shoe rather than in the wellhead. If now the well is started up at a comparatively high production rate. obstructing the choke. The choke is then called a bottom-hole choke. There are several known types of bottom-hole choke. that is. If this drop is brought about at the wellhead. the same relative amount of gas can do round twice as much work. Figure 2. . so that the bottom-hole choke can now be pulled. Figure 2. Thus the flow resistance between valve I and seat 2 will decrease (increase). 2. The difference is that the regulator maintains a constant pressure differential irrespective of the wellhead pressure. 2 .190 2. that is. It may be seated at the desired depth in one of several landing devices not shown in the Figure. 3 4 0 . If in the open state of the valve the pressure differential across the valve is greater (less) than the pressure represented by the spring 3.3 -40 shows the OTIS-E type bottom-hole regulator. OTIS B-type retrievable bottom-hole choke Fig. I Fig. then seat 2 will rise (fall). The regulator can be used to maintain pressure differentials up to a round 100 bars. This type of choke is not recommended for pressure differentials in excess of 120 bars. It is usually combined in use with a rather small-bore wellhead choke. provided the latter is in the lower. closed end position. Valve I is pressed by a rather weak spring load against the choke seat 2. OTIS E-type bottom-hole regulator Removable bottom-hole regulator. too.3 -39. In the absence of flow. the resilient cups will be slack. It serves much the same purpose as a removable bottom-hole choke. the prescribed wellhead pressure can be set by means of the wellhead choke. a bottom-hole choke of a design permitting mechanical locking should be used. For greater differentials. PRODUCING OIL W E L L S X I ) run in likewise on a wire line: a jerk on the pulling tool engaging the fishing neck of the choke will disengage the slips. The constant damping is provided by the regulator. The resultant pressure will displace sleeve 3 to the left.3 . be less in the case of gas flow. 2.3-41.3-42. the pressure differential across orifice 1 will increase.2. then some of the gas may be bled off into the flow line through the partly opened casing valve provided the well has a packerless completion.3. of course. Surge-damping completions. -As stated above. 2. the flow resistance of a choke of conventional design is higher if the fluid flowing through is a liquid rather than a gas.42. and the fluid in the tubing will have the original GOR as delivered by the formation. optimal in the sense expounded in Section 2. If liquid flows through the choke.3-41. Choke of self-adjusting aperture (a) (b) (c) Fig. In order to provide a steadier flow regulation. 2. The pressure differential across orifice I will.3 -(b). FLOWING WELLS PRODUCING GASEOUS FLUIDS 191 As explained farther above. In such wells it may be recommended to change the tubing to a size suited to ensure cooperation between formation and well. a variable-resistance choke described by DeVerteuil (1953) and shown as Fig. a ) . against the spring force 2. 2.3. If the GOR is comparatively high. then the annulus will cease to function as a surge chamber. has been devised. Installing such a packer may radically cure surging ( F i g . after MURAVYEV and K R Y L ~(1949) V opened to let the liquid pass and the flow resistance is thus lessened. The perforations 4 are thus I 1 \ 4 Fig. The gas rising in the annulus . (ii) If the casing annulus is shut off by a packer at tubing-shoe level. a surface choke providing the required damping may bring about a wellhead pressure high enough to kill the well. Supply gas is taken from the casing annulus through filter 13. (iii) By the well-timed opening and shutting of the wellhead it may be achieved that the well starts producing only when a sufficient quantity of liquid has already accumulated. the control valve will open. Also in this case. shut-in controlled by clockwork mechanism. shut-in controlled by a drop in casing pressure. The small clearance between the funnel rim and the casing will damp the flow of gaseous liquid from the annulus into the tubing. fixed to the end of the tubing.42 h). a valve controlled by one of several possible signals is installed in the flow line. therefore. PRODUCING OIL WELLS 41) will entrain a jacket of gaseous liquid. Opening controlled by rise in casing pressure. The valve stem of relay 3 is forced upward by spring 5. a gaseous-liquid jacket will develop in the annulus below the gaslift valve ( F i g . This displaces panel 12 to the left and. h). A Krylov funnel is an inverted funnel. as a result. decrease any further. by its modular structure. according to the signal used. In a third solution.3 . In wells equipped with this device. The valve stem of the relay rises and delivers supply gas to the pressure switch 11. The realization to be discussed here is clockwork-controlled as to opening and controlled by a rise in tubing pressure as to shut-in (see Fig. and so does the supply pressure acting upon the membrane of the control valve in the flow line. which. just before a blowoff of gas from the annulus occurs.2. shuts off nozzle 4. 2. disengaging arm 2 from the cam on timer wheel 1. In this case. the casing annulus is left to bleed as in the foregoing case. When the BHP declines. The valve stem of the relay will more downward and. Pressure in the supply line 6 decreases. a rise in tubing pressure. set so as to pass gas from the annulus to the tubing at a pressure differential from 1 to 2 bars. Now the pressure of the supply gas will increase above the membrane of relay 3. it permits the supply gas from the YES relay 3 (power amplifier) to bleed through no7zle 4. Control systems can. The casing valve is closed in this case at the wellhead. bears cams in a number equal to the daily number of production cycles. valve stem 9 of pressure detector 8 will move upward. a rise in tubing pressure. The pressure of fluid rising in the tubing will not. a gas-lift valve. the arrival of a tubing plunger at the wellhead. Pressure gauges 15 and 16 respectively indicate input supply gas pressure and supply gas pressure over the membrane of the control valve. can be adapted to several of the aboveoutlined combinations. of a rim diameter slightly less than the ID of the casing (Fig. We shall now outline the operation of a Hungarian make of pneumatic control system. by increasing the pressure of supply gas in conduit 6 and above the membrane of the control valve in the flow line. be classified as follows: opening controlled by a clockwork mechanism. supply pressure above the membrane of the NO relay 10 will decrease. As soon as the tubing pressure increases after the liquid production phase to a value set by spring 7. When arm 2 is moved by one of the cams to the left of its position shown in the Figure.3 -42/c). and is shut in as soon as the liquid is depleted. is installed from 30 to 40 m above the tubing shoe. and the annulus will not blow down.3 . brings the control valve to close. a drop in casing pressure. the arrival of a tubing plunger at the wellhead. The timer wheel 1.192 2.43 a. it is this 'reserve oil' that will enter the tubing first. rotated by the clockwork. 2. Bourdon- . Its pressure is reduced to the desired value in reductor 14. -10) ---a) -Cl Fig.3 -43. Optimal operation parameters should be determined starting from reservoir engineering limitations and economic considerations. it is necessary to check (i) whether the well completion and the fittings conform to the prescriptions set down . The greater the permitted pressure drop in the casing annulus. The fact that the gas accumulated in the casing annulus is prevented from escaping will give rise to a rather high B H P and.2. (c) Well check-ups In the course of production. in turn. Checking the well should cover the following. solid line is highpow pressure power gas greater the daily liquid production. When the drilling contractor hands over the well.3. to a relatively low inflow rate. Pneumatic control of flowing wells employed in Hungary: dashed line is high-pressure casing gas. the greater will be the amount of gas escaping without doing useful work. it is imperative to run periodical checks on the condition of the well and also on the parameters of liquid and gas production. 2. FLOWING WELLS PRODUCING GASEOUS FLUIDS 193 gauge recorder 17 records the pressure in the casing head. but the less will be the mean B H P and the . broken line is low-pressure power gas. which permits the establishment of several parameters of the zone of influence of the well. The pressures as well as the internal gas and liquid contents in the wellhead assembly should be checked. (iii)whether the wellhead equipment provides the required packoff without a leak. for a more suitable size. (ii) whether the tubing run in the well conforms to the agreement reached after well testing. If the total production shows a drop. The second group (that of the parameters to be checked at longer intervals) includes the following.g. and tested for composition and physico-chemical properties in order to gather the information required for a satisfactory planning and management of production. The production of individual wells is measured only at rather long intervals. PRODUCING OIL WELLS+]) in the order.6 months apart. If the two pressures vary in opposition. (v) A fluid sample is taken under pressure from every well newly brought in. the position and .. The results may indicate the desirability of exchanging the wellhead choke. The parameters fall into two groups: those that should be recorded at least once a day and those to be recorded at longer intervals.. or indeed. owing to deposits of scale or wax.. remedial operations cannot be started unless the individual well responsible for the drop has been pinpointed. The general rule is that if in a well having a casing annulus open below. it is usual to record a BHP buildup curve. Checks on a producing well include the periodical or continuous recording and evaluation of certain operating parameters. decreases while p.g. this may be due e. or an obstruction of the choke. (vi) On the occasion of every scraping operation. at the casing head). e. increases. The first group includes the pressures in the tubing and casing head. The recording of wellhead pressures sheds light on a number of important circumstances. vary in the same direction. to an increase in reservoir energy.. if the annulus is open below. then the flow resistance of the tubing has increased.g. the cause will usually reside in the well completion. then the cause of the change is to be sought for outside the well completion. (iv) whether the hand-over protocol contains all essential data concerning well completion and testing. (iv) Usually in connection with item (iii). If both pressures increase. and periodically from key wells of the field. or lowered flow resistance of the choke as a result of erosion. and at the tubing head. p. The wellhead assembly and the flow regulation equipment should be checked for good condition. to a decrease in reservoir energy. It is this well that has to be subjected to a closer scrutiny. Looking up the pressure records will at once reveal anomalous behaviour in the responsible well. and p. the tubing. It is but the production of a group of wells producing e. The data recorded at the group of well under consideration are processed into an isobar map which provides useful information as to the stage of depletion of the field.10 days. (i) The oil. Any essential change in the rate of flow and composition of the well fluid is reflected by pressure changes at the tubing shoe (and hence. gas and water productions as well as the sand and/or mud production of the well are measured at intervals of 5 . or deposition of wax in the flow line. (iii) Formation pressure is measured 3 . and the daily duration of production.g. Decrease of both pressures may be due e. If p.194 2. into the same stock tank that is recorded. (ii) It is expedient to run well tests with several chokes at least once a year or after any significant change in well production. which'entails a gradual increase in specific gas requirement. This is how the optimal frequency and method of scraping operations can be determined. Gas lifting Gas lift is a means of artificial production by which the producing well is supplied from the surface with high-pressure injection gas. because this tends to keep specific injection gas requirement low. tubing. insufficient in itself to ensure flowing production. Observations permit us to predict optimum tubing-change intervals. If the flowing B H P were only 30 bars at the same rate of production. and the flowing BHP is 50 bars. There are two main types of gas lift. The fundamental trait of intermittent gas lift is that the injection gas is introduced in to the tubing slugwise rather than continuously. for example. and to change it if need be. the specific gas requirement would be 480 m3/m3. it is necessary to check whether the bore of the production choke has worn down beyond a certain limit. producing a daily 7. During production life.4. then at 1 bar wellhead pressure the specific injection gas requirement is 140 m3/m3. the specific injection gas requirement of a 2000m deep well of modern completion. the production rate and the flowing B H P of gaslifted well will usually tend to decline gradually.9 m3 of liquid at a B H P of 5 bars.4. Scale can often be eliminated only be changing the tubing. The gas requirement ofintermittent gas lift is lower at low rates and Iow BHP's than that of continuous-flow gas lift. The drawback of intermittent gas lift is that-particularly in its modern forms of low specific injection gas requirement. is about 300 m3/m3. whose pressure energy is used to help lift the well fluid. The Gilbert pressure-gradient curves given in the Appendix reveal. notably at the instants when enough liquid has accumulated in the tubing. the specific injection gas requirement would be 350 m3/m3. which permit production also at low producing . acting more or less like a piston. (vii) At intervals depending on the composition and sand content of the well fluid. a steady stream of injection gas is at the surface introduced into the casing annulus. that is continuous-flow and intermittent. GAS LIFTING 195 thickness of the wax. it hardly decreases with decreasing B H P as long as the amount of liquid lifted per cycle remains unchanged. Continuous-flow gas lift can be regarded as an obvious continuation of flowing production. It is most economical where flowing B H P and well capacity are both high. to aerate the well fluid derived from the formation. The specific gas requirement over a day of production equals in a fair approximation the specific gas requirement of each individual production cycle. The injection gas usually enters the tubing through a deeply installed gas lift valve.9 m3. The simplest well completion for intermittent gas lift is the same as that for continuous-flow gas lift. lifts the liquid slug to the surface. also. At a flowing B H P of 30 bars and a daily liquid production rate of 7. For instance.2. sand and scale deposits in the tubing are to be determined. that if a well 2000 m deep produces a daily 95. In order to supplement the formation-gas energy.3 m3 of liquid through 2 718 in. This means of production has the considerable advantage that it uses the total quantity of produced formation gas to lift liquid. The gas slug. 2. the types. generally its length varies in the Fig. The casing annulus is packed off at tubing shoe level by packer 2. factors influencing operation (a)l. Both injection gas flow and well flow are steady or quasi-steady. which is insufficient in itself to ensure flowing production. Relatively long tubing string. 2. The pressure drop offlow in the tubing string can be determined by the methods discussed in Section 1. Insertion of the plunger greatly reduces sliggape. -One of the possible well completions suitable for continuous flow gas lifting in a single-completion well is sketched in Fig. only operating valve 1 is normally open during steady production. Continuous-flow gas lift (a) Theory of production. just as in the case of flowing production. Designing a continuous-flow gas lift operation for a single-completion well means to find the optimal size and length of tubing. the liquid slug and the gas column are separated by a plunger made of metal or some plastic. is led through injection gas line 3 into the casing annulus. formation fluid and injection gas rise together.196 2. the depth of continuous gas injection.1.4.4.4. 2.4 . A peculiar variety of intermittent gas lift is plungerlift production.the formation gas produced is not exploited in lifting the well fluid. also. Of the gas lift valves installed in the tubing wall.1. even if the rate is small.1. sizes and depths of the gas lift valves to be installed. In the tubing. 2. the formation gas produced will contribute to the lifting of the liquid. The main advantage of the method is that the specific injection gas requirement is low at medium BHPs. The tubing is longer than several ten of meters. Continuous gas lift installation range of 100 or 1000 m order of magnitudes. In this method. and the decision . the gas enters the tubing through operating valve I. PRODUCING OIL WELLS--~I) BHPs . The injection gas required to supplement the formation-gas energy. Determining the point of gas injection In early production practice. then the point of injection has to be higher up the tubing. If it is less.. Graph I is the pressure gradient curve. issuing from point A. If the well fluid rises. will fail to be optimal. on the first leg of its journey to the surface. then the length of the tubing string has to be less than well depth. is the least possible value attainable with the given surface gathering and separation equipment. This aperture is usually fitted with a gas lift valve. When choosing the tubing.4. 2. The point of gas injection is at the well bottom if injection gas pressure is equal to-or greater than the flowing B H P to be realized. the tubing string reaches down to the well bottom. determined by the flowing BHP p . lift gas was invariably introduced into the tubing at the tubing shoe. Fig. The annulus was not packed off. In both alternatives it is assumed that the wellhead pressure p. then the specific gas requirement.4-2. the tubing size chosen ensures either a minimum specific injection gas requirement or a minimum flowing pressure gradient.4-2. The correct depth of injection can be designed in the manner shown in Fig. or the flowing pressure gradient. by hypothesis. 2. In modern completions. injection gas pressure is less than the prescribed flowing B H P .2. If. and is provided farther up with an aperture to let injection gas enter. It is assumed first that the injection gas enters at the shoe of a tubing string not reaching down to the bottom of the well. GAS LIFTING 197 whether to use a packerless (open) or a closed gas lift installation. or to make the well produce liquid at the greatest possible flow rate at a given consumption of injection gas. ~ . the criterion of optimization is either to lift the formation fluid at the prescribed flowing B H P under the lowest possible injection GLR. in a casing which has of necessity a larger diameter than the tubing. because. The specific injection gas requirement of continuous-flow gas lift is less if the tubing string reaches down to the well bottom. in such a well completion. 198 2. PRODUCING OIL WELLS 4 1 ) prescribed for the well bottom situated at a depth L,. This combination ofdata will prevail if the well fluid, characterized by a liquid inflow rate q, and a formation GOR R, flows in a casing of diameter d,: Graph I1 shows the injection gas pressure v. depth in the casing annulus. At the point of intersection B of Graphs I and 11, the pressure of injection gas attains the pressure of the well fluid rising in the casing; the ordinate of this point determines the length L , of the tubing; Graph 111 is the pressure traverse in the tubing at a liquid flow rate q, and a combined formationplus-injection GOR (R, + R,). This graph is selected from a set of curves referring to the given q, and the tubing size d,, by finding the curve along which pressure decreases from p,, to p,, over a length L,. Subtraction of R, from the R,, value belonging to this curve yields the specific injection gas requirement R,. Let the tubing string reach down to the well bottom and let the injection gas pass from the casing annulus into the tubing through a gas lift valve. Graph IV is the pressure traverse of flow below the point of injection. Passage through the gas lift valve involves a pressure drop Ap. Hence, a Graph 11' is to be traced parallel to, and at a distance A p from, Graph 11. The point of intersection C of Graphs IV and 11' indicates the depth L, at which the injection valve is to be installed. The pressure traverse valid for the flow of formation fluid plus injection gas (Graph V) is chosen in the same way as the curve issuing from the point B in the previous case. Flowing pressure at depth L, in the tubing is higher than what it would have been in the previous case, when the well fluid rose in the casing to a depth L,. This means that, for rising to a depth L,, the well fluid has consumed less pressure energy. Consequently, lifting it to the surface consumes less injection gas energy, too. In the following we shall analyse the influence of wellhead pressure and injection gas pressure upon the economy of continuous-flow gas lift (McAfee 1961). The aim to be pursued is to make the wellhead pressure p,, as low as possible. Causes for a high wellhead pressure may include a flow line too long or laid over a hilly terrain, or of a diameter too small or reduced by deposits; some fitting causing a significant local rise in flow resistance; an abrupt break of direction; or a separator installed far above the well; or too high a separator pressure. The influence of wellhead pressure upon the specific requirement of injection gas is shown in Fig. 2.4 -3. Let wellhead pressure of 4.4,7.9, 11.3 and 14.7 bars prevail in succession in the well characterized in the Figure. Starting from point C, let us select from the set of curves, in the manner described in connection with Fig. 2.4-2 above, the pressure gradient curves belonging to said wellhead pressures at the given oil flow rate q, and tubing size d. Each curve is marked with the corresponding specific injection gas requirement. At the bottom of the Figure, the energy required to compress the injection gas is shown on a comparative scale; absolute values are not shown either here or in the next few figures. When calculating the compressors' power consumption, the intake pressure was taken to be 2.7 bars in each case. It seen that the power consumption of compression is almost three times as high at a wellhead pressure of 14.7 bars than at one of 4.4 bars. Production is, then, the more economical, the less the flowing wellhead pressure. 199 2.4. GAS LIFTING The effective injection gas pressure at the surface (that is, the pressure to be ensured continuously during production) is to be chosen so that it should equal the flowing BHP at the well bottom. If the injection gas pressure is less than that, then injection should, by the above considerations, take place at a point above the well bottom. The compressor energy required t o compress the injection gas is the greater, the higher up the tubing the point of injection determined by lower injection 0 50 100 150 o ban Fig. 2.4- 3. Influence of wellhead pressure on power demand of injection-gas supply, after MCAFEE (1961) gas pressure. Figure 2.4-4 refers to a well with pressure gradient curves for three values of injection gas pressure. Specific injection gas requirement is the parameter ofthe pressure gradient curves fitted between the point p (,, L;= 0),corresponding to the wellhead, and the points A,, A, and A,, corresponding to the points of injection. In the given example, specific injection gas requirement rises from 43 to 142 m3/m3if the injection gas pressure decreases from 119 to 43 bars. If the injection gas pressure is unnecessarily higher than the flowing BHP (cf. also paragraph (a)2), then part of the pressure energy will escape without doing any useful work. (a)2. Relatively short tubing string. In high rate and high productivity water wells producing from high pressure reservoirs a tubing string of only several ten ofmeters length is run into a comparatively deep well and the well is operated with gas or air lift. The completion of wells of this kind may be "regular", i.e. without gas lift valves and packer (Fig. 2.4 -5, a), or it may contain a separate gas injection string placed the annulus (Fig. 2.4-5, b). While analysing the transport curve of the tubing it becomes clear that in the same dimensionless pressure gradient the specific liquid lifting capacity of the gas flowing in the vertical pipe section of length dl is smaller if the tubing is relatively shorter than if its length ranges in the order of magnitude of 200 2. PRODUCING OIL WELLS { I ) 100 or 1000 m. As an example Fig.2.4 - 6 shows two families of curves. The group of curves A were calculated by applying Krylov's equations, while curves B, though using the same parameters, were determined by laboratory experiments using short tubing. The reasons for the discrepancies are discussed below. In the inflow section of each tubing the flowing gradient is greater, due to the intake losses and the "greater than average" slippage losses, than it would be with 150 p, bars Fig. 2.4 - 4. Influence of gas lift pressure on power demand of injection-gas supply, after MCAFEE(1961) Fig. 2.4-5. Gas lift installations with short tubing strings the same production rate and state parameters some 10 meters above the tubing shoe, among "steady state" flow conditions. The slippage losses are greater because after the intake the gas bubbles are more heterogeneous in size and distribution than with steady flow. The modified Eq. 1.4- 1 1 for short tubing (Szilas and Patsch 1975) states Yk 2.4 - 1 t = C - + <I, Yl where C, the correction factor based on small scale laboratory experiments performed with water and air, is The constants of the equation, K,, K,, K,, K4, which are functions ofd, and f,are determined for a certain well completion. The general application of this equation requires test data from of other well completions also. Both the intake losses and the intake gas bubble distribution are significantly influenced by the shape of the piece 20 1 2.4. GAS LIFTING through which the gas from the annulus, or from the injection string placed in the annulus, flows into the tubing. It turns out, however, even from Eq. 2.4-2, that the gradient-increasing impact of the short tubing with the given configuration is the function of tubing length L, the inside tubing diameter d , , the average'flowing gradient and the gas flow rate at standard conditions, q,,. From the equation it can be calculated what the critical length of tubing is, for which the gradient, at the t, 10-3>/s 20 1 ct = 0.090tn 1= 0.600 qg, , l ~ - ' r n ~ / s Fig. 2.4-6. Transport curves for short and long strings of tubing, after SZILASand PATSCH(1975) end it reaches the steady state value characteristic of long tubing string. Thus it follows that, on the one hand, greater specific gas requirements are encountered for short tubing than for long tubing, and, on the other, the specific gas requirements of the short tubing can be modified by altering the construction of the gas injector piece. (b) Installation design (b)l. Selecting optimal tubing size. - Two parameters of the tubing have to be optimized, viz. its length and its ID. In the foregoing paragraph we have found that length is optimal if the tubing string reaches down to the well bottom. The optimum diameter depends on what is regarded as the optimization criterion of the gas lift operation. (if Dimensioning the tubing for afixed rate of oil production and u minimum specific injection gas requirement with time-invariant parameters. Using pressure gradient curves, the problem can be solved regardless of whether the pressure of the injection gas is greater or less than the flowing BHP unequivocally defined by the oil production rate (McAfee 1961). In Fig. 2.4-7, the point of injection is likewise defined unambiguously by the point of intersection of the prescribed BHP and the given injection-gas pressure, or, retaining the notation of Fig. 2.4-2, of Graphs I and 11'. Between this point, and the points (p,,, L = O), pressure gradient curves 202 2. PRODUCING 011, WELLS+]) referring to various tubing sizes have been fitted. It is clear from the Figure that, under the conditions stated, tubing sizes of 1.9,2 318 and 2 718 in. will respectively result in specific injection gas requirements of 142,44 and 36 m3/m3. Consequently, in the case considered, 2 718 in. size tubing is the optimal choice. The procedure is applicable also if injection gas pressure at the well bottom is equal to or greater than the prescribed flowing BHP, if it is noted that higher injection gas pressures have to be reduced to the desired value. If the injection gas pressure available, pi, is equal to ,bors Fig. 2.4-7. Influence of tubing size on power demand of injection-gas supply, after M r A m (1961) or greater than the BHP, then the tubing size delivering the prescribed oil flow at the minimal injection gas pressure can rather simply be calculated using Krylov's relationships. It is based on the consideration that fcan be calculated from Eq. 1.4 - 12 if the given tubing-shoe pressure p,, and the least feasible wellhead pressure pTo are known. In the knowledge of the prescribed oil flow rate go, do,, can be calculated using Eq. 2.3 - 1. Example 2.4 - 1. Find the optimum tubing size if L, = 1153 m; p,, = 79.5 bars; pwJ= 24.0 bars; pTOmi,= 1-2 bar; J =2.23 x 10- l o m3/(Pas); n = 1; p,= 900 kg/m3; Rf= 15 m3/m3. The oil production rate corresponding to the prescribed flowing BHP is, by Eq. 2.1 - 3, The average pressure gradient is, by Eq. 1.4- 12, 2.4. GAS LIFTING and the optimum tubing size is furnished by Eq. 2.3- 1 as The ID of the next standard tubing size is 0.062 m: its nominal size is 2 718 in. The total specific gas requirement is, by Eq. 1.4 - 19, R,,, = 0,123 1 153(1-0.224)900 x 9.81 = 131 m3/m3, 24.0 x l o 5 0.062°95 x 0.224 x 1.01 x l o 5 lg 1-2 x 105 and the specific injection gas requirement is Ri=131-15=116 m3/m3. (ii) Dimensioning the tubing for the maximum oilflow ratefeasible at a given specific injection gas consumption with time-invariant parameters. Let us solve the problem under the assumption that the injection-gas pressure at the well bottom equals the flowing BHP. Let us trace the inflow performance curve of the well in a bilinear orthogonal system of coordinates calibrated in q, v. pwf. Using a set of pressure gradient curves, let us plot in this Figure the throughput capacity v. pressure curves (q, v. pwf)of various tubing sizes. This is done by choosing from a set of curves valid for a given tubing size d and q, =const. the curve belonging to the prescribed GOR, R,,. The value of pwf, that is, the value to which tubing pressure increases from a prescribed wellhead pressure p,, over a tubing length L,, is then read off the curve. The values thus obtained are plotted against the oil production rate. The plots belonging to one and the same tubing size are connected with continuous lines. The points ofintersection of the inflow performance curve, characterizing inflow into the well, with the throughput capacity curves of the individual tubing sizes, give the rate q, at which the well will produce oil at the prescribed specific gas requirement and wellhead pressure. The tubing size to be chosen is that which ensures the highest oil flow rate. Example 2.4-2. Find the standard tubing size at which a well 2000 m deep, producing an oil that can be characterized by one of Gilbert's set of curves, will produce at the highest rate, if p,, =4.0 bars and Ri= 200 m3/m3.Let the formation gas production be negligible. Tubing available includes the sizes 2 318, 2 718, and 3 112 in., all three in sufficient length to reach down to the well bottom. The inflow performance curve is given as Graph 1 in Fig. 2.4-8/a. The throughput capacity curves are the three top graphs in Fig. 2.4 -8/a, respectively marked 2 3/8,2 718 and 3 112 in. at Ri = 200. The graphs have been plotted using Columns 1,2 and 3 of Table 2.4- I, whose values have in turn been read off Gilbert's pressure gradient curves. The data for 3 112-in. tubing have been taken from a set of curves presented in Gilbert's original work but not reproduced in this book. As revealed by the points of 2. PRODUCING OIL W E L L M I ) Fig. 2.4 - 8/a. I I X) 40 60 80 100 q, , mS/d Fig. 2.4- 8/b. intersection of the inflow performance curve (Graph 1) and of the throughput capacity graphs, the well will deliver a daily 73 m3 of oil through a tubing of 2 3/8 in. size and further 70 m3through 2 7/8 and 67.5 m3 through 3 112 in. size tubing. That is, at a prescribed specific injection gas consumption Ri= 200 m3/m3, it is the 2 318 in. tubing that ensures the highest rate of production. 2.4. G A S LIFTING 1600 1400 1200 1000 800 600 COO 200 I I 1 2 3 4 t. years Fig. 2.4- 8/c. Fig. 2.4 - 8/d. (iii) Dimensioning the tubing for the maximum feasible liquid production rate, with time-invariant parameters. It is assumed that injection gas pressure at the well bottom equals the flowing B H P . Let us trace the inflow performance curve of the well in a bilinear orthogonal q, v. p, coordinate system. Using sets of pressure gradient curves, let us plot in this same Figure throughput capacity curves (q, v. pwf) corresponding to the least feasible flowing B H P for various tubing sizes. The values 206 2. PRODUCING OIL WELLS (I) to be plotted are established by finding among the pressure gradient curves referring to a given tubing size d and various values of q, =const. that curve which has the steepest slope, that is, the one which gives the least pressure at any depth below the surface. Reading off the pressures to which the prescribed wellhead pressure p,, increases over a tubing length L, (that is, the producing BHPs, pWf),let us plot the values thus found against the production rate. The points belonging to a given tubing size are connected with a continuous line. The points of intersection of the inflow performance curve with the throughput capacity curves belonging to the various tubing sizes permit to find the maximum rates of production feasible by continuous flow gas lift through each of the tubing sizes examined. The pressure gradient curves permit us to determine the minimal specific gas requirements of lifting Rpminthe maximum rates of production through each tubing size. Let us point out that this construction cannot be performed with the pressure-traverse curves based on the Poettmann-Carpenter equations, because in any set of curves belonging to a given pair of values d and q,, the slope of the curve invariably increases with the increase of R,,, the production GOR. This situation, which is contrary to observation, is due to certain lacks of the theory expounded in Section 1.4.1(d). Example 2.4-3. For the well characterized in the foregoing example, let us find out, first, which of the tubing sizes 2 3/8,2 718 and 3 112 in. will ensure the greatest rate of production, and second, the specific injection gas requirement of that rate of production. The throughput capacity curves derived from the pressure gradient curves are shown as the lowermost three graphs marked respectively 2 3/8,2 718 and 3 112 in. at R,,,, in Fig. 2.4-8/a. The curves have been plotted using the data in Columns 1, 2 and 4 of Table 2.4-1, which have in turn been read off Gilbert's pressure gradient curves. Also in this case, the data for 3 112 in. tubing have been taken from Gilbert's original work. The points of intersection of the inflow performance curve with the throughput capacity curves give the maximum daily production by means of continuous flow gas lift as 75 m3 for 2 318 in., 82.5 m3 for 2 718 in., and 89.5 m3 for 3 112 in. tubing. The continuous curves in Fig. 2.4-8/b illustrate the q, v. R,,,, relationships for the three tubing sizes. These curves have been plotted using data in Columns 2 and 5 of Table 2.4 - 1. The curves can be used to read off the specific injection gas requirement Rpmi,also for any intermediate value of q,. Accordingly, the 75 m3 maximum daily production obtained in the foregoing paragraph requires 300 m3/m3 of injection gas. The 82.5 m3 produced through 2 718 in. tubing requires 460 m3/m3, and the 89.5 m3 through 3 112 in. tubing requires 670 m3/m3. (iv) Dimensioning of the tubing string, with time-variant parameters. The inflow performance curve of the well will vary during the life of the well, and it is usually possible to predict its variation by reservoir engineering considerations. Solving the problems outlined above'for various instants of time, each instant characterized by its own inflow performance curve, it is possible to derive the changes in time also of the production parameters. Let the formation gas production of the well be negligible. I 3 112 in. Assuming continuous-flow gas lift over the period of time envisaged.4-8/a.0 31.5 60.225 and 42.9 31. q.9 15.5 60.5. d 40 m3/d 2 Pw~200 Pwfmin Rpmin bars 3 bars 4 m3/m3 5 2318 7..5 46.5 16.9.1.4 .0 14.0 42.0 - .3 65 58 51 50 49 15 20 25 31 36 1570 1120 765 578 42 1 3 1/2 7.5 95.7 62.5 95.= 4. The inflow performance curves of a well 2000 m deep at intervals of 2.4 -4. I 3 112 in. what additional supply of injection gas is required to Table 2..0 62.2.0 bars.9 15.5 29.0 82.7 62. 1 Example 2. 2 718 and 3 112 in.9 31. 145. 2.0 300 320 350 400 520 750 460 510 580 660 820 1220 670 730 820 940 1120 1620 m3/m3 %lob 2 318 in.5 months after designing are shown as Graphs 1-6 in Fig. Serial number 1 2 3 4 5 6 2 318 in. GAS LIFTING Table 2.5.2.7 62.5 95. The least feasible wellhead pressure is pTOmi.0 22.3 81 69 59 53 52 11 13 78 23 27 2320 1590 1130 805 644 in..0 89. The flow of the well fluid can be characterized by a set of Gilbert curves. let us answer the following questions: what is the maximum feasible daily oil production rate.5 74.5 69.0 12.0 55. 1 40mas 2 718 in..4. 1 m3/d 2 3 4 5 6 75.0 26.0 50. ( Rpin 2 718 in.9 31.5 39.. at Ri=200 m3/m3..4 .0 480 35.9 15.. rn3/d 7 72. Tubing is available in the standard sizes 2 318.3 50 41 42 45 48 22 28 32 42 47 890 632 445 321 262 2718 7. 2 318 in. which of the tubing sizes will ensure the maximum oil flow rate q. 2. = 200 taken from Table 2.7.4 -3 reveal how far the maximum production rate q.x-qe200. These values after graphical smoothing are carried into Column 2.4 . These data indicate the specific amount of injection gas required to produce oil at any rate higher than what can be produced through 2 318 in. 40 Serial number 2 318 in.. that is. tubing. Table 2. R..0 2. Fig..0 14.. this production.0 22. through any given size of tubing? The throughput capacity curves in Fig. exceeding the maximum feasible production through 2 318 in.4-2. tubing at Ri= 200. Columns 9 . and partly because of the different methods elaborated by the different experts.5 7.5 11. Column 8 lists the values of q.4-8/c. corrected m3/d 3 2 2.13.0 2.2. = Aq..5 12..0 2.. as explained in point (iii).. Columns 13..4-8/b provides the R.6 43. and R.0 q g mar 2 318 in..7 15... Gas lift valve spacing.5 9.0 ( 2 718 in.2 31.. In Columns 5 .9 3 112 in.3 and Column 7 of Table 2.0 7. .3 25. are listed in Table 2. values belonging to the various points of time.1 60...5 2.0 4.. The greatest feasible oil production rate and the corresponding specific injection gas requirement are plotted v..4 49.3..4 -2. through 2 318 in..5 4.0 238 17. and q. It is impossible to discuss all the methods here.0 54. It is seen that the production of more oil requires an additional 2000 -4000 m3/m3 of injection gas over a significant part of the life of the well. taken from Table 2. PRODUCING OIL W E L L S 41) Table 2. and R.11 and 2 -4..4-2 refers to 2 318 in..9 28.5 3. size tubing will permit the greatest oil production rate throughout the producing life of the well.4 -2 are carried into Column 1 of Table 2.0 35. 3 112 in. time in Fig.4-2.. and qO2... . 2 718 in. The differences between the corresponding entries in Columns 1 and 7 of Table 2.4 -8/d is a plot of the data in columns 2.. read-off 1 1 2 3 4 5 6 1.3. -qgm.4. is realized at the considerable expense of a 120-percent increase in GOR...0 38. produce the additional amount of oil between q.11 list Aq..0 10-0 9.. Columns 1-4 of Table 2.4-3.5 19.. 2.. (b)2... respectively. 14 and 15 of Table 2. The values of q.0 42 12. 4 5 lo3 m3/d 6 7 17.8 17.0 14. is the product of q.0 7.The valve string design calculations of both the continuous and intermittent gas lift production differ to some extent partly because of the different valve types applied.2 35./Aq.4-2. It is apparent that 3 112in. tubing at a GOR of 200. tubing by 30 percent.4-8/a have been plotted as explained in points (ii) and (iii). read off the graphs.15 give the ratios of the corresponding entries in Columns 9 .. Figure 2.4 ..0 12. attainable through each of the tubing sizes available exceeds the pruduction rate q. . However.0 9.6 13. 2. AR.. the products of the values q.5 16.. q. let e. (i) Operation and dimensioning ofpressure-controlled gas lift valves.6 - In the present section we shall speak of two design methods that can be applied for casing-pressure operated gas lift valves. Winkler and Smith 1962.2 Q8 2. as shown in the Figure then the pressure acting to open it is composed of the back pressure p. The condition for the valve to open is A.1 9.4 2. Designing production equipment presupposes.).5 42.3 1.~)Pc=ADPD.9 25.9 3.3 21. Various spacing methods are discussed in manuals dealing with gas lifting (e. 2 718 in.0 19.10.2 3.0 7. GAS LIFTING 4. A.3. 4 8 200 2 318 in.4. and some catalogues).A.3 3.4-9 shows a schematic section of a Guiberson A-type gas lift valve (later called basic valve.0 4.1 45. The casing pressure required to open the valve is seen to depend on the pressure acting on the tubing side of the valve. If the valve is in the closed position. We shall therefore discuss at this point.5 12.209 2.0 9. 10' m3/m3 8 9 10 11 12 13 14 15 14.6 9.4 8.9 3. then 2. Figure 2..3 deals in detail with the valves used in modern gas lift operations. Dome 1 is charged with nitrogen gas. however.4 . acting upon the crosssectional area ( A D . The suffixes have been chosen in this way because the valve is usually installed so that the pressure in the tubing acts as back-pressure and the pressure in the casing annulus as gas pressure.73 The relationship is illustrated for p.8 8.8 1. slightly apart from our main trend of ideas. Section 2. Let us express pc from this equation..2 30. 2 318 in.4 40.2 2.4-3 m2 and AD=4.2 3.9 2.= 3.3 0-8 4.7 2. If p.9 3.g. we mention the characteristics to be taken into consideration when designing the valve string. = 4 0 bars in Fig.0 36.2 2.PT+(AD-A. the operation ofa casing pressure-controlled gas lift valve.1 8. Brown 1980.17 x x m2..8 2. read-off lo3 m3/d 1 corrected 2 718 in.2 2. of the valve port 4 and the pressure p. 2 318 in.2 2.4.6 7. AR. 3 112 in. acting upon the crosssectional area A.4. Vol.6 3.= 1 bar.4 17. 2a. In Section 2. a knowledge of at least the fundamentals of valve operation.2 22. 3 112 in. while discussing the more important valve types.5 23. then the casing pressure required to open the valve is pc .2 2. 2. BV).g.0 23. Its pressure pD depresses the bellows 2 of effective cross-sectional area ADand also the valve ball 3 fixed to it..9 3.0 3. 4 . be opened at any back-pressure p . By the general gas law.( ! ) =42-8 bars. such as the cooling effect of the gas flowing through. =40 bars.4-9. If p . Guiberson A type gas lift valve Fig. the pressure in the tubing exerts no control on the moving system. because the area of the valve port 4 is much smaller than the combined sections of the inflow ports 6. <40 bars by bringing pressore in the casing to the appropriate value between 42. it equals 1. for instance. whence . closing of the valve is controlled by casing pressure alone and the valve will close whenever casing pressure drops enough to equal dome pressure. then. The valve can. PRODUCING OIL W E L L S . p c > p .9) approximately equals the casing pressure. It should further be taken into account that establishing the valve temperature in a working valve involves some uncertainties.002.8 and 40 bars. the Fig. then the casing pressure required to open the valve will also be 40 bars. It is therefore usually permissible to regard the ratio zJzi as equal to unity. 2. 2.10. The valve is at a higher temperature when installed in the well than when it has been charged.210 2.4. 2. pc=p. In the open position. The condition for gas to flow through the opened valve from the casing to the tubing is.. that is. If the valve is open. of course. . the pressure of nitrogen in the dome at the temperature prevailing at the depth of installation Li is The change of compressibility factor of nitrogen is small in most cases of practical interest. At 40 "Cand 50 bars pressure. then pressure in cavity 5 (Fig. a =0.4.00118 X 6 7 0 X 2 1 .067 X 29. and temperature T prevailing there. Dome pressure in the valve installed in the well equals. ~~ = 0. 9 3 3 + ~0.. M = 21.. it is Let us add that T can be regarded as the arithmetic average of mean annual temperature on the surface and of formation temperature at valve depth. p2 =pco. +0.. GAS LIFTING In order to control the valve by regulating injection gas pressure on the surface..7 = 37.933 X 40. Example 2. casing-head pressure on closing of the valve is p. Its surface value can be calculated using Eq. pci = 40. = UP..4-5. 2 is the compressibility factor of the injection gas in the casing annulus.38..5. = 29.25.=O yields for the pressure at depth of the gas column Let p .0 "C.2 x 10' Pa. p..: = 30 "C.9. 2=0-87 at T=293.6 X lo5 = Dome pressure in the valve at 20 "C temperature is 293.5 X 10' = 39. pressure in the casing annulus at that depth. the pressure of injection gas is p. on the surface.. = 39. Tco= 11.. Accuracy will not be unduly impaired by assuming B. at the depth L.7 x 10' e 0. back-pressure during continuous production.. = 1.= 288.0 . we have to know the injection gas pressure pci at the depth of installation Li of the valve..0 kg/kmole. pTJi= 16. maximum possible back-pressure during unloading after closing of valve. 8 7 x 293. Find the dome charge pressure p. gas flow rate through valve during continuous operation. at the mean pressure p.5 m3/s. where the gas lift valve is installed. x = 1..2 Closing pressure of the valve is equal to dome pressure. = 0. q. 7. temperature at that depth.3r v. at 20 "C temperature. 2.. discharge factor. of a pressure-controlled gas lift valve of opening equation pc= 1 ...067pTi. pDi= 0 .7 x 10' Pa.21 1 2. 303. = 39. Equation 1. T. mean annual temperature at the surface..2 p. and the choke diameter d. provided the depth of installation of the valve is Li=670 m.7 bars.. provided the casing-head pressure is pco. . .2 K .7 bars. p.7 K and p3rpDi=39.7 x 10' -.4. Hence.5 bars. 0 7 2 p T . = p. h = L. p. the closing pressure as measured on the casing head. Calculation requires the knowledge of T and 5. 0 7 2 ~ ~ .. by the opening equation.2-4 with the assumption q.01 bar. 0 0 ..4 x lo5 Pa.6 bars.. that is.11 gives (p2/pl).11.I 1 shows the main phases of unloading a well provided with three gas lift valves. where. The Figure shows a so-called semi-closed installation which has the casing annulus packed off b u t has no standing valve at the tubing (dl Fig. The simplest way of doing it would be to expel through the tubing the liquid filling the well by injecting gas into the casing annulus. with a number of attendant drawbacks such as the necessity of installing on the surface a separate high-pressure unloading network conduit. by means of a number of gas lift valves installed along the tubing string. In modern practice the well is unloaded in several steps.. shut in or dead for one of a variety of reasons.4. production can be started up only by removing a substantial portion of the liquid column from the well. 1.=0. is carried out in gas lift wells by means of the injection gas.4.412<0-555.4. etc.By Eq. or intentionally filled up with liquid from the surface. by the logic of the situation. (ii) Unloading a well. This operation.25. 1.4. PRODUCING OIL W E L L S { l ) The choke diameter of the valve can be calculated using Eq. Unloading with gas lift valves (a1 (b) Ic . about 9 mm. = d C h iTI .00904 m. = and p1= p c i .212 2. The pressure ratio during production is Table 1. 2. Figure 2.124. the abrupt pressure buildup during unloading may cause caving and a sand inrush at the sandface. however.4. we may use C = 0-465. Since 0. called unloading. d. In a well.555 for x = 1. we may calculate the choke diameter: =0. This would. typically require quite a high injection gas pressure.124. it may be possible to produce the well by injection through any one of the three valves. In the case considered. GAS LIFTING 213 shoe. Tubing pressure opposite valve I decreases to a constant value.g. that a valve . because at the levels of the lower gas lift valves the pressures in the annulus and in the tubing must be practically balanced.11. in order to ensure that. however. in such fashion that gas flow may be started by an initial pressure differential Ap. Tubing pressure opposite valve I decreases.2. This initial stage is shown in Fig. the gas lift valves are provided with reverse check valves. Our considerations can be transferred unchanged to so-called open completions. then pressure in the annulus will start to decrease. to the static level determined by formation pressure.4. The well will now be produced by continuous gas lift by the injection gas entering through valve 3. and the opening pressures acfing upon them are greater than that acting upon the uppermost valve I. the liquid column in the tubing is gradually aerated and the well delivers a gaseous fluid through the tubing head. valve 2 closes under the influence of the annulus pressure's decrease to pD2. Let us assume that the dome pressure of each valve is less by 1 bar than that of the next valve above. In the phase shown as Fig.10 that. From this instant on. b valve I is already uncovered. because their dome pressures are less than that of the uppermost valve. and the liquid level in the annulus sinks to a corresponding constant depth. We shall in the following assume this to be the case. Valve 2 is installed slightly above that depth. This shortens the time required for unloading. As soon as injection gas can enter the tubing through valve 3. there is a gasless liquid column of considerable pressure both in the annulus and in the tubing between the level of the first gas lift valve and the static-pressure level of the liquid. The liquid level sinks largely in the way just described to the depth of valve 3. In modern well completions. 2.4 . As soon as it attains the dome pressure p. e. We have seen in connection with Fig.2. of valve I. The top valve can consequently open even at the beginning of gas injection. similarly to valve I. Gas will continue to flow into the tubing through valve 2 only. After first installation. the liquid level in the annulus keeps sinking. The opening and closing casing pressures of the gas lift valves are set so as to decrease down the hole. 2. there will be at valve depth a pressure differential of say 3-4 bars between annulus and tubing.4 . so that no oil might enter the casing annulus during production. the top valve will open even if the pressure in the tubing opposite it is zero. One thing to avoid is.2.11. c. this valve will close. however. gas injected into the casing head may enter the tubing through two valves. at this gas pressure. by applying the correct injection gas pressure. As a result. Unloading begins by introducing into the casing annulus injection gas at the maximum pressure required to open the top gas lift valve. where the casing annulus is not packed off at the tubing shoe.4. The depth of this valve is designed so that.. The two lower valves will also have opened up. at the time when injection gas begins to flow into the annulus. the well is practically filled with liquid. in order to make gas flow through the valve. at the time the gas attains the valve. Ifnow the surface gas injection rate is less than the rate of gas flow into the tubing through the two valves. After the beginning of gas flow through the valve. however.11. also the casing annulus will be filled with liquid.4. a. In the phase shown as Fig. 3 x lo5 Pa. In the knowledge of this tubing pressure and the casing pressure. = 14.3 bars is required to open the valve. Fig. The casing pressure is already less than the initial value.88 x 39. In order to prevent this. Find the back pressure at which the valve characterized in the previous example will open after closing. If the tubing pressure opposite the valve considered cannot exceed 29.4. a tubing pressure of at least 38. The most unfavourable case as far as the opening safety of the valve is concerned is when the lower valve in question is the next valve below.214 2.6 bars after its closure. the dome pressure can be calculated using the opening equation of the valve.7 bars and the casing pressure is 40.12. choke sizes. PRODUCING OIL WELLWI) should reopen once it has closed and gas flow has started through the next valve below.. because it is in that case that tubing pressure may be highest. we may calculate the tubing pressure at which the valve will open if its dome pressure is 39.4-6. (iii) Valve depths.5 -0-7 = 39-8 bars: p. Calculating the depth of the top valve may involve one of two procedures. say by a value Ap = 0. then injection gas will enter the tubing through one of the valves below. Using the opening equation of the valve. If the valve is in the closed state. already fixed. 'Comparatively low' means that the oil rising in the tubing has not yet attained the wellhead at the . 2. depending on whether the static liquid level prior to unloading is comparatively high or low.7 bar. through whichever lower valve the gas will enter the tubing.8 x 10' = 38. the maximum tubing pressure opposite any valve is calculated for the case that injection gas enters the tubing through the next valve below.13-88 x 39. 'Comparatively high' means that the pressure of gas injected into the annulus will make liquid flow through the tubing head even before gas could enter from the annulus into the tubing. then the valve will stay closed.7 x lo5. That is. Example 2. partly filled with a liquid of gravity y. a liquid column of height 10RAis still missing from the tubing. that of the tubing. the pressure at the liquid level (level 2) will be pc in both the annulus and the tubing. 2. or the well has been filled with liquid from the surface.4-6.. and the weight of the gas column is neglected.. provided no backflow into the formation takes place during the brief period of unloading. if wellhead pressure is pTo. (& If the tubing is 'long'. We may write up for the tubing that. if L.. + p. If gas of pressure p. is longer than the column height hRA of the liquid U-tubed from the annulus into the tubing. the liquid level will sink by a height h. liquid level is at a depth L.At the end of the U-tubing. then.2.. the 10 metres are subtracted.) = hRA.. below the surface in both the tubing and the annulus. A.. The condition for 'long' tubing is.7 Ls > + l)Yl. then the top valve is to be installed at depth .4. and rise in the tubing to a level I. then. The relationship between the level changes in the annulus and in the tubing is h(AT. PC-PTO 2. then the depth of the top gas lift valve is given by theequation In order to provide the pressure differential necessary to make the valve pass gas from the annulus into the tubing. Let us substitute h by the expression in Eq. Figure 2. Let the cross-sectional area of the annulus be AT. PC = hYl+ hRAY. that is.4. is injected into the annulus. If the tubing is 'short'. The tubing is called 'long' if at the initial instant its liquid-unfilled length L. GAS LIFTING 215 instant when injection starts into the tubing from the annulus through the tog gas lift valve.4 . The initial pressure differential is. At the initial instant. As in the case under consideration a static balance of pressures would require the sinking of the liquid level in the annulus by a further 10 m. then.12 is a schematic drawing of the upper part of a well.>hR./A. or the static level is uncertain. then and hence.. of the liquid column reaching to the wellhead in the tubing.4. of the valves. Ap.. The casingpressure traverse reduced by 4. (7) Let us determine for all valves but the last one the maximum tubing pressure that may arise during unloading. The steps of designing are as follows.-Ap. the BHP drops below the formation pressure.. PRODUCING O I L WELLS-(]) This equation is based on the consideration that. depth) is plotted. Let us trace a parallel to Graph I11 through the point (L. at a distance of Ap=3. the pressure drop to be expected across the valve when gas flows through it at the maximum designed rate.. is equal to the the effective pressure in the tubing at valve depth (p. (1) Starting from the point (L =0. the pressure gradient curve (Graph I).216 2. It is assumed that. The reason for the first one-bar reduction is to set the opening pressure of valve 2 one bar below that of valve I. p.124 we calculate the least possible choke diameters d.) hydrostatic pressure L. starting from the point (L=O. . the gas pressure in the annulus will equal the pressure in a tubing filled with oil to the wellhead at a wellhead pressure of p.J.... p. p.. because the well will at a flowing BHP of p...4 bars is intersected by Graph IV/2 at point 2. (8) Using Eq. a pressure p. During unloading. on the other hand.) (Graph IV/2). Now let us draw parallels to the casing-pressure traverse. (4) A Graph IV/l.. In the latter case. is plotted for a continuous-flow gas lift operation into a bilinear orthogonal system of coordinates (p v.4. and another at a distance of a further 3. valid for the size of tubing under consideration. (9) Introducing the values pCiand p. depth) is plotted in the knowledge of y.4 bars.. at the instant when injection starts. is the pressure drop of injection gas across the gas lift valve. still produce less liquid than during continuous flow. so that the formation will deliver fluid to the well at a gradually increasing rate. p.). into Eq. p.. (10) Using the catalogue of a ..... It is the ordinate of this point that defines the depth of valve 2.). one at a distance of one bar.4 .. The depths of the remaining valves can also be established by several means. we calculate the unloading tubing-head pressures pcoi corresponding to the pressures pci. At the point where it intersects Graph 11.4 bars ensures. p. that the valve will pass gas when uncovered and equals.13)..y. will prevail in the tubing at depth L. it is safe at any event to reduce tubing pressure to this value. even at the initial stages of unloading. parallel to Graph 111.4 bars above the point of intersection. The point of intersection I of this last parallel with Graph IV/1 determines the depth L. is defined by the point of intersection of this line with a horizontal line drawn at the depth of the valve under consideration. of the top valve I. L in Fig.(2) Graph I1 (static pressure of gas column in annulus v... (6) The remaining valve depths are determined as for valve 2 above. (3) Graph 111 (pressure of gasless oil v.. 2. modified after Winkler (Winkler and Smith 1962). 2. plus the wellhead pressure p. The procedure to be described below is a graphical one.).starting from the point (L. the depth of the top valve can be established also by a graphical construction. p...). is drawn through the point (L =0. This value is obtained with a fair margin of safety by drawing for any valve a straight line connecting the point marked 2-4 of the next valve below and the point (G-0. on the one hand.5.. The only difference is that casing pressure is reduced by a further one bar for each valve. Let us draw a parallel to Graph 11. (5) In the case ofcontinuous flow gas lift. The pressure differential Ap = 3.. 1. l o m3/(Pas). the filling pressures and choke diameters of the valves. we determine the charged pressures pDnicorresponding to the installed pressures pDi..' Fig. 2. A4 -001) we choose the valve with the next greater port area than the value found in step (9). n = 1.. and the pressure data p.. Do = 900 . = 2. GAS LIFTING 217 manufacturer of gas lift valves (cf.. p.9 bars. p. there is no 'p. p. yo = 95. By the logic of the situation.. Find the depths of the gas lift valves required for the unloading and continuous flow gas lifting of a well of given capacity. 2. Example 2. (1 1) Using the opening equations of we calculate for each valve the domethe valves.1 bars.4.. mean oil density in the well. Using Eq.4.4 . Gas lift valve spacing for continuous flow for the lowermost valve. as well as the surface unloading pressure. and pTmaXi pressures pDi required at valve depth.2. if L. J = 1.13. e. Taking from the catalogue the parameters A.g.4 bars.7. = 92. = 1320 m.3 m3/d. d = 2 318 in.79 x 10. and AD we may write up the opening equation of the valve..4.. = 45. Its actual dome pressure equals that of the next valve above. the CAMCO Gas Lift Manual by Winkler and Smith 1962. p. a = 0..9.4. 0 kg/kmole.. valve.9 47. This will be our Graph I..1 16pT.4 x lo5.. 2. assumed to equal the mean annual temperature.4 42.79 x 10-"(92. = 1. 2.4 .= 1 1 "C. = 5/16 in. at q. 2. The pTfiand p.=0. .4 -5.6 47.=21. T.9 bars. M. geothermal gradient.123 and 1. The results of the graphical construction in Fig.8 20. p.962 .2 26.4-13.4 .. The correction whose results are given in Column 7 is necessary because of overstepping the critical pressure ratio.4. The d. as established from the manufacturer's catalog. Columns 12 and 13 contain the charged and Smith 1962. p. Column 1 1 lists the choke diameters of the valves..4.4 kg/m3. PRODUCING OIL WELL-I) Table 2. so that it starts at pTO= 2. Formation gas production negligible.6 12. = 262 m3/m3.9 30.8 bars.3 25.0 37.13 and the calculation according to steps ( 1 ) -(8) above are listed in Table 2. A4-001).0.0 0 4 0 p. bars 1 2 3 4 466 815 1088 1293 46.3 m3/d and R. Column 4 lists the GORs required according to the pressure gradient curves produce liquid at the rate in question if the tubing pressure at valve depth during continuous flow gas lift is pTfi. values of Column 9 have been calculated by means of Eq. = 0. = 95.1 34. for the 3/16 in.13.04 K/m. The accuracy of the procedure will not be unduly impaired if the actual rate of production is replaced by the rate marked on the Gilbert gradient curve that stands closest to the actual rate.1 44.124. p. The values in question are entered in Column 3.13.8 47.5 62...7 PPO bars 45.4 43. These rates of production are required only for calculating the injection gas requirement which in turn serves to calculate the choke diameter. The flowing BHP will be 30. the least BHP (pwf.p w f i ) . The suitable Gilbert pressure gradient curve set will yield the curve valid for a tubing size d = 2 318 in. corresponding to the values calculated in step ( 1 1).4 . 2.896 pressures at depth and on the surface. The results of the calculations according to steps (9)-(11) above are listed in Table 2. The values of C have been determined by Eqs 1. have been determined graphically by the method illustrated in Fig. Column 5 gives the products of the corresponding entries of Columns 2 and 4.1 43. The opening equations of the valves chosen are (according to data found in the CAMCO Gas Lift Manual. 1. surface gas temperature.4 . The rates of production corresponding to these BHPs and listed in column 2 have been calculated by means of the relationship q. by Winkler . type 5-20. Let us add that the entries in Column 1.6 PC - T "C 29. for the 0.6 54.2. o. valve.Let us copy this curve onto Fig.4-4 Number of valve L m bars PTJ bars Pr.) to be expected while the individual valves pass gas during unloading..4 -4. Valves to be used are: CAMCO Type 5-20.125. data underlying the entries in Column 6 have been read off Fig. chosen 46.6 2 m3/s 40 40 R~ qpm 9. 1/16 10 in.4 64.5 3 250 150 4 1.14 73.7 1 bars PWI 7.5.1 12 bars PD 439 13 bars Pm .04 49.57 9 mm dch calc. 4. dc.4 1 2 Number of valve 88. 0465 8 - c 1. 0555 7 - PTY/PC Table 2. 3/16 11 in.4.76 5 m3/s m3/m3 10-Zm3/s Gilbert 0272 6 - PTI~PC COrT. Second phase. depending on the valve characteristic and the tubing pressure (cf.1 m/s if it is salt water.This phase ends when the top of the slug surfaces. size tubing with a 12.. First phase. The annulus is packed off at the tubing shoe by means of packer 3.4.15 shows gas slippage velocity in a 2 318-in. is the length of the liquid column accumulated above the gas lift valve. its operation is similar to that of the unloading valve shown in Fig.4 . According to White et al.. factois affecting operation The simplest completion used in intermittent gas lift operation is shown in Fig. The liquid slug moves up the tubing at the practically constant velocity 21.6 mm bore choke to be about 0.14.. At the same time.4. There is a standing valve 4 in the tubing string. and is controlled only to some extent by the physical parameters of the liquid. . is independent of the velocity v. the tubing pressure opposite the valve is where h. 2. Four distinct phases of fluid lifting can be distinguished. The length of the surfacing liquid slug will decrease from the h. The casing annulus is filled through regulating device 1 (called the surface controller) with injection gas at a predetermined pressure.I5 v. Section 2. the static pressure of the gas column above the liquid slug. The liquid column of height h. corresponding to the difference of the two values remains dispersed in the gas slug flowing upwards under the liquid slug. The opening pressure of the valve is where ApC is the valve spread.. then the lifted liquid slug will soon enough (in 10 sec or so) attain a constant (terminal) velocity.4 ..) makes gas flow from the casing through the gas lift valve into the tubing.--p.LS {I) 2.3-(a)4).2. PRODUCING OIL WEI. and valve port size d. for a given tubing size d. 2. value accumulated at the bottom of the hole to the h. The pressure difference (p. Intermittent gas lift (a) Theory of production.. because of the break-through of injection gas and the fallback (in the form of mist and of a liquid film covering the tubing wall) ofthe aerated tail ofthe liquid slug.in a tubing of a given size. The latter varies as shown in Fig. The length of the liquid slug will gradually decrease during the lift period. (1963). ofthe liquid slug. The velocity of the liquid slug. depends on the velocity of the gas column lifting it.4. Valve 2 is usually pressure-controlled.. If the valve is a snap-acting one and the operating parameters are suitably chosen.-p. the velocity of gas slippage u. Start of flow. v .9.2. it is possible to make the operating valve open only when a liquid column of sufficient height has built up above it.6 m/s if the liquid is oil. This is the end of the first phase. By suitably regulating the casing pressure from the surface. . Fiyure2. the pressure ratio p.. p. Three of them can be considered as phases of liquid slug lifting while the fourth is the mist production phase. 2. and 1. is negligible in most cases.4. value.. 4 . 2. (ii) the wellhead should present the least possible resistance to flow. The third phase begins at the moment the liquid slug is surfacing and lasts while it leaves the wellhead assembly. within the shortest possible time. It was mentioned that the decrease per unit pressure drop of both the volume and the hydrostatic pressure of the liquid slug may be much greater in the third than in . In the second and third phases of production./p. after its opening. gas should be able to flow at once through the entire crosssection of the valve.4. that is. Given a certain gas injection rate. In this production phase the length ofthe liquid slug in the tubing (assuming a constant rising velocity) decreases much quicker than in the previous phase since it gets shorter. The valve should be snapacting (see paragraph 2.2. 2. p. Intermittent gas lift installation Fig.4.14. Liquid slug and slippage velocities v. this can be ensured in the first phase of production by accelerating the liquid column to its terminal velocity v.4. In the interest of this. not only because of the gas breakthrough at the bottom but also because of its leaving through the wellhead at the top. To achieve this aim the time required to lift the slug to the surface should be minimized.3-(a)l). GAS LIFTING 22 1 Third phase.. the liquid velocity should not decrease. after WHITE(1964) Maximum liquid recovery One of the conditions of economic intermittent gas lift is that the greatest possible fraction of the liquid column accumulated at the bottom of the hole and lifted up should get to the surface in the form of a solid liquid slug.15. I b: --- Fig. (i) the injection of gas into the tubing should be shut off when the volume and pressure of gas in the tubing are already sufficient to keep lifting the liquid slug of decreasing hydrostatic pressure at unchanged speed. -h.. and the less liquid will be produced. plotted by the authors in graph form (Fig..16) make it obvious that. At the end of this phase. and the slower will these pressures decrease. the greater will be the pressure at both ends of the tubing.)AT. for simplicity. by the above consideration. the slug velocity will not decrease. Experiment -has revealed (Beadle et al. on the other hand. gas pressure will thus be (assuming.=(L. Ap. from both the denominator and the numerator of this ratio. 1963)that. therefore.. Let a gas pressure p..y. do not install a production choke in the well-head. Subtracting the same pressure drop... If.4-6. if A p s h. Some production parameters describing the case illustrated are compiled in Table 2. the less the choke diameter. let the gas-filled volume be V. The slug velocity cannot. the higher will be the maximum producing BHP. = p. at the instant when the gas lift valve closes. . if the liquid volume produced per cycle is high and the valve dome pressure p. decrease if its pressure decreases by at least as much as that of the gas column lifting it. Thus the length per unit gas pressure of the liquid column lifted will decrease. the pressure gradient lifting the liquid slug will increase. injection gas supply is correctly controlled if the gas lift valve closes at the instant when the top of the liquid slug surfaces. then.2. or. nor any other wellhead equipment of high resistance to flow. be Vl =(L.y.y. that is.4. is great. we obtain another pressure ratio.)AT. The experimental data. prevail %low the liquid slug of hydrostatic pressure h. lifted out of the well. It is therefore expedient to examine whether the injection of gas into the tubing can be stopped at the beginning of the third phase. which is necessarily less than pJpT. then the gas lift valve should close after the onset of the third phase. a perfect gas and isothermal expansion) The pressure drop in the gas will be If this pressure drop is less than the hydrostatis pressure of the liquid slug of length h. then.2. and the separator . whose value is less than unity. This may be the case when the hJLT ratio is comparatively great. The probability that the expansion of the gas in the tubing will lift the liquid slug without decrease of velocity is thus greater in the third phase than in the second.h. the smaller the choke bore. At the beginning of the third phase.. From this viewpoint. let the tubing volume filled with gas of pressure p ./pT is sufficient to provide the required slug velocity. when the slug has just passed the wellhead. Let us assume that a pressure ratio p.. Ap> h. in other words..Let us add that. Except if unavoidable. PRODUCING OIL WELLS-I) the second phase. This.4 . 0 2 4 6 8 XI 12 14 16 18 20 72 24 26 t . That is why Table 2. respectively.= 3 x . and the actual average gas flow rate.6.4. then. As an explanation for this phenomenon let us look at Fig. after BEADLEet al. .4 - Influence of wellhead choke size upon intermittent gas lift. GAS LIFTING is close to the producing well. 2. should be at the separator station rather than in the wellhead. Let us assume that at the end of the third production phase the dimensionless flowing gradient is [ = 0. (1963) Fourth phase. may increase significantly. . No liquid production takes place (q. If the outflow of the gas from the tubing string continues after the liquid slug has surfaced (while the gas lift valve at the well bottom may remain open for a time). If the separator station is at a higher elevation than the wellhead. due to the reduction of the wellhead pressure. =O!).PTo. To prevent this. however.5 in a tubing string of 2 718" and the gas rate flowing through the m3/s. a certain proportion of the dispersed liquid content will get into the flow line and will be produced. then some of the liquid produced may have a tendency to flow back into the well.. . . the average velocity of the gas flowing in the tubing string. . At the end of the third production phase the tubing string is filled with gas containing dispersed liquid droplets. . If the tubing string is q. 0 1 . a reverse check valve of large liquid throughput capacity should be installed at the wellhead. mln Fig.4-6 which shows Krylov's transport curves as a function of the actual gas flow rate.223 2. . . . it may be necessary for reasons of safety to install a production choke. 1. . 13 Its standard state is V while flowing changes in both the function of the lifting time and pressure and then . on the basis of their experiments performed in the Shell Oil Company's test well in Conroe field (Neely et al. Only approximate relations are known for the calculation offlow parameters of intermittent gas lifting.= O will be reduced to 0. the dispersed liquid volume. the space filled up with gas equals the difference between the total inside tubing capacity and the total slug volume. Based on the above understanding a great part of the liquid production may result from this production phase.224 2. 2.e.). When the top of the liquid slug surfaces. contained in the tubing. considering the increased frictional pressure drop. decreases significantly. Let the first aim of the computation be the determination of the gas flow rate under the liquid slug (the interpretation of the symbols is shown in Fig. PRODUCING OIL WELLS-41) gas rate increases to 18 x m3/s. the liquid volume surfacing in slug form. Fig.15. 2. the flow gradient at the operating point 9. the velocity of the liquid slug lifted with gas. and the changes of the flowing bottom-hole pressure. is possible only if the liquid volume.17. Comparatively accurate equations were elaborated by Neely et al. i.4 . Their results will be discussed below.4. It is easy to see that this. 1973) for the calculation of the gas rate flowing through the gas lift valve.17). 2. V= AT(& h..4 . 2. GAS LIFTING 225 With a good approximation the average gas column pressure is the arithmetic average of the pressure under the slug pTl and the pressure.. Due to the lifting of the liquid slug with velocity v . The surfacing liquid slug length can be calculated from the relative liquid content of the gas column that is where after Neely et al. of valve p. that is from which the differential quotient of Eq. 2.546 . hla-CL hlb = --1-c ' E= 16.4..4. at depth. 2. is constant We obtain the interpretation of the differential of the right-hand side if the liquid volume d v fallen back during the rise dt of the liquid slug is determined as .. that is where the pressure at the top of the gas column and and it means that with good approximation the pressure at the well bottom is the sum of the pressure of the "dry" gas column and the imagined hydrostatic pressure of the dispersed liquid fallen back into the column of height h. assuming that v .15 is To determine the last term of Eq.15 let us first differentiate pTl defined in Eq.17 with respect to time.4.11 (&)0..4. the volume of the gas column increases with volume dVduring time dt. 2. The average flow velocity of the gas in the tubing is the arithmetic average of the above two values..122 the gas throughput rate from the annulus to the tubing is . i. is obtained.4.25 is The flow velocity of the gas column can be determined from the value calculated in Eq.. then the flow velocity of the liquid slug v.15 with If numerical values valid at the top of the gas column are substituted into T ... The pressure change at the well bottom. p. 2.24 and 2. then the pressure change of the gas column expressed as the arithmetic average of the changes given by Eqs 2.. 1. applying C = -is: 24-s where: Assuming that with a good approximation the liquid content in the tubing can be taken as E. will be the result. before that. prevails. On the basis of Eq. the initial velocity of the gas column flowing upwards from the tubing shoe u.4.4 . While on the casing side of the gas lift valve value p. PRODUCING OIL WELLSO) and from here Substituting it into Eq. 2. If the values valid at the tubing shoe are considered.4-22 nv.4.e. on the tubing side..226 2. zi and p. . Flowchart of Neely's calculation method . GAS LIFTING The liquid volume h. 2. The flowchart of Fig.4.4 . Fig.18shows the process ofcomputation. produced in the first three production phases is obviously given by the calculated surfacing liquid slug length.4. more approximate process will be described. a simpler.18. From the above equations the afterflow gas volume can also be determined. 2. Later. where computation can be performed with a pocket-calculator.2.A. for the calculation of production per cycle and the specific gas requirement. Since the calculation includes several iterations it is advisable to use a computer. 4 . Total losses d o not depend on the length of the liquid column to be lifted. There are. the casing pressure p. There is an optimal rate of injection q. PRODUCING OIL WELLNI) According to Muravyev and Krylov (1949). Production is optimal if the specific injection gas requirement is a minimum. however. Total loss of energy is significantly influenced. = 100 m and L. a column of length h. In a well 1500 m deep. = 0-2 x 1500= 300 s. several procedures permitting approximate estimations.. -h. . =(h.g. In our opinion the operating mode which enables us to produce the liquid volume prescribed by the reservoir engineering plan at the least specific cost should be implemented.. for instance. the goal to be attained. however. . t . This occurs when the sum of slippage and friction losses are least as related to the total energy consumption. (b) Intermittent gas lift design The complicated. The desirable lift velocity of the liquid slug is 5 m/s.29 1. transient nature of flow in an intermittent gas lift installation precludes an exact prediction of operating parameters. = 1500 m.. We shall now discuss first the Winkler and Smith relationships (Winkler and Smith 1962). Let e. In chamber installations.228 2. by the mean flow velocity of the liquid slug. consequently. If the conditions are not overly unfavourable (such as a small production choke or considerable emulsification). for a conventional installation. h. The specific injection gas requirement is..6 X 10-4hlaLT<hl. according to Krylov. then the length of the liquid column lost owing to fallback is 2. These relationships provide a rapid first approach to a problem. The specific injection gas requirement may be greater than this if. This is.. the basic consideration in designing an intermittent gas lift installation is the economical exploitation of pressure energy. but the liquid fallback will decrease by the same amount. at which total loss is least.) = 76 (or 65) m can be lifted out of the well. the approximate lift duration is. a greater length h. with certain modifications.. is comparatively low and the tubing diameter d is comparatively great. at the given L. then and Of an accumulated liquid column of 100 m length. of the liquid slug entails a greater friction loss.. True.<2'3 X 1O4hlaLT. the ratio of the casing and tubing pressures. for wells 900-2400 m deep. p. and the available line pressure at the wellhead should exceed this by 7 . Taking the given gas line pressure and choosing a certain tubing size . the procedure to be described below is to be performed for several tubing sizes. To find the most favourable tubing size. or one with a downhole chamber (Figs 2..14 and 2. The surface closing pressure of the so-called operating valve.10 bars.2. The statements to be made apply with slight modifications also to chamber installations. and between 180 and 270 m3/m3 in a chamber installation. = 2. that size is to be chosen which gives the least specific cost of production or the least specific injection gas requirement for a given injection-gas line pressure. in a well 1500 m deep. a specific injection gas requirement between 180 and 360 m3/m3may be expected if the installation is conventional. and the -availableline pressure at the wellhead should be at least 34.45 x lo6 N/m2 = 34. For example.4-51.4.3 x lo3 x 1500= 3.5 x lo5 N/m2 =413 bars.3 x 103Li (Pa). Pci and p ~ iis.4. At the opening of the operating valve.5 bars. then the gas injection rate should be In this case.5 x lo5+ 7 x lo5= 41. We shall discuss below the design of a conventional intermittent gas lift installation. is. If we aim at realizing production parameters optimal in the sense of Muravyev and Krylov (1949). respectively).= 2. the valve controlling the intermittent lift in the well. the column length lost due to fallback is and the pressure drop due to friction is Intermittent gas lift design means in principle the choice of a well completion that will lift oil at the desired rate at the lowest possible specific cost. In the case of a single completion. GAS LIFTING 229 For instance. the installation may be either a conventional one. the wellhead closing pressure of the operating valve in a well 1500 m deep should be p. . p. Liquid recovery v. PRODUCING OIL WELLWI) we design the unloading valves in much the same way as for a continuous-flow well. likewise Fig.3 -(a)l). The choice of multipoint v. Figure 2. 14.1967 (by permission of Prentice-Hall. wellhead choke area. In the case when the surface closing pressures decrease downward by 0..17 mm for 2 318 in. (iv) It is to be decided whether we want the upper valves to open once the liquid slug has passed them (multipoint injection) or not (single-point injection).4-20. New Jersey.4. liable to come about during unloading. tubing size.7 bar per valve. tubing size. Inc.7 bar per valve. In the latter case. (iii) The least back-pressure in the tubing. under given conditions.). starting from a point ( L O .19. the following valve port sizes are recommended by Brown (1967): 10. we trace the pressure gradient curve which would . then determining dome pressures of the unloading valves is usually based on one of the following alternatives (Brown 1967):surface closing pressures decreased downward by 0. is determined by assuming that the well produces the desired rate by continuous flow. shows the recovery of the starting slug length v. surface closing pressures increased downward.19. The differences in design principles are: (i) Valves should be instant-closing and opening (snap-action). (ii) Their gas throughput capacity should be comparatively large. as measured in a valve tester. single-point injection shall be discussed later on. L. after BROWN. In order to prevent a significant fall-back of liquid. all surface closing pressures are identical. If the valves are casing pressure controlled.7 bar per valve and injection is of the single-point type.20 mm for 2 718 in. or surface controlled by a time cycle controller (see Section 2. Englewood Cliffs. the surface opening pressures of all valves are equal: they decrease downward by 0.14 mm for 1.4. 2. 13 . the opening pressures at 1 bar back pressure. design proceeds in the following steps. the dome pressure of the operating valve is to be reduced accordingly. are equal for all valves.1.9 in.230 2.7 . 2. p v. USA) after Brown. (1) In a bilinear-orthogonal system of coordinates..4. shown in Fig. the valve port area. defined by the gravity y.). When injection gas starts to flow through the valve.=O.2.. at the optimal GOR as defined by Gilbert. p. Graph IV/l. the Fig. at a distance corresponding to a pressure difference of 0. in order to ensure that the surface closing pressure of valve 2 be less by approximately 0. 2. pressure in the tubing opposite the valve is p. at the least pressure at any given depth (Graph I). that is. (3) Starting from (L. . pco) we trace an injection gas pressure traverse in the annulus for the instant when the top valve closes. This latter line intersects ..4. .7 bar. The pressure differential required to start the gas flowing through the valve is thus assured. pressure in the annulus is higher by 7 bars than this pressure in the tubing. of the gasless oil.7 bar than the closing pressure of valve I. filled up to the wellhead with gasless oil.) (Graph IV/2). (2) Starting from the point ( L . .4 .. At the instant the valve closes. GAS LIFTING 23 1 apply to the given tubing if the well were produced through that tubing at the prescribed rate. Let pco be less by 7 bars than the injection gas pressure available at the surface (Graph XI). p. Let us draw further a parallel to Graph 11. we trace a line p = Ly. (4) Let us draw a parallel to Graph IV/1 through the point (L. Where this line. =0. intersects Graph XI.20.. the annulus pressure traverse. gas pressure in the annulus is equal to or greater than the pressure in a tubing of wellhead pressure p. equal to the opening pressure of the lowermost valve. 2. The maximum pressure p. 2. is the pressure of the gas column above the liquid slug. (5) The depth of the remaining valves are established similarly to valve 2. over a period of time dt results in an increase of liquid volume by A. (9) Using Eq.and a casing pressure p. At the instant considered. and . permissible opposite the lowermost valve at the instant of its opening is established on the assumption that its value should be about two thirds of the dome pressure in said valve.5 we determine.232 2.1 -7 valid for steady-state flow can then be applied. we have to check whether the opening casing pressures of these valves are not. we may record that liquid flowing into the well at a rate q. then Assuming an installation similar to the one in Fig. 2. on the assumption that pDi= pCLithe surface closing pressures of the individual valves.4 . As a result of the procedure under (6). 2. the liquid into the well is considered incompressible. The annulus pressure is decreased by a further 0.. bottom-hole pressure is where p.6 bars than that of the next valve above. less than the actual casing pressures opposite them. let us calculate the casing pressure pcoi required to open it. . either. dh in a tubing of cross-sectional area A T . (1 1) We determine the daily liquid production of the well. minus a gas-flow pressure drop of. in the extreme case that is most conducive to their opening.4 bars.4-4. For purposes of an estimate. If under the influence of this tubing pressure p. Let us assume that. (8) If the upper valves are not to be opened by the rising liquid slug. (10) Using Eq.JpToiwill be greater than 1. the ratio pC. the unloading valve directly above the operating valve will not open.4. The productivity equation No. (7) Using the opening equation of the lowermost valve. if the lowermost unloading valve does open. (6) Let the dome pressure of the lowermost valve be less by 3. The production cannot in the general case be predicted with certainty. Let us further assume that the exponent n of the productivity equation equals unity. we determine the charged dome pressures phi of each individual valve.7 bar per valve. say.5. The ordinate of this point defines the depth of valve 2. that is. However. then the dome pressure of the operating valve has been correctly chosen.. the pressure in the tubing equals the opening casing'pressure of the lowermost valve. in the said extreme case. 3. It is moreover clear that the valves farther up will not open.14. then the dome pressure of the operating valve is to be reduced and the checking procedure repeated. Flow in the drawdown area of an intermittent well is invariably transient. PRODUCING OIL WELLS { I ) Graph IV/2 at the point 2. the mean drawdown over the period of accumulation of the liquid is most expediently expressed as a logarithmic average. applies in a fair enough ..4 ... Substitution of the expressions of q.as happens rather often -the production period t . after rearranging and writing an integration.4-21).233 2. Figure 2.21 shows the variation of p.4-33 yields. The limits of integration are identified in the Figure. 2. into Eq. and p. ) ~ 0 tl tz t- Fig. as --J Y I ~ ~ Pwf2 = P ~ ~ . can also be considered approximately constant.4-21.( P ~ ~ .4. then Ap. GAS LIFTING Since p. is constant. is short as compared to the accumulation period ti (Fig. and dh. 2. Bottom-hole pressure v. 2. v. time (full line). namely If. Solution of this equation yields the increased bottomhole pressure at the instant t.PA~T . time in intermittent gas lift well The equation can be transformed to yield the drawdown by writing Clearly. .. At the beginning of the accumulation period.and by using a computer. but to simplify the calculations it was neglected. using Eqs 2. More accurate calculation is possible by applying the method of Neely which has already been cited.. can be estimated only. e.JLT. 2.234 2. Relationships for establishing h. The mean pressure of the gas column is. If it is higher up.the less the 'increment of h. One such diagram is shown as Fig.4-29 and 2. shown on the flowchart of Fig. ifpwfl is taken according to Eq.) The tubing pressure opposite the operating valve is at the same instant equal to the dome (that is.4-34.39 So far we have tacitly assumed the operating valve to be installed at the bottom of the well.. and the daily liquid production turns out to be Drawdown at the beginning of the accumulation period is. By our considerations connected with Eq. in the case of an insert chamber installation..~ T o . e. and the gas-filled volume of the tubing is VT=(LT-hla)AT.4 .g. This is not usually taken into account in calculations.. in a fair approximation.h. These provide the ratio hIb/hI. (1963) who have also prepared nomograms based on their equations. h..4..~ ~ ~ 2. (12)The injection gas requirement can now be calculated. then. 2..'. liquid will flow into the well even during the production period. our result will be more accurate if the calculation is perfermed by appfiing the method of Neely et al. . 2.for various values of p. the liquid column above the valve may be higher than h. closing) pressure of the valve.4 . then the bottom-hole pressure will be higher than the above-calculated value by the pressure of the liquid column between the well bottom and the valve.4-22. The pressure under the liquid slug then equals the wellhead pressure pro plus the hydrostatic pressure of the liquid column of length h.. Probably. Ap. 2. because.12. =(h.) have been derived by White et al.JpTi and h. Drawdown at the end of the accumulation period is estimated at - A ~ w =2 ~ w s . (In reality this pressure is enlarged by the frictional pressure drop of the liquid slug.~ I ~ Y I . (1973).g.18. . PRODUCING OIL WELLWI) approximation to the full intermittent cycle. The less tl/t. Regardless of that. minus the pressure drop of gas flow through the valve.4-31. let us assume that the operating valve closes at the instant when the top of the liquid slug has surfaced. The gas used up in any production cycle equals the quantity of gas fed by the well to the flow line after the lifting of a liquid slug of length h. after WHITE(1964) By the combined gas laws.4-22.in a tolerable approximation of the actual situation -that the gravity of the liquid is independent of temperature and pressure and that no gas dissolves in the liquid. GAS LIFTING L1 Fig.2.4. 2. the standard-state volume of the gas in the gas in the tubing is We have tacitly assumed above . The gas-filled volume in the tubing after the period of production is The mean pressure of the gas column is The standard volume of the remaining gas is . Finding the liquid recovery of intermittent gas lift wells. (14) By the above line of thought. injection gas requirement and daily cycle number can at best only be estimated. well production. the duration of the lift period. The unloading valves and especially the operating valve must therefore operate satisfactorily not only at the calculated production parameters but also at slightly different ones.236 2. If. e. If the actual length h. Daily injection-gas requirement is (13) Determining the daily number of cycles. 2. t . It may increase until it attains the opening pressure.. Let further zn= 1.2-(b). then. of the next valve above. PRODUCING OIL W E L L S ~ I ) Gas volume used per cycle is. then sufficient accuracy can be achieved by putting V$. then the opening casing pressure of the operating valve will turn out higher. In practice.35. is comparatively low. estimated from the slug velocity. The theoretical specific gas requirement of daily liquid production is equal to this value.. . =0. The specific injection gas requirement is the ratio of the gas volume used for one intermittent cycle and the liquid volume produced. valid during the rise of the liquid slug. This is the opening pressure that determines the least length of the liquid column to be produced. Another circumstance to be reckoned with is that the performances of well and formation will change in time. It is expedient to consider the calculated production parameters as belonging to the maximum possible starting slug length accumulating prior to opening. the actual specific requirement may be greater.as is frequently the case -the wellhead pressure p. equal to zero. Daily cycle number is By the considerations at the beginning of Section 2. that is. if the tubing and/or casing string is leaking or the operating valve closes only after the top of the liquid slug has left the well.4. then.g. of the liquid slug to be lifted is less than that.2L. is By Eq.4 . 5 40.9 36.7 lists the valve depths read off Fig.17x38.4 .2x pT3=40. 2. = 1.2 60. (4) and (5) Let us determine graphically the depths of valves from 1to 4.237 2. a.4-7 Table 2. p. = 1640m.17 x 36.= 1-17x 41.. = 122. d = 2 718 in.. GAS LIFTING Example 2. estimated oil production rate.4 .1 7 ~ 2 5 . = 2. The least casing pressure required to open valve 3 is.9 32.4.1 x lo5 Pa.17pT for all of the casing pressure controlled gas lift valves. 1. The least tubing pressure at any depth is ensured by a GOR of 765 m3/m3. (1) We take as a basis that Gilbertian set of curves for 2 718411. Starting from this pressure and using Eq.7 36. we calculate the casing pressure v.4 PD.2 PDo bars "C 5 6 7 8 13. 2. Tco = 11.0 . The corresponding section of the curve having this parameter is copied onto Fig.0 3 1.8 25.1 x l o 5 . 4 42. = 30 m3/d.4 x lo5 Pa.7 28.7 38. J = 3-7 x 10.8 x lo5= 4 2 5 x 10' P a . tubing which holds for the liquid production rate q. p.4 x lo5 = 36.1 3 36. = 21. Design an intermittent gas lift installation by the procedure just discussed for a well completion as shown in Fig.5 45. (6): P T=~ (7) (8) Let 38.01 bar. starting from the point defined by the coordinates (L = 0.4-8..0 bars. The opening equation is pc= 1. pc. M . (2) Let '' pD. The value in question is qo=31. p..7 kglkmole.5. 2.2 x lo5-3. depth curve (Graph 11). we draw a pressure traverse for gasless oil in the tubing.. if L.5 38. .= 15 "C.0 bars.1 x lo5-7 x 105=38. Column 2 gives the dome pressures at the respective depths of installation.0 "C.9 41.1 37.m3/(Pas) p.4.4 -20.5 ~ 10Pa.7 m3/d. Graph IV/L). = 3. pc4=1.6 38.17 pD-0. closest to the expected production.9 40. 2.2 36.7. = 850 kg/m3.14.7 x lo5-0.4-20 (Graph I). T. p.1 x 105 = 25. q. Serial number 1 2 3 4 L PD PT PC T P~min bars m 1 2 452 882 1275 1627 39.8 x 10' Pa.=pi-7 x 105=45.1 bars. (3) Using a pressure gradient corresponding to a density of 850 kg/m3. = 2. In the order of the steps outlined above.1 bars. Column 1 of Table 2. pi = 45. the solution is found as follows.88 x lo-' K/m. 4105=40.5 73. then. = 90 m.1 x lo5. =pTfl + ALyl=9.5 x lo5 In 95.2.4 bars. = 0.7. Ap.5 x 10' P a . Column 7 lists the charged dome pressures calculated by means of Eq. 2..29.36.5 x lo5.6 x 10' ..4. Let us choose the less favourable hl. 2. 2. (10) The surface closing pressures calculated using 2.6 x lo5 P a . 2. = 0.5 x lo5+ 1. and assuming p. = 111. =pTf2+ ALy.1627)850x 9.4-31.6 x lo5 = 103-3x lo5 P a .=2x 1 0 . Using Eq. we have with reference to the bottom of the tubing The pressure of the liquid column between the well bottom and valve 4 is. the mean drawdown is Ap. we have The length of the liquid column lost by fallback is. ALyl=(1640. By Eq.1 x lo5= 10. PRODUCING OIL WELL-I) and since valve 3 will not open when the liquid slug has passed it. by Eq.. = 122.1 x lo5 P a .4.1 x lo5= 26.=prf2 = 25. tubing pressure opposite valve 4 is pT.5 are shown in Column 8 of Table 2. provided density is 850 kg/m3 here also.1 x lo5-26.4 . (1 1) At the instant when the liquid slug starts to rise.5 x lo5 =95-6 x lo5 P a .4. and for a constant equal to 2 x h.4-4.4 ~ 2 8 1x 1610=90m.95. we get and Hence and p.34 and assuming p. By Eq.81 = 1.4 .4 .= 25. 2. Referring this to the well bottom.4 . (9) Column 6 of Table 2. Ap. 111. 2.4 x lo5+ 1.34. p. = 122.7 gives the temperature at the depth of each valve.10-6x 10' = 111-5x lo5 P a . By Eq... . and that of valve 4 is pc4= 1-17x 38.4-41.01 x 105 R.4-44.4. The opening equation of valve 3 is p. and by Eq.. 2. We have. 315.92 x 1.64m3.2.4-42. 2. 2. of course. q.4-43 yields (14) Let us find the least liquid column length h.. 2.i.17pT3. VT=(1627-90)30. If.2 x 10' x 288. (13) Determining the daily cycle number. the daily liquid production is (12) The value of figuring in Eq. it is clear that valve 3 will just not open if .17 x 41-7 x 10' -o. we neglect the weight of the gas column in both the annulus and the tubing. 2. = 206 x 33-0= 6796 m3/d . = 1.1 x 1 0 ' . in order to be on the safe side.0 . first. 4.2 x = 206 m3/m3. = By Eq. Substitution of these values into Eq. 119 191 x 30.2 x 10-4=4. that can be lifted from valve 4 without the valves above opening: the critical valve to check is. 2. = 26-2 x lo5 P a .4 -40 and hence.4-37. GAS LIFTING By Eq.64 x 26. the lowermost unloading valve. By Eq.2 = 119 m3. 1 7 ~ ~ ~ .5 x 0. either by applying continuous or intermittent gas lift methods. In the world petroleum industry several valves operating on the basis of rather different principles and designs were applied in the last decades. their design and setting is well calculable. With the different valve designs the prescribed production rate can be realized economically within large ranges. In certain valve types. and the operation of some of them is well modifiable according to the varying production requirements. Several other valve types and designs have developed having in common that the opening. 2. Their application is advantageous for the following reasons. 2. while its closing is controlled solely by the casing pressure.3X . low costs of equipment required both on the surface and downhole.240 Further.lo5 4 The above four equations permit us to calculate the maximum permissible opening casing pressure: and the corresponding minimum tubing pressure at opening is pT4= 13. Gas lift valves (a) Pressure-controlled valves Opening and closing the valves mounted on the connection of the gas injection and production pipes in a well can be achieved in several various ways.4-9.3. Since World War I1 almost all the other types have gradually been replaced by pressure-controlled valves. amongst others: simple construction. The nomenclature of the available gas lift valves is not uniform and unambiguous. The digits in the system are 1. As an explanation here is the following code: . The first type of the pressure controlled gas lift valve is the kick-off valve (later called a basic valve) shown in Fig. however. exceptionally. the flow area are determined by the pressures upstream and downstream of the valve.7 x 1 O5 Pa. The present author has tried to formulate a "tag-code" which facilitates evaluation of the valve types available today. The minimum starting slug length is 2. or.4.2. PRODUCING OIL WELLS { I ) PT3 = ~ ~ ~ . closing and. The meaning of the tag changes according to the order of the digits and their position within the tag. sometimes. 3. the opening of which is controlled by the tubing and by the casing pressure prevailing in the valve setting depth. the influencing impact of the tubing pressure and casing pressure may differ. by hypothesis. the value of the digit is 3. = 5.The basic valve can be used as an operating valve as well.= 5. a spring force A F . = 24.for instance means that the valve in question is not snap-acting.2. a pressure rise ApD in the gas dome. in the metal and.9 bars to balance the forces acting from above and below the inner valve.that is.2. 2.0 bars.$ A F D resulting from the rise of the valve in the highest position. corresponding to a force increase AF. According to Eq. it has spread. on the one hand.9 bars after opening. is greater than the force increase A F . to open "instantaneously".1.if the opening force A F . or p.0 bars before opening. 2. . = AF. e. the valve will fully open . The increment force suddenly hitting the inner valve in the course of opening is. and it is retrievable only with the tubing. According to the above interpretation the tag 2. = 25. of the rising inner valve is p. on the other. in fact.0 bars requires a casing pressure of 25.4-9. rise slightly above the values just stated. the dome is gas-charged. it has got no special opening and/or closing features.2. = 5. Opening and closing of the valve. . A D= 6-2 x Let p.. This force makes the inner valve rise to a height h'. This generates. The opening. it is of the metal bellows type.2. in a valve of a m2 and A. the gas passage are is not influenced by the tubing pressure. These features are characteristic of the basic valve shown in Fig. then. The inner valve will reach its highest possible position in the valve under consideration. that is. GAS LIFTING -- Position of the digit from left to right 1 2 3 4 Is the valve snap-action type? Is it of metal bellows type? Is it a gas charged valve? Is the gas passage area alTected by tubing pressure'! 5 Does the valve spread? 6 Has it got special opening and/or closing features? 7' Is it retrievable by wireline or by pumpdown? --- Value of the digit 1 2 Yes Yes Yes no no no Yes yes no no Yes no Yes no If both answers are possible. in a fair approximation.7 x lo-' m2 then given make. takes place when p. and. p.1. The pressure acting upon the closing surface A.g. Let us examine the process of opening and closing.4.4-3 the opening of the valve for a given dome pressure is influenced by both the casing pressure and tubing pressure..1. (a)l.. If. then a back-pressure of p. The rise of the inner valve compresses the bellows. will be insufficient at a comparatively lower cycle number.) is shown on Fig. Reduction of valve travel to. also on the daily cycle number. Example 2. 30 . =20+47=6? N. respectively. and AF. the limit pressure will be at C' instead of C.57 cm2.5 mm. Full opening at p. Let us draw a line parallel to the abscissa axis through this ordinate value.. will increase.Let us assume a total valve stem travel of h = 3 mm. Let us record the condition of full opening. that is.242 2. = 2 4 bars gives rise to AF. If the cycle number in a given well is decreased. say.23 for dome pressures of 24 bars (Graph I). PRODUCING OIL WELLWI) h. at p. This is the most favourable of all possible conditions as far as full instant opening is concerned.4 -9.. satisfactorily predicted at high cycle numbers. the pre-opening pressure p . resulting from the pressure rise on the dome at 24 bars dome pressure.=47 N. Let us note that valve opening in testers is often checked at atmospheric back-pressure only.4-23. o 10 1'5 io Fig.bars The relationship d F .4 bars and A at 19 bars. For instance.& . consequently. < AF.2cm2 and A.p. 28 bars (Graph 11) and 32 bars (Graph 111). assumed a greater value. a force A F S = 2 0 N resulting from the load rate of the bellows at full opening. = 24 bars. 2.5 bars. . The full instant-operating pressure limit has. 2.4 . in the case of intermittent lift. the valve does not open fully. Zj P. or increasing the dome volume of the valve. Let A D = 6 . 1. Clearly. = A. and its gas throughput capacity will be less than in the fully open position. Intermittent lift requires valves that will open fully under the operating conditions expected. The corresponding points of intersection and limit pressures for 28 and 32 bars are B at 16. 13. the valve will not open fully unless the tubing pressure drops below the abscissa of C. The example reveals that full opening depends not only on valve design but also on dome pressure and. It intersects Graph I at C. It may thus happen that the gas throughput capacity of the valve.. =0. entailing a decrease of AF. entails a decrease of AF. If AF.. then. "in a moment".AF. Then.4.4 -9 the check valve 7 can be pressed by a weak spring (not shown) against the valve port. The check valve will consequently open only when pressure below valve 4 has risen to a higher value. e. the valve will stay in the upper limit position until the decreasing pressure attains the value AFodA.nh') may be so great as to prevent any but the slightest pressure rise in the tubing below the valve. (i) In the valve shown in Fig. The valve stem may start to rise so smoothly that a small initial rise. (0) (b) (Cl Fig.67 = 20 N. either. Instant (snap-action) opening can be ensured in several ways. This transitory balance can. 2.. that is.4 -24). because the resistance to flow of the geometry (d. as the liquid slug rtses. Any further drop is casing pressure will lower the valve stem with a consequent decrease in gas throughput cross-section. may establish itself for a while.1 -(b)2). Part a of the Figure shows the closed valve.4-24. at a pressure of 10-0bars. During this aborted opening. AFpp= 87 .. h'. of course. Once the increase in casing pressure has lifted the valve stem above a limit position . quite guaranteed by the play of forces just described. however. The basic valve is.32 x lo5 N/m2in the present example. . injection gas will enter the tubing to no avail. 2016. (ii) Instant opening is facilitated also by the McMurry-type valve (Fig. Keeping the valve stem in upper (fully open) position requires an excess opening force AFop=AF. Instant opening is not. 2. When the casing pressure starts do decrease. 2. Closing occurs when the casing pressure has dropped to equal the dome pressure.. Continuing the foregoing example let p. instant-opening but not instant-closing.2 x 10-4=0.g. without opening the valve closed by needle 2. Snap-acting valves are when both opening and closing of the valve takes place rapidly. McMurry-type inner valve Example 2. An increase in casing pressure lifts the valve stem 1to the position shown in part b. the valve will close when casing pressure decreases to equal dome pressure (Section 2.4. be upset by a slight shock or vibration.10. boosting the instant-opening action.=24 bars and h = 3 mm. GAS LIFIYNG Closure is unaffected by tubing pressure.4.243 2. 3). Szilas-type magnetic gas 11ft valve Fig. acting on area A.4 -26 (tag: 1. The force needed to part the jacket from the magnet can be set by adjusting an air gap: AF.1.1.244 2. Merla WF gas lift valve Instant closing and opening of intermittent valves is most often ensured by pilot valves.. PRODUCING OIL WELLS+!) depending on the force arising in spring 3. 2. The resultant force will depress and thereby open the main valve and permit injection gas to enter the tubing through inlets 7 and port 6. 2. Not charged with gas.2.1.4-25) (Szilas 1962).2.4-9. The magnet will let go of jacket 2 fixed to the valve stem only when the casing pressure has decreased to equal the closing pressure.1.2. instant closure is ensured by a permanent magnet (1) installed in the dome (Fig. In the Szilas-type gas lift valve (tag 1. of port 2 and a casing pressufe pp. As soon as the casing pressure decreases to equal the "bellows pressure". its effect is substituted with the force of a spring (Section 2. Operation of the pilot is thus the same as that of the valve in Fig.-A.4-26. . Once the pilot valve has opened.4. the casing pressure entering through port 2 will act on the top face of main valve 5.1. the pilot will close.A. + AF.2. Fig. The pilot will open if the algebraic sum of the forces acting on it from the direction of the tubing and the casing exceeds the "bellows pressure force". 2. = A F .4-25. Gas of pressure p. 2.1. As an example consider the Merla WF type operating valve shown in Fig. pilot 1is under the influence of a tubing pressure p .. When the main valve is closed.2). entering through inlets 3 acting on the effective area (A. the spring will jerk the inner valve into the position shown in part c.. = AF.3 -(a)2).2. 2.4. GAS LIFTING 245 trapped in space 8, will space towards the tubing through the bleed bore of the main valve stem, and pressure in space 8 will decrease to pT. Spring 9 then lifts the main valve into the closed position. In addition to safe instant opening and closing, pilotoperated intermitting valves have the considerable advantage that the opening equation and, consequently, the spread are independent of valve port area A,,. (a)2. Main structural parts of gas lift valves. -The bellows are an essential part of gas lift valves so their deformation and damage must be avoided. A conical stem is situated inside the bellows of the basic valve shown in Fig. 2.4-9. In the annular space between the stem and the bellows lube oil of low vapour pressure can be found. If great external pressure is exercised on the bellows, the conical shoulder will be pressed to the rim of the inlet leading to the dome, and the reaction force generated in the liquid closed in the annular space prevents deformation of the bellows. If the state of the bellows is checked on the surface the structural part enclosing hole 5 must be unscrewed. The nut on the extension piece of the steel stem, protects the bellows from being spreaded by the internal pressure. External dirt may settle among the convolutions of the bellows. This may hinder the movement of the bellows and the valve will not open as prescribed. In the Garrett valve of tag 2.1.1.2.1.2.3, shown in Fig.2.4 -27, dome pressure acts on the outside of the bellows. Valve stem I contains a cavity with high-viscosity lube oil. The space between the bellows and the outer surface of the perforated valve stem is filled with a similar oil. Mud, sand grains, scale and rust entering the valve can, at most thus reach only the lowermost convolution of the bellows. In normal operation, no well fluid rises higher than port 4, being prevented from doing so by check valve 5. Still, some inflow of well fluid is possible during installation, and the 246 2. PRODUCINGOIL WELLS -(I) injection gas may also contain some dirt. The bellows cannot be contaminated of the middle part of the valve is constructed as shown in part b of the Figure. The valve stem is provided with an O-ring type seal. The space above the seal is also filled with high-viscosity oil. In some constructions, the bellows are made of several elements so as to minimize deformation (Fig. 2.4 - 25) or leans against a perforated jacket. From the point of view of valve spacing and control the fact that the valve's operational temperature cannot be exactly predicted is disadvantageous. To Fig. 2.4 - 28. Merla L gas lift valve eliminate these disadvantages spring-loaded bellows valves were constructed. A valve of this kind is the Merla L type, having the tag 2.1.2.1.2.1.3,shown in Fig. 2.4 -28. The valve stem is pressed on the valve port not only by the dome pressure but also by the F, force af the spring I . Equation 2.4- 3 of the opening pressure is thus modified to P D A D + F s = P T A , ~ +P C ( A D - A ~ ~ ) . 2.4 - 45 Let P D AD + Fs= P D S A D , where p,, is the joined, imaginary "dome pressure" of the dome and spring. Let us denote, furthermore, the ratio of the valve port area and the effective cross section area of the dome A, J A D by k then the equation of opening can be expressed in the following form: 1 1-k PT= ~ P D s -~ P c . 2.4 - 46 Very frequently the dome is filled, respectively, only with air or gas of zero overpressure. In these cases the "dome pressure" is created solely by spring force. 2.4. GAS LIFTING 247 Still, the important role of the bellows remains unchallenged; without the bellows the casing pressure would act on surface A,, and not on (A,-A,J. The spring force is hardly influenced by changes occurring in temperature, that is why the opening conditions of the valve at the setting depth remain practically the same as in the surface valve tester. The setting of the dome pressure to the right value which is to be effectuated after the well spacing design is a field problem. In valves without springs this setting means that the dome is charged with gas of prescribed Fig. 2.4-29. Gas lift valve tester pressure, taking the ambient temperature into consideration. To determine p,, in spring-loaded valves a special valve tester is required. Figure 2.4 - 29 is a sketch of the Merla-type equipment. With its help p,, can be directly determined assuming that the opening equation, Eq. 2.4-45, is also valid at closing at very low gas flow rates, too. Clearly, if p , = p c then p c = p D , . For the experiment, gas lift valve I is placed into test chamber 2. While valve 3 is open, valve 4 is closed. If pressure rises in the gas chamber, at a certain pressure, valve 2 opens and passes gas on the side closed by valve 4. Then valve 3 is closed and valve 4 is slightly opened; the pressure slowly bleeds down in the equipment and equalizes on the two sides of gas lift valve 1. When the gas lift valve closes, pc =p,= p,,. From the moment of closing the pc pressure of gauge 5 remains constant, and the p , pressure of gauge 6 gradually bleeds down to atmospheric value. Another consequence of the "spring load instead of gas charge" is that with the rising and sinking of the valve stem there is a nearly linear relation between the pressure prevailing in ;he space surrounding the bellows and the valve travel height. On the basis of engineering gas law it is obvious that this relation regarding to gas charged domes is of nearly hyperbolic character. The control of the gas throughput capacity was made possible in equipment with springs (Section 2.4.3-(a)4). The k constant of the opening equation can only be approximately determined from the geometrical data of A,, and A,. The main reason for this is that the bearing perimeter of the valve needle or valve ball differs from the perimeter of the valve port. Figure 2.4-30 shows a possible construction. It can be seen that the cross sectional area, on the bottom of which the tubing pressure is exercised, is greater than the area of valve port of d,, diameter. Thus, the value of k must be taken into consideration at designing according to the manufacturer's catalogue. The shape of the valve stem and port may be different. Conical stem and/or conical port is generally used if the valve is used for throttling control. If we want to 248 2. PRODUCING OIL WELLWI) obtain a great and generally constant gas throughput area immediately after the start of the opening, then the valve port is of a vertically entering edge type and the stem ends in a ball. Also, a check valve belongs to each gas lift valve. Its purpose is to prevent any liquid flow from the tubing into the annulus. When first unloading or working over dirty water or mud, formation treatment treating fluid (e.g. fracturing fluid, Fig. 2.4 - 30. Fig. 2.4 -31. Macco check valve hydrochloric acid) may enter the tubing. If these fluids flow through the gas lift valves, they will erode and corrode them and the life of the valves will decrease. After thedying ofa well due to operational troubles the well fluid would enter not only the tubing but the annulus packed off at the bottom as well. The unloading process would last longer, would require more gas, and the well fluid containing solid contamination would cause erosive damage. The check calves applied in bellows type gas lift valves are balls or closing elements of other shapes with spherical closing surface. Closure is also facilitated by gravitation or by spring force. Figure 2.4 -31 shows the MACCO spring-loaded check valve. In certain cases the drawings of gas lift valves do not include check valves. This is only for simplification of the figures. Check valves are applied practically in each case sometimes even two in series for the sake of greater reliability (a) 3. Pressure controlled gas lift valves without bellows. -The OTIS C type valve, shown in Fig. 2.4-32 (tag: 2.2.1.2.2.2.2) is not mounted in the usual mandrel but threaded between two lengths of tubing as a sort of special sleeve (see Fig. 2.4 -41). The nitrogen-charged dome I is of annular section. If dome pressure exceeds casing pressure, internal overpressure makes the elastic sleeve 2 close the injection gas inlet slots 3. The similarly elastic reverse check valve 4 prevents the well fluid from flowing through, or entering into, the valve. If casing pressure exceeds dome pressure, sleeve 2 assumes the position shown in part (b) of the Figure, and injection 249 2.4. GAS LIFTING gas can flow from the annulus through slots 3, annular passage 5 and bores 6 into the tubing. The only moving parts are the two sleeves made of a rubber or plastic. A feature of the valve is that the opening and closing casing pressures are the same, practically equal to the dome pressure, and they are independent of the tubing pressure. The valve is thus opening at a somewhat greater casing pressure than the charged pressure. A further condition of the beginning of gas injection is that the Section A-A I I (a) (b) Fig. 2.4-32. OTIS C type gas lift valve casing pressure should be greater than the tubing pressure. The opening, or greater than opening, casing pressure holds the valve open. The valve is advantageous because its inside and outside diameters are the same as the inside diameter of the tubing string and the outside diameter of the joint, respectively. Its gas passage area is greater than that of gas lift valves with bellows. A disadvantage of this type is that it can be run and retrieved only with the tubing string. There are also OTIS valves which are wireline or pumpdown retrievable. These must be run inside the tubing, and thus their inner diameter is smaller than that of the tubing string. A flexible sleeve type gas lift valve has been patented by Szilas, the spread of which is time-dependent (tag: 2.2.1.2.1.1.2). The valve forms a part of an assembly comprising 01 a packer and bleed port used for chamber lift (Section 2.4.4-(b)). 250 2. PRODUCING OIL WELLS+I) The OTIS CF type valve sh wn in cut-away form Fig. 2.4-33 (tag: 2.2.1.1.2.1.2) 9 opens and closes upon the impact of the tubing pressure and the decrease of the casing pressure, respectively. The annular dome 2 is surrounded by the flexible sleeve I. The inner valve 3 is intended to be opened by the tubing pressure acting from below and by spring 5, and is intended to be closed by the casing pressure acting from above. If the casing pressure is larger than the charged pressure of dome Fig. 2.4-33. OTIS CF type gas lift valve 2, sleeve 1opens. If, then, the opening forces acting upwards from below are greater than the force from the casing pressure acting downwards, inner valve 3 opens, and the rate of opening depends on the tubing pressure. A gas rate corresponding to the size of the opening will then be passed from the annulus into the tubing through radial slots 6. Gas passage stops if inner valve 3, due to the decreased tubing pressure, or sleeve 1, due to the decreased casing pressure, closes. (a) 4. Main types of gas liji valves with bellows, operational parameters. -The first type of gas lift valve controlled by the casing pressure is the basic valve, i.e. the unloading valve shown in Fig. 2.4 - 9 that can be used as an operating valve as well. The equation characterizing its opening given with Eq. 2.4-46 is 25 1 2.4. GAS LIFTING In this valve type k = A,dA, is very small, e.g. 1 : 16. Line I of Fig. 2.4-34 graphically shows this relation characteristic of the opening. Pressures p , and p, are equal in each point of line 11. In area I above it gas passage is impossible since casing pressure is lower than tubing pressure. Area 2 is bounded by line I1 at the left and by a vertical line passing through the p , = p , pressure at the right. Here gas flow through the valve is also impossible because the valve closes if the casing pressure is 'CI 'c? IC' C ' Fig. 2.4- 34. lower than the dome pressure. The valve can first be applied for intermittent lift. Its range of operation is area 3. Opening is done with the casing pressure controlled from the surface. This opening casing pressure depends on the height h and the corresponding pressure p , of the liquid column at which the gas injection into the tubing should begin. If this value is p,, then p,, casing pressure is required for opening. If the liquid is lifted to the surface by the gas passed into the tubing then the casing pressure is decreased to equal the valve dome pressure by surface control, and thus the valve closes. Due to the steep valve characteristics, by a comparatively small change of the casing pressure liquid slugs of considerably different legths can be lifted to the surface in one cycle. The difference between the opening and closing pressures, p,, and p,=p, , respectively, is the spread of the.valve. The greater the value of this, the more gas bleeds down in intermittent operation from the annulus during one production cycle. This gas volume can be both useful and harmful from the point of view of production. It is useful if the surface gas supply system is unable to provide sufficient gas rate during the short production period and then the additional gas volume determined by the spread and the annular space volume is at hand. It is harmful if more gas bleeds down from the annulus than the quantity required for the lifting the liquid slug. From the point of view of the efficiency of the intermittent production the largest possible gas passage area is advantageous. Due to the impact of the same, however, the steepness of the characteristic line of the valve decreases, thus the spread required for producing the liquid slug of the same height increases. Thus it is expedient to develop a valve construction where the enlargement of the gas passage 252 2. PRODUCING OIL WELLS (I) area is possible without changing the steepness of the characteristic line. One of the solutions is the pilot-operated gas-lift valve. An example of this is shown in Fig. 2.4 -26 and its operation is also described. Another solution is the OTIS gas lift valve supplied with "pilo-port", tag: 2.1.1.2.1.1.3 (Fig. 2.4-35). Other parts of the valve are, principally, the same as those of the basic valve. k of the opening equation (Eq. 2.4 - 45) is determined by the cross-sectional area of the port 2 of cage 1for a given bellows area. If, after opening, due to the increased pressure around the bellows, the valve stem rapidly rises pulling the cage then valve port area 3, of greater diameter, opens. From the shape of the valvecharacteristics it is obvious that the spread of the runin valve increases if we want to open it by a smaller liquid slug head. Because of this the additional gas volume flowing from the annulus after the liquid slug also increases. It may result in a significant increase of the specific gas requirement for Fig. 2.4-35. OTIS gas lift valve with "pilo-port'' Fig. 2.4-36. Guiberson CR type gas lift valve- intermittent gas lifting during the well's production history. To eliminate this problem the Guiberson CR (constant ratio) type valve was developed (tag: 2.1.1.2.1.1.3), and is shown in Fig. 2.4-36. The structure of the valve from the top to line A -A is practically the same as that of the basic valve (Fig. 2.4 - 9 ) . Dome 1 is charged with nitrogen gas. Rods 3 touch the bottom face of valve stem 2 but they are not connected to it. The upper section of rod 5 of the inner valve 4, like a piston, reaches into space 6 filled with gas of nearly atmospheric pressure. If the pressure in the annulus exceeds the dome pressure in the valve, then valve stem 2 travels 2.4. GAS LIFTING 253 upwards while the part under it remains where it was. For this remaining part we can write where AA is the difference between the area of valve port 7 and the effectivearea of the lower bellows, and A,, is the area of valve port 7. Rearranging the above equation we obtain i.e. if the casing pressure exceeds the dome pressure, then the proportion of the opening casing pressure to the tubing pressure depends solely on the structural parameters of the valves, and is independent of the casing pressure p, . The valve always closes at dome pressure. An advantage of the CR type valve is that if the length of the liquid slug h to be lifted changes for a given well, the proportion pc/pT determining the rising velocity of the liquid slug remains the same. Design errors or changes in the casing pressure p, due to the well parameters hardly influence the optimum specific gas requirement. Initially valves controlled by casing pressure were used not only for intermittent but also for continuous flow, as operating valves. It turned out that its application for gas passage control is disadvantageous. If, temporarily, the pressure of the rather gassy wellstream decreases at valve depth, then, because of the increase of the pressure difference between the two sides of the valve, the gas flow through the port of constant area also increases. With greater tubing pressure, however, the gas rate entering into the wellstream decreases. The control, due to the operation of the valves acts in the opposite direction, as is desired. To eliminate these disadvantages there are valves sensitive to tubing pressure. In the literature different names are used. Pressure operated valves are mentioned as well as fluid operated ones. For us it appears to be more logical if both types are called pressure operated valves. The valves belonging to the first type will be named as valves operated by casing pressure. The second group includes valves sensitive to tubing pressure. The family of valves sensitive to tubing pressure includes two different groups. Essentially, the first group comprises those basic valves which are reversely installed as shown in Fig. 2.4-37. The lift gas enters through port 2 under the check valve from the annulus and flows into the tubing through the annular space surrounding holes 3. Certain types are equipped not only with dome and bellows but with springs compensating for the "gas dome pressure". The MACCO RM type valve, tag: 2.1.2.1.2.2.3, can serve as an example. The condition of opening is PDSAD=PT(AD-A,IJ + P C & and from this, by substituting AcJAD= k .g.. Gas passes from the annulus through the valve into the tubing. 2. It is obvious that the valve characteristics are very flat. 2. 2. the tubing pressure decreases the valve ball begins descending. Due to the significant increase in the compressive load effecting the bellows the valve stem rises to the highest structural position. to p>.4-37.38. Within the valid range of casing pressures this opening tubing pressure hardly changes. will increase from p. If.. = p c . PRODUCING OIL W E L L W I ) Valve characteristics of this kind are shown in Fig. in the position before the closure some pressure drop . pressure drop of Ap occurs and so the pressure in the valve and on its tubing side.. This value is about one and a half times as great as the former value. for p. because of the surfacing of the liquid slug. Reversely installed gas lift valve pos Fig. At the valve port of area A. with a fair approximation.4-38.4 . If the casing pressure is the same as it was at the opening. 2. the value of the tubing pressure required for opening is determined. however.4 -48.Ap. Opening takes place if the tubing pressure reaches the value calculated by applying Eq. If.2 54 2. and for a given p. the valve will close at the same value the tubing pressure was at the opening. e.. it is p. a Fig. . 4-39..4 .2. and that is why the characteristic curve of the valve is rather steep. then. Factor k of the valve is comparatively large (112 .. On the other hand.1. reaches the value required for opening but the valve stem does not rise. however. 2. having the tag 2. pDs. . The Merla L-type valve. and the value of gas throughput.4-45.4. This means that in the open state. to a fair approximation. and it can be characterized by Eq. Graph I of the lower diagram shows the relation p. the same as that of the basic valve. Graph I1 is the curve of "equal pressures". 2. the closing tubing pressure will be somewhat larger than the opening value (p.1. then. GAS LIFTING 255 occurs in the valve port due to the passage of gas from the annulus. The same line.).If the tubing pressure reaches a greater value. the valve stem rises higher and more gas is . O n the one hand it differs from the basic valve in that the cross-sectional area of gas intake from the annulus into Opening Fig. because of the actual casing pressure drop. At the intersection of the two straight lines the'casing pressure and the tubing pressure just equal the dome pressure. The opening equation of these type of valves is theoretically. Characteristic curves of this valve type are shown in Fig. in accordance with point D of the upper diagram. the "dome pressure" is secured by a spring and the total valve travel is relatively great. characteristic of the opening condition.1.2. due to the outer force pressing on the bellows. At this pressure the valve with a tubing pressure value p.-p. 2.1/5). the valve is significantly smaller than the valve port area from the valve into the tubing. 2.. p.39.. Let us assume that the casing pressure equals p. equals 0. however.28). characterizes the closing pressure as well. belongs to the other group of valves sensitive to the tubing pressure.4.2. is negligible. the tubing pressure prevails in the valve space surrounding the bellows..3 (Fig. This difference. 1. At the tubing pressure p. It becomes obvious considering the effective operational range lies between points D and C.Pilot valve I operates in the same way as the basic valve. determined by the opening equation. the gas flow rate passed through the valve q. instead of gas of the former tubing pressure.1. At point A the Fig. smaller. the tubing pressure range. is made possible. so that with reduced tubing pressure less. and is at its maximum at point C. then according to the principles of the flow behaviour through chokes. Between the tubing pressure values corresponding to points C and D. changes linearly with the tubing pressure. is the useful throttling portion. the valve stem has reached its highest position. The Figure also shows that with smaller casing pressure p. exercised by the gas lift valve. for which the valve is open. with constant casing pressure. If the tubing pressure is even greater. and gas of greater casing pressure gets into space 3 under the valve.4-40..1. Special operational features characterize the OTIS RS type high-spread valve (spreadmaster) shown in Fig. seemingly inversely to the above explanation.1.. in practice the pressures p.256 2. The "partial opening". since p. Thus the correct control. It should be noted that.. It is used for controlling continuous gas lifting. respectively. corresponding to point B. also marked in the lower section of the Figure. gas should be passed into the tubing string.1. the gas throughput capacity decreases. while with increased tubing pressure more. PRODUCING OIL WELLS ( I ) passed through. thus the passage of gas stops. then the pilot valve opens. decreases.40 (tag: 1. The main valve 4 acts as a differential . are called closing tubing pressures.4 .. OTIS RS type gas lift valve casing and tubing pressures are equal. becomes larger and p. 2.. acts upon pilot valve port 2. If. 2.3). the tubing pressure. is intended to be opened by the joint forces exercised upon area 6 of the tubing pressure and the force of spring 7.4. Run in of an instrument below the valve is not generally possible. but the flow area in the tubing is restricted by the mandrel. In the valve passes the gas lift gas from the annulus into the tubing string. The annulus can be that of the casing but an annular space between the tubing and the injection line can play the same role. and by reducing the tubing pressure. prior to running the tubing. together with the pipe section including the valve mandrel. .4 -41 shows different outside mounted gas lift mandrels.4 -35) for snap opening and closing. when pilot valve 1 closes. The valve can be retrieved only together with the tubing.4-37. on the other. wireline retrievable valves.41. and with ball stemhead. Valves are called balanced when the opening and closing tubing pressures are the same. The valve. or. (a)5. b differs from a because the valve is recessed into the tubing. when main valve 4 closes. on the one hand. The valves are either threaded into the mandrels or they are fixed with small packing elements. which. GAS LIFTING valve. and the well is produced through the annulus. and.257 2. respectively. or with pilo-port 8 (see also explanation of Fig. Conventional gas lift valve mandrels casing pressure. 2. Characterizing the valves in this way seems to be outdated.A. In the first case the installation of the valve into the mandrel takes place on the surface. Figure 2. 2.. . If the tubing pressure is high enough the valve opens and gas will be passed into the tubing. In a the valve is fixed to a full-bore tubing I D mandrel. 2.). the annulus casing pressure acts on the surface ( A D . In this way the space requirement is less. A "reversed" installation is shown in Fig. i.Valves operate within special mandrels run as part of the tubing String. is intended to be closed by the casing pressure exercised upon area 5.4 . In c the gas in conveyed to the valve through an injection line of small diameter. and thus the gas throughput capacity depends on the tubing pressure around it. is suitable for throttling control.e. In case of unbalanced valves the opening and closing pressures are different. in general. It is assumed in each case that the valves are installed "straight". Gas passage may be stopped with a reduction of the (0) (b) (c) Fig. with tapered valve stem. Travel of the main valve stem 4. The literature often uses the classification "balanced" or "unbalanced" for the valves. Installation of gas lift valves. Running and retrieving a Camco gas lift valve.4-42 (tag: 2. PRODUCING OIL WELLS 41) Changing a wireline-retrievable valve is much less costly. a shows the running operation. 2.2. which consists of three centring arms (3) fixed to a sleeve at each end.258 2. after WIELAND(1961) retrieving a CAMCO type retrievable valve is illustrated in Fig. 2. Pulling makes the upper sleeve slide down bar 6.1. Retrieval is shown in b. so that the upper sleeve comes to rest against the knuckle joint. The valve is first run past the valve mandrel and then pulled slightly back. Gas flows into the valve through inlets I.4 . which also provides packoff between tubing and annulus.4.4-43 (Wieland 1961).2. the main components of which are the running tool 5.1).Its operation is the same as that of the OTIS C type valve described in Section 2. Most of today's valves are manufactured in two variants: one wireline-retrievable and the other for outside mounting. Valve I is installed by means of a wire-line tool. On running.4-43.2. On furhter lowering the valve is deflected by the centring arms in the eccentric mandrel so as to slide precisely into the mandrel bore. It is fixed in its seat by packing 6. OTIS wireline-retrievable gas lift valve Fig. Running and Section A-A Fig. 2. the knuckle joint 2 and the kickover tool. and get caught in the position shown in the Figure. A slight jerk will disengage the running tool. Retrieving tool 7 differs from the running tool in that its length is increased by .2. spring 4 pushes the centring arms up. A wireline-retrievable OTIS valve is shown in Fig.42. 2.3-(a)3. 2. Figure 2. If the specific gas content of the wellstream flowing in from the formation into the wellbore increases. then the application of an operating valve sensitive to tubing pressure is the most economical. If a well is continuously produced from one zone. gas lift can be applied in flowing wells. According to Section (a)4 this valve type automatically controls its gas throughput capacity. due to shutdown because of measurements. the density of the rising wellstream and. In a injection gas flows from the annulus into the tubing. or due to dying after operational troubles. then. A valve string can be applied for unloading even if the well is not produced by gas lift. Gas lift valves can also be applied for the selective production of one or more zones of the same well. Application of gas lift valves. e. In c the well is produced through the tubing by means of gas supplied through a separate gas conduit.4.4. Wireline retrievable gas lift valve mandrels 2. (a)6. do not start without an outside energy supply. however. the normal production is done with gas lift. which. In b the gas enters a chamber (cf. Section (0 (b) (c Fig. the type of kick-off valve is the same as that of the operating valve. In this case also. it is advisable to perform unloading through a string of unloading valves as well. Frequently. in most cases. GAS LIITING spacer bar 8. the tool is run past the valve first and then pulled up a small way. thus.4-44 shows three types of mandrels for retrievable valves.g.4-44. The kick-over tool then gets caught in the lowermost possible position. and further lowering of the tool directs the pulling tool exactly towards the fishing neck of the valve.259 2.4-(b). . If. -Gas lift valves are applied for unloading and for intermittent and continuous gas lifting. The valve gets caught and can be retrieved. g.4-45 shows the operation of two upper valves of the same type installed in the well. in order to Plc p~ (a) 21' '1 (b) Fig. Theoretically. Figure 2. If valves sensitive to tubing pressure are also used as kickoff valves. Then the liquid level is depressed below the second valve and gas injection starts through that valve also. Due to the decreasirig pressure the valve will pass and inject less gas rate into the wellstream.4. applying valves of Merla L type. PRODUCING OIL WELLS ( I ) the tubing pressure at the depth of the valve decreases.260 2. To explain this phenomenon we demonstrate the unloading process taking place e. Unloading begins when the gas flow rate passing through the upper valve produces a sufficient tubing pressure decrease to attain pTI. energy used for the compression of gas can also be saved.1 -(b)). the socalled transfer pressure. however. Unloading a gas lifted well with Merla L type valves close the valves we do not have to drop the casing pressure. and so for working the operating valve the available injection pressure can be fully utilized. Due to the impact of the gas injection through the two valves the tubing pressure at the depth of the upper valve .4-45. is somewhat more complicated than the valves controlled by casing pressure (Section 2. The selection and spacing of these valves. 2. Thus. the control of the gas lift from the surface is simple: a gas supply system on the surface must be provided that guarantees the prescribed constant pressure of gas lift injection in the annulus. the valve closes. is that from time to time. Closing is produced by a drop in the tubing pressure after the surfacing of the liquid slug. Due to the gas rate. and the possible solutions can be classified into two groups depending on whether a surface intermitter is used or not. due to opening of the lower valve. also Section 2. If the tubing pressure reaches the value of the opening pressure required for the given casing pressure. It is essential that the operational characteristics of the valves should be properly selected.4-45. If the gas content of the wellstream is constant or changes only slowly and evenly.lo).2. it would inject a sufficient rate of gas into the annulus to lift the prescribed liquid slug during the prescribed time (cf. and closes when the energy of gas contained in the tubing under the liquid slug is sufficient enough to lift the slug to the surface.5 -(a)). but due to their "insensibility" it is not advisable. and injection goes on only through valve 2. A common feature of the solutions belonging to this group is that the gas lift valve automatically opens when a liquid slug of sufficient height has accumulated in the tubing. the valve must ensure that for a given casing pressure it opens when the prescribed volume of fluid (with the right liquid column height and pressure) is accumulated in the tubing. Installations of this kind do not require snap-acting gas lift valves. A basic condition is that at full opening of the valve the gas passage area should be large.g. can also be applied. For this purpose the application of snap-acting valves is expedient. corresponding to the prescribed production rate.4. or by a drop in the casing pressure. From time to time the necessary modification of the injection pressure must be carried out on the surface. then valves not sensitive to tubing pressure. If no surface intermitter is used. it closes. Each valve alone should be able to pass a sufficientgas flow rate to reach the transfer pressure and. Figure 2. the valve opens. passes through the lower valve but the tubing pressure at the depth of the upper valve is reduced only to a p. The opening of valves controlled by casing pressure also depends on the tubing pressure (see Fig. the liquid will be lifted to the surface by the injected gas and then.. GAS LIFTING 261 decreases.and a drop in the casing pressure is required only for closure. due to a decrease. The valve may be either casing pressure controlled or sensitive to tubing pressure.4.4. These requirements can be achieved in several ways. The maximum gas rate q. at p. also Section 2. the closing pressure p. it is possible to control their opening and closing by it. only they are less steep (see Figs 2.. b represents the process shown in a for wrongly selected valve characteristics. At wells equipped with valves of this type the casing pressure is constant. 2. theoretically. Due to an increase in the casing pressure the valve opens and generally.4-(a)). valves controlled by casing pressure or OTIS C type valves. when the tubing . e. The role of the intermitter situated on the surface generally near to the wellhead. value that is greater than p.4-39). injected from the annulus..4-38 and 2. the tubing pressure increases. in principle. injection of gas in the casing is controlled by pressure regulator and choke (cf.4 . The characteristic line of tubing-pressure sensitive valves for opening is similar to that of the valves controlled by casing pressure. They may be less sensitive to changes in casing pressure and that is why. Several valve types are suitable for intermittent lgt. then. a is for continuous flow. if a liquid slug of sufficient pressure and height has accumulated in the tubing. The valve string above the operating valve controllcd by casing pressure is designed so that in the course of lifting the slug none of the valves of the string above the operating valve should open. Spacing of the kick-off valve strings is various according to valve types and deviates from the process discussed in the previous sections concerning casingpressure controlled valves.4-(a)). shows the pressure traverse for normal continuous operation. With relatively small casing pressure and sufficiently high available surface injection rates multipoint gas injection may prove to be economical (see also Section 2. can first be applied in cases of high opening tubing pressure. while b refers to intermittent lift. If the flow resistance of the wellhead and flow line is great. Points p. The length of the liquid column to be lifted cannot be changed in already installed valves.262 2.. the dccrease of the tubing pressure will be slow after the surfacing of the liquid slug.e. the valve closes. Figure 2. Fig.4-46.4-46 shows the main pressure traverses of the unloading valve string sensitive to tubing pressure. Valves sensitive to tubing pressure. In a curve p. show the closing pressure of the valves (see also .4. PRODUCING OIL WELLS { I ) pressure drops to a value practically equal to the opening pressure. i. Gas lift valve spacing procedure for (a) continuous and (b) intermittent installations using Merla R valves thus the gas lift valve remains open for an unnecessarily long time and gas lift gas consumption will be relatively large. 2. It can be used as an unloading valve. p. GAS LIFTING 263 Fig.2. gas lift valves operating on a variety of principles have been used in early production practice (Brown 1967). These latter parameters are shown in a less than L . Its main feature is that it will operate even if casing pressure remains constant. from Eq. pressure of the gassy liquid column fallen back into the tubing (which can be calculated. p. 2.. This point corresponds to the least flowing tubing pressure assumed on the tubing shoe. Tubing pressure .3 -(a).4.4.19 with the interpretation Ap. Krylov-Issakov differential type kick-off valve pressure differential across it is small and closes when it is great.4-(b)). knowing the inflow fluid parameters. The valves.4 -45). e... the Ap.g) and the A p . 2. The closing pressure curve of the valves. tubing depth in the Figure. Of these. open as the liquid slug passes them and later close due to a drop in tubing pressure. (b) Otber types of gas lift valves As stated in Section 2.. drawn starting from A. It opens when the Fig.= h. whereas it was necessary in spacing casing-pressure controlled valves.4..g.. one after the other. 2. 2.. is the maximum injection pressure valid in the annulus. shown open in Fig. from two phase flow gradient curves. As an example consider the Krylov-Issakov U-1-M type differential unloading valve (Muravyev and Krylov 1949).4-47.4.4-47. pressure drop that can be determined. It is ovbious that the effective casing pressure need not be decreased downwards. only the socalled differential type gas lift valve is used to any advantage today. is parallel to this. or in a chamber installation as a bleed valve (Section 2.p.. p. In the example shown the intermittent lift is performed with the help of multipoint injection. It is obtained so that to the gathering system pressure on the surface. are added. of valve I and the pull F.4-1 shows a semiclosed installation.4 bars.4 . Single completion.. Values less than these can be set by reducing the spring force by means of nut 3.4-21. in the closed state. . .5 -(b)l).+F..4.P.The simplest completion used in continuous-flow production is the so-called open completion with a single string of tubing and with no fittings in the well. the load on the well bottom is composed of the weight of the liquid column and of the gas column above it. whereas casing pressure acts on the smaller A . 2. The closing condition is A~P. Section 2. The mean flowing BHP is seen to be . of spring 2 act to open the valve. in the open state and on the greater A.. small and the closing pressure differential Ap. A condition for this arrangement is that the well fluid must not erode or corrode the casing and there must be no paraffin deposits. The annulus is packed off at the well bottom by means of packer 2. Another advantage is that if the well is shut off or dies. and the opening condition of the closed valve is since in the closed valve the casing and the tubing pressure act on equal surfaces A .264 2. PRODUCING OIL WELLS 11) acting on the area A. In the phase of accumulation. the annulus does not get filled with liquid and has not to be unloaded. Figure 2. A solution is shown in Fig. 2. In the production phase. The annulus is packed off by means of packer 3.3. whereas casing pressure acting through the valve port upon a smaller area A. Injection gas passes from the annulus into the tubing through valve I . Back-pressure retarding the inflow offormation fluid into the well varies as shown by the continuous line in Fig. -Intermittent gas lift normally requires a closed completion. standing valve 4 will close as soon as injection gas raises pressure above the standing valve higher than what prevails below it. and hence its greatest opening pressure differential is 4. The nearly constant spring force and the fact that tubing pressure invariably acts on a given surface A.4. Injection gas is admixed to the well fluid either at the tubing shoe or through a continuous gas lift valve installed in the tubing wall. Types of gas lift installation (a) Conventional installation (a)l. The maximum closing pressure differential of this unloading valve is 34 bars. 2.~A. plus the tubinghead pressure. casing flow may be employed.14. on the pear-shaped valve acts to close it. The closed annulus prevents surging of the second type (cf. make the opening pressure differential Apo. If the liquid production rate envisaged is quite high. In the U-1-M valve. with gas supplied through the tubing and fluid produced through the annulus. Injection gas is supplied to the casing annulus and well fluid is produced through the tubing. great. decline of formation pressure will even at a constant formation GOR entail a gradual increase in specific injection gas requirement. (ii) there are two separate injection-gas supplies in the well. The lower zone produces through tubing 2. Dual completions. casing pressure will drop soon enough to close the gas lift valve or valves so that the entire liquid slug will fall back and kill production. The gas injection to the tubing may be single-point or multipoint. (a)2. The increase in mean flowing B H P would reduce the daily inflow of liquid into the well. (iii) In an intermittent installation. the unloading valves above the operating valve open one after another as the rising slug passes them.There are two types of installation.4. (i) Injection gas pressure at the tubing shoe is less than or equal to flowing B H P in the case of continuous flow and greater than the mean flowing B H P in intermittent production. and in wells where fluctuations in flowing B H P preclude designing for optimal-depth single-point injection. delivering additional volumes of injection gas to the tubing.). (ii) In continuous flow. This will remain the case un ti1 the decline of formation pressure or the desire to increase production makes it necessary to reduce initial slug length. as it can be adapted much more readily to a wide range of production conditions. low injection gas pressure. The critical requirement of the method is an adequate supply of injection gas from the surface as. Both solutions in Fig. This solution was popular in early dualcompletion practice. Nowadays the completion shown in part (b) of the Figure is preferred. in the absence of such. all the gas delivered by the formation can be used to lift fluid. 2. In a continuous flow installation. Single-point injection means that gas is fed to the tubing through a single intermitting valve.2. the specific injection gas requirement does not necessarily increase as formation pressure declines. (Largely after Winkler and Smith 1962. In the absence of such a valve. in intermittent production. Multipoint injection is capable of delivering a copious supply of gas to the tubing section below the slug even if casing pressure is comparatively low. GAS IJFTING 2 65 fairly low. The result is a high slug velocity and reduced fallback. The dashed line shows the variation of pressure above the closed standing valve. the upper one through casing annulus 3. The above-outlined differences in well completion entail certain typical features of the two production methods. The Figure reveals also the influence of the standing valve. Valves are usually of the wireline-retrievable type. Its advantages predominate in comparatively deep wells with large-size tubing. This permits a fast valve change if design turns out to be wrong or inflow characteristics . that is (i) both tubing strings are supplied with injection gas from a common conduit or casing annulus. usually the lowermost one.4-48 belong to the first group. the well is provided with two concentrically disposed tubing strings. In solution (a). Gas enters into the tubing annulus I. specific injection gas requirement in a given well producing a given fluid remains constant as long as the initial length h of the liquid slug to be lifted remains the same. as it could be realized with the current types of packer and wellhead equipment then available. In multipoint injection. formation gas hardly affects the specific injection gas requirement. the B H P would vary according to this line (assuming there is no backflow of fluid into the formation). the pressure of injection gas entering the casing annulus is to be stabilized at the surface.4. Fig. 2. because.122). (b) tubing-pressure sensitive valves on both tubing strings. Injection gas flow through the lower-zone valve is regulated by means of slight changes in surface pressure. The production of both zones with casing-pressure operated valves is recommended if the flowing bottom-hole pressure of both zones is so low. The greater the pressure differential over these valves. The gas injection period of the two zones if possible should not be at the same time. This hardly affects gas flow through the upper-zone valve. however. tubing-pressure sensitive. Production is consequently more uniform. that it is impossible to apply . A basic requirement is the selection of such valves. The lower-zone valve has a great gas throughput with a low flowing pressure drop.8 bars. or. beside controlling the production in one zone. or valves of different character to the two above-mentioned types. Both zones intermittent lift. 1. the less the change in gas throughput per unit change in tubing pressure (see Eq. Valve choice may be based on various criteria depending on the inflow characteristics and the production method (continuous or intermittent) to be preferred. The applicable valve types: (a) casing-pressure operated valves on both tubing strings. If both zones are equipped with casing-pressure operated valves. The continuous valves of the upper zone are choked so as to give a pressure drop of 7 . and (d) casing-pressure operated valves on one string while tubing pressure-sensitive valves are installed on the other string. close on casing pressure. which. which. (c) valves sensitive to tubing pressure at both tubing strings. then. or. The design is rather simple.266 2. PRODUCING OIL WELLHI) change. Dual gas lift completion (I) Both zones continuousflow. Several types of gas lift valves can be used.4-48. the gas demand of the surface gas lift line is very great and it could cause a drop in the line pressure to an undesired level. the producing wellhead pressure is so high. At both tubing strings the gas lift valves to be applied can be casing-pressure operated. do not or only negligibly influence production in the other zone. The volume of this excess gas will be less if the opening pressure of the operating valve of the zone with the lower cycle number is higher. GAS LIFTING 267 tubing-pressure sensitive valves for any zone. When. Tubing-pressure sensitive valves can be used if formation pressure is relatively high. say A. The right selection of . No valve is suitable for both continuous and intermittent lift in dual installation. the flowing pressure drop in the wellhead assembly is low. however. the surface intermitter will close the flow line of zone A.4. After the installation the mode of the production cannot be changed. 2.2. Dual gas lift completion but the gas cannot leave the string. When the valve of lower opening pressure opens. One zone continuous-flow. and if the liquid slug length to be lifted and the liquid production per cycle are not intended to change. thus securing the production of the other zone. The opening pressures of the two operating valves are different. and the corresponding zone. Only keeping the casing pressure constant is required on the surface. The selection of valves for such wells is a much more complicated process than in the previous cases. produces. other intermittent lift. the other operating valve with higher opening casing pressure opens. When production from zone B ceases the flow line ofzone A automatically opens and thus the gas stored in the string bleeds down. the other operating valve remains closed. say B.4-49. The tubing string of this zone is also filled with gas Fig. and the operating casing pressure should be lower than the opening pressure of the intermittent valve. In favourable cases. either by continuous flow or intermittent lift. is sensitive to the tubing pressure and can be closed with a drop in casing pressure. A chamber installation at a given specific injection gas requirement gives rise to a lower flowing BHP and hence to a higher rate of production than a conventional one. also.268 2.4. and the daily liquid production rate. Example 2. while the lower zone is of lower productivity and operated intermittently (Davis and Brown 1973). Dual completions will permit the production of one zone by flowing and another by gas lifting. the two zones may be produced independently. Its advantages become apparent primarily if the flowing BHP is low and casing size is large.. The lower zone receives injection gas through annulus I. Several completions are possible. For the intermitting producing zone it is often advantageous to apply tubingpressure sensitive valves. The well contains three strings of tubing. the tubing itself is invariably of 2 718 in.4 . depending primarily on which zone is deeper and also on whether the gas can be produced through the annulus.8 bars. or requires a separate tubing string. through a change in casing pressure. 2. the upper one through annulus 2. let the liquid accumulate in chambers of diameters ranging from 50 to 150 mm. as well as the mean flowing BHP over this period. intended to facilitate intermittent lift. The completion required in this case is a simplified version of the above-described ones. gas from the gas zone may be used to gas lift the other zone. If casingpressure operated valves are used in both zones.8. The case is rather simple if the upper zone is of higher productivity and is continuously produced. This method is relatively immune to errors in design. In a well characterized by the data given in Example 2. The operating valve of the continuous zone. The values of h. The larger amount of piping required makes this completion costlier than the foregoing one. Find the time required for 0. (b) Chamber installation A chamber is essentially a larger-diameter piping attached to the tubing shoe. A chamber installation with its larger diameter makes the same volume of oil represent less head against the formation than a conventional installation. Several methods are available. The intermittent cycle frequency is controlled with a surface intermitter. The operating casing pressure on the surface. then the pressure drop through the port of the continuous zone's operating valve should be 7 . is the same. Dual completions will prove advantageous also in the case when one zone produces gas and the other produces oil by gas lift.849 m3 of oil to accumulate. corresponding to the various chamber diameters . while the operating valve of the intermittent zone is a casing-pressure operated type with no spread. independent of the depth of the gas injection. a given size of production casing will take smaller sizes of tubing. This latter valve's closing pressure is the higher. size. In the solution shown as Fig. PRODUCING O ~ WELLS L 41) the choke size of the operating valve of the continuous flow zone is especially essential.4-49.11. for instance. n. 2. 36 52.4-39 respectively.6 107 110 115 94. over a conventional installation with 2 718 in. 32 44.269 2.5 114 116.5 m3/d.4 . 75 100 I 1.8. I AD..8)=3.. 75 100 150 AP. Let us note that.4 -8.4 115.. n. mm Fig. columns of Table 2.4. The main data of the calculation are listed in Table2. 35 5 0 . GAS LIFTING can be calculated by means of the relationships A. 2.849. =0.8 .281 in each case Ap.2 117. 2.. dr constant 58..5 108 113.2 t ' liquid production.37 for daily Table 2. .. Chamber diameter h.0 192.4 . can be calculated using Eqs 2. 33 96.3-32.2 150 Chamber diameter.. In the knowledge ofthese data.50.5 111. 2. chamber diameter of the t i . The Figure reveals~accumulationtime nc qo I/d m3/d qOc .1 48.2 108.3 37.3 33. tubing (di=0. a chamber of 0.9 47. =0.4 -40.. 31 42.3 281. = 0 bar " .062 m).4 .320hla and Ap.36 for mean drawdown and 2.1 m diameter represents an advantage of (36.2 48. 40 4 s m3/d 1Jd 1640 1503 1443 1387 1358 30. and Ap. and q.1 bars than tubing-shoe pressure..8 .7 103. in conformity with the foregoing example..1 34. a round 11 percent.. mm m AP. 34 48.4-38 and 2.6 36. let 90 h .4 .8 83 95. we may use Eq. that is. In the case examined.1 43.0 50 62 I 107.4 . If the chamber . 50 62 .h. Figure 2. to decrease and daily cycle number and production to increase as chamber diameter increases.58 58 3 7 5 4 . For simplicity.+ bars 432.4-50 shows plots v..8 50.4 -44 to find the span of time needed for accumulation.-h.4 51. was calculated by Eq. 30 4 0 1 . flowing BHP is taken to be invariably higher by 1. it is necessary to decrease the production per cycle. or bleed valve 3.4-51. then other production parameters being equal . by 2. Chamber installations. and remains open until casing pressure drops below its closing pressure. Bleed port 2. Inc. thus permitting most of the chamber to be filled by liquid. Bleed port sizes at low GOR are 2 . Valve 1is opened by periodical injection of gas from the surface.270 2.4-51 shows five modern versions of chamber installations..8 m3. Bleed ports have the drawback that they will bleed also during the liquid production phase.3 mm.4 percent of the initial production. yo. so that the pressure there will be no higher at the end of accumulation than at its beginning. entails an increase in specific injection gas requirement. The common features of all five are that (i) gas injection is controlled by a surface time cycle controller. Texas) Figure 2. and (iv) injection gas fed to the chamber top enters the tubing only after having displaced the entire liquid volume. (0) (b) (C) (d ) (el Fig. 2.1962 (used with permission of CAMCO. lets the formation gas accumulated in the top part of the chamber escape into the tubing. the volume of liquid producible per cycle would be less and the specific injection gas requirement would be greater. that is.. A surface time cycle controller is required in each case because no liquid will rise opposite valve 1. (ii) at the top of the chamber there is a bleed port or bleed valve to get rid of the formation gas accumulated between production cycles: (iii) the chamber practically reaches down to the well bottom. This. this would increase daily production only by a further 0. however. PRODUCING OIL WELLS < I ) diameter could be increased to 150 mm. largely after WINKLER and SMITH. If the formation gas were not bled off. This increases gas . Houston. If the mean flowing BHP is to be reduced in an installation of given chamber diameter. Fig.. the well bottom is not sealed off during production. time of casingand tubing-head pressures. Surface control of intermittent lift installations We have to assure a constant gas pressure upstream of the choke. but entails a higher mean BHP. GAS LIFTING 27 1 requirements somewhat. This results in a larger chamber diameter than in an insert chamber. the choke bore can be calculated using Eq.4-51 are packer chamber installations. 2.2.4.4.4. Figure 2. The scale of tubing-head pressures is greater than that of casing-head pressures. Having casingpressure controlled gas lift valves. also.54 shows a two-pen pressure chart with traces of pco = f(t) and p. 2. pressure regulator I ensures in the line section upstream of a motor valve controlled by a clock-driven time cycle pilot a constant line pressure slightly higher than the maximum opening pressure of the intermitting valve. 1. They can be used if the well is cased to bottom. The most widespread two types are shown in Fig. The ID of the chamber being less than the ID of the production casing. = f ( t ) recorded by a fictive instrument whose period of rotation . 2. by the pressure buildup of starting production. In the knowledge of injection-gas line pressure and prescribed casing pressure and gas injection rate. Injection-gas supply (a) Surface control of wells All the control of a continuous-flow well consists in supplying injection gas at a suitable pressure and rate through a suitable choke to the casing annulus.4.124.4 -52. that is.4. various types of control are used in intermittent lift installations. time cycle pilot 2 opens motor valve 3 and lets gas pass into the well. The so-called bottle-chamber or insert-chamber solutions (c) and (d) are employed when the sand face is uncased. it does not boost production as much as a packer-chamber installation in a cased-to-bottom completion would. Standing valve 4 prevents the pressure rise during production from reacting on the formation.4-53 shows the change v. Cases (a) and (b) in Fig. 2.52. 2. pressure surges at the end of the production phase may trigger sand inrushes or a cave-in of the sand face. Such control does not requires instant-action gas lift valves.5. In (e). At pre-set intervals and over pre-set spans of time. In (a). This drawback is eliminated by the use of bleed valves which can be closed by a pressure differential of about 2 bars. Sector (a) of the two-pen pressure-recorder chart in Fig. 2. then pure gas to the flow line. 2. during one production cycle . The top of the liquid slug surfaces at 3. or by the tubing pressure build-up caused by the surfacing of the slug. The time cycle pilot opens at the instant marked 1and closes at 2. Between 4 and 5. controlled by clockdriven time cycle pilot.272 2. the bottom ofthe liquid slug) surfaces at 4.4 .54. the top of the lift gas (that is. Time cycle pilots of a variety of types are employed. Wellhead pressures of intermittent liR wells under various surface controls Fig. The closing of the line is controlled either by the pins. The clock-driven cycle controller for wells produced by Fig. Wellhead pressure chart of intermittent lift well.4-53. Their common feature is a rotating timing wheel provided with a suitable number of timing pins controlling the opening of the injection-gas line. PRODUCING OIL WELLS ( I ) precisely equals one production cycle. the well delivers first a mist. 2. Supply gas depressing the diaphragm of the motor valve bleeds off through orifice 13. The annulus is filled through the choke comparatively fast to the required injection gas pressure. Valves installed in the well are snap-acting. after WIELAND(1961) annular orifice 11 where the supply gas depressing diaphragm 10 bleeds off. on the one hand. of the liquid slug.55. depressing it to close the motor valve. The diameter of the surface choke is to be chosen so as to be.2.4. 2. If a pin 6 on clock-driven wheel 5 lifts arm 7. Motor valve 1 is closed in the state shown in the Figure. According to whether the choke bore is comparatively large or small. large enough to deliver to the annulus enough gas of sufficient pressure during the accumulation period and. whereupon the regulator shuts off the injection gas line. 2. Production starts when a liquid slug of the required length h. unbalanced. described in connection with Fig. can by a change of assembly be made suitable for controlling gas lift wells also. In the control shown as Fig. GAS LIFTING 273 intermittent natural flow. then needle 8 obstructs orifice 9 and opens an Fig. on the other. Regulator 1 provides upstream of the choke a pressure corresponding to the opening casing pressure required at the prescribed initial length h.4 -55 shows a comparatively simple time cycle pilot that controls both the opening and the shut-off of the injection gas flow (Wieland 1961). Supply gas acts upon the diaphragm through the open valve 4.and casing-head pressure changes during the cycle thus controlled is shown . there are two different types of control. Figure 2. The duration of the open phase may be adjusted by raising more or fewer timing pins 6 on wheel 5.3-43. The push down to close motor valve is now opened by a spring (not shown). A two-pen pressure-recorder chart of the tubing. (i) Comparatively large-bore choke. has built up above the operating valve.. The pressure of injection gas flowing through the supply line 2 is reduced in reductors 3 to round 2 bars. opening the line to the passage of injection gas. it is easy to see that the motor valve will again close.4. not larger than necessary. so as to avoid a slow drop of casing pressure to the closing pressure of the intermitting valve in the production phase. Clock-driven time cycle pilot. When timing wheel 5 has rotated far enough to let fall arm 7 back into the position shown in the Figure. Supply gas now lifts diaphragm 10 making it open the attached valve 12 and close 4..4-52/b pressure regulator 1 provides a constant gas pressure pi upstream of choke 2. There is an uninterrupted flow of injection gas into the casing annulus and a corresponding uninterrupted pressure rise during the phase of accumulation. 2. (b) Analyzing and trouble-shooting gas lift installations Measurements performed to analyse the operation of a gas lift well are of two kinds: (i) subsurface measurements and (ii) surface measurements.4-53. (ii) Bore of choke comparatively small. rather substantially costlier than the choke-type controller. 1967. The survey is performed by lowering a pressure bomb into the tubing through a Fig. 2. The most positive control permitting to attain a minimum of specific injection gas requirement is provided by the clock-driven time cycle pilot.) of Fig.) of Fig. The total injection gas volume used by the wells and supplied by the source is continually measured. however. The most important measurement in the tubing of a continuous flow gas lift well is the pressure bomb survey. A typical two-pen pressure-recorder chart of this type of operation is shown as part (b. by permission of the author) . Checking gas lift valve operation by pressure bomb survey (after BROWN. It can be performed in any well produced through the tubing rather than the annulus and may be expected to provide highly useful information. Intermittent valves installed in the well snapacting unbalanced. The regulator provides upstream of the choke a pressure in excess of the maximum required casing pressure.274 2.53. It is most expedient to supply wells with injection gas through individual lines from a common constant-pressure source.4-56. those of the individual wells can be measured periodically or on a spot check basis. 2.4 . The intermitting valve opens when the resultant of casing pressure and of the likewise rising tubing pressure provides the force necessary to open it. The first group includes pressure and temperature surveys and liquid level soundings. It is. PRODUCING OIL WELLWI) in part (b. . then the instrument should be lowered in the accumulation period and efficient precautions are to be taken to ensure its remaining below the operating valve during the production period. then the valve or the tubing is obstructed. can be decreased. In wells with a fast-rising fluid. (v) If the opening and closing casing pressures have changed. metering liquid and gas production. a tubing leak. The continuous recording of casing and tubing pressures is of a particular importance in intermittent wells. In an intermittent well. (ii) dome pressure of valve 2 has decreased and cannot close valve. then gas will rise in the tubing also in the accumulation period. can be raised above the opening pressure of valve 4. Figure 2. the survey is started at some distance from the surface. then the injection gas has started to enter the tubing through a different valve. This difficulty tends to arise in the top tubing section where low pressure makes the fluid expand and accelerate. and vice versa. If a survey cannot be dispensed with. and tubing pressure exhibits no periodic increase. snarl up or tear the wire line. and pressure measurements. liquid levels may be sounded by means of an acoustic survey. then cycle frequency is too great. (iii) valve 2 is not suitably packed off in its seat. metering injection gas volumes.. or if the valves can be re-spaced so that the depth of valve 4 is less. e. If the leak is between the tubing and the annulus. GAS LIFTING 275 lubricator installed on the well-head. as expansion will reduce temperature below the ambient value. including a point directly below each valve. Undesirable injection of gas may be due to imperfectly sealed tubing joints. Injection gas enters the tubing through two valves. or casing pressure p. Pressures are measured at a number ofpoints. A temperature survey of the tubing string will permit the location of the depth of injection. (iv) If the tubing pressure buildup duiing production is small and very short. This will reduce flowing BHP and increase the rate of production. or dome pressure in the operating valve has changed. contrary to design. Surface measurements to check gas lift wells include measurements of casing and tubing pressures. (ii) If wellhead pressure rises very high during production. after reopening. (i) a dimensioning error (closing pressure of valve 2 less than flowing pressure of gas flowing through valve 3). If required. (iii) If casing pressure is normal. it is inexpedient or indeed impossible to run a wire-line pressure-bomb survey. This may have several causes. mainly with recording pressure gauges. such as: (i) A casing pressure drop between production cycles usually indicates a tubing or casing leak or improper valve closure. then the point of gas injection will be at valve 4..4 -56 is the record of a pressure bomb survey. The liquid slug may rise fast enough to sweep up the bomb. The Figure further reveals injection gas pressure opposite valve 3 to be higher than necessary.g. then the choking beyond the wellhead has to be reduced. The well is then shut off to permit insertion and lowering to a certain depth of the bomb.2. If wellhead pressure p. 2 and 3. Liquid level soundings usually are of a subordinate importance. The recorder charts will show up correct operation and permit the diagnosis of a variety of malfunctions. (vi) The pressure charts will reveal when the well is able to produce also without injection. The pressure traverse is seen to exhibit two breaks. or a valve that has failed to close.4. it may be impossible to lower the bomb against the well flow. For the sake of determining the problem occurring in the quickest possible time. As well as the production tests discussed above the inflow performance of the well has to be analysed regularly. It may occur. that between two measurements of routine type some unfavourable change is experienced in production. it is Fig. The cause of the fault is an inadequate supply of injection gas to the tubing through the intended operating valve and. 1967. Recording tubing and casing pressures in continuous-flow gas lift wells will likewise provide useful information. 2. The tubing pressure diagram shows the production period to be too long. In (a). The continuous recording of wellhead pressures is not usually necessary.4-57. however. Wellhead pressure charts of malfunctioning intermittent lift wells. the total and specific lift gas volumes. some easily measurable well parameters must be taken every day. The rapid drop in both casing and tubing pressure shows liquid production per cycle to be too small.4-57 shows wellhead pressure recorder charts of three malfunctioning wells (somewhat modified after Brown 1967).too low a cycle frequency. a detailed checking of the defective well is required. In (b). the time cycle controller is out of kilter. however. constructed by using parts of flow diagrams 14-14(12) and 14-14(23) (by permission of the author) primarily the casing pressure diagram that reveals two valves to be in simultaneous operation. after BROWN. In part (c) of the Figure.276 2. and the water content of the . because the surfacing of the liquid slug may entail vibrations affecting the record. The regularly measured data are the wellhead and casing-head pressures. PRODUCING OIL WELLS { I ) The pressure recorder is instailed next to the well but not on the wellhead. Figure 2. the well produces at too high a cycle frequency. As the measured values exceed the allowed range. The high cycle frequency entails too high a specific injection gas requirement. 2. are supplied from the . leaks in the tubing and casing. where it is gauged and treated to a certain extent before removal. Inc. or into sales line 7.and a pumped group K . then in order to ensure a smooth supply of gas to the compressor station and an adequate covering of the fluctuating well demands the setting up of a suitable surface supply system is required.) Figure 2.a continuous-flow gas lift group K. heading. If the gas production rate of the well and/or the injection gas requirements of the gas lift wells tend to fluctuate. Fig. Lowpressure gas from the wells is led to compressor station 4. wellhead chokes and flow lines due to deposits.4. . used with permission of CAMCO. The station compresses gas for repressuring and for gas lifting. (c) Gas supply system Injection and lift gas is supplied by a gas well or by a compressor station. changes in the well inflow performance.4.4-58 shows a so-called closed rotative gas lift system in which said functions are discharged by various facilities. are delivered to test separator 1 and production separator 2. 2. The Figure is essentially an outline of possible options.an intermittent lift gas lift group K .. Gas intended for injection enters the intakes of the compressors through conduit 5. A check-up programme is described by Mayhi11 (1974). slightly modified after WINKLER and SMITH-(^^^^. erroneously designed or installed flow line. GAS LIFTING 277 wellstream.58. The latter is fed through line 8 to the gas lift distribution centres 10. Gas lift system. Frequent reasons of well errors: errors in tubing size dimensions and valve spacing. whereas conduit 6 supplies the compressor engines with fuel. .. Oil and gas produced from a number of wells. Oil is collected in stock tank 3. including a flowing group K . . and it is not usually necessary to realize all of them. whereas the former passes through line 9 to the repressuring wells K. The well groups K 2 and K . On the basis of the detailed well analysis the characteristics of the wells are calculated and plotted by computer. According to analyses the most frequent causes of troubles on the surface are: high pressure drop in the wellhead assembly. obstructed gas lift valve ports. 278 2.4-59. If that will not help. or to reach the highest income. Gas production from a number of flowing. requires careful preparation. Economy is evaluated on the basis of other concepts as well.when this has reached a permissible maximum.4. and vent 11. systematic measurements and modification of the production parameters on the basis of them. valve V. PRODUCING OIL WELLS -(I) distribution centres 10. .4. When pressure decreases in this line. to the compressors. up-to-date equipment. The production of the required rate at the minimum possible cost. Some experts and companies intend to use the available gas lift gas volume to reach the maximum rate of oil from one well.ure system grows too high. In the 4. on the basis of Subsection 2. after SIMMONS (1972a) opinion of the author the duty of the production engineer is the realization of the reservoir engineering plan at the minimum cost. The gas storage capacity of high-pressure line 12 is augmented by a buffer tank P 2 similar to P . opens up automatically the high-pressure gas well K g . however. m3/d Fig. from a given group of wells. If the pressure in the system mounts too high. Further smoothing can be achieved by using a high-capacity pipeline or a number of unproductive wells as a buffer gas tank P l . qL. automatically connects it with the repressuring line. It is easy to produce the well by gas lift. If pressure drops too low in lines 5 and 6. valve V. 2. Gas lift well optimization in case of unlimited production rate One of the main characteristics of gas lifting is that production is only apparently simple. . The requirements: sound theoretical knowledge. If pressure in the low-press. continuous-flow gas lift. valve V5 throttles or shuts off the sales line. and pumped wells is likely to give a fairly smooth gas supply to the compressors. automatically supplies make-up gas from the low-pressure gas well K g . can be achieved. Regulators Vl and V2 regulate the pressure of gas entering the compressors. . In the next section. the excess gas is flared through back-pressure regulator B . 2. then by by-pass pressure relief regulator B2 bleeds off the excess pressure into the lowpressure system. This aim. I. or alternatively.6. following Simmons (1972 a. then pressure in the sales line is increased first by means of valve V5. b) and Redden et al. Optimizing a gas lifted well. valve V . . The values. Optimizing a gas lifted well. let the difference between the income and the costs be denoted by AS. . = go. During the producing life the production rate of the well changes. Graph I of Fig. . B.42 m3/d. Let us indicate the increase in daily oil production as Ago. . at different specific gas supply R. methods of this kind are discussed. Figure 2.4-9 gives a summary of the results published by Simmons.. Considering that (R.Rf) = Ri .4-60.29 and 49. the cumulated value by B.. -q. the well produces only waterless oil. The greatest profit can be expected if Bin just equals B. .2. 7he optimum production of one well. The curve obtained is very similar to the Krylov-type transport curves characteristic of the two-phase flow in the tubing. represent the liquid rates q.and the profit by B..i. it differs from the Krylov-type curves because it is characteristic of the interaction of the well and reservoir. after SIMMONS (1972b) well is. 2.e.e.the daily lift gas requirement of production is qgi=41 x Ri . Generally it decreases. for incremental gas lift volumes of 2.4. although we can suppose a certain definite water content as well. .. and wellstreams.83 x lo3m3/d (100 x lo3 cftld). wellhead pressures.4 -59. of the qgi Fig. Let us assume that production and economy of the production of the above mentioned well. Let us assume that the change of the well inflow performance with time is known. 2.=O. however. Thus the optimum gas injection rate is also changing with time. 11. It is assumed tacitly that q. is determined. GAS LIFTING 279 (1974)..4-60 represents curve qo= Kggi)determined by the points of intersection of Fig.. It should be noted that the wells analysed operate with continuous gas lift.4-59 is the inflow performance curve. The family of curves I1 are the transport curves belonging to different gas-liquid ratios at given tubing sizes. i.. In accordance with this the oil rate will fall between 49. shown by the points of intersection. Table 2... In principle. 2. and then yo = q. and the joint value (income) of the produced oil and dissolved gas by Bin. the cost of compression of the lift gas and that of saltwater disposal should be indicated by B. . The expected daily profit values of the total producing life are discounted to the same initial date. the gas requirement will rise to an uneconomical level. but that no more gas than the optimum value must be injected into the well.. B P ~ Bpr max 99 98 40 60 80 100 120 140 160 180 sslyo q g k max Fig. on the one hand. 2. PRODUCING OIL WELLS . several gas lifted wells producing together. after SIMMONS (1972a. the profit decreases slightly and. however.125% range of the optimum value.. not that it is not worth optimizing. There are several schemes for this. on the other. Optimizing gas lifted wells. . Itsis visible that at least 99% of B.2. compared to the characteristics of the point belonging to the greatest profit. can be guaranteed if the gas injection rate is in the 75. Both the abscissa and ordinate values are given as a percentage.4-9. Evaluation corresponding to the above table for different times is to be performed. It means.{ I ) Table 2. Figure 2. If more gas is injected then..4-61. b) In the oilfield there are generally.4-61 represents profit as a function of the gas injection rate.. that is why optimization schemes are developed which determine the optimum gas lift volume distribution for all the gas lifted wells of the field. In the next section the original plunger lifts will be discussed. The process is carried on until the available total daily gas injection rate is distributed. the production scheme that guarantees the biggest daily profit can be also calculated..tubing and separating the rising liquid slug from the gas column lifting it.. Here. value can be determined. however. This process is carried on until the available daily gas lift volume is reached. Gas pressure in the casing annulus acts on the well bottom.4. assuming unlimited gas supply. The EXXON method is described by Redden et al. It is then calculated how large the incremental oil production at each well will be for a given incremental injection gas rate Aq.4. also. Well installations in current use can be classified into two groups: original and combined plunger lift. the volume of the optimum injection rate is calculated for each well. It permits the use of the pressure energy of the produced gas too and can be applied sometimes without gas injection in wells unable to produce by self-flowing. With a similar method. design features The plunger lift is a peculiar version of intermittent gas lift. In some cases the tubing strings are equipped with unloading valves facilitating the kick-off of stopping wells. Packers are not used in wells produced by original plunger lift. 2. The two fundamental types of plunger lift employed in production practice are those without and with time cycle control. The Shell process described by Simmons (1972a. the sum of the optimum characteristics of the individual wells gives the field's optimum. as follows. wherefore plunger lift does not permit the realization of low BHPs. the aim is to reach the maximum daily rate in the case of gas compressors of a given capacity. b) plans the greatest daily production. value is analysed and the gas rate is injected into the well from which the biggest increase in production can be expected. and it is determined at which well this decrease causes the slightest drop in production. the available daily lift gas quantity is limited. Thereafter the production increasing impact of the gas injection rate of the same Aq. Then a Aqgi decrease in the injection rate is assumed. GAS LIFTING 28 1 If the available daily lift gas quantity is not limited then the daily maximum B . is assumed at each well. Plunger lift (a) Operating principles. it has to be used so that it guarantee either the greatest daily oil production or the greatest daily profit. . in the case of a limited gas supply. Thus. Its main feature is a piston (plunger) inserted in the. First. If. (1974).7. . with the effect of considerably reducing gas break-through and liquid fallback. The incremental gas rate will be injected first into the well in which the increase in oil rate is the greatest. available by a considerable small gas injection rate.2. so that for each well the qgi optimum value is determined by applying the previous scheme and each well is produced at this lift gas value. An oil rate. since plunger weight is the same irrespective of the weight of liquid above it.if required -enters the annulus through line 11and open valve 3. Pressure drop under the plunger makes valve 2 open and lets the plunger descend. The plunger cannot rise beyond the bumper spring 12. Let us assume that plunger 1 with its valve 2 closed sits on the bottom shock absorber. It is shown in Fig. When the pressure force of gas accumulating in the annulus and acting upon the plunger exceeds the u Fig. only a small portion of gas energy expended will do useful work. and 7 are closed. (ii) Between plunger and tubing particularly those of the early rigid-seal type . In normal operation. PRODUCING OIL WELLS+]) The operation of the first type essentially agrees with that of the plunger lift patented by Hughes in 1927.4. Liquid flows through the wellhead perforations of the tubing and the open valve 5 into flow line 10.62. Thus if the length of this column is small. the plunger rises. Impact on downhole bumper spring 9 closes valve 2.4-62.6. This type of plunger lift is uneconomical in low-capacity wells because (i) the plunger starts to rise directly after impact on the downhole bumper spring and to lift such fluid as has accumulated during one full cycle of its travel. 2.232 2.there may be a substantial gap permitting the fallback of an appreciable fraction of the liquid slug. this makes the plunger ready to rise again. 2. Hughes' plunger lift weight of the plunger plus the weight of the liquid and gas column above it. injection gas . Valves 4. The relative . There is above it a short liquid column in the tubing. 2.4. GAS LIFTING 283 amount of this fallback is high if the slug is small. Finally, (iii), during the fall of the plunger, gas can escape from the tubing without having done useful work. The economic benefits of plunger lifting can be extended into the low-capacity range of wells by using a plunger lift controlled by a cycle controller. The well completion itself resembles that in Fig. 2.4-62. The surface equipment is shown in Fig. 2.4 -63. Injections gas -if required -flows during normal operation into the Fig. 2.4-63. Surface equipment of plunger lift installation controlled by a time cycle controller annulus through line I and open valve 2. Valves 3 and 8 are closed; valves 11,6 and 7, as well as choked valve 5, are open. The opening and closing of motor valve 9 is controlled by cycle pilot 13. There are two widespread types of control, that is (i) opening is initiated by a clockwork mechanism, (ii) opening is initiated by a rise in casing pressure. Closing is controlled in both cases by the surfacing of the plunger. Regardless of the type of control, the result is the same, namely, a decrease of cycle frequency, by letting the plunger rise only when enough liquid has accumulated in the tubing above it. Lubricator 12 contains a mechanical or magnetic sensor detecting the proximity of the plunger; it is equipped to send a pneumatic o r hydraulic signal to cycle pilot 13 which thereupon instructs motor valve 9 to shut off the flow line. The volume of liquid lifted per cycle can be varied over a fairly wide range; also, no gas can escape from the well during the plunger's descent. In order to ensure a better seal between the plunger and the tubing wall, plasticseal plungers are increasingly employed. The plunger in Fig. 2.4-64 is a construction of the National Co. Split-ring seals I are pushed outward by springs 2. The maximum displacement of the split rings is limited by ribs 3. Valve 4 stays shut during ascent owing to the pressure differential across the plunger; it is fixed in place by hasp 5. The valve opens after surfacing and is kept in the open position by magnet 6. The sealing element of the Merla plunger in Fig. 2.4-65 is the plastic sleeve I . Friction against the tubing makes it close opening 2 on ascent and open it on descent. The plastic seal rings 3 can move sidewise independently of each other. During ascent, the small pistons 4, actuated by the higher pressure within the plunger, push the rings eccentrically against the tubing wall. Section A-A shows in 284 2. PRODUCING OIL WELLS+]) an axial view how the aggregate deformation of the rings manages to obstruct the entire aperture of the tubing. Numerous other solutions are known. Plunger lift represents an advantage when producing waxy oils and those liable to form stable emulsions. Wax deposits in the tubing are scraped off by the plunger as they are formed; mixing leading to the formation of a stable emulsion is limited, because gas and liquid are comparatively well separated during their upward travel. Fig. 2.4- ,154.National elast~c-sealplunger Fig. 2.4-65. Merla's elastic-seal plunger Plunger lift is used also in gas wells producing also water and/or condensate; the latter, settling at the well bottom, result in an increase of BHP. Plunger lift with or' without cycle control removes the liquid as it forms and keeps the BHP at a low value. In certain cases, gas is produced through the annulus, whereas liquid is produced by plunger lift through the tubing. (b) Designing the plunger-lift operation Evaluating operating data of 145 wells, Beeson, Knox and Stoddard (1958) have written up relationships describing the operation of cycle-controlled plunger lifts using expanding positive-seal plungers. Table 2.4- 10 lists some of the typical data 2.4. GAS LIFTING Table 2.4 - 10. Symbol Tubing length Production Production per cycle Oil density WOR L, 4. ~ O C PO R, Unit m m 3/d 930 0.7 m3 kg/m3 0.02 780 0 % d = 2 7/8 in. d=23/8in. min max mean min max mean 3537 10.0 2035 5.1 1038 1.6 3574 17.5 2534 7.1 0.46 850 87 0.1 1 835 17 0-03 797 0 0.86 910 89 0.32 857 13 of the wells analysed. The fundamental equations derived by the authors using the correlation method are, transposed into SI units, as follows. For 2 3/8 in. tubing: 10-3LT (3.018 x i w 3 L T + 1.043 x 10-5pTomin +25.92)+ 117.6; Rg4 = Yoc Pcomax-Pcomin=3'545X 1 0 5 q 0 , + 7 7 . 6 1 ~ T +X2 1 0 - Z ~ T O m i n + 6 . 8X2lo4. 7 For 2 7 / 8 in. tubing: 2.4 - 53 In the above equations, pcOmaxis the maximum and pcomi, the minimum casing pressure, pTOminis the least tubing-head pressure during normal production. Rgo is the total specific gas volume required for production. goma,is the maximum daily production achieved by plunger lifting a given well, it can be calculated from mean data concerning the ascent and descent of the plunger. The authors have found that the mean velocity of plunger ascent is 5 m/s until the liquid plug surfaces. Descent velocity in pure gas is about twice this value. Velocities are less during the evacuation of the liquid, on the one hand, and during descent through liquid, on the other. The minimum cycle frequency determined purely by the ascent and descent times of the plunger - that is, assuming that the pIunger immediately rebounds from the downhole bumper spring without any rest period -is, for 2 3/8 in. tubing. 286 2. PRODUCING OIL WELLS (I) and for 2 718 in. tubing, tc= 0.295LT + 2267qOc. The maximum possible daily production by plunger lift can be calculated by substituting the above expressions into the equation which yields, for 2 318 in. tubing, and for 2 718 in. tubing, 86"qOC m3/d. 40max =0.295LT + 2267qOc Using their own fundamental equations, the authors have prepared nomograms and proposed procedures for operation design. In the following I shall outline a process based on the same fundamental relationships, but somewhat different from the Beeson-Knox-Stoddard method, and in better keeping with our own design principles. The mean flowing BHP is, in a fair approximation, where C is the weight correction factor, of dimension Pa/(Pa m), of a gas column of height of 1 m. Let the daily inflow from the formation be described by the relationship Let us substitute, assuming a 2 318 in. tubing, the expression of pcOmaxfrom Eq. 2.4 - 51 and the expression of (pcomax -pcomin) from Eq. 2.4 - 53. Rearranging, we obtain the relationship go = 86,400[Jpws- J(l CL,) (0.99pTomin+ 148.7LT + 4.307 x lo5)2.4 - 59 -J(1 + CL,) (2577LT+3.198 x 106)q,,] m3/d. + In the same manner, using Eqs 2.4- 54 and 2.4- 56, we may derive for 2 718 in. tubing qo= 86,400[JpWs-J(1 + CL,) (O.975pTomin+ 25.35LT + 7.81 x lO5)2.4 - 60 - J(1-t CLT)(1582LT+6.710x lO4)qOc] m3/d. Example 2.4- 12 serves to elucidate the application of these relationships. Let d, = 2 718 in.; di =0%2 rn;pTomin = 2.0 bars; L, = 1440 m; J , = 7.26 x 10-l2 m S / s ~ ; p,,=53.9 bars and C=8.64 x l/m. Let us calculate the operating conditions 2.4. GAS LIFTING 287 to be expected at p,,=25.5 bars. The tubing is run to bottom. In Fig. 2.4-66, line q,, =f(q,,) is calculated using Eq. 2.4-60. Let us plot the maximum feasible production v. cycle production using Eq. 2.4-58 and specific injection gas requirement, using Eq. 2.4- 55. On the left-hand side of the diagram, the line q,, =f(p,,) characterizing inflow is plotted. It is seen that at a flowing B H P of 25.5 bars, daily production will be 1.8 m3. The cycle production corresponding to point Fig. 2.4-66. Design of plunger lift operation of intersection B , is 0.55 m3; the specific injection gas requirement corresponding to point of intersection C is 200 m3/m3; and finally, the-value of q0,,,=28.6 m3/d corresponding to point of intersection D indicates that the designed production is technically feasible. Let J , = 7.26 x 10- l 1 m3/(Pas), other well parameters being equal. Inflow into the well is characterized by the line q,, = f(p,,). Production, at the same flowing B H P of 25.5 bars, is 17.8 m3; q,,,, and R,, remain constant at 28-5 m3/d and 200 m3/m3, respectively. Figure 2.4 -66 reveals that the flowing B H P can only be decreased by increasing the specificinjection gas requirement. For instance, to establish a flowing B H P of 14,7 bars an increase of gas injection from 200 to 535 m3/m3 is required in the low-productivity well, causing only a very slight rise in production, from 1.8 to 2.0 m3/d. A flowing B H P of 14.7 bars cannot be realized by plunger lift in the higher productivity well since a daily inflow of 24.5 m3 is higher than the technically feasible q,,,,= 16.5 m3/d. The above procedure, as has been shown, permits us to check whether a prescribed flowing B H P can be realized by means of plunger lift, and if so, what specific injection gas requirement is to be expected. 2. PRODUCING 01L W E L L S { I ) (c) Combined plunger lifts Combined plunger lifts are a combination of equipment of original plunger lifting and of intermittent gas lifting using pressure-operated gas lift valves. McMurry's design shown in Fig. 2.4 -67 is of this kind. Standing valve 1is situated on the well bottom to prevent liquid backflow into the formation during production. Fig. 2.4-67. Comblned plunger lift installation Fig. 2.4-68. McMurry combined plunger lift installation w ~ t hchamber Intermitting valve 2 is installed on the tubing under bumper 3. Devices in the tubing are wireline-retrievable. This arrangement can be considered as an intermittent gas lift installation where the fallback of the liquid slug lifted is significantly decreased by the plunger. An advantage is here too that the paraffin deposited on the tubing wall is scraped off by the plunger during operation. Due to the closed installation the flowing bottom-hole pressure is lower than in the case of the original plunger lift, and it is also lower than at intermittent gas lift without a chamber, since the length of the.liquid fallback, and thus the attainable average flowing bottom-hole pressure, is smaller. The production cycles are controlled by the methods applied for intermittent gas lifting (e.g, by surface intermitters) and not by periodically closing and opening the flow line. The end of the production cycles is transmitted by a signal from the surfacing plunger. 2.4. GAS LIFTING 289 Figure 2.4-68 shows a combined plunger lift made by McMurry that is able to reach low flowing bottom-hole pressures. The lift gas is led through motor valve 2 controlled by time cycle intermitter I and through pipe string 3 into chamber 4. The pressure in annulus 5, and thus on the well bottom will be very small because the formation gas will be sucked away by a surface vacuum pump, through pipe 6. Standing valve 7 prevents the gas lift pressure from acting on the well bottom. The tubing string is run with unloading valves only. Specific gas requirements may be increased by the capacity of the gas injection string. CHAPTER 3 PRODUCING GAS WELLS A gas well is a flowing well producing predominantly gaseous hydrocarbons. The gas may contain subordinate amounts of liquid hydrocarbons and water. Condensate, that is, the hydrocarbons produced in gas form but liquid under surface conditions, is a colourless or pale liquid composed of low-molecular-weight hydrocarbons. GOR is in the order of ten thousand at least. Gas wells may therefore be regarded also as oil wells with a high(sometimes infinite) GOR. Our statements in Section 2.3 hold in many respects also for gas wells. In this chapter we shall aim at presenting those features of gas wells which differ from those of flowing oil wells. The first subject to be tackled will be a productivity analysis of gas wells; the compressibility of gas being much greater than that of most well fluids composed of oil and gas, the flow of gas in the reservoir is governed by relationships other than those discussed in connexion with the performance of oil wells. The often very high pressure, high temperature and possible corrosivity of gas raise the need of completing wells with a view to these features. 3.1. Well testing, inflow performance curves At a steady state, the gas rate, flowing from the formation into the well can be characterized by the following LIT (laminar-inertial-turbulent) equation (Theory and practice. . . 1975), where c , and c2 are numerical constants, ji is the viscosity of the gas and k is the actual permeability of the formation at average pressure and at temperature T s is the Van Everdingen constant skin factor, and D is the variable skin, or IT factor, depending on the production rate. Assuming that ji, 2, 7:k, h, re, r,, s and D can be 3.1. WELL TESTING 29 1 considered as constants in the case of a given well, the above equation can be expressed in the following, simplified, form The equation is valid for the following conditions: the flow in the formation is isothermal; the effects of gravity are negligible; the flow is of single-phase type; the reservoir rock is homogeneous and of isotropic character, while the porosity is constant; permeability is independent of pressure; the viscosity and compressibility factor of the fluid is constant, and the compressibility and pressure gradients are small; the radial, cylinder-symmetrical flow model is valid. The hypothesis, assuming the viscosity and compressibility are constant, may lead to significant errors in wells in which the gas, from the formation of low permeability, is entering with a relatively high flow velocity. In these cases the result obtained from is more promising. Here $ is the pseudopressure, which, according to the definition given by Al Hussainy, is $,,and $ ,, are the pseudopressures corresponding top,, and p,,, respectively. aqgn is the pseudopressure drop determined by the laminar flow and well parameters where the dynamic effect bqin,comprising the turbulent flow, is also considered. The equation can be applied so that the Il/-p curve corresponding to the given gas composition and formation temperature is constructed and then the $ corresponding to the given p pressure can be directly read. In practice the Rawlins-Schellhardt equation, although simpler than the LIT equation it is properly accurate, can be used in many cases; it considers the 2 compressibility factor and ji viscosity changing with the average pressure of the gas flowing in the formation, and the dynamic-turbulent effects, by using constants C and n This relationship, which is borne out fairly well by actual fact, is usually plotted in a bilogarithmic system of coordinates, in which case the inflow performance curve is a straight line. (Fig. 3.1 - 1shows the inflow performance curve of the Hungarian gas well OK - 17.)The value of n is in the range from 0.5 to 1.0. If it is outside this range, then the well test has been incorrectly run and has to be repeated. Wrong results will be obtained also if liquid accumulates in the well during the test or, if the steady-flow method has been employed and the flow could not stabilize while testing at each individual operating point. The above relationship will be strictly valid for any given Of the several calculation methods developed to calculate the least gas flow rate that will still Fig.71(67-4-5 x lo-' p)0. also of conditions in gas and oil wells with high GORs.1 . than its steady-state or terminal velocity). 3. 3.1. Substituting these into Eq. In wells producing wet gas it is indicated to produce at a high rate for several hours (up to 24) in order to clean the well.06 N/m and p. Hubbard and Dukler (1969). which is assumed to be spherical for simplicity. = 1007 kg/m3.5 1 0 . =0. and increasing the constant C by 20 percent to be on the safe side. Hungary prevent the condensation of liquid at the well bottom and the formation of a liquid slug. On the basis of these. Inflow performance curve of gas well OK-17. the minimum gas velocity: where C is a constant whose numerical value is provided by the theoretical considerations referred to. we obtain for condensate Vgc min = 1. No liquid will settle at the bottom of a well if the velocity vgminof the gas flow is equal to or greater than the fall velocity of the largest liquid drop (more precisely.25 (4. It is a fair approximation. PRODUCING GAS WELLS gas well if the fluid flowing in the reservoir contains no liquid phase. o = a< approximately equals 0.292 3. the fall velocity of the largest drops has been derived so as to equal. For a hydrocarbon condensate. so that at the velocity ugmindefined by this hypothesis the entire dispersed phase will be lifted to the surface by the gas flow. = p. a = a. The diameter of the largest drop.1 -7 . by hypothesis.1 -6. however. = p . special care must be taken to avoid the formation of liquid slugs in the well during the test.02 N/m and p. For water. = 721 kg/m3. While testing such wells. we shall discuss here the theory and calculation method of Turner. is determined by its kinetic energy and surface tension.~p)0'5 9 3. The fall velocity of smaller dropletsis less. = 100 bars.8 for wells also producing water. 3.47 4 6 lo5 ~ Tc 224 Fig. Little is known to the present author about the accuracy of the various relevant calculation methods published in literature.1 -1. (di= 0. 3. by the expression for vgcmin furnished by Eq.. WELL TESTING and for water For gas of temperature T and of pressure p flowing through a section of area A at a velocity v. .2). The above relationships hold of course for production through the annulus as well as through the tubing. T. the derivation of Eq. in which the slowest gas flow is at the shoe of the tubing through which the gas is Eing produced.= 224 K). the the wellhead pressure will first increase. Section 8.10) gives Replacing o. = 1. qgnmin parameters valid there. The temperature of gas rising in a gas well is influenced by a number of factors even if flow is steady (cf. where pressure is greatest.83.3.1 . M . Find the least rate of production preventing liquid slug formation in a well producing also water. we get q. By Eq. = 21 kg/kmole (p. Testing should therefore be camed out so as to change the temperature of the gas stream little or not at all.= 2 7/8 in.2. If e.=1.01 bar.1 . in order to bring about a comparatively wide warm zone around the well. 8. = qgnmin as the least gas flow rate that will still prevent the formation of a liquid slug in the well.062 m). This can be achieved by producing the well for a longer period at a comparatively high rate before testing..8. p. d. p. T.By Eq.1. furnished by Eq.. Gas flow velocity in steady-state flow in a given well is slowest at the is therefore to be determined using the tubing shoe.= .= . 1.g. Example 3.. T 330 i o o x lo5 =2-18 and T.= 288.1-2 furnishes a z =0.7 for wells producing gas plus hydrocarbon condensate. The results of well tests are affectedalso by the circumstance that the temperature of the flowing gas is modified by the test.1 -9. 3. a flowing gas well is shut in. = 330 K. 3.l.2 K. or by the expression for vgwmi. the general gas law (cf. p p=-= p. =46 bars and T. but may subsequently decrease as the well cools off. The operating points will thus be far enough apait.294 3. PRODUCING GAS WELLS It is best to determine the B H P of the shut-in well by means of a pressure bomb and to calculate the flowing BHPs out of the wellhead pressures. The lengths and consequently the hydrostatic pressures acting on the well bottom of the gas and liquid column in the well are consequently unknown. succesive flow rates should increase as this reduces test duration as compared with the opposite sequence. because in wells producing wet gas the formation of a liquid slug after shut-off cannot be avoided. best suited precisely for the testing of this type of well. . During subsequent production.1 -5 can be established by several well testing methods. which improves the accuracy of establishing the performance curve. The steady-flow test is used only if reservoir permeability is rather high. . as otherwise testing at any operating point may take days and even weeks. If the ID of the tubing is large enough as compared with the OD of the pressure bomb. This is the feature which gave the test its name. then wellhead pressure is to be reduced by at least 5 percent in the first stage and by at least 25 percent in the fourth.1 -5 valid for steady flow is usually established after suitable processing of the data furnished by these one-day or even shorter tests. gas velocities prevailing in the tubing may be high enough to sweep up the conventional wireline-operated pressure bomb. and gas velocities are rather low. in the second. too. and the flowing B H P recorded or calculated for each choke. on the other hand. If the well is in addition of comparatively small capacity. until they become stabilized. This results in any liquid accumulated in the well being swept out without the intercalation of a 'purifying interval' in the first case. After the stabilization of flow and B H P with a given choke in place. flow conditions will not stabilize any sooner. If the. pressures and outflow temperatures are recorded at intervals of 30 minutes.1. the isochronal test and the Carter method.capacity of the well is comparatively high.If the well produces liquid. or if the flowing temperature is comparatively high. Equation 3. one has to be contented with a smaller terminal pressure reduction. the test can be resumed immediately after changing the choke. In wells of comparatively low flowing temperatures producing dry gas. there can be no objection to subsurface pressure surveys. Three methods are widely used: the steady-flow test. The quantity of accumulated liquid is not known. The two other tests are. The steady-flow test This test is called. It fundamentally consists in measuring stabilized open flow of the well with four chokes of different diameter built in succession. During production. also the back-pressure or multipoint test. with some ambiguity.1. flow during these tests is invariably transient. then the flow rate should be highest in the first stage. It is best to carry out the first test 2-4 hours after opening the well. 3. on the other hand. the advantage of this measure lies in the faster stabilization of temperatures around the well. Then the rate of production is measured. The static B H P is determined out of shut-in data. too. Equation 3. 2. a. and the tubing pressure and gas flow rate are measured at predetermined intervals of time. 1.1-2. 3.Surface flow rates with no well-bore storage effects . performed at a larger-than-usual number of operating points. 3. Characteristic curves of gas well testing after FETKOVICH (BROWN1977.5.2. 3. The line shown in Fig. the well is first produced for a while through a comparatively smallbore choke.2 and 3 hours.295 3. test time is shown in Fig.- Fig. has resulted in a plot providing a fair fit to a straight line calculated by Eq.1 . 112. WELL TESTING The characteristic variation of the gas rate and bottom-hole pressure v. tubing pressures and rates of production are measured at the same intervals of time.1. 3. Now the we11 is reopened and produced through a larger-bore choke. The procedure is repeated. (C) t . . The isochronal test In this test. say.1. by permission of the author) 3.I has been established by a steady-flow test that has furnished the points plotted in the Figure.1 .1.Surface flow rates including well-bore storage effects ---. The well is then shut in until the pre-opening wellhead pressure builds up again. The test. provided each test is started from a state of static equilibrium in the formation. -fp. the radius of influence will be the same for each. O n the . decreases with the duration of the test. PRODUCING GAS WELLS usually with two larger-bore chokes. .296 3.] to a given test duration (isochronal points) defines a well performance curve that can be described by Eq. The piezometric surface visualized above the horizontal plane passing through the well bottom is rather simple. q gbelonging . This latter calculation is based on the consideration that the radius of influence re of the well will monotonely increase with time until it attains the radius pertaining to steady-state flow. Figure 3. distortions of the flow pattern in the flow area of the well by previous stages of testing can be avoided. (ii) The performance equation for stabilized flow is determined from the isochronal curve. The equation of the performance curve for stabilized flow can in principle be established in two ways.5 permits us to calculate the value of C. In bilogarithmic representation.3.5 . the curves take the form of parallel lines. By restarting each phase of the test from the initial wellhead pressure. Dimensionless time is Hence.. ran 10' qpn. (i) By producing the well at one of the chokes until the rate of production stabilizes. 3. and not on the rate of production (Cullender 1955). its shape being determined solely by the circumstances of flow in the current phase of the test.1 . Substitution of the q.3 shows the performance curves of such a test. 3.p ~ f ) . and pWf values thus obtained into Eq.1 . if several test of equal duration are successively performed at different terminal rates of flow. m3h Fig. shifting towards lower rates of production as time goes by. The exponent n of the equation is the same for all parameters N. denoted C' to indicate transient flow. and the coefficient.1 -2. flow must not be hampered by any operation. b shows the characteristic change in the gas production rate and bottom-hole pressure during testing.1 ..1 . Figure 3. 3. During production. The instantaneous radius of influence of a given gas well has been shown to depend solely on the dimensionless time N. Isochronal well performance curves Each set of points [ ( p ~ . = 170. The static reservoir pressure determined from the pressure-build-up curve is pws = 173. 1963). which in turn reduces the rate of inflow into the well.1-2.. = 2. it represents no improvement over the isochronal method.4 bars.1 . When rk=r.12(p. B H P prior to shut-in is pwf= 149.Pwf Pws -Pwf 3 where p.4 bars. Example 3. the factor C for stabilized flow is then given as C = c x C' (Hurst et al.1. and pwsis the static B H P .08 1 x 10. flow into the well has stabilized. as far as well performance is concerned.3 bars. c = Pw1. . WELL TESTING 297 circumference of the circle defined by the radius rb reservoir pressure will be p..1 . According to the authors cited. = 3.11. because the rate of pressure build-up is determined by the same parameters as the relationship between the factors C and C'. B H P measured 8 hours after shut-in is p.5 of stabilized performance now becomes q. In the Carter method. 3...The reduction factor can be calculated out of the data of B H P build-up v. .3.By Eq. The increase of r: consequently entails a decrease in the mean pressure gradient of flow within the formation.708 x 10.. -p$f)0'80. time when the well is shut in after a test phase of duration t. Description of the method can be dispensed with as it is more closely related by its nature to the subject of reservoir engineering: also. .P$f)0'80.. pwf is flowing B H P prior to shut-in. q.will remain unchanged. Equation 3. and hence.12(p%. Establish a performance equation for stabilized flow if the 8hour isochronal performance equation is q. =pws. short test runs with just two different bore chokes are sufficient if the rate of production remains unchanged throughout the test (Carter et al.. 1963). is B H P after shut-in of the same duration as the preceding test. and the B H P . pwf. The factor C' derived from production data over a space of time t is to be multiplied by a reduction factor c.. This may be due. N . The subscript number indicates the serial numbers of the successive phases of the steady-flow test.10. and the exponent n of the performance equation will deviate from the true value. In the following I shall describe Clark's method (Katz 1959) of transforming steadyflow performance equations into isochronal.13 where.. e. is the duration of test production through the first choke.. 3.1 . 2 3.10 denotes time passed since the beginning of the steady-flow test. q. Transformation of the performance equation derived from the steady-flow test into an isochronal performance equation When performing a steady-flow test. the well produces some liquid. If e. can be calculated using the equation 1 N..] determined by the steady-flow test is adopted as the first point of the isochronal graph.. given time. Transformation is performed by dividing by the correction factor K ithe values A p i i = (p.t.. 3. If N. to a wellhead pressure change so slow as to 6e mistaken for zero by the observer. -p$. > 100.).g.1. In the case under consideration. which may sometimes prove quite difficult.3. The other points of the steady-flow test have to be transformed into isochronal points valid at the instants ti.1 . The line connecting operating points thus established is of course wrong..3. The significance of the correction resides in the fact that in certain cases it may be an advantage to test the well without intercalated shut-ins.. -ptJi) pertaining to flow rates qgni determined by the steady-flow test. c. . although. then N.g. is the dimensionless BHP at various instants of dimensionless time. = . a liquid column may accumulate on the well bottom during shut-in and fail to be removed by subsequent low-rate production. by Eq. 3. PRODUCING GAS WELLS 3. . The characteristic change of the gas production rate and that of the flowing bottom-hole pressure as a function of time is shown in Fig. The first point [(p. each belonging to a different choke size.(In N . the parameter t in Eq. + 0. The flowing B H P can then be measured only by a pressure survey.1 .80977) . it would build up to a significant value. The correction factor is given by the equation where N .. Points incorrectly determined for the above reaaJn can be converted by calculation into the points of an isochronal graph. it may happen that production through a given choke does not attain a steady state.1-2. 1 Serial number dc.11 (Hungary).299 3. 4e mm 1 2 3 4 10 8 6 4 t m3/s Apt.1 .12. r.223. and K i using Eq. calculate the corresponding values of N. Data measured on the well Algyo .7 53.895 x l o a 5Pi s.1. A&/) data established by the test is Now by Eq. 3. are listed in Table 3.13.322 0.1 .10. Using this equation.1. pg= 1. 3.4 116.1. find N. using Eq. cg=4. WELL TESTING Example 3.=0. The following physical parameters were found to remain constant in a good enough approximation throughout the entire test: kg= 1. @=0.864 0373 262. dJ8 ... for various values of t.77 7 14 21 28 a-' 1 Fig. 49 . and then. lo2 bar2 h 1.1 195.3 (after Mihily Megyeri).532 1.084 m.1 -4.1 .1 .61 x I/bar. established by steady flow interrupted-before complete stabilization. Divide the Table 3. 3. The equation of the line defined by the plot of the (q. 3. Establish the isochronal performance equation for t = 7 h.432 x 10-l4 m2..1. The maximum point of the wellhead pressure curves is called flow point by Green.1 . and the gas rate belonging to it is the smallest rate that can be achieved using the given tubing size (Green 1978).2 . To a gas comparatively rich in liquid. make it reasonable to change the completion quite considerably.1shows the inflow curve of a gas well also producing liquids. are discussed in the next example. values of Aptf by the appropriate correction factors.3. together with any other strings of tubing conduits and other equipment in the well. The equation of the line fitted to the points thus established is q. Pressure drop in a general way is the less. 3. For dry gas or gas very low in liquid."(pts 2 -p. = 2. Maximum feasible tubing size is limited by the ID of the production casing.2 will apply. while curve I1 shows the wellhead pressure curves valid at different tubing sizes. In dimensioning the tubing it is necessary to see that pressure drop due to flow resistance is comparatively low and the wellhead pressure of the flowing gas is the least permissible value or even less.. however. the considerations in Section 1. the greater the tubing size.j) 0. The cuwes can be determined as discussed in Section 2. 3. no flow point of this kind exists. The isochronal performance graphs established by referring data of a steady flow test to t = 7 h are plotted in a bilogarithmic system of coordinates shown as Fig.1 -(b). In wells producing dry gas.754 . one may apply Ros' theory (Section 1. The changed importance of certain production parameters may.4. dimensioning the tubing A gas well may be regarded as a flowing gaseous oil well whose well fluid contains little or no liquid. Curve I of Fig.2. the smallest possible rate can be produced. . The operating curves.3.1 -4. through the tubing string. characteristic of wells producing dry gas.1 -(f)). PRODUCING GAS WELLS Table 3. The results are listed in Table 3. or if the flow in the tubing string is single phase. but. Well completions may thus be identical in principle with those of flowing oil wells.1-2.054 x 10. Well completion. 3. The pressure drop of gas rising in the tubing will have to be calculated differently according as the gas produced is dry or wet.2. p.3. The standard-state density of the gas produced is p.3 -39.301 3.2-3 shows sketches of some typical completions..=0. At a flowing B H P of 90 bars. corrosion and erosion. L . Clearly..2.1 "C. 1. The sealing of the male-female couplings can be improved e.12. Find the optimum tubing size if q.. Figure 3. The surface ( p W f . qgn Fig.2-2.= 69 bars.2 . temperature and pressure changes during production must not result in a loading of the string to yield or collapse. by the use of teflon powder. (iii) the avoidance of the accumulation of a liquid slug on the well bottom during production. = 500. = 2000 m. The least permissible wellhead pressure is pTOmi. tubing. A useful review of modern high-pressure gas-well completions has been given by Speel (1967). Wellhead pressure curves for gas wells. Wellhead pressures p. is expressed by means of Eq. The threads of the tubing string should provide a perfect seal.. The mean flowing temperature is estimated at 86.2 . (iv) also.=69bars in the line A-B.4. a wellhead pressure of 69 bars will be ensured by 4 112in.) is intersected by a plane parallel to the base plane and passing through pTOmi.g.2.000 m3 of gas per day is the greater the less the flowing BHP.I.2-4.d. The pressure energy expended in producing q. = 500. This will flow under pressure and fill out the minor unevennesses of the thread. or by the use of plastic seal rings. 3. The dimensioning of tubing for this type of completion has been discussed early in this section.. Fig. (ii) an automatic shut-off of the gas flow in case of damage to the wellhead.2. The wellhead equipment is similar to that described in Section 2. This is facilitated by special male and female threads (cf. 1.. (v) It should be possible to perform workovers. When designing the well completion it is necessary to bear in mind the need for (i) protecting tubing from damage due to temperature and pressure changes.000 m3/d. repairs and shut-offs simply and safely. however..I .881 kg/m3. tubing only. flowing BHP declines during production from 190 bars to 90 bars. 3. belonging to several BHPs and tubing sizes are calculated using Eq. after GREEN (1978) The results have been plotted in Fig. WELL COMPLETION Example 3. A tubing of size exceeding the maximum prescribed by the . to be used when the well is produced exclusively through the tubing. up to a flowing BHP of 140 bars. Solutions (a) and (d) are single completions. 3. the prescribed gas flow rate can be achieved through 2 718 in. 2-2. b can be used when the casing is not expected to suffer damage during production (Ledet et al. the plunger is out ofthe way in a tubing attachment (lubricator)installed on the Christmas tree (cf. say 2 and 8 times a day. Section 2. 1968). Intermittent production of liquid may be controlled e. can be facilitated e.302 3. so as to preclude appreciable increases in BHP. by the opening and closing of the tubing outlet. which now plays the role ofa 'dewatering string'.A motor valve under time-cycle control shuts off the flow line between. or. the gas lift valve opens as soon as a liquid column of sufficient length has accumulated above it.g. It may be of the differential. The large crosssection of the annulus restricts flowing pressure drop in the gas. by gas lift valves installed close to the tubing shoe. This completion permits the production of gas at a fast rate. 3. The plunger then sinks to the bumper spring installed at the tubing bottom. The controller now reopens the flow line and formation gas lifts up the Fig.2-3. The solution shown in Fig. it may be controlled by a retarder.7).g. The second solution is . in the Baker-Merla system. PRODUCIN(> GAS WELLS criterion of total fluid removal can be used if the well is equipped for plunger lifting (Bennett and Auvenshine 1957). The accumulating liquid is 'blown off rather often. In the first solution. During production. The annulus of comparativ~lylarge cross-section will produce dry gas because the flow section is greater than the maximum permitted by the criterion of total fluid removal. 3. or tubing-pressure-operated type.4. Periodic opening of the tubing head will permit gas pressure in the annulus to remove the liquid through the comparatively small-size tubing. any liquid will accumulate at the well bottom. The economical removal of liquid accumulated in the tubing. sucker-rod pumping or the addition of foam-producing chemicals (Nichols 1968). a plunger lift operated in the tubing. Influence of tubing size and bottom-hole pressure upon wellhead pressure of a gas well plunger together with the liquid column above it. Foam- (a) (b) (c) (d Fig. Density of the liquid is chosen in dependence on formation pressure. to permit the fast killing of the well (by opening the valve in the packer. The main difference is that gas is produced through the annulus and the tubing serves for dewatering only. Gas flow rate in the casing will tend to be below-critical. In the large cross-section ensured by the combination of the two conduits. Low viscosity results in ease of pumping. Also in this case. Higher-density liquids include CaCl. Several types of liquid are used. and easy aeration by inflowing gas. dissolved in fresh water. c. Their thorough mixing with water and gas is ensured by suitable means. to protect the casing string from gas pressures higher than the hydrostatic pressure of the liquid column. and two. the well bottom can be flooded with the liquid stored in the annulus). or ZnC1. This solution might be economical in wells producing both gas and water at comparatively high rates but at a comparatively low flowing BHP. The sucker-rod installation is quite conventional. and unaffected in its properties by the pressures and temperatures prevailing in the well. as well as from gas corrosion.2-3. The liquid in the annulus is of lowviscosity. Foaming water can be removed efficiently from the well by gas pressure. 1978). non-corrosive to the tubing or casing. fast flooding of the well bottom when the well is to be killed. densities may range up to 1900 kg/m3.In the solution shown in Fig. In the solution shown as Fig. The . after SPEEL(1967) le producing chemicals are fed in batches to the well during periodical shut-offs. the casing must not be damaged by the well fluid. pressure drop due to flow resistance is comparatively small. the annulus is packed off at the tubing shoe and filled with liquid above the packer. Periodical shut-offs of the casing head will push the liquid accumulated in the annulus into the tubing whence it is removed by gas pressure. well fluid is produced by continuous open flow through both the annulus and the tubing. This method is most economical in comparatively high G WR wells (Kutuvaya et al. WELL COMPLETION similar to the plunger-lift installation described in the foregoing section. Typical gas well completions. 3. The most important thing to be kept in mind is the choice of corrosion-resistant pumps and rods. d.2-3. 3.2. The solution has two purposes: one.2-3.303 3. Slightly alkaline fresh water or fresh water with a dissolved inhibitor will often do. 3. surmounted by the tubing head 6. however. Tubing 2 are of' '/2 in. size. size each. PRODUC~NGGAS WELLS pH of these solutions is rather low. size can be opened to the surface tJmeans of a bleed valve. their corrosive tendencies have to be kept in check by the addition of an inhibitor. one wing valve 9 and one lubricating valve 10.2 -3. casing string and the production casing can be opened by means of valve pairs 4.2-4 shows the wellhead equipment used in the GFR for a well of this type (Werner and Becker 1968). Christmas tree of high-pressuredual gas well completion. . The outer annulus of 18 5/8 in.304 3. Figure 3. Each string of tubing is provided with a pair of main valves 8. There is a blow-out preventer 5 closing on the tubing attached to the casing head. Figure 3. The Christmas tree assembly 7 is of the monoblock type. Fig. The annulus above the upper packer is filled with liquid. after WERNER and BECKER (1968) Formation pressure in the reservoir traversed by the well is 379 bars at a depth of 2500 m. e shows a high-pressure gas well producing two zones.2 -4. Production casing string I is of 9 5/8 in. 3. the annulus between the 13 3/8 in. The sedimented sulfide scale settles on the well equipment and aggravates. the operation of the safety valve or gas lift valve.3. without the presence of water between 0.g. deposits in pip's In gas wells corrosion hazard usually comes from inside.* The effect of CO.S: one of them is the so-called hydrogen embrittlement. In the presence of water. Corrosion of gas wells. a galvanic cell comes into existence. a current starts from the Fe pole towards the FeS pole.3.. this reduces the tension of the fracture in the immediate neighbourhood but facilitates the progress of the fracture.S content is called sweet gas. the resulting electrolytical corrosion may cause punctures. It has been pointed out that the extent of the fracture and bursting is greater in pipes made of steels of higher strength. becomes corrosive if the well fluid contains water. the other is sulphide stress cracking. Dissolved in water. The reaction equation is The iron sulphide thus formed is a dark powder or scale. and loaded with greater tensile stress. is described by the following reaction equations: CO. which may burst or fracture the pipes. For sulphide stress cracking there are several explanations.S is called sour gas. Greater pressure and temperature and high production rate facilitate corrosion. while above pressures of 2 bars the presence of CO. As well as this hydrogen migrates into the threedimensional stress region joining the fracture front.5 and 2 bars. Corrosion is also possible. however. turns into carbonic acid. CORROSION OF GAS WELLS 3. The reason for hydrogen embrittlement is that due to the reaction the atomic hydrogen that developes diffuses into the undeteriorated steel and.3. having a higher electrode potential than iron. inactive in itself. causing very high local pressures up to lo6 to lo8 bars.S and corrosive formation waters as the main agents. e.1 and 1 kPa. CO. organic acids. entering the crystal lattice of the iron. or sometimes even stops. will surely lead to corrosion. while the gas with no H. and thus further fractures and the progress of fracture is facilitated (Smith 1977). H. . is between 0. in the form of CO. One is that the hydrogen atoms in steel combine into hydrogen molecules. Two further kinds of damages can also be caused by H.S if there is also water present in the wellstream and the partial pressure of the gas is greater than 0. This * In Anglo-American practice the gas containing H. . the operation of some assemblies. Hazardous corrosion is caused by H. significantly decreases its elasticity. According to Casner and Smith hydrogen adsorbs on the surface of fracture or erroneous lattice.01 bar (1 kPa). Corrosion is possible if the partial pressure of CO. recommended for wells with corrosive streams. the tensile strength and yield strength of the material must be relatively small. and H. In the annular space between the two tubing faces that are not in direct connection. Coating the inside of the tubing with plastics may prove an efficient solution to prevent corrosion.3 . great turbulence may emerge that can lead to harmful pitting above the coupling (Gazs6 1980). To reduce this impact several different methods are used.-Significant erosion Fig. Soviet petroleum engineers use completion with the tubing shoe resting on a seat fixed to the casing string (Nomisikov et al. To reduce corrosion. pipe hardness and tension referred to yield strength. . is smaller than that of the greatest strength P-105 steel used in non-corrosive wellstreams. This damage source will be eliminated by using integral tubing joints of internally smooth cross-section (Vaghi et al. Of the API pipe materials shown in Table 2. L-80 and C-95. 1979).1. 1976). while the tubing and annulus are carefully sealed from each other. after HUDGINS(1970) and corrosion can be facilitated by the inner profile of the conventional tubing couplings. The tubing shoe must not be fixed to the packer or tubing anchor if the tubing string is long and a significant temperature variation can be expected due to the opening and shutdown of the well. on the other. PRODUCING GAS WELLS phenomenon is called stress corrosion. the lower end of the tubing can freely move vertically for several meters. The seal element is equipped with multi-unit seals of acid and heat resistant material. 1970). 1970). fixed only at the top. Due to temperature drop a stress rise may occur in the tubing string fixed at both ends that may cause the string to break. The tensile strength generated in the tubing proportionally increases with the length and specific weight of the tubing. 3. on the one hand.3.S resistant must be applied.306 3. Figure 3.1 represents time up to corrosion-controlled fracture v. With suspended tubing strings. For wells of this type the Packer-Bore-Receptacle method is used (Texas Iron Works) where. tensile stress can be reduced by applying so-called telescopic tubing that is adjusted to the wellstream velocity and the diameter gets gradually smaller from the top towards the bottom (Hamby et al. and.3 -5 it can be seen that the yield strength of steels C-75. Incidence of corrosion failure v. through the special plastic coated bore of the packer. rigidity of the pipe (expressed in terms of Rockwell hardness) and tension referred to yield strength (Hudgins. pipe materials that are CO. 10 week interval 8. valves).g. or through a special pipe string. Due to the high pressure gradient emerging around the wellbore in the formation sand grains separating from the reservoir rock may cause grave erosion. The bottom-hole choke is also favourable (see Section 2.g. The greater the wellstream velocity the shorter the life of the inhibitor coating. and from there together with the wellstream it gets into the well. if the gas in the flow line gets so cold that at flowing pressure hydrates may form again. in an 8 . as a solvent.e. CORROSION OF GAS WELLS 307 Corrosion can be successfully reduced by applying suitable inhibitors. while keeping the wellstream and well parameters in question always in mind. these are hydrocarbon hydrates. Due to the cooling caused by gas expansion in the wellhead choke.5-(b)3). Its injection into the well can be achieved in several ways. In this case it gets into the wellstream either through the open annulus at the bottom. The separating solid hydrates may obstruct the gas stream totally. In gas wells the presence or formation of three solid components must be taken into consideration. is injected into the formation. Methods of prevention: the gas must be heated by a heat exchanger upstream of the production choke. thus its formation must be prevented. sand and elementary sulphur. In such well completions a large part of gas expansion occurs at the well bottom. the adjoining wellhead assembly and the inner surfaces of the gathering and separating systems situated on the surface. An instrument for this is a small pipe containing . in the form of batch treatment. and. The sandface of the well must be formed so that no significant quantity of sand can get into the well. At very high production rates. For this reason it is expedient to select a tubing size in which the flow velocity does not exceed 10 .3. This injection can be performed together with the addition of the corrosion inhibitor. In steam-saturated gases at high pressures and low temperatures solid hydrocarbon hydrates may form (e.3. furthermor. however. An often successful way of protection is if the inhibitor. A favourable case for the presentation of the formation of hydrates is a large production rate. it should be remembered that even from properly consolidated sandstone reservoirs some sand may be swept up by the wellstream. e. sedimentation of this kind may be expected in the wellhead assembly and in the front section of the flow line. avoiding the packer.3. I is advisable that the inhibitor should be selected under laboratory conditions. glycol or alcohol. The highest rate that can be produced from the well without sand grains must be determined by experiment. then some chemicals to prevent the formation of hydrates are added at the wellhead. it gets into the injector valve and then into the wellstream. It can be continuously injected into the annulus. see Katz 1959). Its advantage is that it protects not only the inner surface of the tubing but also the equipment attached to it (e. Thus the gas will not cool to the temperature required for the formation of gas hydrates.15 m/s.12 m3 of diesel oil with a ten percent inhibitor content is injected into the producing wells and this provided proper protection (Gazsb 1980). ethylene. In the Schonkirchen reservoir. 5600 m deep. when the surface temperature of the gas is so high that no hydrates form even after expansion. The "inhibitor coating" ofthe inside pipe wall is worn by the wellstream. Presence of sand can be indicated in several ways.g. and how dangerous it is. It can be prevented if sulphur solvent is injected into the wellstream at the bottom. Testing includes caliper surveys of the tubing. PRODUCING GAS WELLS compressed gas. at what distance and to what extent the gas stream of a given concentration is resolved.308 3. i. Smith (1977)describes an equation which can help determine. API Spec. Only metal-to-metal seals may be used as main sealing elements. Basically. Due to this the pressure of the gauge decreases to the flow line pressure. may reduce the flow area or may even plug the tubing. may cause immediate death.025%of the H2S content. then each part of the wellhead assembly must be checked with greaterthan-avarage care. among assumed conditions. i.e. (1976) In natural gas with an H2Scontent the corrosive impact is damaging not only but it can also cause poisoning by getting into the atmosphere. measurement of the inhibitor and iron contents of the liquid in the wellstream. Wells of the deepest hydrocarbon producing formation in Europe. which is installed in the flow line after the wellhead. The wall of the small pipe that faces the gas flow direction is a rather thin membrane that can be punched by sand grains flowing at a high velocity. In GFR for instance monoethylamine is applied and Hofbauer et al. which. the wells of the Malossa . A concentration of 250 ppm. even during production. i. 0. The value bearable by human beings is 10 -20 ppm. the different danger levels due to H2Scontent is the main reason for the continuous checking of wells producing gas with an H2Scontent. 3. but teflon seals are used in addition. Gas treating facilities for gases containing H. Fig. settling on the tubing well.e. If there is a danger of corrosion. after HAMBYet al. (1976) discusses the harmful side effect of this method. The wellstream of gas wells may also contain atomic sulphur. corrosion may emerge. 5AX lists the up-to-date nondestructive testing methods of the tubing.S. The condition of well equipment must be regularly checked. Its pressure is indicated by a gauge. and the installation and checking of corrosion probes.e.3-2. From tank 18 pump 17 sucks alcohol. however.8 m3 water.65% CH. gets'into pit 12. CORROSION OF GAS WELLS 309 field in Italy.4-0. The pressure.1. produce wet gas of 0.3 -2 (after Hamby 1976).3. If. No condensate can be found in the wellstream. or.9% C 0 2 and 45 .59% C 0 2 and 0.6 ppm H2S content. if the surface treating facilities fail (Vaghi et al. The wells can be checked directly and from a distance by applying TV cameras in a check-up cabin. it is necessary. while flow line 3 may produce through the annulus. temperature.Figure 3. flows into the flare. Valve 21 is equipped with a rupture disc. Killing fluid can be pumped into the tubing through line 23. The wellstream is heated in heat exchanger 4. through line 22. inhibiting the formation of hydrocarbon hydrates. but it is saturated with steam and together with 1 million m3 gas it produces 1. The wellstream contains 27 -46% H2S. 1979). bypassing the latter. 3 . .3.4. The wellstream is automatically shut down if the tubing pressure is higher or smaller than the allowable value. which is injected into the system through lines 19 and 20. and in normal operation it flows through line 5 and measuring instrument 6. through line 11. The separated water. . Well 1 through flow line 2 produces through the tubing. it gets into the liquid knock-out 9 through sefety valves 8. is a sketch of the surface treating facilities used in the Thomasville gas field of the Shell company. and from here into the central gas treating station. into line 7. From tank 14 pump 13 sucks corrosion inhibitor through filter 15 and pumps it into the well annulus through line 16. and from there into flare 10 where it can be flared. rate of the wellstream and composition of the water sample is regularly checked. In case of overpressure of the flow line the gas. or. Kastrop 1974). Hydraulic pumps are driven by a hydraulic engine integral with them.The bottomhole pumps of today can be subdivided as follows.CHAPTER 4 PRODUCING OIL WELLS . the bottom-hole pump may be of plunger or centrifugal or some other type. in the decade starting with 1859.The fluid entering the well from the formation is lifted to the surface by a pump installed below the producing fluid level.1.800 artificially lifted wells of the Soviet Union and 85% of the 474. 1961). Of the sucker-rod type of pump. The rotating motion of the motor shaft can be transformed into reciprocating motion in various ways. the installation is called a hydraulic sucker-rod pump. 7he sucker-rod pump is a plunger pump performing a reciprocating motion. and lowered to the well bottom. the installation is called a crank-type or walkingbeam-type sucker-rod pump. In rodless bottom-hole pump installations. . the installation is called a derrick-type sucker-rod pump. . The reciprocating motion of the surface drive is communicated to the pump by a string of sucker rods. According to data for 1974. If the transformation is by wireline and pulley. or in the well. The prime mover of the pump is installed either on the surface. 85% of the 48.000 artificially lifted wells of the United States are produced by walking-beam type rod pumping (Grigoraschenko 1974.deep wells were drilled with wireline rigs whose bit-lifting horsehead was used after well completion also for sucker-rod pumping (History . Its prime mover is installed on the surface. driven in its turn by a power fluid to which pressure is imparted by a prime mover situated on the surface. a hydraulic means of transformation is adopted.(2) 4. Centrifugal pumps integral with an electric motor. it is integral with the pump. This type is called a hydraulic (rodless) bottom-hole pump. Further rodless bottom-hole pumps include electric membrane pumps and sonic pumps. Numerous types of bottom-hole pump have been developed from the mid-nineteenth century onward. are called submersible pumps. We shall therefore concentrate in our following discussion on the peculiarities of walking-beam type sucker-rod pumps. the walking-beam type is most widespread. The bottom-hole pump unit comprises all the mechanisms and equipment serving the purposes of production.. Production by bottom-hole pumps Production by bottom-hole pumps is a mechanical technique. If a crank and a flywheel are used. In long-stroke hydraulic pumps. in the latter case. According to Coberly. . Attached to the tubing shoe installed in the well is pump barrel 10. the polished rod.I). the power of electric motor 1is transferred by v-belts to a gear reducer 2.1.1. 8 and a beam counterweight 9. . . provided that I. The longest stroke that can be realized does not usually exceed 3 m.1. Walking-beam-type sucker-rod pump installation variation of polished-rod load over the pumping cycle is balanced by one of various means. The crank length and hence the stroke are both variable within limits set by the design. is hung from carrier 4. not to be detailed here. PRODUCTION BY BOTTOM-HOLE PUMPS 4. This number determines (is equal to) the number of double strokes per minute (spm) of the sucker rod. in which plunger 11 is moved up and down by the rod string.4. = I . a walking beam 6 and the horsehead 7. The stroke of the polished rod 3 is twice the length r of the crank. The Fig. 3 and 25. The specially made and machined top unit of the rod string. In the case shown in the Figure. This reduces the rather high rpm of the electric motor to between. Sucker-rod pumping with walking beam-type drive Referring to the sketch of a walking-beam type sucker-rod pumping unit (Fig.4. The structure moving the polished rod is composed of a trestle (samson post) 5. During the upstroke.1 .1 . 4. Power is transferred from the crank to the walking beam by the connecting rod (pitman) of length I. say. this balancing is performed by means of a crank counterweight.1. (a) 1. solve some problems also by the new API method. thus providing insight into operating conditions and their control. These can be static and dynamic. travel.The greatest depth of installation of the bottomhole pump in the check wells was 3150 m. Instantaneous load is a function of a large number of factors. we shall d o so in the sequel. it should describe to a fair degree of accuracy the variation of polished-rod load v. F. At the same time. it would have to account for a large number of factors. the static . although presumably less accurate. What is to be expected of such a procedure is that. is deemed to give better insight into operating conditions. can also be neglected. It occurs as a transitory phenomenon at the start of pumping in almost every well produced by a bottom-hole pump. One modern method of calculation is that contained in API RP 11L.312 4. Check measurements on 77 wells showed the mean calculated value of F. however. firstly. in the polished rod. and secondly. It is subject to considerable variation during the double-stroke pumping cycle. In the case of continuous production. however. The deviation between calculated and actual data is often quite large with each procedure. the producing fluid level is high.. to exceed the mean measured value by as little as 1. the travelling valve is open and the standing valve is closed: the plunger sinks in the fluid filling the barrel. The various procedures of calculation are based on various simplifying assumptions. The static polished-rod load during the upstroke is F. One of the reasons for this is that a rigorous treatment would be very complic'ated. and suggests that comparatively simple relationships may be as satisfactory for design purposes as the most complicated ones. If. in which case F.. but sometimes also in continuous-lift ones. and the plunger can lift the fluid filling the annular space between tubing and rod. is usually small enough to be negligible. that it should give results sufficiently accurate to permit the correct choice of the pumping unit to be used on the well under consideration. PRODUCING OIL WELL-2) travelling valve 12is closed. (a) Loads on the rod string and their effects Several methods have been developed for calculating the polished-rod load. During the downstroke.. then. this reveals the limits of sirnulability to be rather narrow. so that fluid may enter the barrel through filter 14. During continuous production.41 percent (Griffin 1968). A high producing level is frequently encountered in intermittent-life wells. first published in 1967. may play a significant role. Rod load for solid-rod strings. We shall. This method requires the use of auxiliary diagrams given in the standard. some of which are or but approximately known or totally unknown at the time of designing. In the following we shall discuss a different procedure based on a consideration by Muravyev and Krylov (1949) which. -Rod load is maximum in the top unit of the string. standing valve 13 is open. that is.. the producing fluid level is very often quite close to the bottomhole pump. = 2.y.33 x lo4 ~ / r n ~ as an average of the data in Table 4.b = GIL GbL.4 The rod string immersed in the liquid is invariably stretched by its own weight. Assuming y. and its wet weight. we get . + F. immersed in the liquid. The ratio Gr/Ar is nearly constant for standard sucker rods (round 8. in a fair approximation. During the downstroke. and hence If there were no rod string in the tubing.I ) . yr=7. 4.-y. PRODUCTION BY BOITOM-HOLE PUMPS 313 upstroke load in most wells produced by sucker-rod pumps is.1 .=F.. that is. = A. 4. reduced by buoyancy.. = G~LFGbL. Since liquid load equals the weight of the liquid of gravity y.weight per metre of the sucker rod in air G. the weight of one metre of liquid column would be G. the static polished-rod load equals the net wet weight of the rod string. =8826 N/m3 and substituting the numerical values into Eq.yr.. . = F.7 x lo4 N/m3 and E. Now where b is the weight reduction factor and static load can be expressed also as + F.+F.4.1 ..5. above the pump operating at depth L. F. is G:= A&. by Hooke's law.1 . F. In general.1. = A. Its stretch is.06 x 10" N/m2.) . for 1 1/8" ** For pin-and-pin rods and for box-and-pin rods L. which is described. mm an2 m Nlm 12. Main data on API sucker rods (after API Spec.2 25. + The basic stretch of the rod string in a given well fluid thus depends essentially on the length of the rod string alone.05 m. which is of a primary interest to our present discussion.07 6-41 6.35 m.43 6. Early in the downstroke of the polished rod.3 53..4 28. and also by the weight of the liquid column acting on the plunger during the upstroke. 11B (1974) and API RP 11L (1977)) Nominal rod diameter (d.1 -2. we shall for the time being identify stretch with the stretch fraction due to load variation.8 32.43 6.5 16-5 23. polished rod.88 5. The change in liquid load entails a change in stretch. e. At the top of the polished-rod stroke (point A). and the plunger stroke equals the polished-rod stroke less the stretch of rod string plus tubing.43 10. This can be verified. likewise by Hooke's law.) 1/2 518 314 718 1 1 1/8 &** G.98 2. rod string and plunger move downwards at the same speed.43 6.7' 15. to which is added the weight of the liquid column during the downstroke.9 1-27 1. In this phase. + 0 3 8 mm. is We have assumed here a pump barrel diameter equal to the ID of the tubing. By Eqs 4.=6.4.43 6. A. as The tubing also has a basic and a variable stretch.4 42.25 + mm for rods up to 1" diameter.4 and 4. the rod string is fully stretched and the plunger is at the top ofits stroke (point B).43 6.85 3. . -0.g. the string is loaded by its own weight only during the downstroke. Leaving the basic strech due to static load out of consideration.6 19G 22. This is when the plunger starts to actually travel downwards. by the following consideration. Tolerance for all lengths 0. because it is loaded by its own weight during the upstroke. the tensile stress in the rod string gradually decreases to zero which it attains after a travel of ALr.1 . The variable stretch.6 * Tolerance rods. . PRODUCING OIL WELLS-42) Table 4. At fairly low pumping speeds (n < 8 spm) dynamic loads can usually be neglected.1.1 . 1 -9 At comparatively high pumping speeds (n> 8 spm) and great depths (L> 1000 m). d.15.1 .71 cm2.g. The values of A.. Other loads can be described at least approximately (e. a sandy well fluid.88 cm2.4.y. by Eq. 4. The basic stretch of the rod string is. In a fair enough approxi- . In reality. Some of them can be calculated to a fair approximation (e. By a similar consideration.06 x 10'' N/m2.1 . = 22. L. while estimating the other factors or determining them by measurement during production. For practical purposes.1 -6. the stroke reduction for the upstroke is where we have assumed Er= E T = E and sf is the stroke length of the plunger. = 8826 N/m3.5 mm diameter is of 3 112 in. those due to the free vibrations of the rod string). the dynamic factors cannot be neglected any more when calculating the polishedroad load. y.g.2 mm. there are loads that defy mathematical treatment. is 3. 4. the plunger will start to move relative to the barrel only when the plunger has 'overtaken' the lowered barrel. such as a crooked hole. the transformation of motor-shaft rotation into a vertical alternating motion of the rod string).1. and intermittent flowing of the well. This makes the pump barrel fixed to the tubing shoe sink by ALTOagainst point B. we find that Example 4. The play of forces transferred from shaft to polished rod can be given a mathematical formulation valid for a large number of cases. size by Table 4.1.The tubing required for a RWT pump of 63. = 63.5 mm. Dynamic loads may be due to various causes. the weight of the liquid column has been transferred by the closure of the standing valve to the tubing string. .. Find the basic stretch of the rod string and the stroke reduction.2. The stroke reduction is by Eq. highly viscous oil. Introducing the expression G.1 .1 A. finally. a gas-rich well fluid passing through the bottom-hole pump. = A. Hence. changes in the load and length of rod and tubing strings occur at the same time and not following each other. The plunger diameter of the RWT type bottom-hole pump is d. By Table 4. A T = 16. E =2. = 1200 m. are listed in Table 4. PRODUCTION BY BOTTOM-HOLE PUMPS 315 Meanwhile. it will usually do to take into account the force transfer relations of the drive unit.1 . The dynamic load is negligible. 1 35.3 37.0 27.5 33.6 95.9 11-4 15.4 37.5 - 27.3 7.4 29.7 463 50.4 93.5 203 25.6 73.7 31.5 88.9 404 45.5 41.0 31.1 44.7 73. 518 3 274 29.8 29.4 65.2 63.5 69.6 49.8 % 314 4 1 45.6 1 Table 4.7 7.3 37.7 82.4 314 33.8 42.9 82. 314 5 222 23.8 33.1 -2.9 17.0 41.4 33.6 4Q8 33.4 304 % 22.8 56.7 38.3 1 1/16 1 114 1 112 1 314 2 2114 2 112 2 314 3 114 3 3/4 5.1 16.4 26.2 % 33.1 % of 3 / 4 rods 314.8 37.44. S i of plunger 33.9 26.3 45.9 52.6 29-2 105 1 718 1 314 1 518 6 .5 68.3 7.2 27.4 24. 112 mm A.4 I 518 I 112 2 34.8 46.5 71.9 718 1 27.2 72.3 41.5 56-4 64.5 508 57.0 58.3 % of 5/8" rods 518.3 47.3 25. Percentage lengths of rod sizes making up tapered string after API RP 11L (1977) 224 24.2 42.5 26.8 38.3 26.7 29.3 53. 1 in d ~ .2 518 285 306 33.3 37.3 % of 718" rods 718. 2 23.3 32.1 17.7 27.9 82.8 25.6 95.9 27.5 24.7 404 34.1 20.3 51. 718 8 19.0 21.8 294 32.7 in.9 406 44.7 12.4 45.4 298 7/8 42.8 26.5 27.7 657 30 1 21.9 % 60.9 51.0 30-0 33.5 22. 1 10 .0 54.5 1 239 24.4 39.3 38.1 W5 508 57.2 36.5 71.4 15.3 53.6 % of 1" rods 1.3 33.2 49.3 26.7 43.3 25.6 33.3 828 cm2 A.3 % 718 7 54.2 635 69.2 36.7 27.28 314 24.3 257 31. 11/16 1 114 1 112 1 3/4 2 2 114 2 112 2 314 3 1/4 3 314 4 314 *P Size of plunger 5.8 27.4 32.7 35.7 7.6 208 22.2 22.6 15.0 31.3 58.7 30.6 61.6 42.6 1 1/8 19.1 27. 22.9 1 118 20.5 50.5 207 22.2 83.5 36.2 32.8 25.8 29.1 35.4 24.5 26.2 239 25.2 46.6 24.6 98 314 19.1 27.4 28.9 11.mm 27.4 302 33.9 307 % 1 9 19.1 29.2 205 225 25.5 20.3 41.3 102.7 38.1 19.3 25.0 27.3 40.8 38.1 42.9 43.7 % of 1 118" rods 1 718 11 1 1/8.0 39. Increasing the pumping speed may raise the acceleration of the rod string aboCe the acceleration of gravity. but slightly later. including the maximal.The plunger will start to lift the liquid column only after that span of time t. travels down the rod string at the speed of sound and attains the plunger after a span of time t = Llv.takes place at the onset of the polished rod's upstroke. PRODUCING OIL WELLS-2) mation valid for many cases. the greatest total dynamic load appears not at the instant when the polished rod starts to rise. If the walking-beam arms are of unequal length. If this assumption is adopted. 1 . . 4. therefore. according to Muravyev.1 -1) reciprocates along a straight vertical line. and this may cause operating troubles. The maximum dynamic load is where is the so-called dynamic factor. if the walking-beam arms are of equal length.25 (this value may change!) we get and the maximum dynamic load turns out to be * n is expressed here and elsewhere in Section 4.318 4. The acceleration at any instant. Hence. then force transfer can be discussed on the analogy of crosshead-type engine drives. we call it simple harmonic motion. of the horsehead . / 1 2 . the maximum allowable dynamic factor is 05. Acceleration will propagate 4. In practice.5 times more slowly in a gaseous fluid than in rod steel: also. the upper bearing of the pitman (Fig. the acceleration of the liquid column can be neglected: the rod string is in the process of stretching when the maximal acceleration is travelling along it. The maximum positive acceleration of the upper pitman bearing -or. .1 in l/min. and this fact serves to damp the displacement of the fluid. Substituting into this formula the values w =(nn)/30*. the liquid exerts a drag on the tubing wall during its rise. then the expression in the brackets is to be multiplied by the ratio of working centres. then. r = s / 2 and r/l=0. In the relationships to be discussed below we shall usually take into consideration the dynamic load on the rod string only because. and v. If the frequency of the free vibration equals. damped otherwise. Satisfactory agreement is confined in any well to comparatively low pumping speeds. giving integer cycle ratios are called synchronous speeds. Charny's formula (Muravyev and Krylov 1949): where p=(wL)/v. or is a multiple of. then the free vibrations. In practice.give rise to significant excess dynamic loads.4.1 . is the speed of sound (5100m/s).15 is the Mills formula (Eubanks et al. . 1958): The free vibrations of the rod string may in unfavourable cases . PRODUCTION BY BOTTOM-HOLE PUMPS 319 The maximum polished-rod load is to be anticipated after the plunger has started to rise. The frequency of the longitudinal vibration depends solely on the length of the rod string (assuming the speed of sound in the steel to be constant at v. The Slonegger of API formula (Eubanks et al. Pumping speeds.1200 m. i. numerous other relationships are used to calculate maximum polished-rod load. according to more recent research (API RP 11L (1977)) that due to the impact of the long and slim rods and the rod couplings the sound velocity is smaller than the above value. and loads may significantly increase. then This latter formula is in a fair agreement with actual fact for rod-string lengths of 1000. it is 4970 m/s. 1958) is It gives satisfactory results primarily for low pumping speeds and shallow wells. = 5100 m/s): It should be noted.at high pumping speeds in particular . are reinforced by further pulses arriving in phase.e. However in further calculations we will use the value of 5100 m/s. and back again after reflection. Let us enumerate some of these. The sudden load changes at the upper and lower ends of the plunger stroke propagate at the speed of sound up the rod string to the point of suspension of the polished rod. The relationship most resembling Eq. when both static and dynamic loads are maximal.1. 4. the pumping speed. If the rod string is long. the formula gives a value lower than the actual load. This is the case especially when gaseous oils are being pumped: loading iS then sudden. The calculation procedure published in API RP.. from Fig. In practice it is usual not to take intc 12 1./sk. no synchronous vibration takes place as a rule. kr= EAr/L is the spring constant of the rod string. 4. respectively.8 as 07 a6 05 a4 03 02 O ' oo O ar a2 a3 a4 Fig. = F r b + k 1 s k r . After API RP 11L o6 o5 it consideration the load increment due to synchronous vibration. 4. because the longitudinal waves generated by the two sudden load changes per stroke usually attenuate each other.. then the pumping speed is changed sufficiently to displace the frequencies so that the vibrations attenuate each other (no n). . 4. but if the dynamometer card reveals the presence of such. and for tapered strings can be calculated from .1 -3. 4.1 kl 11) 0.1 -20 and 9 Factors k . If the oil produced by sucker-rod pump is gasless.11 has been developed by experiments on mechanical and subsequently on electrical analog models.320 4.1 -2 and Fig. whereas oflloading is gradual and comparatively slow.1 -2. values can be read as function of n/n. and k2 at different F. The maximum and minimum polished-rod loads can be calculated by the slightly modified formula F. PRODUCING OIL WELL-2) The above is rigorously valid only if there is only one sudden load change per stroke. 1 . n = 16 l/min.1 .1-2 are shown in Fig.8% 7/8 in.06 x 10" N/m2.1 -3.5 in. y. s = 1. in percentages. d. and 66. the rod string is tapered. for the tapered strings listed in Table 4. 4. The corrected frequency ratio is n n n no 100 n In.1-4. rods.=2.20 and 4. 4. Fig. 4. pump running depth is L.15..1. it consists of 33. = 1525 m. According to API R P 11L free vibration frequency nb for tapered strings is greater than the value calculated from Eq.1 -2.1 . PRODUCTION BY BOTTOM-HOLE PUMPS 32 1 no of the n/no parameter for straight sucker rod strings can be obtained from Eq. if the liquid level in the casing annulus during production is at L.1 . = 1372 m.4.19. The increase.19. 4. After API RP 1 l L Example 4. Let us calculate the maximum polished rod load by using Eqs 4.37m. = 8826 N/m3.= 1.2% 314 in. The weight of the rod string is . E. 37 x 4.1 .38 x lo4 . 4.0. 1.24 1.1 -4.23 x lo4 - According to Eq. 4.22 The liquid load on the total plunger area is F.322 4.19 0 50 100 130 d. After API RP 1 1 L ..1 . PRODUCING OIL WELLS-2) According to Eq. 4. - sk. mm Fig. 15 The difference between the F.. is greater than in the preceding case. At the same time. the liquid rises and accelerates together with the rod string. because the liquid annulus moving together with the rod string also decelerates together with it. and the sign of 6 is positive in the third . it is. (a)2. On the upstroke. independent of the plunger diameter. and the production rises through the hollow rods.. that is.18: where G.> A.1 -5). F.1 . The casing annulus is not packed off in most cases. values calculated by of the two methods is The load FJr due to rod and fluid friction can also be regarded as dynamic. . F / .1 . It is negligible in most cases. Its value may be significant in crooked wells or if the oil is of high-viscosity or tends to freeze at well temperature. as opposed to the liquid load F. for the solid-rod string. If A.... Relative displacement between well fluid and rod string takes place during the downstroke . According to Eq. may equal A.20.1 . 4. then the second term on the right-hand side of the above equation is zero. 4. Rod load for hollow-rod strings (largely after McDannold (1960)). but it may also be greater or less (Fig. 6 appears with a negative sign in the third pair of parentheses. =A. according to Eq. PRODUCTION BY BOTTOM-HOLE PUMPS and thus From Fig. If A. the bottom-hole pump barrel is usually fixed to the production casing. Its presence may be detected from the dynamometer cards.pair of parentheses.. A.In sucker-rod pumping using hollow rods. This friction cannot be described mathematically... is the friction of the unmoving fluid column against the internal surface of the sinking string. then the pressure acting from below on the surface ABCD reduces the rod-string load. The minimum polished rod load on the downstroke is In practice.2 k .L is the weight of the liquid held by the hollow rod string.47 and so.. 4. If A. so that it does not figure in our fundamental formulae.. then the rod string has to carry the additional weight of a 'liquid annulus'..1 .i< A.. 4.4.1.. 4. = 0. Maximum polished-rod load is calculated by means of a slightly modified Eq. 4. when calculating the friction loss. this simplifies to The stroke reduction due to the change in liquid load is A S A=F LP =A k L2. EA.We shall consider solid-rod strings in what follows below. the velocity thus obtained is further multiplied by 1.1 . PRODUCING OIL WELL-2) only. we get the static loads for the up. EA.1 -5. the corrected production used to give the friction loss is (0) (b) (C Fig. (a)3. Rod string design. In order to account for variations in crank speed. and hence.57. 4. after MCDANNOLD (1960) Putting 6 =0 in Eqs 4.. so does liquid production.1 -23 and 4.y. Bottom-hole pumps with hollow rods. The maximum stress in the polished rod is obtained by dividing the maximum polished-rod load given by Eq.and downstroke as The greatest difference is due to the change in liquid load: But since A. Taking production as a basis.G.L.d.15 by the cross-section of the . the relative rate of flow has to be calculated from twice the daily rate of production. .1 -24.324 4. Thus. Employing the substitution Fr= GrL. The reason for this is obvious: the string section directly attached to the plunger. 4.I . Gr= Grl and L. then the string is continued with rods of the next greater standard size. the length of this second section is determined by the repeated application of the same criterion.27 amax =an1. Ar = All. that the maximum stress must be less than the maximum allowable stress must hold separately for any rod of the string. Keeping this in mind. i. If the two sections do not add up to the required total length. PRODUffION BY BOTTOM-HOLE PUMPS polished rod. one of two design procedures is employed: (i) Rods of the least standard size are attached to the plunger. we get The maximum stress must be less than the maximum allowable stress a. Putting in Eq.. the lowermost rod. To this string section. The string is made up of this size rod until the maximum stress arising attains the allowable maximum. rods of the next greater standard size are attached. (ii) Another procedure of tapered string design is to ensure that the maximum stress at the top of each string section be equal. or the actual stress at the top of any of the string sections farther below. 4. that is. This principle yields for a twosection tapered string . is loaded by the liquid column only. that is.string section designed by this procedure is usually less than the allowable maximum. In practice. whereas the sections farther above are loaded also by the weight of the rods below them. .1 .. rod strings are frequently tapered.e.1. composed of standard rod sizes increasing from the plunger up. given by Eq. 4.uppermost .4. The criterion mentioned in connection with Eq.1 -73.1 -27. we get and hence The length of the nth section counted from below can be calculated analogously: The maximum stress in the top end of the last . 1. In the above equations Example 4. 29.9. = 8826 N / m 3 and 6 = 0. PRODUCING OIL WELLS-(2) Let us assume that Ar2/Ar.9. 12=G11.1 . d. L .z G r 2 / G r l= C . The length percentages of the individual string sections (ISS-s).0 mm diameters.5 mm.326 4.1 Grl = 42-3. calculated upwards from the bottom. 22-2 and 19.4.34 are used. .4.1 . Let us design a rod string with equal stresses in the top of each taper section using sucker rods of 25.33 and 4.1 -3.= 44.1 and 44. y.32. Eqs 4.1 . is obtained as Knowing 1 . and according to Table 4. are: 25. O n the basis of similar considerations for three sections tapered rod string and 1 3 = G l I-I2. = 1500 m. 1. then. or smaller) should be equal but that the ratio of the maximum and allowable stresses should equal each other in the top section of each taper. if it contains brinef = 0. using the former design method.18 (after Mills) is used by the author to calculate a. along the length of the rod string. which neglects the buoyancy force. must be set equal to .4. In West's opinion this is permitted.1 -35 can be read.1.1 -(a)4 it is easy to see that the minimum rod load is Let us assume that is valid in the top section of each ISS.5. If.1 .. omindecreases towards the. Section 4. Since.S can also be found in itf = 0. is the cross-sectional area of the uppermost ISS. PRODUCTION BY BOTTOM-HOLE PUMPS 327 (iii) The basic principles of the design methods discussed above were improved by West (1973). bottom..1 . 0. Here f is a service factor depending on the wellstream composition.1. the maximum stress is the same in the top section of each taper.. the smaller is the a. the above value. who thinks that when designing tapered rod strings the aim is not that the maximum stresses (equalling the allowable.38 it follows that where A. allowable stress. since the equation also neglects the friction of the rod string in the inner tubing wall. The allowable tensile stress was determined by the author on the basis of the modified Goodman diagram. Ratio R is equal to or smaller than 1. =- 4 + 0. from Eqs 4. discussed in API RP 11BR (cf. Since a = F / A . Thus the maximum load in the top section of ISS i (numbering starts from the bottom) is Considering also the facts discussed in Section 4. the lower a rod section is.1...65 and if H. According to the principle.1 . calculated for the whole rod string. Equation 4. and the two neglected loads are acting in opposite directions and nearly cancel each other. from which o.35 to 4.56250. If the composition is non-corrosive f = 1..~~ 4.1 -(d)l). then rod loading increases towards the bottom and is highest at the lowest taper section. .1 -40 the length of the bottom ISS is where..( 1 + 0)] 2.5625Rf ( 1 ..39 R is calculated.(. values calculated in the top section of each taper length. = 31. If ZLri# L.. a.) The liquid load is According to Eq. must be selected.L 11.1 . respectively.+ L. and Fmin(... The data of the former example are valid and.85 x Lr1 = According to similar considerations.. 4. f = 1 and L.= 2.. Ja..= LdG. for the second ISS F. The algorithm of the calculation: considering the required rod sizes G.=O. If R > 1.6 ). then a new design.. =2. G.5625 x 0.1 -40 Design starts at the bottommost ISS where FmaX(. Thus the length of the ith (calculated from the bottom) taper is F.80 x 10' 4 = 498 m.. the taper lengths are calculated..0 ).37. Let G. = 580 MPa..05 x 104+498 x 23.9 N/m shown in column 7 of Table 4. x lo4 N and Fmin(..8 CO. other value for G..36 and 4. according to Eqs 4..1 -40.328 4.1 . PRODUCING OIL W E L L S ( 2 ) the R f = a. . Fminc2. on the basis of R determined with the help of Eq. = L.674 x 2.=Lrl Grl =498 x 23....05 5..8 =3.1 -4.39 On the basis of Eq. 4.23 x lo4 N .8 = 1-19 x lo4 N . 23.5625Fmin(i- Gri[0.( I + I. Example 4. 4. but we could start from the value 31. is required.1 . (This value was selected arbitrarily by estimation. is previously assumed and f is selected.2 N/m. 1) 6)] 4. considering the calculated G. furthermore. 4.1 -4.. F.(.=LdG. From Eq.674(1. Let us now design a three sections tapered rod string by applying West's method.05 x lo4-0.1 . = 1 ) -R f Ai - [ ? + 0.=O thus = LdG. If R 5 1. then. The difference between plunger stroke and polished-rod stroke is correctly given by Eq. finally.1.2. and the tubing shoe is not fixed to the casing string.= 528.07~ Lr3 = + Checking the calculations The average specific rod string weight is Repeating the calculation using R = 0.0)-(1 0)] =443m. Influence of dynamic loads. (a)4. The changes in dynamic load due to this circumstance result in a greater rod-string stretch at the lower stroke end and a smaller one at the upper stroke end than if the . PRODUCTION BY BOTTOM-HOLE PUMPS 329 For the third ISS 5. L. the rod string is untapered. the percentages of the ISS lengths upwards from the bottom are 35. from which Table 4.685. and the table of API RP 11L (1977). The discussed method was improved by Neely (1976).1 -2 and 4.674(1. this effect has to be accounted for at comparatively high pumping speeds and great well depths.3..310. The magnitude of the acceleration is greatest at the lower stroke end (where its sign is positive) and at the upper stroke end (where its sign is negative). = 517 and Lr3 =455. i.5625 x 282 x lo4 4 42.1 . .674 ~ 5.5625x 0. As mentioned above. In the course of rod string design Neely considers the impact of the buoyant force upon the static loads and also that dynamic loads in the rod string decrease from the wellhead towards the bottom.10 only if dynamic loads can be neglected. was constructed according to his considerations. 8 6 lo4-0.e. Effective plunger stroke.4. the acceleration of the rod string varies at any instant of the cycle.5 and 30.1-4 of the present work has been developed by formal and unit transcription. assuming harmonic motion of the polished rod. ( 4 .3. Thus the rod string designed by applying West's method is lighter than the rod string calculated in Example 4.80 x lo8 + 0. 4.1 . Lr.34. 3 x 10-10L2n2s. Hence.1 -41 The formula of Coberly (Zaba and Doherty 1956). 4. =2. This is the phenomenon known as overtravel. E = 2. the angular velocity w of the crank is not constant. the plunger stroke becomes The expression in the parentheses.1 .1-11 and 4.. o=(nn)/30. the above formula may accordingly be written as The plunger-stroke formula Eq. r =s/2 m. In SI units. 4. PRODUCING OIL WELLS-(2) basic plus variable static load were only considered.5 x lo4 N/m3.330 4.= 8. by Eqs 4./A. was probably derived by a similar consideration.1-5.06 x 10" N/m2 and g=9. differing from the above only in the coefficient. at the lower stroke end is. Stretch at the upper stroke end is where The difference in stretch between the lower and upper stroke end is Putting G. we get AL.81 m/s2. where AL. assumed to be harmonic. firstly. the plunger or pump shoe passes beyond the end points to be expected under purely static loads: the stroke is somewhat lengthened. it reads Hence. 4.42 is just an approximation in most cases.1-12.+ AL. called the Coberly coefficient.AL. and the consequent changes in dynamic load. = AL.. . the upper end of the pitman travels . The main causes of deviation between fact and formula are that. . secondly. of the polished rod.. is denoted by K. taking into account the changes in acceleration due to the motion. The stretch due to rod-string weight and dynamic loads. It is in particular the top faces of the rod couplings that have to be ploughed through the 'solid' oil above them.7 (line I).1-7. rather than being distributed over the entire string. 4. which means that a force exceeding the static shear force of the oil is needed to start the string moving. Plot this relationship to the scale of the dynamometer card in Fig. the load will concentrate for a while in a certain section of the rod string. 4.. polished-rod travel. If the dynamometer card is near ideal (which may well be the case if the pumping speed is low). this diagram would be a straight line of unity slope (line 11). we obtain a diagram illustrating the probable plunger travel.b of the rod string (line 1'). . It is advisable at intervals to check the calculated value by the method just described. s. the plunger stroke. The oil may then 'grip' the rod string when the polished rod starts on its upstroke: load will then build up steeply for a while before the plunger actually starts moving.6. the oil surrounding the top sections of the rod string may be cold enough to freeze. slight shocks and drag. and thirdly. it can be directly read from Fig. Fig. The intercept a of the line parallel to the axis of abscissae through any point of the chart gives the stretch under the load at that point. When pumping high-viscosity oil. The ordinate difference between the lowermost and uppermost point of this diagram gives s. The procedure expresses the probable plunger travel in terms of polished-rod travel. The known methods of determining plunger travel will of course fail in this case.1 -6. Hence. 4. and plot plunger travel v. On the other hand.4.1 .4. The actual plunger stroke can also be determined from the dynamometer card.7. PRODUCTION BY BOTTOM-HOLE PUMPS 33 1 along a circular arc rather than a straight vertical line. friction between fluid and tubing wall does not in itself limit the applicability of these methods. The stretch of the rod string under the load can be calculated using Eq. is easier to determine.1. there arise complicated vibrations caused by interference.1. Now let uscalibrate the ordinate axis on the same scale as the abscissa axis. Then draw a parallel to I through the starting point of the chart corresponding to the wet weight F. Several graphical methods are known. By adding to each point of this line the corresponding stretch a with the correct sign.1 .4. the one to be discussed below is due to Falk (Szilas Fig. In the absence of stretch. Determination of plunger stroke with Falk's method and Falk 1959). 5 m long 718 in.. 4. k .3 m). and If the rod string is non-tapered and the tubing is not anchored. the plunger diameter of the sucker rod pump is 2 112 in. the stroke length of the polished rod is 3. and the specific weight of the produced liquid is 9810 N/m3./sk. is Example 4. if the rod string is non-tapered and the tubing is anchored. more general form: A./L. as a function of nr/n. Let us calculate the plunger stroke length by using Eqs 4. The nominal size of the unanchored tubing string is 3 1/2 in. For calculating the effective plunger-stroke length is given by API RP 1lL. c = L3/L. If the rod string is tapered.8 m and 539. The spring constant of the tubing string.076 m). then l/AT=O. PRODUCING OIL WELLS-{2) Influence of the well completion. it is advisable to use Eq./L.332 4.= 1248.1 . a = L. If the tubing shoe is fixed to the casing then the tubing string will exhibit no variable stretch: the plunger stroke is thus increased. 4.1 -43 A S = -w E where w is a factor accounting for the type of well completion. where factor k. the two sections tapered rod string consists of 961.1 -42 and 4. rod sections respectively (Lr= 1501.5 m. and C3 = Arl/Ar3.10 in the following. In the general case. (di =0. For the above reasons. L~ 4. while the pumping speed is 8 min-'. then the changes in rod size should be taken into account in calculating stretch. .3 m.?. values can be read from Fig. and 1 in. b= L. = Arl/Ar. which holds for a tapered rod string and a non-anchored tubing. then And finally.1 -44.1 -8. then Here. at different F. If the rod string is tapered and the tubing is anchored. C . the dynamic liquid level is at depth L..1 -5. 1 .5 Fig.5 0.4 0.1 0.7 0.2 0.1 0 0 0.1.8 0.1 -42 where. 4. with the help of Eq. from Fig. 4.3 0.19 and Fig. Using Eq.43 and 4.0 as 0.1 .7 1.2 0. 4.s- Fl -.1 . After API RP l l L 0.7 n /nb By Eq. PRODUCTION BY BOTTOM-HOLE PUMPS 1.6 1. 4. .4 0.=k.1 -4. 4.1 .2 k3 1.6 0.5 1. 4.3 1.6 0. can be determined. according to Eqs 4.1 -8.4.1 -8. kT For tapered rod strings k.1 1.3 0.43/a.44 s.4 1. 22 Applying Eq.19 n From Fig. 4. for this given case practically the same result can be obtained by using any of the two above-discussed calculation methods.67 x EAT kT= -and so =P 1501. For instance. = 2 112 in. . This is the critical tubing length (assuming that the fluid level in the annulus is flush with the top of the bottom-hole pump): . The spring constant of the tubing string is 2. significant friction may arise between the buckled tubing and the rods tensioned by the liquid load: the rods and tubes may undergo excessive wear and may break or puncture. A p in the tubing: this is the force giving rise to buckling. PRODUCING OIL WELLS-2) According to Eq. and with rod strings of 1 in.1 .4 at d . -718 in. The interpretation of multiple buckling in the tubing was given by Lubinski and Blenkarn in 1957. According to them.1 -9). after correction From Fig. (a)5.1 x 10" x 1. A 7'" = 7. 4.1 . The length of the buckled tubing section is determined by finding the depth at which the tubing weight plus the weight of the liquid column equals the buckling force F.1 . 4.1 -8 k . Buckling of the tubing.34 x lo5 That is. i.e.334 4.87. 4. 4. This may entail several types of trouble. the liquid load acting on the plunger generates an upward force F = A .3 =2. =0.Research in recent years has shown that the variable liquid load causes unanchored tubing not only to stretch. but also to buckle during the upstroke (Fig.7%. The analysis of theoretical production capacity is facilitated by considering the volume produced per stroke: . the tubing will not buckle even during the upstroke. it is usual to anchor the lower end of the tubing string to the casing (cf. after LUBINSKI and BLENKARN (1957) cause punctures or breaks in any of these strings.(d)3). . Production capacity of pumping. Tubing buckling during pumping. measured from the tubing shoe determines the neutral point of the tubing. above it.1 -9.The theoretical production capacity of pumping is given by It is assumed that the volumetric eficiency is unity. As mentioned above. (iv) lateral stress on the plunger entails its rapid. (iii) repeated buckling of the tubing may entail wear or failure of the threaded couplings. multiple buckling of the tubing may cause a variety of troubles: (i) friction between tubing and rod string increases the polished-rod load and hence the energy consumption of pumping.1 . (ii) wear of the rod string against the tubing and of the tubing against the casing may Fig. the tubing will undergo multiple buckling.1. Up to that point. PRODUCTION BY BOITOM-HOLE PUMPS 335 Length I.In order to eliminate these harmful effects. uneven wear. . Section 4.4.1. 4. (b) Operating points of sucker-rod pumping (b)l. 1 9.1 . of the pump will be reduced.= 8826 N/m3 sK.1 50.5 500 750 loo0 1250 1500 1750 2000 2500 3000 90.7 60-2 44. the plunger stroke s.7 15.43.1 -3.5 14. we obtain Production is maximum when dV/dA.5 5.3 57.4 30.9 21.1 22.1 14.1 -43.2 mrn.1 25. for d.6 35.75 Higher 79.8 72.7 15.0 12.6 8.8 7. that is. Table 4.4 5.0 7.---. and y.6 2.9 20. E Let us find the plunger giving maximum production for a given polished rod stroke s and a given pumping speed n.8 19.2 36. .W .25 1.3 45.3 7. as opposed to surface reciprocating positive-displacement pumps.1 8.4 10. By Eq.1 18.=22. let us substitute As by its Expression 4.. Then V= A.75 1.5 28.1 -3 Table 4.8 2. that is.1 22.7 12.1 -43 the second term on the left-hand side of this equation equals 2As.7 43.7 11. 4. PRODUCING OIL WELLS 4 2 ) Let us replaces.0 100.5 3.0 6.5 1. and thus the theoretical production capacity is maximum when sK sK = 2As.6 14.9 29.1 16.3 67.4 56.2 40. As = -.4 14.2 28.5 than feasible 90. because increasing the latter increase the liquid load and hence also stroke reduction.336 4. in cm2..0 2. in the latter.2 22. Theoretical values of A.9 21.4 3.4 18.0 11.2 33. we obtain for the cross-sectional area of the plunger providing the maximum theoretical production capacity It is observed that.2 5. Differentiating the above equation with respect to A.8 80.3 40.5 0.4 36. 2 Substituting this into Eq.1 25.0 86.5 60. that is.1 10.0 50. 4.sK . m L m 0. =0. the theoretical production capacity of the bottom-hole pump at a given polished-rod stroke is not a linear function of the plunger's cross-sectional area.1 -42 and.2 33. by its Expression 4..0 1.6 3.9 10.0 . Here. is leakage through the tubing into the casing annulus.= 8826 N/m3 and d.. to the theoretical q. the formation often delivers gas to the well. PRODUCTION BY BOTTOM-HOLE PUMPS 337 lists values of A. for y.. and q.1 -48. so that during the upstroke the liquid 'has not got enough time' to fill the barrel. it will enter the pump barrel and occupy part of the barrel space. Filling effiiency qv. v. cannot be measured either. (i) The theoretical capacity of the pump exceeds the rate of inflow from the formation into the well.The fluid volume actually produced is less than the theoretical capacity furnished by Eq. sK and L. 9. during each stroke. it is justified to assume that the cylinder is sucked full of liquid.:of entry into the pump barrel. and of the efficiency factor q. The fact that q 1 < q. calculated using Eq. The bottom-hole pump barrel does not get filled up with liquid oneach stroke. 9 . The ratio of the effective production q.1. and if no measures are taken to separate and remove it. = 22-2mm. (iv) Even if the well fluid contains no free gas at the pressure pi and temperature 7. Volumetric efficiency of pumping. is slippage past the check valve in the surface conduit connecting the annulus with the tubing. gives the volumetric efficiency of bottom-hole pumping as Volumetric efficiency is a product of the efficiency factor q. (b)2. characterizing the measure to which the pump barrel is filled with an ideal liquid... characterizing the measure of leakage in the 'channel' leading the liquid to the flow line. 4. that is.. (iii) Together with the oil.. The liquid level in the annulus then stabilizes approximately at pump level. The slippage loss of a surface pump can easily be determined. (ii) Inflow of oil into the pump barrel is slower than the upward travel of the plunger. may be due to a variety of causes.. q .. all in m3/d units at stock-tank conditions. whereas in a bottom-hole pump it is not usually possible to separate the slippage loss from the various leakage flows and. . is slippage past the plunger. moreover. The filling factor can be determined by dynamometric measurements or level recording in the annulus. is the amount of fluid sucked into the barrel. The capacity of the pump is to be reduced so as to . and liquid only. in such a surface pump. the volume of stock-tank oil produced per unit time is less by volume factor Bi than the volume of oil at pi and T .1 -46. ad (i). This difference is due to the fact that.4. This interpretation of volumetric efficiency in bottom-hole pump deviates from the one for surface reciprocating positivedisplacement pumps.. and 'lob = qi-qz-q3-q4 41 = 41 . 4. where 9 . 8 35.0 35.7 44.8 34. introducing a solvent.8 46.6 20-0 20.8 37. nearly equal to the pressure of the liquid column of height L in the tubing.8 34.9 32.5 31. Average rod string weights in N/m for tapered strings listed in Table 4.3 20. If there is no dead space between the valves.5 28. During the upstroke. or the viscosity of the oil is too high.1 46.6 19. the space between the travelling and standing valve is filled with this mixture at this pressure pwf.1 19.1 -67 (see later). length of stroke are illustrated by the dashed lines in parts (a) and (b) of Fig. If.3 45.8 35.4 15.3 26.2 Plunger size in 11/16 1114 1112 1 314 2 2 114 2 112 2 314 3 114 3 314 4 314 13.1 31.1 -2. ad (ii).1 39. 17.4 26.2 301 30.6 38.338 4. there is such dead space. the standing valve will open immediately at the onset of the upstroke.3 13. At the onset of the down-stroke.8 21. PRODUCING OIL WELL-2) Table 4.9 28.4 24.7 38.10).9 39.1 . ad (iii).3 27. reduces pressure in the barrel to below the annulus pressure pwf. or increasing the depth of immersion of the pump. however.6 16. 4.2 2 3 4 5 6 7 8 9 10 11.3 19. where 7V means the travelling valve.1 .1 45.4 29. indeed. the barrel is filled with a gas-liquid mixture at a pressure pi almost equal to the pressure of the liquid column in the annulus (or the production BHP) pwf (Fig. slightly exceed p. Incomplete filling of the pump barrel may be due to the hydraulic resistance of the 'suction channel' being too great (either because it is sanded up or because it was too narrow to start with).6 14.4.8 30.6 45.7 42.5 27. is comparatively high.5 40-9 38. but the travelling valve opens up only when the sinking plunger has compressed the gas-liquid mixture between the valves sufficiently for its pressure to attain or. made possible by the rise of the plunger.6 19.4 47.5 35. When the plunger is at the upper end of its stroke. match it to the inflow. Variations of pressure p and polished-rod load F v.9 23.0 26.5 40.0 14. the presence of gas reduces filling efficiency by several causes: during the upstroke. SVdenotes the standing valve. The latter can be remedied by heating.2 35. it is necessary to discuss in some detail the process of pumping a gaseous liquid.5 45.3 25.. In order to clarify the connexion between gas content and filling efficiency. The pressure above the travelling valve.6 38. 0 and C denote opening and closure. The plunger then sinks through this high-pressuremix to the lower end ofits stroke. respectively.0 15.8 27.0 17. some reduction is due to the opening delay Asf .8 361 36.9 35.6 408 34.1 -4.3 22.2 48Q 49.8 * Numbers above each column correspond to those of Table 4.1 27. By the above considerations.4 36.2 409 41.9 45.2 28.7 29.6 43.8 44.8 23. then the standing valve opens only if the expansion of the gas-liquid mixture.3 26. the standing valve shuts off.8 31.8 33.5 26. p.3 21.6 36.7 18.9 27. . Solving for V. part of the effectivebarrel volume is occupied by gas rather than liquid.. Filling efficiency is a function primarily of the gas content of the fluid entering the Fig. Vpis the total stroke volume of the plunger.+v. Rwfis the specific where gas volume in the same space. we have v. A further reduction in the effective downstroke volume is due to the opening delay As.=Vp+4 is the volume of oil in the space between the two valves. and the pressure ratio p. at the pressure p./pwf. the proportion of dead space to the stroke volume of the pump. we have ..4. 4. PRODUCTION BY BOTTOM-HOLE PUMPS 339 of the standing valve. This results in a reduction of the effective barrel volume.. pump. Moreover. expressed in terms of plunger travel.1..Rw. Let us assume that the free gas sucked in at the'pressure pwfis uniformly distributed in the oil.10. and that compressibility of the oil and changes in dissolved-gas content are negligible. With the plunger at the upper end of its stroke. 4 is the dead-space volume.1 .. of the travelling valve expressed in terms of plunger travel. due in its turn to the significant expansion of fluid in the dead space. 1 ... tloa l+k 1 R.340 4.. It is apparent that the smaller the relative dead-space volume k. The latter is increased also by the decrease of k'. of the relative dead-space volume.11... and RL is the specific gas volume in the dead space at the pressure p. will be small if pJpwf is small.53 and 4. which. PRODUCING OIL WELLS--(2) With the plunger at the lower end of its stroke./k' Consequently. equals C p J p W f k' . = V'n into Eq.5 1 and dividing by n.1 .1.and E2as expressed by Eqs 4. in a given well.we get Let VJVp= k and R w f / R L =k'.54. Figure 4.11 illustrates the relationship 4. we obtain the relationship Introducing K. 4. is the volume of oil in the dead space. k'.55 for Fig. Hence Assuming that the filling efficiency is affected by the presence of gas only.1.6 .. . = (K/.1 . we may write where V. = 0 1 with k as a parameter RL =0. tj va as a function of k' at R . = -- + k 1 + R. the filling efficiency is a function of the effective GOR of the liquid sucked into the barrel. k and of the pressuredependent change in GOR.1. Since k' = Rwf/R. the higher the filling efficiency. then..1. ) n and q. 4. introducing q. Leakage through the tubing can be measured rather simply after the running of a new close-fitted sucker-rod pump in which slippage past the plunger may be neglected: the tubing is filled with oil to its open top. In the arrangement shown as Fig. PRODUCTION BY BOTTOM-HOLE PUMPS 34 1 At a given p. stretchings and contractions will cause wear on the coupling threads and this effect may be enhanced by erosive solid particles or corrosive fluids entering between the threads. When pumping a sandy well fluid. increases as the pump wears.. Leakage due to worn threads may be minimized by inverting couplings or by rethreading. These leaks are due to erosion and to a lesser extent to corrosion. with the longest possible stroke at the highest pumping speed. so as to permit the gas entering the well to bypass the bottom-hole pump. quite close originally. and topped up once per minute. If leakage exceeds a certain allowable value.1. then a so-called gas lock comes to exist. Part of the liquid lifted by the plunger may (i) slip back through the clearance between plunger and barrel. Operating point of maximum liquid production. (ii) The number and size of leaks in the tubing wall may be significant particularly if the tubing is old. If the check valve does not close tight. 4. -According the Section (b)l the plunger size for maximum liquid production at a given polished rod stroke and pumping speed can be calculated from Eq. of well fluid into the casing annulus.. the fit between barrel and plunger.pressure gauge 4 will register an increase in pressure after shut-off of the casing valve 3 if the check valve 2 leaks liquid into line I. This leakage 9. For the first approach the maximum production capacity available with a given pumping unit is obtained if production is carried out with this determined plunger size.12. A considerable leak may come to exist also if the threads are not cleaned adequately before make-up.xpi is greater than the pump stroke volume. some liquid will leak through it into the annulus. These leaks may permit a significant flow 9. will deteriorate more rapidly and thus the slippage loss will rapidly increase too. between valve balls and seats. The same clearance will result in a greater slippage loss if oil viscosity is less. In the formulation of Juch and Watson (1969). and may attain quite high values. The very large number of periodic bucklings.4. Realization is limited by the allowable and . Erosion may be due to contact with the moving rod string. 4. is so high that its expansion due to a pressure reduction to p. if the torque used in make-up is insufficient or if the thread compound is not of the right quality. (b)3. If the gas content of well fluid contained in the dead-space pt pressure p. the tubing string must be pulled and pressure-tested length by length. Volume eficiency qob. (iii) The casing annulus of wells pumped by means of bottom-hole pumps is usually connected with the flowline through a conduit incorporating a check valve.1 . and the sucker-rod pump ceases to produce any liquid. and past the seating cone of a rod pump. or to repeated stresses at a coupling. Leakage along the threads may be significant even if the tubing pipe is new.1 -48. this can be attained by increasing the depth of immersion below the producing liquid level.. where d.13b show the flow chart. the pumping speeds are 20.1 . the principle declared above must be modified to some extent.1 .1 -5. s = 1..4 m and 1.15 and 10 I/min. 314 in. That is why in order to determine the operating point of maximum liquid production.12.4 m and n = 20 l/min..1 .342 4. if the allowable load of the pumping unit is exceeded by the calculated maximum polished-rod load.1.= 1550m.4 m3/d.=621 MPa). Let us determine the parameters of the theoretical maximum liquid production capacity if the setting depth of the pump is L. Based on the above the three parameters of the maximum liquid production. and by the allowable structural capacity of the pumping unit. and if the calculated net peak torque exceeds its highest allowable value. While using this method the tapered sucker rod string is designed by West's method (Section 4. and 518 in. PRODUCING OIL WELLS (2) dynamic loads of the sucker rod string. Wellhead connections to flow line at a well produced by sucker-rod pump given by API RP 11L. 2 114 in. the rod string is composed of API C grade rods (a. it is not possible to develop a direct equation for determining the plunger size ensuring maximum liquid production during one pumping cycle. the polished-rod stroke s.13a and b by computer.8 m. That of the maximum liftingcipacity has to be selected.1 -(a)3). Example 4. and the pumping speed n can be determined assuming that the rod loads and the plunger stroke length are calculated with the pumping motion assumed to be harmonic. and the stroke lengths are 1. d. however.. A better model for the actual motion of the plunger as a function of the surface parameters is Fig. = 1 314 in. combinations should be calculated..13a and 4. An operating point must not be realized if the allowable strength of the sucker rod of given grade is exceeded by the calculated maximum rod stress. 4.. It is visible the maximum liquid production within the given load ranges is given by the fourth version. of the calculation.0 m. and 1 314 in. the possible plunger sizes are 2 314 in. the plunger diameter d. and the allowable structural capacity of the pumping unit is 10' N. The rod string has to be made up of rods of 718 in. The operating points determined by all the realizable s.1 -6.1 . . the tubing string is anchored. Calculation is performed according to the flowchart of Fig. Figures 4. Ma. 1. the theoretical liquid production capacity is 51. n. By this method. 4. The parameters of possible versions are collected in Table 4. Calculate F .1 .n pumping modes can facilitate its realization.4. Flowchart of a computer program to calculate maximum liquid production with sucker rod pumping.with max. the minimum net torque.If the required liquid production is less than the possible maximum value.s . L I Calculate sp. Following Byrd (1977) (with . then. . 4. generally. or the most favourable value obtained from a group of the above-enumerated factors can be set as the criteria. the minimum polished-rod power. The minimum polished-rod load. No uniform criteria are settled concerning the determination of the optimum operating point.qt Fig. according to TAKACS (b)4. the maximum lifting efficiency. several d . Operating point of optimum liquid production.1.. PRODUCTION BY BOTTOM-HOLE PUMPS OL@ J 'Jmax n Choose pumplng mode . .13. The subroutine. To numerically solve the relevant function the interval halving method is used.0 31.4 1.3 51. the well is pumped off. In our opinion the optimum operating point of a given pumping unit is that at which the required production rate is lifted to the surface by applying the minimum polished-rod power.6 12. PRODUCING OIL WELL-2) Table 4.000 operating points.. For the selection of the optimum operating point use of this design book is advisable.1 19.. The hydraulic power of fluid lifting is Calculated on the basis of API RP 11L. the required production rate is produced by the .4 32. the liquid pumped is water.2 NO.14a and b.4. is shown in Fig.0 1. assuming that the pump volumetric efficiency is 100%. The flow chart of the main programme.. prepared on this basis..4 1.1 . According to Byrd the most favourable operating and investment costs are assured at the highest value of J. some modification) the required liquid production is optimally lifted to the surface if the economic index is of maximum value.1 -5.4 1. As a result.s -n parameter combinations are determined at which the production capacity of the pumping unit equals the required q. the rate can be realized with the given equipment..0 21. While making up our calculation scheme we made use of the equations of API R P 11L. Parameter J thus attributes equal importance to the net torque M. From the Tables of Bul l l L 3 it can be determined at what pumping parameters the required production from a given depth and rod string combination can be realized. and the tubing string is anchored. API Bul 1lL3 comprises the operating characteristics of some 60. since in this case the production costs are smallest..0 10 15 10 20 15 10 20 15 10 27. 4. and the allowable loads upon the rod string and pumping unit are not exceeded.4 1. Its essence is that all d . . to the maximum polished-rod load F.8 33... calculating q=q. rate.8 1. is shown in Fig.4 46.I5a and b.8 1. 4 s n 4 of case in m I/min m3/d 1 2 3 4 5 6 7 8 9 2 114 1 314 1 314 1314 1 314 1 314 1 314 1 314 1314 1.0 1.4..1 . and to the hydraulic power P. 1. prepared on the above basis.= 800 m. Let us determine the parameters of the optimum operating point if the dynamic fluid level is L. <>-a New case? a C a l c u l a t e Mma.4.= 1000 kg/m3 . Example 4. The calculation scheme neglects the fact that the pumping speed can be set only to discrete values. The actual pumping speed set must be the next greater one to the calculated value. PRODUCTION BY BOTTOM-HOLE PUMPS D a t a input Input Output of r e s u l t s J = J+l n C a l c u l a t e pumplng s p e e d that achleves a Calculate Fma. 4.14.. were assumed.1 -2. according to TAKAG sucker rod pump at a pumping speed of n.7. and in each case taper lengths corresponding to API R P 11L and to Table 4. Flowchart of optimum pumping mode calculations.1 . Fig. To accelerate the calculation process design of the tapered rod string was disregarded. a fluid rate of 15 m3/d with p.1 . 25 in.5 in. Flowchart of a subroutine to calculate the pumping speed required to produce a given rate. 2. with some formal modification..= 1100 m. which. and 718 in..25 in..12 l/min.l Calculate q Colculate spls not be ochieved! a RETURN Calculate s p l s nl = n Calculate q 4.45 m. and 3. 2.37 m. the tubing string is not anchored. 0-75m. The daily liquid production. 2. according to T A K ~ C S density is to be produced from a depth of L. The nominal diameters of the possible plungers are d p = 1-5 in. and the rod string is made of rods of 314 in.1 -46.75 in. while the possible pumping speed is in the range n= 5.07 m and 1. 2.15. 4..- E5... the possible polished rod stroke lengths are s =0. can be calculated from Eq.0 in. 1. considering the volumetric efficiency. 1-76in. is .1 . the expected volumetric efficiency is 80%. 99 2.37 1.93 kW.4 2. d.25 in.4. 4.24 1.3 9.2 57..93 2.5 69.1 .5 1.3 82.2 63.0 l/min.06 209 2..2 or rather 6. Determination of M..25 38.4 7..7 86.96 2.0 614 76.4 40.4 7.22 2. 1.1 47.4 5.37 1. FSm.5 81..2 7.. PRODUCTION BY BOTTOM-HOLE PUMPS Calculate s p l s & Calculate q b RETURN Fig.6 43. Ps in mm m l/min kN kNm kW 1. and n =5.is the smallest.09 1.1.07 1.37 1.0 2. In this case the polished-rod power.75 2.0 8.75 3.07 1.8 57.0 112. 1 2 3 4 5 6 7 8 9 10 1 s n M.37 m.07 9.6. No.= 2. . when d.1 .l(c).5 42.0 69 8.6 51. s = 1.1 5(b) Table 4.7 106 12.07 1. is discussed in Section 4.0 56.37 1.02 1.8 50.75 1.7 46.1 44.5 50.50 2.6 1.2 50. The most favourable required production rate is lifted by version 6.1.0 2.07 1.8 6.07 1.6 74.8 98.86 1 1 1 1 1 1 Results of the calculation are summarized in Table 4.25 2-25 2.6 99.2 89.1 -6.7 78..5 44. 1 - . one has to know the maximum polished-rod load anticipated. contains the Fig. as well as the maximum driveshaft torque required. 4.4. which was introduced in the Soviet Union in 1967. the maximum polished-rod stroke and pumping speed to be used. Standard GOST 5866-66. PRODUCING OIL WELLS-42) (c) Pumping units and prime movers In order to select the correct surface unit. while the third is s.16. q.1 . Table 4.. Example 4. F.17. The code numbers of the Standard are shown in Table 4. = 1..5 -4000 have different arms. discussed below.1 .81 kN in the SI system). The first number after the letters SK is the maximum allowable polished-rod load in Mp ( 1Mp=9.1 . in lo2lb.1 . Supplement. 9 are so-called basic models and 11 are modified models. Columns 1 and 7 carry the markings of the individual models.1 . The fields outlined in full line and marked with Roman numerals are subdivided by dashed lines into smaller fields marked by Arabic numerals. 4. = 8826 N/m3.1 . 4. part (b) to the modified ones. listed in Columns 10 and 11 of Table 4. 50 m3/d of liquid is to be pumped by sucker-rod pump from a depth of 1500m. in in. corresponding to mark 4. The basic models (cf.1 . the drive required can be chosen by reference to Fig. the dynamic loads and the peak torque are smaller than it units of conventional type. optimum plunger diameter is 43 mm. PRODUCTION BY BOTTOM-HOLE PUMPS 349 main parameters of 20 differenttypes of pumping unit. Which is the basic model to be selected?Figure4. Fig. .. Correlation between the Table and Fig. whereas all modified models except 7 SK 12. Hence.1 . 4..2. and due to this. and s. with the arm on the horsehead side longer by 40 .2. Further to be used in selection is Table 4. In the above example. it has been assumed that y.12. Further API calculation methods. Each of these corresponds to a plunger diameter. Part (a) refers to the basic models.1 -25) have equal walking-beam arms.. the second is F. There are three basic pumping units and their schematic drafts are shown in Fig.85 and a..1. in 10' lb..16 a and Table 4. with the difference that the first number of the code is M. units. In constructing the Figure.l. are also valid for conventional pumping units.7 reveal the best suited model to be 7 SK .50 percent. 1972Dec. In the pumping unit shown in c the acceleration.1 .1 -8 and the equations of API Std 11L cited in the present work refer to the so called conventional units shown in Fig.26. Of these.17.4.1 -8.5 -4000.) classificationis also given according to M. The basic models have higher depth capabilities whereas the modified models offerhigher production capacities.17. = 0. For production rates below 150 m3/d. 4. Lukin MARK I1 is the most popular equipment of this type.16 also helps to find the approximate value of the optimum plunger diameter. the third is the maximum torque of the slow shaft of the gear reducer in kp m (1 kp .18 x 10' N/mZ. marked VII. 4.16 is established by means of the Roman numerals in Columns 6 and 9. 4.rn=9. Figure 4.1 -8. inch.. the stroke of the modified model is longer than that of the corresponding basic model..81 Nm in the SI system). In the standard sizes of the surface pumping units given by API Std 11E (1971. Type b is the air balanced pumping unit and one of its versions is shown in Fig. and its allowable polished-rod load is less. a.7. the second number is the maximum polished-rod stroke in metres. 4.16 Modified types :b) Table 4.1 .1 .16 8 9 7 1 2 3 4 5 6 Code . 4.1 -7. mm I I 1 Sucker-rod pump Field of application in the Fig. speed sPm l/min Field of application (a) in the Fig.Type code Speed spm I/min Power of electric mover kW Weight of surface pumping unit kN Basic types (a) 15 15 15 15 14 12 11 11 13 11 8 I I1 111 IV VI VII VIII IX counterweight Combined Crank counterweight v 8 6 Counter balancing Max. Data of Soviet sucker-rod pumping units (after GOST 5866) v VI VII VIII IX VIII X I I1 111 IV 28 32 38 43 55 65 68 82 93 Diam. and the speed. Due to several advantageous properties the latter is used if electric energy is available.4. after GRIFFIN (1976) Calculation of the required power of the prime mover The pumping unit can be driven by gas or by electric engine. An example of the characteristic curves of an electric motor is shown in Fig.86 228-17374 228-200-74 228-213. In the following the electric drive will be discussed. (1972) Size 64-32-16 6.17. the power factor. PRODUCTION BY BOTTOM-HOLE PUMPS Table 4.1. Basic pumping unit types. Generally a three-phase. P.4-21 -24 10 -32-24 10 -40-20 16 -27-30 I6 -53-30 25 -53-30 25 -56-36 25 -67-36 40 -89-36 40 -76-42 40 -89-42 40 -76-48 57 -76-42 67 -89-42 57 -95-48 Size Size Size 57. Here the current consumption. are shown as a function of the torque. i. the useful motor power.1 . The selection of the motor. Standard pumping unit sizes after API Std 11E (1971) and its Sup.120 456-256-144 456-305-144 456-305-168 640-305-120 640-256. cos cp. 4.86 228-246.109-48 57. M. squirrel-cage induction motor is applied as prime mover. the determination of its .76-54 80-109-48 80-133-48 80-119-54 80-133-54 80-119-64 114-133-54 114-143-64 114-173-64 114-143-74 114-119-86 160-173-64 160-143-74 160-173-74 160-200-74 160.144 640-305-144 640-365-144 640-305-168 640-305-192 912-427-144 912-305. 4. n.e.173.1 -8. the tj efficiency of the electric motor. 1.168 912-365-168 912-305-192 912-427-192 Fa Size 912-470-240 912-427-216 1280-427-168 1280-427-192 1280-427-216 1280-470-240 1280-470-300 1824-427-192 1824-427-216 1824-470-240 1824-470-300 2560-470-240 2560-470-300 3648-470-240 3648-470-300 (C) In the glven position Fig.86 228-173-100 228-213-120 320-213. 1..120 320-256-144 456-256-120 456-305-120 456-365.1 -18.86 320-256-100 320-305-100 320-213-120 320-256. 4.1-19.2 0.8 0.4 0.7 k4 0.18. PRODUCING OIL W E L L S ( 2 ) M Fig.5 0.6 nlno 0.5 Fig.6 0.3 0.3 0. After API RP 11L 0.1 0.4 0.1 .2 0. 4. Characteristics of an electric prime mover 0.1 0 0 0. 4.7 . is the conversion factor in Nm/m2. can be read from Fig.= 'lm where fc is the cyclic load factor (CLF) and qm is the mechanical efficiency of the pumping unit.4. after EICKMEIER (1973) In Eq. The polished-rod power can be calculated more exactly using the dynamometer diagram of an operating well. Cyclic load factors for different motor current patterns.1 -20.1 -20. The current consumption of the motor significantly varies in the course of one stroke. Ps. Following Eickmeier (1973) we can see three curves of this type on Fig. At . and FJsk. 4..59 CLF is interpreted in the following way. The first is proportional to the useful output of the motor while the latter is proportional to the heating of the engine.19 as a function of the relations n'ln. is the area of the diagram expressed in m2. 4. when where A. PRODUflION BY BOTTOM-HOLE PUMPS 353 nominal power with the knowledge of the polished-rod power. can be carried out with the help of the following relation: pa fc P.1 . P. 4. i* are defined. on the basis of API RP 1 1L is where k.1.4. and the rms current. Fig. In each case the average current.1 .andf. The beam counterweight is generally applied as an addition to the rotary one. respectively. reduced to the polished-rod attachment point with proper approximatibn. 4. to lift fluids in the course of the upstroke. That is why API RP 11L takes only static loads into consideration when determining the effective counterweight to be applied After mounting the counterweight.1 -62 To prevent the motor from heating above the permitted temperature an engine of f. a dynamometer diagram must be drawn in the course of steady-state operation and from this the torque curve must be plotted for the crankshaft. during a complete revolution of the crank.. which are not easy. The final setting of the . calculated on the basis of the above relation. There are two ways to obtain a flatter curve (because of this an engine of smaller power can be applied): (i) good counterbalancing results in more constant polished-rod load and more constant torque required from the motor in one pumping cycle. in the course of a complete stroke.e. significantly changes.354 4. From now on we shall discuss only problems concerning rotary counterweights.are applied to the pumping unit. creates a torque on the crankshaft defined by the geometry of the pumping unit wheref. and in the case of rotary counterweights it can be changed by moving the counterweights on the crank. F. The polished-rod load. PRODUCING OIL WELLS---(2) variable load. In order to use the bulk of the potential energy of the rod string occurring at the downstroke. in both the upstroke and the downstroke only a force equal to the value of half the fluid load exer'cises torque on the crankshaft. Let the effective counterweight. the smaller thefc value. a so-called counterweight. i. 4. too i* > I. to determine.1 -25) or a rotary counterweight consisting of two pieces attached to each side of the crank. is the so-called torque factor (see later). The quotient of the above two values is the CLF i* fC=T. the most advantageous position of the counterweights. and sometimes is impossible. represented in the Figure. As counterweights we can use a socalled beam counterweight mounted on the end of the walking beam opposite the polished rod (see Fig. or counterweights. sometimes significantly. times higher nominal power must be selected instead of a motor of P. The counterweights also exercise torque on the gear reducer shaft. (ii) with a motor which has a flatter current curve. which. which would be valid and satisfactory with constant loading. The flatter 1curve. output. be equal to the sum of the total buoyant rod weight and half of the fluid load. Due to the dynamic characteristics of the pumping unit the rotary counterweight is the more efficient of the two types. Assuming only static loads. The torque of the counterweight can be changed in beam counterweights by the size and number of the applied discs. In reality even dynamic loads influence. The effective counterweight. This value should be furnished by the manufacturer of the pumping equipment. Figure 4. change in the given case. after API Std 11E (1971) force that should be applied on the polished rod so that the walking beam is in a horizontal position when the pitman is disconnected from the crank. is the so-called structural unbalance. It is equivalent to the Fig. Further factors are explained by Fig. where F: is the actual weight of the rotating counterweight and F. and torque M.4. It can be a positive or negative value depending on the direction of the torque it creates.. is in the conventional pumping unit.1 -21. generated by the polished-rod load F..1 -22 illustrates how the M. . The net torque effecting the crankshaft in any position is the difference of the two torques. PRODUCTION BY BOTTOM-HOLE PUMPS 355 counterweight must be determined so that the maximum torque is the same in the course of the upstroke and downstroke of the rod string. i..caused by counterweight force F. 4. Fig.4. reduced to the place of suspension of the polished rod. Crankshaft torques for one pumping cycle.4..1-22.1.1-21.e. 20 1. .1 -9.55 1.1 s 50. constant. PRODUCING OIL WELLS+2) M .10 1. q. and by the V-belt drive by about 3%. Table 4.356 4.10 1. It means that the mechanical efficiency can be taken as 0.8 50.25 1.20 1.10 1. Values offc according to Howell and Hogwood (1962) fc Average polished rod velocity (2xsxn) I *NS counterweights HS NS motor m/min 38. position (12 hour position).1 . According to Day and Bird (Brown 1980) the transmitted power is reduced by the friction of the rope and bearing by about 3%.35 * NS..40 1.1 38. The shape of the M .9 and this value is. In the conventional pumping unit the net crankshaft torque for a angle is where a is the crank angle from the starting. vertical.. a.5 t 76. = M.59. The figure also shows the change of M . In the case of a given M . HS. Table 4. API Std 11E (1971) requires the manufacturer to give the f. changes with s slip with counterweights of different types and at different average polished-rod velocities.2 beam rotary 1. high slip motor. 4. as a function of the crank angle. F.. the mechanical efficiency of the pumping unit. curve the larger slip the applied electrornotor has the smaller the amplitudes of the I curve (assumed to be of equal size and direction).8 t 63.1 -9 (after Howell and Hogwood 1962)shows how f. according to Eq. with good approximation. The slip of the three-phase squirrel cage induction motor is where n.30 140 I HS motor 1. curve is determined by the pumping unit geometry and the change in the loads of the polished rod and counterweight.05 1. by the gear reducer by about 4%.5 63. is the synchronous speed of the magnetic flux created in the armature gap of the motor by the alternating current supplied through the stator and n is the actual speed of the crank of the electromotor.15 1. can be read from the dynamometer diagram and Fu is considered constant.05 1. To determine the nominal power of the motor we also need to know. factor for each 15" of crank position and also offers methods for its calculation for each pumping unit type.20 1.10 1. normal slip motor.M.. The fluid load -Fl-- 1.22.1 -59 the nominal power of the motor is To determine the nominal power of the prime mover the relation elaborated by AZNII is used in the Soviet Union (Kulizade 1960): where C. which for the earlier Soviet types assumes the q .8 no SO- From Fig.1 . q . and. = 8826 N/m3. 1.19 n 9 n =. modified to a certain extent: . =0. from Fig.96. s = 1.9% 718 in. = 44.4 x 5.= 8%. the rod string is two sections tapered 32.10 to be 0. PRODUCTION BY BOTTOM-HOLE PUMPS 357 Example 4.14. =0.1 . consequently.60 is According to Eq.1 . 4.19 k. A . and thus the polished-rod power by Eq. 4. n = 9 I/min.1 .21. 4.fc = 1. Let us determine the nominal power of the electromotor on the above basis if L= 1200 m. value shown in Table 4. According to Eq.1.0.1% 314 in.4. 67. Factor C2can be calculated from the following relation.The corrected no 63.25. 4.1 -9. 4. d..4 m.5 mm. is the factor depending on the type of pumping unit. y.9.64 x 104 =0.36 x lo4 sk..1 -4. 020 0035 0.100 0.69 =2.358 4.15.220 * The first number is F. Values of C. the last two digits indicate n. PRODUCING OIL W E L L W 2 ) where Example 4. The type of pumping unit should be SKN 5-1812. The input electric power consumed by the pumping unit is .160 0./sk. =0. Let us calculate s. =0. in Mp. From Table 4. the volumetric efficiency is qv=0. in dm.1 . 0. in min-'.1 .83 and that is why s p = 1.33 x According to Eq. TYIJe SKN 2-615' SKN 3-915 SKN 5-1812 SKN 10-2115 SKN 10-3012 c.1 -43 by using the API method. factor is 0-100.10.1 -68 The useful motor power obtained is greater than the value calculated previously using the API method.1 . the first or first two digits after the hyphen indicate s.4 x 0-83= 1-16 m . Let us determine the nominal power of the motor taking the data of the previous example into consideration. 4.. By Eq. Table 4.85.22 and n/nb = 0.10.1 -8 k . On the basis of these data from Fig. 4. 4. 4.. from Eq.1 . When solving the previous problem we already calculated that F.10 the C . The tubing is anchored. 4. The average efficiency during one stroke must be substituted into the formula.1 .18. After learning these values the adequate P.which is assumed to be constant. 4.. values valid for the crankshaft for each 15" crank angle.1 -23. After API RP 11L . no Fig. The exact determination of efficiency q.1 . and r..TOdetermine these values we first compose the M . net torque curve and then from this we read the M.~.1.18. 4. it can change significantly as a function of torque. and qm can be determined in the same way as P. Dividing this with the mechanical efficiency. according to the characteristic curve shown in Fig. values can be read from Fig. PRODUCTION BY BOITOM-HOLE PUMPS P.. is the effective output of the motor at a crank angle when the efficiency of the motor is qea. we obtain the different temporary motor torque valid for different a crank angles. which can be calculated by using the following relation: where P. of the motor is relatively more difficult because.359 4. 8 36.1 1 . PRODUCING OIL W E L L S 4 2 ) Data of the standard gear reducers can be found in Table 4.1 -24.1 -24 k.4 10 16 25 40 57 80 114 0. M. Example 4. In certain sizes the useful power of motors that can be employed. 30 22. 4.11 (after the API Std 11E. 1 1 160 228 320 456 640 912 1280 1824 18.36 x lo4 N/m. 22 15.72 1. + . Since. is also given (after Eickmeier 1973).5% difference between the measured and calculated values of the net peak torque in the 124 conventional pumping units he examined.5. k .360 4. 4. 37 30. . curve composed on the basis of the dynamometer diagram. 7.1 1. With an accuracy satisfactory enough for the selection of equipment it can also be calculated by using API R P 11L (1977). The code number means the maximum allowable net torque expressed in lo3 Ib in..6. = 5.1 . 11.1 25. generated during one stroke.6. =0. 8. 4. and where k6 can be read from Fig. from Fig. is of Table 4. F.3 103 145 206 code kNm 6.6.7.1 . can be calculated with Eq. 16.1 .22 and nlnb = 0.5. 68. difference.5 72.5 6.5 3. 22. 45 great significance.4% of the values calculated by the Mills formula are placed there. can be determined from Fig../sk. together with the gear reducer. 7 5 5. 37. 5. Let us calculate the net peak torque if the characteristic data of pumping are the same as in the previous example.8 4. Its numerical value can be directly read from the M .4% of the measured values were within the range of I@/.1 -22. unit.0 12. and n/nb. 15 11./sk. depending on expressions FJsk.1 -23 as a function of the expressions F. k.15.. on average. Main data of standard gear reducers with applicable motors after API Std. 11E (1971) and after Eickmeier* (1973) Gear reducer Motor* M.7.11.8 2. 5. 4.2 51.35. previously k. and n/n:.9 Gear reducer Motor* Ma P" kW 7. 7. According to Griftin (1976) there was. which must be smaller than the maximum allowable torque of the gear reducer. 1971). P" kW code kNm 3. The greatest so-called net peak torque. = 0.4 9.. 30. Only 8. 1 0.1 .4+ 0.72. 4. 4. Some pumping units feature either the crank or the beam type balance only. .1 -26 on the other hand.6 "0 One of the frequently used pumping units is the SKN type.1 .5 bars pressure is provided by a compressor driven by the pumping unit. 4. Fig. After API RP 11L 0. = 0-22 and thus. Compressed air at 4. shown in Fig. = 1200(0. the role of the balancing counterweight is assumed by compressed air in a cylinder.4 Fig. In the airbalanced unit shown in Fig.1. by Eq. PRODUDION BY BOTTOM-HOLE PUMPS Considering that F.329 x 32. 4.1 .3 0. 4. It has a combined crank-and-beam balance.2 0.1 .23 furnishes k. according to Eq. 4.1 -25.361 4. which belongs to the conventional type. 0 0.24.5 n - 0.72/a.671 x 23-8)= 3-20 x lo4 N and then. 25. of which we should consider here: (i) the hydraulic drive shown in Fig.1 -27. the piston is controlled by Fig. the walking beam is moved by piston 1. the piston is driven by power liquid provided through line 2 by an electrically driven pump. PRODUCING OIL W E L L S d 2 ) Practice sometimes employs special pumping units. 4.362 4. SKN type sucker-rod pumping unit . connected to the beam by a bearing.1 . 4. 1.1 -29). . The total weight of the pumping unit is 92 kN.1 -27. the unit is therefore suited for attaining especially low BHPs.26 x lo4 Nm. The polished rod is suspended from wire rope 1 (Fig. SBN-5-3015drive 350m3 per day of gas. The maximum polishedrod stroke is 3. Hydraulic sucker-rod pump drive Fig. 4.4. 4.28. this reduces the BHP. suction pressure is 0.1 . 4.29. PK-5suction-compressor dnve Fig. pumping speeds can be varied from 5 to 15 spm. the unit marked PK-5-350 moves Fig. (ii) Figure 4. maximum discharge pressure is 5 bars.0 m.9 bar. rod 2 of the piston moving in cylinder 1is connected by a bearing to walking beam 3. the maximum allowable torque on the slow shaft of the gear reducer is 2.PRODUCTION BY BOTTOM-HOLEPUMPS 363 toggle 3.1 . 4. At a pumping speed of 10 spm. The structural steel consumption of this solution is much less than that of the conventional ones. Drive crank 2 is rigidly fixed to counterweight crank 3.1 -28 shows the PK-5 type Soviet make pumping unit with an accessory gas compressor. (iii) A motion transformer significantly different from the conventional ones is incorporated in the Soviet-make pumping unit SBN 5-3015. the double-acting compressor sucks gas from pipe 4 and pumps it into flow line 5. On the tubinghead. 4. A frequently adopted arrangement is shown in Fig. PRODUCING OIL WELL-2) (d) Wellhead and subsurface equipment Wellhead designs for wells produced by means of sucker-rod pumps differ from those of flowing and gas-lift wells. and well fluid starts to leak out. a polished-rod stufing box is installed.4. Axelson's polished-rod stuffing box Fig. Corrosion-resistant . be fixed at any height on the polished rod (Fig. The polished rod is cold-drawn from high-strength alloy steel.12 (see earlier).1 -31. the packings can be compressed and the seal improved by screwing down ear nut 2.and tubinghead often agree with those used in other types of wells. however. Adjustment is usually performed by an Axelson type polished-rod clamp that can. Its suspension from the carrier bar may follow any one of several designs. 4. 4. suspensions using the Galle chain (Fig. Adjustment is performed by changing the number of chain links. The suspension must permit the height of the polished rod relative to the horsehead to be adjusted. One possible polished-rod stufing box Fig.1 -32). by tightening the bolts.The packoff provided by this device prevents the leakage of liquid from the tubing along the moving polished rod.1 -30. In the Soviet Union. 4. 4. It is carried by a carrier bar fixed to a hanger cable depending from the horsehead. The casing.1 . Rod string suspension involv~ngGalle chain design is shown in Fig. The top section of the rod string is the so-called polished rod. 4. If the oil-resistant rubber packings 1 get worn.1 -30.1 -31) are most popular. in order to correctly adjust the plunger stroke within the pump barrel. the number of rod breaks in rod strings equipped with couplings of this type is significantly smaller than in the conventionally made sucker rods (Crosby 1969b). Axelson's polished-rod clamp ( b) Fig. PRODUCTION BY BOTTOM-HOLE PUMPS 365 alloys are used where well fluids are corrosive. The length of rods is standardized. 4. Standards for the dimensions of sucker rods were introduced in several countries. used directly. 4. Due to both reasons. in most Fig. Later. It was found that the build-up of harmful stresses and corrosion had decreased. The sucker rods can be of box-and-pin end type (Fig. the 4 lengths. Since these standards differ only slightly from each other. Sucker rods.1 -33. Table 4. (d) 1. 4.1 -33. API sucker-rod couplings cases.1 -33. Generally API Spec.4. tables and diagrams included in them concerning the dimensioning of the rods can be. . a) or ofpin-and-pin end type.1 -I) is followed. Since the late 1950ssucker-rod pins.32. b).1. the thread of which is machined oversize first and then reduced by rolling. prescribed by the API standard are shown in Table 4. In the latter case they are joined with couplings (Fig. 4. Std 11B (cf.1.too. The diameter of the polished rod is usually greater by 10 mm than that of the sucker-rod directly attached to it. calculations.1 . have been used (McCurdy and Elkins 1967).1 . rod coupling was prepared by applying the same method. . m N/m 26.19 0557 1 9.4 26.43 0198 1 914+005 36.7 33. At first.12 lists some of the main parameters of Varco make hollow rods. successful experiments have been carried out with hollow rods Table 4.3 28.14k0-05 27.14k0-05 18.1 -34 shows the end and coupling design in longitudinal section of a Varco make hollow sucker rod..1.0 8041 Symbol do di A.9 4. PRODUCING OIL WELLS-(2) By the term sucker rod. strings were simply made up of standard external-upset tubing of 1 . kN 53.1 114 in. Table 4.D. however.366 4.7 209 2. Main data of Varco hollow rods Data O. in. These are usually pinthreaded at both ends and joined by appropriate couplings.12. has led to the development of hollow sucker rods. a solid rod is most often meant in practice. In the Soviet Union.1 . I.1 .5 F. and of smalldiameter wells.6 3.34. hollow rod strings made in 1960 could already operate pumps installed up to 2265 m depth. Unit mm mm cm2 107 . Failures in this type of string were very frequent. Fig. 4.15 0344 7/8 9.6 15. Steel cross-section Capacity per unit length API thread on rod end Overall rod length Rod weight per unit length Maximum allowable load for rod made of N-80steel 314 Nominal size. the increasing number of wells producing sandy and heavy crudes. Varco's hollow rod Today hollow rods are made by several manufacturers. Figure 4. I/m in. size. However. 1 1 1/8 G. however. and they usually took place at the last joint. As a result of some high-pressure development work.D. v- L. 4. The type of stress on sucker rods is pulsating tension. is due to Timoshenko .. The plot is constructed as follows. and that the magnitude of this tension varies more or less periodically. The glass has the effect of reducing wax deposits (Zotov and Kand 1967).5 to 2. respectively.Now the value ad4 characterizing the rod material to be used is plotted on the ordinate axis. This line intersects the line of minimum stress in point 2. The maximum allowable tensile stress of the sucker rod is given by where a is a safety factor whose value is in the range from 1. . Modified Goodman diagram for designing sucker-rod strings.. = a. This gives point 1. 'J'rnin Fig. From the origin of coordinates. After plotting aB/1.1. after JeRNlGAN (1971) According to more recent designing principles.accounts for load changes. in its original form. provided no corrosion is to be anticipated. and the fatigue limit. The shaded area is the area of safety. the number of annual load changes exceeds five million.1 -35. Sucker rods are exposed to substantial fatigue due to significant load changes at comparatively short intervals. Designing is facilitated by consideration of the so-called areas of safety shown in diagrams characterizing the individual types of fatigue limit. The orthogonal system of coordinates in Fig. a line is drawn parallel to the abscissa axis through the point thus obtained. This means that the rod is under tension throughout.which. because structural materials have a variety of fatigue limits (Zork6czy 1968).75 on the ordinate axis. Even at the rather low pumping speed of 10 spm. The maximum allowable stress can be determined by means of a modified Goodman diagram. This is the locus of line a. The line connecting points 1and 2 is the graph showing the variation of maximum allowable stress v.4. . In a well 1000-1500m deep.. PRODUCTION BY BOTTOM-HOLE PUMPS 367 glass-coated on the inside.1 -35 is calibrated in minimum stress on its abscissa axis and in maximum allowable stress on its ordinate axis (Jernigan 1971).30 kN. minimum stress. the Complex nature of the recurring stresses forbids us to speak of the fatigue limit of steel. a line of plus unity slope is drawn. the difference between maximum and minimum load is 10. The above formula .. 4. This. In the stress decrease phase. Mo. rod steel should be chosen for corrosion resistance according to the following main viewpoints: . As to composition. rod steels fall into two groups. and to a lesser extent to accessory gases such as hydrogen sulphide. Similar to Mo and V. The harmful concentration of stress and the reduction of the cross-section is further enhanced by the fact that the corrosion pits are deformed by the variable stress on the rods. however. it promotes the formation of a fine-grained texture. Irrespective of strength criteria. A greater tensile stress will distend the pits. Cu. This is a deoxidant that reduces brittleness in the presence of sulphur. The stress in the section of a deep pit may be ten times as much as in a full. is not usually necessary. Added in comparatively small amounts.1-13 shows composition and strength parameters of various rod materials. However.corrosion anticipated may be used anyway. Mo. This is why it is impossible to successfully simulate in the laboratory conditions affected by a number of secondary factors acting over incomparably longer spans of time. A pit so distended may catch a particle of metal or a sand grain. Table 4. Si. M. Cu.5 percent. Otherwise. It is termed an alloy steel if it contains other alloying elements as well. It does not form carbides the way some other alloying elements do. moreover. A variety of steels are used to make sucker rods. Cr. It serves first of all to reduce the grain size of high-strength steels. it improves resistance to atmospheric corrosion. Corrosion results in pitting of the rod surface. this particle prevents the relaxation of the material around the pit and. Cr. Ni. Cracks thus formed tend to propagate until the rod breaks under a stress exceeding the lowered endurance of the material. !I Similar to Mo. the material is called a carbon steel. It inhibits corrosion brittleness caused by hydrogen sulphide gas in corrosion pits. The presence of C in steel considerably increases strength. The pits may. on the other. but considerably improves resistance to corrosive agents other than hydrogen sulphide. The extent of corrosion thus depends in addition to the given rod material and corroding medium also to a significant extent on time and the stress variation range. A hardener in solid solution in ferrite. If the manganese content is less than 0. causes cracking in the surrounding metal. Corrosion is due primarily to formation water. uncorroded cross-section. serving as a wedge. it also increases brittleness and lowers corrosion resistance. entail stress concentration. hardness and the suitability for tempering. B. V and B. on the one hand. and there are no alloying elements other than Si and C. The number of wells producing strongly corrosive fluids is comparatively small. Enables the steel to be heattreated to improve its strength.. start cracks and. and traces of P and S as contaminants. oxygen and carbon dioxide. because only rod materials resistant to the kind of. such as Ni.368 4. strength and/or corrosion resistance of the steel. This element forms carbides and considerably improves the temperability of steel. A very effective deoxidant. To this are added alloying elements increasing the hardness. it plays a role similar to that of carbon. if added in small amounts. All steels contain Fe in a proportion above 90 percent. PRODUCING OIL WELL-2) Corrosion. It does not provide protection against hydrogen brittleness. but there is almost no well in which corrosion is nil. 85 020.40 050:'0.80 1.30 05510.025 max 0025 max 0025max 0..75 1.17'0..70 Mayari 62 5 40 Reliance 77 Hi-Ten Y Special A 4621 Mod A4621 3310 Special Special 80820 0.OX 0. 60.'0.'655 793i897 8281897 793.32..2513.10 1. Brinell hardness 94.8 min 67.30 .50 X Special 0.30 0..260 235 t . 0.8 t 1421115 122i142 136:102 941122 122/81 102 min 113 t 183/207 I85 t 174 min 192 avg 173 t 1761220 1851205 230!260 250.20.90 003 max 004 max 0016 1 0. Chemical and mechanical properties of sucker rods (after Frick 1962) Chemical properties No Manufacturer Grade of rod AlSl specilication C Mn 'I S Si Ni Mechanical properties Cr Mo V 0 '0 I 2 Axelson Oilwell 3 4 5 6 7 8 9 10 avg t = = Bethlehem National Continental-Emsco Norris Continental-Emsco Axelson Continental-Emsco Oilwell average typical 60 N C 1036 C 1036 0.35 025/0. Nm i0 .36 0.35 0. 66/55 60167 63/50 68/73 . 50 min 60 avg 501 70/60 60172.'0.I8..20 020/0..75 080/1..23 055/0.20.13 0.W 3.21..85 0. 19/24 28/35 .20 060.W 070'0.'275 230.23 O..20'0.35 050/0.897 724/793 Elongation on 2in I 8in Red.20..15..40 030/050 030/055 008/015 0201030 020/030 045 min 1. 36/26 22/29 25/16 18/25 16/12 13114.05 015i0.35 0..1 min 104 t .'0.04 max 004 max D04 max 004 max 0.'0.40 0.30..15 QO5min 040.37 1.651200 1.50 1.33.30 020/030 008/0.0.90 045:O.04 max 0017 1 0035 max 005 max 0028 t 005 max 004 max 004 max 004 max 0025 max 0030 max 0025max 004 max 0. .7511.35.15.'0.024 t 020/0.90/1.5 16/12 ..35 020'0..23 O.'67 53/68 32 min 35 avg 32 t 45/32 .M) 1.65!2.'0.40/1.9Q1.'1.32'0.13.'030 020. 67.80 0. .'QlX Q17.'0. in area bod impact o..0.24 Q13.1 .60 Yield point Tensile strength MN/m2 MN/m2 448/497 414/514 6211724 6211724 414 rnin 448 avg 414 t 490/635 4481517 6211724 690/793 6551759 6551745 607 min 655 avg 621 t 6071779 566..'0.0. .'0.2/122 88.'l..50/0.20 0.35 0.Table 4.80 0~70. . 1.'0. 35/25 . The flexible rod. Inhibitors have the drawback that their application is a never-ending job.366 m long. It is liquid-loaded also during the downstroke. heat-treated.25 mm thick (Joy and Coleman 1968).6 mm thick.SI 1036Md) and K (465 1) steels. The wirerope thus made up is encased in an outer nylon jacket about 0. Inorganic inhibitors neutralize the corrosive agent by entering into a chemical reaction with it. and again heat-treated. rolled into an elliptic form. joint failure is about as probable as failure elsewhere along the rod. in a rod of 22. The wirerope is composed of wires 183. The protective action of organic inhibitors is usually due to the fact that their heteropolar molecules.2 mm diameter.14. 4. so that the Flexirod is tensioned throughout (cf. adhering with one end to the metal surface.1. shot-peened.1 -40). Figure 4. whose description was published in 1968. the flexible sucker-rod was introduced into commercial production (Patton 1970).5 m diameter for transport to the wellsite. In the torque range from 206 to 540Nm. Thus ifjoint failures occur fairly often.1 -36 is the sketch of a pumping unit equipped with a Flexirod (Joy and Coleman 1968).M o steel Ni . failures occur predominantly at the joints if make-up torque is less than 206 Nm. so-called differential type. flexible rods have been made of C (AI. each of a round 2 mm diameter and of 1655 MN/mZ tensile strength.Cr steel In order to prevent or limit sucker-rod corrosion. plastic jacketed and wound on a drum of around 5. Rods are particularly prone to joint failure if an insufficient make-up torque is used. It may be of the same material as the solid rod. Pump I is of a special. whereas at 540 Nm the number of joint failures decreases rather steeply. inhibitors are sometimes employed. but-welded. The effective breaking load of the rope is 186 kN. The main dimensions are given in Table 4. As a result of cooperation between Bethlehem Steel and DuPont de Nemours. is made up of 37 strands. It is driven by a 1 kW electromotor with a maximum make up torque of 1080 Nm. it is advisable to employ power sucker-rod tongs ensuring correct and uniform make-up torque at all joints. The inhibitor dosed into the annulus flows down to the well bottom where it mixes with the well fluid. According to Walmsley and Helman.4. Their advantage is that they protect from corrosion not only the sucker rods but all the steel surfaces in contact with the well fluid. The Soviet made ASK type automatic power-tongs belong to this group. also Fig. and encased in nylon 0. In 1970. The full length of line is then qualitycontrolled bv ultrasonic means. PRODUCTION BY BOTTOM-HOLE PUMPS Medium surrounding the md Mildly corrosive Contains HzS Strongly corrosive brine 7he rod is to he made of Carbon steel Ni . form an impermeable film that keeps the corrosive medium from direct contact with the steel. it is transferred to a special well-completion derrick by means of a sheave-like rodguide.1 . At the well. The on of the Flexirod which emerges to the surface is encased in a . a flexible rod built under the trade name Flexirod or Corod has been applied since 1961 in experimental installations. however. The absence of rod collplings permits the selection of smaller-size tubing and hence also of smaller-size production casing.9 25. The probability of failure !s greatly reduced because 65 .0 718 15/16 1 operations by itself.370 4.8 34.g. In 1968.2 39.80 percent of all failures in solid rods occur at the joints.8 25. The upper endof the Flexirod is wound on drum 3 on the Samson post. The smaller rod-string weight entails a smaller load and a lower specific power consumption. the sucker-rod pump was still run and pulled by means of a well-completion rig suited for the purpose.14.7 29. A pumping unit is being developed. that can carry out these Fig. the pump can be run at speeds up to 1. 4. Thus e. it carries no load. The Flexirod has a number of advantages (Patton 1970).36.4 18.1 206 22.2 23. Rodstring weight may be significantly reduced by the fact that standard Flexirod sizes differ by 1-6mm rather than the 3.8 m/s. after JOY and COLEMAN (1968) Table 4. in. a four-stage Corod string may be lighter by 17 percent than the two-stage solid-rod string of the same strength.1 . The role of this latter is restricted to ensuring a satisfactory seal together with the polished-rod stuffing box. Corod sizes and weights (after Patton 1970) d G. Sucker-rod pump with Flexirods.2 mm for solid rods. so that a prime mover of lower rating will do.1 . mm N/m 11/16 3/4 13/16 174 19. PRODUCING OIL WELL-2) hollow polished rod 2.4 21. Running and pulling are simple and fast. The tendency to wax . 1 . The heavywalled full-barrel rod pumps shown in parts (c). Several fundamental types of bdth tubing and rod pumps are known. the plunger. which is an advantage when pumping gaseous fluids. dead space is less. and it is simpler and therefore cheaper. Sucker-rod pumps may be tubing pumps or rod pumps.the lengths of barrel and plunger. and the overall structural length. and slightly modified. These may be classified according to various viewpoints. PRODUCTION BY BOTTOM-HOLE PUMPS 37 1 deposition is considerably reduced because first deposits usually form on the shoulders of the rod couplings. the (basic) plunger diameter. Plunger diameters of standard sucker-rod pumps are listed in Table 4. the API standard designation of the pump (found in Table 4. an efficient joining of broken Flexirod ends at the wellsite is not easy. a certain unavoidable dead space.1 -37 have been taken from API Std 11-AX (1971). Its application. However. and often by means of. The tubing pump has the advantages over the rod pump that it will accommodate a larger-diameter plunger in a given tubing size. This entails. The barrel is scated on and fixed to a conical seat previously installed at the tubing shoe. (d)2.1 . in spite of its relatively high price. The rod weight. It simplifies the use of plastic-lined tubing. The tubing pump owes its name to the fact that the pump barrel is run with the tubing and cannot be removed without pulling it. and the rod string is fixed to it subsequently. In the case of the rod pump. It is needed because the various types of standing-valvepuller mounted on the plunger or the standing-valve cage (not shown in the Figure) also require some space. . The bottom-hole stroke reduction due to the greater rod stretch is made up for by the greater overtravel at the dead points. Experiments were made in wells of 1939 m greatest depth with sucker-rod strings made of glass-reinforced plastics (Watkins 1978).16. but it is invariably removed together with.4. The advantages of the rod pump are. Friction of the rod string against the tubing is likewise reduced.Fundamental types. the plunger is run on the rod string. and/or where steel rod strings frequently break due to great rod loads. The barrel is screwed onto the lowermost length of tubing. on the other hand. The fundamental types shown in Fig. but in some solutions the barrel is run with the plunger in place. however. (d) and (e) of the Figure agree in . The standing valve can be installed with or without the plunger. both the plunger and the barrel can be run or pulled with the rod string. together with the steel sinker bars. that it is not necessary to pull the tubing when changing the pump. In most types of tubing pump.15). is about one-third of the weight of the rods made entirely of steel. The parts (a) and (b) of the Figure featuring pumps of TH and TL type show the plunger and standing valve and barrel. seems to be advisable at wells where the danger of corrosion is significant. certain designs are more trouble-free provided the sand content of the fluid is low. Unequivocal specification ~f a sucker-rod pump includes the nominal size of the tubing. the plunger is not run 'naked' so that its surface will not be damaged on running and pulling. 4.1. which reduces both tubing corrosion and friction loss in the well fluid. There is an insert between standing valve and barrel. and so pump changes are cheaper. Bottom-hole pumps. Sucker-rod pump sizes after API Std 11AX (1971) API code 1. in.1 . however.372 4. The pumps with heavy-walled barrels denoted RH can stand a heavier liquid load without Table 4. 4. PRODUCING OIL W E L L H 2 ) TH (a1 TL RHA RUB (b) (c ) (d I Fig. Basic sucker-rod pump types. They have. RHA RHB RHT RLA RLB RLT RWA RWB RWT TH TL - - - 1 114 1114 - 2 114 2 114 1 114 1 114 1 114 1 114 1 114 1114 1112 1114 11/2 1 314 1 314 1112 1 1/2 1 112 1 112 1112 1 112 1314 1 314 1 314 1 314 13/4 1 314 2 2 2 2 114 2 114 2114 2 1/4 2 114 2 114 2 114 2 1/4 2 112 2 112 2 112 2 314 2 314 . the disadvantage that the reworking of a worn barrel is more difficult.15.1 -37. Full barrels are cheaper than barrels with sectional liners. according to API Std 1lAX RHT (e! general design features with the thin-walled full-barrel pumps of type designation RW.9 Nominal tubing size 2 718 2 318 3 112 plunger sizts. it can be installed and operated without letting the producing fluid level rise. in crooked wells. In the solutions shown as (d) and (g). In the types RHT Table 4. bottom holddown Symbol of full barrel Thin-walled Heavy-walled TH RHA RHB RHT - RWA RWB RWT Liner barrel TL RLA RLB RLT . This is an advantage especially when pumping a sandy crude. The rod pumps shown in parts (c) and (0 of the Figure are provided with top holddown.1 . after pulling the plunger and standing valve of a well previously pumped by means of a tubing pump. and can therefore be used at greater depths. than it would be in the case of a tubing pump. In both cases. the bottom holddown permits such settling of sand. API standard designations of sucker-rod pumps Type of Pump Tubing type Rod type Stationary barrel. the pump has less tendency to seize in the tubing. PRODUCTION BY BOTTOM-HOLE PUMPS RLA (f) RLB RLT :g 1 (h) Fig.4.1. fixation to the tubing is more elastic. It has. for it prevents the settling of sand between the outer barrel wall and the tubing. the advantage that. bottom holddown Travelling barrel. Also. owing to the conic seating surface of the holddown.16. however.37 deformation.1 . 4. top holddown Stationary barrel. 1-39. US1 Axelson TL type sucker-rod pump Fig.1-38. PRODUCING OIL WELL-2) and RLT. Let us add that it is usual to install above rod pumps a ring-type check valve that prevents the settling of sand risen through the tubing in the event of a stoppage. because turbulency about the barrel Fig. these types are better suited for lower-viscosity oils. the plunger is fixed to the seating nipple and the pump barrel is travelling together with the rod string.1 . They are favourable also when pumping a gaseous fluid.1 . 4. In Fig. Because of the smaller standing-valve inlet. standing valve I is simply dropped into the well prior to installing .374 4.38 and the RLA type rod pump shown in Fig. 4. 4. US1 Axelson RLA type sucker-rod pump limits the settling of sand during operation. For structural details let us consider the TL type tubing pump shown in Fig. 4.1 .39.38. both of US1 Axelson make. They are less sensitive to sand than the stationary-barrel types with bottom holddown. 4. to be seated in a nipple in the tubing string. the pump barrel is equipped with mandrel 1. Telescopic or threetube sucker-rod pumps are rod pumps with the middle tube fixed to the tubhg. 4. The absence of the tubing may make this solution highly economical. special pumps. This solution is restricted to gasless wells where the annulus is not required for producing gas.4. The casing pump is a rod pump whose seating nipple is fixed to the casing by means of an anchor packer. it finds its own place. 4.1 -40. Fig.1. falling down the tubing. after HOOD(1968) Besides the fundamental types just described there are other. Contrast between the concepts of plunger . another pump can be installed without damaging the structure. It is pulled together with the barrel by latching onto extension 3 of the standing-valve cage the self-latching standing-valve puller 2 on the plunger.1 -39. Hold-down under operating conditions is provided by the pressure differential acting on the three seating cup rings marked 2. Differential sucker-rod pump. whereas the other two coaxial tubes fitting the stationary one on its inside and outside move together with the rod string. The pump can be pulled with a definite jerk. In Fig. The completion involved is of the tubingless type. PRODUCTION BY BOTTOM-HOLE PUMPS 375 the pump. 1 -41. 4.1 -(d)4 . The advantages of the one-piece barrel are that. The plunger is forced downward by a force proportional to the pressure differential. Main structural parts.and corrosion-resistant alloy steels. Sucker-rod pumps of special design will be discussed in more detail in paragraphs 4. on the other hand. called liner barrel. for a given nominal size (a given tubing diameter). and that it is cheaper. in the same way as a conventional sucker-rod pump. On the down-stroke. or a barrel composed of a number of liners.376 4. The three-tube pump is used to advantage in producing well fluids containing fine sand whose grains are smaller than the operating clearances. The sectional-liner barrel has. but to the pressure of the liquid column in the tubing from above. which permits it to sink at sufficient speed. whereas travelling valves V2and V3open. It operates on the upstroke.40) is used in conjunction with Flexirod-type rod strings (Hood 1968). which is important especially at the high lift . a downward-directed force acts on the plunger. The differential pump has two plungers. 4. The Fig. Because of the considerable tube lengths usual in this type of pump.5. Liners are made of wear. The liners are placed in a close-fitting jacket and held together by two flush collars.1 . nitrated or provided with a hard chrome plating. whereas it is difficult to accurately hone a long one-piece barrel. Oilwell's Neilsen design pump barrel with steel band true plunger lifting the well fluid is the lower one marked I. the plunger may be of greater diameter. PRODUCING OIL WELL-2) and barrel is obscured here. The dflerential sucker-rod pump (Fig. precisely honed liners. standing valve Vl closes. the advantages that any length of barrel may be made up of short. Through orifice 2 the effective cross-sectional area of plunger 3 is subjected to the comparatively small annulus pressure from below.1. the short liners enable machining to closer tolerances. The insides of some liners are specially treated. a relatively greater operating clearance may be permitted between moving parts than in the more conventional pumps. The liner barrel usually contains several cylindrical liners. It has the advantage that. during the down-stroke. each of 1 ft length (or 300 mm according to a Soviet standard). very carefully honed on the inside and at the shoulders. The pump barrel may be a one-piece barrel made of a colddrawn steel tube or of cast iron. the latter are provided with rubber or plastic cups. Standard API barrel lengths include sizes between 1. the plunger is operated so as . Figure 4.4m. on the other hand.1-42 shows a Neilsen type O-ring plunger made by Oilwell. 4. both differing in diameter by 1 mm from the standard size. 4.300m in countries using the metric system.1. Most plungers are machined in one piece. with a hard chrome plating. and matched to the barrel material. or 1. Metal plungers are made of an alloy steel chosen for strength and resistance to wear and corrosion. In order that a worn barrel may be reworked and reused. PRODUCTION BY BOTTOM-HOLE PUMPS 377 pressures encountered in deep wells. and join them together on running by means of a special coupling. liners I are locked together by steel bands 2 that prevent their misalignment even at great depths.g. Barrels of the biggest sizes may pose a handling problem on the surface and also on running in the well. Let us point out that high pressures will tend to misalign liners if these are simply placed end to end. Oilwell's Neilsen design O-ring type pump plunger undersize and oversize barrels. Standard pump barrel lengths are usually multiples of 1 ft (0. The latter may have the advantage that.52and 13. Two types of plunger are distinguished: metal plungers and soft-packed ones.1 -42.04 in.1 -41). the barrel is rehoned and fitted with the standard size plunger.4. The low breaking strength of certain alloys necessitates making up of several piece plungers to be exposed to high loads. sand grains will get caught in the grooves rather than scoring the plunger and barrel full length.305 m). e. On the other hand. Plungers may be plain or grooved. Undersize barrels differing in diameter from the standard API size by 0. and this may cause operating trouble.02 mm are marked '-40'. in the Neilsen type barrel made by Oilwell (Fig. when pumping a sandy fluid. After a certain amount of wear. it is usual to provide undersize barrels. Soviet suckerrod pumps are furnished with Fig. or 0. a worn barrel is comparatively cheaper to rehone. They are case-hardened or provided e.g. If. It is usual to make these big barrels in two halves (each of which may be of the sectional liner type). 1 mm. In the Soviet Union. Example 4.2. 4. They have the advantage of longer life when producing a sandy fluid. the slippage is 100 times this value. Ap = 200 bars. Eq. whereas on the downstroke the contracting cups hardly touch the barrel wall.170 pm). For the 120-cp oil. if d. Such plungers are used at depths less than 1500 m.1 mm. . The correct choice of plunger fit requires consideration of well-fluid viscosity. the liquid weight on the plunger presses the cups against the barrel.28 x lo-' x 86. In Fig. The corresponding plungers are termed . (that is. The correct choice of the plunger-barrel combination best suited for a given well is very essential. so that its viscosity tends to be less than that of the bulk well fluid.1. and packing is provided by valve cups.1 m3/d.12.400=0. 1957). respectively (1 cP = 10. from 25 to 127 pm). The plunger diameter equals the barrel diameter except for a very narrow clearance. 4. there are five nominal clearance groups increasing in 0. in order to minimize slippage past the plunger under the excessive pressure differential building up between plunger ends during the upstroke. and h. -4 and . 1. Ad = 0.1 .120 and 120. that is.001-in. to 0-005 in.011 m3/d. Find the daily slippage loss past the plunger in oil of 120and 1. is plunger length. The advantages of grooved barrels are therefore debatable. its grooves may pick up and carry solid sand particles into the barrel.378 4. PRODUCING OIL WELL-2) to stroke out of the barrel. If the plunger and barrel are not made of the same material differential thermal expansion at the setting depth should be taken into account. rings. respectively. Slippage loss can be estimated by the formula (Oil Well Supply. steps from 0. where Ap is the pressure differential across the plunger in Pa. This design is used at .4 3 a. the . Ad is the diametral clearance (difference in diameters) in m. packing is provided by valve cups 1 made of oil-resistant rubber. They are usually cheaper than metal-to-metal plungers.5 fits.2 cP viscosity.001 in.1 . which would cause a smaller-clearance plunger to seize. whereas the .3.Pas). may pass through a larger clearance. The plunger may even seize up if the clearance is too small. As a rule of thumb. = 57. In soft-packed plungers. Bulletin. Let us point out that oil slipping past the plunger is warmed by friction.1 .22 m. because sand grains suspended in the fluid. and h.1 fit is used with oils of low viscosity (1 -20 cP). For the 1-2-cpoil. Too tight a fit should be avoided. three clearance groups are distinguished (20-70. In the US. in m. = 1. .5 fit may ensure a satisfactory operation even about 400cP.74 gives which equals 1. etc. 70. the diameter of the metal body is significantly less than that of the barrel bore. On the upstroke. because the sealing surfaces are hardly worn by the sand. A considerable drawback is . Type (c) is a combination of cup and ring-type plungers.and corrosion-resistant metal. occasionally case-hardened. so that repair jobs cannot be scheduled in advance. 7hbrbing anchor. The ball is confined in its motion by a cage of 3 or 4 ribs.that cups will fail all of a sudden. This type also permits to detect wear.l. 4. The anchor used in earlier practice was usually of the compression type (Fig.l(a)5) has become widely known.1 -39 illustrate some popular types. without any preliminary warning. Valve balls and seats are made of wear. Progressive wear can be detected well enough. a device designed to fix the tubing shoe to the casing used to be employed even in early practice. The Figuretalso shows the mode of attaching the seat in the sucker-rod pump. Figures 4. . paragraph 4.4. A special type to be mentioned is the combined plunger where the packing is provided by a close . the conical seat is lined with plastic or white metal. in a tubing pump.1 -38 and 4. They are used at comparatively great depth. Oilwell's soft-packed plunger types comparatively low sand contents. which also has favourable adhesive properties.1 -44): it is a device resembling a hook-wall packer.metal-to-metal fit along part of the body and by valve cups along the rest. however. the theory concerning the multiple buckling of the tubing (cf. -In order to increase plunger stroke. It can be used for cleaning up wells following a sand fracturing operation.1. packing is provided by valve rings 2 made of oil resistant synthetic rubber. In (b). Since. In addition to these types of Oilwell make. the standing valve may simply be fixed by adhesion between mating tapers. (d)3. 4. Let us add that. the operation of the anchor was also submitted to a more detailed analysis.1 -43. other types of soft-packed plungers are also known. In this case. PRODUCTION BY BOTTOM-HOLE PUMPS (a (b) (c) Fig. 4. is not stretched. The tubing may therefore undergo multiple buckling during both the up. a tension . During the downstroke. however. This reduces to some extent the buckling of the tubing (part (a) of the Figure). the rod string is pulled straight by the load on the plunger.1-45.and the downstroke (Fig.1 -44.1 -45). nor overloads due to friction (Lubinski and Blenkarn 1957). If a compression anchor is installed upside down. tubing and possibly casing. it does not prevent wear and damage of the rod string. Now 1 Fig. Since the slips are arranged so as to slide freely upwards and seize against the casing downwards. and BLENKARN (1975) after LWBINSKI during the upstroke. The rod string. It can be set at the desired depth by releasing the Jhooks (1. the tubing will stretch. and these will grip the inside of the casing. this holddown will fix the tubing shoe in the highest position occurring after its release.380 4. limited by the casing. but since the downward movement of the tubing shoe is prevented by the compression anchor. in the fully stretched state. Now spring 3 can press up slips 5 on cone 4.2).4. it can therefore follow the curves of the tubing. Compression anchor Fig. 4. The buckling of the latter is. not loaded by fluid. This is the type of buckling discussed in the section referred to above. Buckling of tubing during sucker-rod pumping. Thus even though the compression anchor prevents the movement of the pump barrel. that is. PRODUCING OIL WELLS-42) without the sealing elements. with a compression anchor installed. the tubing will buckle again (part (b) of the Figure). The above circumstances have made it desirable to have an anchor which attaches the tubing shoe to the casing in the deepest position occurring. on the other. and this could result in casing wear or puncture. This makes the expander wedges 1 approach each other (Fig. 4. and this stress will further increase at times of pumping stoppage. Figure 4.1 -47). This type of anchor keeps the tubing from both buckling and shortening. measures were subsequently taken to avoid the anchor's climbing down into the deepest possible position under the gradually increasing loads. the sources of damage associated with the compression anchor. The necessary prestretch is to be determined by calculation. it is rotated to the left from 3 112 to 4 turns. Prestretching increases the tensile stress on the tubing.1 -46 shows a Baker type tubing anchor that can be set at any depth. 4. Setting and releasing Baker's tubing anchor . notably. puts an end to anchor action. the tubing may undergo a permanent deformation and even break.1.1 -46. In the tension-anchor types first employed in practice. a short upward travel was needed to make the slips grip the casing wall. the tension anchor is provided with a safety device that disengages the slips in overstress situations. If the stress exceeds the allowable value. In order to prevent this. when the tubing cools down. In order to prevent this.4. and so limits stroke reduction. These slips are serrated so as to prevent both upward and downward movement. of course.1-47. Calculating the necessary amount of prestretch is facilitated 1 Fig. the anchor was set in a prestretched state of the tubing. Baker's tubing anchor (01 (b) Fig. PRODUCTION BY BOITOM-HOLE PUMPS 38 1 anchor results. on the one hand. Once the tubing is run to the desired depth. these then press the slips 2 against the casing wall. and eliminates. 4. This. the holddown buttons bear against the inside of the casing.1-49 shows the Guiberson type H M .1 -48) is provided with a number of holddown buttons moving in a number of radial cylinders.4.2 hydromechanical automatic tension anchor. Guiberson's hydraulic tubing anchor Fig. forced outwards by cone 5. 4. Figure 4. Guiberson's HM-2 hydromechanical automatic tension anchor down) only in that the upward serrations of the slips immediately grip the casing wall after release. This differs in principle from the basic type (the compression anchor installed upside Fig. Once tubing pressure exceeds casing pressure by about 14 bars after the onset of pumping. The Guiberson type hydraulic tubing anchor (Fig. this type of anchor automatically sets the tubing in the deepest position. PRODUCING OIL W E L L S 3 2 ) by tables and diagrams. cylinder 1 is moved downward by the pressure differential across it. This permits spring 4 to press slips 3 downwards.1-48. Hence. they come to bear against the inside of the casing. the stretch during operation in the tubing is the least possible. If prior to retrieval the pressure differential between tubing and annulus is equalized .1-49. Whenever tubing pressure exceeds casing pressure. no upward movement at all is required to seat the slips. Overstress breaks a shear ring. and the slips may then disengage. Correct operation requires prestretching also in this case. so that.382 4. 4. No prestretching is required if an automatic tension anchor is used. As no prestretching is required. against the force of spring 2. Length m Prior to 2 718 823 Production 95 m3/d.4. substantial'wear on rod and tubing strings Production 111 m3/d. represent a hydraulic resistance high enough to prevent the rod string from sinking during the time available: the carrier bar overtakes the polished rod. (d)4.6 m3/d Production 10 m v d 2 718 1826 Production 34 m3/d.17. (iv) the valve ball moves sluggishly in the narrow cage. the rated polished-rod and prime-mover load have to be exceeded significantly. They will not jell even at 0 O C . Typical jelling crudes are parafin-based. Effects of correctly functioning tubing anchors (after Taylor 1960) Tubing Main operating characteristics Diam.1 . but their comparative significance will be different. and then reworked to install a correctly operating tension anchor (Taylor 1960).(vi) consider able friction between barrel and plunger may lift the barrel off its seat.1. and the valve will not open or close on time. (iii) flow resistance of the standing valve may prevent the barrel from filling with liquid during the upstroke. had to be pulled every 6 weeks No tubing trouble over 15 months 2 718 1890 Rod string had to be pulled every other month No rod string change necessary. because highviscosity crudes tend to be naphthene-based. production increased by 20% 2 318 2743 Marked wear on rod string in deflected hole Wear reduced by half Subsequent to repair rod pumps requires special measures. Equipment for producing high-viscosity and high pour-point crudes. then cylinder 1is pushed up by spring 2 and the slips disengage as above.17lists some operating data on wells provided at first with no anchor. PRODUCTION BY BOTTOM-HOLE PUMPS 383 by pulling the standing valve or by any other means. the viscosity of the oil in the tubing increases. 2-3 rod breakages per month Production 46 m3/d no rod breakage 2 718 1737 Tubing perforated. or an anchor that failed to operate properly. Producing oils of several thousand cSt viscosity (waxy crudes) by means of suckerTable 4. These same difficulties will arise when pumping crudes of high pour-point at well temperature. Table 4. on restarting the well. but may be pretty viscous even at high temperatures. (v) during pumping stoppages.1. so that. . (ii) comparatively narrow travelling-valve inlets may. because (i) high friction losses against the tubing and flow line result in an increased polished-rod load during the upstroke. and their viscosity is then comparatively insensitive to temperature. no wear at all 2 718 3473 Many joints had to be changed each quarter No joint failure 2 318 2179 Production 5. in. during the downstroke. 1 . proportional to the static shear stress. If production is reduced but not halted. and decreasing the viscosity of oil entering the pump. A semi-empirical formula was derived to provide the flowing pressure drop of water-cut oil of 800 c P viscosity in pumps of 2 318 -4 112-in. = 100 m3/day. Example 4. A sketch of pump design is given in Fig. Pumps with large valve ports are to be preferred. the flow properties described are transitional. streamlined. Fiud the flowing pressure drop of water-cut oil.1 -13. . size: 4.By Eq. All these conditions may considerably augment gas pressure below the jelled oil plug in the annulus. API type pumps are listed in Table 4.1. the expansion of gas in the tubing enhances the cooling of the well fluid and thus increases the polished-rod load. in which case the pump produces no liquid at all.1 . .384 4. d3'82 .18. shooting it to the surface or into the flow line with a loud report. . on the other hand. may result in full gas lock. The fluid level will then rise in the annulus. tends to be very high. Valves of conventional sucker-rod pumps will perform better if the clearance between cage ribs and valve ball is at least 2 mm and the cage height is less than usual. then removing the latter through the annulus may cause a special kind of operating trouble if formation pressure is comparatively high and well temperature is comparatively low. Their apparent viscosity may be very high near the pour point.10 "C. 4.1 -75 Ap = 6897 +(Apl ~ q .16 x x 0-0699-3'82= 5.9 mm). This irregular shock load is harmful to both the well and the pumping installation.2 x lo4 Pa = 0 5 2 bar. Cia Shell de Venezuela and US1 Venezolana have developed a modified sucker-rod pump whose flow resistances are less than those of the API types (Juch and Watson 1969). indeed. Pumping will inevitably stop at times during continuous production. = 69. It will not let the gas produced flow out through the casinghead. Ap=6897+(1709 x0.8+ 11. and regularly during intermittent production. 800 cP viscosity. so that the gas in question is deflected into the sucker-rod pump together with the oil. If it attains a height where the temperature is low enough to make the oil jell. size API sucker-rod pump (d. in a 2 3/4-in. too.75. then a 'packer' develops in the annulus and stays there even after pumping has been restarted. This is due to the following phenomenon. PRODUCING OIL WELL-2) on the other hand. If the waxy crude enters the well together with some gas.28 x lo4 x 1. + where the constants A a ~ Bd for the new. 4. ) q . so that the gas may break through the plug. Measures which permit the pumping of high viscosity crudes without the above pitfalls can be subdivided in two groups: installing pumps that operate satisfactorily even if the viscosity of the well fluid is high.In mixed-base oils.It is more difficult to start a well producing a crude of high pour point than a high-viscosity one because the starting polished-rod load. but it will usually decrease rather steeply under a temperature rise as small as 5 . This reduces the volumetric efficiency of pumping and. Friction in continuous operation may. and the conventional. if q.1 -66.16 x l o 3 ) . be less than in the case of a high-viscosity crude. . Shoulder 5 then presses against crosspiece 6 lifting sleeve 2 together with the fluid in it. up= 1-4 m/s (to be expected at about n = 12 m i n l and s.= 1. hp= 1. During the upstroke. check valve 7closes. 11. In Fig.= lo4 cP. During the downstroke.14. Ad= 1. or if the oil is too viscous even at the original formation temperature of the well bottom.The viscosity of oil entering the well may be decreased by heating or by dilution with low-viscosity oil. in order to prevert direct contact between hot-water pipe.1 -50. clap valve 4 opens. or farther up the tubing. The latter can be estimated (Juch and Watson 1969) by the formula Table 4. usually in gas-burner boilers.22 m. rod string 3 moves upwards. Water is heated at the surface. This type of pump comes in three sizes: their parameters are given in Table 4. pipe I is usually heat-insulated on the inside or outside.19. 4.18. usually of 1-in. If this is not the case. It has been used in the German oilfields since 1956 (Briiggemann and de MonyC 1959). PRODUCTION BY BOTTOM-HOLE PUMPS 385 The force pressing the sucker-rod pump into its seat.1 . and sleeve 2 re-enters the liquid. clap valve 4 covers the seat machined in the plane A .4. it is recommended to insert an insulating ring at each coupling. designed for the sucker-rod pumping of heavy crudes.1.8 m). electrical or gas-burner. This pipe is fitted with heatexchange plates 2 in a height corresponding to from one-half to three-quarters of the perforated well section. By the above formula The Pleuger type clad-valve pump. can be employed up to 5200 cSt viscosity.1-51 shows a well completion suitable for hot-water heating (Walker 1959). Find the friction force arising between barrel and plunger if dp= 1 314 in. In order to limit undesirable heat losses. and fed to the well bottom through pipe 1.1 . p. tubing and casing.A and closes. The tubing heater is usually installed at a height where wax would start . The electric heater can be placed either below the pump (bottom-hole heater). Heating may be of one of three types: hot-water.in the tubing must exceed the friction force between plunger and barrel during the upstroke.28 x 10" Example 4. Figure 4.3 x m. so as to envelop the rod string (tubing heater). sleeve 2 performs a reciprocating motion along pump tube I. The rising fluid lifts check valve 7 which permits one strokeful of the oil in the tubing to enter the flow line. The first solution is to be preferred if waxy deposits are to be anticipated even at the well bottom.1 . diameter. 1 . Heating temperature . PRODUCING OIL WELL-2) to deposit in the absence of heating.8 Fig. Pleuger's clapvalve bottom-hole pump. in a well produced by sucker-rod pump. 4. Bottom-hole heating with hot water.5 78.386 4.19.The electric current is led in cable 1 to the six steel clad heater elements.4 38.1-50. The heater elements must therefore invariably be covered with oil.2 4 4 4 14 20 64 26. after WALKER (1959) steel. Figure 4.1 -52 shows an electric bottom-hole heater (Howell and Hogwood 1962). load in.1-51. Data of Pleuger clap-valve pumps (Briiggemann and de Monyk 1959) O' D' Stroke length Speed Capacity Effective valve surface Max. It may return via another cable strand or in the tubing Table 4. Their surface temperature must not exceed that ofthe oil by more than 40'"Cand must not exceed 150 "Cin any case. When designing the heating system one should keep in mind that the oil must not be heated above its coking temperature. 4. after BRUGGEMANNand de MoM(1959) Fig.5 25 39 118 1.2 I . m I/min m3/d cm2 kN 3 4 5 112 1. 1. electric heating at a depth of 600 . and q. 1962) a rough estimate.1 -53 compares the economics of the above two kinds of heating under given operating conditions (modified after Walker 1959).cables insulated with asbestos and lacquered textile in a lead sheath are employed.4.Up to 93 "C. depends on the heat loss to the surroundings. however. At even higher temperatures. 4. Box 1260 Tulsa. if power is bought or produced at 83 Forint per GJ. (Figure taken from Howel and ~ o ~ w o o Petroleum d. The heat supply required is given by where q is the liquid production rate. Oklahoma 74101. It must be protected from both mechanical damage and corrosion. ATis the temperature increase desired. In some well fluids. copper-insulated cables are recommended. For instance. PRODUCTION BY BOTTOM-HOLE PUMPS 387 is a function largely of the rate of production.1 . The cost of electric heating is practically independent of depth and is a function of power cost alone. Figure 4. Publishing Company. it equals 0. the efficiencyof heating. Electric bottom-hole heating in a well produced by sucker-rod pump.The cost of delivering one thermal unit at the well bottom increases in the case of hot-water heating with depth and with the price of gas used to heat the water. these may be damaged by corrosion.52. PVC sheets may be used only up to round 80 "C.5 at Fig. duration of heating and loss of heat to the formation. The choice of the cable requires special care. about 1700 wells were produced with the aid of one type of heating or another. PRODUCING OIL WELL-2) m roughly equals hot-water heating if the cost of gas is 0. s 10. The fuel is a mixture of natural gas and air or propane and air.fW- Electric power price 8s F ~ / G J E 90- -5 so- g E -:: 63 FtlQ3 70- 60- '8 Q 40- :: so's X 20. In California.54. Economics of bottom-hole heating methods. 1965).1 -53. which lets them off .388 4.318 Ft per m3. Burner 1 is installed below the pump. Combustion products are led through pipe 3 to the annulus. 1959. 4. It is fed to the burner through pipe 2. Gas-fired bottom-hole heating In a well produced by sucker-rod pump after BRANDTet al. Bottom-hole heating may also involve direct gas burning. after WALKER Fig.1 .1 -54 is a sketch of a well completion incorporating a sucker-rod pump provided with a gas burner (Brandt et al. --irx3z Well depth 200 400 600 rn Well depth Fig. Figure 4. (1965) . 4. The upper limit in wells producing a fluid of low WOR is about 32 m3/day. it must not be forgotten that some liquid condensate may form during the rise of the combustion product. interacting with the flow resistance of the system.1.1 mm mesh size.The screen is of 0. The diluted oil rises to the surface through annulus 2 between the rod string and the tubing. -The purpose of a sand anchor is to separate the sand in the well fluid before it enters the pump barrel. flow is of the annular type. this type of heating will not usually be applicable in wells producing at rates lower than 0. Through perforations I it enters thecasing annulus where it rises to the surface after mixing with the heavy crude. Two possible designs of the submerged pump and of the well completion permitting the addition of a viscosity-reducing solvent are shown in Figs 4. PRODUCTION BY BOTTOM-HOLE PUMPS 389 into the atmosphere.1 -55 and 4. The fuel feed and the gas-to-air ratio are adjusted by a surface control device. The fuel attains the two opposed burner nozzles through filter 10 and check valve 11. fed with current through cable IS. At comparatively low rates. on the one hand. the well must be filled up with low-viscosity. Figure 4. The solutions outlined above are suited in general also for the pumping of high pour-point crudes. on the other. Hence. The feed rate is controlled by the pressure differential between control valves 6 and the back-pressure valve 9. In the sand anchor shown in pig. Production equipmentfor sandy crudes. its minimum diameter is 19 mm. air through conduit 5 to the pressurecontrol valves 6. Ignition of the fuel is ensured by glow plug 14. and the BHP required to keep it up is therefore fairly high. Incorporated in the heater is a thermometer 16.4. The filter is required to hold back solid impurities which could plug the screen installed to prevent flashbacking. In the application of this type of heater. Low-viscosity oil is pumped to the well bottom through the hollow rods and through port I on the sucker-rod pump. and the pressure gradient required to maintain it is less. that feed them to the pressure balancing valve 7 which ensures that gas and air entering the chokes are of equal pressure. in series with the glow plug (no temperature measurement is possible during ignition). Gas arrives through conduit 4. also the BHP.4 m. Interrupting such wells may be something of a problem. The method can be used even at depths exceeding 1500 m. In Fig. it may be of the slug type. Applicability is restricted by higher water contents. Flow will thus become two-phase. Details of the gas burner are shown in part (A) of the Figure. nonfreezing oil directly after stoppage or before restarting.1 -56 (Walker 1959). This method is excluded if the rod string sinks too sluggishly on the downstroke o r if the oil is gaseous. The combustion chamber is ceramic-lined.2 m3/day. If the annulus risks freezing up during pumping stoppages.1 -56 shows a solution popular in Venezuela.4. 4. and prevents coking of the oil. At higher flow rates. Low-viscosity oil is pumped into the annulus between tubing and rod string. This protects the wall of the heater from direct contact with the flame. therefore. a sucker-rod pump is attached to a hollow rod string. The correct gas-to-air ratio can be ensured by the proper choice of the chokes 8. This has an adverse effect on production. The length of the stepped burner chamber is round 2.1 -55.1 -57. the fluid enters the pump through tube 1and annular . and so is. (d)5. 1-55. Bottom-hole pump suited for solvent injection. after WALKER (1959) Fig. (ii) if pumping is stopped. 4. but the cleaning operation itself will be more complicated. The essential thing is to produce the well without damaging the sand face. The cross-section of annulus 2 is chosen so that the rise velocity of the well fluid in it is less than the settling velocity of the sand. which reduces the likelihood of sand grains settling out during continuous production. The check valve in the hollow rod string .1-58. a tubing pump is fixed to the tubing shoe. after WALKER (1959) intervals. Since the chamber can be emptied only after pulling it together with the tubing. In certain other designs. Hollow rods have the advantage that (i) fluid flows faster in the narrower hollow-rod space than in the rod-to-tubing annulus. the sand in the chamber can be dumped onto the well bottom by a sudden jerk on the tubing string. In the solution shown as Fig. the sand in the hollow rods cannot fall between barrel and plunger. to evacuate it continuously to the surface with the least possible harm to the production equipment. and if some sand is produced nevertheless. Such equipment may prolong cleaning Fig. this solution is uneconomical except if the sand content in the well fluid is rather low. 4. PRODUCING OIL WELL-2) space 2. 4. Well completion suited for solvent injection. Fluid lifted on the upstroke reaches flow line 3 through hollow rod string 1and branchoff 2. The hollow sucker rod has in the first place been developed to facilitate the production ofsandy crudes.1-56. The sand collects in chamber 3. The importance of a sand trap is not too great in most cases.390 4. Sand anchor Fig. produced with hollow-rod pump Fig.1-58. 4. 4.PRODUCTION BY BOTTOM-HOLE PUMPS Fig. 4.1 . 4.1. Completion with tubing.57.1-60.4.1-59. Borger-type Christmas tree for hollow-rod pumping . Bottom-hole design with hollow-rod pump seated on an anchor Fig. 15 and 4. In the Borger type wellhead equipment (Fig.. Eqs 4.23). 4. the annulus between tubing and hollow rod string used to be filled with water (Fig. PRODUCING OIL WELLS (2) further prevents sand settling during stoppages from reaching the pump. 4.l(d)l). Hollow-rod string and flow line are connected by conduit 4.l.1 -5.. 4. There are more recent solutions also for wellhead assemblies. which is polished on the inside. (v) If the well-fluid is non-gaseous.61. The rod-string head is connected to the flow line by a flexible conduit. a tubing used t o be run because the plunger used to be of larger diameter than the ID of the hollow rods (cf.1 . as shown in Fig.1 . (ii) Owing to the greater metallic cross section of the hollow rod string. gas anchor In more recent types of hollow rod (cf. and the absence of tubing eliminates tubing stretch. size solid rod. The wellhead equipment much resembles the one for a solid-rod sucker-rod pump completion. Fig.solid ones for several reasons in addition to the ease of pumping sandy crudes: (i) Solid-rod string plus tubing is replaced by the cheaper hollow-rod string. stretch is less than in a 518-in. (iv) Requiring less space. stroke reduction due to changes in liquid load tends to be less. c). may be less even if rod-string weight is greater (cf. the risk ofjoint failure is rather slight. This hazard was the more grave. The pump can be seated on an anchor fixed to the casing.1 -60). 4. (iii) If plunger size is large enough. polished on the outside.58). paragraph 4. hollow-rod string 1 is surrounded by cylinder 2. which assumes the role of the polished rod. 4.1 . In completions such as these. In order to increase the depth of applicability.62. 4. Canadian-type Christmas tree for hollow-rod pumping Fig.392 4. and the upward force acting during the upstroke caused buckling and early failure in the hollow rods. Modern hollow sucker-rod strings are to be preferred to. it can be produced . this solution is at a distinct advantage in multiple completions and midi wells. F. 4.1 .1 . hence. Fig. In the Canadian type wellhead completion (Fig.1 -61).1 -59. plunger 2 mounted on hollow rod string 1 moves in cylinder 3. the deeper the well. The depth of installation can be increased significantly even if the pump is not loaded by an outside fluid column. (i) In unfavourable cases. . after SCHMOE (1959) friction.. Of course. (vi) The rod string does not have to be pulled if paraffin deposits form. the hollow rod string will rub against the inside of the casing. PRODUCTION BY BOTTOM-HOLE PUMPS 393 through the casing-to-rod annulus. Virnovsky (Muravyev and Krylov 1949). non-corrosive and non-erosive to the casing. The annulus is dimensioned so that the rise velocity of the gas bubbles is greater than the rate of downward flow of the fluid. in which case the hollow rod string can be used as a feed line for inhibitors or low-viscosity oil.4.1. For this reason. may be greater than for a solid rod string.1 -62). F. According to S.Free gas entering the sucker-rod pump reduces its volumetric efficiency (Section 4.1 . The device separating the gas from the fluid at the well bottom is called a gas anchor..1 -64. Gas may thus collect and escape through the entry ports and rise up in the casing annulus. Gas anchor for slim holes. The simplest design is the so-called single-body gas anchor (Fig. Multi-body gas anchor Fig.6 3 . Nevertheless. hollow rods have certain drawbacks as well.1 -(b)2). (ii) At high production rates. fluid friction may be significant in the narrow cross-section of the rod.1. Well fluid enters the anchor through ports 1 from where it moves downward in annulus 2. and no significant deposits of paraffin are to be anticipated. 4. 4. . (111) If plunger diameter is small. or to house electric heaters. it is best to separate as much gas as possible from the liquid entering the well even before it enters the sucker-rod pump and to deflect it into the annulus for delivery to the flow line. (d)6. the well may be produced through the casing annulus if the fluid is non-gaseous. plastic rod-guides are employed. 4. Production equipmentfor gaseous and water-cut oil. Such deposits can be prevented by a paraphobic lining or coating. To reduce Fig.the cross-sectional area A. snv Aa = 1 2 ~ ~ s n 3 A. The length of the gas anchor is to be chosen so Fig.12Aps. PRODUCING OIL WELL-2) of the gas-anchor annulus (in m2) should be for high viscosity oil for low-viscosity oil for water A. 4. The design shown in Fig. furnished by the above formulae cannot be realized owing to the well being too slim. 4. If the A. =0. A.1 -63). A typical port diameter is 2 mm.3 x 104A. two.= 1.394 4. Well fluid and gas flow past the . Installing a gas anchor of suficient diameter may be difficult or impossible in slim wells. In this case. 4.1 -64 may be used even in such cases (Schmoe 1959). Sonic gas anchor that the gas bubbles entering its annulus may rise to the top ports during one full stroke cycle of the pump. The third formula is to be used if the well fluid contains more than 80 percent water. in the above formula means the sum of the cross-sectional areas of the gas passages in the individual anchor bodies. A typical gas anchor length equals 20 times the jacket diameter.1 -65.or three-body gas anchors can be used (Fig. Quite often.1 -67 (for which see also p. 4. a sucker-rod pump design whose volumetric efficiency is not too seriously affected by the gas should possibly be chosen. Both the tubing pump marked Tand the rod pump denoted R are provided with a ring valve 1made of brass. 4. secondly. rod pumps are at an advantage because dead space below the lower end of the plunger stroke is comparatively small.66. This is a multi-body gas anchor in whose annular space gas separation is promoted by disk bafflesmounted on spiral R I Fig. modified sucker-rod pumps have been designed for heavy crudes (Fig. In light oils.1. after JUCHand WATSON(1969) springs. Modified bottom-hole pump. stroke length in the conventional pump (dashed line) and the . 4. the vibration gas anchor (Fig. which in effect turns the pump into a two-stage one. Experience has shown this device to operate satisfactorily even at GORs up to 2000.1 -66). Part (c) shows the variation of polished-rod load v. Well-fluid flow keeps the springs and baffles in continuous vibration. In such cases.1 -65) is often used with success. Of the conventional types. 396). firstly. Oil enters the sucker-rod pump through port 2. to the choking of the comparatively slim conduits and.1.1 -(d)4 that novel. Part (a) shows various plunger positions. the gas anchor will not remove all the free gas from the liquid entering the pump. It has been mentioned in Section 4. Let us consider one of the more advanced designs. Failures may be due.1 .4. PRODUCTION BY BOROM-HOLE PUMPS 395 packer and into the annulus through conduit I. Seyeral special 'gas-insensitive' sucker-rod pumps are also known. to packing breakdown. Operation is analysed with reference to Fig. 4. stroke length in a conventional pump. (ii) the rod string is in tension throughout.1. the standing valve opens earlier. because the . The advantage of the modified design when pumping gaseous fluids is that (i) Fig. (iii) on the upstroke.396 4. Earlier opening improves the volumetric efficiency of the pump. Gas in highviscosity oil is particularly deleterious to volumetric efficiency. the dashed line shows pressure in the space below the plunger v. so that more fluid can enter the barrel. PRODUCING OIL WELLS 42) novel design (full line). 4. In Part (b).1 -(f)2).1 -67. the lower part shows the same for the space between plunger and standing valves. which reduces the risk of its buckling and reduces or eliminates the liability of fluid pound (Section 4. The upper part of the full-line diagram shows pressure change in the compression space between plunger and ring valves. Operation of modified bottom-hole pump (JUCH and WATSON 1969) the plunger valve opens earlier and more smoothly during the downstroke. this makes the oil seep downwards and lubricate the plunger with oil throughout. because the lower viscosity of water permits faster slippage past the plunger. a sizeable pressure differential between the groove and the space below the plunger. Fig. . chamber 4 is under suction pressure. Part of the latter also attains space 1 through port 3. whereas its lower part contains water or watery oil.1 -68. and (ii) it reduces lubrication. 4. whereas groove 5 is under the discharge pressure of the pump. During the upstroke. The upper part of the annulus is filled with oil. Pressures being equal between the groove and the space above the plunger. These difficulties are partly obviated in the oil-lubricated pump of ARMCO. compression during the downstroke will not cause it to redissolve in the crude to any significant extent (Juch and Watson 1969). part of the oil enters space 1directly. During each downstroke. During the downstroke. liquid may enter both the central bore 1and the annulus 2 of the pump (Fig. ARMCO oil-lubricated bottom-hole pump for wet oil During production. oil lost from space 2 is made up from the well fluid.1. There is. which makes the barrel and plunger wear faster. Laboratory experiments have shown that even if the gas will separate rather readily. The presence of water when producing oil with a sucker-rod pump causes two kinds of harm: (i) it reduces volumetric efficiency. no oil seeps from the former into the latter.4. 4. however. PRODUCTION BY BOTTOM-HOLE PUMPS 397 considerabie pressure drop on entrance into the barrel permits more gas to separate.1 -68). the rest enters space 2. Slonegger 1961. Craft et al. as these are discussed in sufficient detail in numerous papers and even books dedicated to this single topic (e. and hence its frequency of vibration.10 is in a general way more of a problem than in flowing or gas-lifted wells. one of whose ends is fixed. Zaba and Doherty 1956. however. The measurement requires a special wellhead completion (Reneau 1953). The assembly permits measurement of BHPs in 3 or 4 wells per day. This procedure is fraught with the risk of the wireline carrying the bomb winding itself around the tubing. or the wireline gets wrapped around the tubing.1 . Such methods have the drawback of being comparatively expensive. the measuring element is an elastic wire. Let us discuss below the potential testing of wells and the means required to perform it. Another design incorporates a Bourdon tube which turns a disk proportionally to the pressure sensed. We shall not. and the most frequent production control procedure is the recording and analysis of dynamometer cards. each 1500-2000 m deep.1 -(f)l). Essentially a plot of polished-rod load v. Far this reason. 1962). Tension in the wire.1. and a special running winch. also. Belov 1960. a tubing string of small enough OD. are proportional to membrane deformation. During a wait of a few minutes. stroke. because no bottom-hole pressure bomb can be installed in the tubing without pulling the sucker-rod string. If the bomb gets caught by a coupling during its pulling. The application of this method is often forbidden by well size and completion type. The winch is provided with a hydraulic torque convertor and a depth and load recorder. enter into details concerning this instrument and its applications. The frequency of vibration triggered in the wire is transmitted to the surface. and featuring an open completion. PRODUCING OIL WELL-2) (e) Well testing One of the most important instruments of testing wells produced with sucker-rod pumps is the dynamometer.4. the bomb will usually disengage itself and pulling can be continued. the card permits determination of numerous parameters of operation of the sucker-rod well. running and pulling the measuring system requires an excess effort. It may be economical to permanently install pressure gauges below the tubing shoes of key wells. In wells with a production casing of large enough size. the BHP can be measured by a pressure bomb run in the annulus. special methods for measuring BHPs have been developed. Figure 4. .7 or 2. In the Maihak type device (one of whose variants is used in process control: cf. Pressures so measured are transmitted to the surface via an electric cable. Pressure gauges installed in the well. Determining performance curves of pumped wells by means of Eqs 2. Section 4. The position of the disk is electrically sensed and transmitted to the surface. which prohibits their use in just any well.1 -69 shows a Halliburton type power-driven measuring assembly and the running of the pressure bomb. the hydraulic power transfer will gradually build up the load in the wireline to the allowable limit and no further. it must therefore be run and pulled very carefully in order to avoid breaking it. the other being attached to a membrane whose deformation is proportional to pressure.g.1 . 4.1 -69.1.PRODUCTION BY BOTTOM-HOLE PUMPS Fig. Halliburton pressure measuring assembly 399 . 4. .h = F.. is From this F. Also.1 . is the weight of the wet rod string and it is equal to the load represented by the bottom line of the dynamometer card (Fig.1 .82. = p W JA. the measurement is carried out shortly after the installation of a new sucker-rod pump).(F.1 . FTo= Appro. Being aware of these parameters pw. 4. F.70). and the plunger load can be calculated from this value. According to the above equations Pw. A common feature of both groups is that the flowing bottom-hole pressure is determined at pump setting depth. 4. 4. = A.F s d ) A.Calculation offlowing bottom-hole pressures from surjhce measurements Several methods are known and. Knowing these values fi can be calculated from Eq. they can be classified into two groups. is the weight of the rod string in air that can be determined if the rod string parameters are known.1 -4.h = Fr --. Agnew's method (1956) belonging to the first group is discussed below. This method can be applied if the pump can be operated at a low enough speed to make dynamic loads and friction losses negligible. with a small modification of Eq.1 .70. From pressure measurements the tubing head pressure p. The accuracy of this method is significantly influenced by the accuracy at which rod loads can be determined from dynamometer cards.vu . 4. .L% + F T .and hence Yr F. It is also known that F. 4.. The conditions are ensured by operating the pump at a low speed (if the well is prone to waxing. Opening the casing annulus and venting the gas is advisable. 4. .3 it can be seen that The downstroke polished-rod load.1 . According to Eq. can be calculated from Eq. is known. logically follows.1 the polished-rod load on the upstroke is then In connection with deriving Eq. the value of F.1 . 4.8 1. can be directly read from a diagram similar to that of Fig. depending whether the dynamometer card is used numerically for the determination of the flowing bottom-hole pressure or not. The dynamic liquid level Ld in the casing annulus is determined by means of an acoustic survey.1 -71.4. 2.1 . The Fig.e. This latter is moved at a constant speed by an electric . 4. 4. Figure 4. sound source 1.Upon the casing head the "gun". is measured by surface pressure gauges.1. is mounted. Changes in microphone current due to the incident sound waves are transmitted by amplifier 3 to pen recorder 4. Acoustical survey (MURAVYEV and KRYLOV1949) reflection of the sound wave generated pneumatically or by exploding some cordite is sensed by microphone 2.e. which traces them on paper strip 5.71 shows the principle of measurement (Muravyev and Krylov 1949). i. The pressure of the gas column can be determined by Eq.70. This is a tungsten filament bent in the shape of the letter w to which current is fed by a low-voltage cell.4-5.. Fig. i.1 . PRODUCTION BY BOTTOM-HOLE PUMPS 40 1 The essence of the methods belonging to the second group is that they determine the flowing bottom-hole pressures on the basis of The casing-head pressure p. or equal to. then (L. g if we know the gas fraction then There are other methods that calculate the flowing bottom-hole pressure also by Eq. by applying Wallis' equations to the foamy liquid column in the annulus.1 -(f)2) the casing pressure is decreased by some tenths of bars and for 1 or 2 hours the production is continued at a steady rate. is less than.61 m/s. of larger-than-usual diameter. so that the liquid level sinks to the pump depth.J. 0. . Then.L. then According to Eq. PRODUCING OIL WELLS--(2) motor.402 4.83. surface casing pressure can be read. the p. by choking. For calibration purposes. while the speed of pumping remains unchanged. The speed of sound is different in different gases at different pressures. Reflections from these couplings permit us to calculate the speed of sound and.. . Thus it is guaranteed that the operating parameters are stabilized.1 and the relation . pressures are adjusted on the casinghead by choking the gas passage from the annulus.and casing-head pressures during the period of the choked casing-head gas passage. but adjust such a casing-head pressure p.4.. the cross sectional fraction of the gas phase is if v. When the diagram begins to get "pistolshaped" (Section 4. hence. if the superficial gas velocity is greater than this value.. and the fluid level should really be at the pump setting depth.)% =0.1 . These latter methods can be applied on wells of relatively greater gas-oil ratios. For the determination of the average specific weight of the liquid column in the annulus several methods are known. According to Nind's method (1964) this can be determined only by continuous dynamometer survey. A sudden increase in the tubing-head pressure indicates that the fluid level in the annulus is depressed to the pump. assumed to be the same in both cases is k= Pcol+ Pg1 -Pcoz .1. so-called marker couplings. 1. are installed at various known depths in the tubing string. the depth of the fluid level. = p . It is obvious that the average specific weight of the liquid. and from the data.. Deax (1972)records the tubing. 4. According to the Walker method (Nind 1964) two different p.Pgz Ld2 -L d l Godbey and Dimon (1977) measure the gas volumetric flow rate produced through the casing head. and adjusting it to the changes taking place during the pumped life of the well.1 -72.the subsurface mechanical loss P. which. . the more economical one is to be chosen. Power consumption of sucker-rod pump. Well depths ranged from 800 to 1100m.. and reducing pump capacity to the desired value.4.. and output power Po. O n the left-hand side of Fig. PRODUCTION BY BOTTOM-HOLE PUMPS (f) Operating conditions Correctly choosing the operating point of a sucker-rod pump installation. then they should equal each other as well as the daily inflow rate. intermittent operation. Some of the results are shown in Fig. is spent to cover the electric loss P.1. Power consumption of 474 electrically driven sucker-rod pump installations was investigated in the Soviet Union (Milinsky et al. The main difference between the two modes is in this case that the same volume of liquid is pumped over 24 h in the continuous mode. after MILINSKY et al..73 (assuming a given well and a given rate of production) daily power consumption v. let us assume as a first approximation that (i) the mode of operation does not affect the daily inflow rate of fluid into the well. and the volumetric loss P. Power consumption is greater in the intermittent mode. or by maintaining the capacity and reducing the duration of pumping per day.. . (ii) the liquid flowing through the sucker-rod pump is gasless. In order to forestall this. and during a number of hours t < 24 in the intermittent mode. . a decline in well capacity entails a gradual decrease in volumetric efficiency. if the capacity of the sucker-rod pump installation is not adjusted to the gradually growing deficiency of well fluid.4. 1970). If both variants are feasible. daily pumping time has been plotted for two values of polished-rot stroke.It often happens that. 4.. This can be realized in one of two ways: either by maintaining continuous pumping. If the daily production rates of the two modes have been correctly chosen. Continuous v. (iii) volumetric efficiency is unity. "v pm2pm1 PC 25-75 5-15 5-25 20-50 % % % O/o Fig. (1970) (01. the surface mechanical loss P. In order to decide whether continuous or intermittent pumping is more economical. The volumetric and electric losses are seen to assume a high significance occasional1y. daily production rates from 10 to 80 m3. involving a higher spm. after continuously producing a well of comparatively high rate with a pump of the correct capacity.. is a highly important task. 4. It is seen that the difference between input power Pi.1 . gives rise to higher dynamic loads. the production rate of the pump is to be reduced so as to match the daily inflow rate.72. a gradual increase in the specific power cost of production will result (Szilas 1964).1 . PRODUCING OIL WELL-2) Fig. 4' = q t ~ J 6 0[NISI Daily power consumption is provided by wherein the P input power of the motor. k 1200 m. = 3 1. after SZILAS (1964) Volumetric efficiency has been assumed to equal unity.=2500 kgid. y = 8826 N/m3. however.1 -46 and 4.4. The figure further shows that. however.8 mm. A further reduction in pumping time. because: (i) the production capacity of the pump decreases in . Daily power consumption of intermittent and continuous pumping at q.68. is derived from Eq. The volumetric efficiencies of the two modes of operation are. d . In the case examined. power consumption is higher at shorter polished-rod strokes. 4. The Figure reveals daily power consumption to be the higher the shorter the daily pumping time.1 -73. power consumption hardly increases while pumping time decreases from 24 to 12 h. 4. different in the general case. with the substitution giving r .1 -49. with an approximation of sufficient accuracy for comparison. entails quite a steep rise in power consumption. the power consumption of a correctly dimensioned continuous pumping operation is less for a given volumetric efficiency than that of the intermittent operation. all other parameters being constant. Since a daily pumping time of 24 h means continuous operation.1 . Pumping speeds have been determined using the relationship implied by Eqs 4. t is daily pumping time in s. since lifting a given liquid volume from a given depth requires in a fair approximation the same total number of strokes at given values of polishedrod stroke and plunger diameter. In continuous operation. The diagram enables us to decide which of the modes is the more economical. the decrease in volumetric efficiency due to the gas content of the well fluid is the greater.4. PRODUCTION BY BOTTOM-HOLE PUMPS 405 time owing to wear of the moving parts.1. now. provided daily production is equal in the two cases. the theoretical capacity must be increased. volumetric efficiency. we find with reference to the diagram that. if the volumetric efficiency ofcontinuous pumping is 0. the daily power consumption of continuous pumping at a volumetric efficiency of q. and the daily production rate is that much lower. mean volumetric efficiency is invariably less than unity. this condition obtains only: if (i) the well bottom is below the sand face (the well ends in a 'sump'): both modes will produce at the same rate if the fluid level cannot rise past the sand face. In the intermittent mode.=0.1. Thus inflow and daily production rates can be equalized. this number of strokes is . For instance. The efficiency of intermittent production is lowered by the missing production.l(b)2. In other words. the automatic control of daily pumping time permits to continuously adjust production capacity to inflow. except for a short while between changes. the producing fluid level is invariably higher. In reality. the volumetric efficiency of intermittent pumping is less than unity. the initial capacity must exceed the rate of inflow.4. too. If the prime mover of continuous pumping is an electric motor. (ii) if the allowable pumping rate of the well is rather low so that the pump is deep below the fluid level.88 equals that of intermittent pumping for lOh/d. then intermittent pumping is more economical. On the basis of the above considerations. The necessarily higher pumping speeds of intermittent operation cause more wear and tear in the pumping installation. in order to deliver the required production. The decrease of volumetric efficiency due to the presence of gas may be more unfavourable in continuous operation. at a polished-rod stroke ofs = laom. Repeated capacity increases may be brought about by increasing the pumping speed of continuous operation. immersion is equal to or less than in intermittent operation.73 the daily power consumption furnished by Eq. (ii) By what has been expounded in Section 4. as regards specific power consumption. the less the BHP and the depth of immersion. We have assumed so far that the daily production rate is not affected by the mode of production. In intermittent pumping. at unity efficiency. with the producing level comparatively high.1 . The mean producing fluid level of intermittent pumping may be adjusted to equal that of continuous production. In an automated intermitting operation (see below). also. In reality. changing the pumping speed requires changing of the v-belt sheave.88. in the given well. the prcducing fluid level usually stabilizes near the pump in continuous operation. In cases other than the above. we have plotted on the right-hand side of Fig.1 . 4. at daily pumping times exceeding 10 h.89 v. Noticing the decrease of production capacity below a given threshold and changing the sheave requires human intervention. the above consideration applies to ideal intermittent pumping. When wear kas reduced capacity to the level of the prescribed production rate. or the daily pumping time of intermittent operation. 1 .4 kNm maximum allowable torque. If the forces involved are significant.. and the dynamic forces acting on the plunger are transmitted to the rod string and also to the surface pumping unit. however. The wearing parts of the pump therefore cover the same aggregate 'friction path'. It is particularly harmful to the surface gear reducer and may. 2 and 3 represent possible cases of fluid pound in one and the same well. If this is the case. shorten life and lead to early tooth cracking and breakage. Intermittent pumping is justified if it significantly improves volumetric eficiency. then the barrel will not fill up completely with fluid during the plunger stroke. 4.74 shows severaldanymometer cards illustrating the 'fluid-deficient' operation of a sucker-rod pump. Determining from these diagrams the peripheral forces on the crankshaft for various shaft positions a. it is usually preferable to operate in the continuous mode. state that if the volumetric efficiency of continuous pumping is comparatively high. Fluid deficiency is not. we see this to be exceeded during the downstroke in cases I and 2. Fluid pound. Figure 4. The force of a plunger hitting a gasless well fluid is approximately. then. 4. but at a faster average speed in the intermittent case. Dynamometer cards indicating fluid deficiency. The situation would apparently improve if a larger effective counterbalance were used.1 . 0 20 40 60 80 100 120 S d . Curves I. and thus the balancing required will change from .=6. after MARTIN(1961) (f) 2. PRODUCING OIL WELLS <2) realized within a shorter span of time. the plunger loaded with the weight of the fluid column in the tubing plus the weight of the rod string suddenly hits the fluid in the barrel after a more or less free drop. automation of the intermittent installation is to be recommended.406 4. We may. Cm Fig.75. Assuming a gear reducer of M. the phenomenon is called fluid pound. Gear-reducer load can be readily analysed by examining crankshaft torque. and calculating torques therefrom. The torque is seen to change significantly and repeatedly during each stroke cycle. At the beginning of the downstroke. -If the production capacity of a sucker-rod pump exceeds the inflow rate of well fluid into its barrel. according to Juch and Watson (1969). and failures are more frequent. a permanent situation.1 -74. No overloading occurs in case 3. This is a dynamic shock as well as a change in static load. Dynamic stresses are also stronger. we obtain the diagrams in Fig. Now wear is about proportional to the square of the relative speed of the moving parts. even in an apparently well-designed unit. the gear tooth on the highspeed shaft pushing the gear tooth on the crankshaft.1 -75. 4. after MARTIN(1961) of consideration here. a shows a normal case. A phenomenon of special interest is the negative torque. b) inverts the role of the teeth. PRODUCTION BY BOTTOM-HOLE PUMPS 407 one stroke cycle to the next. 4. Peak loads and load fluctuations may exceed those shown in Fig. Hence.1 .76. and also of the rod string.4 Upstroke Downstroke I -9 Fig.75 by as much as 50 percent.1 -76. 4. more than once in a stroke cycle.4.1. The phenomenon of fluid pound tends to shorten the life of sucker-rod components. that is.76. primarily because it hastens fatigue. . If the gears are overloaded. Hence. The negative torque (Fig. Variation of net crankshaft torque over one stroke. 4.1. owing to the dynamic effects left out -3 C. it is preferable to follow the API procedure of derating the gear reducer by a factor of two. in sucker-rod pump installations where the occurrence of fluid pound is anticipated. Figure4. after MARTIN (1961) Fig. an abrupt snapover of the crankshaft's teeth from the pushed into the pushing position will occur. this may take the form of a clash cracking or breaking the engaged teeth. It is liable to cause trouble especially at high pumping speeds. Influence of negative torque upon gears.1 . The magnet pulls in and releases the sensor wire. . after DE MOP-& (1959) Figure 4. incorporates pressure sensor 2 (a steel wire. Automatic control. feeds low-voltage pulses to the electromagnet coil. on the other.408 4. the discriminator ignites one of the series-connected thyratrons 7. in cases of liquid deficiency. However. by means of tuning screws 6. 4. and by the latter to discriminator 5.First. Transmitter 1. When the down-hole transmitter wire is vibrating at the natural frequency of one of the two discriminator wires.1 -77. when the well has been pumped off. automatic trigger 3. for intermittent pumping. it must be ensured that the sucker rod pump will operate only as long as the pump barrel is fully filled with liquid during the upstroke. to the least and greatest prescribed pressure. on the one hand. which starts to vibrate at a frequency depending on its constant physical parameters. time cycle intermitters were used. Maihak's SR-1 controller.77 is a diagram of a regulating device built by Maihak AG. Previously. The electric vibrations induced in the coil by the vibrating wire are fed through a cable attached to the tubing to amplifier 4.1 . when the fluid level has attained a predetermined height during a pumping stop and. Mounted next to the wire is an electromagnet. on the one hand. one of whose ends is attached to a membrane whose position is pressure dependent). At predetermined intervals. but very often also at continuous production. or. no long-lasting results can be reached by applying this method. This latter incorporates two wires whose natural frequencies are adjusted. on the other. 2 - I Fig. pumping will stop. Electric signals control the start-up and stopping of the pumping unit's prime mover. installed on the surface. in intermittent pumping. There are several solutions for automatic control: Automatic '5formation control" of intermittent pumping Formation control essentially consists of installing on the well bottom a sensor that signals. and denoted the SR-1 (de MonyC 1959). and on its tensioning by the membrane. installed at the tubing shoe. The winding of the relay in the anode circuit of the thyratron in question receives a current which opens or closes the main winding circuit of the . PRODUCING OIL WELL-2) (0 3. 4. respectively. at the downstroke. the plunger descends into a pump barrel only partially filled with liquid. Westerman (1977) gives an excellent summary of these processes. Fig. or time. and is plotted as function of the polished-rod displacement.4. As a sign of the fluid deficiency. Of the further units shown in the diagram 8 is a counter. These methods are based either on the measurement of the current input of the electromotor or on the measurement and evaluation of the polished-rod load. "Pump-off' control Formation control is rather costly. The principal methods applied even today are shown in Fig. If.78. The control permits us to start pumping when the fluid level has risen to a predetermined value and to stop when the well has been pumped off. respectively. A l l .1. Several methods have been developed that sense the pumped-off condition on the basis of surface recordings. 4.1 -78. The dashed line shows the case of a fully filled barrel and the solid line that of a partially filled barrel. 9 is a recorder and 10 is an adjusting device. "Pump of' control methods after WESTERMAN (1977) . are smaller. 4.1 -78. according to the method shown in Fig. The control methods using the current input are shown in A. "Pump-off' control is the common name for these methods. or pump-off. PRODUCTION BY BOTTOM-HOLE PUMPS 409 prime mover. crank angle. the second peak in the current and the the area below the consumption curve. The current input proportional to the net crankshaft torque is continuously measured.1 . 1 . the pumping time is decreased by 30-35%. automatically shuts the well down or signals to the pumper or supervisor. Fig. The control shown in Figure 4.2 m and a maximum polished-rod load of 196 kN -or a departure from the usual walking-beam drive. while the method presented in Fig. such as failure analysis. and either.1. the options are to increase plunger size. Figure B/1 shows a method. in wells of intermittent operation. The basis of control at method B/3 is the diagram area valid during the downstroke.12).1 . Method B/4 interprets the size of the area under a taken line. Fig. the polished-rod displacement. Beside this. PRODUCING OIL WELLS--<2) the decrease in peak current is indicated. where the dynamometer card can be transmitted to a controlling computer station. 4. respectively. Such a method is described by Hunter et al. and the energy consumption by 10. as expounded in Section 4. as the result of evaluation. the rates lifted increase. 4. The measured input currents and polished-rod loads. where the rod load is measured and checked at a certain point in the downstroke. polished-rod stroke and/or pumping speed. The special duty POC computer has the required computing capability. . A/3 shows the decrease of the average motor current during a complete pumping cycle.1. (1978). Westermann (1977) points out that pump-off control leads to very significant savings in operating costs. The method shown in B/2 considers the difference in the rate ofchange of the rod load for normal and pumped-off conditions. Increasing pumping speeds is primarily limited by the maximum allowable dynamic load (Eq. greater than prescribed at a given polished-rod position. At (a) the pump is full.35%. the operating costs by 10. which exceeds the evaluation of the POC computer and can do other tests. crank angle or time are transmitted into a minidomputer.1 . In certain cases hierarchical systems are applied. v.1 -(b) 1.7818 is based upon the measurement of the rod load as a function of the polished rod displacement or the crank angle. and an earlier recognition of operational failures with an improved possibility of their correction is possible.35%. A/2 shows the decrease in current demand at a given point. respectively. while at (b) the actual measured value.7 of the Soviet unit 9 SK is 3 14 kN for a stroke of 4. Increasing the polished-rod stroke requires either a significant increase in the dimensions and weight of the surface pumping unit -the weight according to Table 4.41 0 4. As compared to the conventional control methods. A larger plunger size will improve capacity only up to the theoretical maximum. refers to pump-off. The long-stroke sucker-rod pump If the production capacity of the sucker-rod pump is to be increased. the use of manpower can be improved. A/4 considers a less than normal value of the current consumption on the downstroke.2. drive motor and gear reducer 3. condensate tank 5. The fluid collecting in the condensate tank is likewise delivered to tank 4 by screw pump 6. a drainage pump. filled with power fluid and gas.1. 4. the pump sucks fluid from under the cylinder and forces it into the gascushioned balancing tank. the control valve rises. balance tank 4. the second by correctly choosing the flow resistance in the path of fluid backflow. housing the piston that moves the polished rod. . 4. the reversing valve sinks and another upstroke begins. Figure 4. Pumping speed is determined by the combined duration of the up.1 . Its main components are hydraulic cylinder 1. Reversing valve 3 now rises and changes the direction of fluid flow.4. The first can be regulated by the rate of flow of power fluid under the piston.79 shows a hydraulic pumping unit. screw pump2. pump 1 A '2 5' Fig. On the upstroke (part a). Operation of the system is explained on the example of an Axelson make hydraulic drive (Fig.and downstroke. When the piston has attained the lower end of the stroke.1 . Stroke can be adjusted by changing the point where power-fluid conduit 7 enters the cylinder. At the upper end of the stroke (part b). On the downstroke. and air accumulator 6.1-80). pressure above the control valve 2 suddenly increases and forces the valve into the lower position. PRODUCTION BY BOTTOM-HOLE PUMPS 41 1 (a) Hydraulic drive The hydraulic drive permits a significant increase in stroke without too great an increase in structural weight.79. Hydraulic long-stroke drive sucks liquid from the balance tank 4 and forces it under the piston in the cylinder. towering above the wellhead. 1 -48). PRODUCING OIL WELLS i 2 ) Table 4.412 4.1 m stroke and 178 kN maximum polished-rod load is only 133 kN. which further increases production capacity. The longer stroke of the hydraulic drive has extended also the depth range of sucker-rod pumping. It is seen that the weight ofeven a unit of 9. Maximum delivery of Pelton's long-stroke hydraulic sucker-rod pumps .1 -20 lists the main parameters of Pelton-made long-stroke hydraulic pumps. Figure 4.1 .1 -81. 4.80. Operation of Axelson's hydraulic drive Fig. round 42 percent of the walking-beam type unit mentioned above. 4. Eq. The longer stroke entails a larger maximum plunger size (cf.1 -81 shows the maximum production capacities at various depths of the units listed Fig. 4. 1. wear of the pump plunger and barrel is reduced. In the smooth-running hydraulic drive.7 63 63 63 102 107 109 111 130 132 133 . Weight I/min kN 14. rod life is prolonged.1 7.and the downstroke. The other diagram shown for comparison is that of a walking-beam-type unit (shaded). stroke reduction is 60 percent of I b S Fig. = 25.'. with s = 1. e.0 9.4 12. the shape of the diagram is near-ideal.0 6. The better utilization of power is revealed also by the dynamometer card.7 5. 4.20 (p.1 m and n = 2 min. and 15 percent if it is 9.1 -82 shows a typical card of a long-stroke hydraulic unit with s = 9. longTable 4. Load is seen to be practically constant during both the up.3 4.1 -(b)2) is more favourable at longer strokes. the diagram deviates strongly from the ideal.8 m and n= 1 0 m i n l . dynamic load on the rod string is less. PRODUCTION BY BOTTOM-HOLE PUMPS in Table 4. The longer stroke decreases the relative stroke reduction. Section 4. Figure 4. In the case of a rod string 2560 m long and a plunger of 1 314-in. In the walking-beam unit. The diagram marked FP shows approximate maximum production rates attainable with walking-beam type pumping units.4 mm. = 1000 kg/m3. d.1 -20.1 m.1 -82. Typical data of Pelton hydraulic long-stroke sucker-rod pumping units Type code 350-6-10 F-P 350-7-10 F-P 350-8-10 F-P 412-7-20 G-P 412-8-20 G-P 412-8. if ensures a more efficient stroke transfer.9 5.1 . the pump has to be changed less often.. the load changes significantly over the up.1. Despite the above advantages. The average upstroke speed is typically the same in both systems. Comparison of diagrams FP and HP reveals a considerable improvement in production capacity. = 1).and downstroke.5-20 G-P 412-9-20 G-P 512-8-30 H-P 512-8. rl.413 4. The volumetric-efficiencyreduction due to the presence of free gas is also less because the Asls ratio (cf.1 9.g. polished-rod stroke if the latter equals 1-9m.5-30 H-P 512-9-30 H-P rims.3 5. size. The grooves holding the wire-rope windings are of a special design: on Fig.414 4. At the top of a derrick. shown in Fig. 4. 4.1 -83 there are two drums turning on the same shaft.1 -83. Ewing 1970). about 16 m high. Oilwell's 3534-type mechanical-drive long-stroke sucker-rod pump . PROIIUCING OIL WELLS (2) stroke hydraulic pumps went out of use early in the nineteen-fifties. One of the products of the resulting development work is the Oilwell rig marked 3534. (b) Mechanical drive The considerable advantages of long-stroke pumping units with hydraulic drive has urged research and design teams to develop a mechanical drive simpler and more reliable than the hydraulic (Metters 1970. because the reliability of the drive was found to be unsatisfactory and its maintenance too costly (Metters 1970). 4. One drum takes the wire-rope hanging the rod string. after EWING.1. The lever arm of counterweight 3 equals the drum radius.84. its lever arm is zero. 4.1 . October 28-30.1970 (presented at the 41st Annual California Regional Meeting of the Society of Petroleum Engineers of AIME. Operation of mechanical long-stroke drive. Winding and unwinding of suspension rope. in Santa Barbara. As soon as this acceleration peaks out. after EWING. the other takes the wire-rope from which depends a counterweight moving up and down in the derrick. in Santa Barbara. California. Figure 4.1970 (presented at the 41st Annual California Regional Meeting of the Society of Petroleum Engineers of AIME. California. an acceleration results purely from the difference in lever arms. whereas they decrease along a spiral on the conical drum portion. 1970) .1 -84 shows three positions during the upstroke. the motor cuts in Fig. 4. likewise installed at the derrick top. October 28-30. rope 1 connected to the rod string is in contact with rod-guide 2. Early in the upstroke. The drum shaft is rotated through a gear reducer by an electric motor. In part (a). groove radii are constant.1 -85. This type of drive permits a very economical utilization of motor power. PRODUCTION BY BOTTOM-HOLE PUMPS 415 the cylindrical part of the drums. 1970) Fig. the rod string continues to rise at that speed.. kN kN* m 156 111 10. shown in part (c) of the Figure. according to part (b) ofthe Figure. PRODUCING OIL WELLS {2) and further accelerates the rod string.8 m before the end of the upstroke.1 -21 Typical data of Oilwell 3534 long-stroke mechanicaldrive pumping units Type code 3534-75 3534-100 Fm.4 * Counterbalance effect Sm. Figure 4..416 4. so that the relative torque of the rodstring side increases. The prime mover switches off and the rod string arrives with a smooth deceleration at the upper stroke end. Maximum delivery of Oilweil's long-stroke mechanical-drive sucker-rod pumps Table 4. . About 1. After having attained a pre-determined top speed.1 .4 156 111 10.. 4. Fcm. while. the lever arms of rod string and counterweight are equal..n I/min 5 5 P kW Weight kN 56 145 75 156 .1 -85 shows the arrangement and suspension of the wire- L. This solution provides uniform lift speed over 80 percent of the upstroke. the lever arm of the counterweight begins to decrease.. m Fig.86. In all solutions. one of the principal aims is to make running and pulling as simple and troublefree as possible. conventional tubing sizes can be used. whose basic principles are outlined in Fig. The relevant pumping methods fall into three groups: selective pumping by tandem sucker-rod pumps. Each pump receives a separate inflow from a separately developed zone.1 -21. even if their fluids are gaseous. The capacity of the units is given in Fig. from the nineteen-fifties on. It has the drawback that gas in the individual zone fluids cannot be separated before entering the pumps. The combined costs of pump changing. work-overs and paraffing removal are about twice higher than the corresponding costs in a conventional single completion. In solution (a) pump 3 producing zone I delivers its fluid through conduit 5 and annulus 6. by double-horsehead pumps. PRODUCTION BY BOTTOM-HOLE PUMPS 417 rope in the spiral groove on the drum in various situations. (a) Tandem sucker-rod pumps The tandem pump is a pair of sucker-rod pumps. Design details of solution (b) are shown in Fig. driven by a common rod string (see Boyd 1960).1 -87.4.7 mm ID). and thus pumping at a favourable volumetric eficiency is restricted to gasless or low-GOR wells. Both zones can be produced at a satisfactory volumetric eficiency. whereas the gas of this same zone reaches the surface through conduit 6.3. 4. Tubing 1 is of 2 3/8-in. and the products of each pump is delivered separately to the surface. are contained in Table 4. In wells less than 1800 m deep. 4. size (125. This solution is costlier than both foregoing ones. The data of the drive unit. 4. 4.1 -88. Solution (b) differs from the above in that the flaid of the lower zone is led by the conduit 5 up to the surface.and 314-in. Thus the upper zone can be produced at a satisfactory volumetric eficiency even if it is gaseous.1. This solution is costlier than the one in (a). Tubing 2 is of . Selective sucker-rod pumping of multiple completions The drive towards reduced production costs has. which has so far been developed in two sizes. completed with a production casing of at least 5 112-in. Dual-zone arrangements fall into four groups. which will fit into a production casing of somewhat smaller size.1 -86 on the assumption of a 90-percent volumetric efficiency. size rods. one below another. and by two separate sucker-rod pumps. more seldom three zones opened in one and the same well. with the liquid and gas of zone I being produced through a pair of coaxial tubing strings.1. The Flexirod has been combined to advantage with the long-stroke mechanical suckerrod pump drive (Snyder 1970). size: it takes a rod string made up of 7/8. The Figure also shows recommended plunger sizes. Zone 2 is produced by pump 4 through tubing 7. This solution is cheaper than the rest of the options. In soiution (c) the fluid of zone 1is produced through conduit 5 by pump 3. promoted sucker-rod pumping techniques which permit the selective production of two. Solution (d) is a variant of solution (c). which makes the annulus available for removing the gas of the upper zone. 1 -88. 4. PRODUCING OIL WELL-2) (a) (b) (C) (d) Fig. 4. Selective production of two formations with tandem sucker-rod pumps.4.87. after BOYD(1960) . "b" arrangement. after BOYD(1960) Fig.1 . 9 4.0 Pump spacing Water content 38.3 1739 65 13. torque MNm 13 18 18 26 73 73 Max.9 3.4 31.9 9.9 3.7 1344 47 1.63 4.7 4.7 3198 2583 25 5.9 3.88 4.7 4.9 9.Max.88 1.5 85 3. Nominal size - '8.1 7.4 31.1 -22.37 1.9 4.7 31.8 .9 38.7 Setting depth m 'Ontent Water % production m3/d mm Barrel Length Data of lower pump 2 2 2 2 2 2 in. stroke m 1.5 568 16 15.9 30 30 5 19 31 26 4.1 m3/d Gross pr*uction 10.88 1.7 4.7 24.1 21 21 25 25 m % 14.7 31.1 38. 38.7 4.9 4.9 7.1 2.1 3.9 m Length ID 38.9 38.7 20 1309 23 2. Operating data of selective production of two zones with tandem sucker-rod pumps (after Boyd 1960) . Nominal size 1760 1365 m Setting depth 3.1 m ID 2590 - 5.88 52 52 29 11 11 11 kW Motor power 2 2 2 2 2 1877 2614 2620 3228 2 in.7 31.1 mm Barrel Data of upper pump Table 4.9 31.7 4. the higher fluid load demands a stronger rod string. size and can be run separately. Section 4.89. As a prevention. Since in deeper wells the casing is thicker-walled. 2 718-in. rods. and even that only within rather narrow limits set by well completion and pump design. Selective productton of three formationswith tandem sucker-rod pumps.1 . size.1 -(f)2). the operating point is sometimes designed with the lower-capacity zone in mind. PRODUCING O I L WILLLS (2) 1-in. The plunger entering the unfilled barrel may give rise to fluid pound harmful to the entire installation (ef. too. The pump producing the lower-capacity zone is therefore often oversized with respect to the rate of inflow. The only parameter that can be varied to affect production capacity is the plunger diameter. this is achiebed for the upper zone by letting the oil produced flow back in the annulus. sucker-rod pumps provided with a special . 7/8 and 314-in. after Boyv (1960) couplings have to be used.22. size tubing will not pass. so that special tubes with slim Fig. in whose bore packer 5 ensures a leakproof pack-OK In wells deeper than 1800 m. The main operating parameters of wells fitted with tandem sucker-rod pumps of this type are given in Table 4.1. in the section of I-in. The pumping speeds of the two pumps in tandem are equal. 4.420 4. To solve the same problem for the upper zone.1 . In solution (b). size tubing is required. the normal 1-in. and their strokes differ only inasmuch as stretching of rod strings and tubings is different. It is sometimes necessary to stop pumping one zone while continuing to produce the other. The two zones are likely to have different fluid inflow rates. The string is usually composed of rods of 1. It can be attached by means of hold-down 3 to cross-over piece 4. production casing. The entire fluid of zone 1 is produced by pump 3 through tubing 5. and the gas from this zone rises through annulus 10. In practice. the pump produces in the usual fashion. tubing is run in a 7-in. tubing filled with liquid. The surface pumping unit is of the walking-beam type with a special horsehead hanging both strings of rods.4. during setting) be exposed to a very high tensile stress. The annulus is packed off above zone 1. All the described solutions have the advantage of permitting the selective pumping of two zones at comparatively low cost. (iii) the production of both formations must be stopped for pump changing. The producing zones are separated by a packer. as external-upset tubes would not go in the casing. 4. In wells close to 2000m deep. two rod strings and two suckcr-rod pumps.g. It is. whereas the gas from zone 2 is removed through annulus 7. so that pipe made of high-strength steel N 80 is employed. 2 3/8-in. Tubing 7 is of 1in. (ii) if inflow from one zone is too sparse. The tubing is of the plain-end type. the edges of the couplings are . PRODUCTION BY ROTTOM-HOLE PUMPS 42 1 travelling valve arc uscd.1. The production casing is of 5 112-in. One relevant Salzgitter arrangement is shown in Fig. high water content. of course. The principle of the solution is shown in Fig. hollow-rod string 9 moves in 2-in. or a gas lock develops in the pump barrel for any other rcason. The main advantage of the solution as compared to the tandcm pump is that pumping one zone can be stopped quite independently of the other one. howcver.1 -90 (Graf 1957). the tubing head is shut off. In order to facilitate running or pulling. If. Their main drawbacks are that (i) the capacities of the two pumps cannot be varied independently. It was in 1959 hat a tandem pump was first used to selectively produce three formations. This arrangement will. (b) Doublehorsehead pumping units The well completion features two independent strings of tubing. Both pumps are thus driven by the same prime mover. tubing 8. size. except within rather narrow limits. much more expensive. the tubing producing the upper zone may under unfavourable conditions (low fluid level in the annulus. work satisfactorily only if the fluid of the lower zone is comparatively gasless. The fluid of zone I enters pump 4 and reaches the surface through tubing 7. however. (c) Tvo pumping units The most elastic method of selectively producing two zones is undoubtedly the one involving two entirely independent sucker-rod pumping units.4. increased pressure keeps the travelling valve permanently open. rod-string load transferred to tubing e. fluid pound may occur and result in rod-string failures. Zone 2 is produced by pump 5 through tubing annulus 8. The liquid of top zone 3 is produced by pump A through holjow-rod string 9. As long as the tubing head is open. size. thus idling the pump. however.1 -89. The fluid from zone 2 is produced by pump 4 through tubing 6. as it needs more pipe and more rods. The bore of the packer is provided with a check valve. 1 . Selective sucker-rod pumping with independent pumps pump installations exceed but slightly the cost of producing two separate wells with independent sucker-rod pumps. In the Soviet Union. This well completion has its advantages even if one zone is flowing.422 4.1 -91. 4. 4.The pumping unit has a single gear reducer for two separate crank-balanced walking beams. One possible wellhead design is shown in Fig. The two cranks are at right angles.1 -90. especially if the upper zone is flowing.4. Pneumatically balanced double walking beam units based on the same idea are also being built. In principle. Its drawback is that both zones have to be produced together. Repair and maintenance costs of producing a single well with two independent Fig. twin wells drilled side by side are produced in the way illustrated by Fig. Running and pulling is performed under protection of a blowout preventer. and only the other one has to be pumped. . Both tubings are hung in the tubing-head by means of mandrel hangers provided with O-ring seals. Tubing axes are deflected far enough to make the least distance between horseheads equal 40 mm. The saving is thus essentially the investment cost of one well. This arrangement keeps the torque almost constant. Carrier bars and polished-rod clamps are designed so as to prevent the rod-string equipment from getting entangled. and thus the utilization of prime mover and gear reducer are more efficient than in the conventional set-up.92 (after German and Gadiev 1960). PRODUCING OIL WELLS--(2) turned down on both tubing strings. this solution can also be employed to selectively produce one and the same well. 4. Wellhead design for selectivepumping with two independent sucker-rod pumps. 4. Soviet drive unit suited for the production of bunched wells . after GRAF (1957) Fig. 4.1.1 -92.1 -91. PRODUCTION BY BOTTOM-HOLE PUMPS Fig. each of which is to tap one of several zones. Both have the advantage that gas can be produced separately and the volumetric efficiency of pumping is thus better than in (a). size. Solutions (b) and (c) employ hollow rods. gas rises in annulus 4. In solution (a). Such wells are cased with tubing-size pipes (3 112. The midi completion can thus be regarded as selective only in the sense that the slim casings. 9 percent of the 21 was due to cheaper tubing and wellhead equipment. size. 4. perfectly independent actually.a travelling-barrel pump 1 is used.1 -93. Size of rod 3 is not restricted.and preferably even 2 718-in. slim-hole or midi (minimum diameter) completions are often advantageous. usually of 1 114-in. between casing and hollow-rod string. size). In (b). after CORLEY and RIKE (1959) and CROSBY (1969b) Figure 4. Special rod couplings causing no wear on the casing are to be preferred.4. are run in a single common borehole. It is the gas that rises in the hollow rods and the . Solution (c) employs a special pump 1fixed to anchor packer 2 that packs off the annulus. (0) (b) (C) (d) Fig. Production capacity is comparatively large. Bottom-hole arrangements for sucker-rod pumping of slim holes. 2 718 in. The maximum nominal size of the pump 2 going into the 2 718-in. and the casing is not exposed to corrosion or erosion.1 -93 has been compiled after Crosby (1969b) and Corley and Rike (1959). A survey (Crosby 1969b)found that completion of midi wells produced by mechanical means cost less by 21 percent than that of normal-size wells. This arrangement has the drawback that it can be employed only if the GOR of the well fluid is rather low. size tubing 1is 2 in. This permits to grout into a bore-hole of suitable size several casings of say. it is held down by an anchor 2 that does not pack off the annulus. PRODUCING OIL WELLS+2) (d) Sucker-rod pumping of slim holes In wells of comparatively small capacity. Liquid rises in the hollow rods 3. a rod pump fixed t o the casing is used. 4. The allowable setting depth is greater in some of the types. the production capacity of sucker-rod pumps decreases significantly at greater depth. size is run in casing I . Both solutions have the drawback of lower production capacity than (a). Hydraulic bottom-hole pumps The common feature of hydraulic bottom-hole pumps is that the pump unit anchored to the tubing shoe incorporates a hydraulic engine whose piston reciprocates in the vertical. Tubing 2 of 1 114. The power-fluid supply rate required to drive the pump is * We shall consistently term 'piston' the piston in the engine and 'plunger' the piston in the pump. is the cross-sectional area of the plunger. in the case of a single plunger. Setting depth is further limited by maximum allowable rod stress. A. and hence stroke reduction.2. ApI is the fluid friction loss in the entire flow string. one or two pump plungers are rigidly attached. but so is most often also the pump-drive unit. Maximum pump size is 1 114 in. In a rodless bottom-hole pump. the rodless pump is at an advantage in inclined wells. Rods 4 are of 112. A.or 518-in. the liquid flows in the channel of lower flow resistance. Production capacity in such an arrangement is less depth-dependent than in the sucker-rod pump. . is that of the piston. As a result. The advantage of the arrangement is that. Its advantage is that the gas can be separated while still in the well.1 -86. Solution (d) is essentially a conventional rod-string arrangement reduced in size. The production capacity of this solution is comparatively small and the completion is comparatively expensive. size. RODLESS BOTTOM-HOLE PUMPING 425 liquid that rises in the annulus.1. and the maximum feasible production rate out of that depth is about 80 m3/d.* The piston is moved by a power fluid supplied to it from the surface through a separate conduit.2. increases with depth. to the other end of its piston rod. the maximum setting depth of the sucker-rod pumps used today is about 3000 m. Lacking a rod string that could rub against the tubing. 4. not only is the pump at the well bottom. and the rod string will not rub against the casing. The pressure of the power fluid in the surface pumping unit is. Rodless bottom-hole pumping All types of sucker-rod pump have the common feature that rod stretch due to the changing fluid load.or 1 112-in.2. As is shown also in Fig. also the rod string may cause considerable wear of the casing. 4. 4. The tubing is usually fixed to the casing by means of anchor 5. here. 4.2-1. A precondition of operations planning is to know beforehand the friction losses of both the power fluid and the well fluid. At the temperatures prevailing in the well. by Eq. then a higher p is Fig. on the other hand.JA..65 on an average). and secondly. that is. PRODUCING OIL WELLS-(2) where q is the overall efficiency of the bottom-hole pump installation (0. and the power-fluid supply rate will be less than the liquid production rate. If the piston diameter is larger than the plunger diameter. must exceed liquid production rate q. poier-fluid supply rate q. 4.2.426 4. This arrangement is therefore to be preferred in wells of smaller depth and higher productivity.< 1. Such arrangements are chosen for deep wells of low productivity. by Eq.. Kobe's B-type hydraulic bottom-hole Pump required for the same well depth. Calculation of these is somewhat hampered by the fact that the temperatures of both fluids are affected by well depth as well as by the duration and rate of pumping.1. Friction loss is composed of the sliding-fit friction of the mechanical parts and of the fluid friction of flow.2-2. is the liquid production rate.2-2. 4.. a lower power-fluid pressure p will do at a given well depth L. Kobe's conventional hydraulic bottom-hole pump Fig. A. and q. The overall efficiency of the pumping installation is significantly reduced by hydraulic losses. then. firstly. These fall into two groups: friction loss and slippage. If. flow properties of both the power fluid and the well fluid may be regarded as . A J A . > 1. 4. 4. At the lower end of the stroke. sucks fluid from space 8 and delivers it into annulus 4. There are various combinations of pump and well completion.2-3. Figure 4. the well fluid mixes with the power fluid in annulus 4 and rises together with it through casing annulus 6 .427 4. (i) bottom-hole insert or tubing pumps run on a pipe string. diagrams or nomograms (Coberly 1961). and (ii) closed systems.2. (a)]. including. and.2-2 shows a so-called Btype Kobe pump for producing high-capacity wells. The pump operates essentially in the same way as the standard pump. Kobe make double-acting pumps were first employed commercially in 1932 (Coberly 1961). The common feature of these is that the spent power fluid and the well fluid get mixed in the well. Plunger 7. and rise in one and the (a) (b) (c) (dl Fig. Seal rings are marked 1. engine valve 3 rises so that the power fluid can now force the piston upwards.2-3 shows designs of open-system completions. Calculation is usually performed with the aid of simplified formulae. Completions involving Kobe's bottom-hole pumps. Piston 1 is forced downwards by power fluid fed to it through conduit 2. Double-acting hydraulic pumps. producing mixed oil .ESS BOTTOM-HOLE PUMPING Newtonian. This is a more recent design. Figure 4. This permits piston and plunger sizes to be greater for a given overall pump diameter. rigidly attached to the piston. on the other (i) open systems in which the exhaust fluid from the engine is mixed with the discharge from the pump. The spent power fluid flows through annulus 4 to port 5 and rises to the surface through casing annulus 6. and (ii) free pumps. ROD1. The double-acting hydraulic bottom-hole pump is the earliest type of rodless plunger pumps. Figure 4.2-1 shows a standard Kobe bottom-hole pump. improved by the use of more modern means of sealing. In this set-up. on the one hand. the spent power fluid rises through annulus 1. three 2 118 x 2 112 pumps (set up as in Fig. 4. In types (c) and (d). which makes it more expensive. Table 4.1 gives sizes and operating parameters of some typical Kobe pumps after catalogues issued in 1968 -69. it should also be warm. (c) and (d) are. b) are used to produce 540 m3/d of oil from a depth of 4604 m. The closed system differs from the types just described in that the power fluid and well fluid are kept separate during their upward travel. In 1968. whereas the well fluid riser through tubing 2. 4.2. PRODUCING OIL W E L L S 4 2 ) same flow channel.2-3. changing it requires none of the usual work-over operations. this was the rodless hydraulic bottomhole pump operating at the greatest depth (Hollis 1968). The valve closes if the power-fluid circulation is reversed for the purpose of pump recovery. Closed type completion involving Kobe's bottom-hole pump pump is installed by placing it into the tubing at the wellhead and letting it sink to its setting depth.It is essential that the power fluid be pure.428 4. its drawback is that it needs more pipe. For recovery.freepump types. power-fluid flow is reversed.2 -I. there is a variety of o t h e ~ solutions including closed systems with free pumps. The production capacity of the pump installation can be further increased by installing two pumps in one well and operating them in tandem. It is assisted in staying open by a magnet placed above the ball. and the spent power fluid plus the wclY fluia rise through a smaller-size tubing in (c) and through the casing annulus in (ci).2-4. The Fig. The free pump is thus very easy to change. 4. (d) is shown in more detail in Fig. the fluid underflowing the pump then raises the unit to the surface. In solutions (a) and (b). the standing valve is permanently open in normal operation. its drawback is that it needs more pipe. The advantage of solution (c) over (d) is that it can also be used to produce gaseous well fluids. (a) has the advantage over (b) that it permits the produciio2 of also gaseous fluids. The . The power fluid attains the pump through a large-diameter tubing. In the Reno field. 4.2-4. the pump can be run and pulled on a nlacaroni tubing string. In the solution shown as Fig. if parafin deposition is to be anticipated. The solution shown is just an example. USA. 2. Sizes and operating parameters 3f Kobe pumps Theoretical capacity m3/d .* The figures denote: tubing ID x piston ** Can be operated below rared speed 'B' double pump end 'B' single pump end Standard double pump end Standard single pump end Small bore Pump size* Stroke m Area ratio O D x first pump ID x second plunger O D Length m spm Rated Table 4.1. . The power-fluid distribution system much resembles the lift-gas distribution systems of gas-lifted wells. after BOWERS(1970) shows a closed power-fluid system after Bowers (1970). Earlier. and rotating it occasionally during operating stoppages. The overall maintenance costs of power-oil and power-water systems are about equal (Bowers 1970). Tank 6 stores makeup to the pump intake. Figure 4.5. The devices marked 7 are gas boots. 4. If the power oil is hot enough. a closed system using water as the power fluid is employed in order to reduce the fire hazard in this rather densely populated region. no parrafin will deposit out of it. Spent fluid returns through lines 4 to the intake manifold of the triplexes. The system actually employed is selected on the basis of economic considerations. Operating costs have turned out to be lower than in systems using power oil. the plug is pumped down to the bottom-hole pump. No paraflin deposition will occur if the pipes are provided with a paraphobic plastic lining. power-fluid treatment is more and more centralized nowadays. PRODUCING OIL W E L L S 4 2 ) power fluid most often employed is simply a purified and heated well fluid.430 4. The tubing strings installed in the well are cleaned by means of a plug of suitable form. each well used to be equipped with a separate heater-treater. In the Wasson field of Western Texas.2. Closed power-fluid system. The power water returning from the well is filtered on a glass filter: the water thus cleaned of solid contaminations and mixed with an inhibitor is then recycled.2-5 Fig. where it dissolves in the hot oil. and central pump stations tend to be installed in most fields using this production method. The elasticity and economy of this system was unsatisfactory. Power fluid is pumped by triplex pumps 1 through distribution line 2 to wells 3. but pump life is shorter. however. nor out of the well fluid. Scraping the annulus is performed in certain wells by mounting scraper blades on the outside of the tubing. made of a special material. so that powerfluid pressure may act on the top of the piston also through conduit 6 and bore 7. ..2. A typical single-acting pump is the Byron-Jackson-make Hydralift. During.1. Byron-Jackson single-acting hydraulic bottom-hole pump improve upon the poor 'volumetric efficiency of short-stroke double-acting pumps when pumping fluidseven of comparatively slight gas content. 4.2-6. The operating parameters of the two types of pump thus exhibit a fairly wide overlap. > 2 in. shown as Fig.2-6.The operating principle of the singleacting hydraulic pump is the same as that of the sucker-rod pump. Since the top area of the piston is greater than its bottom area. and sinks in the fluid sucked into the barrel during the downstroke. stroke range is s=0. too. The stroke and plunger size of a single-acting pump are usually greater. . RODLESS BOTTOM-HOLE PUMPING 43 1 (a)2. the downstroke (Section a).7 m. Single-acting pumps were called into life in order to (0 (b) Fig. travelling valve 2 of plunger I is open. Single-acting bottom-hole pumps. The plunger lifts the well-fluid column in the tubing on the upstroke. the resultant of the '. and pumping speeds range from 6 . Single-acting pumps are usually simpler in design than double-acting ones.4. Plunger sizes are d .4.. rather than by a rod string driven from the surface.30 min . Reversing valve 5 in piston 4 is open. 4. and are consequently less sensitive to sand. The only difference is that the plunger is moved by a hydraulic engine installed directly above the pump. standing valve 3 is closed. but its pumping speed is less than that of the double-acting pump. 432 4. PRODUCING OIL W E L L S ( 2 ) pressure forces acting on the piston is down the plunger will, of course, copy piston motion. On attaining the lower end of the stroke, reversing valve 5 moves into the lower position (part b of the Figure). Power-fluid pressure now makes the piston rise. The power fluid above the piston enters through bore 8 above the plunger, from where, after mixing with the well fluid, it flows into tubing 9. During the upstroke, the standing valve is open and the travelling valve of the plunger is closed. The Fig. 4.2-7. Variation of power-fluid pressure at wellhead, after W m ~ (1961) s Fig. 4.2- 8. fJydraulic dynamometer, after Wmos (1961) Hydralift, just as the Kobe pump, can be tubing-run or used as a free pump (cf. Fig. 4.2-3,c). Nominal pump sizes are from 2 to 5 112 in.; the stroke is 1.53 m; production capacity ranges from 24 to 2400 m3/d; maximum setting depth is 4600 m. The operation of the single-acting hydraulic pump is supervised by means of the hydraulic dynamometer recording pressure changes of the power fluid near the wellhead (Woods 1961). These changes permit the determination of first of all the duration of the upstroke (2 in Fig. 4.2- 7) and downstroke 1 and the detection of fluid deficiency. The principle of the hydraulic dynamometer is illustrated in Fig. 4.2-8. The two faces of piston 1 are exposed to equal fluid pressures. That is, the piston can be adjusted to middle height in cylinder 2 at any pressure. Chamber 3 contains nitrogen gas, whose pressure equals that of the power fluid. Pressure changes affect the volume of the nitrogen, which displaces the piston downwards if 4.2. RODLESS BOTTOM-HOLE PUMPING 433 pressure builds up and upwards if it decreases. The force transmitted by piston rod 4 onto gauge ring 5 varies accordingly. The deformation of the ring, proportional to the force, is amplified and recorded by servo mechanism 6. (a)3. Selective bottom-hole pumping of several zones. - In the solution shown as Fig. 4.2- 9, a, pumps are installed in separate tubings run side by side. The power fluid is fed through conduit 2 to pump 1 producing the lower zone and through (0) (b) Fig. 4.2-9. Selective production of several formations with hydraulic bottom-hole pumps; well completions conduit 4 to pump 3 producing the upper zone. The exhaust of pump I rises through annulus 5 and that of pump 3 through annulus 6. The well fluids are mixed and rise together with the respective exhausts. Gas is removed through tubing 7 from the lower zone and through annulus 8 from the upper zone. In the tandem arrangement shown as Fig. 4.2-9, b, the two pumps are mounted in a single body, end to end along a vertical axis. The fluid of the upper zoneenters the upper pump through port I, and leaves through port 2 into tubing 3. The engine driving the upper pump receives power fluid through port 4 and exhausts it through port 5 into annulus 6. The oil from the lower zone is sucked in by the lower pump through port 7 and pumped through port 8 likewise into annulus 6. The engine driving the lower pump, supplied with power fluid through conduit 9 and port 10, exhausts it through port 11 into the annulus. This solution has the advantage over the preceding one of requiring less space, but it cannot be used in wells producing a gaseous fluid. Other solutions are, of course, also possible. For instance, the completion in Fig. 4.2-9, a 434 4. PRODUCING OIL W E L L S 4 2 ) can be modified to be used with a free pump. The slim powerfluid conduits are dispensed with; power fluid reaches the engines through large-size tubings. The liquid from the upper zone is produced separately. The liquid from the lower zone merges with the exhausts of both engines before rising through the annulus. There are two packers; the gas produced from the two zones cannot be separated. 4.2.2. Electric centrifugal submersible pumps The inventor of the electric centrifugal submersible pump is A. Arutyunoff, whose pumps manufactured by the Reda Company have been in commercial use since 1927 in a variety of oilfields (History . . . 1961).The importance of the submersible pump is illustrated by the fact that in the Soviet Union, where this means of production had first been introduced in the nineteen-fifties, 3400 wells were produced by electric submersible pumps in 1967,which is about 9 percent of all wells produced by mechanical means. The combined output of these pumps was 58 million tons of crude in 1967, about 49 percent of the total amount of crude produced by artificial production methods (Zaitsev 1968). (a) Components of the submersible pumping unit The unit is made up, generally, of three major component: an electric motor, a socalled protector connected to it, and a multistage centrifugal pump. In pumps producing a gaseous well fluid, a gas separator is inserted between the protector and pump. The most typical arrangement is shown in Fig. 4.2-10. Motor 1 is the bottom unit and above it there are the protector 2 and the centrifugal pump 3 attached to the tubing string. The electromotor is fed by current from the surface transmitted by cable fixed to the tubing string. The motor driving the pump is a three-phase, dipole, squirrel-cage asynchronous type. Its performance curves are similar to those of the prime mover of sucker-rod pumps (see Fig. 4.1 - 18).The main difference is that due to the limited well crosssection the diameter of the motor of the submersible pump is much smaller, and power is increased by the increase in length. The cooling of the motor is facilitated by circulating lube oil in it. The heat generated is taken over and carried away by the wellstream around the motor. For efficient cooling the flow velocity of the liquid should be at least 0-3m/s, since overheating significantly decreases motor life. The usual speed of the motors generally used in the U.S., is 3500 l/min, at a frequency of 60 Hz, while at 50 Hz frequency, more generally used in Europe, it is 2915 l/min. The power of the motor significantly changes with the speed i.e. the power of the same motor at 50 Hz is only 58% of the value, valid at 60 Hz. The motors can be constructed as one unit up to about 10m in length. For greater 4.2. RODLESS BOTTOM-HOLE PUMPING 435 performance tandem motors can be applied. The power of the motor depends considerably on the diameter, and thus necessarily on the internal diameter of the producing casing string of the well. At a frequency of 60 Hz the greatest applicable motor power in a casing of 114 mm (4 112 in.) internal diameter is 95 kW; if the diameter is 140 mm (5 112 in.), 178 mm (7 in.) and 219 mm (8 518 in.) the power of prime mover 179, 447 and 760 kW,respectively. Fig. 4.2- 10. Electric centrifugal submersible pump (MURAVYEV and KRYLOV1949) Figure 4.2 - 11 illustrates the dipole, three-phase squirrel-cage asynchronous motor of ECN type applied in the Soviet Union (Bogdanov 1968). The motor built around shaft 1 is split into a number of short sections, separated by bearings to prevent buckling of the comparatively long shaft. Stator windings 3 are separated by non-magnetic bearing support stator lamellae 4. Lube oil is circulated by turbine 5 in the motor's interstices and through bore 6. Power is supplied to the motor through cable 7 and lead 8. The OD of the motor is 103 - 123 mm; its length is 4.2 - 8.1 m; its normal operating speed is 3000 rpm. The protector has several tasks. In rotation of normal direction it generates a reaction force of opposite direction but of equal size to the axial forces that are developing in the pump. It prevents displacing the lube oil of prescribed dielectric character by well fluid. It renders change in its lube oil storing capacity if the volume of the oil varies v. temperature. It ensures that ambient pressure prevails in the 4. PRODUCING OIL WELLS-{Z) Fig. 4.2-1 1 . Motor of ECN electric submersible Fig. 4.2-12. Protector of ECN electric submersible pump, after BOGDANOV (1968) pump, after BOGDANOV (1968) motor, increasingits operating life and safety. The oil chambers of the protector may be open (e.g. as in the Byron Jackson and Centrilift types), or sealed off. The protector unit of the Soviet ECN pumps (Bogdanov 1968), shown in Fig. 4.2- 12, belong to this latter group. Its role is to feed lube grease from chamber 1to the pump and lube oil from chamber 2 to the motor. The pressure required to perform these tasks is applied by coil spring 3 and the fluid acting on plunger 5 through port 4. Grease is pressed into the bottom bearings of the pump. As the grease can also reach the bottom of chamber 2, through slits along the shaft, it keeps the motor lube oil under pressure, too. The pump is a multistage centrifugal type of axial intake and radial outflow. The number of possible stages exceeds 500. The significant axial force must be balanced, otherwise, due to friction of the diffuser and impeller wheels, bthe life of the equipment will be shortened. Balancing can be done by applying either so-called 4.2. RODLESS BOITOM-HOLE PUMPlNG 437 fixed or floating impellers. In the first case balancing takes place in the protector (see above). The advantages of this method are the small wear and long life, though the possible head capacity, for structural reasons, is limited. That is why, in modern units, the other method is used. The impellers may axially shift on the pump shaft while the emerging axial forces are partially taken up by the rotary seal rings mounted into the impellers. The liquid film developing on these rings prevents direct Fig. 4.2- 13. One stage of Centrilift centrifugal submersible pump. after BOLEY(1967) contact of the impeller and diffuser: the impeller "floats". To reach a further decrease in pressure difference balancing holes of small diameters are drilled into the impeller. A section of one stage of a Centrilift pump of this type is shown in Fig. 4.2 - 13. Pump stages are made of corrosion- and erosion-resisting materials. This can be a steel alloy, bronze or plastic. Favourable results were achieved in the Soviet Union with stages made of P-68 plastic. Its weight is only some 9% of the weight of bronze wheels (Bogdanov 1968). The performance curve of one stage of a Centrilift pump is shown in Fig. 4.2- 14. According to the q,- H characteristic, head capacity declines gradually from an initial value as output increases. The centrifugal pump of this type, unlike several other types of centrifugal pumps, applied on the surface has no unstable portion. If it is intended to run into a well from which a required rate must be produced, though the inflow performance is changing, or only approximately known, then it is advisable to select a head curve with steep characteristics. With this kind of curve the producing rate is less dependent on the dynamic fluid level. For economic energy consumption the pump's operating point should be at the maximum of the efficiency curve, or the required producing rate should differ from the value belonging to the greatest eficiency by not more than 15 -20% (cf. range shown in Fig. 4.2 - 14).The pump's greatest possible efficiency depends on the type and construction, and, within a given type, on the throughput capacity. Figure 4.2-15 (after Arutyunoff 1965) shows the efficiency curves of Reda pumps of different capacity. It can be seen that at comparatively high production rates even an efficiency of 75% can be achieved while at rates of up to 1500m y d the greater the capacity of the pump, the more favourable its maximum efficiency. Divine (1979) proves that the production rate of a submersible pump for a given head can be changed most economically by changing the electric frequency, and, due to this, by 438 4. PRODUCING OIL WELLS-42) modifying the pumping speed. The costs of the necessary surface control unit are recorvered within 8 months. The head capacity and efiiciency of the submersible pump are decreased if free gas is present in the wellstream. U p to a 0.1 volume ratio the impact of the gas can hardly be recognized, at greater values, however, the impact of the gas upon the performance is increasingly significant. "Gas sensitivity" differs according to pump q,, m3/d Fig. 4.2- 14. 30 40 60 80100 200 300 5 0 0 1000 2000 4000 q,, m3/d Fig. 4.2- 15. Efficiency of Reda's electric submersible pumps 4.2. RODLESS BO'ITOM-HOLE PUMPING 439 types, it is generally greater at smaller dimensions. The first stages of submersible pumps manufactured by Reda to produce gaseous oil are generally less gas sensitive and they compress the wellstream to buble-point pressure. - It is advantageous if the greatest possible part of the free gas content is separated before the pump intake and this gas, through the casing annulus, is separately led to the surface. For this purpose gas separators of different kinds were constructed. Fig. 4.2 - 16. Reda's gas separator A Reda gas separator can be seen in Fig. 4.2-16. The wellstream enters the separator through ports 1 - 1 . Gas rises in annulus 2 to escape into the casing annulus. The degassed liquid is fed to the main pump by screw pump 3. The pressure increase due to screw pump action may make the liquid dissolve some of the separated gas. - Centrilift pumps incorporate a centrifugal separator. The well fluid entering the separator body gets into a high-speed single-stage special pump, the centrifugal separator. Its liquid fraction rises along the wall of the chamber above the separator into the main pump. The gas rising along the shaft is led through a port into the annulus. The three-core cable feeding the electric power must be made with high-grade insulation. The insulation must be chemically inert to the well fluid, must be corrosion resistant and gas impermeable, and must be protected from mechanical damage. The three conductors of the cable are individually insulated, and then the three-core cable obtained is jointly insulated. The cable can be of round crosssection or flat. In the latter case the conductor axis of the three cores are in the same 440 4. PRODUCING OIL WELLS (2) plane. Use of flat cables is more advantageous because it makas better use of the available space, and they are used first at pumps. A sheath of steel, provided with an alloyed or corrosion-resistant coating offers protection against mechanical damages. The cable is fixed to the tubing string at 4- 5 m intervals and is run into the well together with the tubing string. The allowable ambient temperature of the cable depends on the material used for insulation. The highest temperature Fig. 4.2-17. Submersible pump installation for high-capacity wells, after ARUTYUNOFF (1965) Fig. 4.2-18. Dual zone selective production by sucker-rod and electric submersible pumps, after ARUTYUNOFF (1 965) applicable is 177 "C (Brown 1980). The importance of impermeability of the insulation to gas is especially emphasized. If, under high pressure, gas can penetrate the pores of the insulation, then at a pressure decrease the insulating coating will blister and be ruined. thus running the pump in the opposite direction. if the sandface is surrounded by a casing of smaller diameter. e. It may happen. 4. too. 4. (b) Well testing Economical planning of submersible pump operation requires a fairly accurate idea of the operating point anticipated and a pump to match that operating point. Cable suspended submersible pump construction and installation is also known (Brown 1980). In high capacity wells.2. respectively. generally. This has two important tasks: it prevents the liquid filling the tubing string after production shutdown and flowing backwards through the pump. The pump. that the first-run pump will be suited for a well test only. A production test may be performed as follows. which is greater than the cross section of the tubing. only the high productivity zone is produced by a submersible pump. production testing often requires the use of submersible pumps. This reversed arrangement can be justified at greater casing diameters. can be multiplied. too. A pump thus chosen will produce at a rate corresponding to optimum efficiency. while the upper zone by sucker-rod pump through the tubing string.2 . Electric submersible pump installations. Submersible pumps can also be applied in cases of selective production from one well. however. This is shown in Fig.4. 4. Motor I is above pump 2 and pack-off 3 is inserted between the protector and the pump.pump after shutdown in sand-laden wellstreams. The pump is set into a pipe section of greater diameter and the suction pipe descends to the sand face. With these methods no tubing string is usually applied. In favourable cases the pumping capacity and the production rate of the well.g. to be used for lifting the fluid. This makes it possible for the annulus cross-section area. and that the definitive pump may only be installed after analysis of the test results. This running mode would significantly damage the pump.2 -10. During pulling it can be opened and the possibility of pulling the "wet" string to the surface eliminates. is used in wells with a nominal size production casing of 4 1/2". where the lower zone is produced through the annulus by submersible pump. a ball type check valve is installed. The cable is to be of especially high tensile strength. RODLESS BOTTOM-HOLE PUMPING 44 1 Above the pump. The pump builds up pressure equal to its maximum head capacity H . the tubing is filled with oil taken from the well. After a wait long enough to let the static level establish itself in the well. The other task is to prevent the settling of sand from the tubing into the. differing from that shown in Fig.2-17. Generally. are also known.18 (Arutyunoff 1965). Greater annular area is provided for the zone produced by the submersible pump. above the . the wellhead is shut off and the pump is started. and the outside diameter of the pump should be greater than in the conventional arrangement. The liquid rate has to be sufficient for the cooling of the motor. but gasless liquid rate is intended to be produced (Arutyunoff 1965). while the other zone is produced by flowing or other lifting methods. therefore. shown in Fig. if a considerably high. Above the check valve a drain valve is mounted. the productivity index can be calculated. We may now write PTO 4. resulting in a pressure p. then. we may write. the well is abruptly shut off and the wellhead pressure is measured. Well testing with electric submersible pumps liquid column in the annulus (Fig. J and pws are known. and using the relationship q.4.2 . If the inflow characteristics of the well could not be accurately established beforehand.2. With knowledge of the stabilized rate of production q. Once this rate is stabilized. then formation pressure is and where h . may be taken from the above equations...).19). and h. If this is not the case. . Assuming that the production level is not significantly changed during the short shut-off time.19. It is assumed that the exponent n of the productivity equation equals unity. ... then the production test must be repeated and n calculated from the result. YI + The well is then reopened and produced at a rate q. production may be corrected slightly in some cases by suitably choking the well output (Muravyev 1959). in order to operate the pump at a more economical pumping point. PRODUCING OIL WELLS--(2) Fig.2. on the closed wellhead. in a fair approximation If the well depth is Lw and the mean gravity of the liquid column in the well is fi.= J(pw.-p. 4. 4.3 Ho=hl -. so that the productivity equation characterizing the inflow of liquid into the well may be written. In order to achieve the required production rate q.the pump of q.the setting depth of the pump. If the water content is less than 50 .. within this range. (iii) it is water-cut oil. and (v) it is oil containing gas and water. . There can be five solutions for the first two parts of the problem depending on the composition of the wellstream: (i) it is gasless water.70% then "water in oil" type emulsion develops.. well depth at the required flowing bottom-hole pressure p. p. (c) Selection of a pumping unit and the design of its operation Let us assume.1. Due to mixing oil and water emulsion emerges.70% "oil in water" generally develops. The determination of the density according to the weighted average is simple. 4. the results will be less accurate in cases (iii) and (v). however. that the quantitative and qualitative parameters of the well inflow are known. .2.the type and dimensions of the pump. rate and PTO wellhead pressure. often cannot be accurately determined. The average viscosity of the liquid mixture.frictional pressure drop. = q. The viscosity. The . (ii) and (iv). can be many times that of the oil.. The pressure of the fluid column at height h from the well bottom is p = hp. Communication is realized through the current transporting electric cable (Brown 1980). q. and it leads to no apparent changes in the flow parameters of the water. RODLESS BOTTOM-HOLE PUMPING 443 With modern equipment a pressure transducer as well as the submersible pump is installed in the well. and the flowing bottom-hole pressure p. The small oil content mentioned at (i) means only a small percentage. can be determined by the Weisbach or Fanning equation discussed in Section 1 .4. and its viscosity hardly exceeds that of the water. In water contents higher than 50. . are given. Graph 11 is the pressure traverse of the flow in the tubing string at the required q. this makes reading and recording the measured pressures possible on the surface. ad (i). The equation of the pressure graph is .. (iv) it is gas-cut water. (ii) it is gasless oil. the liquid rate to be produced.g.2-20 illustrates the change of hydrostatic pressure of the liquid column v. Due to more uncertain determination of the viscosity. . usually increases with water content. and . the viscosity ofwhich. Sufficiently accurate design methods exist for cases (i). Accuracy is sufficient if the density and viscosity are calculated at the average temperature of the flowing liquid. The water and oil content of the liquid may influence the density and viscosity of the wellstream. The values to be determined are . perhaps with a small oil content.and the flowing bottom-hole pressure belonging to it. capacity can be installed at any point of the well section of h height. Graph I of Fig.. at a greater water content.the parameters of the electric cable and transformer. where Ap . 444 4.-ppi ....(.2 . 4. . or less frequently.2. and only a given number of stages can be installed in them. 4.. The outside diameter should be the greatest possible that can be installed in the casing string. If the pump is installed at the highest possible level (shown as L. The pressure corresponding to head capacity H(. The pump is selected on the basis of the following considerations. therefore. at the same power. Thus it is ensured that during operation the motor is cooled by the wellstream flowing upwards.2.2..14.. P(.. first. The motor power. n' should be applied. 4.. rate to be lifted corresponds to the greatest efficiency should be selected (see Fig.. That is instead of n. is generally given in the catalogues for one stage. the nearest available number of stages. for 100 stages.20. Head capacity H and motor power p. in the Figure) then the pressure increase to be produced is A p . With the number of required stages can be determined as follows.= lo3 x 9-81H(. because. is p. the greatest required power per stage. = p. is read from the performance curve corresponding to Fig. PRODUCING OIL WELLS-42) maximum depth of installation L. is the level where the pump gets below the dynamic liquid level with sufficient safety (say 30 m). knowledge of head H(. 4. then. The motor power required is to be determined. Pressure traverses of submersible pumping for gas-free liquid production and the electrlc cable are the shortest.6 Pptl) The dimensions of the standard pump housings are given. The minimum allowable setting depth is the upper level of the sandface.14). The size where the q. In this case the length of the tubing string Fig. and the costs of investment and electric power are the lowest. the greater the diameter the smaller the costs of the pump. and the number of required stages is APP n= -. 4.2-21.. from a well with a m2/s production casing string of 7". Influence of liquid viscosity on submersible pump performance known for the user. is only rarely possible. and the head pressure should be corrected by a factor taken from a table. can be obtained from Table 4. as a function of viscosity. The original tables give correction values up to 5000 SSU (1082 cSt). q.73 x kinematic viscosity and p. q. shown in Fig. should be modified by some calculation method. 4. . 4.2.2. Example 4.. 4. In a somewhat modified form the process is as follows: The correction factor f. = 270 m3/d. in the case of q. Another possibility is that with knowledge of viscosity the curves. a. and a..2 .2 . however.2 .1. is 15. The difference is that the performance curves of the pump. will be changed. too. The result of a modification of this kind are the curves plotted with dashed lines in Fig. RODLESS BOTTOM-HOLE PUMPING can be determined from ad (ii). fluid of v.2-21.2. 4. in pressure units.=ao+alv+a2v2 4. = 1.8 where constants a.=850 kg/m3 density is to be produced. The equation is valid up to a kinetic viscosity value of 3 x m2/s (300 cSt). With a fair approximation the effect of the viscosity can be considered in another way. The bp. originally determined for water and published in catalogues...6 MPa. This. The application of these factors is intended to be illustrated by the following example.20). due to the differences between the viscosities of the water and oil. Let us select a submersible pumping unit if. The most accurate method is if the pump manufacturing company determines the performance curves valid for the oil of given viscosity and make them Fig. = 60 and 70%. the production rate to be lifted. head required of the pump.14. The characteristic pressure traverses are the same as in the former case ( F i g . According to the Handbook (1978).2. Legg (1979) suggests that with a water content of 20 .=1. 4.selected is 0. its pressure increase is According to Eq. When calculating the motor power the density of the heavier mixture component.. the efficiency of the pump is greatest at q. Thus the . .14 the highest value of P ( . 4.2 m.2. because viscosity can only be approximately determined. and on this basis ad (iii).. 4.2. i..2.e. is considered.2-6 the number of required stages is The brake power of the motor is According to Fig. that of water. Clearly.15x270=311 m3/d The performance curves of the selected pump are shown in Fig.40% the viscosity of the liquid should be selected to be 2 . i.3 times greater than the in situ viscosity of the oil.410 W. In the case of water-cut oil the process differs from (ii). Selecting a pump of 70% greatest volumetric efficiency the correction factors are The corrected production rate is qcor=fqxq.14.4. The head developed by one stage of the pump with water is 8.e. PRODUCING OIL WELLS+2) Table 4..2. if the flowing bottom-hole pressure is lower than the bubble-point pressure. and. When its pressure during the upward rise decreases to equal the bubble point pressure. The lower section of Fig. In gassy liquids. therefore. q. 4. RODLESS BOTTOM-HOLE PUMPING 447 motor will not be overloaded even during temporary separation of the two liquids in the tubing string. The wellstream flows into the pump with pressure p. gas rate R .4.4.)q. A gasless Fig. 4.2. If it is greater liquid enters the pump. The bubble point is at the unity value of the ordinate. while (R . due to the increased pressure it will leave the pump in an "even more" liquid state. respectively). Pressure traverses of submersible pumping for gaseous liquid production liquid column will be available in the annulus. as stated for (iii).R. and the pressure traverse takes its shape according to the laws of two-phase flow. including oil. the flowing bottom-hole pressure may be higher or lower than the bubble point pressure. gets into the annulus. From the original Rq. the same. gets into the pump.2-22 represents the change of the volume factor compared to the bubble-point value as a function of pressure in cases of a smaller and a greater gas-oil ratio (curves IV and IV'. I is the pressure traverse of the fluid flowing in the production casing from the well bottom to the pump intake. however. In the upper section of the Figure the pressure traverses valid during the operation of the electric centrifugal pump installed at depth L.. gas starts to escape. The design and selection of the pump is. and then into the tubing string. and . can be seen. it can be calculated according to Section 1. The situation is more complicated.2-22. with some modification.. ad (iv). 4.)q. the more costly the current supply. The deeper the pump is installed. Design is generally made by computers. It is proved that with the liquid production rate each cost item. while at greater only liquid. respectively. also decreases. (d) Economy of the operation Figure 4. 111' and IV' show the case when a portion greater than the produced gas rate Rq. -p..R. The gas rate (R . According to the diagram the specific cost of the production increases almost linearly v. i. the fluid volume to be lifted. The most significant item is the cost of electric power consumption. depth at any given rate of production. the total specific production cost. and the smaller the throughput capacity pump required.448 4.and twophase type. Along Graph I1 the flow under and above pressure p. PRODUCING OIL WELLS (2) leaves with a pressure greater than bubble-point pressure p. However. and of these versions the one with the smallest production cost should be selected. getting into the annulus aerates the oil column there. The actual fluid volume lifted by the individual stages of the pump decreases from the bottom upwards. starting from the voltage required at the motor. of the pump and determines how many pump stages and what types are required in order to decrease the wellstream pressure to equal the bubble-point pressure. and thus the type and dimension of the pump can be significantly influenced by the pump setting depth. The significance of cable losses is visible. Manuals of manufacturing companies also give the specific voltage drops of electric cables of different types. The pressure traverse can be calculated as discussed in Section 1. .. and only a smaller portion gets into the annulus. the smaller the production rate at a given depth. in the knowledge of the developing voltage drop. Liquid level is at depth L. p. Thus the required secondary voltage of the surface transformer can also be obtained. Figure 4.. It can clearly be seen that the pressure increase required of the pump (p.2-25 shows the changes in the specific production costs of the Reda pumps at different rates depending on well depths. two phases flow. respectively. the deeper the pump is installed. Curves 11'. p. The power diagram is determined for a pumping well producing 80 m3/d of oil with 1800 m of head. the proper size and type of cable to be used must be selected. is of one... Then the pump stages of. A computing method requiring no iteration is given by Legg (1979).).. rate ofproduction. After determining the parameters of the pumping unit. Figure 4. the greater the proportion of produced gas separated and directed into the annulus.. In cases of a pressure smaller than p. The motor power and current consumption have to be calculated.2 -24 represents the cost of pumping one ton of liquid with a Reda pump v. is led into the pump and tubing string. Such a method is discussed by Hall and Dunbar (1971). Technically and economically several versions must be designed.2-23 illustrates the percentage of the prospective power consumption and various losses of electric submersible centrifugal pumping. gradually increasing liquid capacity corresponding to increasing specific volume are computed and selected. The greater the production rate.e. In this method Legg starts from the discharge pressure. Production cost componen:s of Reda's submersible pumps Fig.23.2-24.2-25. RODLESS BO'lTOM-HOLE PUMPING "I Fig. 4. Comparison of operating costs of Reda's submersible pumps .2.2 .4. Power consumption of electric submersible pumping. 4. after BOLEY(1967) A Electric power B Running and pulling C Reoairs and maintenance \ E Wages F Depreciation Fig. 4. 2 . Check valves. resulting in periodic stretching and contraction in the individual sections between check valves.4. The vibration propagates in the tubing at the speed of sound. . whereas on shrinking they Fig.26. Comparatively few of these have ever found commercial use. One of the shafts is driven by a motor. .27. . the hanger plate starts vibrating at a frequency equal to the rpm of the shafts. On stretching. its commercial applications are mentioned in literature from the late fifties on (Sonic. The tubing is hung from hanger plate 2 resting on coil springs 1. Other types of rodless bottom-hole pumps Bottom-hole pumps operating on a number of principles and designs different from the above-discussed ones have been patented all over the world. Cogwheels 5 keyed onto the excenter shafts ensure the synchronous rotation of the two eccentric weights. Let us now describe some of the more important designs. 7he sonic pump of Bodine was first tested in operation in 1953 (History . PRODUCING OIL W E L L W 2 ) 4. The opposite rotation of the two shafts generates centrifugal forces whose resultant is a reciprocating vertical force. or at least at a large number of these. Sonic pump (Petroleum Engineer 1958) Fig. however. in the US alone. 4.2-26. usually made of plastic. 1961). . For instance. 1961). As a result.2. are installed at each tubing joint. 165 patents for bottom-hole pumps were applied between 1935 and 1960 (History . 4. Its principle is illustrated in Fig. the open valves submerge in the liquid.2 . . . 4.3. Pleuger's diaphragm pump ( B R ~ ~ G G E M A Nand N DE Mo& 1959) . 1958). Mounted on the hanger plate are two eccentric weights 4 suitable for exciting vibrations. The latter. respectively. Temperature and viscosity of the pumped fluid must not exceed 70 "C and 300 cSt. The membrane sucks fluid on the downstroke and lifts in into tubing 10 on the next upstroke.10 times greater than that of gravity. so that producing a gaseous fluid is a rather sensitive job.451 4. made of plastic. including a relationship of production capacity v.The overall efficiency of the sonic pump may attain 0. and thus the fluid will go on rising even when the valve is already sinking on the next half-wave. Neither the tubing nor the annulus is accessible to well testing or dewaxing. it can produce fluids containing up to 80 percent solids. Tubing size is 2 3/8-4 1/2 in. the EDN-1000 type diaphragm pump of somewhat different construction is used.19 mm. pumping speed is about 700 spm.1200 min. are mounted at intervals of about 3 m on the outside of the tubing. close and lift the liquid column. It has the drawback that packing off the casing head is a problem at high pressures. The acceleration of fluid lifted by the check valves is 5.amplitude is 7. . which permits daily rates of production of 30.6. drives membrane 6.2.Plunger size in commercially used membrane pumps is 29-38 mm. In Baku. sonic pumps have been experimented with since the middle fifties.2-27. In experimental wells of 4 m3/d production have been attained. The nearly trouble-free operation and the simplicity in repair are considered to be great advantages (Govberg 1978). It has the considerable advantage of being almost insensitive to sand. The bottom-hole jet pump is one type of rodless bottom-hole pump. The tubing section is open. the excited frequency (Kruman and Geibovich 1970). centralizers 6. of high-pressure liquid is supplied . The entire space is under the pressure corresponding to the setting depth. A flow q. A diagram of the type most preferred in practice is shown as Fig.7. It has been used in full-scale oil production since 1973. Vibration frequency is 600. the Pleuger type membrane pump (Briiggemann and de MonyC 1959) has been employed since 1953. a pump of 136 mm OD may produce 10-20 m3/d against a head of 30 . The principle of the pump is explained by Fig. so that testing and dewaxing is easy enough. 4. by the intermediary of the liquid in sealed space 5. so that life is comparatively long even if the fluid is sandy. a tube several metres long. In the oil fields of the German Federal Republic. in the Soviet Union. 4. The motor space ends in bellows 11. Frequency is chosen so as to equal or to be a multiple of the resonance frequency of the tubing. RODLESS BOTTOM-HOLE PUMPING '. too. In the Soviet Union. Theoretical relationships describing pump operation have been developed. The well fluid reaches intake valve through sheath screen 9. A pair of bevel gears mounted on rotor 2 of electric motor I drives eccentric disk 3 which generates a reciprocating motion in plunger 4. Above the check valve. This pump has the advantage that none of its sensitive component parts is in direct contact with the well fluid.100 bars. The space above the membrane is bounded by intake valve 7 and check valve 8. fitted with a conical cap on its top. is installed to prevent sand settling out of the pumped fluid from settling in the check valve. The space between this latter and the pump jacket is filled with oil. Efficiency presumably drops steeply at low rates of production..2-28. while the intake valve is closed. In order to avoid transverse vibrations resulting in the tubing's rubbing against the casing.160 m3/d. The well fluid joins the high-pressure liquid after the passage of the annular aperture 5. The power and well fluids. flow from the throat into diffusor 6. The efficiency of the pump (the ratio of input work and useful work) depends considerably on the rate of production.2-29.2-0.25 times well depth. the pump is insensitive to the quality of power fluid. mixed together. According to Raabe (1970). the latter by cavitation. after WILSON Fig.15 percent for a . 4. The desirable depth of immersion is 0. In one instance. it was 12. 4.2-28. this liquid jet entrains the well fluid q entering through the sand face into the direction of arrow 4 essentially as a result of its apparent turbulent shear drag. The first is worn largely by the solids contained in the high-pressure liquid. Zones of operation of Kobe's liquid-jet pump and pressure is increased sufficiently to let the fluid rise to the surface. In order to minimize cavitation it is indicated to install the pump as deep below the dynamic level as possible. PRODUCING OIL WELLS (2) through tubing I to nozzle 2. Kobe's liquid-jet (1973) pump. it demands little supervision in operation. from where it flows at a decreased pressure and increased velocity into the throat 3. The wearing parts are primarily the nozzle and the throat. the pump has a broad depth range of application. -The Kobemake liquid-jet bottom-hole pumps have numerous advantages: the bottom-hole equipment includes no moving parts. exchange and repairs are simple. it permits the production of corrosive and abrasive fluids as well as fluids of a high GOR.452 4. Velocity is reduced there Fig. Operation is most favourable in the stippled zone on the right-hand side. but still within tolerable limits if a rather significant throat wear can be accepted. If the coil is fed current from the surface. the plunger then sinks back under its own weight. The pump is of the reciprocating-plunger type. The diagram shows the variation of power fluid requirement v. there are several iron cores surrou~idedby a solenoid coil. Figure 4. then the iron cores will raise the plunger and the fluid column above it.2. A solenoid-driven electromagnetic pump is described by Ioachim (1965). RODLESS BOTTOM-HOLE PUMPING 453 rate of 64 m3/d and 40 . Below the single-acting plunger. The device is comparatively simple and rather insensitive to sand.4.57 percent for 159 m3/d. Current is interrupted at the upper end of the stroke. on a rod fixed to it. . There is some cavitation also within the upper shaded zone.2-29 presents as an example the operating chart of a Kobe-make liquid jet pump. the desired rate of production for the given well dimensions for various dynamic level depths. The line bordering the diagram on the top is where cavitation becomes so intense as to preclude the use of the pump. The above-mentioned procedures permit comparisons of economy only within one and the same group of production equipment. It points out. In the above chapters. calculation procedures are aimed at establishing the least specific injection gas requirement in continuous or intermittent operation that will produce the well at the desired rate and at the desired BHP. Thus e.1 states the economic advantages of the eleven main types of production methods at various well fluid characteristics. in inclined wells and at low well productivities. in continuous gas lift and plunger lift. for choosing between different types of equipment. for instance. that the production of gaseous well fluid is an advantage in flowing production.1. have been discussed at the appropriate places. the most economical operating point is that resulting in the least fluid load. (The type of pump envisaged in the group of rodless hydraulic bottom-hole pumps is invariably the double-acting hydraulic pump. The procedure to be outlined below is suited. to be pondered against economy. more economical than any mechanical means. is immaterial in intermittent gas lift and unfavourable to various degrees in the various types of bottom-hole pumping.) Table 5-2 provides information on the maximum production capacity of the various types of equipment. discussing the various means of production. In sucker-rod pumping. Table 5 . The minimum consumption of injection gas marks the most economical operating point of the production equipment under consideration. at various . grouped in the same way as in Table 5 . In the Chapter on gas lift.Chapter 5 Choice of most economical production methods The rational installation of production equipment requires the selection of such means of production and its operation at such operating point or points as make producing the well under consideration a t the prescribed rate as cheap as possible. in the case of flowing production. on the other hand. the main aim of well design and production planning is to find the tubing size at which flowing production at a prescribed BHP can be maintained for the longest possible time.g. The advantages and disadvantages of the various well completions compatible with this or that means of production. the reader finds calculation procedures and comparative tables which set the choice of finding the most economical operation techniques and the optimum-size production equipment. a 9 F Bii S :: $ 4 3 ? . Selection of production methods (I) C - - A C A A submersible centrifugal A A - c C C B sonic Rodless pumping A A - B A C A membrane pump E 0 z 5 z 0 -1 0 C 0 0 .Rofitable Indifferent Disadvantageous Detrimental Inapplicable Inclined well Stripper well A B C + + A B A - - A C B n tinuous + B B viscous emulsifying gaseous sandy A flowing Well stream parafinous Characteristics A B B A - + C A - plunger lift - C A A intermittent Gas lifting B B B B A A A A A B B A hollow rods B B solid rods walking beam type C B C B A B A A' B - A hydraulic Pumping B B long stroke unit Sucker rod pumping Table 5.1. casing 6 0 1 2 3 4 5 50 20 5 bars Gas lifting 6 3 4 6 2 4 6 6 6 6 6 6 5 6 6 5 6 6 5 2 6 ? 3 ? ? ? 3 ? 1 ? 0 0 1 0 0 1 0 0 3 6 6 6 6 6 4 membrane Pump sonic Rodless pumping hydraulic Pumping submersible centrifugal* long stroke type Table 5-2. Selection of production methods (11) .x .100 100-200 q ~ r n .50 50.1 6 4 5 3 2 6 6 4 1000 2000 3000 1000 2000 3000 200-300 300-400 >400 0 0 . m3/d (within reasonable economic limits) 2 6 0 3000 1 2 3 2 3 3 2 1 2 2 0 0 3 2 3 2 5 3 0 3 1 0 0 solid rods 0 2 3 0 2 3 0 3 1 hollow rods typ Sucker rod pumping walking 1 0 1 plunger lift 3 0 0 1 1 0 1 1000 intermittent 2000 continuous Flowing Lw m x maximum value at 6 in. 1. whereas in bottom-hole pumping the BHP is almost irrelevant.* The items figuring in annual direct cost are the depreciation of the production equipment A repair and maintenance costs B.000 Ft per year and c = 6 Ft/Mg.1 for two different types of production equipment. MOST ECONOMICAL. q.p.= 1800 m. Although the selection tables give but a rough orientation.= 15 bars. and continuous gas lift is liable to be uneconomical. . optimum economy will lie with the means of production having low depreciation and repair and maintenance costs even though specific cost of power is comparatively high. Table 5-2 also gives some indication as to how the economy of the individual production means depends on the rate of production.Table 5-1 states that options are restricted by the sand content to continuous gas-lifting. The annual direct cost is. is cqan. in low-productivity wells. The one is characterized by A + B = 45. we get Figure 5 . Paraffin deposits exclude the sonic pump. and the cost of power c. Kan=(A+B)+cq... The selection table indicates at the same time that q. then. For instance. the low production rate excludes electric submersibles. 5 . The consideration to be given below is aimed at proving that.1is a plot of Eq. in Ft/Mg). In compiling this Table. = 10 m3/m3. A and B are almost independent of the rate of production. sonic and membrane type bottom-hole pumps.. overheads wages of well-maintenance and work-over personnel. and the * Ft is the symbol for Forint. the Hungarian currency unit. Table 5 -2 states membrane-type bottom-hole pumps to be unsuited for a depth of 1800 m. Example 5.. whereas power cost c is an approximately linear function of that variable. . Hence.) are left out of consideration. Dividing both sides of the equation by qan. limits of rational operation have been considered. electric submersible. PRODUCTION METHODS 457 well depths and producing BHPs. in gas-lift type methods of production varies significantly with producing BHP and well depth. at an annual production rate of qan= 365 q. Let the specific cost of power be c Ft/Mg the yearly power cost.. the well fluid contains 2. = 10 m3/d.. Find the most economical means of production. R. and further to hollow-rod. if L. Cost items independent of the type of production equipment (cost of drilling.3 percent sand and paraffin deposits are liable to occur. Economic comparison of production equipment should preferably be based on the so-called direct specific cost (k. . but the specific injection-gas requirement is so high as to be prohibitive in practice.. they usually permit the reduction of the number ofmethods to be given a closer look to just one or two. sucker-rod pumping with a hollow-rod string is the obvious choice. Of the items in the direct cost.5. continuous gas-lifting a well 1000 m deep at a producing BHP of 5 bars may be technically feasible. etc. The ordinate difference between graphs 4 and 5 at various rates of production indicates the injection-gas saving in m3 per Mg of crude against the hypothetical gas-lift . q. (Graph 5).1 merely serves to provide a comparison in principle of two types of equipment. 5 . 5-1. then the specific cost of the crude thus produced is precisely equal to that produced by the sucker-rod pump. Graphs 1and 2 refer to walkingbeam type sucker-rod pumps. Fig. that will result in a cost equal to that of sucker-rod pumping. Equation 5 . Let us plot in this system of coordinates the actual or anticipated specific injection-gas consumption of production v.5 -2. Equipment 1 is seen to be more economical at rates of production above 3 Mg/d.10 Mg/d (Graph 4). gas lift for instance is more economical than bottom-hole pumping. The ordinate difference between Graphs 1 and 3 defines a certain cost fraction. and the amount of gas thus co'mpressed is just sufficient to produce the well. we obtain the specific injectiongas consumption R.. MOST ECONOMICAL PRODUCTION METHODS other by A + B= 7500 Ft/y and c = 40 Ft/Mg. at low rates of production. Part (b) of the Figure is a plot of R.1are plotted in a bilogarithmic system of coordinates. v. If this fraction is spent on compressing injection gas. Graph 3 to an intermittent gas lift.458 5. The relationships imply that. In real-life situations. and vice versa.2and 3 of Fig. Graphs 1. choice between two options is made possible by the procedure illustrated by Fig.. in the range from 1 . In part (a). daily production rate q. Dividing the ordinate differences 1-3 belonging to various rates of production by the corresponding specific costs of compression (corrected for losses). 5 . In the case assumed in the Figure. Multiplying this hypothetical saving by the corresponding annual production rate q. In operations planning Fig. In reality. intermittent gas-lift production of a well is more economical at rates below 8. 5-2. and sucker-rod pumping is more economical above it.00OFt/y is saved by changing over from sucker-rod pumping to intermittent gas lift. after SZILAS (1957) 2 Mg/d. however. each parameter of production changes: the flowing bottom-hole pressure and the daily production rate generally decrease with time. we obtain a graph of annual cost saving Ak/y v. The production costs change as functions of the .2 is to be prepared for various well depths or well groups of various depths. daily rate of production (Graph 6). MOST ECONOMICAL PRODUCTION METHODS 459 operation equal in cost to sucker-rod pumping. In a well producing Fig. and plotting the resulting values.5.6 Mg/d. 45. In the above section it was implicitly assumed that the daily production parameters of the well do not change with time. rate of production in sucker-rod pumping and intermittent gas lift.. Economy v. and the specific cost of compression. The cost of production with a q [m3/dl - Fig. Along the intersection of the surface characteristic of the two lifting methods. the production costs change with the daily production rate and flowing bottom-hole pressure in cases of continuous gas lifting and electric submersible pumping. 5 -3. the production costs of the two methods are the same. .7. Figure 5-3 for example. shown by a dashed line. Production cost comparison of gas lifting and submersible pumping submersible pump at relatively large daily rates and low BHPs is low while vice versa at gas lifting. MOST ECONOMICAL PRODUCTION METHODS above factors. shows how. when selecting the most economic lifting method for a well the expected total life of the well must be considered (see Chapter 6.4and Szilas 1979).460 5. Strictly spoken. for a well of given depth and inflow performance. respectively (Szilas and Takacs 1979). .APPENDIX Fig. Fig. A-1. A-2. A-B Po Mf-8 Fig. Fig. Fig. A-4. A-6 P. .APPENDIX Fig. A-3. A-10. A-9. - '0 50 100 Fig. A-8.APPENDIX - Fig. A-7. Fig.ban Fig. P. 160 200 PIbore 250 . R. N.H. (1963): Evaluation of surface back-pressure for continuous. SPE AMEZCUA. BONSALL.W. June. Journal of Canadian Petroleum Technology. V. (1980): Comparative analysis of pumpoff control systems for field applications..P. API Drilling and Production Practice. & BRILL. NEDRA. 11. (1960): Slim-hole completions reduce well costs 35%. Petroleum Engineer lnt. ADONIN. (1954): Simultaneous flow of oil and gas.. (1957): Dewatering of gas wells. BAKER. A z ~ zK. 10.J. A. R.. (1958): The plunger lift method of oil production.. 1. T. Petroleum Technology. (1969): Vybor novogo oborudovaniya i rezhima otkachki dlya glubinnonasosnykh skvazhin. (1956): Dynamometer stars in a new role. BAN. & STODDARD. Oct. C. P. API RP 39 (1960): Recommended practice standard procedure fo the evaluation of hydraulic fracturing fluids. Prentice-Hall. (1965): Modem aspects of electrical submergible pumps. (1962): Miyanie sooistv gornykh porod na doizhenii o nikh zhidkosti. S. BINDER.A.. . K. G. Englewood Cliffs. (1964): Eksperimentalnoe issledovanie fizicheskikh svoistv emulsionnykh neftei. 5. (1958): Advancedfluid mechanics. Journal of Petroleum Technology. G. Moscow. Vol. KNOX. World Oil.0. D. I.E. Nov. W..D. Vol. (1967): Einsatzplanung und Betriebserfahrung mit elektrischen Tauchkreiselpumpen. Gostoptekhizdat. Gostoptekhizdat.J. P. J. Oil and Gas Journal.-Aug. P. 256. (1980): HOWplunger lift affects production. GOVIFX. & BROWN. July. Journal of BAXENDELL. B. & FOGARASI. BEADLE. M. D. Dallas. ARUTYWNOFF. Neftyanoe khozyaistvo. C.A. G. 8. & AWENSHINE. Izu. 7he Petroleum Engineer. Petroleum Engineer Int. 9362. (1973): A study of two-phase flow in inclined pipes. HARLAN. E. July 18th. BENNEIT. 7. BEAUREGARD. G. M. Aug. BELOV. 3. E.G.M. AGNEW. American Journal of Science. (1958): The distribution of temperature in flowing wells. BENNET. S. (1962-1963): Ways to calculate gas flow and static head. W. BOGDANOV. BOLEY. July.G. J. (1961): Calculation of pressure gradients in highrate oil wells. Oil and Gas Journal. & THOMAS. J. ErdoelErdgas-Zeitschrift. J. . Journal of Petroleum Technology. ASME preprint 54-PET-28. BOLDIZAR. BOYD. Moscow. & FERGUSON. Neft i Gaz. L. Petroleum Engineer. L.and intermittent-flow gas lift. M. .. July-Sept. N. A. July 26th. N. (1968): Pogruzhenenie tsentrobezhnie elektronasosy dlya dobichi ntfti. May. Inc. C. Moscow. (1972): Pressure drop in wells producing oil and gas. BEGGS. (1960): Tandem rod pumps prove practical and economical in deep dual wells. (1980): Artificial lift concepts and timing. 22nd. I. A.REFERENCES ABDURASHITOV. BEESON.B. & AVENESYAN. G. (1960): Issledooanie raboty glubinnykh nasosov dinamografom. H. Oil and Gas Journal. 4. A z ~ z X. (1959):Turbulent flow of non-newtonian systems. Joe Chastain. (1972): A simple low-cost method for determining the productivity index of high pumping wells. . I. 1. Ch. Sept. World Oil. AIME. B. (1977): Pumping deep wells with a beam and sucker rod system. 19th. J. BROWN. June. from short flow tests. California. (1973): Pumping well optimization techiques. A.C. B R ~ E M A NF.R. 3. 4.H.J. J. M. H. Vol. 4. K. H. (1961): 7heory and application of hydraulic oil well pumps. (1974):Two-phase vertical flow in oil wells-prediction of pressure drop. S. ASME 80-Pet-18. June. ESPANOL. Vol. N. (1963): Determination of stabilized gas well performance CARTER. W. W. DAVIS. G. E. G. I . HOLDEN. p. A. N. (1977): The technology of artificial I# methods. R. & GRIFFIN. L. Chapman and Hall Ltd.G. EWING. Petroleum Publishing Co. p. Reinhold P.. COBERLY. FANCHER. R. (1967): Gas lift theory and practice. (1953): The exercise of control of flowing wells and of input to gas lift installations by means of a differential flow control valve. H.-June. & METZNER. FRANKS. (1979): Application and economics of variable speed submersibles. J. Sixth WPC Congress. M. AGA API. J. E. C. & RILLEY. April 20th. Journal of Petroleum Technology. (1969): Gas-liquid flow in pipelines. & BROWN. 204. (1969b): Fully rolled thread: breakthrough in rod couplings. Journal of the Institute of Petroleum. POYNTER. E. DEVERTEUIL. Journal of Petroleum Technology.. DIVINE. Apr. P. J.. C. E.. DUNS.. Thesis. I. D. R. E.D. Y. E.(1963): Vertical flow of gas and liquid mixtures in wells. Journal of Petroleum Technology. DEAX. & MERRYMAN. & HUMMEL. 2a. (1980): Sucker rod pumping offshore. C. & MOORE. Petroleum Engineer. G. DOERR. J. S. FINCHER. Vol. N& . L. (1968):Comparison of three methodsfor calculating a pressure traverse in vertical multiphase flow.D. J.. D. T. CROSBY. Englewood Cliffs. Pans. MILLER.JR. Journal of Petroleum Technology. D. CULLENDER. Houston.K. E. SPE 6436. & RIKE. (1973): Optimum design for dual gas lift. Jan. Journal of Petroleum Technology. PPC Books. CHIERICI. H. Prentice-Hall Inc. L. LAWRENCE. Erdoel Zeitschrift. A. R. BROWN. B. Rheology of disperse systems. New York.. 5. T. (1969a): Miniaturized completions can be artificially lifted.. Midland. SPE preprint 3186. A.K. 8.. W. (1963): Prediction of pressure gradients for multiphase flow in tubing. J. E. EUBANKS. New York. CASSON.REFERENCES 465 BOWERS. C. CROSBY. E. E. 3. (1959): How to save with tubingless completions. Journal. CORLEY. F. K. DODGE. BRANDT. W. J. E. A. (1958): Pumping well problem analysis. BYRD. BROWN. Vol.. BRILL.. 39. J. Texas. L. G.D. & ROS. (1980): The technology of artificial lift methods. P. (1970): Long stroke pumping unit. N. D. CRAFT. C. 12. Oil and Gas Journal. 6.. KOBE Inc. New York.J. 133. & GRAVES. B.. G. Febr. (1962): Viscosity and its measurement. (1970): Shell tries hydraulic lift for high-volume wells in West Texas. G. N. J. Oil and Gas Journal. Petroleum Engineer. K.J. Pergamon Press.F. The University of Tulsa. EICKMEIER. N.(1962): Well design: Drilling and production. C. M . D. L.calculations. London. Tulsa. & HAGEWRN. G. de Mo&. (1975): Practical aspects of predicting errors in two phase pressure-loss .B. Section 11/22. (1959): Neuerungen auf dem Gebiet der Erd6lf"orderung mittels Tiefpumpen. D. (1955):The isochronal performance method of determining the flow characteristics of gas wells. C. Society of Petroleum Engineers Journal. 1417.. CIUCCI. Petroleum Engineer. Huntington Park. Inc. (1966): Practical use of recent research in multiphase vertical and horizontal flow. July. 7he Journal of Canadian Petroleum Technology. Englewood Cliffs. MAXWELL. BROWNE. World Oil. 6. DINSDALE. DUKLER. & BROWN. Prentice-Hall. H. & S ~ C H G. J. Tulsa. Research results. N. (1959): AJow equationfor pigment-oil suspensions of the printing ink type. (1965): Stimulating heavy oil reservoirs with downhole air-gas burners. E. F. P. M. K. L. (1963): Aspects of gas deliverability. CANDY. A. 61. L. GOVIER. W. HEDSTROM. G. R. Oklahoma. R. 1319. p. (1978): Analyzing the performance of gas wells.C. A. (1960): Glubinnonasosnye privodi dlya ekspluatatsii kustovykh dvukhstvolnikh skvazhin. Bucharest. G o v ~ wG. Van Nostrand Reinhold Co. Journal of Petroleum Technology. C'. T. in Sl Salzburg. (in Hungarian) GEIMAN. Short Course.. GRIFFIN. May 10. A. and Eng.S. Okt. A. (1963): Pipeline flow characteristics of crude oils. Petroleum Technology. 4.H. C. J. (2nd ed. Chem. & DUNBAR. B. American Petroleum Institute (API). (1942): Design and construction ofoil pipelines. p. F.L. W. HOOD.. HUNTER. June 26th. HOLLENBECK. Ind. Roy.. 7. Z.466 REFERENCES FRICK. New York. Gemeinschaftstagung ~ G E W I D G M Koom 4. C. Neftepromisloooe Delo. 7. & BROWN. Bohrlochausriistungen in Hochdruckgasbohrungen. S. E. D. & REITER.. (1962): Petroleum production handbook. M. Jan. a long stroke pumper. History of petroleum engineering (1961). 1. Hungarian). (1957): Vereinfachte Sammelstelle im Oelfeld. USI. HURST. D.) Centrilift Inc. & CLARKE. API preprint 801-44F. & TAYLOR. (1976): Uberlegungen zur Verbesserung von HOFBAUER. (1978): 0 rezultatakh opytnoi ekspluatatsii pogruzhnogo diafragrnennogo nasosa.. Mdjraw-Hill B. Oil and Gas Journal. JAGER. 6. high-pressure sour gas.... C. 11. Journal of Petroleum Technology. GRIGORASHCHENKO. K. (1965): Experimental study of pressure gradients occuring during continuous two-phase flow in small-diameter vertical conduits. BKLKBolaj Ps Foldgaz. (1976): Producing Mississippi's deep. API preprint 875GRIFFIN. 3. R. (1968): Deep. (1973):7heflow ofcomplex mixtures in pipes. & DIMON. Garrett Oil Tools. HOLLIS. SPE 9216. CH. & AZIZ. HURBEL. 2. Neftyanoe Hozyaistoo. JR. (1978): Denver unit well surveillance and pump-off control system. HAMBY. G . 22F. L. (1980): Experiences in the deep. Editura Technica. (1942): Proc. BROUSSARD. Erdoel Zeitschrift. p. IOACHIM. Azerbaidzhanskoe Neftyanoe Khozyaistvo. C. ?he Journal oJ Canadian Petroleum Technology. E. high-volume hydraulic pumping Reno-field. sour Schonkirchen gas field. GOVRERG. Sixth WPC. J. & SIMONS. p. GILBERT. P. E. W..K. HOWELL. M. G. J. Journal of Petroleum Technology. G. GRAF. E. (1952): Flow of plastics materials in pipes. (1976):An update on pumping unit sizing as recommended by API-RP-11 L. Handbook oJgas l f t (1959). & HDGWOOI).-March. E. Budapest (in GYULAY. Texas. Tulsa. S. K. Industries. API Preprint 801-44A. Mernoki Tovabbkepzo Intezet. K. Inc. Dec. (1970): Hydrogen sulfide corrosion can be controlled. Section VI1/1. D. G A Z ~E. GOODSON. 8. B. 28-33. R. A. M. 629. (1968): The flexible sucker rod . E. (Edinburgh). SANDK~~HLER. & GADIEV. C . S. & RITTER. (1962):Electr$ed oil production.R. 6. pp. (1974): Osnovnye napravlenii razvitiya tekhniki i tekhnologii dobychi nefti. (1978): How EPNG produces deep high-pressure gas wells.T. Congress. A. Proc. W. U. (1968): New API design calculation for sucker rod pumping systems. P. G. Journal of Petroleum Technology. (1977): The automatic liquid level monitor for pumping wells. Handbook for oiljield subsurface electrically drioen pumps (1978). E. Petroleum Engineer. R. (1965): Extracria perrolului +igazelor. R. bis 6. 1019. HUDGINS. Dallas and Houston. G. (1971): Computer helps select best lifting equipment. New York-TorontuLondon. Journal o/ GODBEY. The Petroleum Publishing Co. of the 25th Southwestern Petroleum GREEN. A.D.W.0 . D. & LEESE. 4.J. Soc.K. HAGEDORN. Tulsa. (1955): Flowing and gas-lift well performance. 792 p. 7. API Drilling and Produc-tion Practice. . W . H. W.. (1980): An alternate approach to high volume. HALL. Dallas. M. 0 . 9.R. F. .an innovation in pumping. Oil and Gas Journal. MCDANNOLD. Dec.S. (1981b): Gas separator performance for submersible pump operation.R. KUTUVAYA. & ELKINS. J. Petroleum Pansaction. 12. C. D. SPE preprint 3193. McGraw-Hill B. A. F. B. 8. & BIRD. Petroleum Engineer..R. V. A. pp. JOY. J.J. (1979): Submersible pump selection 4. r LOCKHART. (1964):Tube flow of non-newtonian polymer solutions. (1967): Impact of new technology on the U. MCCURDY. LEFUR. AIME. nasosa. JUCH. & KATZ. L. European Offshore Petroleum Conference and Exhibition. Gazovaya Promishlennost. Eng. No. METZNER.J. (1977): Critical evaluation of friction pressuredrop prediction methods for gas liquid flow in horizontal pipes. 4.D. petroleum industry 19461965. Petroleum Engineer lnt. METTERS.D. R. R. New York-Toront~LondonSidney. V. A. G.. LEDET. July 9th. & REED. A. controlling it. 63-67.E. A. KANU. M. (1967): Transport en conduite de liquids non newtoniens.40. 12. METER. . 257. Vol. July 15. KULIZADE. 0. J. OBUKHOVA. Z. I . McGraw-Hill B. A. (1958): Fluid dynamics and heat transfer. C .E. R. 27th. & DAY. (1960): How to determine pumping loads with hollow sucker rods. R. Aug. (1972): A comparison of vertical two-phase computation techniques. & WATSON. P. (1969): New concepts in sucker-rod pump design. Prepared by the National Petroleum Council. 3. M. (1957): Buckling of tubing in pumping wells. Journal. KNUDSEN. H. K. B. Inc. E. L. 45. and turbulent-flow regions. F. & BLENKARN. P. 10. July 15th. 210. (1949): Proposed correlation of data for isothermal two-phase. Journal of Petroleum Technology. C. . 1. F..R. KASTROP. 10. June 28th. 5.E. E. C..J. Part ofseries Oil and Gas Journal. T. (1961): Scaleup for non-newtonian fluid flow. M. V. (198ia): Effect of gaseous fluids on subersible pump performance.L. Engineer.correlation of the laminar..A. MANDHANE. KATZ.J. LEUTWYLER. K. Aug..A. Inc. July 23rd. Eur. & MARTIN. (1960): Elektroohorudooanie v neftedohiche. A. ASME preprint 72-Pet-38.CHA. New YorkToront+London. Journal of Petroleum Technology. A. 8. Petroleum Engineer. P. 7-8. (1978): Experience with surface controlled sub-surface safety valves. Progress.. (1974): Simplified method for gas-lift well problem identification and diagnosis. (1955): Flow of non-newtonian fluids . W. & GEIBOVICH. L. W. LEBARON BOWEN. Aznyeftnyesr. Revue de Plnstitute Fran~aisdu Pitrole. (1971): New producers aid optimum design of high-volume pumping systems. E. Neftyanoe Khozyaistvo. J. (1981): Systems analysis hikes well performance. MEDLEY. (1961): Stop pounding that pumping well. S. MARTIN. A. SPE 9219. LEA. June-Sept. two-component flow in pipes. W. (1974): A statistical evaluation ofmethods used to predict pressure losses for multiphase flow in oil well tubing. & BRILL. Journal of Petroleum Technology. (1968): Flexible sucker rod in the works. H. American Institute of Chemical Engineers Journal. Inc. Oil and Gas Journal. New York-Toronto-London.R. Oil and Gas Journal.. Ch. N. Mdraw-Hill B. Aug. transition. ANDERSON. (1970): A new concept in pumping unit technology. 32. D.. & COLEMAN. E. E. A. D. C. Washington.REFERENCES 467 JERNIGAN. LAWSON. (1961): The evaluation of vertical-lift performance in producing wells. & MARTINELLI. (1966):Mechanics offluidflow. (1970): Otkachka vyazkikh zhidkostei s pomochyu vibratsionovo KRUMAN. J. Petroleum K. G. 1st. Chemlcal Engr. G. 1. (1959): Handbook of natural gas enqineering. Journal of Petroleum Technology. SPE 5151.J. P. LEGG. K.L. et al. Vol. p. J. Oil and Gas Journal. LONGWELL. 6th. 5. LEA. L. (1974): World demand puts pressure on production equipment.R. GREGORYG. Chem. & AZIZ. B. R. & TURNER.A. MCAFEE. its effects and means for LUBINSKI. & KUZNETSOV. p. C.D. Baku. J. G. M c L ~ o oW. MAYHILL. MIROSANICHENKO. P. (1978): Zashchita oborudovaniya skvazhin ot uglekislotoi korrozii. F. (1968): Dewater gas wells automatically. May. SPE 9218. B. DE (1959): Regelung des Tiefpumpenantriebes durch den dlzufluss. F. & GOVIER. (1967): Eine Obersicht iiber einige Methoden zur Berechnung des Druckverlustes beim Transport zeitunabhaengiger nicht-Newton'scher Fliissigkeiten in Rohrleitungen. 6. C. Petroleum Engineer. ROS.M. S. Dallas. PERSOZ. KHARLAMENKO.R. API Drilling and Production Practice. & RASIZADE. SPE 8246. Dallas. (1967): Numerical prediction of the flow characteristics of thyxotropic liquids.F. Technical Univ. World Oil.468 REFERENCES MILINSKY. P. VDI-Verlag GmbH. I. C. J. B K L Kdolaj 2s Foldgriz 3 (in Hungarian).. (1970): Puti snizheniya energeticheskikh zatrat glubinnonasosnykh ustanovok. M. 10. E. RITTER.. & VOGEL. & SAMILEV.. PRUTZMAN. R.. A. PATSCH. ZAJTSEV. McGraw-Hill B. The Petroleum Engineer. Inc. (1955): Problems and economics of dual completions. REHER. JR. D. (1969): Non-Newtonian fluid flow in pipes. (1961): Simultaneous flow of gas and liquid as encountered in well tubing. RITTER.R. I. OMANA.D. A. G. J . G. G. P. KBolaj es Fiildgaz. E. (1970): Pumpen. Bulletin 6-956. A. BRILL. Aug. B. B..J. C.R. (1979):System analysis as applied to producing wells.& BUSKUNOV. 232 p. R. SPE 4538.N. NIND.. (1959): Spravochnik po dobyche nefiy (Vol. No. 3. V. Journal of Petroleum Technology. G. J. Dusseldorf. YA. A. Razrabotka neftyanykh mestorozhdenii i dobycha nefti (1972). A.J. & THOMSON.. J. July. 6. (1963): New charts developed to predict gas-liquid flow through chokes. flow strings. 1. PATSCH. (1 970): Steady temperature distributions in producing wells and pipelines. HOUSSI&RE. Miskolc (in Hungarian).A. World Oil.. Gazovay Promyshlennost. (1970): Continuous rod design. & BROWN.E. 12 (in Hungarian). A. NEELY. - . GY. E. R.A. S. P. Oil well supply (1957): Selection and application of subsurface pumps. (1953):The multiphase flow of gas. ORKISZEWSKI.A. & DETTERICK. V. Hydraulische Maschine und Anlagen (Teil3). MACH. Society of Petroleum Engineers Journal. Moscow. P. Moscow. A. API Drilling and Production Practice. & BECK. NICHOLS. F. A.. R. 11. T. A. MURAVYEV. Chem. (1964): Principles of oil well production. (1973): A field test and analytical study of intermittent NEELY. R. MURAVYEV. MONYB.F. M. 99. PAPAY. J. (1960): Introduction a Pitude de la rhiologie. Dec. March. Moscow. PROANO.G. gas lift. (1949): Ekspluatatsiya neftyanykh mestorozhdenii. New York-Toront* London. of Miskolc (in Hungarian). J. Techn.K. M. 3. H. Erdiil und Kohle. I. Dunod. MONTGOMERY. V.. NEELY. D. E.G. M.B. cuts costs. V. (1965): The development and evaluation of theory of thyxotropic behaviour. J. Nedra. API preprint 851-42-A. Congresso Panamericano de Ingenieria del Petroleo. MS Thesis. 3. C. SHERMAN.A. (1969): Multiphase flow through chokes. MINGARAEV. Journal of Petroleum Technology. MIRZADZHANZADE. 58. P. 3. RENEAU. & KRYUIV.. K. (1969): Corrections to and general solution of Krylov's vertical two-phasepow correlations. p. W.. & BLANN. SPE preprint 5150.. Gostoptekhizdat. J. P~ETTMANN. Petroleum Engineer. M. W. Canadian Journal of Chemical Engineering. Mexico. Yu. & CARPANTER. REDDEN.H . (1968): Dewatering gas wells. & BATICKY. KH. Neftyanoe Khozyaistvo. oil and water through vertical POETTMANN. (1967): Predicting two-phase pressure drops in vertical pipe.. (1974): Optimizing gas-lift systems. LUTFULLIN. PATTON. PLACE. BROWN. (1979): Corrosion control deep sour gas production. SPE 8310. 1. B. (1979): Pump-off control system boosts production. 11 (in Hungarian). Gostoptekhizdat. (1979): Utilization of fiberglass sucker rods.R. G. H. (1971): Calculation of pressure distribution in vertical two-phase flow. D.(1970): Research report of the Petroleum Engineering Dept.. 8. (1953): Design and development ofimproved annular survey equipment and techniques. W. RAABE. F. Yu. L. J. B K L KJolaj 2s Fiildgciz. M. p. 10. T . A. (1970): Oborudovanie skvazhiny rekomenduemoe dlya mestorozhdenii soderzhashchikh serovodorodov. H. NOMISIKOV. Paris. KHALICHIN. 48. E.). SAUL.E. MILLEY. & MYLIUS. (1976): Sucker rod string design. Vyp.L. SPE preprint 2682. GURBANOV. A. 6. Industrial and Engheering Chembtry. 2. A.REFERENCES 469 SCHLICHTING. Houston. Vol. SZILAS. (1970): Der Transport von Oel-Wasser-Gas Gemischen in Erdoelfernleitungen. (1957): Dohycha i transport gaza. Oct. p. E.L. 1. 9. Chem. Mining Handbook. p. & SHIRKOVSKY. P. Miiszaki Kiad6.E. 1227. P. ErdoelErdgas Zeitschrift. Co. S. 1789-92. pp. Co. . & PATSCH. Sopron. (1959): Bestimmung des Druckkoeffizienten aus den Betr~ebsdaten der &sonde. P. Petroleum Engineer. R.. 3.F. SZILAS. 3. STEPHENS. Phys. Mitteilungen der Fakultaten fir Bergingenieure und Geo-lngenieure ( X X ) . Publications of the Technical University. (1981): Determination of turbulent pressure loss of nonnewtonian oil flow in rough pipes. SIMMONS. (1963): Changes in the rheoIogical properties of emulsions on aging.. SZILAS. F. Pennsylvania. 2. & NAVRATIL. M. No. SNYDER. World Oil. Aug. & SPENCER. SPEEL.A. Rheologica Acta.A. Gulf Publ. P. 1-4.. Techn. Texas.ekhizdat. SIMMONS. I. A. JR. Miskolc.. pp. 1 (in Hungarian). E. Part 11. 139. 3. 6 (in Hungarian). Rheologica Acta. University of Miskolc (in Hungarian). 3. Geothermics. SZILAS. A. Technical TAKACS.A. (1977): A history of the development of Rule 36. 0. SHAW.L. pp. Inc. W. Universitatsfakultaten. SZILAS. p. Oil Well Supply. (1967): Non-newtonianflow and heat transfer. 12. P. John Wiley and Sons. Vol. p. SNYDER. A.R C.A. SZILAS. Mexico. on the kinetics of globule coagulations. P. 6-956.J. Sopron. P. E. Bdnyaszati Lapok. E. 5. Freiherger Forschungshefte A233. Seventh W P C Proceedings. . %KO. F.A. P. BOBOK. P. (1959): Turbulent flow of pseudoplastic polymer solutions in straight cylindrical tubes. Mitteilungen der Fakultiiten f i r Bergingenieure und Geo-lngenieure ( X V l l l ) . B K L KJolaj b Foldgaz.A. R. (1959): Bottom hole separators increase production. W. Part 2. A. New York. Journal of Petroleum Technology. Vol. (1967): High pressure gas well completions. 16. (1982): Interpretation of oil thixotropy using a grid-shell structure. SZILAS. R. W. Dec. Gulf Publ. (1939): Gas-lift principles and practices. P.. SHAVER.R. and their dependence SHERMAN. (1979): Optimum lift method in forced production. 0. A. Budapest (in Hungarian). (1971): Determining flow curves for pressure drop calculation of thixotropic-pseudoplastic crudes. P. 3. Techn. 1. SZILAS. 68-69.. G. SCHMOE. W. P. (1984): Grid shell theory. Texas.S.. April. Sonic pump bows in (1958): Petroleum Engineer. World Oil. SZILAS. (1961): Dynagraph Analysis of Sucker Rod Pumping. E. S ~ N E G C EJ. 4. (1955): Betriebsverhaeltnisse gasfreies Oel fordernder Sonden. (1972a): Optimizing continuous flow gas lift wells. & MERRILL. Bulletin ONGC (India). World Oil. Oct.A. 9. SMIRNOV. Ch. G. SZILAS. P. (1970): New pumping methods boost oil production. 29 (in Hungarian).G. P.und Plungerliftforderung -zwei rationelle Forderverfahren Wr geringproduktive Sonden. Gostop. W. (1958): The flow of lubricating greases. Houston. Petroleum Engineer. & FALK. 4648. (1975): Computer selection of optimum vertical two-~hasecorrelation. a new concept to explain thixotropy. Vol. SKELLAND. 6. SZILAS. A. The Pennsylvania State College. E. A. & TAKACS. P. (1975): Flow in geothermal hot water wells.A. P. MS Thesis. May. M. Universitatsfakultaten. 1. & SUMAN. B K L Kciolaj i s Fiildgciz. (1980):Basic equation of up-iodate vertical two-phase flow correlations. 47. H. Part I. P.A. Journal. Moscow. (1978): High pressure well completion. Bulletin No. 50. Congresso Panamericano de lngenieria del Petroleo. SZILAS. (1959): Production of oil and natural gas.G. (1964): Kontinuierlicher oder intermittierender Betrieb von Pumpsonden? ErdoelZeitschrift. (1962): Intermittierende Gaslift. P. Selection and application of subsurface pumps (1957).. SZILAS. (1950): Natural gas engineering. 97 (in Hungarian). No. (1979): Optimum system of oil field production equipment. E. (1957): Choosing the most economical production equipment. SZILAS.. (1972b): Optimizing continuous flow gas l i t wells. SMITH. p. A. ROBINSON.G.. L. O'CCONNELL.P. (1964): Friction pressure reducers in well stimulation.I. L. T. WALKER. 21st. 3. July. S P 2. 3. B. (1967): Nagruzki is napryazheniya v polykh nasosnykh stangakh iz osteklovannykh trub. H.K. (1977): Pump-off controllers match pump capacity to production.A. (1973): Improving sucker rod string design. (1974): Evaluation of three new methods for predicting pressure losses in vertical oil-well tubing. WINKLER. Journal of Petroleum Technology.. Camco Inc. WEST. (1973): Research report.470 REFERENCES TAKJ. J. & BILGERI. R. 5. VOHRA.A. E. Journal of Petroleum Technology. 1.. . WHITE.A. Y. and dynamic parameters of intermittent gas lift. R. P..M.G. p. R. M. R. Part 4.D.. G.. J. (1979):Production VAGHI. DAVIS. Izv. VINCZE.. Journal of Petroleum Technology. D.D. Houston. Oil and Gas Journal. Petrochemie. USI. W. L. Trrum~rs. Calgary.R. HERNANDEZ. 731. N. Handbook of gas lift (1959): Garrett Oil Tools. ~R. Budapest (in Hungarian). LYON$J. TEK. Budapest.J. E. New York-London-Sydney.A. K. M. Canada. G. J. Yu. A. May 17th. ZAITSEV. & STACHA. G.. (1930): Mathematical development of the theory of flowing wells. 68. 7heory and practice of the testing ofgas wells (1975).CS. W. R. GIACCA. (1975): Comparison of liquid-holdup and VOHRA. 131. (1978): Fiberglass sucker rods in beam-pumped oil wells. 8. W. 7he Oil and Gas Journal. 12.M. R. World Oil. Pipe Line Industry. PULGA. Nefti i Gaz. Part 3. G. (1960): How and why tubing anchors reduce operating costs of rods. (1961): How to improve your hydraulic pumping operations. Erdgas.G. G. p. 28th. UHL.I.) Gulf Publ. L. AIME (Petroleum Decelopment and Technology) 86. WATKINS. Interscience Publishers. for the continuous removal of liquids from gas wells. & VANDEVIER. C. (1962): CAMCO gas lift manual. Nov. 8.. V. (1961): Wire-line installations are a boost to gas lift. & BECKER. Houston. Journal of Petroleum Technology. J. 5. p.G . WESTERMAN. (1961): Multiphase flow of water. Canadian Oil and Gas TAYLOR. (1954): When do duel completion pay? 7he Oil and Gas Journal.P. (1968): Zweizonenforderung in Hochdruck-Gasbohrungen. (3rd Ed.J. Italy. Oil and Gas Equipment. 10th World Petroleum Congress. WHITE. Journal. OGIL-OKGT. Texas. (1967b): Steady flow in gas pipe lines. in the very deep Malossa field. & KAND. G. May. TURNER. Sept. T.T. C. Tankonyvkiado. (1968): Metallograjia Ps anyagoizsgdlat (Metallography and material testing). 11. & BRILL. Z . E. 6. F. E.) Energy Resources Conservation Board. Journal of Petroleum Technology. Bucharest. UHL. P. r U .. (1963): An analytical concept of the static B.J. Journal of Petroleum Technology. E. 192. 4. US Industries Inc. W. T. WILSON.. (1973): Deep well tests show jet pump advantage. Journal of Petroleum Technology. E. & SMITH. & DUKLER. (1968): Inflow performance relationship for solution gas drive wells. (1979): Progress in the development of submersible pump power cables... MAROANO. SPE 8244. TORRICELLI. WIELAND. (4th ed.. 8. HUBBARD. J. A. TURNER. Texas. B. C. Z O R K ~ Z YB. CO. Neftepromyshloooe Delo. Woous. 10. 1. & BRILL. L. (1966): Mscosity andpow measurement. J. (1967a): Steady flow in gas pipe lines. Pipe Line Industry. W. & DOHERTY. Jan. New York. W. R. WERNER. (1956): Practical petroleum engineers handbook. (1978): Evaluation of ten methods for prediction of pressure drop in oil wells. 9.. VERSLUYS.C.D. ZOTOV. Petroleum Engineer. Trans. Erdoel-Erdgas Zeitschrift. KIM. VANW A ZJ. VOGEL. friction-factor correlations for gas-liquid flow. & COLWELL. 8. (1969): Analysis and prediction of minimum flow rate M. Erdol und Kohle. Journal of Petroleum Technology. (1968): Tekhnika i tekhnologiya podema nefti iz skvazhin i puty ikh dalneishego sovershenstvovaniya. ZABA. (1959): Heavy crude is more attractive now. oil and natural gas through vertical flow strings. World Oil.S.J. CHIERICHI. p.D. 390.regulator 190 capillary vixometer 48 casing . hydraulic 432 .pump 375 chamber installation 268 choke . 395 . 177.card 33 1. 450 . 304 .tension anchor 382 back pressure valve 173 Bingham-plastic fluid 33 blowout preventer 172.heater 385 . 367 annular flow 20.assembly 171.440 dynamic factor 315.84 apparent viscosity 35 apparent yield stress 36 automatic . 385..flowing well 185 .type kick off valve 263 . gaseous 393 -.of pumped wells 272 cycle load factor 353 dead space of pump stroke 339 diaphragm pump 451 differential .417.effect of 150.of gas lift wells 272 .(plastic) viscosity 3 1 dilatant fluid 31 dimensioning the tubing 159. 163.head 166 .safety valve 174 .fittings 172 clap valve pump 385 clock driven cycle controller 272 closed power fluid system 430 closed type completion 197. 265. 371. 324.formation control 408 . 451 cycle control .v. 204 Christmas-tree . 80. high viscosity 383 -. sandy 389.SUBJECT INDEX acoustical survey 401 allowable stress 325. 201. intermittent operation of pumping 403 Corod 370 corrosion of gas wells 305 counterweight 3 1 1. 386. 161. 428 Coberly coefficient 330 compression anchor continuous .of plunger lifts 284 .rodless 425. 318 dynamic load 318 dynamometer .406 -. 455 crude pumping -.pump 310. 304 bottom-hole .diameter 126 . selective) .choke 189 -.gas lift 196 -.completion 171. 355 crank and beam balance 361 crankshaft torque 407 critical pressure ratio 126. 300 dome pressure 247 double-acting hydraulic pump 427 double horsehead pumping unit 421 dual (multiple.sucker rod pump 375 . 1 80. 97. .of plastic fluids 46 .pump 391 flowir~g hydraulic .production's efficiency 144 --.regulation of flowing production -. single acting 43 1 flowing wells producing . volumetric of pumping 337 elastic seal plunger 284 electric .290 froth flow 57.unloading (kick off) 212.of pseudoplastic fluids 42 Goodman diagram 367 . 125.flowing wells 187 .455 -. 137.anchor 320 . 455 .single completion 264 .testing 290 gas-lift --. 158. double acting 427 . 455 . 48 .408 gas-well 290 economic comparison of production methods 457 efficiency .curve 33. 120 inflow performance curve (IPC) 131.treating facilities 308 . 231.of electric submersible pump 437 . continuous 196.prime mover of sucker rod pumping 351 electromagnetic pump 453 eiementary sulfur 307 energy-loss factor 68. 300 .472 SUBJECT INDEX . 76. 455 .corrosion 305 --. 260.flow line 152 .by choke 125 heat transfer correction factor 139 -.of gasless oil production 144 -.flow 22. dimensioning of 300 --.operation checking 274 --spacing 217. 90 -. 83.in horizontal and inclined pipes 110 Halliburtons pressure measuring assembly 399 -. 146.long stroke drive 41 1 . intermittent 220. 260 -.power of sucker-rod pumping 344 fluid pound 406 friction coeflicient (factor) for flow in pipes 17-25.insensitive sucker-rod pump 395 . fundamentals 17 gradient curve (pressure traverse curve) 70. 369 fundamental gradient formula 60 injection gas supply 271 .bottom-hole pressure 132.system 277 Galle chain 364 integral tubing 181 interaction of well with gas .valve 209.by surge-damping 191 hilly terrain 121. 461 . 86. 305 intermittent .containing H. 47.sets of (family of) 73.pump drive 41 1 44. 74 .optimization 278 flow . 262 -.in pipes. 400 . 98.without bellow 248 gas-lift well .heater 385 .in vertical pipe 55 hazardous gas well corrosion 305 heading 80 .S orland CO.bottom-hole pumps 425 .life 156 --.parameters of intermittent gas lifting 224 . 240 -. 116. gas supply system of 277 Flexirod 369 .formation 146 .centrifugal submersible pump 434 .with bellow 250 -.gaseous fluids 146.patterns 57. 185. 124 hollow rod 366 opening and shutting of the tubing 192 . 99 external upset tubing 181 extrusion viscometer 48 .dual completion 265 filling efficiency of pumping 337 -.pumping 403. minimum flow velocity in 292 . 112 inhibitor 307.completion 300 .with chamber installation 268 -.gas lift 220.dynamometer 432 .gasless oil 137 . wireline retrievable 258 -.tester 247 --. .controlled gas lift valve 209. 351. rnultiphase vertical flow 58 . 205. 323 .of gasless oil at flowing 138 .clamp 365 load 312. 455 .for a given polished-rod stroke 336 for sucker-rod pumping 343 of gaseous oil at flowing 163 . 92. volume factor of 71 . 82.liquid throughput 62 production method 454 tubing diameter 159 . 46 plug flow 58 plunger-lift 281. 1 14 liquid-jet pump 452 loads on the rod string 312 long stroke pumping 410 longitudinal vibration of rod string 319 malfunctioning of gas lift wells 276 mass gradient 79 maximum ....well performance curves 296 Kobe's hydraulic pump 426 laminar flow 17.surge 142. 440 multiphase flow 55 .inflow 13 1. 240 . 76.liquid production rate .test 295 .stuffing box 364 power consumption of sucker-rod pumping 351 submersible pumping 449 .allowable tensile stress 367 -.liquid throughput 62 mechanical drive long stroke pumping 319 mechanical efficiency of pumping unit 353. 461 utilization curves 138. most economical 454 . 177.434 -.rodless hydraulic pumping 335 operating points of . mass factor of 68 -. nominal power of 356 production -. 115. 118 monoblock type Christmas-tree 171 Moody-diagram 19 motor of .methods. 154 pressure drop calculation .gas lifting 278 sucker-rod pumping 343 . 319 .flow velocity in gas wells 292 ..in vertical tubing 55 -.a!lowable net torque 360 .bomb survey 275 . 185 traverse curve (gradient curve) 70.-.in inclined pipe line 118 . 265. 41 7.for choke at .at continuous gas lifting 203. 206 .. 74 . minimum of 320.polished-rod load 320 mist flow 58..SUBJECT INDEX isochronal .-..multiphase flow 128 .Newtonian liquid flow 17 plastic oil flow 46 pseudoplastic oil flow 42.multiphase horizontal flow 1 13.average density of 56. 146.Krylov curve 62 sucker-rod pumping 335 - optimum lift performance of wells at . i 18 . 97.for pipe at . maximum of 320. set of (family of) 73..submersible centrifugal pump 434 . 119 .sucker rod pumping unit 351 multi-body gas anchor 395 multiple completion 171. 290 plain tubing 180 plastic fluid 37.spoke 152 protector 435 - - - - - .gas flow 22 .. 44 prime mover 348.gas - peak torque 360 performance curve of centrifugal submersible pump 437 ..in horizontal pipe line 110 . 356 metal-bellow type gas-lift valve 209.-..gas flow 125 . .vertical two phase flow 62 pressure . 1 15. 112. 323 . 21. 42.combined with gas-lift valves 288 plunger stroke length 330 pneumatically balanced pumping unit 362 point of lift gas injection 197 polished-rod -. 241 midi (slim-hole) completion 179 minimum .gas lift 264 .- - nominal power of the motor 356 oil-lubricated bottom-hole pump 397 open completion of wells at .. 92. 424 .Pleuger's diaphragm 45 1 -.sucker rods (Table 4. 102. Pleuger's clap valve 386 -. 44 Pump -. 43 1.liquid-jet 452 .API Std sizes 314 Reda's gas separator 439 .electric submersible centrifugal 434 .maximum allowable tensile strength 367 -.for gaseous oil 395 -.1-13.gas lifted 274 rotational viscometer 50 . 440 hydraulic 426. 79 slug flow 57.string weight 338 -. 212 steady-flow gas well test 294 storm choke 174 stratified flow 112. centrifugal submersible 437 -.Pleuger's diaphragm 451 . sucker-rod 31 1. attached) relative roughness 18 . 116.velocity 56. 440 semiclosed installation 264 s h ~ r tubing t string 199 single-acting hydraulic pump 43 1 slippage .tapered string 316 .tubings 182 stretch of the rod string 314 stroke reduction 315 submersible pumping unit 434 sucker rods 365 sucker-rod . 118 strength of API Std .474 SUBJECT INDEX pseudoplastic fluid 32.sonic 450 -. Varco's hollow 366 .-.in sucker-rod pumping 278 ..for plastic fluids 46 .for sandy oil 378 -.. 26 sucker-rod pump .1-13.tandem 4 17 pumping -.made by Haake 53 . 455 sour gas 305 stable and unstable operating points 150 standing valve 371 starting up (unloading) a well 182. 25.. 120 -.. 118 soft packed plunger 378 solvent injection 390 sonic pump 450. 40 . GOST standard 350 pump-off control 409 sand in gas well stream 307 sandy crude 389.units --.in multiphase flow 56 -.for wet oil 397 --.loss 56 -. rodless -.455 selective well production 171.electromagnetic 453 -. rodless .API standard 372 --.corrosion of 368 removable bottom-hole regulator 190 . 417.centrifugal submersible 435. attached) . 42.flowing 193 rod-pump 371 .hydraulic producing by rodless pump 432 . 41 .for Newtonian fluids 17. sucker-rod -.for multiphase flow 84. 177. 433 . generalized 39. API standard 351 .composition of (Table 4.. 38. 91.API Std sizes 372 rheology 30 ' superficial fluid velocity 80 rheopectic fluids 36 surface control of wells rodless bottom-hole pump 425 .. 21. 265. 85.coupling 365 Reynolds number -.for slim holes 424 -.sucker-rod pump 408 running and retrieving tool 258 surge dumping 191 surging well 185 safety valve 173 swabbing 183 sand-anchor 391 sweet gas 305 .API Std designations 373 rheological models 32 -.hydraulic 425 . 437.for solvent injection 390 . differential 375 -. critical 17. 250. 173. 187 valve 165. apparent 35 volume efficiency 34 1 volumetric efficiency of pumping 337 walking beam-type drive 31 1 Weber number 85 wireline-retrievable gas-lift valve 219 . 161. 380 . external upset 1 8 1 . buckling of 334. plain 180 .dimensioning 159. 257.safety valve 174 - .horizontal pipe line 110 inclined pipe line 118 -vertical tubing string 55 unstable well operation 145.string. integral 181 .anchor 379 -.SUBJECT INDEX tandem sucker-rod pump 417 tapered rod string 316 telescoping sucker-rod pump 375 thermal conductivity coefficient 139 thixotropic-pseudoplastic flow properties 33 torque flow pattern 94 transport curve of the tubing 61. 371 vibration of sucker-rod string 319 viscoelastic fluid 36 viscosity -. 245. 171.pump 371 . 300 -. 240. 163. 63 traveling valve 371 trouble shooting gas lift installation 274 tubing 180 .head 167 .hanger 167 -. 248. short 199 swab 183 two-phase flow in .