' .Explore the Potential of Air-Lift Pumps and Multiphase A This is in accord with analogous experi (5). recycle aeration in sludge digestors (6), deep sea mining (7), and the recovery of manganese nodules (8,9,10) from some amount of scatter in published pplications of so-called "air-lift pumps" in fields other than petroleum (I) have included the handling of hazardous flu ids (2), the design of bioreactors (3,4), the recovery of archeological artifacts Use this new capacity correlation for pump design. f. A.Zenz. AIMS experimental data on air-lift capacity. Since injected gas bubbles are dis placed upwardly by the downward "slip" flow of liquid (that is, dense phase (23)) at the walls, the cross section through an upward moving gas bubble represents a countercurrent flow as depicted in Figure le despite a net upward transport of slugs of liquid. This local countercurrent flow design and operation of an air-lift pump is analogous to the empty pipe flooding The transition to slug flow The entrainment of spray or droplets as occurs from a fractionator tray consti , ..:: ence in the injection of flashing feeds into risers in fluid catalytic cracking units, an alo gously carrying upwardly bulk solids (particles) as opposed to bulk liq uids (molecules), and also accounts for ocean floors. Interest among a host of domestic (//-17,18) and foreign (/9) organizations dates back several decades; having passed EPA hurdles (20), recovery of ocean resources has been further sanc tioned by U.S. legislation (/7). With the exception of "bioreactors" the practical lies in the dense-phase slug-flow regime of cocurrent gas-liquid upflow (21). t'.' phenomena illustrated in Figure Id for which correlations already exist (24). In view of the identical flow phenomena in Figures le and Id, accounting for the sys tem variables should also be identical whether the net flows are cocurrent or countercurrent tutes a form of dilute phase cocurrent gas-liquid upflow. Since bubble caps have been used as foot pieces in gas lift pumps, a pipe set over a cap on a tray, as illustrated in Figure 1 a, constitutes con c e p t u a lly a low efficiency bubbling upflow gas lift operating at very shallow submergence. In practice, a gas lift oper ates with deeper submergence, and more efficiently in slug flow, as depicted in Dense phase liquid transport by gas-lift pumps In Figure I b, gas compressed to a pressure level equivalent to the depth of submergence is introduced to the lift pipe to displace liquid upwardly. As the liquid flows back down into the bubble-form Figure I b where the foot piece is simply voids, more gas is continually introduced to establish a steady state of refluxing of a gas injection nozzle. In practice, multiport injectors have been found to be more efficient (22) in terms of increased capacity, particularly in the bubbling and slug-flow regimes. upwardly displaced liquid. The net rate of conveyance or refluxing decreases with height of lift. If the pipe is cut off at some height, below the maximum commensu rate with the given gas rate, or of the dif- CHEMICAL ENGINEERING PROGRESS • AUGUST 1993 • 51 " · .·� " �. (above) Dilute-dense phase manifestations.... 104 ·... l>j. In Figure 2 gas volume and gas density are based on discharge con ditions. • • • · > . •Figure 1._•' f: . CHEMICAL ENGINEERING PROGRESS .. --. '· . 10 100 1000 10 • Figure 2. :.. - ....� Vo'· 11J3 " .' -..-'' '1·:·} � ' ' �- ' . . Lilt. (right) "Con-elation" ofair-waler lift data. within a long lift pipe these could vary significantly from inlet to discharge. • \· . .. flow.:. h. the significance of "corrections" to the data in Figure 2 would be difficult to evaluate justi fiably when even the best data are subject to experimental error and to the effects of the air injection arrang ments (22). . or conversely giving the same wieght yield at equal air rates. then the net rate of liquid at that height will be continuously expelled from the pipe and hence the action referred to as a lift "pump. S. . .' '. sq. his data are plotted in Figure 3 and show excel- . S . .. h. .-< VL. The ordi nate should be modified by consid ering that increased liquid density would logically result in reducing the effective volumetric yield. Submerguncu. It also reflects the work expanded in compressing the air in an air lift. If S is replaced by log [(S + 34)/34 ] which is pro portional to the work of compression and still reflects the submergence.o . the question arises as to how well this correlation would satisfy other fluids. ·. . The submergence term. p6 Gas density PL = Fluid density _· . Chamberlain (2) obtained air-lift data for both water and a 93.. rather than countercurrent. : ..5 lb/ft3 caustic solu tion in the same pipe.... to 15 in. Multiplying the ordinate and dividing the abscissa by the square root of L results in the correlation of Figure 2. The basis for the choice of coor dinates in Figure 2 lays principally in their ability to correlate maximum countercurrent dilute phase-dense phase flow through empty vertical tubes and packed towers (23. · D PiJ!e Ld� inches l . 52 • AUGUST 1993 • despite the fact that air lift represent overall a net cocurrent ." Experimental air-lift data Figure 2 displays a variety of pub Ii shed a i r-lift data c overing lift heights ranging from 5 in. (bl fa) ' .. However. h. . 10 .'�t. The curves drawn through each investi gator's results f all into a numerical sequence with height of lift. " f 101 101 ' . ·· 11)3 :'��' · · A= Pii>u cross·seelion.FLUIDS/SOLIDS HANDLING.. Effect of fluid density Since all the data in Figure 2 are based on lifting water. T hat these coordinates yield a plot as organized in Figure 2 lends credibili ty to this approach to correlation. then the data in Figure 2 yield a fam ily of parallel curves spaced accord ing to the square root of the lift height. .24). .. . � Vo t ri-VL . ference in hydraulic head. to 65 ft and pipe diameters from � in. in the denomin at or of the ordinate of Figure 2 is based on analogy to cor relating data on entrainment from distillation trays (25).. than near the point of optimum slug-flow operation (28). Band of data ..8 L Cxlog [(34+S)/34] •Equation 7 (VdA)(48/D)112 (pdp!)1121L112 -----. For standard air and 106 Data of Chamberlain [) = 1...IA)(48/D)1f2 L lf2/log ([ S +34}':34] 0. Multiplying numerators and denominators by equal terms.14(6)2 \f._ 1 •Figure 3.7 psia.L (1) W1 =Pa VG In (PIP) (2) The work (isothermal compression) expended by the dilute phase (air) in lifting the liquid is: and the fractional efficiency.in figure 3. . which rep resents a smoothed ban d drawn through the data in Figure 2 may therefore be considered a more gen eralized correlation. x 48 6 1 x. is (4) E= W.0765 •EquationA The Ingersoll-Rand equation The theoretical efficiency of an air lift is simply the work required to lift the liquid to the point of dis c h arge divided b y t h e work of isothermal compression of the air. submer gence. It is evident from Figures 2 and 3 that the water rate falls off sharply when the air rate is either less (in the bubbling (3 ) Since Pa= 34 ft of water or 14._______ ____ to 100 1. From the Ingersoll-Rand equation 62.6" L= 10ft. ___J _ L-________. 'G L '¥. Abscissa ofFigure4 W0= W. P may be expressed as 34 + S.000 Vo� A VDLPL CHEMICAL ENGINEERING PROGRESS • AUGUST 1993 • 53 . S = 10ft.4 • Self= 1 Sft.= (\f. Operationaily deter mined values of E are generally of the order of 40 to 50% at the point of maximum operating efficiency. where S is the submergence in ft.8 L 469 Exlog [ (34+S)/34] •Equalion 6 (SCFM/fr2)(48/D)112 (GPMJJt2)( 48/D)112 = 0.6X4 X 144 � - flow regime) or greater (in the annu lar or mist flow regime)._. and efficiency. ' .7 or Eq.____.4 3. 5 and 6. 8 . 6 see Eq.) The pub lished version of the Ingersoll-Rand equations is simply Eq.. The work required to lift the dense phase (liquid) to the point of discharge is: \. Figure 3.8 (pdpJ c •Equalion8 alone. When analyzed in these terms. it is impossible to predict the variation in a given lift pipe's per formance as air rates are changed.lent correlation.. 6 with the term (469 E) replaced by a constant which in effect amounts to assigning a value to E. The equation gives the air-to-water ratio only at the point of peak effi ciency and would imply that this ratio is constant at all air rates. the Ingersoll-Rand equation can be rearranged for graphical comparison with Figures 2 and 3.7 Exln [(34+S)/34] •Equat ions (SCFM)Air (GPM)Water - 0.27) and is usually accompanied with t a b ul ated v al ues o f a constant derived from experimental data at or near the point of maximum effi ciency of operation as a function of the lift height.. at PL = 93. therefore: E= WJW1 E.=O 0916 � 30 .Effecto/ fluid density. so that 0. at PL= 62.5 o 1� . From Eq.144x14 . This relation ship is generally recognized as the Ingersoll-Rand equation (26. as given in Table 1 (26).. UPa VG In (PIP0) (See Equations A. the air-to-liquid ratio can be expressed as a function of lift height. 000 •Figure 4.. I.- - - 1oe----�---�. ft'lmin = dense phase now. = gas now at discharge conditions. dynes/cm density of lifted fluid.4 101"'========='====� ' 100 10 j4iP.��: - - -.:. Ingersoll-Rand equation -�: t? Slugging plots as a straight line -/· I LA.4... T h e c u r v e rT I .000 that corresponding to the ratio at this point of maximum delivery efficiency.. L . v 0LPr VG A 1.5! �Cl . in..:..0765 Air Rate Air Rate Pr= 62... .___.. = submergence. '. c:::n posed on Figure 3.. lift only under conditions of peak Examples theoretical effici ency... ft. = pressure at point of gas entry.. E=50% ::· . Mist � but then curves away to yield lower water-to-air ratios at values of the abscissa (air rate ) higher or lower than 102 1 10 100 1. ft.. Multiphase cocurrent estimating the yield from an air vertical upjlow regimes. lb/sq. entipoise = surface tension of lifted fluid. d: Ill ing to the ai r-to-water ::I c b N ' ratio at peak theoretical . lb/ft' • AUGUST 1993 • c 62..... 104 � with slope correspondco . lb/ft' gas density.028 cross-sectionul area of annular a A •Figure S..-A 1 .... Nomenclature D now. b u t n o t Consider the operable gas-liquid over the entire range of possible operating conditions .---- �I� 105 1-Bubbling Equation 9 is shown in F i g u r e 4 as s up e r i m2 '" �? . sq. ft. PL = 0. Eq. Pa (9) 10& = .i � � Vo � v OLP. The Ingersoll-Rand A equation is therefore useful in •Figure 6.0765). Air l ifting of water 30 ft than water.' CHEMICAL ENGINEERING PROGRESS -----------· - - ____________ .'. sq. ft.. Significance ofthe Ingersoll Rand equation.lb/min Greek Letters £ = gas void fraction in aerated dense phase µ.\ ---------- ���.... viscosity of lifted fluid. A ir-lift examples.:... I efficiency. Figures 3 solids ratios for two situations illus trated in Figure 5: a n d 4 i n c o r p o r a t e as w e l l the effect of fluids of densities other 1.. fractional efficiency..-----.... P.. ft. = E p atmospheric pressure. 8 is then 0. pipe submerged 50 ft. The lt. w. lb/ft' liquid density. gal/min pounds of dense ph11SC lifted per minute w. L VG VL w..FLUI OS/SOLIDS HANDLING "'-" 'r\\. .. through a 6 in.:.:.. ft.·� 10Wgt % Sand Ingersoll-Rand equation -. s area. f ' . � ::I. = � = P1 Po Pt 54 water (that is. worlc input ft-lb/min = work output ft. pipe cross-sectional = pipe inside diameter.. I. b ased on experimental 103 data exhibits this same >'I< slope at only one point. · soWgt Fluid % Water Rate PG=0... lb/sq. WJW1 lift height. �.-.. and to the right of the curve in Figure 4.162. B and Table 2.Ordinate o/Figure4 = •EquationB Abscissa ofFigure4 •Equation C = \fX4 x144 3.1/165) + (0. pipe submerged 50 ft.30) CHEMICAL ENGINEERING PROGRESS • AUGUST 1993 • 55 .14(6)2 Ordinate =(SlurryGPM)x4x 144 ofFigure4 3.4/66. This region has been explored in some detail by Dukler and others (29.1 =201 v.5 {48 V 6 x 6 66. A. as a slurry containing 10 wt. of a motor driven pump or sim ply by a hydraulic difference in head. Case/. L would be the tube diameter and S would equal Lp/ (1 . See Eqs. for exam ple. D and Table 3. Under such conditions. Case 2.4 At values of the abscissa greater than about 50.e}.4)) = 66.5 62. Air lifting of a sedimented sand.1)112 log{(34+ 46.0844 (ACFM) (33. 'L = 0. Bubbling and annular liquid flow At values of the abscissa less than about 50 and to the left of the curve in Figure 4.0765 48 8 - 6 66.4 112 (30) /og{(34+50}'34] x x -133.14(6>2 '6x4 x144 3. two-phase flow would occur in the form of gas bubbles ris ing in a matrix of liquid forced to flow upwardly by means. Effective Lift = 30 + 50.14(6)2 /f x 0.9= 33.9}'34] =235(SlurryGPM) •Equation D 2. voidage must be so great that liquid can only be dri ven up the pipe in annular flow by the surface drag of the gas core.5)= 46.9 ft. typical in bioreactors (3).% fine sand.46. Slurry density= l/((0.1 ft. See Eqs. C.9/62. a distance of 30 ft through a 6 in.5 lb/ft3 Effective submergence= 50 (62. " 4th Hill pp.' 19. et Res..• . 1980). · m:](''\' \vt _ �� ·:.�::t. :-· 21. ..G.._·. (July 1929) ·. . JmJ. Fax: 914/414���.�..: '" · 195.-::. : �:�i: � ' :-. -- 1 · . anal Achievement Award. Baker.tJ8!Jl: p��t�PJt mot[' •-.FLUIDS/SOLIDS HANDLING � Acknowledgment . Zenz..�nd has been 8 consultant to J and domestic corporations. phase upflow to the extent supported by data published to date . 20 (No' 1980 ).�:��t�t(� iJ. Ingersoll·Rand .. 20.�f�'J... ls:� . Annular Flow. Gas-Uqui4. Morrison. C. sand in the Reader Inquiry card in this Issue with the No. NY (914/424·3220. · ·� r-�. F.io_se portions of this article developed under 'a> (1988). L.385. (May 1965).� 27.=J.:-. · ·· . :���}. Cocurm. ' )_a non· profit industrial consortiu ' ... pm01ilif cation. Equating bubble rise velocity to displacing liquid downflow in a slugging tube. 387-391 (19 " 23. The results are shown in Figure 6 with the ratio of film cross-sectional area to pipe cross-sectional area as a parameter.1'&diii . A. Y.'' Ai PP· 829-843 098ii ' 30. New Yorkpp .0. Taltel. L. �'l 1!$0r Emeritus at Manhattan ��JJ. upward gas stream. In the . to the measured rate of the cocurrent.. : Bureau of Mines.. pp. Chem. �· . corre sponds to an annulus-to-tube area ratio of 0..o. �ldr. • AUGUST 1993 • CHEMICAL ENGINEERING PROGRESS · · 88(10). to several ft in diameter..�.ifllfii.'.· Separation Techni · · ' Chemical En8ii1 �· Hill. ed his PhD in chemical engineering . W. 2bookS. Week. Zenz. • ))' . p.. but also suggests the correla tion of all regimes of cocurrent multi- 56 Equation. �\��� 33-J4'.- �X . carried upward i n annular films of measured thickness inside a vertical 2 in. .. . Zab G et.. .�· who presented experimental data relating measured amounts of liquid.354 (1980)... J.ll!J!i �'. liquid flow inducing..�·· Tit(. 121-126 (1965):{ 25. et � ..Duckworth. 345. . A. "The' . 6-13.. 19 U�Sit :l :� : '. · Cori{�. G. A.. Upward .Garrison. pp.:.\'." Chent. 26. the 1985 recipianf i>t d in chemical engineering �)... Mining Research >\. ow"of the AIChE.i t .. J� 22.'.$86 recipient of Chemical -�.:ZENZ is president and technical dir�cw:�'ft . Chem. . The addition of liquid viscosity and particularly surface ten sion terms to the ordinate of Figure 6 has been. internal diameter (ID) pipe. Cf.� . 1SHS4.. . ��.'. pp.--:' �.'!J Vertical Tubes..� .1ir3t�rUlly acknowledged.7./�:_. J.·�� -·�: �:/'·�i.. Nemet. York. Schweitzer... Sylvan Cromer's kind permission to publiSh/ td.' 29.he has authored 90 papers. - � p����.:\.1t��· :. et al. � echnic University. A. . Eng p..." Patterns Upward _ - Transit!��. :-.'. 53(12)(July 26$f 32.. aras.. ' ' ::�:h?���-- ljfrm � . "Chemical Etl:' Handbook.:_ � : -·: :.. and ·. 31. 93-98'((' 24..'.A. PEMM NY (1986).._ : ' \ . somewhat arbitrarily..··' Column Flows Waill '��JMS.. J. P.. . .. Fi g u r e 6 r e p r e s e n ts n o t o n l y a capacity correlation for gas lift pump design. Di1 To receive a free copy of this article. based on identi cal terms applicable to horizontal multi phase flow (31) and on data obtained for very low surface tension liquids in cocur rent upflow with air (32) in tubes several in..F. . .':'Al pp. fciriiign . pp. 136 circled. Engi11i�T. <� 26. Padan. Literature Cited .o 53(2).c-Ontract with Union C a rbide Corporation '. •. New York. suggesting that these investigators were approaching slugging and that this limit should at some time be established on Figure 6 experimentally.. 63(March1960} 28. � Hydocarbon Proc .·(July 30.