Society of Petroleum EngineersSPE 26244 Improved Matl9rial Balance Calculations by Coupling With a Statistics-BasE~d History-Matching Program R.R. Hwan, Texaco Inc. SPE Member Copyright 1993, Society of Petmieum Engineers Inc. This paper was prepared for pmsentation at the SPE Petroleum Computer Conference held In New Orleans, Louisiana, U.S.A., 11-14 July 1993. This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Pellroleum Engineers, Its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A. Telex, 163245 SPEUT. ABSTRACT This paper describe~1 a new material balance calculation by coupling a statistilcs based history matching program with a material bal~ll1ce program. The procedure is to match the historical reservoir pressure data with the calculated pressures obtained from the material balance program -- the so-caUed pressure match method -- with the help of the history matching program. The combination of the history matching and material balance programs proves to be a very simple and powerful tool for material balance calculations. A user who does not know cillferent material balance methods under various reservoir conditions is able to calculate the material balanc:e with great accuracy. This is because the new procedure is based on the pressure match method which is known to be applicable to all types of reservoirs, Le., oil or gas reservoir with or without gascap and/or aquifer, with accurate results. In this paper, the calculation of pressure in the material balance mlathod is briefly reviewed and the mechanism of pressure history match is cursorily discussed. Three case studies, comprising an abnormally pressul'1ed gas reservoir, a gascap drive reservoir and an aG[Uifer water drive reservoir, are presented to illustrate the use of the new method. The References and illustrations at end of paper. 179 calculation results of these cases are comparable to or better than those of using the material balance program alone. Moreover, the matches were obtained in only a few number of runs. INTRODUCTION Among all the material balance methods, such as, Schilthuis' method!, Havlenaand Odeh's method2, etc., that have been publicized, the most robust and accurate method is the pressure match method. The method is to match the observed reservoir pressures with the calculated pressures. However, the pressure match normally requires a substantial computational time and effort. This paper describes a new procedure that will overeome this shortcoming and provide fast and accurate results for the material balance calculation. With the new procedure, an engineer need not know various methods, such as Ramagost and Farshad3, Havlena and Odeh2, Cole4, or Campbell5 -- just to name a few -- for the material balance calculation. The current procedure can be applied to all the oil reservoirs as well as the gas reservoirs. It is not necessary to distinguish an abnormally pressured gas reservoir from a regular gas reservoir. There is no need to fit the data with a straight line, most conspicuous in the Havlena and Odeh method. Therefore, the current procedure tends to preserve the resolving power of the original material balance In this paper. PREDICTION OF RESERVOIR PRESSURE The current pressure match method requires a generic model which can predict the reservoir pressures based on the PVT and production data. water and formation. The history matching program used in this study is called "Adaptive History Matching (AHM) System" which was developed by Scientific-Software Intercomp (SSI) with the participation of Texaco and several other major oil companies. are further defined as: Et = Eo + mE. In all the cases tested. lIE (1) where F is the underground withdrawal. have di:tTerent aquifer functions 8. The current procedure involves using a history matching program which is commercially available to match the observed reservoir pressures. (BIB" -1) (5) and w. the mechanics ofapplying the new method and several case studies will be presented following a brief discussion of the pressure calculation in OILWAT/GASWAT and the history match mechanism of ARM. including gas reservoirs and oil reservoirs with and without gas cap and/or aquifer. ARM was developed to help the engineer to deal with the problems of history matching reservoir performance data with a reservoir simulation model. Various aquifers. = B. OILWAT7 and GASWAT8. For an oil reservoir. the material balance equation only contains a few variables. These features make the current method a more foolproof procedure for the numerous reserve estimates required in financial planning work. N is the original oil in place (OOIP). F NEt + W. the calculation results of the new material balance method are comparable to or better than those of using the material balance programs alone. infinite linear. used for this study were developed by Texaco and are also commercially available.t) (7) where U is an aquifer constant and S(P. predict the reservoir pressures based on the general material balance equation as described below.t) is an aquifer function. F.Et and W. the number of possible reservoir and fluid parameters that need to be modified for the production history match may go up to a dozen or more. And. + Efw (3) where E. is cumulative water influx from the aquifer into the reservoir. OILWAT/GASWAT. the property values that need to be adjusted are limited to a very few. = U S(P. In addition. This makes the pressure history match in a material balance calculation much more manageable.2 IMPROVED MATERIAL BALANCE CALCULATIONS WITH A IDSTORY MATCHING PROGRAM equation as discussed by Tehrani6 • SPE 26244 reservoir pressures are to be compared with the observed pressures. Fortunately. The material balance equation for a gas reservoir can be written as: 180 . finite and infinite radial aquifers. Et is the overall expansion of oil. All the valid pressure data points can be used in the new procedure instead of only certain data being chosen to fit in a straight line as in most other methods. gas. such as the small pot. and W. The predicted The material balance programs used in this study. the current method does not require engineers to choose data points for calculation like the material balance programs do. One of the major uncertainties in the history match is to decide what property values to adjust in order to achieve a satisfactory match. The material balance programs.. These new values are used to repeat the calculation of the reservoir pressure as described above. The set of values of N (or G). Gp(l).ell (Pi .. Based on the differences between the calculated and historical pressure data. G. where G is the original gas in place (OGIP). etc. and/or U. given the values of N (or G). The reservoir pressures calculated from the previous section are compared with the historical pressure data in AHM. ---=----. W.)/Bgi (11) For a natural depletion gas reservoir. S(P. The methodology of AHM was discussed by Watkins et al. (1) or (9) will be equal to its right-hand side. III. III.R. AHM...p) Zi G -PZ . the expansion of the connate water and reduction in the pore volume is negligible as compared to the gas expansion and there is no water aquifer.. IO• The underpinning of AHM is a statistical analysis method known as Bayesian The Bayes' theorem provides. and/or U that provides a satisfactory history match of reservoir pressures. For instance. fundamental way.G _P . G. however reached. The newly calculated reservoir pressures are then compared with the historical pressure data in AHM. The key to the above process is the capability of the history matching program. and/or U which minimizes the difference between the calculated and the observed 181 . and Eq. (8) can be expressed in terms of P/Z as: Pi G -(1 . and/or U from historical pressure and production data by interpreting the material balance equations (1) and (9) as linear functions. Eq. and then calculate the reservoir pressure as a function of cumulative production or time.G where If there is no water influx in the above calculation. (12) indicates that there is a linear relationship between P/Z and the fractional recovery GJG. Y (9) [1 . And. Because the PVT properties of the reservoir fluids are functions of pressure. one can choose a pressure value so that the left-hand side of Eq. and Y .(l). In other words. the process is continued until the reservoir pressures calculated from a certain set of N (or G). RANDY HWAN SPE 26244 pressure data is regarded as the correct set. _ -p) Z Zi 3 (12) G Most material balance methods calculate N (or G).(I). (8) Eqs. mSTORY MATCH OF RESERVOIR PRESSURE The history match of the reservoir pressure is conducted with the history matching program. and/orU one can calculate the first reservoir pressure P(1) at the first production data point [Np(I). the second pressure value can be obtained from the first pressure value. Wp(l). The procedure is repeated until all the reservoir pressures are calculated. and/or U match the historical pressure data satisfactorily. AHM will suggest a set of new values of N (or G). the calculated pressure will not depend on the past history of reservoir performance or on the path it has followed in reaching a given state.] by trial and error.t). (9) reduces to the popular form Pi ( 1 . to suggest a certain set of N (or G). Once the first point of reservoir pressure is determined. III. AHM. or the cumulative production Gp • Extrapolating the line of P/Z versus Gp to the abscissa gives the value of OGIP. Eq. It depends only on the immediate conditions. (1) and (9) are used to calculate the reservoir pressure for the pressure match method. P(l). 9 and Parish et al. a process of learning from The pressure match method is to assume values for N (or G). and/or U of a particular aquifer model.P)]. (WII - Wp B. III... in a inference. III. and the second production increment using the same procedure. III. The value of N (or G) thus obtained is the OOIP (or OGIP) of the reservoir. III. (13) and specifies the (relative) likelihood of any feasible vector of property values being the solution vector. mean and variance. In our case. it is assumed that the calculated pressures do not sufficiently match the observed data and further revision is required. P(property valueslcalculated pressures) is now a replacement to Eq. AHM is installed on the mM RS/6000 workstation. PROCEDURE OF PRESSURE MATCH The material balance and history match programs may reside on different computer systems. A user can access AHM from his PC through the network with Microsoft's Windows and Visionware's Xvision software loaded on the PC. Again. such as N (or G). the posterior of the first pressure calculation becomes the prior of the second pressure calculation. it can be expressed lated pressures) DC P(2nd calculated pressures\propeTtJ values)P(property valuesllst calculated pressures} (16) (13) P(property values) The property values of the initial estimates are used to calculate the reservoir pressures as described earlier. The information generated from this calculation is then used to revise the estimates of property values.4 IMPROVED MATERIAL BALANCE CALCULATIONS WITH A IUSTORY MATCHING PROGRAM experience. 182 .. The next step is to calculate the reservoir pressures as discussed previously using the revised estimates of property values. via Bayes' theorem. This may be a common occurrence since various computer systems coexist in the work place nowadays. OILWAT/GASWAT. The following operations are performed by AHM and are described here in case the reader is interested. is installed on the PC or available on the mainframe computer. and shows how knowledge about the state of nature can be continually modified as new data becomes available. to vary. In this case. P(property valueslcalculated pressures) is the posterior distribution after the first round of pressure calculation. (13) and (14) can be combined. The results of the calculation are expressed as p(calculated pressures\property values) (14) With proper constraints. With the distributional assumptions. To history match the reservoir pressures. The calculated pressures are used to update the previous property values. The posterior distribution of the second round of pressure calculation which describes various feasible values of the vector of property value can be written as P(property values list calculated pressures. This process will continue till a set of property values which generates a corresponding set of calculated pressures that satisfactorily match the observed data are obtained. The revised estimates of the property values from the second pressure calculation are used in the third round of the pressure calculation. 2nd calc. and/or U. It is assumed that the calculated pressures do not sufficiently match the observed data. to give P(property valueslcalculated pressures) SPE 26244 DC P( calculated pressure \property values)P(property values} (15) The path to an iterative scheme is now established. These estimates reflect the prior ideas of the engineer on possible values for these properties.- The information of the initial estimates and intervals defines the first two moments of a distribution. but a brief description follows which assumes the reader is trained in statistics and Bayesian theory. Eqs. to provide initial estimates of these properties and to place each estimate in an interval. The interval defines a sub-space of the property space that the correct values of these properties will be found. the user has to decide which properties. It is not necessary for the user to understand how AHM converges in order to make the material balance calculation. the material balance program. On the other hand. m. The pressure difference between the calculated values of these runs and the observed data are shown in Fig. CASE STUDIES These cases include (1) an abnormally pressured (pressure gradient greater than 0.5 psi/ft) gas reservoir with no influx. based on the sum of squares for error.437 BCF and 0. gascap and/or aquifer sizes. The calculated pressures are imported and compared with the observed data in AHM. and (3) a water drive reservoir without gascap. A lower quality value means a better pressure match in AHM. Compare the calculated pressures with the observed data in AHM. The procedure can be summarized in a flow chart as illustrated in Fig. respectively (Table 3). The value of pressure match quality. When the process finishes. 1 shows the pressure matches of Runs 1. 4. and 4 until the calculated pressures satisfactorily match the observed data. Besides providing the match quality. RANDY HWAN SPE 26244 With user's manuals of AHM l l and OILWAT/ GASWAT 12 available for reference. This may comprise OOIP or OGIP. Table 2 183 . Obtain updated AHM estimates of the property values. and. e. in AHM.843 psi/ft. 5. The lower and upper limits ofthe OGIP are also shown in the table. The initial pressure gradient of the reservoir was 0. The historical data includes cumulative oil production as a function of the average (G). etc. Then. aquifer constant. Fig. AHM is able to suggest a value of OGIP for the next run. Specify initial estimates of pressure-match properties. . The suggested property value in AHM is based on the results of all the previous runs. The OGIP value and its limits are input to AHM. 2.. an engineer has to estimate the most likely value of the OGIP and its upper and lower limits. OOIP or OGIP.2193. This result from the current procedure is slightly better than that from GASWAT alone (Ramagost and Farsluld's method). After comparing the calculated pressures with the observed pressures.679 BCF. The reservoir and production data are listed in Table 1. (2) a gascap drive reservoir. 3. the procedure of applying AHM in material balance calculations is summarized below: 1.R. Calculate OGIP for An Abnormally Pressured Reservoir With No Influx The material balance calculation for the Anderson "L" gas reservoir as reported by Ramagost and Farshad3 is conducted with the current procedure. the revised property values giving the satisfactory pressure match are the result of the material balance calculation. 2. The values of the OGIP and pressure match quality of the run are 73. . The starting OGIP which is considered as the most likely (expected) value is used in GASWAT to calculate the reservoir pressures.1017.391 BCF (Table 3).g. Case 1: 5 shows that the initial estimate of OGIP is 70 BCF. Run OILWAT or GASWAT with the current estimates of property values and generate the corresponding pressure results. Case 2: Since the property value to be determined is the OGIP Calculate OOIP and Gascav Size for a Gascap Drive Reservoir This example of an oil reservoir with a gascap is presented in Reference 13. 1) are imported into AHM to compare with the observed pressure data which were entered in AHM beforehand. etc. of Run 2 and the revised value of OGIP for Run 3. This value is then used in GASWAT to calculate the reservoir pressures for Run 2. The value for Run 2 is 70. as shown in Table 3. In AHM. AHM yields a value of match quality. Repeat Steps 2. All the valid data points of the observed pressure are included. The volumetric estimate of OGIP was 69 BCF. 3. the set of the property values in Step 4 that provides the best pressure match are the result of the material balance calculation. 4 and GASWAT alone versus the observed data. 3. The above procedure is repeated for Run 4. the data were not pre-selected for the pressure comparison. The calculated pressures (Run 1 in Fig. the user can examine the match after every iteration (and modify AHM's selections if desired).1917. gascap and/or aquifer size. 71. or he can tum AHM loose at anytime to run on "automatic pilot" if the material balance program is linked with AHM by an interface program. are also shown in Table 3. 5. This is because the water and formation expansions are neglected in Dake's example. for the next run. 6. The process continues till Run 6 of which the OOIP and mare 116. ratios available in the material balance program for the influx calculation for a radial aquifer. These values are used in OILWAT to calculate the reservoir pressures for Run 2 and the calculated pressures are imported and compared with the observed data in AHM.. AHM then suggests the values of DOIP and gascap size ("').3 rb/psi. equal to discrete values. To further improve the pressure match. the value of rJr. The estimates of aquifer size are based on the seismic and geological evidence. There is no initial gascap and the DOIP. The value of pressure match quality.5. reservoir pressure. The results of this case study also indicate that with a faster and more accurate procedure like the current method. for Run 3. respectively. 4. Case 3: Calculate Aquifer Properties for a Water Drive Reservoir with Known OOIP SPE 26244 The results of pressure matches and pressure difference between the calculated and the observed pressures of this case are shown in Figs. 5. 4. are also shown in Table 6.6 IMPROVED MATERIAL BALANCE CALCULATIONS WITH A HISTORY MATCHING PROGRAM radial aquifer shown in Reference 13. when better results are concentrating near the boundaries or within a narrow range of the interval. r Jr. and aquifer constant of Run 6 are 5. 4 shows the pressure matches of all the runs versus the observed data.88.61 MMstb and 0. The value of pressure match quality is 0. The results of the these runs (Table 9) show that the aquifer constant of the best run <Run 10) is 6296.76 MMstb and 0. 1. respectively.00144 (Table 6).3 rb/psi for the next series of AHM/OILWAT runs.5. 5. over the first few years of production. the interval of the property value may be widened or narrowed. Nevertheless..to a water influx function with a continuous rJr. The reservoir. accordingly. 100.47.454. The pressure difference between the observed data and calculated values of Run 6 and the OILWAT enmples are shown in Fig.influx values only available at rJr. as shown in Table 6.469. and 6. The aquifer size in terms of rJr. such as 4. such as 4. Fig. With the current procedure. Currently.. Because OILWAT only calculates the water influx at selected values of ratios of aquifer and reservoir radii.19 MMstb and 0. the pressure increases at the end of the production history when the aquifer is too large.. which is close to the theoretical value of 6446 rb/psi and agrees very well with the result of OILWAT. The most likely values of these properties and the upper and lower limits of the values are estimated and shown in Table 5.. Note that the value of OOIP in the final pressure match. both the aquifer size and aquifer constant could be determined at the same time. respectively. respectively. 6 and 7.).452 (Table 6). is set to be 5 and the aquifer constant starts from 6152. the results of the existing runs are still valid in guiding the subsequent runs with the AHM algorithm. the value of pressure match quality could not be reduced below certain limits. 312 MMstb. The production data and the relevant PVT data are shown in Table 4.6. -.70. As one expects. etc.. the water influx calculation for the radial aquifer in the material balance program needs to improve from the discrete point results -.. 14. Both results of the current procedure and OILWAT alone (FE method7) are better than that calculated bl Havlena and Odeh's method in Dake's example1 . Comparison of the calculated pressures of Run 1 with the observed pressures in AHM yields a value of match quality.9 rb/psi. This is an example of a water drive reservoir with a 184 . 6296 rb/psi. The initial estimates of DOIP and the volume ratio of gascap to reservoir are 70 MMstb and 0.. PVT and production data are presented in Table 7. etc. The results of the AHM/OILWAT calculation are shown in Table 9 with the procedure illustrated in the previous cases. respectively.90. is determined from the volumetric calculation.173 and 6152. the new procedure is limited to the rJr. Run 6. The property values to be determined in this case are OOIP (N) and gascap size (". In other cases. The aquifer size was the only aquifer property determined in the reference. of Run 2 and the revised values of OOIP and ". is quite different from that of the initial estimate but it is still within its limits (see Table 5). The initial estimated values with the limits of these aquifer properties are shown in Table 8.. Tehrani6 realized that the material balance calculation with pressure match is the most accurate method. Moreover. Freedom from data point selection would not only save the engineers' time and effort in material balance calculations but also provide an opportunity to automate the computation process with minimum engineer intervention. the material balance calculation using AHM could be an efficient method for the numerous reserve estimates required by annual reserve updates. Initial estimates of the hydrocarbon in place are normally available through the volumetric calculation of the reservoir. With the network :tile transfer programs. Unlike the classical material balance calculations and by OILWAT and GASWAT alone. The new method is able to overcome the timeconsuming trial-and-error process of the pressure match method by using the history matching program while retaining the robustness and accuracy of the pressure match method. With the current procedure. (18) 185 . However. these results are obtained in just a few runs. An engineer need not know different material balance techniques in order to make material balance calculations. Good initial estimates of the property values will go a long way in pinpointing the sizes of reservoir fluids in place. The procedure is based on the pressure match method. For example. This is because most OILWAT/GASWAT solutions are determined through the plots of straight lines while the pressure match is based on the original material balance equation. an oil reservoir with both gascap and aquifer present. RANDY HWAN SPE 26244 DISCUSSION This material balance calculation uses the history matching capability of the AHM program. especially for oil reservoir with water intlux. Without the uncertainty in deciding which data points to use. the best source of information for history matching still resides in the professionals who are responsible for the reservoir. The current method simplifies the procedure of material balance calculation.t) (17) 7 as reported by Havlena and Odeh2 will reduce the resolving power. e. It is not necessary to have both material balance and history matching programs coexist in the same platform.R. (1) and (7» F = NEt + U S(P. Since an engineer does not need to choose the data points for the material balance calculation. he argued that Eq. However. PC's and workstations.I) Et The results of the case studies demonstrate that the new procedure is a fast and accurate material balance method. The values of aquifer properties may be derived from the theoretical calculation or from initial runs of the material balance program alone. such as drawing straight lines through data sets. generally there is no need to exclude any pressure data points for the pressure match by AHM. and directly focus on the pressure match to obtain a good material balance calculation. the current· procedure could provide more consistent results among different engineers.. CONCLUSIONS A new procedure of material balance calculation by coupling a material balance program with a statistics based history matching program is presented. g. initial estimates for pressure match in AHM. to the conventional form F Et =N + U S(P. He showed that rearranging the material balance equation from the original form (the combined equation of Eqs. the result :tiles of the material balance calculation can be transferred between different computers. The professional input to the history match process becomes more critical when more matching parameters are involved. The calculation results of the new procedure are comparable to or better than those of using the material balance program alone. this would provide good. the aquifer in most cases is ill-defined. Thus. In general. linking these two programs with an interface program would enhance efficiency and usability. AHM was designed to provide a system to integrate this knowledge into the match process. However. (18) is not suitable for calculation of OOIP and aquifer constant. he can by-pass the intermediate steps. l/psi. F. and Bowman. 3 Cumulative water influx. BCF Cumulative gas production. n: "OILWAT: Microcomputer Program for Oil Material Balance With Gascap and Water Influx. MMstb Cumulative water production. Vol. 3 Time. water and formation. for numerous reserve estimates it would be advisable to develop an interface program between the material balance and history matching programs. ft Cumulative gas-oil ratio." J.: "P/Z Abnormally Pressured Gas Reservoirs. MMrb Cumulative water injection.: "The Material Balance as an Equation of a Straight Line. BCF Initial gascap size. Tech. 5. F. G. Pet. (8) Expansion of oil and solution gas. The current method demands high accuracy of the water influx calculation. 1963) 896-900. P. = C..t) . (Sep." paper SPE 10125 presented at the 1981 SPE Annual Technical Conference and Exhibition. 4. == B. rb/stb Water formation volume factor. rb/MCF Oil formation volume factor. (3). L. Houston (1969). Houston. (10) Formation compressibility. However. Campbell Petroleum Series (1978)." paper SPE 24437 presented at the 7th SPE Petroleum Computer Conference. 1981. for permission to prepare and publish this paper. rb/stb. (3). fraction Aquifer function. F. G. Ramagost. San Antonio. years Aquifer constant. (3) Underground withdrawal. MMstb Water influx function defined in Eq. psia Aquifer radius. rb/stb in Eq.:Mineral Property Economic8. 3: Petroleum Property Evaluation. gas. 118:33-52. B. (4) Overall expansion of oil. NOMENCLATURE B. volume ratio of gascap and oil reservoir Original Oil In Place. 2. Tehrani. Pet.." Trans. Oct. MMstb Average reservoir pressure. R• == == == . = E. D.:Reservoir Engineering Manual. The material balance calculation with the current procedure can be conducted with the material balance and history matching programs loaded in different computer systems. M. see Ref. = E. W.: "Active Oil and Reservoir Energy. R. defined in Eq. AIME. scf/stb Solution gas-oil ratio. Litvak. rb Original Gas In Place. BCF Cumulative gas injection. 3... = F = G - .. (Aug. Swl == S(P." J. 1985) 1664-1670. ft Radius of oil reservoir at original oil water contact.H. MMstb Cumulative oil production. see Ref. defined in Eq. Campbell. rb/stb. J. rb/stb Effective compressibility. Havlena. scf/stb == = w. == G - m == N -. l/psi Expansion of water and reduction in pore volume. Sr. rb/MCF in Eq. and Farshad. == Cw = Efw == E. Texas. AS. Tech. P ro r. (11) Gas deviation factor Subscripts = Initial condition ACKNOWLEDGEMENTS The author wishes to thank Texaco Inc. 7. Schilthuis. rb/stb in Eq. REFERENCES 1. R A and Campbell. Wang. = Bw = C. N.: "An Analysis of Volumetric Balance Equation for Calculation of Oil in Place and Water Int1ux. B. l/psi Water compressibility. WI' t Jv. Gulf Publishing Co. The author is also grateful to Dr. W. = U Y Z = = = = SPE 26244 Initial water saturation. Texas. Cole. The result files of the calculation can be transferred through the network file transfer programs. and Odeh. Gas formation volume factor. rb/MCF in Eq. 6.. defined in Eq. R J.. B. D. (8) Expansion of gas..IMPROVED MATERIAL BALANCE CALCULATIONS WITH A HISTORY MATCHING PROGRAM 8 The results of the case study involving water influx from a radial aquifer indicate that the water influx calculation in the material balance program needs to improve from the discrete point results to a continuous water influx function. 186 . Ben Wang for his assistance in using OILWAT/GASWAT programs. 260 5. March 8-11.218 1." paper SPE 23738 presented at the 1992 Latin American Petroleum Engineering Conference. 1990. Dake.440 1.418 1. 317. Venezuela.:"Application of the Laplace Transform to Flow Problems in Reservoirs. T. R. and Teasdale. published by Boffin Inc. F.5 1255.:"GASWAT-PC: A Microcomputer Program. Muggeridge. B. J. A. Adaptive History Matching (ARM Version 1. A.854 G (BCF) 0.:"Effective History Matching: The Application of Advanced Software Techniques to the HistoryMatching Process.344 1. and Modine. Calderbank.393 1.9 561. 9. Texas. Texaco Inc.SPE 26244 R.176 1.127 1. R. and Robinson. J. RANDY HWAN 9 July 19-22. 1993. R. Elsevier Scientific Publishing Co.1) User's Guide: Release Date: June 1992. OILWAT/GASWAT <Version 4) User's Manual by Ben Wang.. 267 <T 9507 psia 11167 ft 20% 35% 0. A.387 1.. L. 583 13. PRODUCTION AND PVT DATA OF CASE 1 Calculate OGIP for an Abnormally Pressured Gas Reservoir Time @wl 0 69 182 280 340 372 455 507 11.749 10.3 1615.758 12. Parish. Scientific Software-Intercomp. W..9 122. A.928 . G.. 10.509 11. G. van Everdingen..977 . TABLE 2 LIMITS AND INITIAL ESTIMATE OF OGIP Lower Limit Expected OGIP(BCF) 187 60 70 Upper Limit 80 . Goode.: Fundamentals of Reservoir Engineering. Watkins. D.8 • Liquid condensate production.8 1913. E&P Technology. Louisiana.890 28.. Inc." Trans.789 17.P.538 8. A.9 317." paper SPE 25250 presented at the 12th SPE Symposium on Reservoir Simulation. June 23-26.504 7. P. 1992.0 0. AIME. Watkins.144 32.262 22. H." paper 14684 presented at the PetroleumIndustIyApplications ofMicrocomputers held in Del Lago on Lake Conroe.0 29. S.891 . Parish. Wang.282 1. (psia) 9507 9292 8970 8595 8332 8009 7603 7406 7002 6721 6535 5764 4766 4295 3750 3247 ~ 1.. Montgomery.147 1. 14. A.239 1. New Orleans..4 2136. 12. V. and Hurst.3 939.048 . New York City (1978) 90. TABLE 1 8. J.7 846.316 1. Caracas. February 28-March 3. 1987. 186 (1949) 305-324.9 240.554 rbjMCF 3x10-6jpsi 15x10 /psi 69BCF Reservoir temperature Initial pressure Depth Porosity Initial water saturation Initial gas formation factor Water compressibility Formation compressibility Original Gas In Place (by volumetrics) 628 663 804 987 1183 1373 1556 Press.8 776.642 3.2 650. T.0 2307.1 406.:"A Stochastic Role for Engineering Input to Reservoir History Matching.820 • G Ip (Mstb) 0. for Gas Material Balance With Water Influx.567 36..226 4. 10 IMPROVED MATERIAL BALANCE CALCULATIONS WITH A InsTORY MATCHING PROGRAM SPE 26244 TABLE 3 TABLE 5 VALUES OF OGIP CHOSEN BY AHM & USED IN GASWAT AND MATCH QUALITY LIMITS AND INITIAL ESTIMATES OF OOIP AND GASCAP SIZE Run No.040 Lower Limit Expected Quality .1294 .71 Gascap Size 0.2122 1.462 0.00144 0.47 0.5 (Approximated) Rs ~ 510 477 450 425 401 375 352 B rbfscf .2353 1.1017 .00113 .1922 1. 1 2 3 4 GASWAT Alone OGIP<BCF) 70 70.7<m8 0.2511 1.59280 0.00101 .00096 .469 0.456 0.2022 1.01815 0.437 74.50 Quality 6.2222 1. Ratio of Gascap and Oil Reservoir) .391 71.61 108.452 0.47 .81 114.513 2400 17.01341 .454 0.295 3000 5.54 0.1917 .19 111.2193 .679 73.60 TABLE 4 TABLE 6 PRODUCTION AND PVT DATA OF CASE 2 PROPERTY VALUES CHOSEN BY AHM & USED IN OILWAT AND MATCH QUALITY Calculate N and m for a Gascap Drive Reservoir Reservoir temperature Formation compressibility Water compressibility Initial gascap volume fraction Pressure N MMstb psia 3300(Pi=PJ) 3150 3.503 2550 14.14 116.00107 .8847 1.903 2850 8.76 100.00100 0.730 Ru ~ 1050 1060 1160 1235 1265 1300 Bo rb/stb 1.45 .852 2700 11.00092 .1065 Upper Limit OOIP(MMstb) 60 70 130 Gascap size (V01.00120 188 Run No.00087 .1822 200 «T 3x10-6/p si 3x10-6/psi 0.63 108. 1 2 3 4 5 6 OILWAT Alone Dake's Example OOIP(MMstb) 70 90.14594 0. 404 650 0.4 6228. 1 2 3 4 5 6 7 8 9 10 OILWAT Alone Aquifer Size 10 11.0 5.390 1.3 6146.SPE 26244 11 R.5 975. RANDY HWAN TABLE 7 TABLE 8 PRODUCTION AND PVT DATA OF CASE 3 LIMITS AND INITIAL ESTIMATES AQUIFER SIZE AND AQUIFER CONSTANT Calculate Aquifer Size and Aquifer Constant for a Reservoir with Known OOIP Lower Limit Expected Reservoir temperature Original Oil In Place Initial gascap volume fraction Connate water saturation Aquifer porosity Aquifer permeability Aquifer thickness Water viscosity Water compressibility Formation compressibility Oil reservoir radius For radial aquifer: Encroachment angle Dimensionless time coefficient Theoretical aquifer constant.67/yr 6446 rb/psi PROPERTY VALUES CHOSEN BY AHM & USED IN OILWAT AND MATCH QUALITY ~ B rb/stb scf/stb rb cf 1.675 4.42 65.273 364 1. U Time years 0 1 3 4 5 6 7 8 9 10 Press.0 Aquifer Const.00700 OJX1275 0. 189 .287 398 1.374 592 0.88 29. psia 2740 2500 2109 1949 1818 1720 1608 1535 1480 1440 ~stb ~ scf stb 0.280 1.0 6693.54 77.0 5. 6500 6355.00065 0.5 6189.294 418 1.251 (9*) 8.0 7.74 74.280 383 1.452 0.170 1.5 6296.0 5. 5% 25% Aquifer constant o 3 10 15 6000 6500 7000 r.0 5.630 (9*) 6.0106 0.173 (6*) 5.820 o I Upper Limit Rs Run No.69 50.621 (7*) 5.14 58.600 1.760 1.700 1.3 6359.303 442 1.500 1.) (u) 200md 100 ft 0.276 371 1.577 3.329 507 1.1 1025 1065 1095 1120 1145 1160 200~ Aquifer size 312 MMstb (r.980 1.43 0 760 920.636 1.395 (12*) 8.55 Cj 4x10· /psi 3x10-6/psi 9200 ft TABLE 9 140 degree 5.316 471 1..15 40.3 6152.5 6152.930 1.591 4.39 70.9 6296 Quality 4.553 0.00275 * The actual values of aquifer size used in the OILWAT calculation. Gas Production (BCF) Figure 2. Gaa Producllon (BCF) to o Import the values of the calculated pressure into AHM to compare with the observed data Figure 1.Compile and review reservoir fluid. Pressure ditTerence between the calculated and observed data of an abnormally pressured gas reservoir. I AHM generates the value of pressure match quality and revises the property values 200 100 i is I No Is the value of pressure match quality satisfactory? D. such as OOIP. to be determined ----Runl 9 -Run4 OASWAT IlIone 'i .• So Ob&P 7 • Estimate the most likely values and limits of property values J1 i• 6 i 4 Calculate reservoir pressures with the most likely or revised property values using OILWAT/GASWAT 3 2 I I 10 o I I I ) 20 30 40 50 Enter the most likely values and limits of properties and import the observed data into AHM Cum. 300 . OGIP. etc. gascap size. pressure and production data 10 I I I Select property values. . PVT. Schematic diagram of the material balance calculation by coupling OILWAT/GASWAT with ARM. Figure 3. ~ ~I o GASWATeIone ro I 20 30 40 ~ Cum.. Pressure matches for an abnormally pressured gas reservoir. Obe.......Ex.. ....-Obo..Run 1 -f:r.-. lL r l...Run 10...1one -*.Run 5 -II.- -+-llelol·. 011 ProduclJon (MMstb) -a...nd OILWAT _ 20 I i..RunS ··---··Run 1&00 I 8. -----:r----....... Pressure difference between the calculated and observed data of an aquifer drive reservoir.. o I I I 10 18 20 CO ~ OlLWAT....Run 2 ~Run3 -+-Run4 -*..-.....!!. -.. -a.g. ·~----.. I I ! i o 10 20 30 40 50 50 70 80 90 Cum.3500 I I 3000 r . 01 Production (MMstb) Figure 7. I I 40 50 J 60 70 so 90 on Production (MMBtb) Figure 6....... OlLWAT oIono I 1800 Run 10.. :::- 3000 A I 2500 l! I 1 j 1 2000 d! 2000 I ....... P 1000 ' I o Cum... -+... 150i 30 I ____ I i i Run 8 -+.. Pressure matches of an aquifer drive reservoir.. ~u 50 ! . .~ i. -so I ! I ! ! . ExM1ple . --·.. •20 I -6....... 011 ProducUon (MMstb) Figure 15..... .OlLWAT_ ____ -30 Run 8 I o I 8 ' 10 I I 18 20 Cum.. -Dake'..P -+. Figure 4.---~ -10 .. "i s 10 1 lL 100 o ~ . Pressure difference between the calculated and observed data of a gascap drive reservoir. Pressure matches of a gascap drive reservoir...Run 4 10 20 30 Cum..