Society of Petroleum Engineers

SPE 26244

Improved Matl9rial Balance Calculations by Coupling With aStatistics-BasE~d History-Matching ProgramR.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 reflectany 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 Societyof 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 acknowledgmentof 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~1a new material balance calculationby coupling a statistilcs based history matchingprogramwith a material bal~ll1ce program. The procedure is tomatch the historical reservoir pressure data with thecalculated pressures obtained from the materialbalanceprogram -- the so-caUed pressure match method -- withthe help of the history matching program.

The combination of the history matching and materialbalance programs proves to be a very simple andpowerful tool for material balance calculations. A userwho does not know cillferent material balance methodsunder various reservoir conditions is able to calculatethe material balanc:e with great accuracy. This isbecause the new procedure is based on the pressurematch method which is known to be applicable to alltypes of reservoirs, Le., oil or gas reservoir with orwithout gascap and/or aquifer, with accurate results.

In this paper, the calculation of pressure in thematerial balance mlathod is briefly reviewed and themechanism of pressure history match is cursorilydiscussed. Three case studies, comprising anabnormally pressul'1ed gas reservoir, a gascap drivereservoir and an aG[Uifer water drive reservoir, arepresented 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 orbetter than those of using the material balanceprogram alone. Moreover, the matches were obtainedin 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 andaccurate method is the pressure match method. Themethod is to match the observed reservoir pressureswith the calculated pressures. However, the pressurematch normally requires a substantial computationaltime and effort. This paper describes a new procedurethat will overeome this shortcoming and provide fastand accurate results for the material balancecalculation.

With the new procedure, an engineer need not knowvarious methods, such as Ramagost and Farshad3,Havlena and Odeh2, Cole4, or Campbell5 -- just toname a few -- for the material balance calculation. Thecurrent procedure can be applied to all the oilreservoirs as well as the gas reservoirs. It is notnecessary to distinguish an abnormally pressured gasreservoir from a regular gas reservoir. There is noneed to fit the data with a straight line, mostconspicuous in the Havlena and Odeh method.Therefore, the current procedure tends to preserve theresolving power of the original material balance

2 IMPROVED MATERIAL BALANCE CALCULATIONS WITH A IDSTORY MATCHING PROGRAM SPE 26244

reservoir pressures are to be compared with theobserved pressures.

The material balance programs used in this study,OILWAT/GASWAT, predict the reservoir pressuresbased on the general material balance equation asdescribed below.

equation as discussed by Tehrani6

In addition, the current method does not requireengineers to choose data points for calculation like thematerial balance programs do. All the valid pressuredata points can be used in the new procedure insteadof only certain data being chosen to fit in a straight lineas in most other methods. These features make thecurrent method a more foolproof procedure for thenumerous reserve estimates required in financialplanning work.

For an oil reservoir,

F lIE NEt + W., (1)The current procedure involves using a historymatching program which is commercially available tomatch the observed reservoir pressures. The historymatching program used in this study is called"Adaptive History Matching (AHM) System" which wasdeveloped by Scientific-Software Intercomp (SSI) withthe participation of Texaco and several other major oilcompanies.

where F is the underground withdrawal, N is theoriginal oil in place (OOIP), Et is the overall expansionof oil, gas, water and formation, and W. is cumulativewater influx from the aquifer into the reservoir. F,Etand W. are further defined as:

where

E, = B. (BIB" -1) (5)

(7)w. = U S(P,t)

Et = Eo + mE, + Efw (3)

and

The material balance equation for a gas reservoir canbe written as:

where U is an aquifer constant and S(P,t) is an aquiferfunction. Various aquifers, such as the small pot,infinite linear, finite and infinite radial aquifers, havedi:tTerent aquifer functions8.

The material balance programs, OILWAT7 andGASWAT8, used for this study were developed byTexaco and are also commercially available. In all thecases tested, including gas reservoirs and oil reservoirswith and without gas cap and/or aquifer, thecalculation results of the new material balance methodare comparable to or better than those of using thematerial balance programs alone. In this paper, themechanics ofapplying the new method and several casestudies will be presented following a brief discussion ofthe pressure calculation in OILWAT/GASWAT and thehistory match mechanism of ARM.

The current pressure match method requires a genericmodel which can predict the reservoir pressures basedon the PVT and production data. The predicted

PREDICTION OF RESERVOIR PRESSURE

ARM was developed to help the engineer to deal withthe problems of history matching reservoirperformance data with a reservoir simulation model.One of the major uncertainties in the history match isto decide what property values to adjust in order toachieve a satisfactory match. And, the number ofpossible reservoir and fluid parameters that need to bemodified for the production history match may go upto a dozen or more. Fortunately, the material balanceequation only contains a few variables; the propertyvalues that need to be adjusted are limited to a veryfew. This makes the pressure history match in amaterial balance calculation much more manageable.

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SPE 26244 R.. RANDY HWAN 3

where G is the original gas in place (OGIP). Eq. (8)can be expressed in terms of P/Z as:

For a natural depletion gas reservoir, the expansion ofthe connate water and reduction in the pore volume isnegligible as compared to the gas expansion and thereis no water aquifer, and Eq. (9) reduces to the popularform

The pressure match method is to assume values forN(or G), III, and/or U of a particular aquifer model,S(P,t), and then calculate the reservoir pressure as afunction of cumulative production or time. The set ofvalues of N (or G), III, and/or U which minimizes thedifference between the calculated and the observed

Most material balance methods calculate N (or G), III,and/or U from historical pressure and production databy interpreting the material balance equations (1) and(9) as linear functions. For instance, Eq. (12) indicatesthat there is a linear relationship between P/Z and thefractional recovery GJG, or the cumulative productionGp Extrapolating the line of P/Z versus Gp to theabscissa gives the value of OGIP, G.

where

and

Pi Gp-(1 - -)

P Zi G- .. ---=-----Z . Y[1 - ell (Pi - P)]- G

Y .. (WII - Wp B,,)/Bgi

P Pi Gp_ .. _(1--)Z Zi G

(8)

(9)

(11)

(12)

pressure data is regarded as the correct set.

Eqs. (1) and (9) are used to calculate the reservoirpressure for the pressure match method. Because thePVT properties of the reservoir fluids are functions ofpressure, given the values of N (or G), III, and/orUone can calculate the first reservoir pressure P(1) atthe first production data point[Np(I), Gp(l), Wp(l), W,(l). G,(I), etc.] by trial anderror. In other words, one can choose a pressure valueso that the left-hand side of Eq. (1) or (9) will be equalto its right-hand side. Once the first point of reservoirpressure is determined, the second pressure value canbe obtained from the first pressure value, P(l), and thesecond production increment using the sameprocedure. The procedure is repeated until all thereservoir pressures are calculated.

If there is no water influx in the above calculation, thecalculated pressure will not depend on the past historyof reservoir performance or on the path it has followedin reaching a given state. It depends only on theimmediate conditions, however reached.

mSTORY MATCH OF RESERVOIR PRESSURE

The history match of the reservoir pressure isconducted with the history matching program, AHM.The reservoir pressures calculated from the previoussection are compared with the historical pressure datain AHM. Based on the differences between thecalculated and historical pressure data, AHM willsuggest a set of new values of N (or G), III, and/or U.These new values are used to repeat the calculation ofthe reservoir pressure as described above. The newlycalculated reservoir pressures are then compared withthe historical pressure data in AHM. And, the processis continued until the reservoir pressures calculatedfrom a certain set of N (or G), III, and/or U match thehistorical pressure data satisfactorily. The value of N(or G) thus obtained is the OOIP (or OGIP) of thereservoir.

The key to the above process is the capability of thehistory matching program, AHM, to suggest a certainset of N (or G), III, and/or U that provides asatisfactory history match of reservoir pressures. Themethodology of AHM was discussed by Watkins et al.9and Parish et al. IO The underpinning of AHM is astatistical analysis method known as Bayesianinference. The Bayes' theorem provides, in afundamental way, a process of learning from

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4 IMPROVED MATERIAL BALANCE CALCULATIONS WITH A IUSTORY MATCHING PROGRAM SPE 26244

experience, and shows how knowledge about the stateof nature can be continually modified as new databecomes available.

To history match the reservoir pressures, the user hasto decide which properties, such as N (or G), m,and/or U, to vary, to provide initial estimates of theseproperties and to place each estimate in an interval.The interval defines a sub-space of the property spacethat the correct values of these properties will befound.

The following operations are performed by AHM andare described here in case the reader is interested. Itis not necessary for the user to understand how AHMconverges in order to make the material balancecalculation, but a brief description follows whichassumes the reader is trained in statistics and Bayesiantheory.

The information of the initial estimates and intervalsdefines the first two moments of a distribution, meanand variance. These estimates reflect the prior ideas ofthe engineer on possible values for these properties.With the distributional assumptions, it can beexpressed

P(property valueslcalculated pressures) is now areplacement to Eq. (13) and specifies the (relative)likelihood of any feasible vector of property valuesbeing the solution vector.P(property valueslcalculated pressures) is the posteriordistribution after the first round of pressurecalculation.

The next step is to calculate the reservoir pressures asdiscussed previously using the revised estimates ofproperty values. In this case, the posterior of the firstpressure calculation becomes the prior of the secondpressure calculation. Again, it is assumed that thecalculated pressures do not sufficiently match theobserved data and further revision is required. Theposterior distribution of the second round of pressurecalculation which describes various feasible values ofthe vector of property value can be written as

P(property values list calculated pressures, 2nd calc,,-lated pressures) DC P(2nd calculated pressures\propeTtJ

values)P(property valuesllst calculated pressures}

(16)

P(property values) (13)

The property values of the initial estimates are used tocalculate the reservoir pressures as described earlier.It is assumed that the calculated pressures do notsufficiently match the observed data. The informationgenerated from this calculation is then used to revisethe estimates of property values. The results of thecalculation are expressed as

p(calculated pressures\property values) (14)

With proper constraints, Eqs. (13) and (14) can becombined, via Bayes' theorem, to give

P(property valueslcalculated pressures) DC P(calculated pressure \property values)P(property values}

(15)

The path to an iterative scheme is now established.The revised estimates of the property values from thesecond pressure calculation are used in the third roundof the pressure calculation. The calculated pressuresare used to update the previous property values. Thisprocess will continue till a set ofproperty values whichgenerates a corresponding set of calculated pressuresthat satisfactorily match the observed data areobtained.

PROCEDURE OF PRESSURE MATCH

The material balance and history match programs mayreside on different computer systems. This may be acommon occurrence since various computer systemscoexist in the work place nowadays. In our case, AHMis installed on the mM RS/6000 workstation. A usercan access AHM from his PC through the networkwith Microsoft's Windows and Visionware's Xvisionsoftware loaded on the PC. On the other hand, thematerial balance program, OILWAT/GASWAT, isinstalled on the PC or available on the mainframecomputer.

182

SPE 26244 R. RANDY HWAN 5

With user's manuals of AHMll and OILWAT/GASWAT12 available for reference, the procedure ofapplying AHM in material balance calculations issummarized below:

1. Specify initial estimates of pressure-matchproperties, e.g., OOIP or OGIP, gascap and/or aquifersizes, etc. in AHM.

2. Run OILWAT or GASWAT with the currentestimates of property values and generate thecorresponding pressure results.

3. Compare the calculated pressures with the observeddata in AHM.

4. Obtain updated AHM estimates of the propertyvalues.

5. Repeat Steps 2, 3, and 4 until the calculatedpressures satisfactorily match the observed data. Then,the set of the property values in Step 4 that providesthe best pressure match are the result of the materialbalance calculation. This may comprise OOIP or OGIP,gascap and/or aquifer size, aquifer constant, etc.

In AHM, the user can examine the match after everyiteration (and modify AHM's selections if desired), orhe can tum AHM loose at anytime to run on"automatic pilot" if the material balance program islinked with AHM by an interface program.

CASE STUDIES

These cases include (1) an abnormally pressured(pressure gradient greater than 0.5 psi/ft) gas reservoirwith no influx, (2) a gascap drive reservoir, and (3) awater drive reservoir without gascap.

Case 1: Calculate OGIP for An AbnormallyPressured Reservoir With No Influx

The material balance calculation for the Anderson "L"gas reservoir as reported by Ramagost and Farshad3 isconducted with the current procedure. The initialpressure gradient of the reservoir was 0.843 psi/ft.The volumetric estimate of OGIP was 69 BCF. Thereservoir and production data are listed in Table 1.

Since the property value to be determined is the OGIP(G), an engineer has to estimate the most likely valueof the OGIP and its upper and lower limits. Table 2

shows that the initial estimate of OGIP is 70 BCF.The lower and upper limits ofthe OGIP are also shownin the table. The OGIP value and its limits are inputto AHM. The starting OGIP which is considered asthe most likely (expected) value is used in GASWAT tocalculate the reservoir pressures.

The calculated pressures (Run 1 in Fig. 1) are importedinto AHM to compare with the observed pressure datawhich were entered in AHM beforehand. All the validdata points of the observed pressure are included; and,the data were not pre-selected for the pressurecomparison. After comparing the calculated pressureswith the observed pressures, AHM yields a value ofmatch quality, .2193, based on the sum of squares forerror, as shown in Table 3. A lower quality valuemeans a better pressure match in AHM.

Besides providing the match quality, AHM is able tosuggest a value of OGIP for the next run. The valuefor Run 2 is 70.391 BCF (Table 3). This value is thenused in GASWAT to calculate the reservoir pressuresfor Run 2. The calculated pressures are imported andcompared with the observed data in AHM. The valueof pressure match quality, .1917, of Run 2 and therevised value of OGIP for Run 3, 71.679 BCF, are alsoshown in Table 3. The suggested property value inAHM is based on the results of all the previous runs.

The above procedure is repeated for Run 4. The valuesof the OGIP and pressure match quality of the run are73.437 BCF and 0.1017, respectively (Table 3). Thisresult from the current procedure is slightly betterthan that from GASWAT alone (Ramagost andFarsluld's method). Fig. 1 shows the pressure matchesof Runs 1, 4 and GASWAT alone versus the observeddata. The pressure difference between the calculatedvalues of these runs and the observed data are shownin Fig. 2.

The procedure can be summarized in a flow chart asillustrated in Fig. 3. When the process finishes, therevised property values giving the satisfactory pressurematch are the result of the material balancecalculation.

Case 2: Calculate OOIP and Gascav Size for aGascap Drive Reservoir

This example of an oil reservoir with a gascap ispresented in Reference 13. The historical data includescumulative oil production as a function of the average

183

6 IMPROVED MATERIAL BALANCE CALCULATIONS WITH A HISTORY MATCHING PROGRAM SPE 26244

reservoir pressure, over the first few years ofproduction. The production data and the relevant PVTdata are shown in Table 4.

The property values to be determined in this case areOOIP (N) and gascap size (",). The most likely valuesof these properties and the upper and lower limits ofthe values are estimated and shown in Table 5. Theinitial estimates of DOIP and the volume ratio ofgascap to reservoir are 70 MMstb and 0.47,respectively.

Comparison of the calculated pressures of Run 1 withthe observed pressures in AHM yields a value ofmatchquality, 6.88, as shown in Table 6. AHM then suggeststhe values of DOIP and gascap size ("'),90.76 MMstband 0.452 (Table 6), respectively, for the next run.These values are used in OILWAT to calculate thereservoir pressures for Run 2 and the calculatedpressures are imported and compared with theobserved data in AHM. The value of pressure matchquality, 1.70, of Run 2 and the revised values of OOIPand ", for Run 3, 100.61 MMstb and 0.454, are alsoshown in Table 6.

The process continues till Run 6 of which the OOIPand mare 116.19 MMstb and 0.469, respectively. Thevalue of pressure match quality is 0.00144 (Table 6).Both results of the current procedure and OILWATalone (FE method7) are better than that calculated blHavlena and Odeh's method in Dake's example1 .This is because the water and formation expansions areneglected in Dake's example. Fig. 4 shows thepressure matches of all the runs versus the observeddata. The pressure difference between the observeddata and calculated values of Run 6 and the OILWATenmples are shown in Fig. 5.

Note that the value of OOIP in the final pressurematch, Run 6, is quite different from that of the initialestimate but it is still within its limits (see Table 5). Inother cases, when better results are concentrating nearthe boundaries or within a narrow range of theinterval, the interval of the property value may bewidened or narrowed, accordingly. Nevertheless, theresults of the existing runs are still valid in guiding thesubsequent runs with the AHM algorithm.

Case 3: Calculate Aquifer Properties for a WaterDrive Reservoir with Known OOIP

This is an example of a water drive reservoir with a

radial aquifer shown in Reference 13. The reservoir,PVT and production data are presented in Table 7.There is no initial gascap and the DOIP, 312 MMstb,is determined from the volumetric calculation.

The aquifer size was the only aquifer propertydetermined in the reference. With the currentprocedure, both the aquifer size and aquifer constantcould be determined at the same time. The initialestimated values with the limits of these aquiferproperties are shown in Table 8. The estimates ofaquifer size are based on the seismic and geologicalevidence.

The results of the AHM/OILWAT calculation areshown in Table 9 with the procedure illustrated in theprevious cases. Because OILWAT only calculates thewater influx at selected values of ratios of aquifer andreservoir radii, rJr,., such as 4, 4.5, 5,6, etc., the valueof pressure match quality could not be reduced belowcertain limits. The aquifer size in terms of rJr,., andaquifer constant of Run 6 are 5.173 and 6152.3 rb/psi,respectively.

To further improve the pressure match, the value ofrJr,. is set to be 5 and the aquifer constant starts from6152.3 rb/psi for the next series of AHM/OILWATruns. The results of the these runs (Table 9) showthat the aquifer constant of the best run

SPE 26244 R. RANDY HWAN 7

DISCUSSION

Tehrani6 realized that the material balance calculationwith pressure match is the most accurate method,especially for oil reservoir with water intlux. Heshowed that rearranging the material balance equationfrom the original form (the combined equation of Eqs.(1) and (7

The current method simplifies the procedure ofmaterial balance calculation. An engineer need notknow different material balance techniques in order tomake material balance calculations. With the currentprocedure, he can by-pass the intermediate steps, suchas drawing straight lines through data sets, anddirectly focus on the pressure match to obtain a goodmaterial balance calculation.

Initial estimates of the hydrocarbon in place arenormally available through the volumetric calculationof the reservoir. In general, this would provide good.initial estimates for pressure match in AHM.However, the aquifer in most cases is ill-defined. Thevalues of aquifer properties may be derived from thetheoretical calculation or from initial runs of thematerial balance program alone.

A new procedure of material balance calculation bycoupling a material balance program with a statisticsbased history matching program is presented. Theprocedure is based on the pressure match method.The new method is able to overcome the time-consuming trial-and-error process of the pressurematch method by using the history matching programwhile retaining the robustness and accuracy of thepressure match method,

CONCLUSIONS

It is not necessary to have both material balance andhistory matching programs coexist in the sameplatform. With the network :tile transfer programs, theresult :tiles of the material balance calculation can betransferred between different computers, e. g., PC'sand workstations. However, linking these twoprograms with an interface program would enhanceefficiency and usability.

Since an engineer does not need to choose the datapoints for the material balance calculation, the currentprocedure could provide more consistent results amongdifferent engineers. Freedom from data point selectionwould not only save the engineers' time and effort inmaterial balance calculations but also provide anopportunity to automate the computation process withminimum engineer intervention.

as reported by Havlena and Odeh2 will reduce theresolving power. Thus, he argued that Eq. (18) is notsuitable for calculation of OOIP and aquifer constant.

Unlike the classical material balance calculations andby OILWAT and GASWAT alone, generally there is noneed to exclude any pressure data points for thepressure match by AHM. This is because mostOILWAT/GASWAT solutions are determined throughthe plots of straight lines while the pressure match isbased on the original material balance equation.Without the uncertainty in deciding which data pointsto use, the material balance calculation using AHMcould be an efficient method for the numerous reserveestimates required by annual reserve updates.

(17)F = NEt + U S(P,t)

This material balance calculation uses the historymatching capability of the AHM program. However,the best source of information for history matching stillresides in the professionals who are responsible for thereservoir. AHM was designed to provide a system tointegrate this knowledge into the match process. Theprofessional input to the history match processbecomes more criticalwhen more matchingparametersare involved. For example, an oil reservoir with bothgascap and aquifer present. Good initial estimates ofthe property values will go a long way in pinpointingthe sizes of reservoir fluids in place.

to the conventional form

F = N + U S(P,I)Et Et

(18)

The results of the case studies demonstrate that thenew procedure is a fast and accurate material balancemethod. The calculation results of the new procedureare comparable to or better than those of using thematerial balance program alone. Moreover, theseresults are obtained in just a few runs.

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8 IMPROVED MATERIAL BALANCE CALCULATIONS WITH A HISTORY MATCHING PROGRAM SPE 26244

ACKNOWLEDGEMENTS

Subscripts

= Initial condition

The results of the case study involving water influxfrom a radial aquifer indicate that the water influxcalculation in the material balance program needs toimprove from the discrete point results to a continuouswater influx function. The current method demandshigh accuracy of the water influx calculation.

The material balance calculation with the currentprocedure can be conducted with the material balanceand history matching programs loaded in differentcomputer systems. The result files of the calculationcan be transferred through the network file transferprograms. However, for numerous reserve estimatesit would be advisable to develop an interface programbetween the material balance and history matchingprograms.

Swl ==S(P,t) ..t ==U =w. =Jv, =WI' =Y =Z =

Initial water saturation, fractionAquifer function, see Ref. 3Time, yearsAquifer constant, see Ref. 3Cumulative water influx, MMrbCumulative water injection, MMstbCumulative water production, MMstbWater influx function defined in Eq. (11)Gas deviation factor

NOMENCLATURE

B, ==B. =Bw =C. =

C, ==

Cw =

Efw ==

E, =

E. =

E, =

F =G -G. ==

G -,m ==

N ==N,

-

P ==ro ==

r.-

R, ..R ..

Gas formation volume factor, rb/MCFOil formation volume factor, rb/stbWater formation volume factor, rb/stbEffective compressibility, l/psi, defined inEq. (10)Formation compressibility, l/psiWater compressibility, l/psiExpansion of water and reduction in porevolume, rb/stb in Eq. (3); rb/MCF in Eq. (8)Expansion ofgas, rb/stb in Eq. (3); rb/MCFin Eq. (8)Expansion of oil and solution gas, rb/stb,defined in Eq. (4)Overall expansion of oil, gas, water andformation, rb/stb, defined in Eq. (3)Underground withdrawal, rbOriginal Gas In Place, BCFCumulative gas injection, BCFCumulative gas production, BCFInitial gascap size, volume ratio of gascapand oil reservoirOriginal Oil In Place, MMstbCumulative oil production, MMstbAverage reservoir pressure, psiaAquifer radius, ftRadius of oil reservoir at original oil watercontact, ftCumulative gas-oil ratio, scf/stbSolution gas-oil ratio, scf/stb

The author wishes to thank Texaco Inc. for permissionto prepare and publish this paper. The author is alsograteful to Dr. Ben Wang for his assistance in usingOILWAT/GASWAT programs.

REFERENCES

1. Schilthuis, R J.: "Active Oil and Reservoir Energy,"Trans., AIME, 118:33-52.

2. Havlena, D. and Odeh, AS.: "The Material Balanceas an Equation of a Straight Line," J. Pet. Tech.(Aug. 1963) 896-900.

3. Ramagost, B. P. and Farshad, F. F.: "P/ZAbnormally Pressured Gas Reservoirs," paper SPE10125 presented at the 1981 SPE Annual TechnicalConference and Exhibition, San Antonio, Texas,Oct. 1981.

4. Cole, F. W.:Reservoir Engineering Manual, GulfPublishing Co., Houston (1969).

5. Campbell, R A and Campbell, J. M., Sr.:MineralProperty Economic8, Vol. 3: Petroleum PropertyEvaluation, Campbell Petroleum Series (1978).

6. Tehrani, D.H.: "An Analysis ofVolumetric BalanceEquation for Calculation of Oil in Place and WaterInt1ux," J. Pet. Tech. (Sep. 1985) 1664-1670.

7. Wang, B., Litvak, B. L. and Bowman, G. W., n:"OILWAT: Microcomputer Program for OilMaterial Balance With Gascap and Water Influx,"paper SPE 24437 presented at the 7th SPEPetroleum Computer Conference, Houston, Texas,

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SPE 26244

July 19-22, 1992.

R. RANDY HWAN

TABLE 1

9

PRODUCTION AND PVT DATA OF CASE 1

Calculate OGIP for anAbnormally Pressured Gas Reservoir

Time Press. G G Ip@wl (psia) ~ (BCF) (Mstb)0 9507 1.440 0.0 0.0

69 9292 1.418 0.393 29.9182 8970 1.387 1.642 122.9280 8595 1.344 3.226 240.9340 8332 1.316 4.260 317.1372 8009 1.282 5.504 406.9455 7603 1.239 7.538 561.2507 7406 1.218 8.749 650.8583 7002 1.176 10.509 776.7628 6721 1.147 11.758 846.3663 6535 1.127 12.789 939.5804 5764 1.048 17.262 1255.3987 4766 .977 22.890 1615.8

1183 4295 .928 28.144 1913.41373 3750 .891 32.567 2136.01556 3247 .854 36.820 2307.8

Liquid condensate production.

TABLE 2

LIMITS AND INITIAL ESTIMATE OF OGIP

Lower Limit Expected Upper Limit

OGIP(BCF) 60 70 80

8. Wang, B. and Teasdale, T. S.:"GASWAT-PC: AMicrocomputer Program. for Gas Material BalanceWith Water Influx," paper 14684 presented at thePetroleumIndustIyApplications ofMicrocomputersheld in Del Lago on Lake Conroe, Montgomery,Texas, June 23-26, 1987.

9. Watkins, A. J., Parish, R. G. and Modine, A. D.:"AStochastic Role for Engineering Input to ReservoirHistory Matching," paper SPE 23738 presented atthe 1992 Latin American Petroleum EngineeringConference, Caracas, Venezuela, March 8-11.

10. Parish, R. G., Calderbank, V. J., Watkins, A. J.,Muggeridge, A. H., Goode, A. T. and Robinson, P.R.:"Effective History Matching: The Application ofAdvanced Software Techniques to the History-Matching Process," paper SPE 25250 presented atthe 12th SPE Symposium on Reservoir Simulation,New Orleans, Louisiana, February 28-March 3,1993.

11. Adaptive History Matching (ARM Version 1.1)User's Guide: Release Date: June 1992, ScientificSoftware-Intercomp, Inc.

12. OILWAT/GASWAT

10 IMPROVED MATERIAL BALANCE CALCULATIONS WITH A InsTORY MATCHING PROGRAM SPE 26244

TABLE 3

VALUES OF OGIP CHOSEN BY AHM &USED IN GASWAT AND MATCH QUALITY

TABLE 5

LIMITS AND INITIAL ESTIMATES OFOOIP AND GASCAP SIZE

Run No.1234

GASWATAlone

OGIP

SPE 26244

TABLE 7

R. RANDY HWAN

TABLE 8

11

PRODUCTION AND PVT DATA OF CASE 3

Calculate Aquifer Size and Aquifer Constantfor a Reservoir with Known OOIP

LIMITS AND INITIAL ESTIMATESAQUIFER SIZE AND AQUIFER CONSTANT

Lower Limit Expected Upper Limit

PROPERTY VALUES CHOSEN BY AHM &USED IN OILWAT AND MATCH QUALITY

TABLE 9

Reservoir temperatureOriginal Oil In PlaceInitial gascap volume fractionConnate water saturationAquifer porosityAquifer permeabilityAquifer thicknessWater viscosityWater compressibilityFormation compressibilityOil reservoir radiusFor radial aquifer:

Encroachment angleDimensionless time coefficientTheoretical aquifer constant, U

200~312 MMstbo5%25%200md100 ft0.55 Cj4x10 /psi3x10-6/psi9200 ft

140 degree5.67/yr6446 rb/psi

Aquifer size 3(r.. I r.)

Aquifer constant 6000(u)

10

6500

15

7000

Run No. Aquifer Size Aquifer Const. QualityTime Press. ~ ~ Bo Rs ~ 1 10 6500 4.591years psia stb scf stb rb/stb scf/stb rb cf 2 11.395 (12*) 6355.0 4.6750 2740 0.0 0 1.404 650 0.930 3 8.251 (9*) 6693.3 4.5771 2500 7.88 760 1.374 592 0.980 4 8.630 (9*) 6359.4 3.6363 2109 29.15 920.5 1.329 507 1.170 5 6.621 (7*) 6228.5 1.5534 1949 40.69 975.1 1.316 471 1.280 6 5.173 (6*) 6152.3 0.4525 1818 50.14 1025 1.303 442 1.390 7 5.0 6152.3 0.000656 1720 58.42 1065 1.294 418 1.500 8 5.0 6146.5 0.01067 1608 65.39 1095 1.287 398 1.600 9 5.0 6189.5 0.007008 1535 70.74 1120 1.280 383 1.700 10 5.0 6296.9 OJX12759 1480 74.54 1145 1.276 371 1.760 OILWAT 5.0 6296 0.00275

10 1440 77.43 1160 1.273 364 1.820 Alone

* The actual values of aquifer size used in theOILWAT calculation.

189

Compile and review reservoir fluid. PVT.pressure and production data

10 I I I

6

Estimate the most likely values and limits ofproperty values

Enter the most likely values andlimits of properties and import theobserved data into AHM

Select property values. such as OOIP. OGIP,gascap size. etc., to be determined

Calculate reservoir pressures withthe most likely or revised propertyvalues using OILWAT/GASWAT

OASWAT IlIone

. Ob&P

-Run4

----Runl

4

9

3

'iSo 7

J1ii

50403020102 I I I I I )

o

Cum. Gaa Producllon (BCF)

to Figure 1. Pressure matches for an abnormally pressured gas reservoir.o

Import the values of the calculatedpressure into AHM to compare withthe observed data

300 , I

200

100

iis

ID.

~ GASWATeIone~I I

o ro 20 30 40 ~

Cum. Gas Production (BCF)

No

AHM generates the value of pressure matchquality and revises the property values

Is thevalue of pressure match

quality satisfactory?

Figure 2. Pressure ditTerence between the calculated and observed data of anabnormally pressured gas reservoir.

Figure 3. Schematic diagram of the material balance calculation by couplingOILWAT/GASWAT with ARM.

3500 I I 3000 r,------------------------------,

2000 I I

3000

Ij1

...-Obo,P

~Run3

-+- Run 1

-+-Run4

-f:r- Run 2

-*- RunS

:::-

A 2500l!

I12000d!

1800 Run 10.-+- Run 4 ~ OlLWAT.1one

---Run 8. OlLWAT oIono .. -Dake'. ExM1ple -*- Run 5 -II- Obe. P90so7030 40 50 60

Cum. on Production (MMBtb)2010

1000 ' I I I Jo

2018101&00 I , I I I

o

Cum. 011 ProduclJon (MMstb)

-a.

CO-a.

Figure 4. Pressure matches of a gascap drive reservoir. Figure 6. Pressure matches of an aquifer drive reservoir.

150iii

30 I I ____ Run 8

-+- Run 10.nd OILWAT _

20

10

100

"isi,g, 50~u

!lL

o~--..-----:r----.---~ ..........-- .. -- ..-....~----- ..-- ..........~

-+-llelol.Ex.......20 I -6- OlLWAT_

Ii.!!.

1lL -10 rl--------,____ Run 8

908070505040302010-so I ! I ! ! , I I ! i

o-30 I I' I I

o 8 10 18 20

Cum, 011 ProducUon (MMstb) Cum. 01 Production (MMstb)

Figure 15. Pressure difference between the calculated and observed data of a gascapdrive reservoir.

Figure 7. Pressure difference between the calculated and observed data of an aquiferdrive reservoir.

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