Material balance

SPE 35589

MB Solution for High Pressure Gas Reservoirs

by Adel M. Elsharkawy, Petroleum Engineering Department- Kuwait UniversitySPE Member

COPwubI19%.SOCICIYofPeIIoleum Etwucm. Inc.

lhia paper w- prepared for presentation at Oie SPE Gas Technolqy Conference held m CalSWY,

Canada, 28 April to I May .t99b

IiIM papa was selected for wtabon by m SPE PM@III Commmee follomng rewew of in fornuhon

contmcd h an &.tract subimtted by tbe auOIcH(s) Content.! of the paper. IM prcsenterl have been

revwwed by the SOCKIY of Pekokum Engmem and we subject to correction by the moJIor(s) lhe

mattid w presttksi does ml nc.=smry re!kct any p.omti of the Sccwty of PIXIVkUm En@mcm os

officers, or member! papers Wesentcd at SPE mccdngs arc subject to pubbcaiion review by Editond

Cotnmuttms of the Soaety of petroleum Engtwen Pemusswtt 10 copy M restricted to m abstract of nol

more than 300 words [email protected] may not be COPA The Ibsbscf should contwt cc+IspictIoiM

acknowledgment of where and by whcin IA. paper u pr-ted Write Libranm MaI!sser SPE, P O

sOX 833s36 Nchdson. TX 750S3-3836. U S A , Ftx 01-2 i 4952-9435

ABSTRACT

Accurate estimation of the initial gas in-place for high--pressuregas reservoirs is quite oflen diflicult because of theeffect of formation compressibility and the uncertain presenceof water influx from small, associated aquifer or adjacentshales.This paper presents a material balance solution for estimatingthe initial gas in-place and predicting the prevailingproduction mechanism for high-pressure gas reservoirs. Thematerial balance solution incorporates water influx fromaquifer, water intlux from shale, formation expansion,connate water expansion, and formation of condensate.Application of the proposed solution to four case histories ofhigh-pressure gas reservoirs shows that this solution wouldsuccessfirllyestimate the IGIP after production of 15°/0 of theinitial gas in-place and predict the prevailing reservoirproduction mechanism. In comparison with the availablemethods, the proposed solution requires no prior assumptionsabut the formation compressibility, aquifer size, or volume ofadjacent shales.

INTRODUCTION

Accurate estimation of the initial gas in-place (IGIP) plays anessential role in the evaluation. analysis, prediction of tirtureperformance, and making economic decision regardingdevelopment of gas reservoirs. Estimation of lGIP is alsoneeded for planning long term gas contracts andcommitments to supply gas to users.

Giila. m

Sodety of Petrdem Engineers

The principle methods for predicting lGIP are the volumetricmethod and the material balance method. The volumetricmethod is based on geological data to define the reservoirareal extent and also on core and log data to define thereservoir rock properties and distribution of fluids inside thereservoir. The volumetric method provides a sketchy estimatefor the IGIP, specially in the early history of the reservoir, andprovides neither prediction of the future production as afunction of the reservoir pressure nor interpretation of theresewoir producing mechanism. However, the materialbalance method is based on pressure-production data forestimating the initial gas in-place. The simplest method is toplot P/Z Vs Gp and extrapolate to zero-pressure. The methodis derived from the material balance equation with theassumption that gas expansion is the sole driving mechanismresponsible for gas production from gas reservoir. Thisassumption is valid for low pressure, completely sealed off“Volumetric” gas reservoirs. However, if the gas reservoir isin contact with an aquifer or a massive amount ofuncompacted shale, the pressure drop in the gas reservoir,may cause water influx because of gas production, As aresult of this pressure support from water influx, theextrapolation of the P/Z Vs Gp of the early data to zeropressure is not a valid means to estimate the IGIP. Further, ifthe reservoir initially has abnormally high formationcompressibility, as observed in some high pressure gasreservoirs, the rate of pressure drop may increase with gasproduction. This is due to the fact that the compaction of thereservoir rock will provide pressure support at the highpressure level. Some of these abnormal pressure gasreservoirs contain retrograde gases. If the reservoir pressuredrops below the dew-point pressure, retrograde condensationoccurs. Because the liquid condensate has lowercompressibility than the gas, the rate of pressure declinewould accelerate. Atso, the formation of condensate insidethe reservoir rock might reduce the gas permeability resultingin less gas production and hence an accelerated pressure dropin a unit’s gas production.Several material balance methods have been proposed toestimate the initial gas in-place for abnormally high pressuregas reservoirs1-7. These methods can be divided into three

201

2 MB SOLUTW-J FOR HIGH.PRESSURED GAS RESERVOIRS SPE 36689

groups. The first group comprises the methods described byHammerlindl 1, Ramagost and Farshad3, and Begland andWhitehead4. These methods use knowledge of formationcompressibility to estimate the initial gas in-place. Thesecond group uses graphical or least square solution tosimultaneously determine the IGIP and the overall formationcompressibility. These methods, however, do not quanti~ theprevailing production mechanism. This grou comprises the

5material balance solutions described by Roach for the formerand Bernard5for the latter. The third group uses type curvematching or matching overall reservoir compressibilitycalculated from the material balance equation to thatcalculated based on rock and water compressibilities andvolume of non-pay sand or aquifer, This group comprises thesolution described by Ambatha6 for the former solution andFetkovitch et al. 7 for the latter solution. The type curvematching solution provides a range for possible answers forthe IGIP and the total reservoir compressibility. Thecompressibility matching solution, however, provides IGIPand aquifer or non-pay sand to reservoir size. This solution issometimes d~fllcult and time consuming because of the non-unique matching and the sensitivity of the pressure data, theassumed IGIP, the formation compressibility and the aquifersize8.

The objective of present study is to develop an easy materialbalance solution that incorporates all possible sources ofexpansion in a high-pressure gas reservoir. This solution canbe used to estimate the IGIP, predict the productionmechanism and calculate the volume of the aquifer or non-pay sands associated with the gas resewoir.

THE MATERIAL BALANCE SOLUTIONS

In order to develop a general material balance solution, allsources of expansion such as water influx from aquifer, shalewater influx, formation expansion, connate water expansionand the formation of condensate must be considered.

1) Water Influx from Associated Aauifer

Water influx from the aquifer into the reservoir can begenerally expressed as;

we = a q(p,t) (1)

Where a is an aquifer constant and P is aquifer function.

However, if the aquifer associated with the abnormal pressuregas reservoir is small, then it can be modeled as a tank9~10,otherwise as an unsteady state involving pressure gradient.Irr this tank model, water influx from the associated aquifer tothe reservoir can be described by;

we = CaVa (pi -P) (2)

Where Ca is the effective compressibility of the aquifer, Ca =~ + Cf, Va is the aquifer pore volume, and (Pl -P) is thecumulative pressure drop.

2) Shale Water Influx

Water influx from shale into the gas reservoir (caused byshale compaction adjacent to the gas reserwoir) can bemodeled as barrier type11 as,

Ws = Csvs ( Ps - P) (3)

In such case the amount of water irdlux from shale (Ws), isproportional to the difference between shale pressure (p~)which is assumed to be equal to the initial reservoir pressure(pi) and the current reservoir pressure(p). The constant,CsVs, is a fimction of the pore volume and compressibility ofthe shale.

3) Formation Ex~ansion

The formation expansion can be treated as a linear function ofpressure. However, some authors 1~3*12 interpreted thedownward curvature in the P/Z Vs Gp plot as caused bycompaction of the formation resulting m changing rockcompressibility as a t%nction of pressure. 0thers5,7interpreted the curvature as characteristics of the high--pressure gas reservoirs not necessarily resulting fromchanging rock compressibility or rock collapse. The theo~ ofchanging rock compressibility as a fimction of pressure haslittle suppon. Jogi et al, 13 and Sinha et al, 14 measured rockcompressibility for samples taken from abnormally highpressure resemoirs. They reported rock compressibility athigh pressure in the order of 2 to 5X104 psi-l. If the rockhas been compacted or average effective rock compressibilityis assumed, the expansion in reservoir pore volume can bedescribed as.

Al’p=(GB.--&-’)[c~~ - z’)]

w

(4)

4) Connate water ExDansion

The change in the volume of conmte water within the gasreservoir because of the pressure drop can be described as afhnction of the volume of the connate water, the watercompressibility, and the pressure drop in the reservoir as,

~B

AVW=( --&’xswc’w(~ - P)] (5)w

202

SPE 35688 ADEL M. ELSHARKAWY 3

The water pressure is assumed to be the same as the reservoirpressure because of the equilibrium condition and neglectingthe capillary pressure effect.

5) Expansion of Condensate

Theexpansion of the condensate can be incorporated in thegas expansion by using the two phase gas deviation factor inplace of the gas compressibility factor below the dew-pointpressure.

The Material Balance Eauation

The material balance equation which accounts for all sourcesof expansion which are previously discussed, can beexpressed as,

G(Bg-Bgl)+We+W~ +AVW+ AVP =

(Gp + %JWg Bg‘Wp Bw (6)

Substituting equations (1) through (4) in equation (6) resultin:

G B,,G(Bg - Bgl) + Ca Va ( PI -p) + Cs Vs (p] -p)+ (~)

w

GBSwCw(Pi-P)+( ~) Cf(Pi- P)

w

= (Gp + ~L Kc) Bg + Wp BW (7)

Equation (7) is a material balance for high-pressure gasresewoirs that incorporates shale water influx, connate waterand formation expansion. These terms are significant forhigh-pressure gas reservoirs. Usually, they are neglected fromthe material balance equation for normal pressure gasreservoirs.

Collecting the pressure drop terms together and defining SwCw + Cf = Ce in equation (7) result in ;

G (Bgl -Bg)+{( ~) Ce + Ca ‘a+ Cs Vs}(Pi -P)=w

(8)(Gp + GPL ‘c) Bg ‘Wp BW

Arrangement of the material balance equation as a straightline had been made long agol 5-17 but it was not untilHavlena and CMeh18 presented their work that the methodbecame fully exploited 9.

Dividing both sides of equation (8) by (Bg - Bgi) results in,

G+a (t-n . (Gp + GuKc)Bg +WPBW(9)

B, - B,, (Bg-Bg,)

GBwhere o = {(H) Ce+ Ca ‘a + Cs Vs}

w

The above equation can be solved graphically or using leastsquare. However, initial scatter in the pressure-productiondata might tiect the answer from least square.Equation (9), shows that the solution plot as;

(Gp +G.p)Bg+ ‘PBW on the y-axisY=

B, - B,,versus X=

(~ -P)on the x-axis result in straight line with intercept

Bg - Bg,at the y-axis equal the initial gas in place and a slope equalthe constant CT Thus the initial gas in-place can beestimated from the intercept, without prior assumptions aboutvalue of the aquifer size, shale volume, or formationcompressibility, In addition, the slope can be used as anindication of the reservoir driving mechanism,

Amlication of the General Material Balance Eauation

The Solution plot of equation (9) results in simultaneousestimation of the IGIP and prediction of the productionmechanism. This would be illustrated by application of thebefore-mentioned solution technique to some well-known,high pressure gas reservoirs. Pressure production data forthese reservoirs are given in tables(1) through (4).

NS2B RESERVOIR

The north Ossum field, NS2B reservoir is located inLafayette, Parish, Louisiana, The reservoir was discovered in”1959, It has an initial pressure of 8921 psi at 12,500 feet.The reservoir history was originally reported by Harville &Hawkins12 and analyzed by Ramagost & Farshad3. Connatewater saturation was reported as 3Lt0/0 and average porosity as2Lt~0. The resewoir permeability is 200 md, Initial gas in-place was calculated from good volumetric data, based oncore and well logs, as 114 BSCF. Harville and Hawkinsproposed that during early life, pressure was partiallysustained by high rock compressibility resulting from rockfailure. After the production of 20 BSCF, rock failure was

203

4 MB SOLIJTIONFOR HIGH-PRESSURED GAS RESERVOIRS SPE 36689

essentially completed to normal rock compressibility of 6 x10-6 psi-l. However, Burgoyne et al.20 proposed waterintlux from shale as a possible explanation of such pressuresupport,

P/Z Vs Gp plot for this reservoir, Figure (l), exhibitsdownward curvature indicating some pressure support as thereservoir is depleted. Extrapolation of the early data for thisreservoir yield apparent gas in-place of about 220 BSCFwhich is nearly twice the volumetric estimate of the IGIP.After production of 20 BSCF (17 % of the IGIP) at 6500 psi(27 V. pressure drop), the second slope of P/Z Vs Gp plotstarted. Extrapolation of the production data from 20 to 40BSCF yields gas in-place of 118 BSCF which is in goodagreement with the volumetric estimate. Thus, the true gas inplace could not be estimated from P/Z plot until ss~. of theIGIP was produced.

Application of the material balance solution discussed in thispaper, Figure (2), yields an IGIP of 121 BSCF and slope of1983 bbl/psi. If the reservoir is assumed to be depletiondrive, an effective compressibility in the order of 18.36 (lOA)psi-l is calculated from the slope. This high compressibilityis an indication of pressure support from water infiux. Basedon rock compressibility measurements reported by Jogi etal. 13 and Sinha et al, 14, a formation compressibility of 3.5(10+) psi-l from Hall’s2‘correlation is used to calculate thevolume of the water body responsible for that pressuresupport. An aquifer pore volume of 188 MM bbl’s iscalculated that is equivalent to an aquifer to reservoir ratio of1.74. It is important to note that the reservoir has GWC, at12,580 ft. which was not considered by other authors3~12~20in their analyses.

Our material balance analysis indicates that the majorproduction mechanism is water influx, from aquifer toreservoir volume ratio of 1.74, is supported by the presence ofGWC at 12,580 ft. The material balance solution discussed inthis paper could estimate the IGIP after 13’%gas productioncompared to 35!40gas production from the P/Z plot. A samplecalculation of the aquifer to reservoir volume ratio is given inthe appendix. Comparison of the results from this study andpervious studies for this reservoir is presented in table (5). Itis clear that the proposed material balance solution is able toestimate the initial gas in-place and predict the prevailingdriving mechanism.

Caiun Field

This is a Louisiana offshore gas reservoir discovered in 1966.The reservoir has initial pressure of 11,450 psi at 13,300 feet.The pressure-production history of the field from Jan. 66 toSept. 73 was introduced by Stelly & Farshad22. The

complete pressure-production data was presented byRamagost & Farshad3. Volumetric estimate of IGIP is 470BSCF based on core and log data, Many authors3~22havestudied the pressure-production history of the field. Theyestimated an IGIP of 470 BSCF assuming abnormalformation compressibility of 20 x 104psi-1. Ambatha6,however, calculated IGIP between 410-760 BSCF but did notexplain the reservoir producing mechanism. The averageporosity for this reservoir is not reported and Fetkovitch e~af, 7 used formation compressibility of 4 (104) Psi-1 toestimated IGIP of 650 BSCF and an associated water volumeratio of 0,2 using the pressure data above 6850 psi. Theseestimates could have been different if the reservoir pressuredata down to 4170 psi, (Gp = 52% of IGIP), had been used.

P/Z Vs Gp plot of Cajun reservoir, Figure (3), showsdownward curvature, The curvature started at 5827 psi afterthe production of 182 BSCF which represents 39% of theinitial gas in-place. Estimation of IGIP based on early datayield lGIP of 680 BSCF, which is 140?4. the volumetricestimate. Extrapolation of the pressure production data,148-246 BSCF, yield an IGIP of 480 BSCF. Thus, the P/Zplot can not be used to estimate the true initial gas in placeuntil 50°4 of the initial gas in place is produced.

Application of the material balance solution for this reservoir,Figure (4), yields an estimate of IGIP of 462 BSCF and slopeof 5184 bbl/psi, (correlation coet%cient, R=O.9114). Thisestimate of IGIP from material balance agrees with thevolumetric estimate, Analysis of the slope, assuming thereservoir is volumetric, indicated that the reservoir has totaleffective compressibility, 18.37 (10-6) Psi-l, indicatingsupport from water influx. If the reservoir porosity isassumed to be 24°/0 ( Cf =3.5 X 10-6 psi-l), a water volumeof 561 MM bbl is calculated from the slope. This watervolume is equivalent to water to reservoir volume ratio of 2.0.

The downward cuwature in this reservoir of the P/Z Vs Gpplot, Figure (3), was caused by water influx as indicated fromanalysis of the slope of Figure (3). The material balancesolution presented in this paper could estimate the IGIP after16% gas production of the initial in-place compared to 50%gas production from the P/Z Vs Gp plot, Comparison of theresults from the present study as well as the others, table (6),indicate the advantage of the proposed solution to the priorsolutions.

Anderson “L” Reservoir

The Anderson “L” reservoir is an abnormally high pressurediscovered in 1965, with initial pressure of 9507 psi at 11,100ft. The reservoir data and history were presented byDuggan23, It was assumed that the resewoir was depletion

204


drive because the reservoir is separated from other blocks byfaults and analysis of the fluids from surrounding blocksshowed different fluids. The reservoir has 1000 feet or moreof uncompacted shales. It contains retrograde gas that has adew point pressure of 6700 psi. Some wells were producedwith as much as 50 percent draw down. All wells producedwith more than 25 percent draw down are off production.The reservoir was completely abandoned after production of55 BSCF because of excessive water production. The

;;y;-:$;!$’,:,y%y:f ‘he ‘e=woir~kn analyz*The Production mechanism ofthis reservoir is ve~ controversial. Begland and Whitehead4matched the production history using IGIP of 70 BSCF andassuming changing formation compressibility. Poston andChen24, Rarnagost and Farshad3, and Ambatha25 estimatedthe IGIP in the range of 65 to 75 BSCF and reservoircompressibility of 14 (104) Psi-1, but they give noexplanation for the high compressibility. On the other hand,Fetkovitch et al. 7 calculated an IGIP of 76 BSCF and anassociated water volume of 2.25 the reservoir volumeassuming formation compressibility of 3.2 (104) psi-1 byusing a total compressibility match procedure.

The pressure-production history of the reservoir, Figure (5),shows downward curvature. The curvature started at 5764 psiafter production of 257. of the IGIP. Extrapolation ofpressure-production data from P/Z plot below 4766 psi (Gp =23 to 38.6 BSCF) project an lGIP of 75 BSCF. Thus, the P/Zplot could not estimate the true IGIP until 40-50% of theinitial gas in place was produced.

Our material balance solution, Figure (6), shows an interceptof 77 BSCF and slope of 878 bbl/psi, (correlation coefficient,R= O .8276). This estimate of IGIP agrees with those reptedby previous authors3~4~7125.If the reservoir is assumed to bedepletion drive, a total effective compressibility of 13.4 (104)Psi-l is calculated from the slope indicating support fromshale-water influx. A formation compressibility estimatedfrom Hall’s correlation 1 of 3.25 (104) Psi-1 is used tocalculate the volume of the water body from the slope. Watervolume of 60.52 MM bbl’s is calculated. This volume isequivalent to a non-pay sand to reservoir ratio of 0.92.

The estimated IGIP and the non pay sand to resetvoir ratiofrom the current materia[ balance analysis agree with thoseestimated by Fetkovitch et cd,’, table (7). However, thecurrent material balance method is simpler and require noassumption for the IGIP or the size ratio to find a match.The material balance solution discussed in this pa~r couldestimate the IGIP after 150/’ of the initial gas in place isproduced as compared to the 40-50’%. gas production from theP/Z Vs Gp plot. Water influx from non pay sand (Shale) inaddition to the formation of condensate below dew point

have reduced the gas permeability and caused the downwardcurvature of the P/Z Vs Gp.

Miocene Reservoir

Miocene reservoir is abnormally high pressure with an initiatpressure of 10,984 psi. The reservoir is located in SouthLouisiana. Pressure-production data for this reservoir isreported by Burgoyne et al. 20 and Hubble26. The reservoirhas a dew point pressure of 7000 psi. Porosity and watersaturation are not reported but assumed to be 24’XOand 34°/0respectively, as a typical of values for Gulf Coast Reservoirs.IGIP from volumetric data is estimated to be 16 BSCF.

P/Z Vs Gp plot for this resewoir, Figure (7), showsdownward curvature. Extrapolation of pressure productiondata above 8789 psi projects IGIP of 47 BSCF which isoverestimated by a factor of 3, Extrapolation of the lateproduction data (7064 -2723 psi) yield IGIP of 16.2 BSCF.Thus, the correct IGIP could not be estimated from thepressure versus production plot until 40!7. of the IGIP wasproduced.

The result obtained using the material balance solutionpresented in this paper, Figure (8), shows an intercept of11.75 (IGIP) and a slope of 564 bbl/psi. However the plotshows a lot of scatter (coefficient of correlation, R=O.8512).A total effective compressibility of 59.09 ( IOA) psi-l wascalculated from the slope indicating high pressure supportfrom water influx. A formation compressibility of 3.5 (10-

“-1 from Hall correlation 16)psl was used to catculate thevolume of the water body. A pore volume of 77.59 MM bbl’sof aquifer or non pay sands was calculated. This watervolume is equivalent to aquifer to reservoir volume ratio of8.13.

This volume of none-pay sand (shale) is slightly greater thanthe size assumed for the proposed solution in equation (3).Probably, this is the reason for the scatter and lack of fitnessin figure (8). The curvature of the P/Z plot for this resemoirwas caused by intrusion of water influx and formation ofcondensate inside the reservoir. The materiaJ balance solutionpresented in this study could estimate the IGIP after 22?4.gasproduction compared to the P/z plot which could not estimatethe IGIP until 40% of the IGIP was produced. Comparison ofthe results from this study and others are presented in table(8).

CONCLUSIONS

Initial gas in-place for abnormally high-pressured gasreservoirs can not be estimated, from the P/Z Vs Gp plot untilas much as 40 to 507. of the IGIP is produced. The material

205

6 MB SOLUTION FOR HIGH-PRESSURED GAS RESERVOIRS SPE 3ss89

balance solution plot presented in this paper requires neitherprior assumptions (formation compressibility, or aquifer size)nor matching procedure. However, it can be used tosimultaneously estimate the IGIP and a constant (slope) thatcan be used to calculate the aquifer size or non-pay sand, andpredict the reservoir prevailing production mechanism. Thecase histories discussed in this paper showed downwardcuwature of the P/Z Vs Gp plot. These curvatures are causedby water influx from aquifer, water irdlux from shales, andthe formation of condensate below dew-point which reducedthe gas permeability.

ACKNOWLEDGMENT

The author wishes to thank Kuwait University for thefinancial support for this study, research grant No. EPO06.

NOMENCLATURE

aBc

PG

+%pKcMPRsavWeWs

.

.

.

.=

.

.

.

.

.

.

.

.

.

.

.

Aquifer constantFormation volume factorCompressibilityAquifer fimctionInitial gas in-placeCumulative produced gasCumulative produced condensateConversion factorAquifer to reservoir sizeReservoir pressureCoefficient of CorrelationSaturationSlope of MB solutionPore volumeWater intlux from aquiferWater inilux from shale

SUBSCRIPTS

a = aquifere = effectivef = formation

g = gasi = initial

P = pores = shalew = water

1-

2-

3-

4-

5-

6-

7-

8-

9-

lo-

11-

12-

13-

14-

Hasmnerlindl,D. J.: “PredictingGasReserves in AbnonrmllyPressured Reservoirs”, SPE Paper 3479 Presented at the 1971SPE Annual Meeting, New Orleans, Oct. 3-6, 1971.

Roach, R. H.: “Analyzing Geopressured Reservoirs A MaterialBalance Technique”, Unsolicited paper SPE,8868, 1981,

Raraagost, B. P., and Farshad, F. F. : “P/Z AbnormallyPressured Gas Reservoirs”, SPE 10125, Presented at the 50thAnnual Meeting, Ssta Antonio, TX, Oct. 5-7, 1981.

Begland, T. F., and Whitehead W, R., :“Depletion Performanceof Volumetric High Pressure Gas Reservoirs”, SPERE, August1989.279-282

Bernard, W. J.: “Reserve Estimation and Performance Predictionfor Geopressured Gas Reservoirs”, Journal of Pet. Science&Eng, 1(1987) 15-21.

Ambatha, K. A. :“A Type-Curve Matching Procedure forMaterial Balance Analysis of Production Data fromGeopressured Gas Reservoirs”, JCPT, Vol. 30, No. 5, Sept,-Get. t991,61-63.

Fetkovitch, M, J., Reese, D. E., aad Whitson, C, H.:“Application of a General Material Balance for High PressureGas Reservoir”, Paper SPE 22921, Presented at the 66th,%mual Tecluical Conference and Exhibition, Dallas TX, Oct,6-9, 1991.

Elsharkawy, A. M. “Analytical and Numerical Solutions forEstimating the Gas Ia-Place for Abnormal Pressure Reservoirs”,SPE paper No. 29934, 1995.

Rossen, R. H. : “ A Regression Approach to Estimate Gas ln-place for Gas field’, JPT, Oct., 1975, 1283-1289,

Wang, B. and Teasadle, T. S. :“ GASWAT-PC: AMicrocomputer Program for Gas Material Balance with waterIntlux,” SPE 16484, Presented at the Petroleum IndustsyApplication in del Lage On Lake Conroe, Montgomery.

Wallace, W. E.:” Water production from Abnormally Pressuredgas Reservoirs in South Louisiana”, JPT, August 1969,969-983.

Harville, D. W., and Hawkins, M. F.: “Rock Compressibilityand Failure as Reservoirs Mechanisms in Geopressured GasReservoirs”, JPT, Dee., 1969, 1528-1550.

Jogi, P. N., Gray, K. E. , and Ashman, T. R.: “ CompactionMeasurements on Cores from the Pleasant Bayou Wells”, Proc.of the 5th Conference of Geopressured-Geothermal Energy,Oct. 13-15, 1981, Baton Rouge, Louisiana

Sinha, K. P. , Holland, M. T., Borschel, T, F. and Schatz, J. P.:”Mechanical and Geological Characteristics of Rocks Samples

206


15-

16-

17-

1tl-

19-

20-

21-

22-

23-

24-

25-

26-

from Sweezy No, I Well at Parcperdue GeopressuredGeothermal Sit. US Department of Energy, 1981.

Brown-Scomb, E. R., Collins, F. :“Estimation of Reserve andWater Drive from Pressure and Production Historyn, Trans.AIME ( 1949), Vol. 186,92-94.

Van Everdirgen, A, F., Timmerman, E. H., and Mc Mahen, J. J,“Application of Material Balance Equation to Partial Water”,b(1953) Vol. 198, 51.

Mc Ewerr, C. R. :“Material Balance Calculations with WaterJnflux in the Presence in Uncertainty in Pressures”, Sot. Pet.Eng. J. , June 1962, 120-128.

Havlena, D., and Odeh, A. S. :“The Material Balance Equationas an Equation of Straight Line”, JPT (August 1963), 896-900.

Wall, C. G., and Craven-Walker, A. :“Material BalanceAnalysis of Partial Water Drive Reservoirs”, Journal of theInstitute of Petroleum, Vol. 53, No (528) December 1967,408-412.

Ehrrgoyne, A. I., Hawkins, M. F., Lavaquail, F. P., andWickenhauser, T. L. :“Shale Water as a Pressure SupportMechanism in Super Pressure Reservoirs”, SPE 3851,1972.

Hall, H. N. :“Compressibility of Reservoir Rocks”, Trans.,AJME(1953), 198, 309-311.

Stelly, O. V., and Farshad, F. F. :“Predicting Gas In-Place inAbnormal Reservoirs”, Pet. Eng. M., June 1981, 104-110

Duggan, J. O.: “The Anderson L - An Abnormally PressuredGas Reservoir in South Texas”, JPT, Feb. 1972, P 132-138

Poston S. W., and Chen, H. Y.: “The SimultaneousDetermination of Formation Compressibility and Gas Irr-Placein Abnormal Pressure Reservoir”, SPE 16227, 1987.

Ambatha, A. K.: “Evaluation of Material Balmce Analysis forVolumetric Abnormally Pressured Gas Reservoir”, JCPT, Vol.32, No. 8, 1993, 19-2

Hubble. O. A. :’in Situ Calculation of Average Effective ShaleCompressibility”, MS thesis, IJniversity of H;uston, 1971.

APPENDIX-SAMPLE CALCULATION

NS2B Reservoir

Intercept (IGIP) = 121 BSCF

Slope = 1983 bbl/psiInitial pressure = 8921 psiTemperature = 240 Deg. FGas Dev. Fat., Z = 1.473

7Z 5.04 (240 + 460) 1,473Bgi= 5.04— =

~ 8921

‘gi = 0“589 bbw CF

~B

slope = (—,_~’’)ce+cava+csv5w

1. Assuming no water influx from shale or aquifer

G Bg,slope = — Ce

l-SW

1983 =121(109) 0.589(10-3) c

(1 - 0.34) e

Ce = 18.36 (10-6) Psi-l

The effective compressibility is high indicating support

from aquifer,

II. Assuming water influx from aquifer(GWC at 12,580 ft).

SWCW+ Cf 0,34x3,0528Ce = 6.916 (10-6)Psi-1

l-SW = 1-0,34 =Ca = Cw + “Cf =3.05 +3.58 = 6.S78 (10-6 )Psi - 1

,

slope = (~ ) Ce + Cavaw

121(10’ )0.589( 10-3)1983 =

(1-0.34)6.916 (10+) +

6.578(104) Va ‘

Va = 188 MM bbl’s

Reservoir pore Volume = (G Bgi/l-Sw)

= 121.589/(1 - .34)

= 108 MM bbl’s

Aquifer to reservoir vohrme ratio,

~=1.74‘alvRes, = ,08

207

8 MB SOLUTION FOR HIGH-PRESSURED GAS RESERVOIRS SPE 36689

Table 1- Pressure-production History for NS2B Reservoir

I Pressure z Cumulative GasPsia Production **

BSCF8921 1.473 0.008845 1.465 0.668322 1.400 3.337417 1,288 10.406838 1.219* 15.596064 1.130* 23.975490 1.075* 27.85478 I 0.967 33.7

I 4104 0.887 40<1* two phase Z factor** include condensate

Table 2- Pressure-production History for Cajun Field

Pressure z Cumulative GasPsi Production BSCF

11444 1.496 010674 1.438 101013192538574790673806847

.397 29

.330 56

.280 78

.230 101

.192 120

.154 1456388 1.122 1615827 1.084 1825409 1.057 1985000 1.033 2164500 1.005 2364170 0,988 246

208


Table 3- Pressure-production History for Anderson “L” Reservoir

BHP z Cumulative Condensate(Psia) Factor Gas (M bbl’s)

productionm cm

950792928970859583328009760374067002672155355764476642953750

1.4401.4181.3871.3441.3161.2821.2391.2181.1761.1471.1271.0480.9770.9280.891

0392.51642.23225.84260.35503.57538.18749.210509.311758.912789.217262.522890.828144.632566.7

029.9122,9240,9317,1406.9561.2650,8776,7864,3939.51255.31615.81913.42136.0

3247 0.854 36819.9 2307.8

Table 4- Pressure-production history for Miocene Reservoir

Pressure z Total Gas ProductionPsi BSCF

10984 i .650 0.00010156 1,580 0,4829924 1.560 0.6489703 1.540 0.8508936 1.490 2.5059222 1.460 2.6348789 1.440 3.3668313 1,390 3.9577064 1.250 5,2516250 1,150 6,0864928 0.960 7,6082723 0.880 10.589

209

10 MB SOLUTION FOR HIGH-PRESSURED GAS RESERVOIRS SPE 355B9

Table 5- Material Balance Results for NS2B Reserwoir (Volumetric estimate = 114 BSCF)

I IGIPAuthors BSCF

Ramagost & Farshad (1981)Present study

114121

Assumptions I Production Mechanism

Cf-= 28xIO+ Psi-l Assume rock collapseShale prOpWtleS, Csh, Ksh, Shale water influxVshCf =25 x 10-6 Psi”l... .. .. .. .. . . . .. . . . . . .. . . . . .. . .

Assume reek collapseWater to reservoir volume= 1.74

I

Table 6- Material Balance Results for Cajun Field ( Volumetric estimate = 470 BSCF)

Authors

Stelly & Farshad (1981)Ramagost&Farshad(1981)Fetkovitch et al, (1991)Ambatha (199l)Present study

IGLP,BSCF

470470650410-650462

Assumptions

Cf = 26x104 Psi-lCf= 19x10% Psi-lWater to reservoir volume= 0.2Volumetric reservoir.. .. ..... .. ..... ...... .. .. ..- ----

Production Mechanism

Assume rock collapseAssume rock collapseWater influx----------------------------

Water to reservoir volume= 2.0

Table 7- Materiat Balance Results for Anderson “L” Reservoir ( Volumetric estimate= 70 BSCF)

Authors

Ramagost&Farshad(1981 )Begtand & Whitehead (1989)

Fetkovitch et al. (J991 )Ambatha (1993)Present study

IGIP,BSCF

7070

7657-103

77

Assumptions

Cf = 15x10-6 Psi-lVariable rock and watercompressibilitiesWater to reservoir volume= 2.25Volumetric reservoir-------------------------- -------

Production Mechanism

Assume rock collapseAssume rock collapse

Water influx. .... .. .. .-----------------

Water to reservoir volume= 1.92

Table 8- Material Balance Results for Miocene Reservoir (Volumetric estimate= 16 BSCF)

IGIP, BSCFAuthors Assumptions Production Mechanism

Burgoyne et al (1972) 16 Shale properties, Csh, Ksh, Shale water influx

VshPresent study 11.75 . ..... .. . . . . . . . . . . . . . . . .. .. . . . . . . Water to reservoir volume= 8.13

210

SPE 3S589 ADEL M. ELSHARKAWY 11

7000

6000

5000

“~ 4000

$3000

2000

1000

0

8000

6000

z‘- 4000&L

2000

0

0 50 100 150 200 250Gp, BSCF

Fig. l-P/Z Vs Gp for NS2B reservoir,Ossun field

~-----

0 100 200 300 400 500 600 700GP , BSCF

Fig. 3-P/Z VS Gp for Cajun reservoir

200

I

7.~ 15(J

(IJ Y =1983x+121m R2 = 0.8276>“ 100

IO* —+––——--–-+-—--—–—0.00 0.02 0.04 0.06

X, PS1/BBUBSCFFig. 2- Material Balance Solution plot for

NS2B Resetvoir

4500

; 400

:. 300 I

I200

y = 5184.3x+ 462.04

R2 = 0.9114

{100 IIo -—----- - -—+---~–– 1

0.00 0.02 0.04 0.06X, PS1/bbl/Bscf

Fig. 4- Material Balance Solution Plot forCajun Reservoir

211

7000

6000

5000

zn 4000

NQ 3000

2000

1000

0 1

0 20 40 60 80 100 120 140GP, BSCF

Fig5-P/Z VSGPfor Anderson “L”Reservoir

7000

6000

5000

‘g 400(3

g 3000”

2000

1000

005101520253035404550

GP, BSCF

Fig. 7-P/Z Vs Gp for Miocene Reservoir

120

100- -

~80- -

~60- - y= 878.34X+ 77.282

’40- -R’= 0.9324

20t i

0.00 0.01 0.02 0.03 0.04 0.05

X, PWBBUBSCF

Fig. 6-Material Balance Solution plot forAnderson “L” reservoir

50 1 f

45

40

1/

@35

~ 30 e y=563.94x+ 11.75

~ 25 R2 = 0.8512

>- 20

‘L-J2d0.00 0.02 0.04 0.06 0.08 0.10

X, PSHBBUBSCF

Fig. 8- MaterialBalance Soltuion Plot forMiocene Reservoir

212

Documents

Material balance