spe-56690-ms

Copyright 1999, Society of Petroleum Engineers Inc.

This paper was prepared for presentation at the 1999 SPE Annual Technical Conference andExhibition held in Houston, Texas, 3–6 October 1999.

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AbstractThis work presents application of a new material balancemethod to detect aquifer influence and calculate water influxand original gas in place for four over-pressured reservoirs.Calculation of water influx needs to satisfy a set of threeequations as opposed to the existing method of one equationof unit slope. In each application, the presence of aquiferinfluence was identified first, and then material balance wasused to determine original gas in place and water influx. Theoverpressure effect was handled by integrating rockcompressibility over operating reservoir pressure.Compositional effects were modeled with Rv (volatile oil/gasratio) by matching PVT data using Walsh-Towler algorithm oran Equation-of-State. This new method is internallyconsistent, which avoids potential pitfalls of existing methods.Comparison with other methods in analyzing overpressurereservoirs shows this new method is more robust andcomprehensive.

IntroductionOne of the most difficult problems in material balancecalculation is to determine the original gas in place (OGIP)and water influx for over-pressured, retrograde gas condensatereservoirs with water influx effects. The technical difficultiesinclude (1) how to estimate an effective average rock orformation compressibility, (2) how to incorporatecompositional effects and (3) how to detect and estimate waterinflux effects for over-pressured reservoirs. The theory of ageneralized material balance method (1, 2, 3) has recentlybeen developed to incorporate all of these effects into a linearequation.

This work applies the newly developed method to detectaquifer influence and calculate water influx and original gas in

place of four over-pressured reservoirs. Calculation of waterinflux needs to satisfy a set of three equations as opposed tothe existing method of one equation of unit slope.

In each application, the presence of aquifer influence wasidentified first, and then material balance was used todetermine OGIP and water influx. The overpressure effectwas handled by integrating rock compressibility overoperating reservoir pressure or by using higher effectiveaverage rock compressibility. Compositional effects weremodeled with Rv (volatile oil/gas ratio) by matching PVT datausing Walsh-Towler algorithm or an Equation-of-State.

The first reservoir is non-volumetric and produces rich gascondensate. The initial gas in place was estimated withvariable rock compressibility, and late-time water influx. Thesecond reservoir is also non-volumetric, producing rich gascondensate and the overpressure effect was modeled by amethod similar to the first example. This new methodpredicted strong aquifer influence, which was confirmed laterby additional production data.

The third reservoir is tight and non-volumetric, producinglean gas condensate from two wells. We estimated OGIP withaverage effective rock compressibility and late-time waterinflux. Detection of aquifer influence by this new method wasalso supported by analysis of two pressure build-up tests forone of the major producers.

The fourth reservoir is volumetric, producing lean gascondensate. A P/Z vs. Gp plot shows a line with dual slopes.The new method, after correcting the overpressure effect,gives OGIP in excellent agreement with extrapolated P/Z plotfrom the normal pressure gradient segment.

Comparison of this new method with other existingmethods is included in this work. It will become clear in latersections that many of the existing methods can only handlesome but not all of the technical difficulties mentioned above.

ObjectivesThe objectives of this study are (1) to apply a newly developedmaterial balance method to determine the initial fluid in placeof over-pressured gas condensate reservoirs, (2) to present arefined method to estimate water influx for over-pressuredreservoirs, and (3) to compare this new method with existingmethods in estimating effective rock compressibility for over-pressured reservoirs.

SPE 56690

Analysis of Overpressured Reservoirs with A New Material Balance MethodS. W. Wang, SPE, V. M. Stevenson, SPE, C. U. Ohaeri, SPE, D. H. Wotring, SPE, Unocal

2 [S-W Wang, V. M. Stevenson, C. U. Ohaeri, D. W. Wotring] [SPE 56690]

FormulationThe following equations summarize the newly developedmaterial balance method for normally and abnormally-pressured gas condensate reservoirs. Detailed derivation ofthese equations is given in reference (1, 2, 3) and definition ofeach symbol is given in nomenclature.

pegfgiofoi WWEGENF −++= (1)

The plotting variables F, Eo, and Eg are expressed inequations (2) through (6), which can be calculated fromproduction data, PVT data, and rock compressibilityexperimenrt.

−−+−=

sv

gspspsvop

RR

BRRRRBNF

1

)()1((2)

[ ]βα −−−= 1oioo BBE (3)

[ ]βα −−−= 1gigg BBE (4)

wc

P

Pi

f

S

dPC

−

−=

∫1

)exp(1

α (5)

wc

iwwc

S

PPCS

−−=

1

)(β (6)

. Notice that the initial gas in place of gas-condensatereservoirs calculated by this method is the amount of free gas,not wet gas originally in the reservoirs. The condensatecontent in the initial reservoir fluid can be calculated by theproduct of Gfgi* Rv or G*Rv.

Detection and Calculation of Water InfluxA refined method to estimate water influx can be derived byrearranging equation (1) as follows:

g

e

g

ofoifgi

g

p

E

W

E

ENG

E

WF ++=+(7)

If there is no free oil initially in the reservoir, thenequation (7) can be degenerated to equation (8).

g

e

g

p

E

WG

E

WF +=+(8)

The advantage of equation (8) is its sensitivity in detectingpresence of aquifer influence. In order to detect presence ofwater influx, one can plot (F+Wp)/Eg vs. Eg by assuming We

=0. If there is no water influx, equation (8) will yield a

horizontal line. Otherwise, it suggests presence of waterinflux. This method can be used to diagnose presence ofaquifer influx at its early stage.

According to equation (8), a plot of (F+Wp)/Eg vs. We/Eg

will yield a straight line of unit slope and the intercept givesthe initial gas in place, G, if an appropriate aquifer model ischosen to fit the production data. In tuning the aquifer model,the calculated water influx, We, should satisfy two additionalequations to ensure a physically correct aquifer model asfollows:

0≥−+ ep WWF (9)

GE

WWF

g

ep =−+(10)

Since regression analysis is used to find a best fit ofequation (8), it often occurs that a straight line can be obtainedwith a nonzero intercept G but with water influx We beinggreater than total fluid withdrawal, (F+Wp). When thishappens, equation (10) can not be satisfied because it givesnegative G. Equation (9) must be satisfied to ensure thatequation (10) will give the same initial gas in place as thatobtained by equation (8). Therefore, equations (8), (9), and(10) should be satisfied simultaneously when tuning an aquifermodel in material balance calculation.

Comparison of this new method with Fetkovich and Reesemethod (4) and Guehria method (5) is described in reference(1). In this work, we focus our comparison with Ramagostand Farshad method (6), and solution plot method.

Ramagost and Farshad MethodIn 1981, Ramagost and Farshad (6) developed a calculationprocedure for analyzing the performance of over-pressured gasreservoirs under pressure depletion. Their equation is givenbelow:

( )GZ

GP

Z

PPP

S

CSC

Z

P

i

pi

i

ii

wc

fwcw −=

−

−+−

11 (11)

The above material balance equation permits calculation ofG (OGIP) when Gp, Cf, Swc, and Z values are treated as inputvariables. The plotting variable are X = Gp and Y = left handside of equation (11). G can be calculated from the slope ofthe X-Y plot.

However, it is not easy to apply equation (11) to gasreservoirs when compositional and water influx effects arepresent. The modified version of Ramagost and Farshadmethod (6) is the solution plot method.

Solution Plot MethodOne major difficulty in studying over-pressured reservoirs isto estimate effective rock compressibility. The generalizedmaterial balance equation can be reformulated so that it can be

[SPE 56690] [Analysis of Overpressured Reservoirs with A New Material Balance Method] 3

fC

fC

used to estimate effective rock compressibility independent ofestimating initial gas in place. This concept was firstrecognized by Roach (7) and the utility of the concept wasexpanded by Poston et al. (8) and Poston and Chen (9, 10).Roach’s concept is to formulate the generalized materialbalance method so that the input variables are production,pressure, and Z-factor and the outcome variables are initial gasin place, rock compressibility, and water influx.

We can obtain Roach’s formula by reformulating equation(1) as follows: For gas reservoirs, Nfoi is zero and equation (1)can be simplified to become equation (12).

peggp WWGEBGF −+== (12)

The gas formation volume factor Bg can be expressed as

PP

ZTTB

sc

scg = (13)

When Cf (P) in equation (5) is replaced by an averagevalue, and use first order approximation of the

exponential function in equation (5), weobtain equation (14).

wc

if

S

PPC

−−=

1

)(α (14)

Combining equations (6), (12), (13), and (14), we haveequation (15).

( )e

gi

pe

i

ip

i

iC

PGB

WW

PPZ

ZP

G

G

PPZ

ZP −∆

−−∆

=

∆

− 11

1 (15)

where ∆P = Pi – P and Ce is defined as

wc

wwcfe

S

CSCC

−+=

1(16)

Equation (15) is the formula originally proposed by Roach(7). We define two plotting variables X and Y as follows:

P

G

PZ

ZPX

p

i

i

∆

= (17)

PPZ

ZPY

i

i

∆

−= 1

1 (18)

A plot of Y vs. X will give a straight line whose interceptis Ce under pressure depletion production, i.e. We - Wp= 0.Then can be calculated from Ce via equation (16).

ApplicationsExample 1: Over-Pressured, Rich Gas CondensateReservoirThe reservoir temperature is 2290F and the initial pressure was7,244 psia at depth of 10,400 ft, which gives a pressuregradient of 0.697 psia/ft. The reservoir is a rich gascondensate with an initial yield of 169 STB/MMSCF dry gas.

Pore volume compressibility and excess stress of coresamples were measured in laboratory. Table 1 shows themeasured excess stress, hydrostatic pore volumecompressibility, calculated uniaxial pore volumecompressibility, and their corresponding reservoir pressure.The uniaxial pore volume compressibility (Cf) is modeled witha third order polynomial of fluid pressure, shown in equation(19). Equation (5) was used to integrate Cf from Pi to P inorder to correct pore volume reduction due to pressure declinein production.

The hydrostatic pore volume compressibility isapproximately twice the uniaxial pore volume compressibilityfor net overburden pressure from 1000 to 9000 psi. Initiallywe thought the uniaxial pore volume compressibility wasmore representative of rock compacting process. Due todrastic pressure reduction observed since 1998, we increasedCf by two folds, which is almost the same as hydrostatic porevolume compressibility in final material balance calculation.

69213317 100.2100.4100.9100.6 −−−− −+−= xPxPxPxCf (19)

PVT properties consist of measured CCE (constantcomposition expansion), CVD (constant volume depletion)and separator tests. Walsh-Towler algorithm (11) was used totransform compositional effects into pseudo-black oil PVTproperties for material balance calculation.

The initial connate water saturation was estimated at 45%and expansion of formation water (Cw = 3.0x10-6 1/psi) wasincluded in material balance calculation. Presence of waterinflux can be detected by plotting (F+Wp)/Eg vs. Eg, whichgives a non-horizontal line as shown in figure 1. The water-influx effect can also be inferred from the solution plot, figure2. According to Poston and Berg (12), the early horizontalpart of figure 2 represents a transient period, the curve thenmoves upward diagonally, representing a pressure-depletionperiod, finally, the curve diverges rightward from thediagonally upward trending line, representing water influxeffect

The inverse slope of the solution plot method gives theinitial gas in place. However, it does not give the same initialgas in place as that obtained by this new method. Thedifference may be caused by retrograde condensate behavior,which can not be handled by the solution plot method.

A finite aquifer with RD=5 and Carter-Tracy method wereused to calculate water influx. Results of material balancecalculation and PVT properties are shown in table 2 and figure3. Using production data from 1994 to March 1998, weestimated IGIP to be 101.5 BSCF dry gas. However, pressuresurveys in 1998 suggested a smaller reservoir than we


estimated earlier. The final estimated IGIP was reduced to 72BSCF dry gas as seen from the last flattened section of figure3. The estimated original condensate content is 12.2 MMSTB. This sudden reduction in estimated OGIP is probablylinked to formation failure since ductile failure was observedat net overburden pressure of 7,000 psi (equivalent to fluidpressure = 3,520 psi) in laboratory. In addition we alsoobserved significant increase in sand production since 1998.

In this example, we also examined the trend of P/Z plot,shown in figure 4. In analyzing P/Z plot, cumulative wet gasproduction is the sum of cumulative dry gas and equivalentgas of retrograde condensate liquid and Z factor should betwo-phase Z factor since reservoir pressure has dropped belowdew point. Results of P/Z analysis is shown in table 3. TheP/Z plot shows a line of dual slopes. Using the last four datapoints in table 3 or figure 4, we estimated IGIP to be 74.4BSCF wet gas. The mole fraction of dry gas in the originalwet gas is 88.15%. Hence, P/Z plot predicts IGIP to be 65.6BSCF dry gas.

Example 2: Over-Pressured, Rich Gas CondensateReservoirThe reservoir temperature is 2380F and the initial pressure was8,973 psia at depth of 11,414 ft, which gives a pressuregradient of 0.786 psia/ft. The reservoir is a rich gascondensate with an initial yield of 169 STB/MMSCF dry gas.

In this example, CVD test was not measured. Peng-Robinson EOS (equation-of-state) was first used to matchCCE test, and then it was used to predict CVD test atunmeasured pressures. Walsh-Towler algorithm (11) wasused to transform compositional effects (simulated CVD test)into pseudo-black oil PVT properties for material balancecalculation.

Pore volume compressibility was not measured inlaboratory. Rock compressibility was modeled by the samepolynomial as that used in example 1. This assumption isbased on geological interpretation that this reservoir isseparated from the reservoir in example 1 by a fault.

Detection of aquifer influence can be seen from plot of(F+Wp)/Eg vs. Eg, and plot of P/Z vs. Gp as shown in figures 5and 6, respectively. Figure 5 shows an upward trending, non-horizontal curve and P/Z plot shows a curve with multiplesegments of reduced slopes. Both plots suggest presence ofwater influx. In this example, the solution plot shown infigure 7 is not very informative because it is essentially ahorizontal line.

The initial connate water saturation was estimated at 45%and expansion of formation water (Cw=3.0x10-6 1/psi) wasincluded in material balance calculation. Carter-Tracy methodand an aquifer of infinite strength were used to calculate waterinflux. Results of material balance calculation and PVTproperties are shown in table 4 and figure 8. Figure 8 shows astraight line with unit slope and an intercept, which gives theinitial gas in place to be 27 BSCF dry gas. The initial gascondensate content is 4.6 MM STB. OGIP derived fromfigure 8 is consistent with that from figure 9, a plot of (F+Wp-We)/Eg vs. Eg.

Example 3: Over-Pressured, Lean Gas CondensateReservoir

The reservoir temperature is 2800F and the initial pressurewas 11,384 psia at depth of 11,640 ft, which gives a pressuregradient of 0.8346 psia/ft. The reservoir is a lean gascondensate with an initial yield of 32 STB/MMSCF dry gas.

PVT properties consist of measured CCE, CVD andseparator tests. Walsh-Towler algorithm (11) was used totransform compositional effects into pseudo-black oil PVTproperties for material balance calculation. Pore volumecompressibility was not measured in laboratory. A rockcompressibility, Cf = 3.7x10-6 1/psi, was used in materialbalance calculation over the entire pressure range of interest.

The initial connate water saturation was estimated at 55%and expansion of formation water (Cw = 3.5x10-6 1/psi ) wasincluded in material balance calculation. Presence of waterinflux can be detected by plotting F/Eg vs. Eg and P/Z vs. Gp asshown in figures 10 and 11, respectively. Figure 10 shows anupward trending, non-horizontal curve, and figure 11, P/Zplot, shows a curve with multiple inflection points, i.e. a curvewith gradually reduced slopes. Both figure 10 and figure 11indicate presence of water influx effect. However, thesolution plot is not indicative for water influx because the Yvalues are almost constant as shown in the last column of table5. According to Poston and Chen (8, 9, 10) that the initial flatregion in solution plot could mean transient behavior orpossible influence of water influx. Carter-Tracy method and afinite aquifer with RD = 5 were used to calculate water influx.

Detection of aquifer influence is also supported by resultsof pressure build-up tests. Figure 12 is a buildup testconducted on a major producing well in 1993 prior to puttingthis well on production. Figure 13 is a buildup test conductedon the same well in 1998. In figure 12 a radial flow period isevident in the segment labeled AB. After this, a slight upwardtrend can be seen on the pressure derivative. Because noknown geological feature could explain this pressure response,we suspected this might be due the influence of an aquifer onthe gas reservoir pressure response. The estimated distance tothe water zone was 484 feet. The buildup response in figure13 is very different from figure 12. It confirmed the presenceof an aquifer near the well. There is no distinguishable radialflow period as the pressure buildup response is dominated firstby changing well bore storage and immediately after by thewater zone. Our best estimate of the distance to the waterzone at this time is less than 50 feet. Notice that figures 12and 13 are placed after figure 20 at the end of this paper due totheir sizes.

Results of material balance calculation and PVT propertiesare shown in table 5. Estimated IGIP can be derived from theintercept of a best-fit straight line shown in figure 14.Consistency check is shown in figure 15, which gives almostidentical result as that obtained from figure 14. The estimatedinitial gas in place is 21.3 BSCF dry gas. The initialretrograde gas condensate content is 0.68 MM STB.


Example 4: Over-Pressured, Lean Gas CondensateReservoir

The reservoir temperature is 2500F and the initial pressurewas 10,485 psia at depth of 14,000 ft, which gives a pressuregradient of 0.749 psia/ft. The reservoir is a lean gascondensate with an initial yield of 8.5 STB/MMSCF dry gas.

No PVT tests is available for the reservoir fluid. Gasphase Z factor was calculated from gas analysis andcorrelations. Liquid condensate has an estimated molecularweight of 159.2 and a gravity of 44.1 API. Cumulative liquidcondensate production was converted into equivalent gasproduction, shown in “equivalent gas” of table 6 and wasincluded in cumulative gas production (Gp) to obtain totalfluid withdrawal, (Ftotal = Gp + equivalent gas + Wp) in table 6.

Pore volume compressibility was not measured inlaboratory. Rock compressibility was modeled with highaverage rock compressibility (Cf = 2.5x10-5 1/psi) over theentire pressure range of interest. Rock compressibility wasestimated to be 1.5x10-5 1/psi from the solution plot, figure 16,which shows only the last four data points.

The initial connate water saturation was estimated at 20%and expansion of formation water (Cw = 2.85x 10-6 1/psi) wasincluded in material balance calculation.

Presence of water influx can be detected from figure 17, aplot of (F+Wp)/Eg vs. Eg. It is believed that influence of waterinflux is insignificant in this example since the data points infigure 17 essentially form a horizontal line. The solution plot,figure 18, also shows no water influx effect since the curvedoes not develop clearly rightward divergence.

Results of material balance calculation and calculatedPVT properties are shown in table 6. The initial gas in placewas estimated to be 48.1 BSCF dry gas according to figure 19,a plot of (F+Wp) vs. Eg. The initial gas condensate content is0.41 MM STB. When we extrapolate the second segment ofthe P/Z plot, figure 20, the intercept gives an initial gas inplace of 47 BSCF dry gas. The agreement between P/Z plotand this new method is very good.

Conclusions(1) This work presents an improved method to detect and

calculate water influx for over-pressured reservoirs,retrograde gas condensate reservoirs in materialbalance calculation.

(2) When tuning an aquifer model, equation (8), a plot of(F+Wp)/Eg vs. We/Eg, yields a straight line of unitslope and an intercept which gives G, original gas inplace. Equations (9) and (10) then serve asconsistency check for the validity of G calculatedfrom equation (8). The aquifer model must satisfythese three equations simultaneously.

(3) This new method is more robust and comprehensivethan other existing methods in analyzing water influxand compositional effects.

(4) The effective rock compressibility can be determinedindependently by equation (15), which also known assolution plot method suggested by Roach (7) and

Poston et al (8, 9) with sufficient and well-behavedpressure data.

(5) However, the solution plot method is not alwaysindicative and conclusive in calculating rockcompressibility and in detecting water influx effect forfollowing reasons: (a) it requires many good pressuremeasurements which are often not available, (b) astraight line can not be drawn definitely to determineeffect rock compressibility, (c) the method does notinclude retrograde condensate effects, and (d) it is notcapable of predicting future water influx.

(6) If laboratory measured Cf is not available, we suggestuse Cf in the order of 10-5 1/psi for over-pressuredreservoirs in material balance calculation to avoidoverestimating OGIP. Our suggestion seems to beconsistent with the examples presented in this workand those listed in reference (12).

NomenclatureBg = gas formation volume factor, RB/SCFBgi = Bg at initial reservoir pressure, RB/SCFBo = oil formation volume factor, RB/STBBoi = initial oil formation volume factor, B/STBCf = rock compressibility, 1/psiCw = water compressibility, 1/psi

CGP = cumulative gas production COP = cumulative oil production CWP = cumulative water production

Eg = net gas expansion, RB/SCFEo = net oil expansion, RB/STBF = total hydrocarbon withdrawal, RBG = original gas in place, SCF

Gfg = gas in free-gas phase, SCFGfo = gas in free-oil phase, SCFGp = produced wellhead gas, SCFN = initial oil in place, STB

Np = cumulative produced oil, STBNfo = oil in free-oil phase, STBNfoi = initial oil in free-oil phase, STB

P = pressure, psia PD = dimensionless pressure

Psc = Fluid pressure at standard condition, 14.7 psia RD = ratio of radius of aquifer to radius of reservoir Rp = cumulative produced wellhead gas-oil ratio,

SCF/STBRps = cumulative produced sales gas-oil ratio, SCF/STBRs = solution oil-gas ratio, SCF/STBRv = volatile oil-gas ratio, STB/SCF

Swc = connate water saturation TD = dimensionless time

Tsc = temperature at standard condition, 0R We = water influx, RB

Wp = water production, RBZ = gas compressibility factorZ2 = two-phase compressibility factor


AcknowledgmentsThe authors thank Unocal Corporation for permission topublish this paper.

References:1. Wang, S. W., “A General Material Balance Method

for Normally and Abnormally Pressured PetroleumReservoirs”, SPE48954, 1998 SPE Annual TechnicalConference, New Orleans, LA, 27-30 September1998.

2. Walsh, M. P. Ansah, J., and Raghavan, R., “The New,Generalized Material Balance as An Equation of aStraight Line: Part 1 – Application to UndersaturatedReservoirs”, SPE27684, 1994 SPE Permian Basin Oiland Gas Recovery Conference, 16-18 March 1994.

3. Walsh, M. P., Ansah, J., and Raghavan, R., “The New,Generalized Material Balance as An Equation of aStraight Line: Part 2 – Application to Saturated andnon-Volumetric Reservoirs”, SPE 27728, 1994 SPEPermian Basin Oil and Gas Recovery Conference, 16-18 March 1994.

4. Fetkovich, M. J., and Reese, D. E., “Application of aGeneral Material Balance for High-Pressure GasReservoirs”, SPE-22921 presented at SPE 66th AnnualTechnical Conference, Dallas, Texas, October 6-9,1991.

5. Guehria, F. M., “A New Approach to P/Z Analysis inAbnormally Pressured Reservoirs”, SPE 36703presented in 1996 SPE Annual Technical Conferencein Denver, Colorado, October 6-9, 1996.

6. Ramagost, B. P., and Farshad, F. F., “P/Z AbnormallyPressured Gas Reservoirs”, SPE-10125, 1981 SPEFall Meeting, San Antonio, Texas, 5-7 October 1981.

7. Roach, R. H., “Analyzing Geopressured Reservoirs –A Material balance Technique”, SPE-9968, 1981

8. Poston, S. W., Chen, H. Y., and Akhtar, M. J.,“Differentiating Between Formation Compressibilityand Water Influx in Overpressured Reservoirs”,SPERE (August 1994), 183.

9. Poston, S. W., and Chen, H. Y., “The SimultaneousDetermination of Formation Compressibility and Gas-in-Place in Abnormally Pressured Reservoirs”, SPE-16227, 1987 SPE Production Operations Symposium,Oklahoma City, Oklahoma, 8-10 March.

10. Poston, S. W., and Chen, H. Y., “Case History studies:Abnormal-Pressured Gas reservoirs”, SPE-18857,1989 SPE Production Operations Symposium,Oklahoma City, Oklahoma, 13-14 March.

11. Walsh, M. P., and Towler, B. F., “Method ComputesPVT Properties for Gas Condensate”, Oil and GasJournal, July 31, 1995, pp. 83-86.

12. Poston, S. W., and Berg, R. R., “Overpressured GasReservoirs”, Publisher: Society of Petroleumengineers, 1997, Richardson, Texas, U.S.A.

Table 1: Rock Compressibility Measurement,Example 1

(Reference depth at 10520.5 ft)net stress hydrostatic Cf uniaxial Cf fluid pressure

psi 1/psi 1/psi psi

200 4.70E-05 2.68E-05 10,321

1,000 4.35E-06 2.48E-06 9,521

2,000 2.86E-06 1.51E-06 8,521

3,000 3.05E-06 1.74E-06 7,521

4,000 4.15E-06 2.37E-06 6,521

5,000 5.61E-06 3.20E-06 5,521

6,000 7.30E-06 4.16E-06 4,521

7,000 1.35E-04 7.68E-05 3,521

8,000 7.22E-05 4.14E-05 2,521

9,000 4.41E-05 2.51E-05 1,521

Table 3: Analysis of P/Z Plot, Example 1

Date P/Z2 cum drygas

cum oil cum oil cum wetgas

BSCF moles bscf bscf

2-Jul-94 5700.6 0.00 0.00E+00 0.00E+00 0.000

1-Mar-95 5682.7 0.00 1.52E+05 5.75E-02 0.058

28-Jun-95 5679.1 0.73 2.44E+05 9.26E-02 0.826

7-Dec-95 5660.9 1.15 3.78E+05 1.43E-01 1.294

3-Mar-96 5574.3 3.07 9.88E+05 3.74E-01 3.445

11-Jul-96 5471.5 5.96 1.89E+06 7.16E-01 6.676

18-Dec-96 5307.2 10.16 3.19E+06 1.21E+00 11.371

15-Aug-97 4888.2 19.82 5.77E+06 2.19E+00 22.006

18-Mar-98 4536.0 23.84 7.62E+06 2.89E+00 26.726

19-Jun-98 3908.2 28.09 8.31E+06 3.15E+00 31.238

30-Oct-98 2802.7 41.20 9.07E+06 3.44E+00 44.638

Table 2: PVT Properties and material Balance Calculation of Example 1

Date cum oil cum gas cum water P Z2 Rps Rs Rv Bo Btg F+Wp Integ2(Cf)

bbl MCF bbl psia SCF/STB scf/stb stb/mmscf RB/STB RB/MSCF MM RB

2-Jul-94 0 0 0 7229 1.2682 0 5889 169.8 0.689580 0.000 0.0

1-Mar-95 70,980 378 352 7151 1.2584 6425 5889 169.8 0.692668 0.001 -0.00040

28-Jun-95 114,411 733,246 537 7135 1.2564 6409 5889 169.8 0.693283 0.509 -0.00048

7-Dec-95 177,161 1,150,426 713 7057 1.2467 6494 5889 169.8 0.696359 0.802 -0.00087

3-Mar-96 462,236 3,070,937 2,017 6702 1.2023 6644 5889 169.8 0.710367 2.184 -0.00262

11-Jul-96 883,956 5,959,786 4,690 6312 1.1536 6742 5889 169.8 0.725755 4.330 -0.00453

18-Dec-96 1,492,479 10,162,021 10,295 5750 1.0834 6809 5889 169.8 0.747918 7.611 -0.00740

15-Aug-97 2,699,895 19,819,945 92,847 4705 0.9625 7341 1999 154.8 1.9880 0.801270 15.768 -0.01345

18-Mar-98 3,566,520 23,838,000 279,326 4077 0.8988 6684 1567 131.7 1.8034 0.844678 20.673 -0.01757

19-Jun-98 3,888,100 28,090,000 284,267 3263 0.8349 7225 959 77.8 1.5327 0.987268 29.095 -0.02329

30-Oct-98 4,246,000 41,200,000 327,294 2227 0.7946 9703 358 43.3 1.3099 1.327838 57.122 -0.03034

Table 2: PVT Properties and material Balance Calculation of Example 1 (Continued)Date exp(-2Cf) alpha beta Eg (F+Wp)/Eg We We/Eg (F+Wp-We)/Eg X Y

RB/MSCF B SCF rb bscf bscf mmscf/psi 1/psi

2-Jul-94 1.0 0.0 0.0 0.000000 0.0 0

1-Mar-95 0.99960 0.0007218 0.000192 0.003718 0.2 0 0.000 0.2 0.74 4.03

28-Jun-95 0.99952 0.0008646 0.000230 0.004458 114.1 3,799 0.852 113.3 8.83 4.04

7-Dec-95 0.99913 0.0015746 0.000422 0.008156 98.3 11,918 1.461 96.9 7.58 4.08

3-Mar-96 0.99739 0.0047493 0.001294 0.024954 87.5 26,025 1.043 86.5 6.68 4.30

11-Jul-96 0.99548 0.0082207 0.002252 0.043397 99.8 60,372 1.391 98.4 7.58 4.56

18-Dec-96 0.99262 0.0134114 0.003631 0.070091 108.6 124,160 1.771 106.8 8.26 5.01

15-Aug-97 0.98664 0.0242821 0.006196 0.141086 111.8 273,857 1.941 109.8 10.17 6.58

18-Mar-98 0.98258 0.0316737 0.007737 0.205296 100.7 425,514 2.073 98.6 10.65 8.14

19-Jun-98 0.97698 0.041855 0.009735 0.391509 74.3 510,481 1.304 73.0 11.49 11.56

30-Oct-98 0.97011 0.0543366 0.012278 0.791456 72.2 662,223 0.837 71.3 18.15 20.67


Table 4: PVT and Material Balance Calculation of Example 2

Time P Z2 CGP COP CWP Bg Bg' Eg Integ(Cf) Exp(-Cf) Alpha Beta

Date days psia mm scf stb stb rb/mscf rb/mscf rb/mmscf

26-Feb-96 0 8973 1.4628 0 0 0 0.5735 0.6506 0 0 1.00000 0 0

18-Jun-96 113 8698 1.4304 412.7 68999 330 0.5762 0.6537 2.7 0.00020089 0.99980 0.000365 0.000676

11-Oct-96 228 8421 1.3979 1069.6 176112 2556 0.584 0.6625 10.5 0.00035555 0.99964 0.000646 0.001355

14-Jan-97 323 8197 1.3715 1602.7 265133 5190 0.5886 0.6677 15.1 0.00044729 0.99955 0.000813 0.001906

5-Feb-97 345 8148 1.3658 1718 284528 5778 0.5897 0.6690 16.2 0.00046406 0.99954 0.000844 0.002025

17-Jun-97 477 7810 1.3259 2561.1 428708 14282 0.5972 0.6775 23.7 0.00053072 0.99947 0.000965 0.002855

20-Jan-98 694 7728 1.3162 3559.2 593822 109147 0.5992 0.6798 25.7 0.00052153 0.99948 0.000948 0.003056

9-Feb-98 714 7754 1.3193 3636.4 607157 122414 0.5986 0.6791 25.1 0.00051371 0.99949 0.000934 0.002992

Table 4: PVT and Material Balance Calculation of Example 2 (Continued)

Et F+Wp (F+Wp)/Et tD PD dPD We We/Et (F + Wp)/Et (F+Wp-We)/Et P/Z2 X Y

Date rb/mscf m rb mm SCF rb b scf bscf mmscf/psi 1.0E5 1/psi

26-Feb-96 0.0000 0 0.0000 0.0000 0 0 6134.1

18-Jun-96 0.0037 270 72,208 1.2131 0.8774 0.2471 119,882 32.0 72.2 40.2 6080.5 3.234 3.203

11-Oct-96 0.0132 711 53,822 2.4477 1.1019 0.1388 327,637 24.8 53.8 29.0 6024.0 4.222 3.311

14-Jan-97 0.0189 1075 56,900 3.4676 1.2237 0.1037 548,892 29.0 56.9 27.9 5976.3 4.533 3.401

5-Feb-97 0.0202 1155 57,058 3.7038 1.2475 0.0981 602,462 29.8 57.1 27.3 5965.7 4.582 3.421

17-Jun-97 0.0294 1749 59,562 5.1209 1.3681 0.0745 1,019,128 34.7 59.6 24.9 5890.3 4.907 3.559

20-Jan-98 0.0318 2529 79,614 7.4506 1.5150 0.0540 1,652,650 52.0 79.6 27.6 5871.4 6.391 3.593

9-Feb-98 0.0310 2592 83,530 7.6653 1.5264 0.0527 1,708,808 55.1 83.5 28.5 5877.4 6.662 3.584


Table 5: PVT and material Balance Calculation of Example 3time P Z P/Z Bg(dry) Gp Wp F=Gp*Bg+Wp alpha beta Etdate psia rb/mscf bscf rb mm rb rb/mscf

2-Sep-93 11384 1.48052 7689.2 0.49668 0 0 0.000 0.00000 0.00000 08-Dec-93 11165 1.47855 7551.3 0.50575 0.264 543 0.134 0.00180 0.00094 0.0104263-Aug-94 9862 1.37674 7163.3 0.53315 1.297 2,700 0.694 0.01251 0.00651 0.0459125-Aug-95 8487 1.26429 6712.8 0.56892 3.361 7,541 1.920 0.02382 0.01239 0.09022417-Jun-96 8298 1.26345 6567.7 0.58149 4.881 12,019 2.850 0.02537 0.01320 0.10396930-Jan-98 7938 1.22631 6473.1 0.59000 6.919 20,973 4.103 0.02833 0.01474 0.114707

Table 5: PVT and material Balance Calculation of Example 3 (Continued)time (F+Wp)/Et Delta T DeltaP TD PD dPD/dTD We We/Et (F+Wp-We)/Et X Y

date bcf days psia mm rb bscf bscf mmscf/psi E-5, 1/psi2-Sep-93 0 0 0.0008-Dec-93 12.9 97 219 0.3312 0.20605 1.789917 0.000 0.00 12.9 1.227 8.3353-Aug-94 15.1 335 1522 1.1438 0.80975 0.348288 0.000 0.00 15.1 0.915 4.8235-Aug-95 21.3 702 2897 2.3970 1.08523 0.151156 0.000 0.00 21.3 1.329 5.02017-Jun-96 27.4 1019 3086 3.4794 1.22432 0.112415 0.630 6.06 21.4 1.852 5.53330-Jan-98 35.8 1611 3446 5.5007 1.42439 0.090625 1.656 14.44 21.3 2.385 5.452

Table 6: PVT and Material balance Calculation of Example 4time P Gas-Z Bg Gp(dry) COP CWP CGP equ. Gas

date psia rb/mscf b scf m stb m stb mm rb m scf04-Dec-96 10485 1.418 0.4839 0 0.00 0 0.000 0.001-Jan-97 10256 1.401 0.4888 0.43 3.36 0.35 0.212 2256.326-Sep-97 9372 1.335 0.5097 3.72 31.93 2.72 1.894 21441.720-Feb-98 8893 1.300 0.5231 5.84 50.06 4.68 3.057 33616.515-Jun-98 8689 1.285 0.5292 6.79 58.72 5.49 3.591 39431.820-Jul-98 8000 1.235 0.5524 9.73 82.32 8.44 5.374 55279.8

05-Sep-98 7405 1.192 0.5760 11.25 94.83 11.609 6.478 63681.9

Table 6: PVT and Material balance Calculation of Example 4 (Continued)time equ gas alpha beta Eg Ftotal Ftotal/Eg P/Z Gp (wet)

date m rb rb/m scf m rb b scf bscf04-Dec-96 0.00 0.00000 0.0000000 0 0 7394.2 0.0001-Jan-97 1.10 0.00716 0.0001633 0.00842 213.1 25.3 7320.5 0.4426-Sep-97 10.93 0.03478 0.0007936 0.04300 1907.3 44.4 7020.2 3.7420-Feb-98 17.58 0.04975 0.0011351 0.06378 3079.3 48.3 6840.8 5.8815-Jun-98 20.87 0.05613 0.0012805 0.07304 3617.0 49.5 6761.9 6.8220-Jul-98 30.54 0.07766 0.0017718 0.10691 5412.9 50.6 6477.7 9.78

05-Sep-98 36.68 0.09625 0.0021960 0.13972 6526.1 46.7 6212.2 11.31

Figure 3: (F+Wp-We)/Eg vs. Eg Plot, Example 1

30

50

70

90

110

130

0 0.2 0.4 0.6 0.8 1

Eg, RB/MSCF

(F+W

p-W

e)/E

; BS

CF

Figure 2: Solution Plot of Example 1

-15

-10

-5

0

5

10

15

20

25

0 5 10 15 20

X, MM SCF/psi

Y, 1

.0E

-5 1

/psi

Figure 5: (F+Wp/Eg) vs. Eg Plot of Example 2

20

30

40

50

60

70

80

90

0.00 0.01 0.02 0.03 0.04

Eg, RB/MSCF

(F+

Wp)

/Eg,

BS

CF

Figure 6: P/Z Plot, Example 2

5850

5900

5950

6000

6050

6100

6150

0 1000 2000 3000 4000

Gp, MMSCF

P/Z

, psi

a

Figure 1 :Plot of ( F+W p)/Eg vs. Eg, Example 1

40

50

60

70

80

90

100

110

120

0 0.2 0.4 0.6 0.8 1

Eg, RB/MSCF

(F+

Wp)

/Eg,

B S

CF

Figure 4: P/Z Plot of Example 1

0

1000

2000

3000

4000

5000

6000

0 10 20 30 40 50

Gp (w et gas), BSCF

P/Z

, psi

a

Figure 8: (F+Wp)/Et vs. We/Et, Example 2

y = 1.0055x + 27.307

R2 = 0.9877

0102030405060708090

0 10 20 30 40 50 60

We/Et, mm SCF

(F+

Wp)

/Et,

BS

CF

F ig u re 1 0 : F /E v s . E P lo t, E x a m p le 3

0

5

1 0

1 5

2 0

2 5

3 0

3 5

4 0

0 0 .0 5 0 .1 0 .1 5

E , R B /M S C F

(F+W

p)/E

, BS

CF


-3

-1

1

3

5

7

0 2 4 6 8

Gp(PiZ/ZiP)/DP, MMSCF/psi

(PiZ

/(Z

iP)-

1)/D

P, 1

.E-5

psi

-1

Figure 14: (F+Wp)/E vs We/E Plot, Example 3

y = 1.0035x + 21.299R2 = 1

0

10

20

30

40

50

0 10 20 30 40 50

We/E, BSCF

(F+W

p) /E

, BS

CF

Figure 11: P/Z vs. Gp Plot, Example 3

6400

6600

6800

7000

7200

7400

7600

7800

0.0 2.0 4.0 6.0 8.0

Gp, BSCF

P/Z

, psi

a

Figure 9: (F-We+Wp)/Et vs. Et Plot, Example 2

20

25

30

35

40

0.000 0. 005 0. 010 0. 015 0. 020 0. 025 0. 030 0. 035

Et, R B /M S C F



y = 1.7612x - 1.9497

R2 = 0.6209

-101234567

0 1 2 3 4 5(Gp/DP)(PiZ)/(ZiP), mmscf/psi

(1/D

P)[

(PiZ

/(Z

iP)-

1],

1.0E

5 1/

psi


01234567

0.0 2.0 4.0 6.0(Gp/DP)(PiZ)/(ZiP), mmscf/psi

(1/D

P)[

(PiZ

)/(Z

iP)-

1], 1

.0E

5 1/

psi

Figure 17: (F+Wp)/Eg vs. Eg Plot (Ce = 2.5E-5 1/psi), Example 4

0

10

20

30

40

50

60

0 0.05 0.1 0.15

Eg, rb/mscf

(F+

Wp)

/Eg,

bsc

f

Figure 19: Plot of F vs. E Plot , Example 4

y = 48136x

R2 = 0.995

0

2000

4000

6000

8000

0 0.025

0.05 0.075

0.1 0.125

0.15

Eg, rb/mscf

F, m

rb

Figure 20, P/Z Plot of Example 4

600062006400660068007000720074007600

0 5 10 15Gp, BSCF

P/Z

, psi

a

Figure 15: Plot of (F+W p-W e)/Et vs. Et Plot, Example 3

0

5

10

15

20

25

30

0 0.05 0.1 0.15

Et, rb/mscf

(F+

Wp

- W

e)/E

, BS

CF

14 [S-W Wang, V. M. Stevenson, C. H. Ohaeri, D. W. Wotring] [SPE 56690]

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