Copyright 2000, Society of Petroleum Engineers Inc.

This paper was prepared for presentation at the 2000 SPE Annual Technical Conference andExhibition held in Dallas, Texas, 14 October 2000.

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AbstractGas material balance in conventional, volumetric reservoirs isdescribed by a linear relationship between pressure/z-factor(p/z) and cumulative production. Unfortunately, tight gasreservoirs do not exhibit this type of behavior, but insteaddevelop a nonlinear trend, which is not amenable toconventional analysis. The nonlinearity is a function of twoitems: the testing method (time) and the reservoircharacteristics. For these type of reservoirs the testing time isinsufficient to reach average reservoir pressure and from apractical viewpoint, it is not possible to shutin for extendedperiods of time. Therefore, a method has been developed touse key intersection points and slopes from a tight gas materialbalance plot to better understand the reservoir behavior.

This work begins by explaining the nature of the nonlineartrend in terms of flow regimes. The primary objective is toimprove the estimate of gas-in-place and recovery in a tightgas reservoir. Typically, gas-in-place is underestimated usingconventional techniques. It is demonstrated that by using theappropriate slope with the initial pressure an improved(increased) estimate of gas-in-place is achieved. Furthermore,it is possible to distinguish the effect of infill wells andsubsequently determine the incremental recovery. Includedare field examples from the San Juan Basin and southeast NewMexico, which demonstrate the technique.

IntroductionThe widely known gas material balance equation for a simple,volumetric reservoir, is given by;

=

GpG

izip

z

p 1 ,. .(1)

Consequently, a common tool in reservoir analysis of gaswells is to plot p/z vs. the cumulative gas production (Gp). If aconstant slope develops it is possible to ascertain the recoveryand gas-in-place. Equation (1) is constrained by isothermaltemperature conditions, no phase changes, no water influx,and no compressibility effects; i.e., water and formationcompressibility, respectively. Ikoku1 provides details ofreservoirs with water influx and compressibility effects.

Unfortunately, in low permeability gas reservoirs thisbehavior is not exhibited, but instead, a nonlinear trendprevails as shown in Fig. 1. This trend has been recognized bypast authors 2-4 and has been discarded as unuseable. It is theobjective of this work to use this data to obtain informationpertaining to the reservoir.

The nonlinear trend is a function both of the pressuremeasurement technique and the reservoir characteristics.Typical shut in periods are not of sufficient duration toachieve a representative average reservoir pressure. Thisconcept can be reinforced by examining the criteria forreaching pseudosteady state flow.

DApsstkAtici

psst

3790= ,.(2)

Assuming a well located in the center of the drainage areaand substituting typical reservoir and gas properties for a tightgas formation ( = 11%, k = 0.1 md, gi = 0.012 cp., cti =0.001 psi-1), results in a time to reach pseudosteady state of 2years for an 80 acre drainage area and 16 years for a 640 acredrainage area. Subsequently, a single buildup pressuremeasurement after seven days of shut in will not achieve sucha boundary condition.

ApproachTo analyze low-permeability reservoirs the followingconstraints are applied: (1) no water influx, (2) constantreservoir temperature, (3) no rock compressibility effects, and(4) only single phase dry gas; i.e., no phase changes occur inthe reservoir. Many reservoirs exhibit these constraints suchas the Dakota and Mesaverde of the San Juan Basin, or thePecos Slope Abo of southeast New Mexico to name a few.

Furthermore, to simplify the analysis the bottomholeflowing pressure will be assumed to be constant over the lifeof the well. A reasonable assumption for dry gas wellscontrolled by surface line pressure. The Pwf of the examples

SPE 62883

A New Approach to Gas Material Balance in Tight Gas ReservoirsThomas W. Engler, SPE, New Mexico Tech

2 THOMAS W. ENGLER SPE 62883

discussed later meet this criteria; however, if the pressurevaries significantly then superposition is recommended.

Referring to Figure 1, three trends are exhibited on the p/zplots for low permeability reservoirs. During the early timeperiod a rapid decrease in pressure occurs. If this trend isextrapolated to p/z = 0, the gas-in-place (G) will be seriouslyunderestimated. The behavior has been previously explainedas the response to transient flow profile3; however, additionalanalysis did not confirm this hypothesis. An alternativesolution is the rapid depletion of a stimulated well in areservoir consisting of a natural fracture network; in simpleterms, the flush production associated with such a condition.Coupled with this behavior is the inability of the pressuremeasurement technique to capture reservoir pressure withinthe testing time. Subsequently, as the drainage radius isexpanding the testing pressure deviates more and more fromthe average reservoir pressure.

The intermediate period exhibits uniform slope over anextended period of time, even though, the magnitude of thepressure measurement observed is significantly below theaverage reservoir pressure. During this period, the test time istoo short to capture the average pressure response; however,consistency of the data suggests that a similar region is beingrepeatedly investigated by the pressure test. For example,notice in Figure 2 the difference in pws and pr is approximatelyconstant for an extended period of time. Several researchers2,5have presented methods to correct measured data to averagereservoir pressure by pressure buildup techniques.

The constant slope provides an opportunity to estimate thehydrocarbon-pore volume, Vhc. Defining the slope (m) as;

pG)z/p(

m

= , ..(3)

and substituting into the gas material balance equation, resultsin an expression to determine Vhc.

m

1*

scT

scTP

hcV = , .(4)

From volumetrics,

)w

S1(Ah43560hcV = ,(5)thus providing a method to determine the drainage area.

Furthermore, from the observation of a constant slope,three scenarios can be developed to determine the gas-in-placeas illustrated in Figure 3. The problem is defining therelationship between the determined slope and the actual slopeif one could measure the actual reservoir pressure. Case Aexhibits two parallel trends of constant slope; i.e., m1 = m2.Gas-in-place can readily be obtained from,

m

1*

izipG

= ,(6)

The difference in gas-in-place between the two lines is dueto the initial reservoir pressure difference; and not thehydrocarbon pore volume, which is the same for both lines.

To have equal slopes suggests the radius of investigationof the pressure test is expanding at the same rate as the radiusof drainage of the reservoir. That is, ri constant* re over anextended period of time. The magnitude of gas-in-place willbe overestimated by this method and therefore provides anupper bound to the well.

In case B the slopes are different, but the intersectionpoint occurs at the same gas-in-place. Subsequently, thehydrocarbon pore volume is corrected to reflect the differencein reservoir pressures. Estimation of G is obtained by,

2

1*

1

1*

int mizip

mz

pG

=

= ,(7)

where the (p/z)int is the intercept value from the identifiedpressure trend. To solve for the correct Vhc requires thesubstitution of m2 into Eq. (4). For this behavior to occurmeans the investigative volume seen during subsequentpressure tests is approaching the average drainage volume ofthe well. In other words, ri 0.472re. This is as expected fordepleted reservoirs where the pressure gradient isapproximately uniform throughout the reservoir.

The third and final scenario (Case C) exhibits both adifferent slope and intercept between the measured pressuretrend and the actual reservoir behavior. Unfortunately, themeasured data does not reflect the actual reservoir behavior.The best is to estimate a range for gas-in-place using Case Aas the upper bound and case B as the lower bound

A final stage of the life of the well occurs when depletionhas been significant (see Fig. 1). At this time the measuredpressure curve flattens and becomes constant; converging tothe actual average reservoir pressure. In many cases the gas-in-place was estimated by extending a straight line from theinitial p/z point through this late time point. Experience hasshown this method typically underestimates gas-in-place, dueto the late time measured pressure slightly underpredicting theactual reservoir pressure. Also, as Fetkovich, et.al.4 correctlypoint out, a rise in pressure can be a rebound effect due to adecrease in withdrawal from the reservoir.

ApplicationsPictured Cliffs. The first example well produces from thePictured Cliffs sandstone in the San Juan Basin of northwestNew Mexico. Picture Cliffs is a low permeability, sandstone toshaly sandstone gas reservoir found at a depth ofapproximately 3200 feet and developed on 160 acre spacing. 6The example well (No.114) was initially completed in 1958and included a hydraulic fracture treatment to becommercially productive. Other well and reservoir data arelisted in Table 1. The long history of production and pressuredata along with a pressure buildup test, make this well anexcellent candidate for investigation.

SPE 62883 A NEW APPROACH TO GAS MATERIAL BALANCE IN TIGHT GAS RESERVOIRS 3

Figure 4 is the p/z vs cumulative production plot for thiswell. In the San Juan Basin, pressure data is recorded over a7-day shut in period and reported annually until 1974 andevery other year until 1990. The primary purpose ofcollecting this information was for deliverability testing andproration. Notice the typical tight gas well response of a rapiddecrease in pressure within the first year. This behavior doesnot correspond to the end of the transient period, which occurs8 to 10 years later according to decline curve analysis. Themajority of time and hence cumulative production exhibitscase B behavior; i.e., constant p/z decline. Applying Eq. (7)this trend results in an estimate of 660 mmscf of gas-in-place.

Also shown on Figure 4 is an extrapolation between theinitial p/z and the anomalous increase in p/z found in the latestdata points; resulting in 520 mmscf of gas-in-place.Frequently this extrapolation is applied to tight gas wells toestimate gas-in-place and recovery. The validity of the lastpoints is pivotal to this method being successful or not. Thesepressure points were acquired during a time of extended cyclesof shutin and production due to external constraints. Theresulting bottomhole flowing pressure is increased whichsubsequently translates into an increase in recorded shutinbottomhole pressure. This is the same conclusion as drawn byFetkovich, et al.4 in 1987. Unless this pressure data isobtained very late in the life of the well it is likely this methodwill underestimate gas-in-place and reserves.

Cumulative production (as of mid 1999) for this well is480 mmscf; therefore 73% of the gas-in-place has beenrecovered. A rate cumulative plot (Figure 5) also provides alinear trend, which when extrapolated results in gas-in-placeof 700 mmscf or 69% recovery. Both methods are withinreasonable agreement. Results are given in Table 2 forcomparison.

A key to tight gas development is the drainage area ofexisting wells and the feasibility of infill drilling. Estimationof drainage area was performed by both decline curve analysisand the modified material balance method. Type curvematching on a log-log scale as originally proposed byFetkovich7,8 and later expanded by Sunde9, identified bothtransient and boundary dominant flow present in this well(Figure 6). Drainage area was estimated to be 90 acres by thedecline curve method. The example well illustrates a case Bbehavior, i.e., unique G but a variable slope (m). UsingEquation (7) to adjust the slope, the hydrocarbon pore volumeis calculated to be 7.544 mmrcf. Substitution of the knowngas and well properties results in a drainage area calculation of70 acres.

To further investigate the tight gas, pressure behavior, asingle well, simulation model was developed for single-phaseflow. As a simplification, the reservoir properties wereassumed to be homogeneous and isotropic. The well wasbottomhole pressure constrained, initially at 250 psi and thenreduced to 150 psi ten years later. This change reflects theactual pressures measured during the annual deliverabilitytests. Figure 7 illustrates the excellent match between theresults from the simulator with the measured data for both gasrate and shutin bottomhole pressure. The success of the model

verifies the linear trends seen on the gas material balance plotsand the slow pressure response of tight gas reservoirs.Furthermore, to obtain this match the areal extent of thesimulation model was 86 acres, which is in agreement with theprevious methods.

The analysis suggest this well has drained 70 to 90 acres ofthe dedicated 160-acre proration unit and has recoveredapproximately 70% of the gas-in-place within that volume.The paradox is the boundary-dominated flow exhibited by thedecline curve. The nearest well is approximately 1850 feetaway from the subject well, farther than the estimateddrainage area. Two explanations can be given. First, thedrainage calculations are based on isotropic conditions andtherefore a circular drainage pattern. However, if anisotropyexists, then the two wells are sufficiently close enough toprovide interference. Investigation of production andgeological trends show a dominant northwest/southeastdirection, the exact direction of these two wells. Second, athinning of the reservoir net pay thickness over the arealextent of this well would increase the drainage area. Forexample if thickness is reduced by half then the drainage areadoubles to approximately 160 acres.

A second example producing from the Picture Cliffsreservoir is Well No. 88 shown in Figure 8. Reservoir andwell properties are listed in Table 1. Again the behavior issimilar to the first example. Extrapolation of the pressure/ztrend results in an estimate of 988 mmscf of gas-in-place.Cumulative production has been 705 mmscf, thereforerecovery has been 71%. If an extrapolation between the initialpoint and the last set of test points is drawn the gas-in-place is820 mmscf, or 86% recovery. From production declineanalysis the gas-in-place is estimated to be 920 mmscf (Fig.9).

The slope of the line extending from the initial pressure/zand intersecting the extrapolated gas-in-place is given by Eq.(7);

mmscfpsim /286.16312.*624

12722 ==

Substituting into Eq. (5) results in a calculated drainagearea for this well of 70 acres. In comparison, analysis of thedecline curve resulted in a drainage area of 77 acres for thiswell.

The next example illustrates the usefulness of this methodfor a pair of wells; the original well and a replacement well664 ft apart. The original well produced 132 mmscf for 15years, but was abandoned due to mechanical problems. Thereplacement well was drilled 8 years later and has cumulativeproduction to date of 350 mmscf. Figure 10 is the p/z plot forboth wells combined. Several interesting features can be seenon this figure. For the initial well, note the typical response ofhigh initial p/z followed by a period of declining slope. Thelast three tests show a rapid decrease in pressure andproduction, verifying the mechanical problems. For thereplacement well, note the initial pressure was almost identicalto the first well, 897 vs 876 psia, respectively; thus illustratingthe low permeability of the Picture Cliffs reservoir. Limited

4 THOMAS W. ENGLER SPE 62883

data for the remaining life of the replacement well makeanalysis difficult, however the late time increase in p/z isexhibited and is due to shutin periods as described previously.

An extrapolation of the pressure trend results in G = 783mmscf. Total production for this proration unit is 480 mmscf,or 61% of the gas-in-place. At the end of the initial well,recovery would have been 17% of the gas-in-place. This lowrecovery coupled with the estimate of gas-in-place providesevidence to drill a replacement well. Drainage area isestimated to be 78 acres and 104 acres by material balance anddecline curve analysis, respectively.

Dakota Sandstone. The Dakota is a prolific, gas-bearingsandstone to shaly sandstone reservoir located in the San JuanBasin. The subject well was completed in the Dakota in 1968at a depth of approximately 7300 feet. Figure 11 illustratesthe pressure/z behavior with respect to cumulative production.Unlike the Picture Cliffs examples, this well exhibits twoparallel straight lines as described by case A. Following theguidelines presented for case A, the gas-in-place is given bythe straight line through the initial pressure point and is 3.951Bcf. The cumulative production is 3.31 Bcf, thereforerecovery to date is 84%. From the slope the drainage area isestimated to be 165 acres. A match of the production rate datain Figure 12 results in significantly greater gas-in-place anddrainage area; 7.0 Bcf and 296 acres, respectively.

This well was part of a 15 well simulation study of theDakota reservoir.10 A reservoir pressure contour map at theend of the simulation (current time) confirms the well hasdrained approximately 160 acres. It was one of the first wellsdrilled in the area and has cumulative production which is 3 to10 times greater than the adjacent offset wells.

Pecos Slope Abo. The last example is from the Abosandstone formation, which is productive near Roswell insoutheastern New Mexico. This reservoir was one of the firstto be designated as tight gas and current spacing is 160 acres11.For the subject well, input data is found in Table 1 and resultsare summarized in Table 2.

Figure 13 is the gas material balance plot for the givenwell. The pressure data was obtained from recording themaximum surface pressure from periodic 24-hour builduptests. These pressures obviously do not reach averagereservoir pressure; however, they do delineate a trend asclassified by Case B. Gas-in-place is estimated to be 975mmscf. Cumulative production has been 615 mmscf, orrecovery to date is 63% of the gas-in-place. An attempt toconfirm this analysis by decline type-curves was not possiblesince the well did not reach pseudosteady state flow (see Fig.14) during the wells 17-yr history.

Using Eq. (7) to estimate the slope (m2), the hydrocarbonpore volume is calculated to be 9.162 mmrft3. Solving forarea in Eq. (5), results in 259 acres as the area of influencefrom the material balance analysis. This solution issignificantly greater than the 160 acres dedicated to the well.If porosity or thickness increase away from the wellbore, like

lenticular sands found in the Abo tend to do, then thecorresponding area would be reduced.

ConclusionsA method is proposed to evaluate historical shutin pressuredata for low permeability gas reservoirs. This data is typicallyignored due to the inadequate buildup time to measure a trueaverage reservoir pressure. However, it was shown that eventhough the magnitude of the pressure measurements is inerror, the trend can be applied to obtain an improved estimateof gas-in-place. Three cases were identified of tight gasbehavior and relationships developed with the desiredresponse.

Benefits of the method are improved estimates of gas-in-place; thereby enhancing the accuracy of forecasts andreserves. Also obtained is an estimate of drainage area, whichis used to determine the availability of infill drilling prospects.As shown in the first example, only one-half of the dedicatedacreage has been drained by this well; leaving the remainingarea available for future development.

This method is best applied when coupled with othertechniques; thereby verifying or adding new information to theunderstanding of the reservoir. Decline curve analysis andsimulation were two additional tools used for comparisionwith the proposed method. Unfortunately, decline curves havea tendency to be erratic in tight gas reservoirs and aretherefore sometimes difficult to evaluate.

NomenclatureA = drainage area, ft2cti = initial total compressibility, psi-1h = reservoir thickness, ftk = permeability, md.

G = gas-in-place, mmscfGp = cumulative gas production, mmscfm = slope of p/z vs. Gp plot, psia/mmscfp = pressure, psi

pr = average reservoir pressure, psipwf = wellbore flowing pressure, psipws = measured shutin bottomhole pressure, psi

re = reservoir radius, ft.ri = investigative radius, ft

Sw = water saturation, dimensionlessz = gas compressibility factor or z-factorT = temperature, Ft = time, hours

tDA = dimensionless timeVhc = hydrocarbon pore volume, res. ft3

= porosity, dimensionless

Subscriptsi = initial

pss = pseudosteady statesc = standard conditions

SPE 62883 A NEW APPROACH TO GAS MATERIAL BALANCE IN TIGHT GAS RESERVOIRS 5

AcknowledgementsI like to thank New Mexico Tech for allowing me to publishthis paper. Also, I.H.S/Dwights for providing the productiondatabase and Gemini Solutions, Inc for the reservoir simulator.

References1. Ikoku, C.: Natural Gas Reservoir Engineering, Krieger

Publishing Co., Malabar, FL (1992)2. Stewart,P.R.: Low-Permeability Gas Well Performance at

Constant Pressure, JPT, (Sept. 1970) 1149-1156.3. Slider,H.C.: Worldwide Practical Petroleum Reservoir

Engineering Methods, Pennwell Publishing, Tulsa, OK (1983)4. Fetkovich,M.J., Vienot,M.E., Bradley,M.D. and Kiesow, U.G. :

Decline-Curve Analysis Using Type Curves-Case Histories,SPEFE (Dec. 1987) 637-656.

5. Brons,F and Miller, W.C.:A Simple Method for CorrectingSpot Pressure Readings, (1961) Trans., AIME 222, 803-805.

6. Dutton,S.P.,Clift,S.J.,Hamilton,D.S.,Hamlin,H.S.,Hentz, T.F.,Howard, W.E., Akhter,M.S., and Laubach,S.E.: Major LowPermeability Sandstone Gas Reservoirs in the ContinentalUnited States, GRI/BEG Report No. 211 (1993)

7. Fetkovich,M.J.:Decline Curve Analysis Using Type Curves,JPT (June 1980) 1065-77.

8. Fetkovich,M.J., Fetkovich,E.J. and Fetkovich,M.D.:UsefulConcepts for Decline Curve Forecasting, Reserve Estimation,and Analysis, SPE 28628 (Sept. 1994) presented at the AnnualTechnical Conference in New Orleans, LA.

9. Sunde,A., Chen, H., and Teufel,L.W.:Producing Char-acteristics and Drainage Volume of Dakota Reservoirs, San JuanBasin, New Mexico, SPE 60288 (Mar 2000) presented at theSPE Rocky Mountain/Low Permeability ReservoirsSymposium.

10. Jaramillo, M.: Integrated Study of the Dakota Formation: EastHalf of the Gas Project Area, San Juan Basin, New MexicoM.S. Thesis, Petroleum Engineering (May 2000)

11. Bentz,L.M.:Pecos Slope Abo, Chaves County, New Mexico,Roswell Geological Society (1988) 22-43.

No. 114 No. 88 No. 18 Dakota Abo, % 11 11 11 5 12.3gi, cp 0.0112 0.0118 0.0114 0.019 0.014h, ft 40 67 73 125 11cti, psi-1x 10-4

8.8 9.6 12.8 3.22 8.86

g 0.67 0.67 0.67 0.68 0.675Tr , F 106 103 106 200 98Sw, % 44 44 44 50 40rw, ft. 0.229 0.229 0.229 0.229 0.333Pi, psi 1131 1045 762 2856 1239

Table 1. Input well and reservoir properties

No.114

No.88

No.18R

Dakota Abo

G,mmscf 660 988 783 3.951 975Recovery,% 73 71 61 84 63

P/z

anal

ysis

A, acres 70 70 78 165 259

G,mmscf 700 920 1110 7000Recovery,% 69 77 43 47

Rat

eA

naly

sis

A, acres 90 77 104 296

Table 2. Results and comparison of p/z analysis with rate timeanalysis.

Figure 1. P/z response for conventional gas reservoir and a tightgas reservoir.

Figure 2. Schematic of a partial buildup response in a tight gasreservoir, indicating the difference in measured pws and averagereservoir pressure, pr.

Gp

p/z

Conventional response

G

Tight gas response

(p/z)i

(p/z)intm

1

m2 =

m1

?

Gp

p/z

Conventional response

G

Tight gas response

(p/z)i

(p/z)intm

1

m2 =

m1

?m2 =

m1

?

Pi

rw

.472rere

Pwf ri

Pi

rw

.472rere

Pwf ri

6 THOMAS W. ENGLER SPE 62883

Figure 3. Three possible relationships between the conventionalresponse and the tight gas response.

Figure 4. Field example of tight gas response (Case B) on p/z plotand estimation of gas-in-place.

Figure 5. Extrapolation of Rate cumulative trend for gas-in-place.

Figure 6.. Rate time log-log type curve of Well No. 114.

G1 G2Gp

P/z m1 =

m2

Case A

Gp

P/z m1 m

2

G1= G2

Case B

G p

P/zm

1 m2

G1 G 2

Case C

G1 G2Gp

P/z m1 =

m2

Case A

Gp

P/z m1 m

2

G1= G2

Case B

Gp

P/z m1 m

2

G1= G2

Case B

G p

P/zm

1 m2

G1 G 2

Case C

G p

P/zm

1 m2

G1 G 2

Case C

P /Z vs. C umula tive P ro duc tio nN o . 11 4

y = -0.8367x + 552.88R2 = 0.9580

200

400

600

800

1000

1200

1400

1600

0 100 200 300 400 500 600 700

Cumulative Production, mmscf

P/Z,

ps

ia

N o. 114 - P icture C liffs

0500

10001500200025003000350040004500

0 100 200 300 400 500 600 700C umulativ e Prod, mmscf

Pro

duct

ion

Rat

e,

msc

f/mo

bas ed on day s on

1

10

100

1000

10000

1 10 100 1000cumulative time,months

mcf

/mo

annual average

Fetkovich Decline Curve

0.0 01

0.0 1

0 .1

1

10

0.0 001 0.0 01 0.0 1 0 .1 1 10 100 1000tDd

qDd

SPE 62883 A NEW APPROACH TO GAS MATERIAL BALANCE IN TIGHT GAS RESERVOIRS 7

Figure 7. Comparison of simulation results with measured datafor Pictured Cliffs example.

Figure 8. Second Pictured Cliffs example of tight gas response onp/z curve.

Figure 9. Extrapolation of rate cumulative trend for the secondfield example.

Figure 10. Determination of gas-in-place for two wells in the sameproration unit, original well and a replacement well.

Figure 11. Dakota field example exhibiting Case A tight gasbehavior.

Figure 12. Rate time log-log type curve of Dakota Well

1

10

100

1000

0 5 10 15 20 25

time, years

pro

duct

ion

ra

te,

msc

f/mo

0

200

400

600

800

1000

1200

SIBH

P, p

si

simulated

measured

P /Z vs. C um ula tive P ro d uc tio nN o . 8 8

y = -0.6312x + 623.98R 2 = 0.9173

0

200

400

600

800

100 0

120 0

140 0

0 100 200 300 400 500 600 700 800 900 100 0

C umulativ e Production, mmscf

P/Z,

ps

ia

N o. 8 8 - P ic tured C liffs

0

2000

4000

6000

8000

10000

12000

0 100 200 300 400 500 600 700 800 900

C umulativ e Production, mmscf

Pro

duct

ion

rat

e,

mcf

/mo

based on day on

N o . 1 8 a nd 1 8 R

y = -0 .7 2 35 x + 56 6 .9R 2 = 0 .5 28 6

0100200300400500600700800900

1000

0 100 200 300 400 500 600 700 800

Cumulative production, mmscf

P/Z,

psia

P/z vs. Cumulative ProductionDakota Example

y = -0.8264x + 3264.6R2 = 0.999

0

500

1000

1500

2000

2500

3000

3500

0 500 1000 1500 2000 2500 3000 3500 4000

Cumulative Production, mmscf

p/z,

ps

i

100

1000

10000

100000

1 10 100 1000cum ulative tim e, m o

mcf/

mo

annual average

Fetkovich Decline Curve

0 .001

0 .01

0 .1

1

1 0

0 .000 1 0 .001 0 .01 0 .1 1 1 0 1 00 1 000

tDd

qDd

8 THOMAS W. ENGLER SPE 62883

Figure 13. Pecos slope Abo example of Case A tight gas behavior.

Figure 14. Rate-time Log-log type curve of Pecos Slope Abo well.

P e co s S lo p e A b o W e ll

y = -0 .98 63x + 96 1 .27R 2 = 0 .98 66

0

200

400

600

800

1000

1200

1400

1600

0 200 400 600 800 1000

Cu mulativ e p ro duction , mmscf

P/z,

ps

i

Fetkovich Decline Curve

0.001

0.01

0.1

1

10

0.0001 0.001 0.01 0.1 1 10 100 1000

tDd

qDd

10

100

1000

10000

100000

1 10 100 1000

time,months

mcf

/mo

Annual average

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