Unconventional Oil & Gas
Unconventional Oil & Gas PETR 571
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Chapter 1 GAS MATERIAL BALANCE 11 Introduction Material balance is the application of the law of conservation of mass to oil and gas reservoirs and aquifers It is based on the premise that reservoir space voided by r quot is 39 J39 39J and r39 39y lled by the expansion ofremaining uids and rock As demonstrated later in this chapter material balance is a useful engineering method for understanding a reservoir s past performance and predicting its future potential To understand and analyze gas reservoirs the following conditions will be applied 1 Reservoir hydrocarbon uids are in phase equilibrium at all times and equilibrium is achieved instantaneously after any pressure change 2 The reservoir can be represented by a single weighted pressure average at any time Pressure gradients in the reservoir cannot be considered by the method 3 Fluid saturations are uniform throughout the reservoir at any time Saturation gradients cannot be handled 4 Conventional PVT relationships for normal gas are applicable and are sufficient to describe uid phase behavior in the reservoir Material balance calculations can be used to 1 Determine original oil and gas in place in the reservoir 2 Determine original water in place in the aquifer 3 Estimate expected oil and gas recoveries as a function of pressure decline in a closed reservoir producing by depletion drive or as a function of water in ux in a water drive reservoir 4 Predict future behavior of a reservoir production rates pressure decline and water in ux 5 Verify volumetric estimates of original uids in place 6 Verify future production rates and recoveries predicted by declinecurve analysis 7 Determine which primary r J 39 drive 39 39 are 1 r quot 39 for a reservoir s observed behavior and quantify the relative importance of each mechanism 8 Evaluate the effectiveness of a water drive 9 Study the interference of fields sharing a common aquifer Data requirements to accurately apply the material balance method consists of l cumulative uid production at several times cumulative oil gas and water 2 average reservoir pressures at the same times averaged accurately over the entire reservoir 3 uid PVT data at each reservoir pressure as well as formation compressibility 12 Basic concepts The general materialbalance equation for a depletiondrive gas reservoir neglecting water and formation compressibilities is expressed by G 1P 11 Z Z G It is one of the most often used relationships in gas reservoir engineering It is usually valid enough to provide excellent estimates of original gasinplace based on observed production pressure and PVT data During the life of a gas reservoir cumulative production is recorded and average reservoir pressures are periodically measured At each measured reservoir pressure the gas zfactor is determined to calculate Pz and the result plotted as shown in Figure 11 below Notice that Equation 11 results in a linear relationship between Pz and GP That is as gas is produced from the reservoir the ratio Pz should decline linearly for a volumetric reservoir Note that for an ideal gas pressure alone would decline linearly 4000 3500 3000 2500 2000 plz psia 1500 1000 500 0 0 1 2 3 4 5 6 7 8 9 10 11 12 Cumulative gas producedBscf Figure 11 Example of linear relationship between pz and gas produced for a volumetric reservoir Example 11 Determine the original gasinplace and ultimate recovery at an abandonment pressure of 500 psia for the following reservoir Gas speci c gravity 070 Reservoir temperature l50 F Original reservoir pressure 3000 psia Abandonment reservoir pressure 500 psia Production and pressure history as shown in the following table Gp mmscf P psia z pz psia 0 3000 0822 3650 580 2800 0816 3431 1390 2550 0810 3148 3040 2070 0815 2540 Steps 1 Determine zfactor and calculate Pz 2 Plot Pz versus Gp Example shown in Fig 11 3 Draw a straight line through the data points 4 Extrapolate the straight line to pz 0 where Gp must equal G the OGIP From Figure 11 G 100 Bscf 5 Ultimate recovery is estimated from an abandonment pressure of 500 psia and z 0945 thus pza 529 psia From Fiqure 11 the ultimate recovery is estimated to be 85 Bscf or 85 of the OGIP In the example the data points formed a easilyrecognizable straight line but in practice this may not always be the case Theoretically there should be a linear relationship between pz and G However in practice there are several factors that may cause the relationship to be nonlinear Formation compressibility may be significant as in an unconsolidated sand reservoir If this extra stored energy is not accounted for the measured data points will be extrapolated to an optimistically high value of OGIP In the example if the reservoir actually had an OGIP of 100 Bscf but the formation was unconsolidated and had significant compressibility the three measured reservoir pressures after production had begun would have been greater and extrapolation to OGIP would have exceeded 100 Bscf Secondly average reservoir pressure may not have been accurately determined This is a common problem and the plot of pz versus Gp frequently shows more fluctuations from a straight line than in Figure 11 Finally if a water drive were acting on the gas reservoir pressure support would occur and the plot of pz versus Gp would give an overly optimistic OGIP In this example the recovery factor was estimated simply by the ratio of ultimate recovery to the original gasinplace Alternatively it is possible to estimate ultimate recovery efficiency RE in a depletiondrive gas reservoir with negligible water and formation compressibilities by B p 2 RFVOZ1 g 1 a 12 Bga Za pi For the example ultimate recovery efficiency can be estimated from Equation 12 529 RF 1 l 85ofOGIP V0 3650 The decision on selection of an appropriate abandonment pressure is dependent on operational considerations reservoir variables and economics In general the higher the reservoir permeability the lower the abandonment pressure However in tight gas sands where permeability is in the milli to microdarcy range abandonment pressures are being reduced by a variety of methods targeting bottomhole owing pressure These methods can be on the surface such as adding compression or in the wellbore such as adding plunger lift or capillary tubes The added benefit can be quite substantial For instance in the previous example if the abandonment pressure could be reduced in half the incremental gain in recovery would be approximately 1 Bscf 13 Advanced Topics The previous section provides the basic concepts in material balance for simple volumetric gas reservoirs However nonlinearity can occur in the pz vs Gp relationship as a result of water in ux or changes in rock and water compressibilities in geopressured reservoirs or the inability to achieve average reservoir pressure such as in low permeability reservoirs A comprehensive form of the gas material balance equation is given by P Ell ceppi pl 13 p PZ39 1 2 TI Gp Ginj Wpst B WpBw Winij We 1 g where GM and WM are gas and water injection respectively RSW is solution gas in the water phase and cm is an average effective compressibility term From this general material balance equation we will investigate the affects of water in ux rocldwater compressibilities and lowpermeability systems 131 Waterdrive Gas Reservoir The impact of water in ux is to provide pressure support resulting in slower pressure decline Subsequently gas reservoirs associated with aquifers show a attening of the pz curve Figure 12 shows pz curves for gas reservoirs with varying strengths of aquifer support In all cases linear extrapolation of the waterdrive cases to determine OGIP would lead to optimistically high values strength pZ water drive pZ Depletion drive V Figure 12 Water Drive Gas Reservoir pz Curve The rate of the gas withdrawal is directly proportional to the ability of water to encroach For example a high withdrawal rate coupled with a strong aquifer could lead to early coning andor pockets of trapped gas Agarwal et al in 1965 attributed the low gas recovery in water drive reservoirs to the trapped residual gas saturation and a volumetric displacement efficiency less than unity They showed that the size and properties of the aquifer and the withdrawal rates along with residual gas saturation and volumetric sweep efficiency impact the ultimate gas recovery and thus are major factors in designing field development strategy When water invades a gas reservoir the net volume of water in ux reduces the gas volume The material balance equation must re ect this addition subsequently we can write original volume remaining volume net water of GIP rcf of GIP rcf in ux rcf Assuming no injection has occurred that rock and water compressibility changes are small and the solubility of gas in the water is negligible then the general material balance equation reduces to G p p p 1 1 W W B 14 2 2M G GBg e P VJ where We cumulative water in ux into the gas reservoir rcf Wp cumulative water production rcf Note an alternative expression is WPBW where BW is the water formation volume factor in rbblstb Then Wp can be expressed in stb Rearranging Eq 14 to solve for gasinplace results in the following expression GpBg lWe Wp 15 B B g g1 Early in the producing life of a reservoir the difference in the denominator is small and therefore could lead to erroneous values of gasinplace Subsequently to obtain accurate results Eq 15 should be used over longer periods of time To estimate the ultimate recovery efficiency in a waterdrive gas reservoir requires an estimate of residual or trapped gas saturation In a waterdrive gas reservoir gas saturation at abandonment called residual or trapped does not equal original gas saturation SIgr Sgti Sgi therefore B 39 S S RFwd 1 g i 1 P aZ 1 gr 16 Bga Sgi Za Pi Sgi Implicit in the derivation of Equation 16 is the assumption that volumetric sweep efficiency for gas Ev is 100 This assumption is optimistic as frequently the displacement of gas by water results in unswept bypassed portions of the reservoir increasing the trapped gas saturation Subsequently a modified form of Eq 16 is Bgi Sgr 1 EV B Sgi EV RFWd 1 EV 17 g8 Some published values of residual gas saturation were given by Geffen 1952 and are shown in Table 11 below Porous Material Formation Sgr Unconsolidated sand 16 Slightly consolidated sand 21 synthetic Synthetic consolidated sand Selas Porcelain 17 Norton Alundum 24 Consolidated sandstones Wilcox 25 Frio 3038 Nellie Bly 3036 Frontier 3124 Springer 33 Torpedo 3437 Tensleep 4050 Limestone Canyon Reef 50 Table 11 Residual gas saturation after water ood as measured on core plugs Geffenet al 1952 Example 12 The reservoir is the same as described in the previous example except that pressure is fully maintained at its original value by a strong water drive Assume that the entire gas reservoir is swept by water Given Sgi 75 and Sgt 35 respectively What if EV 60 Since the pressure is constant for the life of the reservoir a simpli ed form of Eq 16 becomes S RFWd pi 1E 53 S gi 075 Similiarly if the volumetric sweep ef ciency is accounted for then Eq 17 results in RFwd 32 Both are much less than typical recovery ef ciencies in depletiondrive gas reservoirs Note that a partial water drive does not maintain pressure completely and thus would allow some gas production by pressure depletion and recovery ef ciency would improve In general recovery ef ciency in a gas reservoir is much better under depletion drive than under waterdrive A modi ed material balance for water drive gas reservoirs was proposed by Hower and Jones 1991 and Schafer et al 1993 to account for pressure gradients that develop across the invaded region Previous theory assumed the invaded zone pressure is equivalent to the reservoir pressure and is constant The modi ed approach accounts for pressure gradients in the invaded zone due to capillary pressure The method predicts a higher pressure at the original reservoir boundary and a much lower pressure in the uninvaded region of the reservoir Both water in ux calculations and reservoir performance predictions are in uenced by the pressure gradient term The pressure drop in the invaded zone is given by the steady state radial ow equation 1412quw lnr0 rt Ap p p 18 mv o t krwkh where p0 pressure at the original reservoir boundary pt pressure at the current reservoir boundary r0 radius at the original reservoir boundary rt radius at the current reservoir boundary The relative permeability to water is evaluated at the endpoint ie at residual gas saturation therefore it is not required to obtain the entire relative permeability curve The residual gas saturation is assumed constant throughout the entire invaded region The water ow rate can be estimated using the water in ux term qW dWedt The resulting modi ed material balance equation becomes GpBg GBg BgiGtBgt BgWe BWWP 19 here G 15 the volume of trapped gas m the mvaded regron of the reservorr and 15 a funcuon of 5a and average pressure m the mvaded regron Resu1ts from the proposed mod ed matena1 ba1anee method agreed wrth a numenea1 mm 1 Wm 01 performance Frgure 1 3 from Hower and Jones 1991 r11ustrates the eneeuent mateh wrth the srmu1ator 1f a kn 0 0 15 ass med 1so ee m rese u u performance between the eonvenuona1 and modfredmaterra1 ba1anee teehmques Mml uunlulhm 39 a ton zen mm 4110 son 9911 7 cumummsssmmmm Frgure 1 3 Companson ofreservorr performance for eonventrona1 and mod ed matena1 ba1anee methods and numenea1 srmu1auon Hower and Jones 1991 Example 1 3 GWLUX 15 a so ware appheauon for the moddfxed gas matena1 ba1anee method promded by GRI Use the DEMO DAT le and determrne the 06 When applymg the matena1 ba1anee equatrons for 011 and gas reservoer the typrea1 so1uuon 15 to rearrange to solve for N and then used to eompute 001 or 06 at ddfferent umes dunng a reservoxr s hfe Natura11y the resu1ts of eaeh ea1eu1atron vary somewhat from one trme to another Thus there are o en major questrons about the n tam tr uorOG A powerful method of removing much of the doubt concerning the accuracy of computed results was presented by Havlena and Odeh in two papers in 1963 and 1964 Th e first paper presents the theory the second presents eld case studies Havlena and Odeh39s method rearranges the material balance equations into an algebraic form that results in an equation of a straight line The procedure requires plotting one variable group versus another The shape of the plot and sequence of plotted points provide important insight into the validity of the assumed reservoir drive mechanism The linearized material balance equation for gas reservoirs is F Er WQBW Er 6 where G represents the original gas in place at standard conditions and F total net reservoir voidage F G B W B P g P W E Elg ch total expansion Elg expansion of gas in reservoir E B B g g g1 ch connate water and formation expansion Bgi Pt 1 Swicwcf 1 Swi chngigtxlt 110 111 112 113 Since G and GF are usually expressed in SCF the units of BIg and Bgi are in RCFSCF A plot of FEt vs WeBw E1 should result in a straight line with intercept of G the original gas in place and slope related to water in ux see Figure 14 Wz too small Wz correct FEstb InfemepFG Figure 14 Material balance linear plot for gas reservoirs with aquifer support 19 To appropriately interpret Figure 14 the material balance equation must be coupled with a water in ux model For example for the Fetkovich aquifer model the slope of the straight line should be equal to one If not different aquifer properties must be used Others are the unsteady state Van Everdingen and Hurst and steady state Schilthuis water in ux models In the former a straightline slope provides an estimate of the water in ux constant B If the data does not plot as a straight line then different aquifer properties must be estimated In the latter the slope is equal to the water in ux constant k Further discussion on water in ux properties is beyond the scope of this chapter For details the reader is directed to the references at the end of this chapter The drive indices for a gas reservoir are defined as follows GE Gas drive index GD G Bg 114 P g W B W B Water drive index WDI w 115 G B P g GE cf Compressibility drive index CD W 116 P g Where the sum of the drive indices is equal to one 110 Example 14 The performance history for a gas reservoir with water in ux is given in Table 12 below Solve for the correct gasinplace using the linearized method time Gp Bg Wp days msof rbblmsof stb 1 816 0837 0 31 25299 0843 0 61 52191 0849 0 92 83814 0855 0 123 140817 0868 16563 153 210174 0885 37934 184 260921 0894 54497 214 313742 0905 75868 245 392389 0925 108994 276 429366 0930 120036 304 504400 0952 144969 335 618738 0993 183615 365 733260 1035 221015 396 825832 1067 259662 426 909022 1098 297061 457 949839 1104 335708 488 991534 1117 385396 518 1031923 1132 396082 549 1074335 1152 478896 579 1109657 1167 516296 610 1145626 1185 554942 641 1196897 1221 571505 670 1275411 1289 612823 701 1315925 1316 651469 731 1353185 1340 688869 762 1385369 1360 721995 792 1427744 1407 754052 823 1463357 1442 853428 854 1501825 1488 958326 Table 12 Performance history data for Example 14 The example is setup to demonstrate the in uence of water in ux on identifying the correct straight line A cumulative water in ux of 831 mbbl results in a straight line and estimate of 2107 Bscf of gasinplace See Figure 15 A decrease in cumulative water in ux of 484 mbbl resulted in a concave upwards trend and an increase in cumulative water in ux of 1427 mbbl resulted in a concave downwards trend The GDI is approximately constant at 60 and the WDI at 40 for the 2 years of production history 10602x 210394 R2 09843 FEt A o 10 15 20 25 30 WelEt Figure 15 In uence of water in ux on gas material balance for Example 14 Note if no connate water and formation expansion occurs then Eq 110 reduces to Eq 15 the standard expression for gas material balance with water drive Also if the reservoir drive mechanism is purely by gas expansion depletion drive then Eq 110 reduces to F GEt 117 A plot of F vs El should be a straight line through the origin with slope of G 132 Abnormally pressured gas reservoirs In highpressure depletion drive type reservoirs formation and uid compressibility effects result in a nonlinear pz vs cumulative plot Figure 16 is a schematic illustrating this behavior The rate of decrease of pressure during the early time is reduced due to support of these compressibility components Extrapolation of this initial slope will result in an overestimation of gasinplace and reserves As pressure reduces to a normal gradient the formation compaction in uence on the reservoir becomes negligible and thus the remaining energy comes from the expansion of the gas in the reservoir This accounts for the second slope in Figure 16 112 Gas ex ansion I7 p Z 1 Formation compaction Water expansion pz Gas expansion Overestimate of G L r G P Figure 16 nonlinear pz vs Gp plot due to formation and water compressibility effects Assuming no water in ux or production and no injection then the general material balance equation 13 reduces to n1GP zi G p 118 2 1Ceppip where cm is a pressuredependent effective compressibility term An early definition of cm by Ramagost and Farshad 1981 where in terms of constant pore and water compressibilities cwswi cf 1 Swi Average values were assumed thus removing the complication of pressure dependency To determine gasinplace the pz term yaXis is linearized by plotting 1 wswicfPi P Z 1 Swi ce 119 vs Gp Example 15 Estimate the original gasinplace for the data given by Duggan 1972 for the Anderson L sand Apply both the conventional and geopressured material balance equations Given pi 9507 psia cW 32 X 10396 psi391 Swi 024 cf 195 x 10396 psi391 Original pressure gradient 0843 psift 113 sia 2 G Bof 9507 1 440 0 9292 1418 03925 8970 1387 16425 8595 1344 3 2258 8332 1316 42603 8009 1282 5 5035 7603 1239 75381 7406 1218 87492 7002 1176 105093 6721 1147 117589 6535 1127 127892 5764 1048 17 2625 4766 0977 22 8908 4295 0928 281446 3750 0891 32 5667 3247 0854 368199 Figure 17 displays the results of the conventional material balance Gasinplace is estimated to be 893 Bcf Volumet ic normal pressured 8000 7000 6000 5000 4000 3000 2000 1 000 74679X 6667 R2 09929 pz psia 0 20 40 60 80 100 Gp Bcf Figure 17 Conventional material balance solution for Example 15 Figure 18 shows the results when using the geopressured approach The resulting gas inplace is 707 Bscf Thus if the conventional approach is taken the gasinplace will be overestimated by more than 25 114 Volumet ic geopressured 5 8 92336x R2 09979 modi ed pz psi 8 8 S 8 8 8 8 8 8 8 6 8 O 0 20 40 60 80 100 Gp Bcf Figure 18 Highpressure material balance solution for Example 15 The above example assumed that formation compressibility was both known and constant However frequently formation compressibility varies during pressure depletion and is difficult to obtain in the laboratory Roach 1981 developed a material balance 39 39 J for 39 quot 39J quot quot formation compressibility and gasin place and was later applied by Poston and Chen 1987 to the Anderson L example The revised material balance equation is 1 m J GP m Swi w f L20 pip PZi G pippzi lSwi If the formation compressibility is constant then a straight line will develop with a slope lG and an intercept Swicw Cf1Swi Example 16 Repeat example 15 and estimate both gasinplace and formation compressibility Figure 19 shows the results from this analysis The original gasinplace is estimated from the slope 1000 13199 and the formation compressibility from the intercept 6 6 cf bx10 l Swi Swicw125x10 psz The deviation from the straight line at early time is due to the pore uids supporting the overburden pressure However as uids are withdrawn the formation compacts thus transferring more of the support on the rock matrix 758 Bscf 1 Geopressured 150 1 1 y 13199x 17511 R2 0993 100 3 gt39 50 I 0 0 2 4 6 8 10 12 14 X mmscfpsi Figure 19 Simultaneous solution of gasinplace and formation compressibility for a volumetric geopressured gas reservoir Example 16 Fetkovich et al in 1991 further expanded the effective compressibility term by including both gas solubility and total water associated with the gas reservoir volume The resulting expression accounts for pressure dependency c S c M c c 2 two wz ma Mp fp 1 SW The cumulative total water compressibility ctw is composed of water expansion due to pressure depletion and the release of solution gas in the water and its expansion The associated watervolume ratio M accounts for the total pore and water volumes in pressure communication with the gas reservoir This includes nonnet pay water and pore volumes such as in interbedded shales and shaly sands and external water volume found in limited aquifers The authors defined both terms as M MNNP Ma cm 121 q 2 mp l hnhg haq rel q 1 122 r hquot mg wt rr where nnp nonnet pay property r reservoir net pay property aq aquifer property hnhzg net to gross ratio The proposed method of obtaining gasinplace requires a trial and error solution Historical pressure and production data is coupled with an assumed gasinplace value to 116 backcalculate values of effective compressibility from a rearranged material balance equation 13 Zi Gp 1 c 1 1 123 e backcalculated pZ G pi p The effective compressibility from Eq 123 can be plotted as a function of pressure and compared to values determined from rock and uid properties in Eq 121 A reasonable fit between the two methods provides an estimate of gasinplace and a measure of physical signi cance to the results Example 17 Fetkovich et al tested their method on the Anderson L sand data from Duggan 1971 Additionally they calculated total water compressibility as a function of pressure Using their values of ctw a G 72 Bscf Cf 32 X 10 396 psi 391 and M 225 the following results were obtained 50 45 7 cEpgeneratedfromrockamp 40 39 water properties 35 A E 30 A 3 25 7 839 20 7 0 15 camamassum39ng OGIP 0 00 10 A 5 e I 0 1 1 1 1 0 2000 4000 6000 8000 10000 pressure psia Figure 110 Comparison of backcalculated effective compressibility assuming OGIP with the rock and uid property derived values Figure 110 shows best fit results after varying M Cf and G respectively The authors also varied Swi and decided on Swi 035 In Fig 110 the original Swi 024 was maintained Figure 111 shows the performance match and prediction using the variables listed above The estimated gasinplace of 72 Bcf is within the range of the previous methods Notice the first data points at high pressure in Figure 110 do not fit the correlation drawn These points correspond to the same data points which deviate from the straight line in Figure 19 and thus the same explanation is believed valid for this method as well The disadvantages of the Fetkovich et al method are the requirement of rock and water properties to build the effective compressibility correlation the assumption that Cf is constant and the nonuniqueness of the solution since multiple combinations of the 117 variables can yield the same outcome The advantage is the addition of the pressure dependency of the water compressibility and the development of a physical basis for the analysis historical pz psia 0 20 40 60 80 100 Gp Bscf Figure 111 Performance match and prediction for the Anderson L reservoir 133 Low permeability gas reservoirs Gas material balance in conventional volumetric reservoirs is described by a linear relationship between pressurezfactor pz and cumulative production Unfortunately tight gas reservoirs do not exhibit this type of behavior but instead develop a nonlinear trend see Figure 112 which is not amenable to conventional analysis Figure 112 Pz response for conventional gas reservoir and a tight gas reservoir The nonlinear trend is a function both of the pressure measurement technique and the reservoir characteristics Typical shut in periods are not of sufficient duration to achieve a representative average reservoir pressure This concept can be reinforced by examining the criteria for reaching pseudosteady state ow Wicn39A 124 k t 3790 3 ps tDApss Assuming a well located in the center of the drainage area and substituting typical reservoir and gas properties for a tight gas formation cl 11 k 01 md pgi 0012 cp ct 0001 psi39l results in a time to reach pseudosteady state of 2 years for an 80 acre drainage area and 16 years for a 640acre drainage area Subsequently a single buildup pressure measurement after seven days of shut in will not achieve such a boundary condition To analyze lowpermeability reservoirs the following constraints are applied 1 no water in ux 2 constant reservoir temperature 3 no rock compressibility effects and 4 only single phase dry gas ie no phase changes occur in the reservoir Furthermore to simplify the analysis the bottomhole owing pressure will be assumed to be constant over the life of the well A reasonable assumption for dry gas wells controlled by surface line pressure Referring to Figure 112 three trends are exhibited on the pz plots for low permeability reservoirs During the early time period a rapid decrease in pressure occurs If this trend is extrapolated to pz 0 the gasinplace G will be seriously underestimated The behavior has been previously explained as the response to transient ow Slider 1983 however additional analysis did not confirm this hypothesis An alternative solution is the rapid depletion of a stimulated well in a reservoir consisting of a natural fracture network in simple terms the ush production associated with such a condition Coupled with this behavior is the inability of the pressure measurement technique to capture reservoir pressure within the testing time Subsequently as the drainage radius is expanding the testing pressure deviates more and more from the average reservoir pressure The intermediate period exhibits uniform slope over an extended period of time even though the magnitude of the pressure measurement observed is significantly below the average reservoir pressure During this period the test time is too short to capture the average pressure response however consistency of the data suggests that a similar region is being repeatedly investigated by the pressure test For example notice in Figure 113 the difference in pWS and pr is approximately constant for an extended period of time Several researchers Stewart1970 Brons and Miller 1961 have presented methods to correct measured data to average reservoir pressure by pressure buildup techniques 119 m1 p U HH wf 394 J H w H H Figure 113 Schematic of a partial buildup response in a tight gas reservoir indicating the difference in measured pWS and average reservoir pressure pr The constant slope provides an opportunity to estimate the hydrocarbonpore volume th De ning the slope m as m M 125 AGp and substituting into the gas material balance equation results in an expression to determine th TP 1 i gtxlt th T m 126 sc From volumetrics th 43560Ah 1 SW 127 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 gasinplace as illustrated in Figure 114 The problem is de ning the relationship between the determined slope and the actual slope if one could measure the actual reservoir pressure Case A exhibits two parallel trends of constant slope ie m1 m2 Gasinplace can readily be obtained from P39 1 G 1 128 z m 1 The difference in gasinplace between the two lines is due to the initial reservoir pressure difference and not the hydrocarbon pore volume which is the same for both lines 120 Grp G1 G2 Figure 114 Three possible relationships between the conventional response and the tight gas response To have equal slopes suggests the radius of investigation of the pressure test is expanding at the same rate as the radius of drainage of the reservoir That is r m constant re over an extended period of time The magnitude of gasinplace will be overestimated by this method and therefore provides an upper bound to the well In case B the slopes are different but the intersection point occurs at the same gasin place Estimation of G is obtained by G J 129 2 int m1 2 m2 where the pzim is the intercept value from the identified pressure trend To solve for the correct th requires the substitution of m into Eq 126 Subsequently the hydrocarbon pore volume is corrected to re ect the difference in reservoir pressures For this behavior to occur means the investigative volume seen during subsequent pressure tests is approaching the average drainage volume of the well In other words r gt 0472re This is as expected for depleted reservoirs where the pressure gradient is approximately uniform throughout the reservoir The third and nal scenario Case C exhibits both a different slope and intercept between the measured pressure trend and the actual reservoir behavior Unfortunately the measured data does not re ect the actual reservoir behavior The best is to estimate a range for gasinplace using Case A as the upper bound and case B as the lower bound A nal stage of the life of the well occurs when depletion has been significant see Fig 112 At this time the measured pressure curve attens and becomes constant converging to the actual average reservoir pressure In many cases the gasinplace was estimated by extending a straight line from the initial pz point through this late time point Experience has shown this method typically underestimates gasinplace due to the late time measured pressure slightly underpredicting the actual reservoir pressure Also as Fetkovich etal 1987 correctly point out a rise in pressure can be a rebound effect due to a decrease in withdrawal from the reservoir Example 18 The example well produces from the Pictured Cliffs sandstone in the San Juan Basin of northwest New Mexico Picture Cliffs is a low permeability sandstone to shaly sandstone gas reservoir found at a depth of approximately 3200 feet and developed on 160 acre spacing Dutton et al 1983 The example well No114 was initially completed in 1958 and included a hydraulic fracture treatment to be commercially productive Other well and reservoir data are listed below The long history of production and pressure data make this well an excellent candidate for investigation d2 11 pg cp 00134 h ft 40 cu psi39l x 10394 577 yg 067 Tr deg F 106 SW 44 rw ft 0229 Pi si 1131 Table 13 Input well and reservoir properties Figure 115 is the pz vs cumulative production plot for this well In the San Juan Basin pressure data is recorded over a 7day shut in period and reported annually until 1974 and every other year until 1990 The primary purpose of collecting this information was for deliverability testing and proration Notice the typical tight gas well response of a rapid decrease in pressure within the first year This behavior does not correspond to the end of the transient period which occurs 8 to 10 years later according to decline curve analysis The majority of time and hence cumulative production exhibits case B behavior ie constant pz decline Applying Eq 129 this trend results in an estimate of 660 mmscf of gasinplace 122 PZ vs Cumulative Production N 0 114 PIZ psia Curmlative Production rmscf Figure 115 Field example of tight gas response Case B on pz plot and estimation of gasinplace Also shown on Figure 115 is an extrapolation between the initial pz and the anomalous increase in pz found in the latest data points resulting in 520 mmscf of gasinplace Frequently this extrapolation is applied to tight gas wells to estimate gasinplace and recovery The validity of the last points is pivotal to this method being successful or not These pressure points were acquired during a time of extended cycles of shutin and production due to external constraints The resulting bottomhole owing pressure is increased which subsequently translates into an increase in recorded shutin bottomhole pressure This is the same conclusion as drawn by Fetkovich et al in 1987 Unless this pressure data is obtained very late in the life of the well it is likely this method will underestimate gasinplace and reserves Cumulative production through 2006 for this well is 526 mmscf therefore 80 of the gasinplace has been recovered A rate 7 cumulative plot Figure 116 also provides a linear trend which when extrapolated results in gasinplace of 700 mmscf or 75 recovery Both methods are within reasonable agreement 123 4500 4000 7 3500 7 3000 7 2500 7 2000 7 1500 7 1000 7 u 500 7 ow rate mscfmonth o 0 1 1 1 1 1 1 0 100 200 300 400 500 600 700 Cumulative production mmscf Figure 116 Extrapolation of Rate 7 cumulative trend for gasin place A key to tight gas development is the drainage area of existing wells and the feasibility of in ll drilling Using Equation 129 to adjust the slope the hydrocarbon pore volume is calculated to be 7544 mmrcf Substitution of the known gas and well properties results in a drainage area calculation of 70 acres To further investigate the tight gas pressure behavior a single well simulation model was developed for singlephase ow As a simpli cation the reservoir properties were assumed to be homogeneous and isotropic The well was bottomhole pressure constrained initially at 250 psi and then reduced to 150 psi ten years later This change re ects the actual pressures measured during the annual deliverability tests Figure 117 illustrates the excellent match between the results from the simulator with the measured data for both gas rate and shutin bottomhole pressure The success of the model veri es the linear trends seen on the gas material balance plots and the slow pressure response of tight gas reservoirs Furthermore to obtain this match the areal extent of the simulation model was 86 acres which is in agreement with the previous methods The analysis suggests this well has drained 70 to 90 acres of the dedicated 160acre proration unit and has recovered approximately 70 of the gasinplace within that volume The paradox is the boundarydominated ow exhibited by the decline curve The nearest well is approximately 1850 feet away from the subject well farther than the estimated drainage area Two explanations can be given First the drainage calculations are based on isotropic conditions and therefore a circular drainage pattern However if anisotropy exists then the two wells are sufficiently close enough to provide interference 39 39 quot of r J quot and 39 39 39 trends show a dominant northwestsoutheast direction the exact direction of these two wells Second a thinning of the reservoir net pay thickness over the areal extent of this well would increase the drainage area For example if thickness is reduced by half then the drainage area doubles to approximately 160 acres 124 1000 7 1200 l simulated I 1000 o E I I A measured u a 100 7 800 E 395 3 E 7 600 g s i E 395 0 g 10 7 400 5 e a i 200 1 i i i i i i i i i i i i i i i i i i i i 7 0 0 5 10 15 20 25 timeyears Figure 117 Comparison of simulation results with measured data for Pictured Cliffs example References Agarwal RG AlHussainy R and Ramey Jr HJ The Importance of Water In ux in Gas Reservoirs JPT Mar 1965 BronsF and Miller WC A Simple Method for Correcting Spot Pressure Readings 1961 Trans AIME 222 803805 CarterRD and Tracy GW An Improved Method for Calculating Water In ux JPT Dec 1960 Duggan 10 The Anderson L 7 An Abnormally Pressured Gas Reservoir in South Texas JPT24 No 2 pp 132138 Feb 1972 DuttonSP CliftSJ HamiltonDS HamlinHS Hentz TF Howard WE AkhterMS and LaubachSE Major Low Permeability Sandstone Gas Reservoirs in the Continental United States GRIBEG Report No 211 1993 Engler TW A New Approach to Gas Material Balance in Tight Gas Reservoirs SPE 62883 presented at the ATCE in Dallas TX 2000 Fetkovich MJ A Simpli ed Approach to Water In ux Calculations Finite Aquifer Systems JPT July 1971 p814 FetkovichMJ VienotME BradleyMD and Kiesow UG DeclineCurve Analysis Using Type CurvesCase Histories SPEFE Dec 1987 637656 Fetkovich MJ Reese DE and Whitson CH Application of a General Material Balance for HighPressure Gas Reservoirs SPE 22921 presented at the ATCE in Dallas TX October 1991 Geffen TM Parrish DR Haynes GW and Morse RA Efficiency of Gas Displacement from Porous Media by Liquid Flooding Trans AIME 195 pp 2938 1952 Hammerlindl DJ Predicting Gas Reserves in Abnormally Pressure Reservoirs paper presented at the SPE ATCE in New Orleans La Oct 1971 Havlena D and Odeh AS The Material Balance as an Equation of a Straight Line Trans AIME Part 1 2281896 1963 Part 2231 L815 1964 Hower TL and Jones RE Predicting Recovery of Gas Reservoirs Under Waterdrive Conditions SPE 22937 presented at the ATCE in Dallas TX Oct 1991 126 Ikoku CU Natural Gas Reservoir Engineering Krieger Publishing Co Malabar FL 1992 Lee J and Wattenbarger RA Gas Reservoir Engineering SPE Textbook Series Vol 5 Richardson TX 1996 Poston S W and Chen HY Simultaneous Determination of Formation Compressibility and GasinPlace in Abnormally Pressured Reservoirs SPE 16227 presented at the 1987 Production Operations Symposium in OKC OK March 1987 Ramagost BP and Farshad FF pz Abnormal Pressured Gas Reservoirs SPE 10125 presented at the ATCE in San Antonio TX Oct 1981 Roach RH Analyzing Geopressured Reservoirs 7 A Material Balance Technique SPE paper 9968 Dallas TX Dec 1981 Schafer PS Hower TL and Owens RW 39 WaterDrive Gas Reservoirs published by GRI 1993 SliderHC Worldwide Practical Petroleum Reservoir Engineering Methods Pennwell Publishing Tulsa OK 1983 StewartPR LowPermeability Gas Well Performance at Constant Pressure JPT Sept 1970 11491156 Van Everdingen AF and Hurst W Application of the Laplace Transform to Flow Problems in Reservoirs Trans AIME 186 pp 305324 1949 127 Problems 1 N E One well has been drilled in a volumetric closed gas reservoir and from this well the following information was obtained Initial reservoir temperature Ti 175 F Initial reservoir pressure p 3000 psia Speci c gravity of gas yg 0 60 air 1 Thickness of reservoir h 10 ft Porosity ofthe reservoir 10 Initial water saturation Swi 35 After producing 400 MMscf the reservoir pressure declined to 2000 psia Estimate the areal extent of this reservoir Reservoir temperature is 180 F Reservoir pressure has declined from 3400 to 2400 psia while producing 550 MMscf Standard conditions are 16 psia and 80 F Gas gravity is 066 Assuming a volumetric reservoir calculate the initial gasinplace and the remaining reserves to an abandonment pressure of 500 psia all at the given standard conditions A gas field with an active water drive showed a pressure decline from 3000 to 2000 psia over a 10month period From the following production data match the past history and calculate the original hydrocarbon gas in the reservoir Assume z 08 in the range of reservoir pressures and T 600 F 4 The material balance plot below is for Well No 88 completed in the Picture Cliffs Formation in the San Juan Basin as described in Example 14 Well and reservoir properties are given below d2 11 pg cp 00131 h ft 67 cu psi39l x 10394 622 yg 067 Tr deg F 103 SW 44 rw ft 0229 Pi psi 1045 Estimate the gasinplace and drainage area for this well If cumulative production was 752 mmscf what has been the recovery factor 1400 1200 1000 pz psia 0 200 400 600 800 1000 cumulative production mmscf 5 Ramagost and Farshad 1981 provided the following information for an offshore Louisiana gas reservoir pi 11444 psia Cf 195 X 10396 psia391 Swi 022 cW 32 XlO396 psia391 sia 2 G Bcf 2 11444 1496 0 7650 10674 1438 992 7423 10131 1397 2862 7252 9253 1330 5360 6957 8574 1280 7767 6698 7906 1230 10142 6428 7380 1192 12036 6191 6847 1154 14501 5933 6388 1122 16063 5693 5827 1084 18234 5375 5409 1054 19773 5132 5000 1033 21566 4840 4500 1005 23574 4478 4170 0988 24590 4221 Estimate the original gasinplace a assuming a normally pressured gas reservoir b assuming a geopressured reservoir and known Cf c assuming a geopressured reservoir with an unknown but constant Cf 129
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