Rock Compressibility and Failure as~=e~ervoirM-echanismsin Geopressured

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Gas ReservoirsDavid W. Harville,* SPE-AIME, Louisianastate U.Murrsy F. Hawkins, Jr., SPE-AIME,Louisiana State U.

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IntroductionRock compressibility has long been recognized as animportant factor in material balance calculations ofQfl im place for closed reservoirs producing abovebubble-point pressure. 1 For example, if the pore vol-ume compressibtity of the reservoir rock is half oft~e g~m-pm~sih~ty Of tie undersaturated oil, neglectof the rock compressibtity term results in about a 50percent overestimation of oil in place. In general, itmay be stated that in material balance calculations onclosed reservoirs, consideration of rock compressibti-ty becomes increasingly importantas the fluid com-pressibility decreases. For this reason the effect ofrock compressibility is commonly neglected in studieson gas reservoirs where gas compressibfity is usuallygreat.

Because gas compressibilities decrease with in-creasing pressures, the consideration of rock compres-sibility becomes increasingly important for deeper,high pressure gas reservoirs. For example, the com-pressibility of the gas in the reservoir to be discussedis 30 microsip** at an initial reservoir pressure of8,921 psia. For a nominal pore volume rock com-pressibtity of 6 microsip, neglect of rock compressi-bility in material balance calculations on a closedreservoir will result in a 20 percent overestimation ofinitial gas in place. If the rock compressibfity islarger than 6 microsip, then a still larger overestima-dcn ~f ~u~~ ~!ace ~.~l~t~$In this study we propose

Now with Phillips Patmleum Co., Mo~an City, La.. .Abb~aVia~~n f~~ 10-6 ~i-1, ~i~m being 10-c and sip (aqll are

inches per pound) being psi-l.

that because of low net Overburden pressures, mekcompressibilities in geopressured reservoirs are con-siderably greater than for similar rocks in normallypressured reservoirs. We further suggest that as reser-voir pressure is depleted, the increase in net over-burden pressure initially causes inelastic rock com-paction or rock failure. As failure continues with de-creasing pore pressure, rock compressibility deaeaaesand eventually reaches normal values in the range of6 microsip.

North Ossun F]eld, LouisianaThe mechanisms proposed in the previous paragraphare believed to be illustrated by the performance ofthe NS2B reservoir of the North Ossun field, Lafay-ette Parish, La. This is a geopressured gas reservoirwith an initial pore pressure of 8,921 psia at 1Z,5Wft subsea depth, or a gradient of 0.725 psi/ft. Table1 gives pertinent data on this reservoir. Oood geologiccontrol is indicated by the structure map, Fig. 1. Al-though a gas-water contact exists, it is doubtful thatthe associated aquifer is very large because the rese-rvoir appears to shale out on the west. III addition,considerable complex faulting in the area almost eer-tairdy closes the reservoir with a small aaswiatedaquifer.

Good core and log data have been used to cakm-1... . . ;.;t;~l hvtkmarkn nnre volume of 583 mil-lCWall -u- ..J.--.-- r -lion cu ft, and, with PVT dataj to calculate an initialgas in place of 114 Bscf. The pressure-production

r

A study of the North Ossun field, Louisiana, reveals that as reservoir pressure isdepleted the increase in net overburden pressure initially causes rock failure and as thefailure continues with decreasing pore pressure, rock compressibility decreases untileventually it reaches a normal value.

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TABLE 1-RESERVOIRDATANORTHOSSUNFIELD*LAFAYEITE PARISH, LA., NS2B RESERVOIR

Depth, ft 12,500Pressure, psia 8,921Gradient, psi/ft 0.725Temperature, F 248Gas-water contact, ft 12,580Average gross sand, tt 100Porosity (33 s% quite uniform) 0.235

(electric ioga) 0.24Connate water (eiectric logs) 0.34Permeability, md (33 SS) 200Producing walls 4Geologic controi weils 18Dew-point pressure, psia 6,920initial GOR, bbi/MMacf 160Condensate gravity, *APi 47Net bulk gas volume, MMcf 2,480inithi Z fSCtO; 1.472Initiai gas in piace, Bscf (volumetric) 114Initial gas compressibility 30 X iO-O p~i- at 8,S$2i @a

history of the reservoir is shown in Fig. 2, and p/zvs cumulative production is shown in Fig, 3. For pres-sures below the dew point, two-phase gas deviationfactors were calculated from the PVT data as de-scribed in Chapter 2 of Ref. 1,

Fig. 3 indicates, from extrapolation in the earlylife, an initial gas in place of 220 Bscf, almost twicethe volumetric estimate of 114 Bscf. It is proposedthat during the early life the pressure is partiallysustained by high rock compressibfity resulting fromrock failure as described previously. After the pro-duction of some 20 Bscf, rock failure is essentiallycompleted and rock compressibfity drops to a nor-mal value of about 6 microsip, at a pore pressure ofabout 6,500 psi. At thk pore pressure the gas com-pressibility is up to about 75 microsip, which makesrock c.ompressibfity a comparatively small factor.Thus extrapolation of the curve after about 20 Bscfhas been produced should be valid, and in fact it ex-trapolates to 118 Bscf to agree well with the volu-metric estimate of 114 Bscf.

A further analysis of thk reservoir includes thecalculation, with the following equation, of total ap-parent reservoir pore volume as a function of pres-sure.

414

Ig lg.*

*> ,;%--...:: w cb~,6* . . . . .k --------2i . . . . 3418 .00 a s ,)1 .* 12---#--.--------------.. .07 6. . . . . ..-Q---1:

+:~~~o

II& lStructure mep, top of sand, NS2B reservoir,North Oesun field, Le.

~_GBSP ~ y[l + c.(P, p)] + (G G,)%

(l?ater) (Gas). . . . . . . . .. (1)

As used in this study, tbe connate water Sw includedonly that water in the gas reservoir. In other calcula-tions presented by Harville2 the connate water valuewas increased to include water in associated limitedaquifers. In one case the aquifer size was assumed tobe equal to the size of the gas reservoir, and in an-other case is was assumed to be twice the size of thegas reservoir. Pressure equalization between the res-ervoir and the aquifer was shown to be a valid as-sumption for these small aquifers and for the indi-cated rock and fluid properties.

Fig. 4 shows the pore volume calculated by Eq. 1~~ ~ $GEc~oEof pm ?~ssu~, ~&g no aaeoci-ated aquifer and using for the i&ial gas in place the

. . . . . .

volumetric estimate of i 14 BSCI. The d=rivau.. .- . ..nti..r.a nfthis curve may be used to calculate the rock com-pressibility at each point. As indicated in Fig. 4, therock compressibfity reaches a maximum of 28 micro-sip during the early depletion where rock failure ispresumed to occur. Below about 6,000 psi, accordingto thk interpretation, rock failure is essentially com-plete and the calculated rock compressibility dropsto a more usual I alue of 6 microsip. Because of lowerrock and h@er gas compressibilities at lower porepressures, reservoir performance is very close to thatof a constant volume system, and the p/z extrapola-tion is reasonably accurate. It may be only coinci-dental that rock compressibility drops to more usualvalues when the pore pressure reaches a normal valuefor the reservoir depth; i.e., a gradient of about 0.50psi/ ft.

The foregoing presentation does not prove, ofcourse, that rock failure is the major source of pres-sure support of this reservoir during depletion. (How-ever, Fig. 5, taken from work by Fatt,a provides astriking similarity in the behavior of a Sespe sand-stone sample that had not undergone high overburdenpressures during its geologic history.) Corroborationfor the suggestion that rock failure is a majorsource of pressure support during depletion is

20~

g9 0----25 ~

0

1 \Gas Production ( BCF)

Fig. 3-p/z vs cumulative production for theNS2B reservoir.

W2

Pressure, PSIA (000 s)

Fig. 4-Calculated pore volume of the NS2B resenroir,assuming no water influx and G = 114 Bcf.

0 2 4 6 e 10 12 14External Pressure, PSI (000 s)

Fig. 5-Bulk volume change of a Seapa sandstone sample,zero pom pressure (after Fatt), Pore volume compreasi.

bilities are based on porosity of 25 percent.

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found in the difficulty of explaining the character ofthe support by generally accepted water influx the-ories, because the strong initial support rather sud-denly drops to a very small value. In the additionalstudies by Harville, not presented here, which con-sidered small associated aquifers, the character of thepressure support was unchanged, and only the valuesof the rock compressibil@ were reduced, during boththe initial assumed rock failure interval and the laterstage.

It has been suggested that pressure support in this~~ of reservoir may be water influx from the over-lying and underlying shales. Preliminary studies ofthis possibility indicate that the adjacent shales canprovide neither the volume nor the character of thepressure support indicated by Fig. 4. On the otherhand, rock failure rather nicely explains both.

l~~efiyei ~~ fi~f ~~ f~~.~ oc~~-rsh tajs tyrpeofreservoir, it should not be forgotten that normal rockcompressibtity and connate water expansion are im-portant reservoir mechanisms at higher pore pressuresbecause of decreasing gas compressibility. It shouldalso be realized that what we have just said is evenmore important with oil reservoirs because of theirvery low fluid compressibilities.

With regard to geopressured gas reservoirs, it is .understood that many that we bdieved to be essen-tially closed systems exhibit a large discrepancy be-tween the volumetric estimate of gas in place and thatestimated by extrapolation of the p/z plot. Commonlymentioned is a ratio of about 2 between the figmes,which is the ratio found in thk study. We hope thatthis study will encourage other studies that may shedmore light on this discrepancy and the reservoirmechanism or mechanisms controlling productionfrom geopressured reservoirs.

NomenclatureB, = gas volume factor at pressure p, cu ft/8cf

B,l = gas volume factor at initial pressure,Cuft/scf

c* = connate water compressibtity, psi-i(used 3 X 10+ psi-)

G = initial gas in place, scfG, = gas produced when pressure is p, scfp = average pore pressure at later time, psia

Pi = initial reservoir pore pressure, psia& = connate water saturation, fractionv, = total pore volume, cu ft

References1. Craft, B. C. and Hawkins, M. F., Jr.: Applied Petroleum

Reservoir Engineering, Prentice-Hall, Inc., Engiewoodcliffs, N. J. (1959) 135-138.

2. Harville, D. W.: Rock Collapse as a Producing Mechsn-ism in SuperpressureReservoira,MS thesis, LouisianaStateU., BatonRouge(1967).

3,Fatt, I.: Compreasibdityof Sandstonesat Low to Mod-:~5~ Preasuses,Bull., AAPG (1954) 4% No. 8, 1924-

JWT

Original manuscript raceivad March 24, 1969. Raviaad manu-script received July 9, 1969. Paper (SRZ 2600) wos pmntad atSymposium on Abnormal Subsurface Praasum held st LouiaismaStste U., Baton Rouga, April 28, 1967.0 copyright 1969 Amaricsnhsatituta of Minin& Matelluraicsl, and Petroleum Ssseineass, k.

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