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Pore-Volume Compressibility ofConsolidated, Friable, and UnconsolidatedReservoir Rocks Under Hydrostatic LoadingG. H. Newman, SPE-AIME, Chevron Oil Field Research Co.

IntroductionThe ~Seof pOre.vQ!Urn.~~~rn.nrewihilitv-norositv cor-d----------= =_. --.-, ___relations in engineering calculations is well known.The correlations developed by Hall’ for both sand-stones and limestones have been widely distributed.Van der Knaap’ published a similar correlation usinglimestone samples from a single well and also corre-lated the data with net pressure.

Such correlations are attractive because of thesimple relationship established. However, those cor-relations were intended only for well consolidatedsamples; correlations for friable or unconsolidatedsamples have not been published.

This study compares our laboratory data with thepublished correlations of consolidated samples aswell as with values for friable and unconsolidatedsandstones. Compressibility values are presented for256 rock samplesfrom 40 reservoirs — ]97 samplesfrom 29 sandstone reservoirs and 59 samples from 11limestone reservoirs. Porosities ranged from less than1 percent to 35 percent. Compressibility values fromthe literature*3,s.$ for 79 samples are added, includ-ing Halls and Van der Knaap’s.

The ExperimentsSampliig

To obtain a representative sample of a formation fortesting, one must avoid grain rearrangement. Thisproblem is unlikely to occur with consolidated sam-ples or friable samples containing some cementation,although the effect of removing the overburden is still

unknown. Unconsolidated samples, on the otherhand. present a much more complex problem, in thatgrain rearrangement is very likely during either coringor subsequent handling. The advent of the rubber-sleeve core barrel much improved the chances of ob-taining representative samples. We have some evi-dence that, if carefully handled, rubber-sleeve coreswill provide reasonably undisturbed samples. How-ever, even if the sand is captured undisturbed in therubber sleeve, internal gas can expand the core duringthe trip to the surface.

The history of all the samples used in this study isnot complete, but most of the unconsolidated sampleswere obtained from rubber-sleeve cores.

Preparing the Samples

The consolidated and friable samples used in thisstudy were generally plugs 1 in. in diameter and 3 in.long. and their condition ranged from well preservedto dry and weathered. The core plugs were extractedin solvent to remove water and hydrocarbons, putinto a flexible jacket, and saturated with a refined oil.

The unconsolidated samples of about the samedimensions were generally cored from rubber-sleevecores that had been frozen in liquid nitrogen and forwhich liquid nitrogen had been used as a drillingfluid.” The frozen samples were placed in a Teflonsleeve and allowed to thaw. End plates and screenswere then placed on the ends of the samples. At thispoint the bulk volume of the sample was determined

The pore-volume compressibilities and porosities presented here were derived from 256samples of sandstone and limestone representing 40 reservoirs. These and previouslypublished data are in poor agreement with compressibility-porosity correlations in theliterature. The salient conclusion is that to evaluate rock compressibility for a givenreservoir it is necessary to measure compressibility in the laboratory.

FEBRUARY. 1973 129

from linear dimensions and the sample was placed inthe test cell. A hydrostatic overburden pressure ofabout 50 psi was exerted on the samples before theywere cleaned with solvents and resaturated with arefined oil. The change in the bulk volume at about50 psi was recorded. At the end of the compressibilitytest the sample was extracted in toluene and the sand-grain volume was determined. The sand-grain vol-ume was subtracted from the initial bulk volume toobtain a pore volume (porosity) at zero effective pres-sure. This porosity value at zero pressure was chosento compare with pore-voiume compressibility becausethe zero pressure porosity is normally what the reser-voir engineer has available from routine core analy-sis data.

Measuring Porosity

With the exception of the unconsolidated sandstoneporosities previously discussed, initial porosities weredetermined by API-approved methods,’” which con-sisted of determining the pore volume by resaturationand the bulk volume by either displacement or calibermeasurement.

Applying Stress

Overburden Pressure. All of our data were obtainedfrom samples under uniform hydrostatic stress. Thiswas accomplished by transmitting the overburdenpressure to the jacketed test sample with hydraulicfluid. The tests were conducted under either constantor varying overburden pressure.

Pore Pressure. The pore pressure was controlled.L--.. -I. +L ..== . i..kat wa]l and omlld he variedLll IUU&fl Llle wll~p!e ,CM- ,. . . . . . -- --

independently of the overburden pressure duringtests. The tests were conducted with either constantor varying pore pressures.

Effective Pressure. The ability to vary the overburdenand pore pressures independently made it necessaryto express the data at a common stress condition.This was established as a function of the effectivepressure, defined as the difference between the over-burden (lithostatic) and pore pressures.

Determining Volume Changes

The change in sample pore volume as a function ofeffective stress was obtained by various laboratorymethods.:” These included (1) direct measurementof fluids expelled from the samples, and (2) inferredpore-volume changes determined by measuring di-mensional changes of the samples. The values wereobtained during both increasing and decreasing effec-tive stress. A pore-volume vs effective-stress relation-ship was found for each sample by increasing theeffective stress in about 500-psi increments to aneffective stress equal to or greater than lithostaticpressure based on individual sample depths. Litho-gatic pressure was assumed to be 1 psi./ft.

Calculating Pore-Volume Compressibility

The compressibility values shown in Fig. 1 wereobtained by graphically differentiating the pore-volume: effective-pressure relationships by means of

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the following:

~=ldv.—— ,.. . . . .0P (1)Vp dpeff

where

Co = pore volume compressibility, vol/vol/psiVP = pore volume of the sample at a given

effective pressuredVp = incremental change in pore volume re-

sulting from an incremental change ineffective pressure

dp,ff = incremental change in effective pressure.

Eq. 1 contains the assumption that most of the pore-volume change results from efiective pressure differ-ence. This is a valid approximation for higher-porosity samples. A more comprehensive discussionhas been given by Geertsma.*2

Effects of Cycling, Time, and TemperatureCycling

Cycling is defined as a repeated application of thestress cycle. In other words, the sample is placed inthe test cell and the effective pressure is increased tosome predetermined value. (This value is sometimeshigher than any stress the sample will ever be sub-jected to during reservoir depletion.) The pressure isthen released and a second, third, or even fourthcycle can be performed. Except for the case of ex-ceedingly high-strength elastic rocks, each cycle pro-

CODE

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INITIAL POROSITY &T ZERO NET PRESSURE

Fig. l—Porevolume compressibility at 75 percentIithostatic pressure vs initial sample porosity for

both sandstone and limestone samples.

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\

vides a lower compressibility value as a result of anirreversible change in the rock’s internal structure.Some investigators’ found it necessary to cycle thesamples in order to form a copper jacket around thetest sample. This was done so that the pore volumesexpelled during subsequent loading were not affectedby the penetration of the copper jacket into the an-nular space between the jacket and the sample, aswell as into the surface pores. Other investigators,including King,’ have cycled the samples until theyexhibit elastic behavior; that is, until there is no addi-tional pore-volume hysteresis between cycles. Cycling,for either reason, can result in lower compressibilityvalues on a rock that has failed internally, and theresulting condition is certainly not the condition ofthe sample as it is received in the laboratory. Thisinternal failure is easily exposed with scanning elec-tron micrographs, with thin-sections, or in the caseof unconsolidated sands, with grain-size anaiysis be-#--- ....~ o%-. -1,-l;-” A n .avr-.antinn tn thic wmJh+ helUIG cI1lU tZILG1 &y b,,,,,& fi,l WAW&y U”Jl .“ .s..- . . “ . . “-

in a compacting reservoir that had failed in situ dur-ing pressure depletion or a highly fractured reservoirthat had failed as a result of tectonic forces duringits hi~t~ry: The effects of cycling can be even moreserious on friable or unconsolidated sands because oftheir inelastic behavior.

We have only one example where cycling may leadto a closer approximation of in-situ compressibility,and that is in testing highly disturbed unconsolidatedsands, when grains have been rearranged during cor-ing. Rearrangement of grains from that in-situ condi-tion generally tends to provide a looser packing,which results in a higher pore-volume compressibilityvalue during the laboratory tests. We have demon-strated this by taking sets of adjacent samples froma carefully handled and preserved rubber-sleeve core.One set of samples was carefully handled and theother set was purposely rearranged. The results haveshown that the disturbed samples had much highercompressibilities. Cycling the ‘disturbed samples- re-+,,eo,-1 +h.arn rnnv PICK-IV tn tha in-ck nat.kino rnn -LuLll&u .I, w,li ,tlv. e -, V=W.J .V ...w... ---- ~-- .....a ----dition, but significant internal failure occurred.

The values of pore-volume compressibility in thisstudy were obtained by methods that did not requirecycling. In addition, the reported compressibilityvalues were obtained during the initial application ofeffective pressure.

Time

Our pore -volume compressibility values presentedhere were obtained from pore-volume: effective-stressrelationships that had been obtained using pressureincrements of about 30 minutes (30 min/500 psi).This time was generaiiy sufficient to reach a practicaistress equilibrium for most samples. We are awarethat true stress equilibrium cannot be obtained in thelaboratory in any practical time. However, the most-:--: c--- . -1------- .,.1.,. ..1 ..,. h., +L - G-t f=,,,slgnlll~iint ~diiine Gilttll&GS 1-G pl~d 111 LUG 111OL Iew

minutes of applied stress. It is not within the scopeof this report to investigate these time effects; we onlypoint out that they exist.

Temperature

Of the compressibility values presented in Fig. 1, 81

percent were measured at 74”F; the remainder weremeasured between 130° and 275 ‘F. While we havenot made a systematic study of the effect of tempera-ture, a statistical analysis of pore-volume compressi-bility conducted on a suite of sandstone and lime-stone samples at various temperatures within theindicated temperature range showed no significanttemperature effects. The results, however, were notconclusive, since the scatter of the compressibilitydata at any one temperature was as great as anyobservable temperature effects, or greater. Von Gon-ten and Choudhary,’ in discussing the effects of tem-perature on compressibility, show increases as highas 12 percent at 400”F. We recommend, therefore,that all compressibility measurements be made atreservoir temperature.

Presentation of Data

ihe pore-voiume compressibility vaiues shown in this~~ld~y~~~, in !n.o~t ~a~e~, nressure dependent. Tor.---_.-compare samples that had been obtained from variousdepths. which means the samples were subjected tovarious effective stresses under reservoir conditions,a common effective pressure base of 75 percent ofthe lithostatic pressure was used. This value wasseiected as the most probal.ie average efiective stressthe sample would encounter during reservoir deple-tion. The lithostatic pressure was assumed to be 1psi per foot of depth.

The values obtained at this pressure base, plottedagainst the initial sample porosity, are shown on Fig.1, along with Hall’s correlation. Compressibility-porosity values obtained from the literature, for bothsandstones and limestones, are shown on Fig. 2.

Analysis of DataLimestones

The limestone values shown on Fig. 1 are comparedwith both Hall’s and Van der Knaap’s correlationson Fig. 3. No attempt was made to separate the lime-~?~~~ ~~rn.pi~~ by geography Or litholoe~.

Sandstones

To analyze further the porosity and pore-volumecompressibility of the sandstone samples shown inFig. 1, we used a qualitative rock-typing system. Thesamples were grouped as consolidated, friable, orunconsolidated:

1. Consolidated samples consisted of “hard” rocks(thin edges could not be broken off by hand).

2. Friable samples could be cut into cylinders, butthe edges could be broken off by hand.

3. Unconsolidated samples would fall apart undertheir own weight unit?% they had iiiidergull~ SpCLldI---- --,. ...,.1

treatment such as freezing.Each rock type was replotted under this crude

classification system (Figs. 4 through 6). HaiYs cor--~lmt;-” 99A hk .anrlctnne data nnint~ are alcn chmw~-.1b,,=””.. “. w SJ>.7 Ji-11..s>”..w . . . y--...” --- ---- “.. -

The results of this classification system are com-pared in Fig. 7 by “class averaging” the compressi-bility values from Fig. 1 and Figs. 3 through 6 inporosity increments of 5 percent. For example, thecompressibilities for each rock type having betweenO and 5 percent porosity were averaged and piotteci

FEBRUARY, 1973 131

at 2.5 percent porosity. Hall’s correlation is alsoshown.

These class-averaging curves are intended for in-ternal comparison of the data only. They are not forcorrelation, because of the wide variations in thecompressibility values. This wide variation can beseen on Fig. 8, which shows the range of the datapoints making up the class average for the consoli-dated sandstones.

DiscussionFig. 1 shows that our lower-porosity limestone andsandstone samples follow the general trend obtainedby Hall: the pore-volume compressibility values in-crease with decreasing porosity. This is more pro-nounced on Fig. 3, where only the consolidatedlimestone data are compared with Hall’s and Van derKnaap’s correlations, and on Fig. 4, where only theconsolidated sandstones are compared with Hall’sdata.

The individual compressibility curves for theseconsolidated samples showed substantially elastic be-havior; most of the volume was recovered when thepressure was released.

The samples with the higher porosity in Fig. 1 tendto be unconsolidated, and behave contrary to HalI’sgeneral trend; compressibility tends to increase with

!000 . I I I I Io 14ALL1. SANDSTONES

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Hg. 2—F’ore-volume compressibility vs initial sample

porosity obtained from literature source as indicated.

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porosity. This is evident on Fig. 6 as well. The un-consolidated samples also show significant inelasticbehavior (permanent volume reduction with pressur-ization, resulting from internal grain failure).

The friable samples in Figs. 1 and 5 also show thisinelastic behavior, but there is apparently very littlecorrelation between compressibility and initial sam-ple porosity.

Besides showing wide variations in compressibilityas a function of porosity and rock type, our results- -- ..;are in poor agreement wth Halls correlation. ~ltem-ture values of compressibility for 79 samples (in-cluding Hall’s data), shown in Fig. 2, support ourresults and have about the same scatter. Van derKnaap obtained a good correlation for 23 limestonesamples taken from a single well; but his values arealso in poor agreement with Hall%.

We believe the poor agreement between our dataand Hall’s is in part because Hall’s are based on only12 samples — 7 limestones and 5 sandstones in theporosity range of 2 to 26 percent. Our data are basedon 256 samples, 194 in the same porosity range asHall’s.

Conclusions1. The pore-volume compressibility-porosity val-

ues obtained in this study are in poor agreement with

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15 20 25 35INITIAL POROSITY AT ZERO NET MESSURE

Fig. 3-Pore-volume compressibility at 75 percentIithostatic pressure vs initial sample porosity

for limestones.

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CONSOLIDATED SAMCSTONES

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INITIAL POROSITY AT ZERO NET PRESSURE

Fig. 4-Pore-volume compressibility at 75 percent

Iithostatic pressure vs initial sample porosity for

consolidated sandstones.

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0 c

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Fig. GPorwrolume compressibility at 75 percent

Iithostatic pressure vs initial sample porosity for

unconsolidated sandstones.

FEBRUARY, 1973

1!

0

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INITIAL POROSITV AT ZERO NET PRESSURE

Fig. 5-Porewolume compressibility at 75 percent

Iithostatic rwessure vs initial sample porosity forfriable sandstones.

uNCONSOLIOATEO —

TOTAL ALL SAMPLES

lALLSORRELATION

CDNSULIOATEDSANDSTONES

-\A

,.o~o 5 10 15 20 25 30

INITIAL POROSITY AT ZERO NET PRE~RE

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Fig. 7-Class averages of pore-volume compressibilityvs initial sample porosity.

133

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AVERAGE FOR CONSOLIDATEDSANDSTONES

IT\/RANGE OF THE

I

CLASS AVERAGE

.

1.0I I I I 1 I I !

o 5 10 15 20 25 34INITIAL POROSITYAT ZERO NET PRESSURE

Fig. II-Class average of pore-voiume ccmipwssibiiitj W

initial sample porosity for consolidated sandstones.

published compressibility-porosity correlations. Thisis also supported by values in the literature. Thereis a need, therefore, for laboratory compressibilitymeasurements in evaluating rock compressibilityy fora given reservoir.

2. Pore-volume compressibilities for a given po-rosity can vary widely according to rock type.

3. Attempts to correlate the data showed thatconsolidated sandstones differed greatly from lime-stones and friable and unconsolidated sands, but thedata are too widely scattered for correlations to be.-1; nhle. we!! ~efin~~ trends were found only in theL“’IQ.”consolidated sandstones and limestones and in theunconsolidated sands, whereas the compressiiiiiity ofthe friable samples showed little or no relationship

to initial sample porosity.These data- suggest that correlations might be ob-

tained for both well consolidated limestones andsandstones with similar lithologies. That is, correla-tions may be obtained from samples within a givenreservoir, provided lithologic variations are sm@l.This would be similar to Van der Knaap’s correlationfor limestones from a single well. Much the sameapproach is recommended for the friable and “uncon-solidated samples, but here the pore-bolume com-pressibility is not merely porosity dependent; otherstress parameters need to be investigated.

References

1. Hall, H. N.: “Compressibility of Reservoir Rocks,”Tnzm., AIME ( 1953) 198, 309-311.

2, Van der Knaap, W.: “Nonlinear Behavior of Elastic Po-rous Media.” Trans., AIME ( 1959) 216, 179-187.

3. Fatt, I.: “Pore Volume Compressibilities of SandstoneReservoir Rocks: Trans., A-ME ( i95tl j 213, 362-364.

4. King, M. S.: “Wave Velocities in Rocks as a Functionof Changes in Overburden Pressure and Pore Fluid Satu-ration: Geophysics ( 1966) 31, No. 1.

5. Dobrynin, V. M.: “Effect of Overburden Pressure onSome Properties of Sandstones: Sot. Pet. l%?. J. (Dec.,1962) 360-366.

6. Kohlhaas, C. A. and Miller, F. G.: “Rock-Compactionand Pressure-Transient Analysis with Pressure-DependentRock Properties,” paper SPE 2563 presented at SPE 44th;;6xd Fall Meeting, Denver, Colo., Sept. 28-Ott. 1,

7. Von Gonten, W. D. and Choudhary, B. K.: “The Effectof Pressure and Temperature on Pore-Volume Com-

@nc 9C9C . . . . -t..+ *t CPF AA~~ .&&pressibiiity,” Paper ~r~ /-.-” FIw<...w.. U. - _

nual Fall Meeting, Denver, Colo., Sept. 28-Ott. 1, 1969.8. Carpenter: C. B. and Spencer, G. B.: “Measurements of

Compressibility of Consolidated Oil-Bearing Sandstones,”RI 3540, USBM (Oct., 1940).

9. Jennings, H. Y.: “How to Handle and Process Soft andUnconsolidated Cores,” World Oil (June, 1965 ) 116-119.

10. API Recommended Practice for Core-A nalysis Procedure,API RP40, 1st cd., New York (Aug., 1960).

11. Mann, R. L. and Fatt, I.: “Effect of Pore Fluids on theElastic Properties of Sandstone” Geophysics ( 1960) 25,433-444.

12. Geertsma, J.: “The Effect of Fluid Pressure Decline onVolume Changes of Porous Rocksfl Trans., AIME (1957)-’la 2?1 720ALU, JJ, -J2Z. .m~

Original manuscript received in Society of Petroleum Engineers. . . - -- . .,, --..: --- --- ...-+”. -.-m;”.rl F.@” ~~, ~Q7~,omce uec. 44 19JJ. IWVISW ,,l-{lb=u, ,w, ,--. .-W . . . .

Paper (SPE 3S35) was presented at SPE Rocky Mountain RegionalWzeti rig, he!i! in 2!enver, (%!0., April 10-12, 1972, Q Copyright1973 American Institute of Mining, Metallurgical, and PetroleumEngineers, Inc.

134 JOURNAL OF PETROLEUM TECHNOLOGY