spe 26647 application of variable formation compressibility for improved reservoir analysis

7/30/2019 SPE 26647 Application of Variable Formation Compressibility for Improved Reservoir Analysis

1/16

SPE 26647Application of Variable Formation Compressibility for ImprovedReservoir Analysisf3.P. Yale, G.W. Nabor,* and J.A. Russell, Mobil R&D Corp., and H.D. Pham q andMohamed Yousef,~Mobil E&P US. inc.SPEMembersqNowretired

qqNowwithAbuDhablNatl. OilCo.tNowwithSaudiAramcoCopy@ht 1S53,SocMy of Petroleum Engineer% inc.

Sooktvof PetroleumrIQWrs !

This paper wee prepared for praeematlon at the SSlh Annual Tecfmlcal Conference and Exhibllion of the SocIeIy of Pelrofeum Engineers held IrrHouatom Texas, 3-6 October 1993.This paper wee eelectmf for presenla!ion by an SPE Program Committee followlng review of information contained In an abetract aubmltfed by the author(s). Contents 01the paper,aepresented, have not been reviewed by the Soclaly ot Petroleum Englneare end are aubjecf to correction by the author(e). The material, ae presented, does not necessarily retlwtany poaltlon of the SocIefy of Petroleum Engineers, Iteofficers, or mambera. Pa?erapresented al SPEmeetings are subject to publication ravlewby Edltorlal Commitleea of the Societyof PetroleumEnglneeta. PermleelorrtoCOPYareefrlafed!0 enabatracfof notmore than300words. Illuatratlonemay notbe copied.Tha abatractshould contain conspicuousacknowledgmentof where am by whom ma paper fepreeerded.Write Ubrarlan, SPE, P.O. Box S32438, Richardson, TX 76083-3S3S,U.S.A. Telex, 16324SSPEUT.

ABSTRACTFormationcompressibilityhas long been recognizedasan importantfactor influencing production behaviorfromoverpressuredoil and gas reservoirs. However,forrmtfon compressibii~ data are not routineiycollectedand the us~of formationcompressibilityin reservoiranalysisand simulation is often oversimp!ifjed.This paper discussesmore accuratemethodstodetermine fomation compressibilityand introducesanewmethodfor anafyzing overpressuredoii and gasreservoirswttkh utilizes the variabilityof formationcompressibilitywith declining resefvoir pressure. Thenewiydeveioped method departs from earlier proposedmethods in the use of _ rather than &@ fomtationcompresslbiiii by empfoyinga pore volume formationvoiume factorn,13f,hat propertyintegratesporevoiumecompressibilityeffects over the fuli pressure rangeofinvestigation. Using the newconceptof Elf,the materiaibalance equation (MBE) can be modifiedto inciude theeffects of pressuredependent formation compressibiiiiy.Wefind that the formationcompressibilityin highiyoverpressured unconsolidated reservoirscan be thesameorder of magnitude as gas compressibilityandsignificantlyhigher than oil compressibility. in sometypes of reswvoirs, an order of magnitudechange informationcompressibilitycan occur during drawdown.Weshowthat in many ove~ressured andlorunconsolidated reservoirs, proper integrationof accurateformationcompressibilities is importantfor resetveestimates,determination of drive energies, and overallreservoirdevelopment plans. Forexampie,we find thatthe useof compressibilityvaiues in the MBEwhich aresignificantly fewerthan those which exist in the reservoircouid suggest a strongwaterdrive where one does notexist.

1. lNTRODUCTIONit is recognizedthat a decrease in pore voiumeaccompaniesa decilne in reservoirpressure. Therelativechange in pore volume per unit of pressurechange, i.e., the formationcompressibility,depends onthe rock type, its degree of competence,andthe tectonicsetting. Laboratorymeasurementsshowa wide rangeofcompressibilityievels over the spectrumof rocksfromcompetent carbonatesto unconsolidatedsands,Compressibilitydeclines, sometimesdrastically,aslaboratorystress is increasedto correspondto reservoirpressurechangesfrom discoveryto abandonment.Formationcompressibilityis a source of drive energy inaddition to that provkfedby expansionof fiuids. its effect,and also that of water, are often ignored in anaiyzingreservoirperformancesince the contribution is minorcomparedwith that of gas or oii plus soiutlongas. Theeffects are usuaily considered,however,whenundersaturatedoii resewoir performance is analyzedandthe contributionsof rock and water expansioncan easilyexceed 10percentof the totai.The conditions found in abnormallypressured reservoirsaiso lead to greater significanceof formationcompressibilityas a source of expaneion energy,particularlyif the formation is pooriy consolidated.Abnormaipressureat discoverymeans a lower effectiveresewoir stresscondition, and a higherformationcompressibility. Sincepressure ievei is often high, gascompressibility[ ( l@)- ( IL?)[ dtidp )] is relativelylow,and formationcompressibilitymay in fact be of the sameorder of magnitude;it wlli often exceedoiicompressibiiiiy. Formationcompressibilitycontributionsmay be further magnified if an aquifer--evena smali one--is present since aii of the water-bearingrock presentwiiiprovide fomnationcompressibilitydrive,energy.

Referencesand illustrationsat end of paper. 435


2/16

? APPLICATIONOFVAFtll$LE FORMATIONCOMpRESSl131Llw SPF 266

Where resemolrconditions are such that compressibilityis expected to be relativelyhigh, and variable with stresslevel, taboratoly measurementsare definitely indicated.Use of the data In reservoiranalysis is not routine,andapproximationsare often used. in this paper,we addressboth the laboratorymeasurementsand also a method foraccurately incorporatingthat data in resetvoirperformanceanafysis. The resuft is one which is quitegeneral and whkh can be incorporatedin existingmateriaibalance or resewoir simulation formulationswithonlyminormodifications. Futier, methodspreviouslyproposed byotiter investigatorsprove in fact to bespecial cases of the generaiapproach developed here.2. FOtlMATiON COMPRESSIBILITYPorecompressibilityis a laboratorymeasured rockpropertywhkh is defined as the relativechange in porevolumecda rocksampledivided by the change inlaboratorystress whkh caused the change in porevoiume:

A ~pl Vpcp= AIM) 1

Formationcompressibility,however, is defined in mostreservoir engineering handbooks as the relative changein pore volume divided by the change in reservoirpressurethat caused the change in pore voiume:C,=4.!!M?

A/) 02

The difference between pore compressibilityandformation compressibifiiytherefore is reiatedto thedifference between reservoirpressureand laboratorystress. There are four mainstresseswhichact onanyvolumeof reservoirrock. The overburdenstress,az,thehorizontriistresses,ax,Cp and the pore pressureorreservoirpressure,p, wtuchpressesout against theoverburdenand horizontal resemoirstresses. [n thelaboratory,however,mostoverburdentests are run usinga hydrostatk confining pressureand ambient porepressure. The reservoirstressstateand changes in thatstressstatemustbe convertedto effectiie hydrostatklaboratorystress to understandthe laboratorydata. Thefoilowing equation has been proposedand derived bymany (Geertsma, 195Z Jaeger and Cook, 1976;Teeuw,1971; Nurand Byeriee, 1971):

where KI, K2, and K are constants dependent on rocktype and pi and p are the reservoirpressureatd=overy and at the presenttime respective~. ~eb isthe hydrostaticconfining pressureappiiedto the coresample (minusany pore pressure)to simulatethe in-situ

stressconditions. Equation3 is sometimesreferredtoas the effectivestress equation. Tabie 1 gives KI, IQ,KS for various rock types. KI and K,, relatehow thethree confining stresses in the reservoirand the reservpressureinteract. KI can be defined asKI=(CrX+ ay+IYZ) /(3 CYZ). . . . . . . . . . 3a

oz can be estimatedusingan overburdengradientof 1psi per foot of depth or from integratinga density log. Kis equivalent to the Biot alpha parameter and is defineby Geertsma(1957) and Nurand Byertee(1971)as:K2 = (f cb/cg~), . . . . . . . . . . . . 3b

& relates how the drawdownof the reservoirpressureincreasesthe stresson the formation. it can be definedas:K3 = K2[(l+v)/(3 - TV)] . . . . . . . . 3CEquation3Cis identicalto the uniaxial correctionfactoderiied byTeeuw (1971)with the exceptionthat heassumesK2to be unity.FromEquation3, we can see that hydrostaticpocompressibilitytests, therefore,can be correctedtofomation compressibility through the foilowing equatiocf=&cp . . . . . . . . . . . . . . . . . . 4r TABLE 1

I OsoRvTHW.AIl&I Bock WIQ K h &IConsolidated Sandstones* 0.85 0.80 0.45IFriabie Sandstones 0.90 0.90 0.60IUnconsolidated Sands 0.95 0.95 0.75ICarbonates 0.85 0.85 0.55*TheseK2constants for are vaiid for many consolidatesandstonesand carbonates. Forweii cementedfomations with porosities iower than 15%, the Kzfactocan be between0.4 and 0.8 due to the formationslowbuik compressibility (see Equation3b).2.1 Uniaxial CompactionAs fluidsarewithdrawnfrom the reservoir, it is assumeto compact only in the verticaidirection (uniaxiaicompaction)becausethe verticai extent of the reservoso smalicomparedto its iateral exient (Cieertsma,195Teeuw, 1971; deWaal, 198$). This leads to a decreain the horizontal stressesand therefore to a decreaseithe averageconfiningstress. This has the effectof

436


3/16

ABOR.RUSS~. PHAM.ANDYOUSAF 3fessenfngthe increase in effectivestressas the fluidpressurein the resetvoir is decreased.The fi constantin equation 4 accounts for the changes in horizontalstresses (see Equatfon3c). The variation in Poissonsratio, v, between consolidatedand unconsolidatedclasticwdments leads to a variationIn Kj of 0.45 forconsolidatedsandstones to 0.75 for completelyunconsolidatedsediments. Therefore, for a consolidatedsand, a drawdownof 2000psi Is simulated in the labor-atory by an increasein effective stressof only $00 psi.This lmlaxfal compaction of the reservoirduringdrawdownhas led someto suggest that thecompressibility shoukf be measured unkodaliy,mimkking the no fateral deformationbounda~condition and allowingthe sample to deformonly in thevertkal direction &achance and Andersen, 1987;Andersen, 1985 de Waal, 1986). Theoretkaliy, however,(G$ertarna,1957 JaegerandCook, 1976)the volumetricchange in porevolume Isdue only to the change IntheJWQ5WQolumetrk stresseson the sample,thereforepropertycorrected hydrostatic tests should be equivalentto uniaxialtests.We argue that the diffkutties in maintainingthe no fateraldeformationboundary condfiion along the entire lengthof a sampledurfnga trkudaitest aswell asthe cost anddiffkufty of the tests make uniaxialtests unfavorable.Publisheddata on unkaxialcompaction (Lachance andAndersen, 198* Andersen, 1985) showdata whkh areboth signifkantly 1sssand signfficantfymore than aspredictedby theoreticallycorrectedhydrostaticcornpressibiiff tests. We suggest,therefore, thatformationcornjmssibility be calculated by performinghydrostaticpore compressibilii tests and correctingtoformation compressibilityusing Equation4.2.2 Laboratory Methods forPcw CompremdbilityLaboratory pore compressibilitymeasurementsare doneby determiningthe porevolumeof a core sampleas afunctbn of effective laboratorystress. The porevolume isusualfydetermined eftherby measuringthe total fluidsqueezedout of a Ifqdd saturated sampleandsubtractingit from the pore volumeat ambient condfiionsor by measuring the pore volumedirectly of a driedsampleat eachpressure level using the Soyles faw gasexpansion technfque.Since pore compressibNtyis related to the derivativeofthe pore volumeversus stresscurve, the accuracyofcompressfbijitydata is dependent on the ability of theapparatus to measurevery small changes in porevolume. For thfs reason, Ikjukfsqueezeout on sampleswithmore than 10CCpm volume gfvesbettercompressibility results than Boyles fawmeasurementsortests on small samples.We have found that on samplesfrom friable orunconsolidatedformations, sampteintegtity as well assamplevolume is a concern. Porecompressibilityis verysensftiveto the degree of damageor disturbanceof the

437

samplein weak sediments. ASshown in Figure1,fujldiameter samples from the same unconsolidatedformationas a set of plug sampleshave significantlylowercompressibilities. We suggest that core damageduring plugging and cleaning disturbed the samplesenoughto csuse this difference. The authors havefoundthat ambient pressureporositiesof the plug sampleswere2 to 8 porosity units higher than the full diametercore samples,To maintainsample integrii to insurevalid porecompressibilitymeasurements,the authors recommendthat unconsolidatedcore samplesbe frozen on well siteto prevent sampledisturbanceand desiccation duringshipping; that fulj diametersamples be used to preventdisturbance from pluggingand to maximize accuracyand that the frozen samplesbe placed in the pressurevessel before cleaning and allowed to thaw under someminimumstress (100to 300 psi, generally). Brfnesqueeze-out pore volume testing can be done beforeanycleaningprovidedcare b taken to fully liquid saturatethesampleand that ambient pore volume is measuredafterthe test is complete.We havealso found that the creep associatedwiththedeformationof unconsolidatedrockscan causecompressibilitytests runat high ratesof pressureincreaseto be invalid. One of the authors and others (deWaal, 1985) have observed creep in unconsolidatedcoresamplesto be logarithmicwith time. The magnitudeofthe creep being the most signffkant in poorly sorted,clayrich unconsolidatedcore samples. It is unfeasibleto runtests at reservoirdrawdown rates of 100 psi per monthbut standard laboratoryrates of 1000to 2000 psi perhourdo not allowthe creep to occur, We suggestthatcompressibilitytests on core samples run at ratesbetween 50 and 5 psi per hour for unconsolidatedsamplesand 500 to 50 psi per hour for weaklyconsolidatedformationsallow a significant portionof fhecreep to occur thus improvingthe accuracyof thecompressibilitydata.2.3 Variability of Formation CompressibilityOneof the reasonswhy formationcompressibilityhasbeen left out or underestimatedin reservoiranalysisisthat it has been assumedthat pore compressibilitykfairlyconstantwith stressandof the sameorder ofmagnitudeas the compressibilityof water. EvenHammerlindl(1972)who recognized the importanceofcompressibilityin resetvolranalysis, used a constanthigh formation compressibilityvalue. Figures 3 through5 showthe varjabitityof pore compressibilitywithpressureand rock type. Thefigures representcompilationsof data for consolidated, friable, andunconsolidatedciastic sediments.Definftkmsof the degreeof consolidationare vague. Forthe pwpose of our compilationsthe following generalguidelines apply. Consolidatedsandstones haveundergonesigrdfkant diagenesis and have thek grainswell cementedand dropping a core sample on the floordoesnot cause ft to disintegrate. In the consolidated


4/16

4 FORMATIONCOMPRESSIBILITY SPI?P66sandstonestested, porosityranged from less than 1Ye to25%witha meanporosity of 15%.Wedefine friable samplesas having Iit!leor no cementbetweenthe grainsbut holding together evsn aftercleaning and drying. Friablecores, howe~er,willgenerallybreak or disintegrate if dropped onto the floor.Porosityof the samples tested rangedbetween20% and33Y0,with the mean porosityfor our data set at 23.1?4.Wehave found that the compressibilityof very clean,wellsorted unconsolidatedsands generally fall into thisfriablencategoryeven if they have no cement.Wedefine unconsolidatedsamplesas those which fallapart completely after drying ancVorcleaning withporositlesbetween 27% and 40Y0. They generally havenocement between tho grains and are poorly sortedan~or have large clay iractbns. Our data set ofunconsolidatedsampleswas populated primarilywithturbidite-typeGulfCoast sands with a mean porosityof32.5?40.Figure2a and 2b showthe differences in grain sizedistributionsbetween a clean,well sorted sand (whosecompressibilityfalls into our friible category) and a clayrich,poorly sorted sand (whichfalls into ourunconsolidatedcategory). Both sands are uncon-solidatedfrom the point of viewof having no cementbetween their grains, but they have widely dflerentformationcompressibilities. We have found this strongcorrelationbetween degree of sorting and compressibilityin a number of unconsolidatedformations.Figure3 shows formation compressibilityversuspressureon a toglog plot for a collectionof 121consolidated sandstonesfrom over 45 formations fromaround the workf reported in the published literature(Chieriii et. al. 1967, Dobrynin 1963, Fatt 1958a, 19513b,Wyble 1958,Yale 1984)and measuredby the authors.Notethe general downwardtrend versus pressurewithan order of magnitudechange in compressibilityover thepressure range. Note the order of magnitudevariationofcompressibilitywithin rockswhich are all conskferedconsolidated sandstones.Figures4 and 5 show the formation compressibilityoffriable to unconsolidatedrocks whichmake up asurprislngtylargenumber of resemoirs. These ranges offormation compressibilitiesare large enough to figureprominentlyinto the total compressibilityequation forboth oil and gas reservoirs,especiallythose which areoverpressured. The data in Figure4 are from 140coresamplesfrom7 reservoirsin the North Sea,Afriia, andthe U.S.Gulf Coast whichweconsider%iable. The datain Figure5 are from 14full diametercore samplesfrom4reservoirsin the CM of Mexko and Afrka whichareunconsolidatedand poorly sorted. Note from Figures4and 5 that neady all the sampleshave compressibilitiesgreaterthan that of water at stressesup to 10000psi.Comparingall three figures,we see over 2 ordersofmagnitudevariation in compressibilii at any givenpressuredepending on rock type. Also note that theslopesof the threedata sets aredflerent.

Thesethree figures show the importanceof includingvariable fonmationcompressibility in reservoiranalysisGas compressibilityat 8000 to 15000PSIcan be in therangeof 200 to 20microsips. In overpressuredreservoirs,where the effective stress (seeEquation3)can be 3000 to 1000PSI,formation compressibilitycanbe 1 to 50mlcrosips.Wefind that it is the change in gas and formationcompressibilitywith pressurewhich causes the familiachange in slope of the p/zversus cumulativeproductioplots in overpressuredreservoirs. As reservoirpressurdecreases, gas compressibility increasesand formatiocompressibilitydecreases. The change in slopeof plzversus productionplots for overpressured reservoirscabedue to a change from a formation compressibilityinfluencedsrdem to a gas compressibilitydominatedsystem,2.4 Type Curves for Formation CompressibilityPorecompressibilitymeasurementsare not performedroutinetyfor all reservoirsand data are especiallysparfor those formationswhere it is most important(i.e.friaband unconsolidatedformations). Figure6 and Table 2give TypeCurves which can be usedto estimateformation compressibilityin clastic formations if cwe daare not available. The three type curves (andtheequationsgiven in Table 2) are least square fits througthe data compiledin Figures3,4, and 5.

W= CURVES FWMAIW COwFtE~CL~STIC RESERVOIRSCf = A(cr-B)~+D

he typecurvesinFigure6 aredefinedbytheabovequationwhenxr = KI* (overburdenstress)- K2q ~ + /(3 q (pi -p) (pmdII,B, C,D are constants depending on rocktype asIescribedbelow.

Unconsol Fri$bk(poorly s;~ed)ate~ (&well sortedunconsol.)A -2.805X 10s 1.054X 10~ -2,399X105E 300 500 300c 0.1395 -0.2250 0.06230D 1.183X 104 -1.1(X4Xo~ 4.308X 105

Wecautionagainst the use of type curvesunlesscoredata is not available. Manytimes in unconsolidatedorfriable reservoirs,very little if any core is availableso thestimatesfromtype curvesare necessary. We remind438


5/16

YALE.NABOR.RUSSELI PHAM.ANDYCXJSAF 5the reader that the unconsolidatedand friabledatasetsdo not cover a widevariety of reswvoirs and therewill be formatkms which can be consideredunconsolidated or friablewhich have compressibilitiessignifkantly differentfrom those presented in the typecurves. Wedo belleve,however,that the quality of thedata Inthe formationstested isvery gooddue to themeasurementprocedures followed.3. THE PORE VOLUME FVF - A NEW CONCEPTIn order to easily incorporatevariable formationcompressibilityinto reservoiranalysis we define a porevolume FVF(formationvolumefactor) as:

~,sv/v ., OO. O., . . . .. O.. O 5It is convenient,though not strictly necessary,to chooseoneatmosphereand reservoirtemperatureas thestandard or reference condition, where Br= 1.0. Theporevolume FVF is easify related to formationcompressibilii. In differential formthe formationcompressibilityequation (Equation2) can be written as

Cfdp=dVp/Vp= d~lnVP~ . . . . . . . 6whichcan be integrated between limitspscand p to giveJh (b/ VPSC)= cfop=/(P) . . . . . . 7Pscor equivalently8f=el@~ . . . . . . . . . . . . . . . . . 8

The laboratorytest from which CPis determineddoes, infact, givea nearlydirect determinationof Bt. The ratioofsamplepore volumeat any stress level to porevolumeata stress tevel correspondingto that reached in theresewolr when pressuredeclines to standard pressuregivesthe pore volumeformation volumefactoq the dataneededare an inftfalpore volume and fluid volumeexpelledas a function of stressapplied to the sampleand, of course, a refationsuch as Equation3 whichtiesreservoirpressureto laboratorystress. The laboratorymeasurementdoes not evenhaveto be carried to thestandardcondtiion stress level; it needonfy cover astress rangewhich encompassesthe expected rangeofreservoirpressure. This amountsto defininga referenceconditfontied to the hjghest stress level reached (i.e.,reservoirpressure below the lowest expectedoperationalpressure).3.1 Modified Fluid Formation Volume FactorsBasedon the above formulationswe defi a modifiedgae/oil/waterFVFas

l&fj/& . . . . . . . . . . . . . . . . . . 9

wherej refersto gas, oil, or water. Withthis definition,we have the advantage of simultaneouslyconsideringthe changes,with pressure, of both fluid and the porespaceassociatedwith that fluid. in material balancework, useof these factors allows us to centerattentiononfluid volumechanges, knowing that pore spacechangesare being carried along automatkalty, The resuft,as weshall see, is a compact form of equationwhich accuratelyconsidersall facets of the formation and fluid expansionprocesseswhite retaining an appearancesimilar to thatwith which reservoirengineers have long been familiar.4. MATERIAL BALANCE EQUATIONWewill derive the materfalbalance equation (MBE) for ablackoil system, using the modified formationvolumefactors just introduced. Thesystemmay be comprisedofthree zones gas cap, oii zone, and pot aquifer. Phasespresent consist of hydrocarbonvapor, hydrocarbonliquid,and brine which are morecommonlycalled freegas,oil, and water. Gas is also lookeduponas acomponent,andmay be present either in free form ordissoived in oii and water. Oil and water are not solublein gas or in eachother. A common (average)pressurecharacterizesail zonesand phases.Since the contributionof water-saturatedformation todrive energymay be considerable,the distributionofwater inthe systemisof Importance. First,averageconnate water saturationmay be different in the gas capand oii zone. Second,we allow for the presenceof a potor steady stateaquifer which is in immediatepressurecommunicationwith the hydrocarbonzones. This couldbe underlyingwateror simplya small aquifer. In theusual analysis,the energycontributionfrom a smallaquifer might be neglected,but the possibilityof highandvariable formation compressibility enhances theimportanceof such a contribution, especially inoverpressuredsystems. Fina!ly,we will allowfor watarand gas influxfrom a transientaquifar. Precisetreatment of such influx requires separateanalysiswhichisbeyondthe scopeof this paper, but the overall effectsare easily included in the general formulation.The analysisbegins by relating the porevolumesof theoil, water,and free gas phases to the total porevolumeofthesystem.

Nt30/+WBW~+GF/Bgj=VPSCB/j . . . . . . . 10from which

VP3C=N&j+W~Wi+@j&i . . . . . . . . 11After somedepletion, influx of water and gas,andshrinkageof pore volume, the followingwill apply:(N- Np)13. +(w-wp+w..)B.+(GFI+G~I-G~-GP )13a= VXcBj . . 12

439


6/16

$ APPI l~F VARlw FORh&TiONCOMEJ3EWlRlL11Y SP-The term (GsI- G9)representsthe difference in solutiongas content between initkd and current conditions andcanbewritten aftercombining like terms tw(3s/- (3,= N(F/s/-Rs)+Np F?s. . . . . . s 13We now go through the algebraic steps of solvingEquation12for VP8C,quating the resultto Equation11,and then gathering all terms dealing with productionorinfluxon the right hand side of the equationwhile allothersare gatheredon the left we get:(A/ {[ E.+(/?#?.)Bg] -E.,}) +

W {~W-~Wl} + GFI@a-~~l)=Np(Bo-Ffs E#) +

(WP-We)EW+Gp E9 . . . . . 14we can define a modified two-phase formation volumefactor bydividingthe standardtwo phase factor by Bfi

Bt=@(R#?s)Eg . . . . . , , . . , 15Notethat ~ti = ~01A final step to reachthe form desired requiresrelating Wand GFito N. Wedefine two quantities

Fe =& pore volume ratio, gas cap/oil zone= pore volume ratio, pot aquifer/oilzoneThen

*[ I+ FW+F] . .0 16~iVP% = - h{and the pore volumeof water can be found bymultiplyingeachof the termswithin bracketsby the appropriatewater saturationfor each zone:

~ [ SWI+ FgcSwgi+ FXJ ..17lwjw = _After dwisionby f3~j,substitutions and rearrangement:

w= [ 1I@ Swi+ FcSvgi+F / )ii . . . . 1 8Ew j 1 - sw~

For free gas,

@, = [@ Fw(l-swiBgi 1_sw,~)o 19

Whenthe appropriatesubstitutionsare made in Equation14, the final result is:

N (g.- I@g)+(W- We)& + G#gN= P*(( )Br/ f-l +

[ 1( )Swi+ FgcSwg\+ FW - 20aY_l +

I-swi -[%$Q$J][*-l))Whilethe precedingequation is a very generalform, itdoes requirea calculationof Weby othermeans, Inaddition, usingthe produced_ ratio:

Rp = Gp/Np, . . . . . . . . . . . . . 21we can rearrangeterms to yield:

The numerator is sometimesreferredto as the expandenet=production-plus-excess-gasormulation.Forgas reservoirswith associatedaquifers,the sameapproachmay be used to derive the analog of Eq. 20::zi!i%The terms appearing Inthe denominatorof the Equation20,22, and 23 are worthyof examination. Eachof theterms[( ~1 E1ji) 1] representsthe expansionof a unttvolumeof initial fluid, including itsdissotvedgas, and thecontractionof itsassociatedpore space. The factorswhich multiply[(@ Ej] -1] are volume ratiosat initialconditionsfor (water/oil),(freegas/oil)or (watdfree gas)the multiplierfor the first term is unityof coursesincetheamatysiss based on a unitof eitheroil or of free gas.The water term is often neglected inmaterialbalanceformulations,but It shoukt not be. Inthe generalformshownhere, its significancebecomesmoreobvious,especially in overpressured reservoirswhere formationand gas or oil compressibilitiescan be comparable inmagnitude. The water termmay in fact bedominantforquitemodestvaluesof FpThis can be demonstratedby notingthat

In EW = lnBw-ln~


7/16

Y~R. RWWHUkiAM. ANDYOUSAF 7

and taking the derivative and rearranging:

(%/BW,) = @ - (Pi-p)The exponent is srnaii,since compressibilitiesaretypically 106 in order of magnitude while pressurechanges are 10+3in magnitude, so:

Bw/E#l+ m (lx-p)or()*-1 & m (Pi-P) . . . . . 24B~j

Similarexpressionsmay be developed for oii and itsdissotvedgas, and also for free gas, and the pore spaceassociatedwith each.Someorder~f-magnitude cakulations can now bemade. if we choosea systemat 10,000psi and 225Fastypical ef an overpressuredresetvoir settingwithaweakly consolidatedor unconsolidated formation, we canestimate:

Cw s 3(10+) pShl (Ostf, 1984)Cg = 37(10~ pshl (Bradley, 1987)C?(frbl) =10(10~) ps~l (friable sand)Cf (Uc) =35(10~ pstil (unconsolidated sand)

it foitowsthatCW+ C~(frbi) = 13(10~ psklc~+Cf(lJc) = 38(10*) psi-l

comparedtoCu+ Cj(frbi) = 47(104) psi-lCe+ Cf(UC) = 72(10+) pSt

Tim, the unit expansibilityof water and its pore space isnearty30 percentof that of gas and its pore space for aweakiyconsolidatedsand and over 50% for anunconsolidatedsand. if SWI= 0.2, the water termappearing in the denominator of Equation23, for gasresewoirs, wiil dominate if FW>2.7 for a weak sandand for FW >1.3 for an unconsolidatedsand. For oilreswvoirs, an estimate of two-phasecompressibilitywiilbe system-spectfb, but we can reasonablyargue that itwiii be lessthan gas compressibility. The water termwiiithen exceedthe oii term at even lowervaluesof Fpa.While the precedingdevelopmentaimedto illustratetheneed to account for water-bearingformation in materialbalanceanatysis,the key issue is actuaily the highformationcornpressibiiity. in the example,formationcompressibiiii contributesover 20 percent of theexpansionenergy associated with gas-bearingrock, andover75 patent of the energy associatedwith water-bearing rock for weak fofrnations. Forunconsolidatedformatbn, fonmationcompressibifii contributesnearly

!50%of the energyassociatedwith gas-bearingreservoks. Formationcompressibilityeffects should beincluded,and water-bearing rock shouid not be ignored,eventhough its total voiumemay appearto be quitemodest.These facts have long been recognizedin anaiyzingperformanceof overpressured gas reservoirs(Hammeriindi,1971; Bass, 1972). However,these andother investigators (Ramagostand Farshad,1981;Bernard,1987) have suggested onty approximationsfordeaiing with the problem. The fownulationproposedhereexplicitlyincludesthe effects of ali contributingfiulds andtheir assodated pore space, and has the added attractionof allowingvariable compressibilities to be includedwithrelative ease.5. MBE ANALYSISThe MBE presented in Equations20and 23 Ismorecomprehensivethan those usuaiiy presented, but it hasthe sameformat exceptfor the use of the modifiedformationvoiurnefactors ~O,W,un place of the BO,W,g,Themodifiedfiuid formationvolume factors can be cafcuiatedindependentlyas a pre-analysisstep, and used in placeof the usual fiuid volumefactors in MBEsin current use.it is readityapparent this MBE formulationwiii reducetoconventionalpresentationsof the MBE(see, for example,Dake, 1978; Bradiey, 1987) if appropriate simplifyingassumptionsare made.As an example,considerthe gas materiaibaianceEquation23. if we divide both numeratoranddenominatoron the right hand sideby Eg,solve theresuftingexpressionfor ( 1/ ~g) and then substituteBt(p/z) = (constant)s( 1/ ~g),we obtain, after somealgebra:

ifweassumeWtt= O,then GF1= G. Wealsointroducethe approximations:Bf = M 1 -cf(PFP)lBW = 8~J 1+ Cw(p-p)]

where C~and Cware taken to be smailand constant,Theequationwhich ultimately resuits b:p , _ Gv(~pt?+)+cd~w+1)(p;_p)=()[ 1- s~j 1

(9,-(*)(9J%+%%) 26

441


8/16

lLllY SPF 26The preceding equatfon is that developed by f3ass(1972). If, F-= Oand #Yp=O,then:( )[ ,_& ]=(9,-(?)/(%)71 -(Q+ cwav/ ) (p / -p~whichwas proposedby Ramagostand Farshad (1981).Any one of the Equations25 through 27 can be plotted ascorrected ( ph ) versus corrected t3Pand the lineextrapolatedto an intercept to estimate@Jor (3,provkfedof coursethat FWcan be estimatedwithsufficientaccuracy to allow an accuratecorrection to becalculated. Equation25 has an advantagafor caseswhere Influxcan reasonablybe taken as zero, and theoverpressuredgas resewoir maywell fit this case. Sinceall variable effects are properlyallowed for, F maybe1%eterminedby trial and erroras the value wh h leadstothe best straight-line fit of the pressureand productiondata. Equations 26and 27are not really suitablesincecfwill in fact change rather rapidfyas ( pi - p ) increases.& SIMULATION CONSIDERATIONSVariablecompressibility Is easlfyhandled at the partialdifferentialequation level by substitutingOSCf~orporositywherever ff appears in the equations.Manipulationof@ as a pressuredependent variableshouldbe straightforward. it maybe preferabletoreformulatethe equations In terms of the modifiedfluidvolumefactors B,since these variables can be developedoutsfde the context of the simufatlonequations,therebyreducingthe numerkal cafculatlon required. Since Eltisa continuous, stowtychanging function of resewoirpressure,there is no reasonto anticipate that the ~functions will be any more diffkuft to handle numericallythan the B] functlcmsthemselves.7. CASE HISTORIESTwentyover-pressuredgas reservoirswere selectedandanalyzedwith a computer program developed by usingthe newmethodand the rock compressibilitycorrelationsdiscussedabove. Followingare two of the case historiesstudied.One factor needed in the anafysis is a determinationofrocktype so the propers orP relationshipcan be used.If coredata are not avalfable,type curvesfor formationcompressibiiifycan be used although it is aiwayspreferable to use fabomiorycompressibilitydata from theformatfcnof interest. If type curve compressibilityis usedyet the degree of consoildatton is not certain or avaiiable,one shoufdconduct sensitivity studies for ail appropriaterocktypes to determinethe best sultabie solution. Forthese case histories, formation compressibilityis takenfrom the type cuwes presented earlier.7.1 Caso 1The first selectedcase histoty wasthe AndersonLreservoirfrom the Mobii-Davkffieid presented by Duggan

(1972). The Anderson L is an wer-pressured gasresewoir having an InftlaipressutQof 9507 psia at11,167feet subseadepth, or a gratiient of 0.843 psilftTabie 3 provides other pertinent data on this reservoin this case, ft Isassumedthat FW, WO, Geand RSWezero, and the L sand is weakly consolidated.Thepore vo!umeformation voiumefactors (B~arecalculated from Cf vaiues by using Equations7 andFigure7 shows a graphkai presentationof the rockcompressibilityas a function of reservoirpressure. Wcan use the 13fconceptto correct the p/z versusproduction piot to account for formationand watercompressibility. As shown Inthe bracedterm on the Isideof Equation25, we can use a factor C:

C = (Bf/Bf~(Fpa + 1) - (Bw/BW~*(Fpa + Swfl(1-sw/j

as a muftip!lerfor p/z. Figure8 shows the actuai andcorrected@zdata plotted against the cumulativewetproduction. The eariy extrapolationof the actuaip/zcurve Indkates an apparent gas-inepiaceof 112 Scf,whkh Is about 61 percent higher than the estimatedvoiumetrk gas-in-placeof 69,6 Bcf. However,theextrapolationof the correctedp/z curve using iinearregressionon ail data points yields a correetedgasinplaceof 83,6 Bcf. The gas-in-piaceof 83.6 Bcf was thinput into Equation25 and the estimatedgas productat each time step was calculatedand plotted in FigurAs shown in Figure8, the calculated gas productionshowsan exceiient match to the actualdata.To determinethe degree of confkfence in predkting toriginai gas-in-piaceearly in the productive iife of thereservoirwhen a few data points are availabie,asensitivity studywas conductedwhereoniy the first sidata pointswere considered Inthe evaluation. in thiscase, the origlnai gas-in-piacedeterminedby iinearregressionon the first six correctedp/z data points isestimatedat 76,0 Bcf. Tabie 4 shows the regressionanaiysis resultsfor the six and the ail=data-pointcaseAithough the six-data-pointcase shows a higherstandarddeviation, both cases give an exceiientbestto the straightiine, This seemsto implythat the gas-ipiace tends to be under-estimatedwhen consideringetwiydata points. To verffythis point,we performedadditional evacuationsbased on data groups from aminimumof three to a maximumof sixteendata pointThe resultsfrom these evaluationsandour experiencwith other case histories indicatedthat gas=in-piaceestimatestend to increasewhen moredata pointsareinciudedand become stabie as reservoirpressure drto about 70 percent of the originai resewoir pressureCurrentiy,we are evacuatingthe possibiecausesof thempirical resuftso7.2 Case 2The NorthOssun NS2tYreservoir (1-iarviiieandHawkIns,1969) k an over-pressuredgas reservoirhavingan initlai pressureof 8921 psi at 12,500feetsubseadepth, or a gradientof 0.725 psMt. Tabie 5

442


9/16

providesother pertinent data on this reservoir.Furthermore,gaod geologic data and considerablecomplex fmdffng in the area suggest a closed reservoirwitha limited wateraquifer. in this case, wealsoassumethat W* Gormd l?Wequaizero.As in Case 1, Bf is calculated from c~via Equations7and 8 for consolidated and unconsolidatedsandstones.Figure9 shows ct as a function of pressure. (p/2)C iscalculatedfor the two selectedcases(a) unconsolidated sandstone with no associated wateraquifer (Fm = 0), and (b) consolidated sandstone witha water aquifer equai five times the porevotumeof thegas reservoir (F@= 5).Figure10shows the actual and the modifiedg%!zata forCase (a)plotted against the cumulative gas production.The early extrapolationof the actuai p/z curve indicatesanapparent gas-fn-pfaceof 210 Bcf. However,theextrapolationof the modifiedp/z curve @/z)C yieidsacorrectedgas-in-placeof 105 Bcf whkh is close to thevoiumetdcestimate of 114 Bcf. Aiso, as shown onFigure10, the cakuiated p/z curve, based on the gas-in-piaceof 105 Bcf,matchesvety weiiwith the actuaidata.To study the contribution of formationcompactionandwater expansion from a smaii aquifer to the drive energy,a sensitivitystudy of this resewoir wasconducted usingdifferent aquifer sizes (F and rock compressibilities.Foreach combinationof rocktype and aqutier size (Fw),the @/zjC data was cakufated and fromwhkh acorrected gas-in-place can be determined. Table 6summarizesthe resultsobtained from twelve differentcasesanalyzed. Comparingthe first unconsolidatedcase (Fpa= O)and the iast wnsoii~ted case (~PtJ= 5)1if is seenthat both cases give the ioweststandarddeviationswhkh indicate the correct gas=in-piaceiswithinthe range of 104 to 108 Bcf. i30thcases providesimilarcafcuiationresults of @/2)C.7.3 Drhm Energy Partitioning and ReserveEstimationThe resultsfrom this sensitivitystudy indicatethat avarying combinationof rock compactionand waterexpansion from a small water aquifer couid provide thesameperfownanceeffects to the reservoirsystemas iorigas the total energycontributionfrom these two factors isthe same. This observation is consistentwith thespeculationraised in the MBEAnalysissectionof thispaper. Therefore, it is important to utilize knowiedgeofthe geofogkai setting as weii as knowledge of reservoirrockpropertiesto evaluateand confickmtiypredict gas-in=piace frompressureperformanceof over-pressuredgasreservoirs. Correct partitioningof drive energies,therefore, is dependent in many cases on accuratemeasurementsor estimatesof formationcompressibility.Underestimationof formationcompressibilitymaysuggest a waterdrive where one does not exist and viceversa.Profitabledevelopmentof overpressuredancUorunconsolidatedresewolrs is dependent on an accurateunderstandingof drive mechanismsand totai reserves.

This is especiaifytrue sincemany if not mostof thesetypes of reservoirsare iocatedoffshore. Accurateformationcompressibilitydata and appikation of thatdata in MBEanaiysis and reservoirsimuiatkmcansignificantly improve reservoirdevelopment in thesetypesof fieids.8. CONCLUSIONS

q Incorporationof variable formationcompressibilityintoreservoir performanceanatysis is important foroverpressuredand/or weakly to unconsolidatedreservoirs.q Accurate laboratorymeasurementsof porecompressibilityare important and standardmethodsformeasurementof pore compressibilityon friable tounconsolidatedcores are often inadequate. Tests onfuii diameter, fresh core samplesfrom unconsolidatedformations are preferableto plug samplesand slow ratetests are necessaryto account for theaneiastic natureof these formations.. Useof the modifiedFormationVoiume Factorasdefined in this pape; ailowsvariable formationcompressibilityto be incorporated into the MBEandother reservoirperformanceanalyseseasily andeffectively.gUseof variable formationcompressibilityin materiaibaianceanalysis for initiai reserves leadsto moreaccurateestimatesof resetves. Useof accuratelaboratorypore compressibilitydata canaiiow accuratereserve estimatesfrom earfytime data in overpressuredsystems.. incorporationof accurate formationcompressibilitymeasurementsin reservoirperformanceanaiysis canaiiow for the correct partitioningof drive energies andestimatesof remaining reserveswhichcan aid in themost efficient developmentof the resewoir.$. ACKNOWLEDGMENTSWewouid liketo thank the managementsof MobiiResearchand DevelopmentCorporationand MobiiExplorationand Producing,U.S. inc. for permissiontopubiish this paper. Wewould a!so liketo thank MartyCohen, RonMoore,J. Michael Rodriguez,and all theothers who helped on this project.

10. NOMENCLATUREA =constantinTable2B =constantinTable2e = porevolumeformationvoiurnefactor(FVF),RWSTB& = iniiiaiporevolumeFVF,FiB/STS!$!

= gasFVF,RWSTB= iniiiaigasFVF,RWSTB= oiiFVF,FiWSTBf% = initiaioiiFVF,REVSTB& = two-phaseFVF,RB/STB


10/16

10 APPLICATIONOFV~ FORMATQNCOMPRESSWIW= irtttiaiwo-phase FVF,RB/STB=waterFVF,RB/STB= hitiafwaterFVF,RB/STB= ~/&= &/&=@/@= &/*= &/@= &/@= &l@: t%:gt ~ ?dle *= constanth Equation28andFigures8 and10= iltlk Comprwhiiityof thefofrrtation,Vowovpsi=formatbnCornprssstiliii,VoiNOvpsi= gasV-MIM*VWM= fyairl~e66ibiiity Oftiwfofmation,Vowovpsi= w --wt vo~o~m= totatwatercornpmssibitity,otvo~psi=conskmt=porevalue ratb, gascap/oilzone= porevalueratio,potaquif~oflzone=Mafhitiaigasklplce,scf= inftialfmefjas inplace,ecf=totat gasprodhced,Scf=Soiutbngashpiace, scf=Mtiatsotutiongashface,scf= htegratedfotrnatiortcornpressblihy= oonstmth Equath 3= constantin Equation3=constrmtfnEquatbn3= oii inplace,STB= N/@= Poissons ratio= total oil produced, STB= porosityat standardcondfiions, fraction= reservoirpressue, psi= initial resewoir pressure, psi= gas in soluftionin oil, scf/RBf?~ = ~itia! gas in solution in oil, scf/Rf3

Swgi = initiaiwater saturation,gas cap, fractions~i = initiaiwater saturation,oii zone, fraction@ = initaieffective Iaboratofy stress, psiau = effective laboratorystress,psiUJr,y = horizontalstresses,psia- = overburdenstress, psiv1? =pore volumeat resetvoirconddion,RBd Sc= porevoiume at standardcondition,STB= water in place,STBwe = cumulativewater infiux, STBWp = cumulativewater produced, STi3z = gas deviation factor

11. REFERENCESAnrhreen,M. A; PredictingReaeivolrConditionPore-VolumeCompressibilityromHydrostatio4Xmseaboratoryatt%apeSF%14213 presentedat the 1985SPE 60thAnnualMeeting,La6Vega%Sept.22-26.~as, t), M.: AnSiyd6ofAbilOmld!yPme8uredGasRaserwrhWithPartialWaternfluxtpaperSPES650presentedat the1972 3SymposiumonAbnormatSubsuflacePorePressure,LouiaianStateUniversity,Mayl&16.Bernard,W. J.: ResenresEstimationandPedormanca Pmdi@n fGeopreawed GasReeervoiratJ. Pet.Sci.Errg.(Aug.19S7)115-21.f3radley,.B.(Editor-fn-Ohlafietmbum E~ineerirrg Hmrdbook,SPE, Richardson,Texas(1987).Chlerioi,G.L.,Ciuod,G.M., Eva,F., andLong,Gt.1967)Effectofoverburdenpreaswuonaornafmtmphy8kelparemeteraofreservoirrocks,Proo. 7#rWorfdP6froteumCongress,z 309.Dake,L. P.: Func&nental# of ReservoirEhgineedng,EleevterScientificPubtishlngCo., Amsterdam(1978).deWaal,J. A,: Or Rate Tjpe CompactionBehatior of SandstoneReservoirRock,Ph.D. thesis,TeohnlacheHogeachoot12alft,(19s6).Dobrynln,V.M. (1663)qEffectofovetirden pressureonsomepropertleaof sandstones,SPfZ/, 2,360,

Dug9an,J. 0.: TheAndereonL* -An AbrronnallyPmssuradGasReswvoirin SouthTexas, JPT(Februery1%2) 132-1SS.Fam1.(195S8)Carrpmseltilltyofarmdstonest lowto rncderatepressures,EMi.AAPG, 42,1924.FattjL (1958b)Porevotumecompressibilitiesf sandstonereservreeks, Trans.,AIME, 213,362.Gewtame, J,: TheEffeotofFluidPmaure DeclineonVolunwtrioChenge8ofPorousRooks,Trans.,AlME(1957) 210,331-340Harrnarlind,D. J.: I%adiotingaaReservesinAbnrmnatlyPnssauradReaervdrsspaperSPE 3479 preeentedat the 1971SPEofAIME46thAnnualMeeting,NewOrleans,Oct.3-S.Harville,D.W.,andkiawkirra,M. F; RockCompreseMityandFalluas ReservdrMeohsniarnsnGeopressuredGasRa.servoire;JP(December,1969) 1528-1530.Jaeger,J. C.,andCook,N. G.W.: Fundamentalsof RockMeohanChapmanand Hall, London(1976).Kaelan,D.K. (19S5)Automatedwe measurement6ystemforenharwcfooredataatoverburdenonditions,aperSPE15165.Koger,K.M.,SaomJ. D.,andMogenstem,N. t%: Te8tiWoDeterminetheGeoteohnioelPropertiesofOil Sends,paperPBiCIM87-38.59 preisentadat tha 1987 PetroleumSodetyofCIM 36thAnnualMeeting,Calgary.Lschwwe,D. P.,andAndarsen,M.A: CemparfaonofUnlaxlalStrandHydrestaticrtressPore-Volume(krnpressibilityntheNuggetSandstone,paperSPE 11971 presentedat the1$SSSPE5SthAnnualMeeting,SanFmndsoo,Oct.5-S.Nur,A. andByerfee,J.D. (1971) Anexactefteotivestresslawforelatitiedeformationof rookwithflulds,Jour. Geophys. i?es.,76414-6419. . .Osif,T. L.: TheEffectsofSaIt Gas,Te$nperatum,ndPressureontheComrxessibllitvfWater. rmeerSPE 13174 rxeeentedat t19~ &PE59thA&uel Technics](%nferenceandExhibitionHouston,Texas, Sept. 16-19.Ramsgost,B.P.,andFarehed,F. F; PiZAbnormallyPressuredGaReservoiretpaperSPE 10125presentedat the 1981SPEofAIME66thAnnualTeohnioalConference,SanAntonio,Ootob5.7.Teeuw,D.: PredictionofReservdrCompactionromLakwatoryCornpressibllityata, SPEJ, (September,1971) 263-271.Teeuw,D.: LaboratoryMeasurementsof (%oningenReswvdrRock,Trans.,RoyalDutchSo&of (iieologiatsandMiningEng.(1973) 28, 19-32sWytie, D.-O.(1958) Effeotofappliedpressureontheconductiviporosity,and permeabilityof sandstones,Trans.AiME, 213,430.Yale,D.P. (1964)NelworkModeilingof Flow,Storage,endDeformationin Porou$Rooks,Ph,D,theds, StanfordUnlverdt


11/16

Y&E. NAKM+RMSELL pHAM.ANDy~ $A~ 11

.-

TABLE 3ANDER ON u n RESFRVOIR DATA

Depth 11167 feetInitialBHP 9507 psiaPressureGradient 0,843 psi/foOtBottom-holeTemperature 266 FNetGas PayThickness 75 ftPorosity 24 ~0Water Saturation 35 %VolumetricGas In Place 69.6 Bof

TABLE 4

EstimatedOGIP(Bcf) 83,6 76CorrelationCoefficient 0.9982 0.9922Standard Deviation (Yo) 0,91 6,85

TABLE 6JJ~~T~ OS~UN M S2Bw IERVQIR DATADepth 12500 feetInitial BHP 8921 pslaPressureGradient 0.725 psVfootBottom-holeTemperature 248 FNetGasPayThickness 100 ftPorosity 24 ~0Water Saturation 34 %Volumelrlc Gas in Place 114 Bcf

TABLE 6

NORTH O!5SUN *NS2B RESERVOIR ANALYSIS RESULTS

[O(3IP @cf) / correlation eoeff./ std.dev.(%)]Fpa = 0 Epa = 1 Fpa = ~ Fpa =5

Consolidated 15810.986J 1.4 143I 0.991I 1.4 120I 0.995 I 1.2 104/0 .997/1.1WeaklyConsol. 149I 0.990/ 1.4 12910.994 / 1.2 10210.99611.1 8410.99411.7Unconsolidated 10510.99611.1 7410.99212.3 4610,982113. 3210.975133.

445


12/16

*M APPLICATIC)N0FVAt31W FORMATIONCOMP~m sP-

FULL DIAMETER VERSUSPLUGSAMPLECCIMPFIESSZBILITY120

80

40

A UNCONSOLIDATEDFORMATIONSA A A

ACLEANED PLUF&lINDUSTRY STANDARDA AA A A

A A

Pti-uL- ~& ~~ A

o0 3000 6000 9000PRESSURE (PSI)FIGURE 1Comparisonofcompmsibility from cleaned plugs versus fresh, fulldiameter coresshowing effectofplug damage on pore compressifdlitiy

.10, vchm9 *9

3a10 0.2 0.4 1. oa4@loao 1 0 0 2 0 0 400 100

? a r t l e l o DisMt.r turn)

FIGURE 2AGrain size distributionfor clean.we!lsorted unconsolkfated sand 2.4, vOllJa*a.a1 P La.o1 .0v 1.6 il; 1.4: l.2-

FIGURE 26Grain size distribution for c!ay rich,mdy sorted UtICOtN301h%kt0Cfand

q 0.80.60.4o.ao 0.2 0.4 1.@a4610a040 1 0 0 aoo 4 0 0 1 0 0 0? ut ie lo Di4 0c t .r Iu mi446


13/16

~~R Rl=~NDyOusAF 13WELL CONSOLIDATED SANDSTONES

.-~ 1- 1 . -13IL J.__---. : 2;00-!500 2000 5000

EFFECTZVELAS STRESS(P5$1FIGURE 3Log-1ogplot of FormationCompressibilityversus EffectiveLaboratoryStress(121 weli consoikfated sandstone samples)

4

FRIA9LE SANDS a WELL SORTED UNCONSQLIDATM

2. E-5

2. E-6

2.E-4 ~ 1 ~

AA 1bA4AA

i?.E-7~ #500 2000 5000 20000EFFECTIVE LAB STRESS(fJsi)

FIGURE 4Log-fogpiot of FormationCompressibilityvarsus EffectiveLaboratory Stress(140 friable sandstone and weil sorted unconsoikfatedsand sampies)447


14/16

q

M APPI ICATK)N OF VAFi,@ F FORMATiON C~lRILITY SPF a

UNCONSOLIDATED SANDS (POORLY SORTED)2. E-4t I jzw~. 4~ &2 . E-5 ;d 4g~ ~ AAafo0 2. E-6 :zgbi!9k 2. E-7 i!500 2000 5000 20000

EFFECTIVE LAB STRESS (PS5)FIGURE 5Log40gplot of FormationCompressibilityversus EffectiveLaboratoryStress(14 unconsolidatedsand samples)

TYPE CLfFiVES FWt CLASTIC RESERV(IIRS50, I. # 1 1

zEf-ii0IL

} .. 4.

. .

40 - ....... ..O-..,30 -

................. .... .20 - ..........

10 -\\\ --c_OTx&T~- ______ .

0 t 1 --T-o 2500 5000 7500 10000EFFECTIVE LAB STRESS(P5$)

FIGURE 6Typecwvesbased on non4inearregression ofdatain Figures3, 4,and5448


15/16

NAE30R.13LlSSW PHAM.AN~ fOUSAF 15

14

9

ANDERSON L RESERVOIR, I 1 1 1 1 1

~~3000 4000 5000 6000 7000 Booo 9000 10000RESERVOIRPRESSURE[PSIIFIGURE 7Formationcompressibil~ as a function of reservoirpressurefor AndersonL

ANDERSON L HESERVOXR7000 ~~6000

z: 50009 4000*QQ 3000

100C

c

e ACTUALA P/z*c cALGULATEO---- P/z*c6 tJoints-- P/z*call points- P/z

~\\

\ \\ \ 120 40 60 80 100 120-.

CUMULATIVE PRODUCTION (Ecf)

FIGURE $P/Zasafunctionof cumulativegaspmduction(standard and variablecompressibill~ analysis)449


16/16

~6 APPJJQYllON OF1/AW FORM~ON COMPRl=SSIBILllY SPF 266

Nf3F+THOSSUN NS2B RESERVOIR

UNCONSOLIDATED

CONSOLIDATE

AI 1 t I

:000 5000 7000 9000RESERVOIR PRESSURE (Psia)

FIGURE 9Formation compressibility as afunctlon ofrese~oir pressureforNorth Ossun(fromType Cutves)

NORTH OEWJN NS2B RESERVOIR7000 I 1 1 I 1 I I I I 1 i

Ie ACTUAL J6000 A P/z*c%j CALCULATED -

& 5000 - P/z?ic- ?/2 -1: i~ 40(3(J - Jn ALQ 3000 - \ \ d$ \ \ \ i2000 - \ \ \ 4\

\i\1000 - \ \ \

, \,, , -,0 L t I 1 Io 20 40 60 $0 100 120 140 160 180 200 220 240CUMULATWE PIWJOUCTION(BCf)

FIGURE 10P/Zasafunctionof cumulativegasproduction(standard and variable compressibilityanalysis)

spe 26647 application of variable formation compressibility for improved reservoir analysis

Documents