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SPE-7609-PA

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SPE 7609 PA
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InfluenceofVeryLowInterfacialTensionsonRelativePermeabilityCharlesBardon,Ins!.Fran95.010000.1110-224010-7C1-nC5Systemat37.7'C2,350162.030.21500.02000.34500.0480.13002.400.04931.6415.8764.077230.1810-421.310-7C1-nClOSystemat37TC73050.330.03260.01250.68500.5750.652446.0017.0001,27087.600.06110.01390.67720.4150.615129.9012.500'Pc=244.7bar;Su=100%.variesintheratioof1.6x104,avariesintheratio1.2x104,whereas1-'2/1-'1variesonlyintheratioof12.Therelativepermeabilitycurvesfirsthavetobedeterminedwithaccuracyfromthedisplacementexperiments.4,J3,14Theyarecalculatedbyagraphicmethod15,16fromtherecoverycurvesandpressuredropvs.time.Theserelativepermeabilitycurveswereadjustedeventuallytoachieveagoodcorrelationbetweentheresultsobtainedwithatwophase-flownumericalmodelandtheexperimentalresults.AnexampleofthemethodusedisdescribedinAppendixB.Forthethreeexperimentsclosetothecriticalpoint,inwhichaiscalculatedtovarybetween0.038and0.001mN/m,itisverydifficulttodefinetheslopesofthecurvesofliquidrecoveryandofpressuredropbecauseoftherapidfalloffinrecordingaccuracyduetothelowlevelofliquidrecoveryafterbreakthroughandthelowviscosityoftheliquidphase.Furthermore,determiningthepositionoftheliquid/vaporinterfaceisratherdelicate.Intheimmediatevicinityofthecriticalpointthereisapiston-typedisplacement,withliquidrecoverycloseto100070atvaporbreakthrough.Soitisdifficulttocalculate,withgoodaccuracy,therelativepermeabilityvaluesbyusingonlythegraphicmethod;adjustmentwiththenumericalmodelbecamemoreandmorenecessary.Wedidnotintroducecapillarypressurecurvesintothenumericalmodel,sincewehaddeterminedtheirinfluencetobenegligiblewithregardtotheviscosityandgravityforcesforthesehigh-speeddisplacements.Inthecourseofthenumericalsimulations,wesoonnoticedthewidespreadofnumericaldispersion,which,withconstant-spacesteps,isobviouslyallthegreaterasthedisplacementfrontismoreabrupt-i.e.,whenthemixtureusedisclosetocriticalconditions.Eachexperimentwassimulatedwithasmaller-andsmaller-spacestep.Whenthis39442.6021.5819.960400.4410-70.3010-710.805.4733.20.1110-72.731.3847.80.02810-70.600.3054.70.00610-736.0718.2528.965350.5810-70.3910-7reductionnolongerinfluencedthesolution,thelatterwasconsideredcorrect.Intherangeofinterfacialtensionsbetween12and0.04mN/m,wefoundanexcellentcorrespondencebetweensimulationandexperimentalresults,withspacestepsof10mm,ontheI1p,oil-recovery,andVLRparameters,ascanbeseeninFigs.2through5.Therelativepermeabilitycurves(Fig.9)calculatedfromthedisplacementtestswerepracticallyunchangedinthenumericalmodel.Fortheotherthreeexperimentsclosetothecriticalpoints,inwhichavariesbetween0.038and0.001mN/m,wehadtoreducethespacestepto1mmtoobtainsolutionsnotaffectedbythenumericaldispersion.Buttheadjustmentoftherelativepermeabilitycurveswasnotsoeasy,andthecorrespondenceofthenumericalsimulationwiththeexperimentswasnotasgoodforthereasonsmentionedearlier.TheseresultsaregiveninFigs.6through8.TherelativepermeabilitycurvesafteradjustmentareshowninFig.10.DiscussionConsideringtheliquidrecoverycurvesvs.injectedvolume(Fig.11),wecanobservethat(1)therecoveryatvaporbreakthroughbecomesgreaterastheinterfacialpropertiesofthevaporandliquidcomeclosertogether(38.7070forthetestat27.6barand>95070forthetestat242.7bar),and(2)theresidualliquidsaturationlevelsalsorangefrom35070(at27.6bar)to0070forthelasttwotests.TheseresultsconfirmthoseobtainedbyWagnerandLeach,2atleastfortheresidualliquidsaturationatbreakthrough.Theseauthorsalsoobservedthat,whentheinterfacialtensionisintherangeof10-3mN/m,liquidrecoveryapproaches100070.Anothercommonpracticeistocomparetheresidualliquidsaturationwiththecapillarynumber.17-20Abrams21introducedamodifiedcapillarynumberthattakesintoconsiderationtheviscosityratiointhecaseofoil/watersystems.ThisnumberisSOCIETYOFPETROLEUMENGINEERSJOURNAL>~~100i!~1OO(!50HSYSTEM~_nCr27.8bor.1I.1·Cv-12.SmN'm_SirrMIlotion.4,\•V.l.REJ.perimfi\f....30zod,10!1lKledvolumeofvapor,PV•Fig.2-Vaporfloodingat400psia(27.6bar).SYSTEMC(.nC769.0bor-7'1·C.u08.6mNlm~lO-'baf__Snnulation...I•'ll.RExp.nment>0.0"101nte..~i~1OO1:::;507550I.jSYSTEMCI_nCr23Ibor.711"Ctoplo-3bor3°1(TzOO6~mN/m__SunulottOll•A,\•VLR("penmenl•RK2010A,J~t.dvolumeofvapor,Pv•Fig.5-Vaporfloodingat3,350psia(231bar).VLRm3/m375r50SYSTEMC,_nC7AplO-5txJrVLRm3/m32344bor.71~C(T~O.038mN/m__StmulahondpI•VLRExperiment•Rte10Ap253lnJtcttd~mtofvapor,PVFig.6-Vaporfloodingat3,400psia(234.5bar).15151010VLR25·~----~~~-~-~-----'~5-----~2-~--­Injectedvolumeofvapor,PvFig.7-Vaporfloodingat3,450psia(237.9bar).395F=(~)(~)0.4.ao-wIloAbramsobservedthatafterawaterfloodtheresidualoilsaturationdecreasessignificantlywhenFisaboveabout10-4.ThisresultwasobtainedbyaddingsomechemicalstothewaterphasetoincreasethewaterviscosityanddecreasethewaterIoilinterfacialtension.Inourcase,inwhichthedisplacingfluid(vaporphase)isthenonwettingphase,wefirstwillexaminetheevolutionofresidualliquidsaturationwithregardtothecapillarynumberandmorespecificallytointerfacialtension.Thenwewillexaminetheinfluenceoftheviscosityratio.Fig.12showsSLRintermsof(Ill'u)/a.Wefindthatthereisacleanbreakbetweentheexperimentsat234.4and237.9bar,withajumpfrom15to0070.8T~""SYSTEMC,.nC72427bar]1l"CCi':o!OOOlmNmI-E.~ment_Alatan!Nurnencolsimulations0-----0A•..01em-----...:1p10-'bOf10°O~------~~~------7-------~,,~----~,-----+1~¥OIumeofvopor,PVkrLFig.8-Vaporflodingat3,520psia(242.7bar).SYSTEMC,_nC7IT>o..04mN/m·o.0.7mN/mkrvConsideringtherelativepermeabilitydeterminations,theseexperimentsshowedusthatwecanclassifytheexperimentsintotwogroupsaccordingtothevalueofinterfacialtension.FirstGroup:u:::::0.04-0.07mN/mWefindinthiscaseasinglecurveofrelativepermeabilitytovapor(nonwettingfluid)andafamilyofrelativepermeabilitycurvestoliquid,withahigherandhigheraveragelevelwhentheinterfacialtensiondecreases(Fig.9).Weevenfindalinearrelationbetweentherelativepermeabilitytoliquidandinterfacialtensionatconstantvaporsaturation(Figs.13and14).SecondGroup:u95070);thenthepressuredropdecreasedlinearlyduringvaporflooding.Ontheotherhand,wehavetoconsiderthatthecapillarypressureisnegligibleandthatthedisplacementisstabilizedbygravity.Itappearsthattherearegreatvariationsintheshapeoftherelativepermeabilitycurveswhentheinterfacialtensiondropsbelow0.04mN/m.Suchvariationsalsohavebeenobservedforwater/oilsystems.3,19Notethatthevalueof0"""'0.04mN/mdoesnotconstituteanabsolutelyclearboundarybetweenthetwodomains.Forlowinterfacialtensions,thevalueswerecalculatedandnotmeasured.Ontheotherhand,thisfindingshouldbeconfirmedwithdifferentkindsofcoresamplesandotherpairsoffluids.Forpracticalapplicationsitappearsthatthiskindofdeterminationshouldbeperformedwithreservoirfluidsunderconditionsascloseaspossibletothoseprevailinginthefield.InfluenceoftheVelocityToillustratetheprimeimportanceofinterfacialtensioninthecapillarynumber,severalexperimentswereperformedwiththesamepairoffluidsatdifferentflowrates.Flowratesrangedfrom1.66x10-4to1.2X10-2cm3/s(i.e.,anaveragefrontvelocityadjustedfrom0.8x10-4to5.6X10-3cm/s).ForthispurposewechosethemixtureC1-nC10at50.3bar,forwhichtheviscosityratiowasthemostunfavorable.ThepropertiesofthismixtureandtheresultsofthevapordisplacementaregiveninTable2.TodetermineultimateliquidrecoveryweusedthemethoddescribedbyJonesandRoszelle.16Weobservedanimportantdifferenceconcerningliquidrecoveryatbreakthrough,butultimaterecoveryand,ofcourse,residualliquidsaturationarepracticallyunchanged(Fig.15).InfluenceofViscosityRatioTotesttheinfluenceofthisparameter,additionalexperimentswerecarriedoutwiththefluidsystemsC1-nCIOandC1-nC5at37.rc.DisplacementsweremadewithaC1-nC10mixtureat87.6bar.TheinterfacialtensionandthecapillarynumberofthissystemwereapproximatelythesameasthoseoftheCI-nC7mixtureattheequilibriumpressureof27.6barandat71.10C.TheresultsaregiveninTable2.AOCTOBER1980~WRFOSTER~LEFEBVREDUPREYBARDON_LONGERON10-310-·--------~--~-----~--~-@~---~--~--­--~--~-~--10-710--Caplllorynumber.iffFig.12-Capillarynumbervs.residualliquidsaturation.-\\"'\\\\\\\\\\\\\\\\\\\\\\\\1510.•krl·0.&krL·a.ar5...krL·o.m•krL·0.10o)(rt·O.l~•krL·0.20ckrl·0.25•krls03Q...krl·0.40-1379bor\\\\o.o.~____~~~-L~~-L~__=-~\~_~2~3W~OO~'~__~~~~~.V_7!;100Fig.13-Relationinterfacialtension-vaporsaturationfordifferentvaluesoftheliquidrelativepermeability.o;mN/m20.%-276bar690bar-13791)or\\\\\\\\\\\\k.L0.0.0.10.20.3Q4""Fig.14-Relationinterfacialtension-liquidrelativepermeabilityfordifferentvaluesofthevaporsaturation.397~..(!~SYSTEMC,_nCIO503bof_377·Cu"J7mN/m;:t~~1'-------r--_~~_O.O}6S)()-Scrn'{s_O.07610-'cm'I,_a~297Xl-'cm'/,t----fQ.II.83)C)-Scm'l,In,ec:ftodyo/um.ofvapor,PV4•Fig.15-InfluenceofthevelocityontheliquidrecoveryfortheC1-nC10systemat730psia(50.3bar).SYSTEMC,_n~816bor.377·C
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