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Improvingsweepefficiencyofedge-waterdrivereservoirsusinginducedformationdamageAbbasZeinijahromin,HammamAl-Jassasi,SteveBegg,PavelBedrikovetskiAustralianSchoolofPetroleum,TheUniversityofAdelaide,AustraliaarticleinfoArticlehistory:Received14January2015Accepted9April2015Availableonline20April2015Keywords:waterproductionedge-water-driveinducedformationdamagelowsalinitywaterinjectionfinesmigrationEORabstractAcommonprobleminedge-waterdrivereservoirsisoilbypassingbyaquiferwater.Theencroachingwaterfromtheadjacentaquiferovertakesoilphaseandleavesasignificantvolumeoftrappedresidualoilbehind.Earlyarrivalofthesewaterfingerscausespre-maturewaterproductionthatleadstowellabandonment.Onesolutiontotheproblemiscreatingabarrieragainsttheencroachingwater.Incurrentstudythepossibilityofusinginducedformationdamagecausedbyinjectingasmallvolumeoflowsalinitywaterintoabandonedwellsisinvestigated.Formationdamageasaresultofinjectionoflowsalinitywaterintothewatered-upwellscreatesalowpermeablebarrieragainstthewaterfingers.Themethodologyofmodelingthistechniqueusingacommercialreservoirsimulatorispresented.Themodelingresultsshowthatinjectionofsmallvolumeoflowsalinitywaterresultsinprolongationofwells'lifewhichresultsinC243–5%incrementalrecoveryifcomparedtonormaldepletion.&2015ElsevierB.V.Allrightsreserved.1.IntroductionOnaverage,morethanthreebarrelsofwaterisproducedforeachbarrelofoilanditcostsbillionsofdollarseveryyeartodisposetheunwantedwater(Baileyetal.,2000).Manyoilreservoirsderivetheirnaturalproducingenergyfromadjacentaquifers.Oilbypassingduetowaterinvasionisamajorprobleminedge-waterdrivereservoirs.Inedge-waterdrivereservoirs,watertonguemayunderrunoilcausingearlywaterproductionatthewellandlowproductivityoftheoilwithconsiderableunrecoveredoilleftbehind(HernandezandWojtanowicz,2006).Encroach-mentofedge-waterresultsinpre-maturewaterproductionfromwellslowonstructureandearlyterminationofwells'life.ThewaterproductioncontinuestoincreaseuntiltheeconomiclimitofWORofthewellisreached.Atthetimeofabandonment,theremaybeconsiderableunsweptoilstilltrappedbehindthewaterfront.Dependingonthereservoirheterogeneity,theresidualoilsaturationmayreach60%(Kumar,1977;Braedley,1987;Hernandezetal.,2006).Hence,itisofagreatinteresttoascertainwaystoretardthewaterencroachmentandcontrolearlywaterproductionandbypassedoilinedge-waterdrivereservoirs.Manydifferentmethodsareusedtoslowdownthewatertongueincluding:productionratecontrol,managementofthetotaloilproductionpatternandinjectionofbarrierfluids.Mostcommonlyusedbarriersfluidsarecement,gels,resins,foamsandpolymers(Karpetal.,1962;Serightetal.,2001;ZaitounandPichery,2001).Alargetreatmentvolumeisrequiredtodivertwaterawayfromtheareathathasbeenalreadysweptbywater,whichisgenerallyuneconomic(Baileyetal.,2000).Reductionofrockpermeabilityduetolowsalinitywaterinjectionhasbeenobservedinseverallaboratoryandfieldstudies(Mungan,1965;Khilaretal.,1983;LeverandDawe,1984).Itisexplainedbymobilizationofin-situfinesandsubsequentpluggingofporethroats.Naturallyin-situfineparticlesareinitiallyinmechanicalequilibriumofdrag,lifting,electrostaticandgravita-tionalforces.Injectionoflowsalinitywaterweakenstheelectro-staticforceandperturbstheequilibriumoftheparticleonporewall.Asaresultthefineparticlesaredraggedwiththeflowingwaterandblocknarrowporethroats(KhilarandFogler,1998;OchiandVernoux,1998;Bedrikovetskyetal.,2012;Husseinetal.,2012).Mobilizationoffineparticlesandsubsequentporepluggingresultsinpermeabilityreductionwhenlowsalinitywaterisinjected.Bedrikovetskyetal.(2012)introducedmaximumreten-tionfunctionformodelingoffinesmigrationinporousmedia.Theproposedapproachallowsapplyingthetorquebalanceofforcesonsingleparticletocalculatethemaximumconcentrationofparticlesthatcanremaininaporousmedium.Thevalidityofthisapproachwasconfirmedbycomparisonwithseriousofdirectlymeasurecoredata(Lemonetal.,2011;Zeinijahromietal.,2011;Husseinetal.,2012).Thepermeabilityreductionvaluesof40–100timeshasreportedinvariouslaboratoryexperiments(Mungan,1965;Khilaretal.,1983;LeverandDawe,1984;SarkarandSharma,1990;ContentslistsavailableatScienceDirectjournalhomepage:www.elsevier.com/locate/petrolJournalofPetroleumScienceandEngineeringhttp://dx.doi.org/10.1016/j.petrol.2015.04.0080920-4105/&2015ElsevierB.V.Allrightsreserved.nCorrespondingauthor.Tel.:þ61883138014;fax:þ68883134345.E-mailaddress:abbas.zeinijahromi@adelaide.edu.au(A.Zeinijahromi).JournalofPetroleumScienceandEngineering130(2015)123–129Husseinetal.,2012);thatmotivatesapplicationoflowsalinitywaterinjectionasapossiblemethodtocreateabarrieragainstwatertongueinedge-waterreservoirs(Nguyenetal.,2013).ModelingresultsbyNguyenetal.(2013)haveshownthatinjectionofsmallvolumelowsalinitywater(LSW)intoabandonedwellscanreducetheencroachingwatervelocityandenhancestheultimatesweepefficiencyby15–18%.ThecurrentstudyfollowsonfromthemethodofapplyinglowsalinitywaterinjectiontocontrolwaterencroachmentbyNguyenetal.(2013).Whilstthisearlierworkhasstudiedthemethodofcreatingbarrieragainstaquiferwatertongue,itassumedasimplifiedtwodimensionalreservoirmodel.Thecurrentpaperextendsthepreviouswork(Nguyenetal.,2013)addressing3Dfivespotpatternwhichiscommonlyusedinfielddevelopmentstoincreasethearealsweepefficiency.ThecurrentworkfollowsBedrikovetskyetal.(2012)inmodelingparticledetachmentduringlowsalinitywaterinjection.Thusthemaximumretentionfunctionisappliedtomodelthefinesdetach-mentduetoinjectionofalternatingbrinesalinitywhennon-swellingmobileclayfinesarepresent.IncurrentpapertheapproachbyZeinijahromietal.(2013)isappliedtoimplementedEclipseblackoilsimulator(Schlumberger,2013)inordertomodellowsalinitywaterflowwithinducedfinesmigration.Zeinijahromietal.(2013)devel-opedanewmethodforimplementingcommercialreservoirsimu-latorstomodelwaterinjectionwithinducedfinesmigration.Frompracticalpointofview,theadvantageofthemethodisthatitcanbereadilyincorporatedintotheexistingpolymersimulatortomodellowsalinitywaterinjectionwithouttheneedfordevelopingnewsoftwareormodifyingthecurrentsimulators.2.Inducedformationdamagemethodtodecelerateedge-waterencroachmentInthissectiontheconceptofusingpermeabilitydeclinebylowsalinitywaterinjectiontocreatelowpermeabilitybarrieragainsttheencroachingedge-waterisdiscussed.Fig.1ashowsaschematicforencroachmentofedge-waterduringoilproductionwithfullorpartialpressuremaintenancebytheaquiferatdifferentstagesofthefielddevelopment.Thelightblueandredcolorsrepresentwaterandoilrespectivelyandblacklineshowsaquiferwaterfront.Waterfromtheadjacentaquifer(purplearrows)encroachesintotheoilreservoirduetopressuredropbetweentheaquiferandtheproductionwells.Atthemomentt1,minimumpressureduringwater-drivenproductionisreachedneartoproductionwells;hencethestreamlinesfromtheaquifercrossthelocationpointsforwellslowonstructure.Thus,thecentrallinesofthewatertonguesalsocrossthelocationpointsforstructurallylowwells.Thelowstructurewellsareaboundedatsomehighwater-cutvalue,whenthecostofwaterproductionanddisposalexceedstheeconomicallimit.Pressurebuildsupnearthelowstructureproducersaftertheirclosure;thus,minimumpressuresovertheareaarereachednearthehighstructureproducingwells(momentt2).Watertonguescontinuetomovetowardsthewellshighonstructureandleaveasignificantvolumeofresidualoilbehind.Fig.1bshowsthesimilarscenarioofoilproductionwiththeshort-termLSWinjectionintheabandonedwells.Similartothe‘normal’productionscenario,atthemomentt1minimumpressurereachesneartowellslowonstructureandthepressuregradientsfromtheaquifercrossthelocationpointsforwellslowonstructurecausingwatertonguestocrossthesewells.Asmallvolumeoflowsalinitywaterisinjectedintostructurallylowwellsaftertheyhavereachedtheeconomicallimitofwaterproduction.Itinducespermeabilityreductionduetofinesmigrationandcreatesalowpermeablezoneinwellvicinity(darkblueareaaroundstructurallylowwells).Thecreatedlowpermeablezonecanslowdownthewaterfingersfrommovingtowardsup-structureproducers.Ithomogenizesmovementofwaterfrontandprolongswater-freeproductionperiodofwellshighonstructurethatleadstotheultimaterecoveryimprovement.3.PhysicmechanismsofinducedformationdamageSeveralstudieshaveshownthatlowsalinitywaterinjectionintoreservoirsrockscancausereductionofrockpermeability.Thephenomenonisexplainedbymobilizationofreservoirfineswhichplugthenarrowporeconstriction(KhilarandFogler,1998;OchiandVernoux,1998;Bedrikovetskyetal.,2011).Themechanicalequilibriumofanattachedparticleisdeterminedbytorquebalanceoffourmajorforces;dragforce,liftingforce,gravitationalforceandtotalelectrostaticforces(Fig.2).FdUðÞldþFlUðÞln¼FeγC0C1þFgC0C1lnð1ÞNomenclatureLatinletterscconcentrationofsuspendedparticlescapolymeradsorptionconcentrationcppolymerconcentrationsintheaqueousphasecp0polymerconcentrationsintheinjectedwaterFddragforce,MLTC02,NFeelectrostaticforce,MLTC02,NFggravitationalforce,MLTC02,NFlliftingforce,MLTC02,Nkabsolutepermeability,L2,mDkoinitialabsolutepermeability,L2,mDkrooilrelativepermeabilitykrwwaterrelativepermeabilityldleverfordragforce,L,mlnleverfornormalforce,L,mppressure,MLC01TC02,PaRkresistancefactorSwatersaturatinUoverallflowvelocity,LTC01,m/sGreeklettersγbrineionicstrength,molLC03,mol/lγ0ionicstrengthoftheinjectedbrine,molLC03,mol/lγireservoirinitialbrineionicstrength,molLC03,mol/lμooildynamicviscosity,MLC01TC01,cpμwwaterdynamicviscosity,MLC01TC01,cpβformationdamagecoefficientεtorqueratio(erosionnumber)σvolumetricconcentrationofcapturedparticlesσavolumetricconcentrationofattachedparticlesσaoinitialvolumetricconcentrationofattachedparticlesσcrmaximumvolumetricconcentrationofcapturedparticlesσsvolumetricconcentrationofstrainedparticlesAbbreviationsLSWlowsalinitywaterA.Zeinijahromietal./JournalofPetroleumScienceandEngineering130(2015)123–129124Here,γissaltconcentrationandUistheDarcyvelocity,ldandlnareleverarmsfordragandnormalforces,respectively.LefthandsideofEq.(1)definesthedetachingtorqueofdragandliftingforceswhilerighthandsideshowstheattachingtorquebygravitationalandelectrostaticforce.Theparticleremainsontheporewallonlyifthemechanicalequilibriumcondition(Eq.(1))onaparticleisfulfilledi.e.theattachingtorquesislessthanorequaltothedetachingtorque.Ifnot,thehydrodynamicforcescandislodgetheparticle.Hydrodynamicforces(dragandliftingforce)dependonflowvelocity,U(Saffmann,1965;O’Neill,1968);while,totalelectro-staticforceisafunctionofparticleandrockmineralogicalcompositionsandalsofluidcomposition(pH,salinity(γ)andtemperature);seeIsraelachvili,1992.ThetotalelectricalforceisthesumofthevanderWaals,electricaldoublelayerandBornforcesasdescribedbytheDLVO(Derjaguin,Landau,VerweyandOverbeek)theory(Derjaguin,1989;Israelachvili,1992;KhilarandFogler,1998).Thetotalelectrostaticforcechangeswithparticle-surfaceseparationdistance.Attachingtorqueisweakenedwithdecreaseofbrinesalinitywhichyieldsinincreaseoftheseparationdistance.Increaseoftheflowvelocityalsohasthesameeffectonseparationdistancebyincreasingthedetachingtorque.Electro-staticforcesareshortrageforces;hence,thefineparticleremainsattachedtothesurface,aslongastheseparationdistanceissmallerthanthatwheretheelectrostaticforcereachesmaximum.Therefore,Eq.(1)expressestheconditionofparticledetachmentforthemaximumvalueofelectrostaticforce.Furtherinthetext,Fedenotesthemaximumvalueoftheattachingelectrostaticforce.Alternationofeitherflowvelocityorfluidchemistrymayresultinperturbationoftorquebalancethatcanleadinparticledislodgmentfromtheporewalls.Flowvelocityincreaseresultsinhigherdetachingtorque(seelefthandsideofEq.(1))andconsequentparticlemobilizationifitexceedstheattachingtorque(seerighthandsideofEq.(1)).Similarly,decreasingsalinityofbrinecausesthetotalelectricalforcetodecreasewhichleadstomobilizationofparticlebyhydrodynamicforces.Dimensionlesserosionnumberεisintroducedastheratiobetweenthedetachingandattachingtorquesε¼FdldþFllnFeþFgC0C1lnð2ÞIn-situfinesarenotmobilizedunlessthetorquefromdetach-ingforcesisgreaterthanthatforattachingtorque,i.e.thevalueofεexceedsthatcorrespondingtomaximumelectrostaticforce,seeBedrikovetskyetal.(2012).Introducingtheerosionnumberεallowscalculationofthemaximumconcentrationofparticlesthatcanexistinaporousmediumσaforeachflowcondition(velocityUandsalinityγ).σa¼σcrεU;γC0C1C0C1ð3ÞFig.3showsthemaximumretentionconcentrationσavstheerosionnumber.Reducingofsaltconcentrationfromformationwaterγitoinjectionwaterγ0perturbsthebalancebetweenattachinganddetachingtorqueandresultsinfinesrelease.ThevolumeofreleasedparticlesΔσ,isequaltothedifferencebetweeninitialconcentrationofattachedparticlesσa0(ε(γi))andmaximumconcentrationofparticlesforinjectedfluidcompositionσa(ε(γ0)),thatcanbedeterminedusingEq.(3).Thedistancethatreleasedparticlestravelbeforebeingcap-turedattheporeconstrictionsissignificantlysmallerthanreferencereservoirsize.Itcorrespondstoinstantstrainingofmobilizedfineparticleatlargescaleapproximationimplyingthatthevolumeofstrainedparticlesσs,isequalvolumeofreleasedparticlesΔσduringalternationofsalinityfromγitoγ0:σsεγ0C0C1C0C1¼Δσεγ0C0C1C0C1¼σa0εγiC0C1C0C1C0σaεγ0C0C1C0C1ð4ÞFollowingPangandSharma(1997)andMojaradandSettari(2007),itisassumedthattheinversetonormalizedpermeabilityk(σs)/k0isalinearfunctionoftheretainedparticleconcentration:k0kσsðÞ¼1þβσsεðÞð5Þwhereβisformationdamagecoefficientwhichshowsthedegreeofdamageduetoporepluggingandk0istheinitial(notdamaged)rockpermeability.4.Mathematicalmodelfortwo-phaseflowwithfinesmigrationParticledetachmenttakesplacewhendetachingtorqueisgreaterthanattachingtorqueintheporeswhichareoccupiedInducedformationdamagearoundtheinjectorst1t3t2FlowdirectionWellsFig.1.Schematicforinducedformationdamagemethodtodecelerateedge-waterencroachment:(a)normalpressuredepletionand(b)pressuredepletionfollowedbyinducedformationdamage.(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.)Fig.2.Forcesactingonanattachedparticle.A.Zeinijahromietal./JournalofPetroleumScienceandEngineering130(2015)123–129125bylowsalinitywater.Therefore,inthissectionthedetachmentofin-situparticlesfromwater-exposedsurfacesisdiscussed,i.e.theparticlemobilizationbydragforceinoilphaseisignored.Volumeofexposedparticletolowsalinitywaterisfunctionofwatersaturation;thus,Eq.(3)canberewrittenasσ¼σcrε;SðÞð6ÞInreservoirscale,theparticlefreerunlength(thedistancethatparticletravelsbeforebeingstrained)isgreatlysmallerthanthereservoirsize.So,itisassumedthatthereleasedfinesarecapturedinstantlybyporousmedia,leadingtoinstantpermeabilityreduc-tioninwatersweptzones.Theinitialconcentrationofin-situparticles,σa0isassumedtobeequaltomaximumparticleconcentrationforinitialreservoirsaltconcentration,σa0¼σa0(γi)whichcanbedeterminedusingEqs.(1)–(3).Modificationsarerequiredtothestandardtwo-phaseflowsystemofequationstodescribetheflowofbrinewithintheporousmediumwithfinesreleaseandcapture.Thissystemofequationsfortwo-phaseflowwithfinesmigrationinlargescaleincludes:C15volumetricbalanceequationforincompressiblefluxoilandwater,C15volumetricbalanceforincompressiblewater,C15massbalanceequationforattachedandstrainedparticles,C15maximumconcentrationofattachedparticlesasafunctionofwaterflowvelocity,salinityandsaturation,C15advectivemasstransferofsaltinporousspacewithfines,andC15andmodifiedDarcy'slawfortwo-phaseflowwithstrainedparticles.∇UðÞ¼0ð7Þϕ∂S∂tþU∇fS;σsðÞ¼0ð8ÞfS;σsε;SðÞðÞ¼1þkroSðÞμw1
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