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eneouscoleum,ChinaArticlehistory:Received2February2015Marzouqietal.,2010;Leastetal.,2013;Mayeretal.,2014).etal.,).Waterbreak-ICDs(Hen-etal.,2011;thehorizontalyears.Moenandwellclean-upbytheinfluxalongandHarelandwhenfluidflowreasonsofun-planningforICDscompletion.Fernandesetal.(2009)presentedContentslistsavailableatScienceDirectJournalofPetroleumScienceJournalofPetroleumScienceandEngineering146(2016)971–982http://dx.doi.org/10.1016/j.petrol.2016.08.007quidinflowevenly.TheprincipleoftheICDsistobalanceorequalizewellborepressuredroptoachieveanevenlydistributedthekeyfactorsofusingICDsornotandaffectingwaterdelayingeffectsbysimulation.Zadehetal.(2012)developedasime-ana-lyticalmathematicalmodelforcalculatingtheoptimalICDscon-figurationsforlonghorizontalwell.Mayeretal.(2014)studiedthe0920-4105/&2016ElsevierB.V.Allrightsreserved.nCorrespondingauthor.ICDreferstoasequalizerisacompletionhardwarethatisde-ployedasapartofwellcompletionsaimedatdistributingtheli-desiredwater/gasbreakthroughinhorizontalwell,suchastheICDtypes,theICDcompletionmodels,andtheappropriatedesignand1.IntroductionHorizontalwellhasbeenwidelyusedtodevelopoilreservoirswithbottomwater.Althoughitseffectsarebetterthanverticalwell,water-crestisstillseriousinheterogeneousoilreservoirswithbottomwater(Wangetal.,2010;AlblooshiandWojtanowicz,2014).Inpastfewyears,manyanti-water-coningtechnologieshavebeenusedtodelaywaterbreakthrough(Pangetal.,2007;Daietal.,2011;AlblooshiandWojtanowicz,2014).ICDswereinitiallydevelopedtodealwithwaterconingproblemsinlonghorizontalwells.Ithasbeenprovensuccessfulinthefield(Madsen1997;Henriksenetal.,2006;AadnoyandHareland,2009;Ouyang,2009;inflowprofilealongthewellborebycreatingdifferentlpressuredrops(AadnoyandHareland,2009;Fernandes2009;Daneshyetal.,2012;Mayeretal.,2014throughwasactuallydelayedinmanyoilfieldsusingriksenetal.,2006;Medhatetal.,2010;RamirezMahmoudetal.,2013;Carvajaletal.,2003).ManyaspectsaboutequalizingtheinfluxalongpathusingICDshavebeenperformedinrecentAsheim(2008)presentedthatICDscanimprovereducingtheimpactofformationdamage,balancethewellbore,andreduceannulusflow.Aadnoy(2009)calculatedaseriesofpressurelossesthroughanICD.Ouyang(2009)summarizedtheyadditionalReceivedinrevisedform27July2016Accepted5August2016Availableonline5August2016Keywords:InflowcontroldevicesReservoir-ICD-wellborecoupledmodelHorizontalwellBottomwaterMechanismSensitivityanalysisabstractTheimprovedoilrecovery(IOR)mechanismofICDsisusuallycontributedtoequalizingpressuredroptoachieveanevenlydistributedinflowprofilealongthehorizontalsection.Substantially,inheterogeneousoilreservoirswithbottomwater,theintrinsicmechanismischangingthepressuredistributioninfor-mationtoeffectivelyutilizetheenergyofbottomwater.Inthiswork,areservoir-ICD-wellborecoupledmodelwasestablishedandthecorrespondingsimulatorwasdeveloped.Intherestofthepaper,thismodelwasusedtodiscoverthemechanismsofICDsinheterogeneousreservoirwithbottomwater.Finally,thesensitivityofmanyfactorsonoilrecoveryfactorandIORofICDsweredemonstrated.TheresultsshowthatICDscanimprovetherecoveryanddelaythewaterconing.TheintrinsicmechanismsofICDscontainsbothequalizingpressuredroparoundthewellboreandchangingthedirectionoflateralflowtoincreasethesweepvolumeofbottomwater,butICDsisessentiallyashallowprofilecontroltechnique.TheIORofICDsissignificantinstrongheterogeneousoilreservoirs;theIORincreasesasthewellproductionrateandoilviscosityincrease;asKv/Kh(theratioofverticaltohorizontalpermeability)andHD(dimensionlesswateravoidanceheight)increase,theIORfirstincreasesandthendecreases,theoptimalvaluesarerelatedtothepermeabilityheterogeneity.&2016ElsevierB.V.Allrightsreserved.articleinfoMechanismandsensitivityanalysisofanforreducingwaterproductioninheterogbottomwaterJingWanga,n,HuiqingLiua,YonggeLiub,YuweiJiaoaMinistryofEducationKeyLaboratoryofPetroleumEngineering,ChinaUniversityofPetrbChinaUniversityofPetroleum,EastChina257061,ChinacPetroChinaResearchInstituteofPetroleumExploration&Development,Beijing100083,dPetroChinaDagangOilfieldCompany,Tianjin300280,ChinaePetroChinaTarimOil&GasCompany,Kurla,Xinjiang841003,Chinajournalhomepage:www.elsevinflowcontroldevices(ICDs)oilreservoirwith,JungangWud,AihongKangeBeijing102249,Chinaier.com/locate/petrolandEngineeringmultiphaseflowperformanceinICDsbyexperiments.Generally,mostoftheresearchesfocusontheICDtypes,theinflowandpressurealongthewellbore,andtheeffectsofICDstechnique.Somesimulationstudiesconcentratesonthelocalpressurelosses.Althoughthecapacitanceresistancemodel(CRM)couldhelptoseparatethewellborephysicsandthecouplingtotheformation(Valdoetal.,2000;Sayarpouretal.,2007;Caoetal.,2014,2015),therearefewresearchesonreservoir-ICD-wellbore→+→=→vvAv.ICDandelement;A2isthecross-sectionalareaofthescreen-innerannulus,whichisequalsto()Απ=−′()DD4,722212whereD2istheinnerdiameterofscreentube,and′D1istheouterdiameterofinnertube.Eq.(6)canbeconvertedintothefollowing→+→=→+→()−vvAAvvAA.82,i2in,iS22,i12out,iICD2Basedonthemomentumtheorem,thepressuredropfromitoJ.Wangetal./JournalofPetroleumScienceandEngineering146(2016)971–982972()−A21,i1in,i11,i1Basedonthemomentumtheorem,thepressuredropfromitoiC01ininnertubeis()ρτπρθΔ=−−Δ−Δ()−pvvDxAgxsin,3w1,i1,i21,i12111whereΔp1,iisthepressuredropfromitoiC01;D1isthediameterofinnertube;θisthedipangleofwellbore;τw1isthefrictioncoupledmodelorcouplingbetweencompletionsimulationsoft-wareandwithareservoirsimulator.Inourwork,acoupledmodelofreservoir,ICDs,andwellborewasestablished.Fluidflowinre-servoir,formation-screenannulus,screen,screen-innerannulus,andinnertubewascoupledandincorporatedinthemodel.Then,thecorrespondingsimulatorwasdevelopedandusedtounder-standthemechanismsofICDstechnologyinheterogeneousre-servoirwithbottomwater.Thesensitivityanalysisofoilproduc-tiontomanyfactorswasdemonstratedaswell.2.ModelingoffluidflowfromreservoirtowellborethroughICDsThestructureofICDsusedinsomeoilfieldsofChinaisshowninFig.1(Lietal.,2010).Thefluidflowsfromformationintotheformation-screenannulusfirst;afterthat,itflowsintothescreen-innerannulusthroughthescreen;finally,itflowsintotheinnertubethroughthenozzlesafterlateralflowinannulus-2.Evenpressureandproductionprofilesarerealizedbyadjustingthenozzlediameter.Thus,thewholeflowprocessisacomplicatedlycoupledflowincludingseepageflow,pipeflow,nozzleflow,variable-massflowininnertube,andmanylocalpressurelosses.2.1.Variable-massflowmodelininnertubeThefluidflowininnertubeisvariable-massflow,asshowninFig.2.Assumingthatthefluidflowissingle-phase,in-compressible,andisothermal,anelementwiththelengthofΔxiscutout.Basedonthemassconservationprinciple,ρρρ→+→=→()−vAvAvA,11,i11in,iICD1,i11whereρisthefluiddensity;A1isthecross-sectionalareaoftheinnertube;v1,iandv1,i-1aretheflowrateatiandiC01,respec-tively;v1in,iisthemeanrateoffluidflowfromannulustotheelement;AICDistheflowareabetweenannulusandelement.Eq.(1)canbeconvertedintothefollowingFig.1.Theflowstructureofhorizontalresistanceofinnertube.Hence,Eqs.(2)and(3)constitutethevariable-massflowmodelininnertube.Ifthebottom-holepressureisconstant,theboundarycondi-tionsare=→=()ppvand0.4N1,0wf1,Ifthewellproductionrateisconstant,theboundaryconditionsare=→=()vvvand0.51,0c1,N2.2.Variable-massflowmodelinthescreen-innerannulusThefluidflowinscreen-innerannulusisalsovariable-massflow,asshowninFig.3.AnelementwiththelengthofΔxiscutoutaswell.Basedonthemassconservationprinciple,ρρρρ→+→−→−→=()−vAvAvAvA0,62,i22in,iS2,i122out,iICDwherev2,i,v2,iC01aretheflowratesatiandiC01,respectively;v2in,iisthemeanrateoffluidflowfromformation-screenannulustotheelementthroughscreen;v2out,iisthemeanrateoffluidflowfromtheelementtoinnertube;ASistheflowareabetweenscreenFig.2.Theschematicdiagramoffluidflowininnertube.Fig.3.Theschematicdiagramoffluidflowinthescreen-innerannulus.wellcompletionwithICD.()π=−′()ADD4,1233222whereD3istheinnerdiameterofformation-screenannulus;D2′istheouterdiameterofscreen.Eq.(11)canbeconvertedintothefollowing→+→=→+→()−vvAAvvAA.13FS3,i3in,i33,i13out,i3Basedonthemomentumtheorem,thepressuredropfromitoiC01intheannulusis()ρτπρθΔ=−−′Δ−ΔpvvDxgxsin22w3e→=→=vv0and0.Fig.4.Theschematicdiagramoffluidflowsintheformation-screenannulus.J.Wangetal./JournalofPetroleumScienceandEngineering146(2016)971–982973iC01intheannulusisρτπρθΔ=(−)−Δ−Δ()−pvvDxAgxsin.9e2,i2,i22,i12w22whereDeistheequivalentdiameterofscreen-innerannulus,=−′DDDe21.Eqs.(8)and(9)constitutethevariable-massflowmodelinscreen-innerannulus.Theboundaryconditionsare→=→=()vv0and0.102,02,N2.3.Variable-massflowmodelintheformation-screenannulusFig.5.Theschematicdiagramoffluidflowsinreservoir.Fluidflowintheformation-screenannulusisshowninFig.4.AnelementwiththelengthofΔxiscutout.Basedonthemassconservationprinciple,ρρρρ→−→+→−→=()−vAvAvAvA0,11FS3,i33,i133in,i3out,iwherev3,i,v3,i-1aretheflowrateatiandiC01,respectively;v3in,iisthemeanrateoffluidflowfromformationtotheelement;v3out,iisthemeanrateoffluidflowfromtheelementtoscreen-inneran-nulusthroughscreen;AFistheflowareabetweenformationandelement;A3isthecross-sectionalareaoftheformation-screenannulus,whichisequalstoFig.6.Theschematicdiagramof()15N3,03,2.4.FluidflowinthereservoirTheessentialpurposeistodelaythewaterconinginthefor-mation.Fluidflowintheformationistwo-phaseflowforbottom-waterflooding.Thefluidflowfromformationtoformation-screenannulusisshowninFig.5.BaseonDarcy'slawandmasscon-versionprinciple,()ρμΦρρϕ∇⋅→+=∂∂()⎛⎝⎜⎜⎞⎠⎟⎟KKqStgrad.16lrlllllllThus,theflowrateis=()vqA,17LlFwhereρlisthedensityofphasel;qlisthesource/sinkterm;ϕistheporosity;Slisthesaturationofphasel;Kisthepermeability;Krlistherelativepermeabilityofphasel;μlistheviscosityofphasel;Фlisthepotentialfunctionofphasel;plisthepressureofphasel;Disthereservoirdepth;vListheflowratefromformationtoformation-screenannulus.2.5.CouplingmodelsbetweendifferentflowchannelsDiscretesolutionisusedforalltheflowchannels,andtheelementsindifferentchannelsareshowninFig.6.ThehorizontaltubeisdividedintoNelementsandNþ1groupsofpressureandflowrate,(pi,vi),areobtained,where(p0,v0)islocatedintheheel.()−A143,i3,i3,i13where′Deistheequivalentdiameterofformation-screenannulus,′=−′DDDe32.Eqs.(13)and(14)constitutetheflowmodelinformation-screenannulus.Theboundaryconditionsareunitstructureinthechannel.etal.(1986)isusuallyused.Becausetheflowrateintheannularismuchsmallerthantherateofflowthroughanozzle,theflowratecanberegardsaszero.Hence,basedonBernoulliequationInitialpressure(MPa)8Initialoilsaturation0.7Depthofaquifer(m)1025Kv/Kh1Porosity0.25Oilviscosity(mPas)30Oildensity(kg/m3)850Lengthofhorizontalwell(m)240θ(deg)0D1(cm)12.5D2(cm)14D3(cm)16Frictioncoefficientofwellbore0.01J.Wangetal./JournalofPetroleumScienceandEngineering146(2016)971–9829742.5.1.Couplingequationsbetweenformationandformation-screenannulusBecausetheoutflowfromformationisequaltotheinflowofformation-screenannulus,thefollowingequationscanbeob-tainedbasedontheseepagemechanics,∑∑==(−)()⎡⎣⎤⎦qqJpp,18ll3in,io,wilo,w3,il3,i===∑(−)()=vvqAJppA,19l3in,iL3in,iFo,w3,il3,iF()πμμ=Δ−⋅+()⎛⎝⎜⎜⎞⎠⎟⎟JxKKrrKK2ln/0.75,203,iyzewroorwwwhereq3in,iistheinflowfromformationtoformation-screenan-nulusati;J3,iistheliquidproductivityindexati;p3,iandv3in,iareElementsofICDsandreservoirsplitSettheinitialpressureandflowrateinICDschannelsandreservoirpressureandsaturationCalculatetheJacobianmatrixJSolvepandvinICDchannelsandpandSwinreservoirGotothenexttime-stepSettheerrorlimitationσandcheckconvergenceYesNoUpdateFig.7.Thecalculationprocedureofthecoupledsimulator.thepressureandflowrateintheformation-screenannulusati,respectively.2.5.2.Couplingequationsbetweenformation-screenannulusandscreen-innerannulusBecausetheoutflowfromformation-screenannulusisequaltotheinflowofscreen-innerannulus,thefollowingequationscanbeobtained,=(−)()qJpp,212in,i2,i3,i2,i===(−)()vvqAJppA,222in,i3out,i2in,iS2,i3,i2,iSwhereq2,iistheinflowfromformation-screenannulustoscreen-innerannulusati;J2,iisthetransmissibilityofscreentube;(p2,i,v2,i)arethepressureandflowrateinthescreen-inneran-nulusati,respectively.2.5.3.Couplingequationsbetweenscreen-innerannulusandinnertubeThefluidinscreen-innerannulusflowsintoinnertubethroughthenozzles.ThepressuredropacrossanozzlefromBourgoyne0123456050100150200250300350400Qo,m3/(day·m)Distancefromheel,mProductiondata-OpenholeSimulationdata-OpenholeProductiondata-ICDs(2nozzles)Simulationdata-ICDs(2nozzles)Productiondata-ICDs(3nozzles)Simulationdata-ICDs(3nozzles)Fig.8.ComparisonsofQocalculatedbythecoupledmodelwiththeproductiondatainliterature(Mahmoudetal.,2013).Table1Petro-physicalpropertiesandwellparameters.ParametersValueModelscale(m)300C220C225Reservoirdepth(m)800ρρ++=++()ZpgZpgvg02,23i22,11,i1in,i2toignorethevariationofheight,theaboveequationcanbesim-plifiedasρ−=()ppv2,242,i1,i1in,i2whichissimilarwiththeexpressionofAadnoyandHareland(2009).Therefore,themeanrateoffluidflowthroughnozzlesisρ==(−)()vvpp2.251in,i2out,i2,i1,iTheaboveequationisthenozzleflowmodelofICDs.2.5.4.PackertreatmentThechannelsaredividedintoseveralindependentpressuresystems.Becausethereisnofluidexchangethroughthepacker,themomentumconservationequationsatthepackershouldbe()ρτπ−=→→−→→−′Δ()+++ppvvvvDxA,26w3,i,R3,i13,i13,i13,i,R3,i,R3e3()ρτπ−=→→−→→+′Δ()−−−ppvvvvDxA,273,i,L3,i13,i13,i13,i,L3,i,Lw3e3wherep3,i,R≠p3,i,L,v3,i,R¼0,andv3,i,L¼0.()ρτπ−=→→−→→−′Δ()+++ppvvvvDxA,282,i,R2,i12,i12,i12,i,R2,i,Rw3e3()ρτπ−=→→−→→+′Δ()−−−ppvvvvDxA,292,i,L2,i12,i12,i12,i,L2,i,Lw3e3Fig.9.Thedistributionofpermeabilityandnozzlediameteralongthewellbore.y11.522.5312Ql,m3/dayOpenholecompletionICDsFig.11.ComparisonofproductionbetweenopenholecompletionandICDs.J.Wangetal./JournalofPetroleumScienceandEngineering146(2016)971–982975(a)Earl00.51234567891011Distancefro(a)Latestage00.511.522.5312345678910111Ql,m3/dayDistancefromFig.10.Wellproductionratealongthewellborstage131415161718192021222324mtheheel,m2131415161718192021222324theheel,mOpenholecompletionICDseforopenholecompletionandICDs.J.Wangetal./JournalofPetroleumScienceandEngineering146(2016)971–982976(a)Openholecompletionwherep2,i,R≠p2,i,L,v2,i,R¼0,andv2,i,L¼0.2.6.ModelingoffrictioncoefficientforpipeflowwithradialinterferenceBecausetheradialflowratethroughthenozzlesisverylarge,theradialinterferencecannotbedisregardedwhencalculatingthesurfaceresistanceofhorizontalwell(SuandGudmundsson,1994;Liuetal.,2013).Fluidflowinahorizontalwellboreisconsideredassumingsingle-phaseflowofanincompressibleNewtonianfluidunderisothermalconditions.Thefrictionresistanceofwellboreis(Liuetal.,2013)τρρ=¯=(+)()+fvfvv28,30w2ii12whereflocalfrictionfactor.Kinney(1968)numericallyfoundthattheratioofthelocalfrictionfactor,f,totheno-wall-flowfrictionfactor,f0,isdependentonthewallReynoldsnumberforlaminarflow.Ouyangetal.(1998)proposedacorrelationbasedonKin-ney’sdata,=(+)≤∼()fNNN1610.0430420003000,31ReRe,w0.6142Re3.Solvingmethod(b)ICDsFig.12.ComparisonofpressureprofilebetweenopenholecompletionandICDs(Unit:Pa).3.1.EquationscouplingInnertube,screen-innerannulus,andformation-screenannu-lusarelabeledasj¼1,2,and3,respectively.Theflowcross-sec-tionalareasareAj,inandAj,out;flowratesarevj,inandvj,out;thediameterorequivalentdiameterofthechannelsareDej,andcross-sectionalareasareAj.3.1.1.Equationscouplingintheformation-screenannulusSubstitutingEqs.(19)and(22)intoEq.(13),thegeneralformulaforsolvingflowrateinformation-screenannulusis()()→=→+¯−−−()++++++vvJppAJppA.37l3,i3,i13,i13,i132,i13,i12,i
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