• / 10
  • 下载费用:5 下载币  

1-s2.0-S092041051631422X-main

关 键 词:
s2 S092041051631422X main
资源描述:
ContentslistsavailableatScienceDirectJournalofPetroleumScienceandEngineeringjournalhomepage:www.elsevier.com/locate/petrolFracturedhorizontalwellproductivitypredictionintightoilreservoirsJinghongHua,⁎,ChongZhangb,ZhenhuaRuic,⁎,YanlongYud,ZhangxinChendaBeijingKeyLaboratoryofUnconventionalNaturalGasGeologyEvaluationandDevelopmentEngineering,ChinaUniversityofGeosciences,Beijing,ChinabThe7thProductionPlantinDaqingOilField,Daqing,ChinacUniversityofAlaska,Fairbanks,AK,USAdDepartmentofChemicalandPetroleumEngineering,UniversityofCalgary,Calgary,CanadaARTICLEINFOKeywords:HorizontalwellProductivitycalculationNumericalmodelPowerlawmodelInfluencesanalysisABSTRACTHorizontalwellsproductivitypredictionanditsinfluencefactorsanalysishaveimportantmeaningsindevelopmentoftightoilreservoirs.Thepurposeofareservoirengineeringstudyistomaintainastableproductionrate.Althoughascientificdevelopmentplancanbenefityieldstability,itneedstomatchwithadjustmentsofawellproductionsystem.Especiallyforextralowpermeabilityandtightoilreservoirs,anunsteadywellproductionsystemmayincreasedifficultiesofwellproductivityprediction.TakingatightoilreservoirinDaqingoilfieldastheresearchsubject,onthebasisofanunsteadypercolationmechanicstheoryandthesuperpositionprinciple,anumericalmodelisbuilttocalculateandanalyzethefracturedhorizontalwellproductivity.Inordertostudyhorizontalwellproductivitybetter,apowerlawexponentialdeclinemodelisalsousedtocalculateandpredictwellproductivity.Comparingwiththenumericalmodelandthepowerlawmodel,theresultsshowthatthenumericalmodelcanbeusedtoanalyzeproductivityinfluencefactors,andbothmodelshaveagoodmatchwithactualproductiondataforwellswiththestableproductionsystemwells.Consideringawell'sunsteadyproductionsystemandamodel'spracticability,thepowerlawmodelcanalsobeusedtocalculateandpredicthorizontalwellsproductivityinthisresearchoilfield.Theresultsofthisstudyprovideareferenceforhorizontalwellproductivitycalculationsandpredictioninsimilarreservoirs.1.IntroductionAtightoilreservoirisdefinedasareservoirwhoseporeairpermeabilityisbelow2×10−3μm2(Yaoetal.,2013a,2013b;Kuangetal.,2012).Intightoilreservoirs,singlewellproductivityisalwaysverylow.Horizontalwelldrillingandhydraulicfracturingtechnologiesarewidelyusedtoimprovewellproductivity.Thenhorizontalwellproductivitycalculationsandpredictionbecomeaverytopicissueforreservoirengineers.PenmatchaandAziz(1998)presentedacomprehensive,transient,semi-analyticalmodelforpredictingtheperformanceofhorizontalwells.Byusingtheprinciplesofsuperpositioninspaceandtimeandbyusingmassbalanceequationsinareservoirandwellbore,theysolvedthismodelinanimplicitmanner.EgbertsandFokker(2001)presentedananalyticalmethodtocalculatetheproductivityindexofaverticalorhorizontalwelltakingintoaccountdifferenthorizontalandverticalpermeabilityandmultiplelayers.WanandAziz(2002)describedanewsemi-analyticalsolutionforhorizontalwellswithmultiplehydraulicfractures.Thefracturescouldberotatedatanyangletoawell,andtheydidnotneedtofullypenetrateaformationintheverticaldirection.Al-KobaisiandOzkan(2004)presentedahybridnumerical-analyticalmodelforthepressure-transientresponseofafinite-conductivityverticalfractureinterceptedbyahorizontalwell.Thismodeldynami-callycoupledanumericalfracturemodelwithananalyticalreservoirmodel.Thisapproachallowedustoincludedetailsofthefracturecharacteristicswhilekeepingthecomputationalworkmanageable.Valkó,Amini(2007)proposedaDVS(DistributedVolumetricSources)methodtopredictproductivityfromahorizontalwellwithmultipletransversefracturesinaclosedouterboundary.Brownetal.(2009)andStalgorovaandMattar(2012)usedaclassicaltri-linearflowmodeltosimulatefluidflowandproductionbehaviorsofmulti-frachorizontalwellsinatightreservoir.BasedonFick'slawinthematrixandDarcy'sflowincleatsandhydraulicfractures,Wangetal.(2013)presentedasemi-analyticalmodelconsideringtheeffectsofboundaryconditionstoinvestigatepressure-transientbehaviorforasymmetri-callyfracturedwellsincoalreservoirs.Luoetal.(2014)studiedthepressurebehaviorofahorizontalwellinterceptedbymultiplenon-planarfractures.Bymeansofconformaltransformationandanequivalentflowresistancemethod,Dengetal.(2014)obtainedtheproductivityformulaforverticalandhorizontalfracturedwellscon-http://dx.doi.org/10.1016/j.petrol.2016.12.037Received10August2016;Receivedinrevisedform26October2016;Accepted27December2016⁎Correspondingauthors.E-mailaddresses:hjhwhat@163.com(J.Hu),zrui@alaska.edu(Z.Rui).JournalofPetroleumScienceandEngineering151(2017)159–168Availableonline30December20160920-4105/©2016ElsevierB.V.Allrightsreserved.MARKsideringdiffusion,slip,desorptionandabsorptionwasobtained,whichcouldpredictaproductionrateoffracturedwells,andprovidesatheoreticalbasisforproductionoptimization.Wangetal.(2015)builtasemi-analyticalmodelbasedonfractaltri-linearflowformulti-stagehydraulicallyfracturedhorizontalwellsintightoilreservoirs.ToaccountfortheheterogeneityofaStimulatedReservoirVolume(SRV),theyusedporosityandpermeabilityfunctionsthatreflectedthefractalnatureofafracturenetworkintheSRV.Liuetal.(2016)investigatedtheimpactofthisflowconsistencyonaproductionratethroughthedevelopmentofanumericalsimulationmodelanditsapplicationtoashalegasreservoir.Mostofthesepapersfocusedondimensionlessvariablesandanalyticalmodel.AlvaroandFaruk(1999)indicatedthatafluidcanflowthroughaporousmediumonlyifthefluidforceissufficienttoovercomeathresholdpressuregradientand,therefore,Darcy'slawshouldbecorrectedforthiseffect.Lietal.(2008)studiednonlinearseepageflowinultra-lowpermeabilityreservoirs.Theresultsshowedthattheproductivitydecreasingrateinlowpermeabilityreservoirwasfasterthanthatinmiddleorhighpermeabilityreservoir.Meanwhile,non-linearfactorshadasignificanteffectontheoil-watertwo-phaseseepagewhentheseepageratewaslower.Zengetal.(2012)designedexperimentalequipmenttoinvestigatesingle-phaseoil/waterflowinultra-lowpermeabilitycoresbyusingacapillaryflowmetertoachieveaccuratemeasurementsofafluidvolume.Theresultsconfirmedthatthesingle-phaseoil/waterflowinultra-lowpermeabilitycoreswasnotconsistentwiththatfromDarcy'slaw.Yaoetal.(2013a,2013b)presentedanumericalmethodforthesolutionofamovingboundaryproblemofone-dimensionalflowinsemi-infinitelongporousmediawithathresholdpressuregradient(TPG)inthecaseofaconstantflowrateattheinnerboundary.Guoetal.(2015)studiednon-Darcy'sflowinwater-bearingcoresfromatightsandstonereservoir,anddevelopedandvalidatedanumericalsimulatorformulti-stagefracturedhorizontalwellsbasedonalowvelocityofanon-Darcy'sflowmodel.Onthebasisofgraphicallyextrapolatingproductionsemi-logplots(logqvst)toabandonment,Arps'sdeclinecurveanalysiswasestablished(1945).Therearethreetypesofdeclinemodelsusingtheconceptofaloss-ratioanditsderivative:Exponential,Hyperbolic,andHarmonic.Forunconventionaloil-gasreservoirexplorationanddevel-opment,especiallyfortightandshalegasreservoirdevelopment,severaldeclineanalysismodelsweredeveloped,andthedifferencesbetweentheempiricaldeclinecurvemodelshadbeencomparedandanalyzed(Ilk,2008;Kabiretal.,2011;KanfarandWattenbarger,2012;Nobakhtetal.,2012;Clarksonetal.,2015;Zhangetal.,2015).However,thesepapersfocusedonshalegasreservoirs,andperformedlimitedresearchontightoilreservoir.Inthispaper,tostudythecharacteristicsoftightoilflowandproductionbehaviorinDaqingoilfield,anumericalmodelandanempiricaldeclinemodelaredeveloped.Thispaperwasorganizedasfollows:Firstly,thenumericalmodelisestablishedtocalculateandanalyzefracturedhorizontalwellproductivityonthebasisofanunsteadypercolationmechanicstheoryandthesuperpositionprinci-ple.Then,powerlawdeclinemodelispresentedforthesamepurpose.Finally,takingatightoilreservoirinDaqingoilfieldasanexample,thesetwomodelsareusedtocalculatehorizontalwellproductivity,andsomeconclusionsaredrawn.2.ProductivitycalculationmodelforafracturedhorizontalwellAccordingtothecharacteristicsoffluidflowinatightoilreservoir,thefluidflowinafracturedhorizontalwellcanbedividedintothreeregions.Thefirstregionisanon-Darcy'sflowregion,whichisfarawayfromhydraulicfracturesandconsiderstheeffectofathresholdpressuregradientonfluidflow.Thesecondregionisanellipticflowregion,whichiscontrolledbyhydraulicfracturesandthematrixaroundthesehydraulicfractures.Thelastregionisalinearflowregionfromwhichthefluidflowsintoawellbottomalonghorizontalwellbore.Someassumptionsaremadetobuildahorizontalwellproductivitymodel.(1)Thereservoirrockandfluidarecompressible.(2)Thehydraulicfractureheightisequaltothereservoirthickness.(3)Asingle-phasenon-Darcy'sunsteadyflowinthereservoirisconsidered.(4)Thefluidflowingalongthefracturesurfacescanenterthewellborebutitdoesnotdirectlyenterthewellbore,whichmeansthatthefluidflowsfromthematrixtothehydraulicfracturesfirst,andthenintowellbore(Fig.1).Multi-stagehydraulicallyfracturingisalwaysusedintightoilreservoirstoimprovesinglewellproductivity.Duetotheinfluenceofdifferentstressdistributionsalongthehorizontalwellbore,thelimita-tionofthefracturingtechnologyandtheirconnectionwithnaturalcracks,hydraulicfracturesmayhavedifferentlength,azimuth,andconductivitycapacity.Thesewillbringmoredifficultiesinbuildingahorizontalwellproductivitymodel.DifferentrelationshipsbetweenfracturesandhorizontalwellborecanbeseeninFig.2.Apressuredeclinemodelinaninfinitehomogeneousformationisusedinthefundamentaltheorywhentimeisveryshort,andproduc-tioncanbeassumedtobeconstant.Apressuredeclineequationcanbeexpressedasfollows:⎡⎣⎢⎛⎝⎜⎞⎠⎟⎤⎦⎥ppxytqμπkhEirηt−(,,)=4−−4i2(1)whereη=k/(ϕμCt),piistheinitialreservoirpressure,Pa;p(x,y,t)isthereservoirpressureatpoint(x,y)inthereservoir,Pa;qisundergroundproduction,m3/s;μisthefluidviscosity,Pas;kisthereservoirpermeability,m2;histhereservoirthickness,m;ristheradialdistance,m;ϕisthereservoirporosity;tisproductiontime,s;Ctisacompressioncoefficient,1/Pa;ηisapressuretransmittingcoefficient,m2/s.Avolumecoefficientandathresholdpressuregradientshouldbeconsidered,andusingarectangularplanecoordinatesystem,Eq.(1)ischangedto:⎡⎣⎢⎛⎝⎜⎞⎠⎟⎤⎦⎥ppxytGrqBμπkhEixxyyηt−(,,)−⋅=4−−(−)+(−)4ic0202(2)whereBisavolumecoefficient;Gisathresholdpressuregradient,Pa/m;qcissurfaceproduction,m3/s;(x0,y0)arethecoordinatesofthepointsink.InaCartesiancoordinatesystem,theanglebetweenthehorizontalwellbore(they-axis)andhydraulicfractureisdefinedasα.ThetwoFig.1.Adiagramofreservoir-fracture-horizontalwellborefluidflow.J.Huetal.JournalofPetroleumScienceandEngineering151(2017)159–168160wingsofthehydraulicfractureare,respectively,dividedintonsegments(Fig.3).ThelengthoftheleftwingisLfliandthatoftherightwingisLfri.Thecoordinatepositionofpointj(1≦j≦n)ontheleftwingcanbeexpressedby:⎛⎝⎜⎛⎝⎜⎞⎠⎟⎛⎝⎜⎞⎠⎟xynjnLαiynjnLαi(,)=−122−2+1sin(),+122−2+1cos())lijlijflififli(3)SubstitutingEq.(3)intoEq.(2),accordingtothesuper-positionprinciple,thetotalpressuredropatanypoint(x,y)inthereservoirfromthen-pointsinkontheleftfracturecanbeexpressedasfollows:⎡⎣⎢⎢⎛⎝⎜⎜⎞⎠⎟⎟⎤⎦⎥⎥ppxytGrEi(−(,,)−⋅)=∑−−iljnqflijμBπkhxnjnLfliαiyyfinjnLfliαiηt=14(+12(2−2+1)sin()2+(−(+12(2−2+1)cos()))24(4)Accordingtothedescriptionoftheaboveequation,therectangularcoordinatesofpointjontherightfracturecanbedescribedby:⎛⎝⎜⎛⎝⎜⎞⎠⎟⎛⎝⎜⎞⎠⎟xyjnLαiyjnLαi(,)=122−1sin(),−122−1cos())rijrijfrififli(5)SubstitutingEq.(5)intoEq.(2),accordingtothesuper-positionprinciple,thetotalpressuredropatanypoint(x,y)inthereservoirfromthen-pointsinkontherightfracturecanbeexpressedasfollows:⎡⎣⎢⎢⎛⎝⎜⎜⎞⎠⎟⎟⎤⎦⎥⎥ppxytGrEi(−(,,)−⋅)=∑−−irjnqμBπkhxLαiyyLαiηt=14(−()sin())+(−(−()cos()))4frijjnfrifijnfri122−12122−12(6)2.1.ProductivitymodelestablishmentandcalculationsAttheithfracturetherearetheflowingradiusRi,formationthicknesswfi,boundarypressure(thesameasthefracturetippressure)p(xfi,yfi,t),andflowingbottomholepressure(thesameaspressureinthehorizontalborehole)pwfi.Theflowpatternnearafracturecanbedeemedasaradialflow.Therefore,thecoursefromafracturetoawellborecanbedescribedasfollows:⎛⎝⎜⎜⎜⎞⎠⎟⎟⎟pxytpqμBπkwrs(,,)−=2ln+fifiwfififiixxhπw(+)flifri(7)whererwistheradiusofwellbore,m;sistheskinfactor.Inreality,hydraulicfracturesarenotalwayssymmetricalalongahorizontalwellbore;therefore,theaveragepressureatthetipofafracturecanbeseenasthetippressure,whichcanbecalculatedbycombiningEqs.(4)and(6).SpecificequationsaregiveninAppendixA.Assumingthatproductionfromfracturekisqfkandthelengthsoftheleftandrightwingsare,respectively,LflkandLfrk,theproductionfromtheleftandrightwingsoffracturekcanbeexpressed,respectively,asfollows:qLLLq=+flkflkflkfrkfk(8)qLLLq=+frkfrkflkfrkfk(9)Productionfrompointsinkjattheleftandrightwingsoffracturespotkcanbeexpressedasfollows:qnLLLq=1+flkjflkflkfrkfk(10)qnLLLq=1+frkjfrkflkfrkfk(11)Exceptforthejuncturepointbetweenthefractureandhorizontalwellbore,thehorizontalwellboreisclosed.Thenthehorizontalwellproductioncanbedescribedasfollows:∑qq=iNfi=1(12)Fig.2.Afluidflowmodelofafracturedhorizontalwell.(1)Fracturesperpendiculartohorizontalwellbore(2)Fracturesandhorizontalwellborehaveacertainangle.Fig.3.Pointsinkonahorizontalwelllength.J.Huetal.JournalofPetroleumScienceandEngineering151(2017)159–168161Areasonableintervaltimeisselected:Aprevioustimeisti,thecurrenttimeisti+1,andthecumulativeproductionqcanbedescribedasfollows:qqtqttt=()+()2(−)iiii+1+1(13)AppendixAwillgivethedetailedsolutionprocedure.Intheaboveequations,kfiisthepermeabilityoffracturespoti,m2;kfiisthewidthoffracturespoti,m;Lflistheleftwinglengthoffracture,m;Lfristherightwinglengthofafracture,m;qfiistheproductionoffracturespoti,m3/s;qflkistheproductionoftheleftwingoffracturespotk,m3/s;qfrkistheproductionoftherightwingoffracturespotk,m3/s;qflkjistheproductionfrompointsinkjattheleftwingoffracturespotk,m3/s;qfrkjistheproductionfrompointsinkjattherightwingoffracturespotk,m3/s.2.2.HorizontalwellborefrictionHydraulicfrictioncanbecalculatedusingEq.(14):ΔpλρυDΔL=2fiih2(14)⎪⎪⎧⎨⎩λRRR=64/,2100eeRe0.3164e4RρυDμ=eihυqπD=15iih2whereΔpfiisthehorizontalwellborefriction,Pa;λisapipelinefrictioncoefficient;ΔListhelengthofthehorizontalwellboresegment,m;υiisthefluidvelocity,m/s;Dhisthepipediameter,m;ReistheReynoldsnumber,dimensionless;qiistheflowrateoffracturei,m3/min.Thecriticalvalueof2100canbeusedforthepipelinefrictioncoefficient(Joshi,1991).PuttingλintoEq.(14),thehorizontalwellborefrictioncanbecalculated.3.PowerlawexponentialdeclinemodelThepredictionofsinglewellproductioninanunconventionalreservoirisahottopic.Anunsteadyflowcharacteralwaysoccursduetolowreservoirpermeabilityandporosity.Inthisresearchfield,adjustingofaproductionsystemisoftenusedtomaintainthesinglewelloutput,whichincreasesthedifficultiesforwellproductivityprediction.Itisdifficulttomatchactualproductiondatausingaconventionaldeclinemethod(Arps),andproductivitypredictionmaybecomeunrealistic.Thus,powerlawmethodisappliedtomatchandpredictwellproductioninthisfieldstudied.TheconceptsofadeclinerateanditsderivativewereproposedbyArps(1945):Dqdqdt1=−/(15)Therelationshipbetweenproductiondataandtimeshowsthatthewellproductionrapidlydecreasesinthefirststage,andkeepsaslowerdeclinevelocityinthelaterstage.Therefore,anewdeclinerateisdefinedasfollows(Ilketal.,2008):DDDt=+n∞1−(1−)(16)SubstitutingEq.(16)intoEq.(15)andmakingcertainthearrangementsgive:⎛⎝⎜⎞⎠⎟qqDtDntqDtDt=ˆexp−−=ˆexp(−−ˆ)iniin∞1∞(17)whereD∞isdeclineconstantdefinedinEq.(16),asgoestot=∞;D1isdeclineconstantdefinedinEq.(16)att=1day,D⌢iisadeclineconstantdefinedinEq.(17)equaltoD1/n,tistheproductiontime,d;nisthetimeexponent;q⌢iistheinitialproductionratede
展开阅读全文
  石油文库所有资源均是用户自行上传分享,仅供网友学习交流,未经上传用户书面授权,请勿作他用。
0条评论

还可以输入200字符

暂无评论,赶快抢占沙发吧。

关于本文
本文标题:1-s2.0-S092041051631422X-main
链接地址:http://www.oilwenku.com/p-70398.html

当前资源信息

吾王的呆毛

编号: 20180607204444704142

类型: 共享资源

格式: PDF

大小: 1.36MB

上传时间: 2018-06-08

广告招租-6
关于我们 - 网站声明 - 网站地图 - 资源地图 - 友情链接 - 网站客服客服 - 联系我们
copyright@ 2016-2020 石油文库网站版权所有
经营许可证编号:川B2-20120048,ICP备案号:蜀ICP备11026253号-10号
收起
展开