production forecasting methods for horizontal well

SPESocietyofPetroleumEngineepsSPE17580ProductionForecastingMethodsforHorizontalWellsbyS.D.Joshi,PhillipsPetroleumCo.SPEMemberCopyright1988SocietyofPetroleumEngineersThispaperwaspreparedforpresentationattheSPEInternationalMeetingonPetroleumEngineering,heldinTianjin,China,November1-4,1988.ThispaperwasselectedforpresentationbyanSPEProgramCommitteefollowingreviewofinformati0ncontainedinanabstractsubmittedbytheauthor(s).Contentsofthepaper,aspresented,havenotbeenreviewedbytheSocietyofPetroleumEngineersandaresubjecttocorrectionbytheauthor(s).Thematerial,aspresented,doesnotnecessarilyreflectanypositionoftheSocietyofPetroleumEngineers,itsofficers,ormembers.PaperspresentedatSPEmeetingsaresubjecttopublicationreviewbyEditorialCommitteesoftheSocietyofPetroleumEngineers.Permissiontocopyisrestrictedtoanabstractofnotmorethan300words.Illustrationsmaynotbecopied.Theabstractshouldcontainconspicuousaoknowledgmentofwhereandbywhomthepaperispresented.WritePublicationsManager,SPE,P.O.Box833836,Richardson,TX75083-3836.Telex,730989SPEDAL.ABSTRACTThispapersummarizesproductionforecastingmethodsforhorizontalwells.Theforecastingmethodsarebasedonanalyticalsolutionsandcorrelationsofnumericalmodelresults.Methodsaresuggestedforsinglephaseflow,solutiongasdrive,naturallyfractured,andbottomwaterdrivereservoirs.Theseforecastingmethodscouldbeusedforaninitialevaluationofhorizontalwelldrillingprospects.Ahorizontalwellcanbelookeduponasacontrolledinfinite-conductivityverticalfractureoflimitedheight.Therefore,thispapercompareshorizontalwellproductivitywithfiniteandinfinite-conductivity,anduniform-fluxfractures.Achoicebetweenhorizontalwellsandstimulatedverticalwellsshouldbedeterminedbyconsideringlocalfracturingexperienceandlocalcostsforstimulation·treatmentsandhorizontaldrilling.INTRODUCfIONDuringthelasteightyears,technologytodrillhorizontalwellshasadvancedsignifi~antly.Presently,variouscommercialtechniquesareavailabletodrillhorizontalwells.TableIliststhesetechniques,whichareclassifiedonthebasisoftheirturningradius.Turningradiusisdefinedastheradiusofcurvatureofawellthatisrequiredtoturnthewellfromaverticaltoahorizontaldirection.Referencesandillustrationsatendofpaper.Horizontalwellsareusuallynewwellsandare300m(1000ft)to1000m(3000ft)inlength.Drainholesareusuallydrilledthroughexistingverticalwellsandaretypically50m·to200m(150to700ft)inlength.1-3Inthispaperthetermhorizontalwellappliestobothtypesofcompletionsunlessnotedotherwise.Fromthereservoirstandpoint,ahorizontalwellrepresentsacontrolledverticalfracture.Thefractureheightisequaltothewellborediameter.Moreover,horizontalwellsofferaninfiniteconductivityflowpath,Le.,thepressuredropwithinthewellborefromoneendtotheotherisminimal.4-6Incontrast,inaconventionalfracturejob,itisdifficulttoobtaininfinite-conductivity.Additionally,theconductivitymaydropovertime,resultinginlossofwellproductivity.Inthefuture,horizontalwellsandfracturingtechniqueswillcompetewitheachother.Therefore,thispaperincludescomparisonsofproductivitiesforverticalstimulatedwellswithhorizontalwells.Thecomparisonsarerestrictedtothinreservoirs,Le.,reservoirthicknessesupto50m.Figure1showsaschematicdiagramofahorizontalwell,drainhole,fullypenetratingfracture,andaninducedfracture.Horizontalwellshaveadistinctadvantageoververticalwellsinreservoirswithgasandwaterconingproblems,wherefracturingcouldposepotentialdifficulties.Instimulationtreatments,controloffracturedirectionandheightisdifficult.Afracturetreatmentmaycreateadirectcommunicationwiththetopgasorbottomwater3032PRODUCTIONFORECASTINGMETHODSFORHORIZONTALWELLSSPE17580(4)rwe=rwexp(-8),Foraverticalwell,an'increaseinoilproductionrateduetowellstimulationisrepresentedbyanegativeskinfactororbyawellborediameterlargerthanthatofaconventional,unstimulatedwell.TherelationshipbetweenskinfactorandeffectivewellborediameterisdefinedasHORIZONTALWELLPRODUCTIVITYForsteadystate,singlephaseflow,severalauthorshavereportedequationstocalculatehorizontalwellproductivity.4,7-13Thefollowingequationscanbeusedtoestimatesteadystateoilproductionfromahorizontalwel1.4resultinginlossof.·:oilrecovery.Incontrast,discussionisrestrictedtosinglephaseflowunlessrecentadvaq..ces,in'drillingtechnologyofferanotedotherwise.fairlygoodvertical(depth)controlonhorizontalwe~lplacementwithinareservoir.Thus,inEFF~CTIVEWELLBORERADIUSANDSKINreservoirswithtopgasandbottomwateraFACfORhorizontalwellcanbedrilledattheappropriatelocationtominimizeconingproblems.orforL~hItisimportant,tonotethattheaboverelationshipisvalidforeithers.teadystate,pseudo-radialflowinan,infinitereservoirorforpseudo-steadystateflowinaboundedreservoir.Forsteadystateconditions,.wecancalculateanequivalentve-rticalwellborediameterofahorizontalwellbyassuming:1)equaldrainagevolume,re,h=re,yand2)equalproductivityindex(q/Ap)h=(q/L\p)v·(5)reh(L/2)rwe=.'ta[1+.J1-(L/2a)2][h/2rw]~2h/LWiththeseassumptions,itcanbeShownthat4(1)(2)where~.=.Jkh/kv,khishorizontalpermeabilityinmd,kyisaverticalpermeabilityinmd,hisreservoirthicknessinm,Jlisviscosityincp,t.\pispressuredropinkPa,BoisinRm3/STm3,and~isflowrateinm