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1、INTERNATIONALJOURNALFORNUMERICALANDANALYTICALMETHODSINGEOMECHANICSInt.J.Numer.Anal.Meth.Geomech.2013;37:993–1015Publishedonline4February2012inWileyOnlineLibrary(wileyonlinelibrary.com).DOI:10.1002/nag.1131Afiniteelementapproachtothesimulationofhydraulicfractureswithlag121,,†MichaelJ.
2、Hunsweck,YongxingShenandAdrianJ.Lew*1DepartmentofMechanicalEngineering,StanfordUniversity,Stanford,CA,USA2LaboratorideCàlculNumèric,UniversitatPolitècnicadeCatalunya(UPCBarcelonaTech),Barcelona,SpainSUMMARYWepresentedafinite-element-basedalgorithmtosimulateplane-strain,straighthydrau
3、licfracturesinanimpermeableelasticmedium.Thealgorithmaccountsforthenonlinearcouplingbetweenthefluidpressureandthecrackopeningandseparatelytrackstheevolutionofthecracktipandthefluidfront.Itthereforeallowstheexistenceofafluidlag.Thefluidfrontisadvancedexplicitlyintime,butanimplicitstrateg
4、yisneededforthecracktiptoguaranteethesatisfactionofGriffith’scriterionateachtimestep.Weenforcedthecouplingbetweenthefluidandtherockbysimultaneouslysolvingforthepressurefieldinthefluidandthecrackopeningateachtimestep.Weprovidedverificationofouralgorithmbyperformingsamplesimula-tionsandcom
5、paringthemwithtwoknownsimilaritysolutions.Copyright©2012JohnWiley&Sons,Ltd.Received7July2011;Revised5October2011;Accepted16November2011KEYWORDS:finiteelement;hydraulicfracture;fluidlag1.INTRODUCTIONHydraulicfracturingisinvolvedinverydiverseapplications,rangingfromtheflowofmagmathrought
6、heearth’scrusttothefailureofdamsduetounderwatercracks[1,2].However,perhapsthemostrelevantandmostinvestigateduseofhydraulicfracturingtodayisinitsapplicationtotheextractionofnaturalgasfromshale[3].Inthiscase,waterathighpressureispumpedseveralmilesthroughtheearth’scrustthroughapredrill
7、edborehole.Whenthewaterreachesthepay-zonelayerwherethenaturalgasistrapped,cracksareformedintherock.Then,beforetheappliedpressureiscompletelyreleased,atreatmentofproppant(sandslurry,etc.)isinsertedintothenewlyformedcrackstopreventthemfromcompletelyclosing.Afterwards,thefreednaturalga
8、scanflowbackupthebor
