ICHF2013001

Chapter19InitiationandBreakdownofanAxisymmetricHydraulicFractureTransversetoaHorizontalWellboreSafdarAbbasandBriceLecampionAdditionalinformationisavailableattheendofthechapter‐bilityisalsotakenintoaccount.Theformulationaccountsforthestrongcouplingbetweentheelasticityequation,theflowoftheinjectedfluidwithinthenewlycreatedcrackandthefracturepropagationcondition.Dimensionalanalysisoftheproblemrevealsthatthreedi‐mensionlessparameterscontroltheentireproblem:theratiooftheinitialdefectlengthoverthewellboreradius,theratiobetweenthewellboreradiusandalength-scaleassociatedwiththefluidstoredbycompressibilityintheinjectionsystemduringthewellpressurization,andfinallytheratioofthetime-scaleoftransitionfromviscositytotoughnessdominatedpropagationtothetime-scaleassociatedwithcompressibilityeffects.Afullycouplednu‐mericalsolverispresented,andvalidatedagainstsolutionsforaradialhydraulicfracturepropagatinginaninfinitemedium.Theinfluenceofthedifferentparametersonthetransi‐tionfromthenear-wellboretothecaseofahydraulicfracturepropagatinginaninfiniteme‐diumisfullydiscussed.1.IntroductionInthisstudy,weareinterestedintheinitiationofhydraulicfracturesfromanopen-holehorizontalwell.Horizontalwellsaredrilledpreferablyinthedirectionoftheminimum©2013AbbasandLecampion;licenseeInTech.ThisisanopenaccessarticledistributedunderthetermsoftheCreativeCommonsAttributionLicense(),whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.ProceedingsoftheInternationalConferenceforEffectiveandSustainableHydraulicFracturing.AnISRMspecializedConference,Bunger,McLennan,andJeffrey(editors).Brisbane,Australia,May2013.horizontalstressinordertocreatehydraulicfracturesperpendiculartothewellboreandthereforemaximizethedrainagefromthereservoir.Duringthepressurizationofthewellbore,tangentialtensilestressisgeneratedwhichcanresultintheinitiationoflongitudinalfracturesparalleltothewellboreaxis[1,2].Inanisotropicelasticmedium,dependinguponthestressfield,theinitiationoffracturestransversetothewellboreaxisisfavoredbycreatinganinitialflaw,i.e.anaxisymmetricnotch,ofsufficientdepth[3](seeFigure.1forasketch).Wefocussolelyontransversehydraulicfracturesinthiscontribution.Intheinitialstageofpropagation,thesetransversefracturescanbeidealizedasaxisymmetric(radial)fracturesaroundthewellboreuntiltheyhitastressbarrierorothertypeofheteroge‐neities.WeinvestigatetheinitiationandpropagationofsuchafractureunderconstantinjectionofaNewtonianfluid,focusingonthecaseof“tight”rockswhereleak-offistypicallynegligible.Inparticular,weareinterestedinclarifyingwhentheeffectsassociatedwiththenear-wellboreregiondissipateandnolongeraffectthehydraulicfracturepropagationandhowthistransitiontakesplace.Theinitiationandtheearlystageofthepropagationofsuchahydraulicfractureisaffectedbytwo“nearwellbore”effects:i)thefinitenessofthewellboreandtheinitialflawlengthandii)atransientphenomenonassociatedwiththereleaseofthefluidstoredbycompressibilityinthewellboreduringthepressurizationphasepriortotheinitiationofthefracture.Thissecondeffectisultimatelylinkedtothecompressibilityoftheinjectionsystem(i.e.mostlythefluidvolumestoredbycompressibilitywithinthewellbore).Theseeffectshavebeeninvestigatedforthecaseofplane-strainfracturesin[4,5]andforthecaseofaxisymmetrichydraulicfracturesdrivenbyaninviscidfluid(i.e.zero-viscosity)in[6].Inthispaper,weextendthesecontribu‐tionstothecaseofviscousflowinaxi-symmetricfractures.Adetaileddimensionalanalysisisperformedindicatingvarioustimescales,lengthscalesanddimensionlessnumberscontrollingtheproblem.Anumericalsolver,alongthelinesofpreviouscontributions[7,8],ispresented.Aseriesofnumericalsimulationsareperformedinordertostudythetransitionfromthenear-wellborepropagationregimetothecaseofaradialhydraulicfractureinaninfinitemediumunderconstantinjectionrate.2.ProblemstatementLetusconsiderahorizontalwellofradiusadrilledinthedirectionoftheminimumhorizontalstressσh.Inthisidealconfiguration,weareinterestedintheinitiationandpropagationofahydraulicfracturefromaradialaxisymmetricnotchoflengthlotransversetothewellbore(Figure.1).Aspreviouslymentioned,weassumethattheradialnotchlengthissufficienttofavoratransversefractureascomparedtoalongitudinalone(see[3]fordiscussionontheeffectofthestressfieldonthecompetitionbetweentransverseandlongitudinalfractureinitiation).Intheabsenceofanystressbarriersorotherheterogeneities,thisaxisymmetrictransversefractureofradiusRwilltransitiontowardapenny-shapedgeometrywhenitsradiusismuchgreaterthanthewellboreradius(Figure.1).Wewilldenoteaspfthefluidpressureins