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CHeterogeneitypermeabilityfracturtypeofanisotropy,three-plugmethodisusuallyapplied.However,thevariationofpermeabilitywithlocationcausesthismethodtobeunreliableinheterogeneousformations.Similarly,thepresenceof(O’Brienattributnaturareducescomparedclayparticletheclayalignmentmodels.Thediscrepancywasattributedtotheclayalignmentcanbealsosourceofanisotropyinorganic-richintroducedtothecoring;orystudies.suctionofwateroftheshaleficantanisotropyintheillite-richshaleofWilcoxformationwasreportedatlowbehaviorwasattributedtotheclosureofcrack-likevoidsparallelContentslistsavailableatScienceDirectlJournalofPetroleumScienceJournalofPetroleumScienceandEngineering133(2015)496–506http://dx.doi.org/10.1016/j.petrol.2015.05.024shales,itshouldbeconsideredthatorganic-richshalesusuallyaretobeddingwithstress.Boltonetal.(2000)observedpermeabilityanisotropyinfine-grainedsedimentsthatdidnotshowparticlealignmentusingSEManalysis.Thesignificantanisotropywasat-tributedtotheparallelmicro-fracturesbasedonmercury-0920-4105/&2015ElsevierB.V.Allrightsreserved.nCorrespondingauthor.E-mailaddress:mmokhtar@mines.edu(M.Mokhtari).particleclusteringandirregularitiesinparticlepacking.Althougheffectivestresses(Kwonetal.,2004).Permeabilitybecamein-creasinglyisotropicwiththeincreaseintheeffectivestress.Thissignificantvariationinpermeabilityatspecificporositywasat-tributedtothegrainsizevariationsinthemudstones.Thecoarser-grainmudstonesaremorepermeablebutthedifferencedimin-ishedathighereffectivestressesduetothecollapseoflargerpores.ConsolidationtestsonseveralartificialclaysbyClennelletal.(1999)showedthatuniaxialconsolidationaloneproduceslittleanisotropywhichismuchlowerthanthepredictedvaluesbycurrentmaximumhorizontaldirection(LaubachOntheotherhand,fracturescanbeartificiallyshalesamplesasaresultofthestressreleaseduringcoretransferandcoreplugpreparationforlaboratShalescanbefracturedinwaterduetocapillarycausinggasentrapmentandfinallytensilefracturingsample(Schmittetal.,1994;Mitchell,2001).SigniordersofmagnitudedifferenceinthepermeabilityofmudstonesatagivenporositywasreportedbyDewhurstetal.(1999).Thisstructuralactivitiescancreatenaturalfractures(Gudmundsson,2011;Fossen,2010)whicharenotnecessarilyalignedwiththeetal.,2004).1.IntroductionWell-developedlaminationsoriginateanaerobicdepositionalenvironmentminationinshalereservoirsisusuallyofplatyparticlessuchasclays.Theticlestobealignedinparallelorientationthedirectionofparticlealignmenttheperpendiculardirectiontotheartificialmicro-fracturesaffectsthereliabilityofthepermeabilitymeasurementinshales.Usingvarietyofmethodstomeasurepermeability,theeffectsoftheseanisotropicandheterogeneousfeaturesunderstressarediscussed.&2015ElsevierB.V.Allrightsreserved.fromquietanddeepandSlatt,1990).La-edtothealignmentltendencyofclaypar-thetortuosityintothetortuosityinalignment.Tennotdominatedbyclay(Hartetal.,2013),thustheiranisotropicfeaturescanbedifferentfromthesealshaleswithhighclaycon-tent.Micro-fracturesareabundantinorganic-richshales.Micro-fracturescanbecreatedduringhydrocarbongenerationandex-pulsion(BergandGangi,1999;LashandEngelder,2005;LewanandBirdwell,2013;AlDuhailanetal.,2013).Thelenticularshapeofkerogenhasanimpactontheshapeofcreatedmicro-fractureandthislenticulardistributionofkerogencancauseanisotropyinwavevelocity(VernikandMilovac,2011).Moreover,regionalCharacterizationofanisotropyinthepermeabilityshalesMehdiMokhtarin,AzraN.TutuncuPetroleumEngineeringDepartment,ColoradoSchoolofMines,1600ArapahoeSt.Golden,articleinfoArticlehistory:Received11March2015Accepted19May2015Availableonline6July2015Keywords:PermeabilityMicrofractureOrganic-richshaleAnisotropyabstractAccuratedeterminationoftightandheterogeneousnaturenaturalfracturesandthesensitivitymakesthetraditionalsteady-statpulsedecayorcrushed-samplestilltimeconsumingandtheshow.Asanalternativemethod,presenceoflaminationandjournalhomepage:www.eoforganic-richO80401,UnitedStatesisessentialandchallenginginorganic-richshalesduetotheofshaleformations,thepresenceoflaminationaswellasinducedoroffracturepermeabilitytostress.Thetightnatureofshaleformationemethodnottobepractical.Therefore,unsteadystatemethodssuchashavebeenpracticedforshales.However,thepulsedecaymethodcanbecrushed-samplemethodissize-dependentasournumericalsimulationstheresultsofcomplextransientmethodarepresented.Moreover,theescausesdirectionaldependencyofpermeability.Tocharacterizethissevier.com/locate/petrolandEngineeringhydraulicfracturing(Clark,1949).Similarlyinshalereservoirs,closureofmicro-fractureswithoutproppantshasbeenaconcernkqLAP1μ=−Δ()where“k”isthepermeability,“q”istheflowrate,μisthefluidFig.1.ComparingthetimerequiredtosaturateasampleofDarcypermeabilitywiththesampleofnano-Darcypermeability.Fig.2.Configurationofpermeabilitymeasurementinsteadystatemethod.M.Mokhtari,A.N.Tutuncu/JournalofPetroleumScienceandEngineering133(2015)496–506497(Nguyenetal..2013).Ontheotherhand,equalorbetterperfor-mancewithlow-proppantconcentration(waterfracs)comparedtoclassicalfracturingintightformationswasreportedbyMayerhoferetal.(1997).Thisphenomenoncanbeattributedtothefracturesheardisplacement(Freddetal.,2001)inaroughfractureandthecomplexfracturenetworkthatalow-viscosityfluidcancreate.However,oneshouldconsiderthatwaterdamagetomatrixandfracturecanbeanissueinshalereservoirs(Bertoncelloetal.,2014)butthisissueisnotdiscussedheresincetheexperimentsareconductedwithgas.2.TheoryandtheexperimentalprocedureforpermeabilitymeasurementShalereservoirshaveextremelylowpermeabilitywhichmakethepermeabilitymeasurementchallenging.Forinstance,thetimetosaturateashalesampleissignificantlyhigherthanthetimerequiredsaturatingaconventionalcoresampleassimulatedinFig.1.FluidflowincoresamplesissimulatedusingCOMSOLMultiphysicsinwhichthetransientpressurediffusionequationsarenumericallysolvedusingfiniteelementmethod.Thesimula-tionresultsshowthatittakes42htoincreasetheporepressureofa1nD(nano-Darcy)samplefrom5MPato6MPawhilethesampleof1D(Darcy)permeabilitytakes150mstoapplysimilarpressureincrease.Therefore,severalothermethodsbesidestheconventionalsteadystatemethodhavebeendevelopedtoaddresstheultra-lowpermeabilitymeasurementsuchasthepermeabilitymeasurementinshalereservoirs.Inthissection,areviewofthesemethodsandtheirsimulationarepresented.2.1.SteadystatemethodSteadystatemethodistheroutinemethodtomeasureper-meabilityofconventionalcoresamples.Insteadystatemethod,fluidflowsthroughcorecross-sectionalareaasshowninFig.2.Pressurelossalongthecoreismeasuredtocalculatepermeabilityintrusionporosimetrydata.Itiscriticaltodistinguishnaturalfracturesfromtheinducedoneasthepresenceoffracturesandheterogeneitycanhavesignificantimpactonthelaboratoryeva-luationofpermeabilitydata(Kamathetal.,1992;Honarpouretal.,1995;Suarez-Riveraetal.,2012;Sinhaetal.,2012;Cuietal.,2009).Fractographictechniquesareusefultodistinguishbetweennaturalfracturesandthecoringorhandling-inducedfractures(Kulanderetal.,1979).Horizontalnaturalfracturesoftenshowtheindica-tionsofpasttectonicactivity.Thefrictionalmovementoffracturesurfacescausesdirectionaldependencyofsurfaceroughnesscalledslickenside.Moreover,thereisoftensecondaryfibrousornon-fibrousmineralgrowth.Verticalnaturalfracturesareveryuncommoninconventionalcoringsincethereislowpossibilityofdrillingwidely-spacedverticalfracturesinaverticalwellbore.Handlinginducedfracturesusuallyindicateapowderzoneatthepointofimpactontheoutercoresurface.Thesensitivityoffracturedmediuminporousmediaisim-portantasdiscussedbyBestandKatsube(1995),Walsh(1981),Dewhurstetal.(1999),Boltonetal.(2000),Kwonetal.(2004),Gudmundsson(2011),Choetal.(2013),Honarpouretal.(2012),BedayatandTaleghani(2012)andBedayatandDahiTaleghani(2015).Thisstresssensitivityisevenmorecriticalinorganic-richshalessincetheproductionfromsuchtightformationtotallyde-pendsonmassivehydraulicfracturing.Classically,aproppingagentsuchassandhasbeenusedtoavoidfractureclosureinaccordingtoDarcy'slaw.viscosity,“L”isthelengthofthecore,“A”isthecross-sectionalarea,andPΔisthepressurelossalongthecore.InthesimulationexampleinFig.2,theinjectionvelocityis104−m/s,viscosityis0.001PaC2s,thecorelengthis0.0762mandthesimulationprovidesthepressurelossalongthecoretobe7620Pa.Therefore,thepermeabilityiscalculatedtobe1012−m2whichisexactlysimilartotheinputpermeabilityinthesimulation.Sincesteadystatemethodissignificantlytimeconsuminginshales,transientmethodsofpermeabilitymeasurementhavebeendeveloped.However,steadystatemethodisstillrecommendedbysomeauthorsduetothedeficienciesintheothermethodsandtheconsistencyoftheresultsfromthesteadystatemethod(Berton-celloandHonarpour,2013).Duetothesmallporesizeinshalereservoirs,Knudsendiffusion(Darabietal.,2012)andadsorption(Cuietal.,2009)canbeacontributingfactorinfluidflowinshaleswhicharenotconsideredinthispaper.2.2.Crushedsample(GRI)methodprofileofanartificialhighporosityandunconsolidatedcoreisFig.4.Theupstreampressuredeclineinthecrushedsamplemethod.M.Mokhtari,A.N.Tutuncu/JournalofPetroleumScienceandEngineering133(2015)496–506498Toreducetheexperimentaltimeforthemeasurementofper-meabilityintightformations,crushingtherocksampletosmallpieceswasproposed(Luffeletal.,1993).Theconfigurationofthecrushed-samplemethod(orGRImethod)andsimulationoffluidflowinthisexperimentisshowninFig.3.ThecrushedsampleisplacedinthedownstreampressurevesselanditispressurizedtoPdown0.TheupstreampressurevesselispressurizedtoPup0.Aftertheupstreampressureisstabilized,thevalvebetweentheup-streamanddownstreamreservoirsisopened.Gasflowfromtheupstreamreservoirtodownstreamreservoiranddiffusesveryrapidlytothevoidspacesinthedownstreamreservoirfollowedbygradualflowtothecrushedcoresamplesuntilthepressureinbothvesselsreachequilibrium.UsingBoyle'slawandconstantcompressibilityfactor,porosity(∅)canbecalculated(Cuietal.,2009)usingEq.(2)⎡⎣⎤⎦VPPVVPPPPV/2upup0edownbdown0eedown0b()()()()∅=−+−−−()whereVupisthevolumeoftheupstreamreservoir,Vdownisthevolumeofthedownstreamreservoir,Pup0istheinitialupstreampressure,Pdown0istheinitialdownstreamreservoirpressure,Vbisthebulkvolumeofthecrushedsamples,andPeistheequilibriumpressure.InsimulationofFig.4,theequilibriumpressureis81.75Pa,whiletheinitialpressureintheupstreamreservoiris100Paandtheinitialpressureinthedownstreamreservoiris20Pa.Moreoverthereservoirvolumeis0.0015m3andthebulkvolumeis0.001178m3.Consequentlytheporosityiscalculatedtobe0.103comparedtotheinputporosityof0.100inthesimulation.Fig.3.Time-dependentfluidflowinTheupstreampressuredecline(Fig.4)canbeusedtocalculatepermeability(Cuietal.,2009).However,theresultofpermeabilitymeasurementsvariesbydifferentvendorsusingcrushedsamplemethod(Tinnietal.,2012;Sinhaetal.,2012).ThesimulationofcrushedsampletestattwodifferentsamplesizesisshowninFig.5.Thediffusionisfasterinthesmallersamplessincethesurfaceareaishigher;however,theequilibriumpressureissimilar(Fig.6).Therefore,permeabilitycalculationusingcrushedsamplemethodissample-sizedependentbutporositymeasurementisnotafunctionofsamplesize.2.3.Pore-scalemodelingmethodWiththeadvancesinimagingtechniques,itispossibletocapturehighresolutionimagesofsmallporesinshalesusingfo-cusedionbeam(FIB)SEMasreportedformanyorganic-richshalesbyCampetal.(2013).AFIBSEMimageofanEagleFordshalesampleisshowninFig.7.Thesamplewasionmilledtoobtainthenextimage;subsequentlythestackoftheseimagescanbeusedtocreateathree-dimensionalporenetworkbyimageanalysis.However,theseimagesareinverysmallscale,sothereisun-certaintyintheupscalingofpermeabilityresultsfromFIBSEMimages.Whentheporenetworkgeometryisconstructed,itispossibletodofluidflowsimulationusingcomputationalfluiddynamics(CFD)techniquesasdiscussedbyDewersetal.(2012).Thevelocitythecrushedsamplemethod.M.Mokhtari,A.N.Tutuncu/JournalofPetroleumScienceandEngineering133(2015)496–506499Fig.5.EffectofcrushedsampleshowninFig.8.Pressurelossalongthecorecanbeobtainedfromthissimulation(Fig.9)andpermeabilitycanbecalculatedaccordingly.2.4.PulsedecaymethodInpulsedecaymethod,anapparatusisconsistedofanup-streamandadownstreamreservoirandacoreholderinthemiddle(Fig.10).InitiallyallthreecomponentsarefilledwithgastoFig.6.Acomparisonofthepressuredeclineasafunctionofcrushedsamplesize.Fig.7.FIBSEMimageofashalesample(right)sizeonpressurediffusion.reachanequilibriumstateof5.0MPaandapressurepulseof0.5MPaisappliedtotheupstreamreservoir.Insteadofaconstantvolumeupstreampressurepulse,itispossibletokeeptheup-streampressureconstant(MetwallyandSondergeld,2011;Helleretal.,2014).Thevalvebetweenupstreamreservoirandcoreisopenedandgasflowsfromtheupstreamreservoirtothecoresampleandfollowedbyflowtothedownstreamreservoir.Pres-suretransducersareinstalledontheupstreamanddownstreamreservoirs.Upstreampressuredecreasesanddownstreamin-creaseswithtime(Fig.11).ThepressurediffusionisbasedonEq.andthecreatedporenetwork(left).Fig.8.Velocityprofileinporescalemodeling(thegeometryiscourtesyofCOMSOLMultiphysics).Thewhitecolorisgraincomponentsoftherocksample.M.Mokhtari,A.N.Tutuncu/JournalofPetroleumScienceandEngineering133(2015)496–506500(3)(Braceetal.,1968)⎜⎟⎛⎝⎞⎠⎡⎣⎢⎛⎝⎜⎞⎠⎟⎤⎦⎥PxkPt1322effssμββββββ∂∂=−+∅−∂∂()whereμistheviscosity,∅istheporosity,βisthefluidcom-pressibility,effβiseffectiverockcompressibility,tisthetime,PisFig.9.Pressurelossinporescalemodeling.Fig.10.Theconfigurationofpulsedecaymethodandthepressureresponsewithtime.Fig.11.Thesimulationofupstreamanddownstreampressureresponsesinthepulsedecaymethod.thepressure,xisthedistanceandkisthepermeability.Braceetal.(1968)assumedthetermsinthebracketstobenegligibleandsolvedEq.(4)toreachEq.(5)topredictthedeclineoftheupstreampressure.SemilogarithmicplotofEq.(5)shouldbelinear(Fig.12)withslopeofɑtocalculatepermeabilitybyEq.(6).Px0422∂∂=()⎡⎣⎢⎢⎛⎝⎜⎜⎞⎠⎟⎟⎤⎦⎥⎥PPpVVVe5tupeqdownupdown()−=Δ+()α−⎛⎝⎜⎜⎞⎠⎟⎟kLVVVV6downupdownupαμβ=+()wherePupistheupstreampressureasafunctionoftime,Peqistheequilibriumpressure,pΔisthepressurepulseatthebeginningoftheexperiment,Vdownisthedownstreamreservoirvolume,Vupistheupstreamreservoirvolume,andListhesamplelength.Per-meabilitywascalculatedtobe1.831019×−m2whichis8.35%lowerthantheinputpermeabilityinthesimulation.Thedis-crepancybetweenthenumericalsimulationandtheanalyticalsolutionisduetoboththenumericalerroraswellastheanalyticalerrorinthederivationofEq.(6)(Hsiehetal.,1981).Fig.12.Semilogarithmicplotrequiredtoobtainpermeabilitybythepulsedecaymethod.2.5.ComplextransientmethodInthecomplextransientmethodorpressureoscillationmethod(Fischer,1992;Boitnott,1997;Bernabeetal.,2006;SongandRenner,2007),upstreampressureisoscillatedinsinusoidalorstepwisemannerandtheresponseindownstreampressureisusedtocalculatepermeability.InthesimulationinFig.13,theupstreampressure,coreporepressureandthedownstreampressureareallheldconstantinitiallyat5MPa.Theupstreampressureisthendecreasedto4.5MPaandisheldconstantforaconstantperiodoftime.Then,theupstreampressureisincreasedto5.5MPaanditisheldconstant.Finallytheupstreampressureisbacktoitsoriginalvalueof5MPaanditisheldconstantforthespecificperiodoftime.Thedownstreampressureresponseisre-corded(Fig.14)tohistorymatchforcalculatingpermeability.Thismethodisquickandthefinalpressureissimilartotheinitialpressure,sothenextexperimentcanbeimmediatelystartedwithouttheneedtosaturatethecoreagain.Aspermeabilitydecrease,thepressurediffusiondecreases,sothereisadelaybetweenth
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