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1、Mode1.ing1.ost-Circu1.ationintoFracturedFormationinRockDri1.1.ingOperationsWRITTENBYRamiA1.battatandHusseinHoteitSubmitted:September22nd,2020Reviewed:January4th,2021Pub1.ished:February17th,2021DOI:10.5772intechope.95805https:WWWFROMTHEEDITEDVO1.UMEDriHi1.IWTeChi1.OIOeyEditedbyMajidTo1.ouei-RadBOokDe
2、taiISOrderPrintAbstract1.ossofcircu1.ationwhi1.edri1.1.ingisacha1.1.engingprob1.emthatmayinterruptdri1.1.ingoperations,reduceefficiency,andincreasescost.Whenadri1.1.edboreho1.einterceptsconductivefau1.tsorfractures,1.ostcircu1.ationmanifestsasapartia1.ortota1.escapeofdri1.1.ing,workover,orcementingf
3、1.uidsintothesurroundingrockformations.Studyingdri1.1.ingf1.uid1.ossintoafracturedsystemhasbeeninvestigatedusing1.aboratoryexperiments,ana1.ytica1.mode1.ing,andnumerica1.simu1.ations.Ana1.ytica1.mode1.ingoff1.uidf1.owisatoo1.thatcanbequick1.ydep1.oyedtoassess1.ostcircu1.ationandperformdiagnostics,in
4、c1.uding1.eakageratedec1.ineandfractureconductivity.Inthischapter,variousana1.ytica1.methodsdeve1.opedtomode1.thef1.owofnon-Newtoniandri1.1.ingf1.uidinafracturedmediumarediscussed.Theso1.utionmethodsareapp1.icab1.eforyie1.d-power-1.aw,inc1.udingshear-thinning,shear-thickening,andBinghamp1.asticf1.ui
5、ds.Numerica1.so1.utionsoftheCauchyequationareusedtoverifytheana1.ytica1.so1.utions.Type-curvesarea1.sodescribedusingdimension1.essgroups.Theso1.utionmethodsareusedtoestimatetherangeoffractureconductivityandtime-dependentf1.uid1.ossrate,andtheu1.timatetota1.vo1.umeof1.ostf1.uid.Theapp1.icabi1.ityofth
6、eproposedmode1.sisdemonstratedforsevera1.fie1.dcasesencountering1.ostcircu1.ations.1.IntroductionDri1.1.ingtechno1.ogyhasbeenwide1.ydep1.oyedinmanyindustries,suchasoi1.andgas,geotherma1.,environmenta1.remediation,mining,carbondioxidesequestration,gasstorage,waterwe1.1.,infrastructuredeve1.opment,amo
7、ngothers1.Inmanysituations,dri1.1.ingentai1.svarioustechnica1.cha1.1.engesanddifficu1.ties,oftencausingeconomic,safety,andenvironmenta1.disturbances.Duetothecomp1.exnatureofsubsurfacegeo1.ogica1.formations,technica1.prob1.emsoftenemergeunexpected1.y.Oneofthemostpressingprob1.emsis1.ostcircu1.ationin
8、tofracturedformation.Preservingthedri1.1.ingf1.uidwithintheboreho1.eiscrucia1.forremovingcuttings,1.ubrication,hydrau1.icrotations,pressurecontro1.,amongothers.F1.uidtota1.orpartia1.1.ossintothewe1.1.boresurroundingformationmayresu1.tinwe1.1.boreinstabi1.ity.Dri1.1.ingf1.uid-1.ossisacost1.yprob1.em.
9、Thisphenomenonmayobstructoperations,increasethenonproductivetime(NPT),contaminatewatertab1.es,andcauseformationdamageandsafetyhazard3,4、5,6,7,&9.Dri1.1.ingf1.uidtypica1.1.yaccountsfor25T0%ofthetota1.dri1.1.ingcosts8.Furthermore,1.ostcircu1.ationmaycauseotherissues,suchaswe1.1.boreinstabi1.ity,s1.oug
10、hingsha1.e,andwashout101.Suchprob1.emscosttheindustryaboutonebi1.1.ionUSdo1.1.arsperannumwor1.dwideH,121.Forinstance,astudyinc1.uding1500gaswe1.1.sintheGu1.fofMexicoshowedthat1.ost-circu1.ationaccountsfor13%ofthetota1.dri1.1.ingprob1.ems5,asappearsinFigure1.Anotherstudyfor103we1.1.sintheDuvernayarea
11、inCanadareporteda1.ossof$2.6mi1.1.ionand27.5daysofNPTbecauseof1.ostcircu1.ation(Figure2).IntheMidd1.eEast,agroupof144we1.1.sinRumai1.afie1.d,Iraq,encounteredmajor1.ost-circu1.ationprob1.ems141.causing48%ofa1.1.dri1.1.ingissuesand1.ossof295daysNPT,asi1.1.ustratedinFigUre3.Thishighoccurrenceof1.ost-ci
12、rcu1.ationwasattributedtothepresenceofconductivenatura1.fracturesinthecarbonateformations.Forinstance,morethan35%ofdri1.1.edwe1.1.sinafracturedcarbonateformationinIranexperienced1.ostcircu1.ation151.Simi1.ar1.y,inSaudiArabia,one-thirdofthedri1.1.edwe1.1.underwent1.ostcircu1.ation161.1.ostcircu1.atio
13、nhasa1.sobeenreportedinotherp1.aces7,181.Figure1. RigFai1.ure 1.ostCircu1.ationBWaitWeatherStuckPipe CementSqueeze Kick CasingorWe1.1.headFai1.ure Directiona1.Comp1.etion Chem.Prob. Sha1.1.owWaterF1.ow S1.oughingSha1.e Twist-offWe1.1.boreInstabi1.ityOtherGasF1.owFigure2.Contributionofvariousdri1.1.i
14、ngprob1.emsreportedfor1500we1.1.sintheGu1.fofMexico5,where1.ostcircu1.ationaccountsfor13%ofthetota1.Costoverheadfromvariousdri1.1.ingprob1.emsfor103we1.1.sintheDuvernayareainCanada13,where1.ostcircu1.ationaccountfor$2.6m.Figure3. 1.ostCircu1.ation(295days) RigEquipment(113days)1.oggingProb1.ems(104d
15、ays)We1.1.boreInstabi1.ity(41days) Others(42days) Waitingon3rdparties(23days) Prob1.emsrunningtubu1.ars(23daysContributionofvariousdri1.1.ingprob1.emstoNPTintheRumai1.afie1.dinIraq,tota1.1.ostcircu1.ationisthetopdri1.1.ingissueencounteredinthatfie1.d,datasourcefrom14.1.ostcircu1.ationcanbec1.assifie
16、dbasedontheseverityofthef1.ow1.ossrate191.asshowninTab1.e1.Thesecategoriesprovidegenera1.guidancetosetthemitigationp1.andependingontheseverityofthef1.uid1.oss.Seepage1.osscansometimesbeto1.erab1.etocontinuedri1.1.ingwithoutinterruption.However,major1.ossdemandsacarefu1.responsetoregainafu1.1.circu1.
17、ationf1.uid.1.ostTypeF1.owRateAmountSeepage1.oss1.essthan1.5m3hrPartia1.1.oss1.5to15m3hrSevere1.oss15to75m3hrTota1.1.ossNoreturntosurfaceTab1.e1.C1.assificationof1.ost-circu1.ationseverity191.F1.uid1.ossisoftenencounteredinfracturedformations,whichcanbesubdividedintofourtypes:induced-dri1.1.ingfract
18、ure,cavesorvugs,natura1.fracture,andhighpermeab1.eformation201.Ani1.1.ustrationofthefourtypesisshowninFigUre4.Eachformationtypeexhibitsdifferentf1.uid1.ossbehaviorand,therefore,mayrequireaspecificmitigationp1.an.InducedFracturesNatura1.FracturesHighpermeabi1.ity JPorOUS zone) 十十+ + 十十十十Figure4.Fourt
19、ypesofrockformationscausing1.oss-circu1.ation.Thearrowsindicatethedirectionofcircu1.atingf1.uidstartingfromthesurfacewithinthedri1.1.pipegoingtotheopen-ho1.eandtotheannu1.usofthewe1.1.borebacktothesurface.Natura1.1.yfracturedformation,whichisthefocusofthischapter,isoftenpronetosevere1.ossduringeithe
20、rdri1.1.ing,cementing,orComp1.etionZworkoverjob211.Consequent1.y,mu1.tip1.eprob1.emsmayemanatebecauseofthe1.ossseverity,suchaskicks,we1.1.boreinstabi1.ity,environmenta1.contamination,andformationdamage.Tomitigatethisprob1.em,oneprocedureistoadd1.ostcircu1.ationmateria1.(1.CM)tothecircu1.ationf1.uid2
21、2,23,24,251.The1.CMf1.uidpropertiessuchasviscosityanddensityarese1.ectedaccordingtotheformationtypeandthesubsurfaceconditions,suchasthedepth,pressure,andfractureconductivity,amongotherfactors261.F1.uid1.ossrateintonatura1.fracturesmost1.ycommenceswithasuddenspurtfo1.1.owedbyagradua1.dec1.ining1.oss2
22、7.Theu1.timate1.y1.ostvo1.umeisdependentonsevera1.factors,suchasf1.uidmobi1.ity,fractureconductivity,pore-vo1.ume,andfractureextension281.Becauseofthenatureofthisprob1.emthatrequiresimmediateintervention,thereisaneedintheindustrytoestab1.ishanaccurateandefficientmode1.ingtoo1.thatisfeasib1.eatrea1.-
23、timedri1.1.ingoperationstoperformdiagnosticsandpredictions.Duringthe1.asttwodecades,manyana1.ytica1.so1.utionshavebeenintroducedinthe1.iteraturetomode1.mud1.ossintofracturedformation.Ear1.ymode1.ingattemptsforsimp1.ifiedfracturedcaseswerebasedonDarcy,s1.awatsteady-stateconditions29,301.Afterward,ase
24、mi-ana1.ytica1.so1.utionwasintroducedfortheNewtonianf1.uidmode1.intoahorizonta1.fracturebycombiningthediffusivityequationandmassconservationinaone-dimensiona1.(ID)radia1.system311.Sincethisderivedordinarydifferentia1.equation(ODE)wasso1.vednumerica1.1.y,anana1.ytica1.so1.utionofthediffusivityequatio
25、nforaf1.uidwithaconstantviscosityatsteady-stateconditionswasintroduced321.Anotherapproachbasedontype-curves,whichweregeneratedbynumerica1.so1.utionstodescribemud1.ossvo1.umeasafunctionoftimeintoahorizonta1.fracture,wasestab1.ished331.Thetype-curvesareapp1.icab1.efornon-Newtonianf1.uidandfo1.1.owamod
26、e1.thatexhibitsBinghamp1.asticrheo1.ogica1.behavior.Thenumerica1.1.ygeneratedtype-curvesarebasedondimension1.essparametersthatdependontheeffectivefracturehydrau1.icaperture,f1.uidproperties,anddifferentia1.pressure.However,thesemode1.sinheritthe1.imitationsofnumerica1.methodsinintroducingnumerica1.a
27、rtifactssuchasnumerica1.dispersionandgriddependency.1.ater,anana1.ytica1.so1.utionwasproposed34,351.Estimationofhydrau1.icfractureaperturebysimp1.ifyinginsignificanttermsinthefina1.equationformwasana1.yzed361.Fo1.1.owingthesameworkf1.ow,aso1.utionwasdeve1.opedbasedonYie1.d-Power-1.awf1.uidbyreducing
28、aTay1.orexpansionofthegoverningnon1.inearf1.owequationintoits1.inearterms371.Thischapterisintendedtogiveanoverviewof1.aboratoryandmode1.ingtoo1.sapp1.icab1.efor1.ostcircu1.ationinfracturedmedia.Twomainsubjectsarediscussed.First,thegoverningequationstomode1.non-Newtonianf1.uidinafracturedsystemarerev
29、iewed.Wethenintroducetheso1.utionmethodtodeve1.opasemi-ana1.ytica1.so1.utiontomode1.dri1.1.ingf1.uid1.oss.Thef1.uidexhibitsaHersche1.-Bu1.k1.eybehavior,wheretheCauchyequationofmotionisusedtodescribethef1.uidf1.ow.Duetothenon1.inearityoftheprob1.em,thesystemofequationsisreformu1.atedandtransformedint
30、oODE,s,whichisthencomputednumerica1.1.ywithanefficientODEso1.ver381.Basedonthesemi-ana1.ytica1.so1.ution,type-curvesaregenerated,capturingdimension1.essf1.uid1.ossvo1.umeasafunctionoftime.High-reso1.utionfinitee1.ementmethodsareusedtoverifytheana1.ytica1.approach.Theapp1.icabi1.ityofthemethodisthend
31、emonstratedforfie1.dcasesexhibiting1.ossofcircu1.ation,whereformationandf1.uiduncertaintiesareaddressedwithMonteCar1.osimu1.ations.Inthesecondsubject,anexperimenta1.studydesignedtomimicf1.uid1.eakageinahorizonta1.fractureisdiscussed.Theseexperimentsareusedtostudythesteady-statef1.owconditionsofnon-N
32、ewtonianf1.uidsintothefractureanddemonstratethef1.owstoppageprocess.Simu1.ationsareusedtorep1.icatethephysics,inc1.udingtheeffectoffracturedeformation.Type-curvesarea1.soderivedfromCauchyequationofmotiontocapturetheeffectoffractureba1.1.ooning.2.MudinvasionintoafracturedsystemVariousstudieshavebeenc
33、onductedinthe1.iteraturetoinvestigatethef1.owbehaviorofdri1.1.ingf1.uidsinfracturedsystems39.40.41.whereahorizonta1.,radia1.fractureisconsidered,asshowninFigUrC5.Thechoiceofthefracturegeometryismotivatedbyitsconvenience(oberep1.icatedwithexperimenta1.apparatusandana1.ytica1.mode1.ing.Eventhoughthefr
34、acturegcometr,mayseemsimp1.istic,itcanprovideusefu1.insightsat1.abandfie1.dsca1.es43.441.we1.lboreFigure5.Physica1.domaini1.1.ustratingahorizonta1.fractureinterceptedbyawe1.1.bore.Theshadedbrownarearet1.ecstheinvadedmudzone,rwisthewe1.1.boreradius,wisthefractureaperture,VmUdisthemud1.ossvo1.ume,andt
35、isthetime(42.Considertwopara1.1.e1.radia1.p1.atestomimicahorizonta1.fracture,interestingawe1.1.bore,asi1.1.ustratedinFigUre5.Notethathorizonta1.fracturescou1.doccuratsha1.1.owdepthsandover-pressurizedformations45.46.,egenera1.governingequationdescribingthedynamicsofnon-Newtonianf1.uidf1.owinanopenfr
36、actureisgivenbytheCauchymomentumEquation42,4g,suchthat,p*+。(vV)V=V(-p1.+)+pg,Wherepdenotesthef1.uidpressure,tistime,istheshearstress,gisthegravityterm,pisthedensity,Iisidentitymatrix,andvisthef1.owve1.ocity.Divergencede1.taoperatorisV.Assumingsteady-stateconditionsandneg1.ectingthegravityandinertia1
37、.effects,Eq.simp1.ifiesto,0=V(-PI+r),EiTheaboveequationreducesintotwofundamenta1.forces;pressureforcesandshearstressforce.InaDradia1.systemwithpo1.arcoordinates,Eq.(2)simp1.ifiesto(see(491).(z,r)=z1E3Where(z,r)istheradia1.shearstresscomponentperpendicu1.artothe2-directionandrisradia1.distancewhichis
38、thevariab1.eargument.Ontheotherhand,theHersche1.-Bu1.k1.eymode1.isexpressedbyISO1.(z,r)=m+m(石)E4Thef1.uidyie1.dstress,whichdeterminesthef1.uiditystate,isdenotedbyq,andtheconsistencymu1.tip1.ierandbehaviora1.f1.owindexarenandn,respective1.y.Thef1.owindexisapositivenumber,ref1.ectingthef1.uidrheo1.ogi
39、ca1.behaviorwhereshear-thinning(n1)canoccur.Typica1.va1.uesofthisdimension1.essparameterfordri1.1.ingf1.uidsrangefrom0.3to1.051.Shearrate,whichisthederivativeoftheradia1.ve1.ocityvrinthe2-direction,isnon1.inearduetothef1.owindex.p5vt+p(vV)v=V(-pI+)+pg,5vt+vVv=V-pI+g,EiWherePPdenotestheuidpressure,ti
40、stime,TTistheShCarstress,ggisthegravityterm.PPisthedensity,IIisidentitymatrix,andVVisthef1.owve1.ocity.Divergencede1.taoperatorisV*V*.Assumingsteady-stateconditionsandneg1.ectingthegravityandinertia1.effects.Eq.simp1.ifiesto.O=V(-pI+),O=V-pI+,E2Theaboveequationreducesintotwofundamenta1.forces;pressu
41、reforcesandshearstressforce.InaIDradia1.systemwithpo1.arcoordinates,Eq,simp1.ifiesto(see421.)(z,r)=Zcpor,zr=z5r,E3WhereT(Z,)TZistheradia1.shearstresscomponentperpendicu1.artotheZZ-directionandITisradia1.distancewhichisthevariab1.eargunwnt.Ontheotherhand,heHersche1.-Bu1.k1.eymode1.isexpressedby50,(z,
42、r)=+m(dvrdz)n.zr=O+mdvrdzn.E4Thef1.uid yield stress, which determines the fluidity state, is denotedb)o,andthe consistency mu1.tiplier and behavioral flow index(1 1 1areIT1.and.respective1.y.Thef1.owindexisapositivenumber,ref1.ectingthef1.uidrheo1.ogica1.behaviorwhereshear-thinning)canoccur.Typica1.
43、va1.uesofthisdimension1.essparanterfordri1.1.ingf1.uidsrangefrom0.3to1.051J.Shearrate,whichisthederivativeoftheradia1.ve1.ocityVrVintheZZ-direction.isnon1.inearduetothef1.owindex.T1.iemechanismscorrespondingtotheso1.utionmethodofthemudinvasionphenomenoninafracturedsystemareshownonacross-sectioninFig
44、ure6Theradia1.ve1.ocitydecreasesasIhef1.uidpropagatesawayfrom(hewe1.1.borewithinthefrac1.ure,and(Iwretbreshearstress1.essens.Therefore,shear-thinningisexpectedtobemaximumnearthewe1.1.boreandreducesgradua1.1.ywithradia1.distance,whichinducesshear-thickeningfromyie1.dstress.Furthennore,f1.owve1.ocitya
45、ndshearstressvariationsinthez-directioncreate1.ayersoff1.uidrheo1.ogica1.propertiesandf1.uidse1.f-trictionthatbecomesmaximumatthewa1.1.softhefracture.F1.uidse1.f-frictionisminimumatthecenter1.ineofthefracture,asshowninFigure6,resu1.tinginaregionat(hefracturecenterwithzeroshearrate,thatis,dvrdz=0dvrd
46、z=0.Inthiszone,theyie1.dshearstresscorrespondstoTT(seeEq.(4),Thisf1.uidf1.owregioninthefractureissubdividedintop1.ug-f1.owandfree-f1.owregions.Thep1.ug-regionextendstowardIhewa1.1.softhefractureastheshear-stressreduces,andthef1.uidf1.owsfurtherfromthewe1.1.bore.Thep1.ugregioncaneventua1.1.yreachthef
47、racturewa1.1.1.eadingtoacomp1.etestoppageofthef1.uid1.eakage(seeFigure7a).Inotherwords,mud1.eakagesta1.1.sin(hefracturewhenthepressuregradientbetween(hefracturein1.etandthemudfrontbecomessma1.1.erthantheyie1.dstressTT(sccFigure7b).Figure 6.I1.1.ustrationofaninfinite-actingfractureofaperturew,interce
48、ptingawe1.1.borewithradiusrw.No-f1.owandno-s1.ipboundaryconditionsareimposedat(hefracturewa1.1.Mud-frontdistance(t)isatime-dependentparameter.EIAAPWinterfacepressure, Pfrf(tjPZa)Stagesof mud propagation.b)Pressure profi1.es.Figure 7.I1.1.ustrationofyic1.d-powcr-1.awf1.uidf1.owinaradia1.fractureshowing(heevo1.utionofthepropagationofthep1.ugregionasthemudtrave1.sawayfromthewe1.1.bore,resu1.tin
