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hydrMatteoMarongiu-Porcua,*,MichaelJ.Economidesb,StephenA.HolditchcarticleinfoArticlehistory:Received17May2013Receivedinrevisedform7June2013Accepted9June2013Availableonline5July2013Keywords:PhysicaloptimizationofhydraulicfracturingEconomicoptimizationofhydraulicfracturingC2112013ElsevierB.V.Allrightsreserved.Arguably,withtheexceptionofsomerarelocationsorcom-panies,thepetroleumindustryhasfinallyreachedthestagewherehydraulicfracturingisnolongerconsideredasastimulationtech-niqueexclusivelysuitableforlow-permeabilityformations.Thistookacoupleofdecades,atleast,followingthedevelopmentoftheofworkinplacesBetteryet,fracturingisnowviewedasanintegralpartofwellandreservoirmanagementandamainstayofproductionen-gineeringratherthanachoiceoflastresortfordepletedorinex-plicablyunderperformingwells.Fracturinghascontinuouslyexpandeduntilithasbecomethecompletionofchoiceforalltypesofwellsbut,particularly,forgaswells.Shaleformations,perhapsthemostimportantnewtypeofpetroleumapplicationsindecadescanbemadecommercialonlythroughthemassiveapplicationofmultiplehydraulicfracturinginhorizontalwells.*Correspondingauthor.Tel.:þ17137226413(office);fax:þ17137229907.ContentslistsavailableatJournalofNaturalGasScienceJournalofNaturalGasScienceandEngineering14(2013)91e107E-mailaddress:matteo.porcu@xgasltd.com(M.Marongiu-Porcu).1.Introductiontipscreenout(TSO)andthevoluminousbodysuchastheGulfofMexicoandRussia.lowerpermeabilityfields,althoughthelattercanbemadeeconomicallyattractiveonlythroughhy-draulicfracturing.NPVNaturalgasreservoir1875-5100/$eseefrontmatterC2112013ElsevierB.V.http://dx.doi.org/10.1016/j.jngse.2013.06.001abstractOptimizationhastakenseveraldifferenthuesinallareasofengineering.Hydraulicfracturing,asappliedtooilandgaswells,hashaditsshare.Inthepast,andbeforethematuringofhigh-permeabilityfracturingandthetipscreenouttechniques,thiswellstimulationprocedurewaslimitedtolow-permeabilityreservoirsandunrestrictedfracturing.Insuchcases,thefracturelengthwouldbeanappropriatedesignoptimizationvariableagainstaneconomiccriterion,e.g.,theNetPresentValue(NPV).Thisinvolvedthebalancingofincrementalfuturerevenueagainstthecostofexecution.Alsointerestingwouldbeparametricstudies,allowingthevariationofexecutionvariablesandthedetectionofdifferencesintheirrespectivedesignNPV.Suchdifferenceswouldbeusefulindecisionstomeasureavariableorstaywithinreasonableassumptions.Theemergenceofhigher-permeabilityfracturingandtheUnifiedFractureDesign(UFD)conceptallowedtwoimportantno-tions.First,thereisnodifferencebetweenlowandhigh-permeabilityreservoirsintermsofbenefitingfromfracturing.Justexecutionissuesneedtoberesolved.Second,andmoreimportant,foranymassofproppanttobeinjectedinanywell,thereexistsonlyonefracturegeometrythatwouldmaximizeproduction.Thisgeometry,consistingoflengthandproppedwidth(withheightasaparasiticvari-able)canbereadilydeterminedand,ifplaced,itwillprovidethemaximumproductivityindex.Allothercombinationsoflengthandwidthwouldresultinlowerproductivityvalues.Thisisphysicaloptimization.Inthispaperwecombinethetwo:theeconomicandphysicaloptimizations.Foreachproppantmasswefirstoptimizethefracturephysicalperformance,andthenweapplytheNPVcriterion.Weperformaseriesofparametricstudiesforarangeofgasreservoirsandweuseeconomicvariablesthatdifferinvariouspartsoftheworld.Weshowhowtodeterminetheoptimumfracturesize.Wethenshowhowfracturetreatmentsmaybeattractiveincertainreservoirsinmatureareasbutnotattractiveelsewhere.Wealsoshowthatforadiversifiedcompany,giventhechoice,fewsuccessfulfracturesinhigh-permeabilityreservoirsarefarpreferabletofracturinglargenumbersofwellsinbUniversityofHouston,USAcTexasA&MUniversity,USAaEconomidesConsultantsInc.,800GessnerRd.,Ste220/240,Houston,TX77024,USAEconomicandphysicaloptimizationofjournalhomepage:www.elsAllrightsreserved.aulicfracturingSciVerseScienceDirectandEngineeringevier.com/locate/jngseGasThechoicetodevelopafieldeitherwithconventionalcom-pletionsorthroughtheapplicationofhydraulicfracturinghasabigimpactonthenumberofwellstobedrilledandonthein-fillplanofafield.Thetremendousadvantageinfracturingmostwellsisnowlargelyaccepted,evennearwatercontacts,consideredthebaneoffracturing.High-permeabilityfracturingisfindingappli-cationbecauseitofferscontrolledfractureextentandlimitsdrawdown.Aproperdesignandexecutionofafracturingtreatmentinvolvesseveraldisciplinessuchasreservoir,productionandcompletionengineering,requiresabackgroundinrockmechanicsandfluiddynamics,isconstrainedbythephysicallimitsofthematerialsandequipmentusedaswellasbytheoperationalissues,andlastbutnotleastmustsatisfycertaineconomiccriteria.Insuchacomplexmulti-subjectenvironment,itisnotatrivialexercisetodetermine“optimum”conditionsforthedesign,theexecutionandthepost-treatmentbehaviorofthewell.Clearly,whatrepresentsanoptimumconditionfromacertainstandpointmaynotbeasfavorablefromotheraspects.SincetheintroductionoftheUnifiedFracturingDesign(UFD)approach(Economidesetal.,2002a),thedesignoffracturingtreatmentsheadstowardthemaximizationofthewellproductivity(quantifiedbytheDimensionlessProductivityIndex,JD).Anotherclearlyimportantapproachisthemaximizationoftherevenuesaccordingtocertaineconomiccriteria(forinstance,theNetPresentValue).ThegoalofthisworkistoshowhowtheUFDapproachcanbeusedtoachieveadualphysicalandeconomicoptimization,invirtuallyanyreservoirtypeandundermostrealisticconstrainsthatarisefromexecutionissues.Wewillseelateronthattheoptimi-zationprocedurepresentedisconsistentandsystematic,andmakesuseoftheoutputparameterscomingfromthephysicaloptimizationasinputfortheselectedeconomiccriterion.ThecentralideaoftheUFDtechniqueistoselecttheappropriateoptimumcompromisebetweenproppedfracturelengthandwidth,foragivenproppantvolumeanddependingonthepropertiesofthereservoirandtheselectedproppant.Adimensionlessparameter,theProppantNumber(Np)wasintro-ducedfirst.TheProppantNumberistheratiooffractureandreservoirdrainagevolumesadjustedbythereservoirperme-abilityandtheproppant-packpermeability,anditiscompletelyindependentfromfracturegeometry.ItwasfoundthatforagivenvalueofNpthereisanoptimalDimensionlessFractureConductivity(CfD),atwhichthedimensionlessproductivityin-dexJDismaximized.Theoptimizedandspecificdimensionlessfractureconductivityleadsalsototheuniqueoptimalfracturegeometry(widthandlength).Wideandshortfracturesareclearlyappropriateforhigh-permeabilityreservoirswhilenar-rowandlongfracturesareforlow-permeabilityreservoirs.Anessentialelementoffieldexecutiontoobtaintheindicatedge-ometriesisthetipscreenout(TSO)technique,whichallowsthearrestofthelateralgrowthinordertoincreasethewidthofthefracture.TheUFDmethodhasalreadybeenusedinawiderangeofrealfieldapplicationswithexcellentresults.Evenmore,insomeveryprogressiveareasthisdesignapproachhasbeenusedto“pushthelimits”oftoday’spracticesinhydraulicfracturing.Demarchosetal.(2004)showed,forexample,howrelevantthemassofproppantisforthemaximizationoftheproductivityindex.DiyashevandEconomides(2005)presentedfieldcasestudiesofalmostathousandhydraulicfracturetreatmentsinWesternSiberia,providingaveryvaluableexperimentalsupportfortheUFDapproach.Romeroetal.(2002)accountedfortwotypesofflowimpedi-M.Marongiu-Porcuetal./JournalofNatural92ments,fracturefacedamageanddamageatthefractureewellboreinterface(“ChokeSkin”,firstlyintroducedbyMukherjeeandEconomides,1991).Economidesetal.(2002b)showedhowtheUFDapproachcanbeappliedtogaswells,especiallyinhigh-permeabilityreservoirs,wherefracturingisthemostappropriatewaytoslashnon-Darcyeffects.Lopez-Hernandezetal.(2004)appliedthemethodologytocompensatefornon-Darcyeffectsinthefracture.WeiandEconomides(2005)presentedtheapplicationsoftheUFDtechniquetohorizontalwellswithmultiplefracturesforbothoilandgasreservoirs,whileDaalandEconomides(2006)furtheradaptedtheUFDtechniquetoin-filldrillingandtotransversallymulti-fracturedhorizontalwellsbyconsideringnon-squaredrainageareasandthesliced-partitionofthedrainageareaalongthehorizontaldrain.Demarchosetal.(2006)presentedasetoffield-provenpro-cedurestooptimallyimplementtheUFDtechniqueduringthesequenceofoperationsrequiredforamulti-fracturingtreatmentonahorizontalwell.Economidesetal.(2010)presentedacompellingsetofselectioncriteriaforhorizontaltransverse,horizontallongi-tudinalandverticalWells,whileMarongiu-Porcuetal.(2010)studiedindetailthemostcommonflawsinhydraulicfracturede-signsrevealedbytheUFDapproach.2.EconomicoptimizationThecruxofhydraulicfracturingisproductionenhancement,meaningacceleratingproductioninadepletingdrainage.Thequestionofcourseiswhetherthisaccelerationoftheproduction,comparedtoanunfracturedwellandassessedthroughtheirrespectivepresentvaluesoftherevenuestreams(oneforafrac-turedwellandanotherforanunfracturedwell),canbebalancedagainstthecostsofthetreatment.Inadditiontotheincreaseinproduction,anevaluationoftheeconomicsofahydraulicfracturingtreatmentmustconsidermanyfactors,includingtreatmentcosts,additionalreservesthatmaybeproducedbeforethewellreachesitseconomiclimitandreservoirrisksassociatedtomechanicalproblemsthatcouldcausethetreatmenttobeunsuccessful.Whilethereareothercriteriaforassessingeconomicattrac-tivenessorlackthereof,forthepurposesofthiswork,wewillusetheNetPresentValueasthecriterionfortheoptimizationandtheevaluationofthedesirabilityofthespecifichydraulicfracturetreatment.TheNPVcriterionhasbeenalreadyselectedbyseveralre-searcherstomonetizetheincrementalproductionobtainedafterafracturingtreatment,butithasneverbeenassociatedtoarigorousphysicaloptimizationsuchastheUFDapproach.Nomatterhowsophisticatedthemodelusedtopredictfracturepropagationandperformancetheeconomicoptimizationrequiresatrialanderrorprocesstodeterminetheoptimumtreatmentdesignfromasetofthecalculatedphysicaldesigns.Forinstance,Britt(1985)usedtheNPVto“showaprocessbywhichtheoptimumfracturelengthandfractureconductivitycanbedeterminedforwellsinmoderate-permeabilityoilreservoirsunderprimarydepletionandsecondaryrecoveryprocesses”.Veatch(1986)presentedacomprehensiveoverviewoftheeco-nomicsoffracturingandcritiquedthemethodsofdesignoptimi-zation.Warembourgetal.(1985)presentedanoutlineofadesignoptimizationprocesswiththeproperidentificationofcriticaltreatmentvariables.AndersonsandPhillips(1988)usedtheconceptoftheNPVtocalculatetheappropriateamountofproppant.AparticularlyrelevantworkinthisstudywaspresentedbyBalenetal.(1988),whodevelopedacomprehensiveengineeringScienceandEngineering14(2013)91e107methodology.Theirprocedureinvolved:-thedeterminationofoptimalpumpingparametersandmaximumproppantcoverageforagivenhydraulicpenetration;-linkingthereservoirdeliverability,wellproducingsystemsandtheoptimizedfracturegeometry;-economicanalysisperformedtocalculatetheNPVforvariousdesignoptions.Wewillseelaterinthispaperhowtheuniquenessoftheso-lutionstotheoptimizationproblemprovidedbytheUFDapproachgreatlysimplifiesandmakesstraightforwardtheexecutionofNPVcalculationsforfracturingtreatments.Thephysicaloptimizationofthefracture,foragivenproppantmassandsatisfyingtheimposedphysicalconstraints,providesablue-printtofollowinthefieldduringthetreatmentinordertomaximizetheJD.UsingtheNPVcriterion,theoptimalamountofproppantatwhichtherevenuescomingfromtheenhancedpro-ductionminustheinvestmentnecessarytoperformthefracturingtreatmentaremaximized,isdetermined3.TurbulenceinnaturalgaswellsandUnifiedFractureDesignapplicationsThissectionexplainshowtheUFDapproachcanbeappliedtoaProppantmassfor(twowings),lbm200,000M.Marongiu-Porcuetal./JournalofNaturalGasSpgravityofproppantmaterial(water¼1)2.65Porosityofproppantpack0.38Proppant-packpermeability,md150,000Maxproppantdiameter,Dpmax,inch0.031Permeable(leakoff)thickness,ft50Wellradius,ft0.4Welldrainagearea,acres320Pre-treatmentskinfactor0Fractureheight,ft100Injectionrate,bpm30Rheology,K0,(lbf/ft2)*sn00.018Rheology,n00.45Leakoffcoeff.inpermeablelayer,ft/min0.50.004Poissonratio,n0.38Reservoirpressure,psi4000Reservoirporosity,%20Bottom-holeflowingpressure,psi1500WaterSaturation,%20Reservoirtemperature,C14F120Gasviscosity,cp0.015Gasdeviationfactor(Z)0.910Gasspecificgravity(gg)0.71Cooke’sconstant(a)1.54naturalgaswell.Inthiscase,theeffectiveproppant-packperme-abilitythatisaveryimportantquantityinfracturedesignwillhavetobeadjusteddownwardsbecauseofturbulenceeffects.Thetroubleisthattheadjustmentdependsontheexpectedrateitself.Economidesetal.(2002b)presentedatrialanderrorprocedurecombiningtheUFDmethodwiththeGidley(1990)adjustmenttotheproppant-packpermeabilityandtheCooke(1993)correlationsforflowinfractures.Althoughthereisturbulenceinthefractureandthedesignwillcompensateforit,primarilybywideningthefracture,thepres-enceofthefractureitselfhasaprofoundimpactonthereductionofreservoirturbulence,perhapsthemostimportantvariableaffectingtheperformanceofmediumtohigh-permeabilitygaswells.Table1Designvariablevalues.Cooke’sconstant(b)110,470Acalculationwasperformedtoillustratetheiterativeapproachtofracturedesignforgaswellsand,atthesametime,toshowtheeffectsthatfracturinghasonthereductionofreservoirturbu-lence,perhapsasimportantaroleasstimulationitself.Table1summarizestheimportantvariablesforthisexercise.Arangeofpermeabilityfrom0.05to100mdisused.Topresenttheresultsinaconvenientway,thefoldsofincrease(FOI)betweenfracturedandunfracturedcaseareused.ThefirstresultsareshowninFig.1,andinadditiontothegaswell,alsothefoldsofincreaseforanoilwellarepresented.Asthereservoirpermeabilityincreases,fortheoilwellthefoldsofproductionin-creaseoveranon-fracturedwellwilldecline.IntheexampleshowninFig.1,for0.1mdthefoldsofincreaseareover10,whereasat100mdthefoldsofincreaseapproach2.FornaturalgaswellsthebehavioroftheFOItrendsatlowreservoirpermeabilitymimicsthatofoilwellsbutasthepermeabilityincreases,thetrenddiverges:afracturedgaswellstartstoperformfarbetterthananon-fracturedhigh-perme-abilitywellbecauseoftheconsiderablereductioninturbulenceeffectsthatadverselyaffectwellperformanceanddominateradialflow.ThedifferencebetweenthesolidanddashedbluecurvesinFig.1isduetotheintroductionofphysicalconstraintsinthecal-culations.Forthedashedcurve,asthereservoirpermeabilityin-creasesandflowintothefractureincreases,theturbulenceinthefracturewouldreducetheeffectivepermeabilityoftheproppantpack.This,inturnwouldrequireafracturewidththatwouldbehighlyunrealisticinpractice,especiallyasitmanifestsitselfashydraulicwidthduringexecution.Sincethehydraulicwidthandthenetpressurearedirectlyrelated,ifduringexecutionanetpressureconstraintofforexample,1000psiisimposed,thenthesolidcurveisobtained,(i.e.,forthesameproppantnumber,theresultingwidthoftheactualfractureisreducedandthemassofproppantisredis-tributedonalongerfracturelength).Thisdesignadjustmentresultsinasub-optimalmaximizedJD,butoneasclosetothetheoreticalmaximumaspossible,andthus,inasetofsmallervaluesofFOI.Selectingahigher-quality(high-perme-ability)proppant,alowerfracturewidthisindicatedandcanbeexecutedwithoutviolatingthenetpressureconstraint.Infact,asuperficialparadoxresultingfromthisworkisthat,con-trarytoconventionalindustrypractices,usinghigher-permeabilityproppantstheindicatedsizesofhydraulicfrac-turesshouldincreaseratherthandecrease(subjecttoeconomicconsiderations).Inconclusion,fromFig.1itisclearthatanygaswellabove5mdwillbegreatlyhandicappedifnothydraulicallyfractured.4.PhysicaloptimizationprocedureThekeyconce
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