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SPE-59095-PA

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SPE 59095 PA
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GelTreatmentsforReducingChannelingtotravelbetweenaninjector-producerpairoftenprovidesausefulcharacterizationofafracturedreservoir.10-13Ofcourse,thetracertransittimedependsonanumberofvariables,includingthepres-suredropbetweenthewells(Dp),thedistancebetweenwells(L),thenumber,orientation,andconductivity(kfwf)ofthecon-nectingfractures,andtheviscosityofthefluidinthefractures~m!.Copyright©1999SocietyofPetroleumEngineersThispaper(SPE59095)wasrevisedforpublicationfrompaperSPE39802,firstpresentedatthe1998SPEPermianBasinOilandGasRecoveryConferenceheldinMidland,Texas,25–27March.Originalmanuscriptreceivedforreview23March1998.Revisedmanuscriptreceived3June1999.Paperpeerapproved12July1999.SPEProd.&Facilities14~4!,November19991064-668X/99/14~4!/269/8/$3.5010.15269inNaturallyFracturedR.S.Seright,SPE,andR.L.Lee,SPE,NewMexicoSummaryThispaperconsiderssomeofthereservoirvariablesthataffecttheseverityofchannelingandthepotentialofgeltreatmentsforre-ducingchannelingthroughnaturallyfracturedreservoirs.Weper-formedextensivetracerandgelplacementstudiesusingtwodif-ferentsimulators.Weshowthatgeltreatmentshavethegreatestpotentialwhentheconductivitiesoffracturesthatarealignedwithdirectflowbetweenaninjector-producerpairareatleast10timestheconductivityofoff-trendfractures.Geltreatmentsalsohavetheirgreatestpotentialinreservoirswithmoderatetolargefrac-turespacing.Producedtracerconcentrationsfrominterwelltracerstudiescanhelpidentifyreservoirsthatarepredisposedtosuc-cessfulgelapplications.Oursimulationstudiesalsoshowhowtracertransittimescanbeusedtoestimatetheconductivityofthemostdirectfracture.Theeffectivenessofgeltreatmentsshouldbeinsensitivetofracturespacingforfracturesthatarealignedwiththedirectflowdirection.Theeffectivenessofgeltreatmentsin-creaseswithincreasedfracturespacingforfracturesthatarenotalignedwiththedirectflowdirection.IntroductionSomeofthemostsuccessfulgeltreatmentshavebeenappliedtoreducechannelinginnaturallyfracturedreservoirs.1-5Therefore,aneedexiststoidentifywhichcharacteristicsofnaturallyfracturedreservoirsindicategoodcandidatesforgelapplications.Thispa-perconsiderssomeofthereservoirvariablesthataffectthesever-ityofchannelingandthepotentialofgeltreatmentsforreducingchannelingthroughnaturallyfracturedreservoirs.AvailableCharacterizationMethodsAtleastthreebooksdescribereservoirengineeringinnaturallyfracturedreservoirs.6-8Thesebooksconcentrateonoilandgasrecoveryduringprimaryproduction.Incontrast,thispaperfo-cusesoncorrectingchannelingproblemsduringsecondaryrecov-eryoperations.Variousloggingmethodshavebeenusedtodetectandcharac-terizefractures~Chap.3ofRef.6,Chap.2ofRef.7,andChap.5ofRef.8!.Thesemethodsmustbeusedwithcautionsincetheyusuallymeasurepropertiesatorverynearthewellbore.Thevalueofthesemethodscanbeincreasedifthewellboreisdeviatedtocrossthedifferentfracturesystems~i.e.,fractureswithdifferentorientations!.Pressuretransientanalyseshaveoftenbeenusedtocharacterizefracturedreservoirs~Chap.4ofRef.6,Chap.4ofRef.7,Chaps.6through8ofRef.8,andRef.9!.Reportedly,thesemethodscanestimatethefracturevolume,thefracturepermeability,and,pos-siblyundersomecircumstances,theminimumspacingbetweenfractures.Pressureinterferencetestscanalsoindicatefractureori-entation.Inadditiontounsteady-statemethods,steady-statepro-ductivityindexeswerealsosuggestedasameanstoestimatefrac-turepermeability.Interwelltracerstudiesprovidevaluablecharacterizationsoffracturedreservoirs,especiallyinjudgingtheapplicabilityofgeltreatmentstoreducechanneling.10-13InterwelltracerdataprovidemuchbetterresolutionofreservoirheterogeneitiesthanpressureReservoirsPetroleumRecoveryResearchCentertransientanalysis.14Tracerresultscanindicate~1!whetherfrac-turesarepresentandifthosefracturesarethecauseofachannel-ingproblem,~2!thelocationanddirectionoffracturechannels,~3!thefracturevolume,~4!thefractureconductivity,and~5!theeffectivenessofaremedialtreatment~e.g.,ageltreatment!inreducingchanneling.Severalmodelsareavailabletoanalyzetracerresults.13-19Inthispaper,wepresentsomesimpleconceptstoassesstheapplicabilityofgeltreatmentsinnaturallyfracturedreservoirs—inparticular,whenchannelingoccursbetweeninjector-producerpairs.RepresentationofaNaturallyFracturedReservoirWhenmodelingnaturallyfracturedreservoirs,thefracturesys-temsgenerallyhavebeenenvisionedasslabs~i.e.,onesetofparallelfractures!,columns~i.e.,twointersectingsetsofparallelverticalfractures!,orcubes~i.e.,threeintersectingsetsofparallelfractures—twoverticalandonehorizontal!.Geostatisticshavealsobeenusedtodescribefracturedistributions.Inthispaper,wefocusonthecolumnmodel.Forsimplicity,assumethatanatu-rallyfracturedreservoirconsistsofaregularpatternofnorth-southfracturesintersectedbyeast-westfractures~seeFig.1!.Foragivennumber,n,offracturesthatareorientedinthenorth-southdirection~theydirection!,2n21fracturesareorientedintheeast-westdirection~thexdirection!.Fig.1illustratesanumberingschemeforthefractures~specificallyforthecasewheren511!.Forourbasecase,oneinjectionwellandoneproductionwellwerelocatedateitherendofthecentraleast-westfracture.Also,thedistancebetweenfractureswasthesameinboththexandydirections.~Later,wewillconsiderwellswheretheproducerisnotonthecentraleast-westfracture.Also,fracturespacingwillbevariedindifferentdirections.!Weassumedthatflowthroughtherockisnegligiblecomparedwiththatthroughthefracturesandthatthesystemisincompressible.Furthermore,fracturesintheydirectionareassumedtohaveaconductivity,(kfwf)y,andfrac-turesinthexdirectionareassumedtohaveadifferentconductiv-ity,(kfwf)x.Aconductivityratio,R,isdefinedusingEq.1.R5~kfwf!x/~kfwf!y.~1!InRef.20twosimulatorsweredescribed~denotedCandE!thatwereusedtodeterminepressures,flowrates,andfrontposi-tionswhenawatertracer,agelant,oragelwasinjectedintoafracturepattern.SimulatorCassumedthatgelantortracerwasinjectedcontinuouslywithaunit-mobilitydisplacementwithoutdispersion.Incontrast,SimulatorEwasmoresophisticated—allowinginjectionofbanksofgelant,gel,ortracerandalsoac-countingfordispersionofthebanks.SimulatorEwasmostusefulforsystemswithrelativelyfewfractures~i.e.,withnvaluesof21orless!.SimulatorCwasusefulforobtainingrelativelyrapidresultsforsystemswithlargenumbersoffractures~i.e.,withnvaluesupto101!.TracerTransitTimesinaSingleFractureDuringaunit-mobilitydisplacement,thetimerequiredforatracerWeusethetransittimeassociatedwithasingledirectfractureasameanstonormalizetransittimesforourfracturesystems.Ifareservoircontainsonlyonefracture~withfractureheight,hf!thatleadsdirectlyfromtheinjectortotheproducerandflowthroughtherockmatrixcanbeneglected,theDarcyequationdeterminesthevolumetricflowrate(q):q5Dpkfwfhf/~Lm!.~2!Thetransittime(t)foratracerisestimatedfromthefracturevolume(hfwfLff)dividedbyq:t5hfwfLff/q5wfL2mff/@Dp~kfwf!#.~3!Giventhefractureconductivity,theeffectiveaveragefracturewidth,wf,canbeestimatedusingEq.4ifwfisexpressedinfeetandkfwfisexpressedindarcy-ft:21wf55.0331024~kfwf!1/3.~4!Fig.2plotsexpectedtracertransittimesfromEq.3versusfractureconductivityandpressuredropwhenL51,000ft,m51cp,andff51.Asanexample,forapressuredropof80psi,Fig.2predictsatransittimeofonedayfora1,000-ft-longfrac-turewithaconductivityof1darcy-ft.Fig.1–Planviewofaninjector-producerpairinasimplenatu-rallyfracturedreservoir.Fig.2–Transittimesthroughasingle1,000-ft-longfracture.270R.S.SerightandR.L.Lee:NaturallyFracturedReservoirsAlthoughtheaboveanalysisprovidesasimpleandusefulmeanstoroughlyestimatetracertransittimes,oneshouldrecog-nizethatdispersionaffectstheprofileofproducedtracerconcen-trationsversustimeorvolumethroughput.Forexample,Fig.3~fromRef.13!showsfieldresultsfromtwointerwelltracerteststhatwereperformedbeforeandafterapplicationofageltreatmentinalimestonereservoir.Forbothtests,aslugofradioactivetracerwasinjectedoverashorttimeperiod,butthetracerwasproducedoverthecourseof140days.Inbothcases,thefirsttracerwasproducedonlyfourdaysaftertracerinjectionintoawellthatwas450ftfromtheproducer.Thepeakconcentrationwasobservedafter10daysforthetracerstudybeforethegeltreatmentandafter37daysforthestudyafterthegeltreatment.Usingtracerresults,Testeretal.11consideredseveralmethodstoestimatethevolumeassociatedwithafracturechannel.Theysuggestedthatthebestestimateofthevolumeofafracturepathisprovidedbythemodalvolume~i.e.,thevolumeassociatedwiththepeakconcentrationintheproducedtracerdistribution!.Forexample,inFig.3,thepeakconcentrationduringatracerstudybeforethegeltreatmentwasnotedabout10daysaftertracerinjection.BasedonotherinformationprovidedinRef.13,about20%oftheproductionrateof550BWPDwasattributedtothewellwheretracerwasinjected.Thus,theestimatedvolumeofthedominantfracturepathwas0.23550310or1,100bbl.Testeretal.11notedthatothervolumemeasurescouldbede-terminedfromthetracercurves.However,theyobservedthatthesevolumesareweightedtooverestimatethefracturevolumeinmostcircumstances.Ifdispersionduringflowthroughasinglefracture~withnoleakoff!wascausedonlybylaminarmixing,atracerwouldfirstarriveattheendofafractureafterinjectingtwo-thirdsofonefracturevolume.22,23IntheexamplesshowninFig.3,tracerbreakthroughoccurredat40%and11%ofthetimes~andvol-umes!associatedwiththepeakconcentrations.Theseresultssug-gestthatconsiderabledispersionoccurredinthefieldexamples.Also,thetracerbankshouldcompletelypassafterinjectionofafewfracturevolumes~i.e.,afewthousandbarrels!.Insteadthetracerprofilewasdispersedover140days~’70fracturevol-umes!.Thisdispersionreflectstherangeofpathwaysfromtheinjectionwelltotheproductionwell.11,13Earlytracerproductionreflectsthemostrapidpathways,whilelatetracerproductionin-dicateslongorcircuitouspathways,deadends,orpossiblychemi-calexchangeinthereservoir.11,13Aswillbeevidentinthenextsection,awiderangeofpathwaysareavailableinnaturallyfrac-turedreservoirs.TransitTimesinaFractureSystemSimulatorCwasusedtodeterminetimesrequiredforatracertotravelfromaninjectionwelltoaproductionwellinanaturallyFig.3–InterwelltracerresultsbeforeandafterageltreatmentafterRef.13.Injection:250BWPD;production:550BWPD.SPEProd.&Facilities,Vol.14,No.4,November1999fracturedsystem.Thesecalculatedtransittimesreflectthemostrapidpathwaysbetweenthewells.Inallcases,the‘‘reservoir’’lookedlikeFig.1.Also,aunit-mobilitydisplacementwasused,andafixedpressuredropwasappliedbetweenthewells.ThetransittimesfromthisprogramwerenormalizedbydividingbythetimecalculatedusingEq.3.~ThetimecalculatedusingEq.3representsthetransittimewhenthesystemcontainsasinglefrac-ture.!ThesedimensionlesstransittimesareplottedinFig.4forfractureconductivityratios,R,rangingfrom0.001to1,000.Thenumberoffracturesorientedintheydirection,n,rangedfrom3to101.SimulatorEwasusedtoconfirmtheresultsshowninFig.4.Similarconditionswereappliedforbothsetsofsimulations.De-tailsofthesesimulationscanbefoundinRef.20.Asmentionedearlier,SimulatorEconsideredinjectionofatracerbankthatcanexperiencedispersion,whiletheSimulatorConlyconsideredcon-tinuoustracerinjectionwithnodispersion.ForrunsmadewithSimulatorE,thevolumeoftheinjectedtracerbankwas10%ofthetotalfracturevolumeofthesystem.Fortherangeofconditionsexamined,Fig.4suggeststhatthetransittimeisnotgreatlysensitivetotheRornvalues.Inpar-ticular,wesee,atmost,afour-foldvariationindimensionlesstransittimes.TheseresultsindicatethattracertransittimeswillnothelpmuchindeterminingRornvaluesinfieldapplications.Withincreasingnvalues,thegreatestvariationsoccurwhenR51~fracturesinthexdirectionhavethesameconductivityasthoseintheydirection!.ThesmallestvariationsoccurwhenRisverylargeorwhenRisnearzero.Incidentally,underourconditions,thedimensionlesstransittimeisunitywhenn10,oursimulationsindicatedthatvirtu-allynoflowoccursthroughmostofthex-directionfractures.20Inthesecases,mostflowoccursthroughthemostdirectfractureorthroughfracturesclosetothemostdirectfracture.20Ofcourse,thesearetheconditionswhereageltreatmentisexpectedtoworkbest.WhenR51~allfractureshavethesameconductivity!,ourstudiesrevealedthattheflowrateintheleastdirectfractureisabout20%ofthatinthemostdirectfracture.20@Theleastdirectfractureisdefinedasthefracturepathway~s!thatfollowstheouterboundaryofthefracturepattern.#Thus,thesweepefficiencyisstillreasonablygood,andwesuspectthatageltreatmentmaynotprovidemuchbenefit.Fig.5wasgeneratedusingSimulatorC.Asacheckfortheseresults,simulationswerealsoperformedusingSimulatorE.Thisprogramcalculatedthetracerconcentrationsthatwereproducedafterinjectingatracerbankequivalentto10%ofthetotalfracturevolume.Fig.6wasgeneratedusingSimulatorE.Thisfigureplotstheproducedtracerconcentrationwhenn511forRvaluesrangingfrom0.001to1,000.Inagreementwiththepreviousresultsandconclusions,Fig.6demonstratesthat~1!thetracertransittime~asdeterminedbytracerbreakthrough!wasnotsensitivetoRvalue,~2!producedtracerconcentrationswerelow~lessthan10%oftheinjectedvalues!whenR10.Theseconclusionsweresupportedbyresultsusingbothsimulators.20272R.S.SerightandR.L.Lee:NaturallyFracturedReservoirsEffectofPluggingtheMostDirectFractureIdeally,ageltreatmentshouldplugthemostdirectfracturewith-outenteringordamagingthesecondaryfractures.Ifthisgelplace-mentcouldbeachieved,howwouldsweepefficiencybeaffected?Morespecifically,howrapidlywouldawatertracertravelbe-tweenaninjectorandaproducerafterversusbeforeageltreat-ment?ThisquestionisaddressedinFig.7forRvaluesrangingfrom1to1,000andfornvaluesrangingfrom3to101.~Fig.7wasgeneratedusingSimulatorC.!Theyaxisplotstheratioofbreakthroughtimes,i.e.,thetransittimeforatracerafterthemostdirectfracturewaspluggeddividedbythetracertransittimebe-forethemostdirectfracturewasplugged.Fig.7indicatesthatgeltreatmentshavethegreatestpotentialforreservoirswithhighRvaluesandlowtointermediatenval-ues.Geltreatmentsarenotexpectedtoprovidemuchsweepim-provementwhenR10!.Whyshouldthebreakthrough-timeratiobesensitivetothespacingofy-directionfracturesbutnotx-directionfractures?They-directionfracturesprovidepathwaysforaninjectedtracertobedrainedawayfromthecentralx-directionfracture.Thus,asthespacingbetweeny-directionfracturesdecreases,moreopportuni-tiesexistfortracerdiversionfromthecentralx-directionfracture,andthetransittimeincreases.Incontrast,thetracerbreakthroughtimeisinsensitivetothespacingbetweenx-directionfractures.AthighRvalues,flowinthexdirectionisdominantthroughthecentralx-directionfrac-ture.Sincethisfractureprovidesthemostconductivepathwaythroughthepattern,itdeterminesthefastesttransittime.Theotherx-directionfracturesplayamuchlesssignificantrole.ArealGelFrontProfilesHowwillageldistributeinafracturesystemduringageltreat-ment?Inaddressingthisquestion,wenotethatduringgelinjec-tion,thepressuredropinthefracturesystemisgreatestacrosstheviscousgelbank.ForthefieldapplicationsdiscussedinRefs.1,3,and4,aformedgel~ratherthanafluidgelantsolution!wasex-trudedthroughthefracturesduringmostoftheplacementprocess.Thisgelwastypically1,000to100,000timesmoreviscousthanwater.24,25Therefore,inthevicinityofthegelbank,thepressuredifferencesinpartsofthefracturesystemthatdonotcontaingel~i.e.,whereonlywaterorhydrocarbonflows!arenegligiblecom-paredtothepressuredropsinthefracturesthatcontaingel.Thus,weassumethatthepressuredropisthesamefromtheinjectionwelltoanypointatthegelfront.Inouranalysis,weassumethatgelonlyflowsthroughthefracturenetwork.Thisassumptionisconsistentwithexperimentalobservations
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