An Improved SAGD analytical Simulator：Circular Steam Chambe

An Improved SAGD analytical Simulator：Circular Steam Chamber Geometry

JournalofPetroleumScienceandEngineering82-83(2012)27–37

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JournalofPetroleumScienceandEngineering

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AnimprovedSAGDanalyticalsimulator:Circularsteamchambergeometry

AliAzad?,RickJ.Chalaturnyk

DepartmentofCivilEngineering,UniversityofAlberta,Edmonton,AB,CanadaT6G-2W2

articleinfoabstract

AnelegantanalyticalmodelfortheSteamAssistedGravityDrainage(SAGD)processwas?rstlyproposedbyButlerandhiscolleaguesforoilsandsreservoirsinCanada.Someyearslater,ReisproposedtwoadditionalanalyticallinearandradialgeometrymodelsthatwereabletomimictheSAGDprocesssatisfactorily.Sincethen,othermathematicalmodelshavebeendevelopedallwithsimilarapproachesconsideringthatsteamchamberhasreachedthecaprock.Thisassumptioncausesthemodeltopredictaconstantoilproductionrate,whichisnotcloselythecaseinreality.

Toovercomethisshortcomingforpracticalhistorymatchingpurposes,thecurrentstudymodi?estheButler/ReismodeltosimulatetheSAGDprocessfromthebeginningofthesteamchambergrowth.Thestudyoffersacirculargeometryformulationusingadiscretemethodofanalysis,calledthemethodofslices,tosolvetheanalyticalequations.TheproposedgeometryandformulationshowbettercapabilitytoreproducetheSAGDprocessanalytically.

?2012ElsevierB.V.Allrightsreserved.

Articlehistory:

Received27July2011Accepted3January2012

Availableonline15January2012Keywords:

analyticalmodelSAGDoil–sand

circulargeometrysimulator

1.Introduction

SteamAssistedGravityDrainage(SAGD)isathermalrecoveryprocessdevelopedinearly80'sforCanadianoilsandreservoirs.Theprocessincludesapairofhorizontalboreholesdrilledoneontopoftheotherwithsomeverticalspacingnearthebottomofthereservoir.Steamisinjectedthroughthetopborehole,calledtheinjector,andthelowerborehole,theproducer,isresponsibleofcollectingoil.SAGDisusuallydeployedinthereservoirswhentheoilsandforma-tionliesindepthanditisnotminable.Con?gurationofaSAGDpro-cessisillustratedinFig.1.ThefundamentalSAGDconceptisthattheinjectedsteamtransfersinternalheatintothereservoirandthesteamisthentransformedtoliquidphase.Theheatlosswillmobilizethebi-tumenlockedintheoilsandstructurebydecreasingtheviscosity,andthendrainstotheproducerundergravity.Thisprocessgenerallyhappensinaregionin?uencedbytheinjectedsteamaroundthein-jectoratthesteamtemperature.TheaffectedregioniscalledthesteamchamberanditisusedtodemonstratetheSAGDprogressin-sidethereservoir.Inthepreheatingperiodatthebeginningoftheprocess,steamiscirculatedinbothwellstoestablishthecommunica-tionbetweenthetwoboreholesandtoincreasetheinjectivity.Ittakesseveralmonthsuntiltheinjectorisopenedforinjectinghighpressureandhightemperaturesteamintothereservoirandthebot-tomboreholeisconvertedintoaproductionwell.Steaminjectioncausesthesteamchambertogrowanditgraduallyoccupieslarger

?Correspondingauthor.Tel.:+1780492-3861.

E-mailaddresses:ali.azad@ualberta.ca(A.Azad),rjchalaturnyk@ualberta.ca(R.J.

Chalaturnyk).

0920-4105/$–seefrontmatter?2012ElsevierB.V.Allrightsreserved.doi:

10.1016/j.petrol.2012.01.003

regionsofthereservoir.ThephysicsoftheSAGDprocessappeartobesimpleandthepredominantproductionmechanismisthermalheattransfer.However,othermechanismsarealsoinvolvedinSAGDprocess.Asanexample,geomechanicalreactionsofthereser-voirsystem(reservoir,caprock,overandunderburden)areshowntooccursimultaneously(Chalaturnyk,1996).

Butleretal.(1980,1981)werethe?rstteamtoworkonSAGD.Focusingonsmallscaleexperimentaltests,theyinvestigatedthedevelopmentofSAGDforindustrialpurposes.Moreover,theypro-posedananalyticalmodel,commonlycalled‘Butlermodel’,thatwasabletogenerallypredicttheprocess.Butlermodelwasfoundedontwosimpletheories:(a)onedimensionalheattransfer(thermal)thatsolvestheheatdistributionforamovingfront,and(b)Darcy'slaw(?ow)tocalculatethepotentialandmagnitudeofthe?owofoil.Usingthesetwotheoriesandanon-linearassumptionforvaria-tionofviscosityinfrontofthesteamchamber,ButlermodelisthemostelegantdrainagemodelforSAGD.Themodelhowever,hadsomeshortcomings.Intheoriginalmodel,thesteamchamberwasnotconstrainedforpassingacrosstheproducer.ThisproblemwaslatersolvedinTANDRAINmodel(ButlerandStephens,1981)byconsideringareductionfactortooilproduction.Anotherconcernwasaboutthegrowthofthesteamchamberbeforetouchingthetopofthereservoir(caprock).Butlermodelassumesthatthepro-ductioninitiateswhenthesteamchambertouchesthecaprockandthelateralgrowthisstarted.Therefore,themodelwasregularlyrevisedandmorefeaturesoftheprocesswereappendedtothemodelinseparatetheories.TherisingsteamchambermodelandamodeltoconsidertheeffectofboundarieswereproposedlaterbyButlertocapturemoreessentialphenomenaoftheSAGDprocess(Butler,1997).

28A.Azad,R.J.Chalaturnyk/JournalofPetroleumScienceandEngineering82-83(2012)27–37

Fig.1.BasicelementsofaSAGD

project.

ExperimentalworksbyButleretal.(1980,1981),ChungandButler(1988),andtheresultsoftheUndergroundTestFacility(UTF),PhaseA(e.g.,reportedbyEdmundsetal.,1994;Chalaturnyk,1996)showedthatthegrowthofthesteamchamberhasdifferentstages.Whenthecommunicationbetweentheinjectorandtheproducerisestablished,thesteamchamberrisesuptotouchthereservoircaprock,andthenbeginstogrowlaterally.

AlthoughButlertheoryassumesthatthesteamchambergrowslaterallyonly,itisstillthefoundationofallothertheoreticalmodels.BasedonthefundamentalsofButlertheory,Reis(1992)proposedanewmodeltosupportthedrainagemechanismofSAGDbycon-strainingtheshapeofthesteamchambertoalineargeometryandfoundsimilarresultstoButlermodel.HeindicatedthathismodelisafunctionofButlertheoryandtheycanbetransformedtoeachotherbyaconstantmultiplier.Eq.(1)showsthemathematicalformoftheButlermodelforoilproductionrate.Eq.(1)canbecom-paredtotheReistheoryinEq.(2)toshowthatbothmodelsevenwithdifferentsteamchambergeometrybutwiththesameapproachobtainsimilarresults.Thetwomodelspredictaconstantvaluefortheoilproductionandadditionalmodi?cationsareneededtobeemployedtosimulatethetruthoftheprocess.s?????????????????????????????q?2L

2kgαρ?ΔSoH

e1T

oss??????????????????????????q?2Lkgαρ?ΔSoH

2amμ:

e2T

os

qoilproductionrateLlengthofboreholeskpermeability

αthermaldiffusivityofthereservoirρoildensity?porosity

ΔSo(initial?residual)oilsaturation

μosdynamicoilviscosityatsteamtemperatureHreservoirheight

mcoef?cientofviscosityacoef?cientofvelocity

OtherresearchesonanalyticalmodelingofSAGDincludesReis(1993),Akin(2005),Liang(2005),Nukhaevetal.(2006),andAzadandChalaturnyk(2010)allofwhichstudieddifferentaspectsofsteamingthehorizontalwells.However,thefundamentalassumptioninallcasesistheconceptintroducedinButlertheorywithone-waysteamchambergrowth.Asanexample,AzadandChalaturnyk(2010)proposedanimprovedmodelforSAGDbyconsideringgeomechanicsinthetheory.TheytooktheReismodelwithlineargeometryandusedanumericalapproachtosolvetheequationstocountforthegrad-ualchangesoftheoilsaturationattheedgeofthesteamchamber.Al-thoughtheirmodelwassuccessfultocaptureessentialfeaturesoftheSAGDphysics,itneedstobedevelopedtorealisticallymimicthediffer-entstagesofthesteamchamberexpansion.

TheworkpresentedhereimprovestheanalyticalButler/Reisdrainagesolutionbyremovingthepreviousgeometricalassumptions.Themodelbene?tsfromadiscretemethodofanalysis,calledthemethodofslices,for?owsimulationinSAGDandusesthegrowingcircularsteamchambergeometry.Thecirculargeometrycanmodelthewholeprocesssincethesteamchamberappears,graduallyrisestotouchthecaprock,andthenitexpandslaterallytocoverlargepartsofthereservoir.2.Methodofslices

WhenadditionalfeaturesoftheSAGDprocessarecombinedtotheReisorButlermodels,theintegralsarenotusuallysolvableinclosedform.Hence,anumericalapproachisrequiredforintegration.Awellestablishedtechniqueinmathematicsforsolvinganintegralistodi-videtheareaundertheintegralfunctionintolimitedslices(e.g.rect-anglesortrapezoids).Itisofinteresttode?netheequationvariablesandtheintegrallimitssothattheslicesunderthefunctiongetaphys-icalmeaningtoo.ThisideawasadaptedinthemodelproposedbyAzadandChalaturnyk(2010),calledthemethodofslices.Fig.2showstheframeworkofthemethodofslicesproposedforlinearge-ometryofthesteamchamber.Eachsliceinadvanceofthesteamchamberrepresentsaregionofinterestfornumericalcalculation.Theresultsofcalculationineachslicearethenaddeduptothoseofotherslicestoformanumericalsolution.Itshouldbenotedthattheequationsarederivedinacontinuummediumandarenotdividedintoslicesfromthebeginning.Therefore,slicesaretheresultofmath-ematicalsolutionratherthanphysicalseparation.

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