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Enhanced co2 storage in confined geologic formations

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Title:
Enhanced co2 storage in confined geologic formations
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English
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Okwen, Roland
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Subjects / Keywords:
Greenhouse gas
Horizontal wells
Carbon Capture and Storage (CCS)
Global climate change
Deep saline aquifer
Dissertations, Academic -- Civil and Environmental Eng -- Doctoral -- USF   ( lcsh )
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non-fiction   ( marcgt )

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Abstract:
ABSTRACT: Many geoscientists endorse Carbon Capture and Storage (CCS) as a potential strategy for mitigating emissions of greenhouse gases. Deep saline aquifers have been reported to have larger CO2 storage capacity than other formation types because of their availability worldwide and less competitive usage. This work proposes an analytical model for screening potential CO2 storage sites and investigates injection strategies that can be employed to enhance CO2 storage. The analytical model provides of estimates CO2 storage efficiency, formation pressure profiles, and CO2-brine interface location. The results from the analytical model were compared to those from a sophisticated and reliable numerical model (TOUGH2). The models showed excellent agreement when input conditions applied in both were similar. Results from sensitivity studies indicate that the agreement between the analytical model and TOUGH2 strongly depends on irreducible brine saturation, gravity and on the relationship between relative permeability and brine saturation. A series of numerical experiments have been conducted to study the pros and cons of different injection strategies for CO2 storage in confined saline aquifers. Vertical, horizontal, and joint vertical and horizontal injection wells were considered. Simulations results show that horizontal wells could be utilized to improve CO2 storage capacity and efficiency in confined aquifers under pressure-limited conditions with relative permeability ratios greater than or equal to 0:01. In addition, joint wells are more efficient than single vertical wells and less efficient than single horizontal wells for CO2 storage in anisotropic aquifers.
Thesis:
Dissertation (Ph.D.)--University of South Florida, 2009.
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Includes bibliographical references.
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by Roland Okwen.
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ABSTRACT: Many geoscientists endorse Carbon Capture and Storage (CCS) as a potential strategy for mitigating emissions of greenhouse gases. Deep saline aquifers have been reported to have larger CO2 storage capacity than other formation types because of their availability worldwide and less competitive usage. This work proposes an analytical model for screening potential CO2 storage sites and investigates injection strategies that can be employed to enhance CO2 storage. The analytical model provides of estimates CO2 storage efficiency, formation pressure profiles, and CO2-brine interface location. The results from the analytical model were compared to those from a sophisticated and reliable numerical model (TOUGH2). The models showed excellent agreement when input conditions applied in both were similar. Results from sensitivity studies indicate that the agreement between the analytical model and TOUGH2 strongly depends on irreducible brine saturation, gravity and on the relationship between relative permeability and brine saturation. A series of numerical experiments have been conducted to study the pros and cons of different injection strategies for CO2 storage in confined saline aquifers. Vertical, horizontal, and joint vertical and horizontal injection wells were considered. Simulations results show that horizontal wells could be utilized to improve CO2 storage capacity and efficiency in confined aquifers under pressure-limited conditions with relative permeability ratios greater than or equal to 0:01. In addition, joint wells are more efficient than single vertical wells and less efficient than single horizontal wells for CO2 storage in anisotropic aquifers.
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EnhancedCO 2 StorageinConnedGeologicFormations by RolandTenjohOkwen Adissertationsubmittedinpartialfulllment oftherequirementsforthedegreeof DoctorofPhilosophy Departmentof CivilandEnvironmentalEngineering Collegeof Engineering UniversityofSouthFlorida MajorProfessor: JereyA.Cunningham,Ph.D. AlexanderDomijan,Jr,Ph.D. MarkRoss,Ph.D. MarkStewart,Ph.D. MayaTrotz,Ph.D. DateofApproval: September30,2009 Keywords:Greenhousegas,Horizontalwells,CarbonCaptureandStorageCCS,Global climatechange,Deepsalineaquifer c Copyright 2009 ,RolandTenjohOkwen

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Dedication Tomygrandmother, ComfortEngwari, forshowingmethevalue ofeducationasakid. Andtomyparents, JamesandPaulineTenjoh fortheirencouragementsand commitmentineducatingtheirchildren.

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Acknowledgements Iwishtothankmycommitteemembersfortheirtimeandcontributionsonthedevelopmentandcompletionofthisdissertation.ManythankstoDr.AlexanderShapiro,at theTechnicalUniversityofDenmarkforencouragingmetopursueaPh.D.Ialsowish toexpressmyimmeasurablegratitudetoDr.JeffreyCunningham,mymajoradvisor,for givingmeagreatdealoffreedomtoexploredifferentideasandprovidingconstructive suggestionsandguidanceinthisnewandchallengingareaofresearch.Iamalsothankful toDr.MonicaGrayforintroducingmetoDr.Cunningham,whenshewasstillagraduate student,forwithoutherhelpImayhavemissedthislife-changingopportunity.Mysincere gratitudealsogoestoProfessorMarkStewartforexposingmetoindustryrelatedresearch. IsincerelyappreciateProfessorMarkRossfortreatingmeasoneofhisgraduatestudents. ThankstoDr.JanNordbotten,attheUniversityofBergen,Norway,forhismanyhelpful discussionsonanalyticalmodelingofCO 2 storageindeepsalineaquifers. ItwouldbeunfairnottoacknowledgetheunendingassistancefromMr.BernardBatson Mr.B.Mr.Biseverything,hisendlessassistanceinhelpingmeovercomeacademic, social,andnancialhurdlesishighlyappreciated. Thegreatestsocialsupportmechanismonecanhaveis`people'. Igivecredittomywife,BerylForewah,myboysOkwenOkwen,TangohOkwen,andTebit Okwenfortheirmoralsupportandunderstanding.ThesocialsupportfromtheCamerooniancommunityinTampaBayisalsogreatlyappreciated. ThismaterialisbasedonworksupportedbytheFloridaEnergySystemsConsortium FESC.FinancialsupporthasbeenprovidedtoRolandOkwenbytheAlfredP.Sloan FoundationviatheNationalActionCouncilforMinoritiesinEngineeringNACME,NationalScienceFoundationNSFS-STEMgrantsDUE#0807023&0324117,andDiverseStudentSuccessDSSscholarshipattheUniversityofSouthFlorida.Anyopinions, ndings,conclusions,orrecommendationsexpressedinthisdissertationarethoseofthe authoranddonotnecessarilyreecttheviewsofFESC,NSF,USF,ortheAlfredP.Sloan Foundation.

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TableofContents ListofTables......................................v ListofFigures......................................vii Abstract.........................................ix Chapter1Introduction................................1 1.1GeologicSequestrationofCO 2 .......................1 1.2Motivation...................................3 1.3Objectives...................................4 1.4Overview...................................5 1.5ReferencesCited...............................6 Chapter2Background................................10 2.1ConceptualModel...............................11 2.1.1StorageEfciency..........................11 2.1.2FormationAnisotropy........................13 2.1.3TrappingMechanisms........................13 2.1.3.1PhysicalTrapping.....................14 2.1.3.2ResidualTrapping.....................14 2.1.3.3SolubilityTrapping....................15 2.1.3.4MineralTrapping.....................16 2.2VerticalvsHorizontalWells.........................16 2.3MultiphaseFlowEquationsTOUGH2...................17 2.3.1DevelopmentofFlowEquations...................17 2.3.2MassTransportandMassBalance..................18 2.4NumericalMethods..............................20 2.5NumericalErrors...............................22 2.6MassBalance.................................23 i

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2.7ReferencesCited...............................24 Chapter3AnalyticalSolutionforEstimatingCO 2 StorageEfciency 2 ......28 3.1Abstract....................................28 3.2Introduction..................................29 3.3ModelDevelopment.............................29 3.3.1ConceptualModel..........................29 3.3.2MathematicalModel.........................32 3.4Results.....................................34 3.5Discussion...................................36 3.6SummaryandConclusions..........................37 3.7ReferencesCited...............................38 Chapter4AnalyticalModelforScreeningPotentialCO 2 Repositories.......41 4.1Abstract....................................41 4.2Introduction..................................41 4.3ModelDevelopment.............................43 4.3.1ConceptualModel..........................43 4.3.2CurrentFormofAnalyticalModel..................44 4.3.3DevelopmentofBoundaryConditiontoPredictFormationPressure46 4.3.4BrineSaturationProle.......................47 4.4TestCasesforComparisontoTOUGH 2 ...................48 4.5ResultsandDiscussions............................51 4.5.1ValidationofAnalyticalModel....................51 4.5.2SensitivityAnalysis.........................53 4.5.2.1Effectof P cap .......................54 4.5.2.2Effectof k r ........................54 4.5.2.3GravityorBuoyancyEffect................54 4.5.2.4CO 2 PlumeExtent, r max .................57 4.5.2.5StorageEfciency, s ...................57 4.5.3Summary...............................59 4.6Conclusions..................................61 4.7ReferencesCited...............................62 2 Okwen,R.T.,Stewart,M.,andCunningham,J.A.,, AcceptedonAugust27,2009:International JournalofGreenhouseGasControl ii

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Chapter5StorageofCO 2 inIsotropicAquifersviaHorizontalInjectionWells..64 5.1Abstract....................................64 5.2Introduction..................................64 5.3Approach...................................67 5.4ResultsandDiscussions............................70 5.4.1AnalysisoftheMetrics........................70 5.4.2SensitivityAnalysis.........................71 5.5Conclusions..................................77 5.6ReferencesCited...............................78 Chapter6StorageofCO 2 inAnisotropicAquifersviaHorizontalWells......82 6.1Abstract....................................82 6.2Introduction..................................82 6.3Approach...................................83 6.4ResultsandDiscussions............................87 6.4.1AnalysisoftheMetrics........................87 6.4.2SensitivityAnalysis.........................90 6.4.3EmpiricalRelationshipsBetween P Q ,and k vh .........93 6.5Conclusions..................................98 6.6ReferencesCited...............................98 Chapter7StorageofCO 2 inAnisotropicAquifersviaJointInjectionWells....101 7.1Abstract....................................101 7.2Introduction..................................101 7.3Approach...................................103 7.3.1CO 2 DistributionBetweenInjectionWellSegments.........103 7.3.2DescriptionofSimulations......................104 7.4ResultsandDiscussion............................106 7.4.1AnalysisoftheMetrics........................107 7.4.2SensitivityAnalysis.........................109 7.4.2.1Injectivity.........................109 7.4.2.2ComparisonofWellPerformances............109 7.5Conclusions..................................112 7.6ReferencesCited...............................113 iii

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Chapter8TemporalVariationsinNear-wellborePressuresDuringCO 2 Injection.115 8.1Abstract....................................115 8.2Introduction..................................116 8.3Background..................................117 8.4Approach...................................118 8.5ResultsandDiscussions............................120 8.5.1DensityEffect............................120 8.5.2EffectofVerticalPermeability....................121 8.5.3EffectofCO 2 MassInjectionRate Q ...............121 8.5.4Mechanism..............................127 8.6Conclusions..................................128 8.7ReferencesCited...............................129 Chapter9Conclusions................................132 Nomenclature......................................135 Appendices.......................................139 AppendixA:ValidationofGridMesh.......................140 AppendixB:DerivationofFormationPressureEquations.............141 AppendixC:FortranCodeforAnalyticalModel..................148 AppendixD:EmpiricalRelationshipsBetween P Q ,and k vh .........169 AbouttheAuthor.................................EndPage iv

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ListofTables Table1ListofcurrentCO 2 storageprojects......................2 Table2DensityandviscosityofCO 2 andbrineincoldandwarmbasins......13 Table3CO 2 massbalanceontestproblem 3 ofthecodeintercomparisonproject..24 Table4Conditionsforarealisticinjectionscenario..................36 Table5Aquiferpropertiesemployedinallsimulations................48 Table6InputparametersandconditionsusedinTOUGH2simulations.......50 Table7EstimatesofCO 2 storageefcienciesfromanalyticalmodelandTOUGH2.52 Table8Estimatesof r max fromanalyticalmodelandTOUGH 2 simulations.....57 Table9Comparisonof s underdifferentphysicalconditions............58 Table10Relativedifferencein P well t ataquiferbottom...............59 Table11Hydrogeologicandnumericalparametersappliedinallsimulations....68 Table12Variationsof P w M CO 2 ;aq ,and s with Q at t equalto50years.......71 Table13Performancesofsimulationsusingverticalandhorizontalwells......71 Table14Comparisonofpressurespredicted.....................75 Table15 Q max M CO 2 ;aq ,and s atdifferentvaluesof L w ...............76 Table16Matrixofsimulationsthatwillbeconductedinphase3...........84 Table17Inputparametersappliedinallsimulationschapter6...........86 Table18Variationsof P w and M CO 2 ;aq with k vh at t equalto 50 years........91 Table19Variationsof and s with k vh at t equalto 50 years............93 Table20Valuesof P barfordifferentvaluesof k vh and L w at 50 years.....93 v

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Table21Valuesof P 0 fordifferentvaluesof k vh and L w at 50 years.........94 Table22ValuesofcoefcientsA andB asfunctionsof .............95 Table23Valuesof P fordifferentvaluesof k vh andwelllengthat 50 years....96 Table24Simulationmatrix Q = 200 kg/s......................105 Table25Inputconditionsappliedinallsimulationschapter7............106 Table26ComparisonofperformancesofCO 2 injectionstrategies..........112 Table27Inputparametersappliedinallsimulationschapter8...........119 Table28Sensitivityof P w onhydrogeologicparameters Q =100 kg=s ......126 Table29 P w t barasafunctionofpermeabilityreduction k vh =1 : 0 ......126 Table30 P w t barasafunctionofpermeabilityreduction k vh =0 : 001 ....127 Table31Comparisonof P w barbetween 10 and 20 layer 2 Dmeshgrids......140 Table32Comparisonof P w barbetween 10 and 20 layer 3 Dmeshgrids......140 Table33Valuesof A for equalto 1 40 ......................169 Table34Valuesof B for equalto 1 40 ......................169 vi

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ListofFigures Figure1ConceptualmodeladaptedfromNordbottenetal..........12 Figure2TimescalesofCO 2 trappingmechanismsadaptedfromIPCC...15 Figure3SchematicrepresentationofCO 2 injectionintoaconnedaquifer.....31 Figure4Storageefciency vsmobilityratio ..................35 Figure5Storageefciency vs.gravityfactor )]TJ/F40 11.9552 Tf 7.314 0 Td [(.................35 Figure6SchematicrepresentationofCO 2 -brineinterfaceduringinjection......44 Figure7ResultsobtainedfromanalyticalmodelandSim1A............52 Figure8Comparisonofpressureprolesfromanalyticalmodel...........53 Figure9Comparisonof P r;t and S w r;t proles.................55 Figure10Schematicrepresentationofmeshgrid...................68 Figure11SchematicrepresentationofCO 2 injectionviaahorizontalwell......69 Figure12 S g spatialdistributionsafter 50 yearschapter5..............72 Figure13 P spatialdistributionsafter 50 years....................73 Figure14AdditionalmassofCO 2 thatcanbestored.................77 Figure15 S g spatialdistributionsafter 50 yearschapter6..............88 Figure16 X CO 2 spatialdistributionsafter 50 years..................89 Figure17Graphsof , ,and against .....................92 Figure18 Q max asafunctionof L w and k vh for P aniso equalto 200 bar......96 Figure19 Q max asafunctionof k vh for P aniso equalto 200 bar..........97 Figure20A 2 DschematicrepresentationofCO 2 injection..............102 vii

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Figure21Gassaturationdistribution t =50 yearschapter7...........108 Figure22Effectsof I vh ona P w ,b M CO 2 ;aq ,andc s ..............110 Figure23 atbottomofwellboreasafunctionof I vh ................111 Figure24Effectofdensityonnear-wellborepressures................122 Figure25Effectof k v onnear-wellborepressures...................123 Figure26Gassaturationdistributionovertimeat k vh equalto 0 : 01 .........124 Figure27Effectof Q perunitwelllengthonnear-wellborepressures........125 Figure28ProposedmechanismdepictingmajorforcesactingonaCO 2 bubble...128 viii

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EnhancedCO 2 StorageinConnedGeologicFormations RolandTenjohOkwen ABSTRACT ManygeoscientistsendorseCarbonCaptureandStorageCCSasapotentialstrategy formitigatingemissionsofgreenhousegases.Deepsalineaquifershavebeenreportedto havelargerCO 2 storagecapacitythanotherformationtypesbecauseoftheiravailability worldwideandlesscompetitiveusage.ThisworkproposesananalyticalmodelforscreeningpotentialCO 2 storagesitesandinvestigatesinjectionstrategiesthatcanbeemployedto enhanceCO 2 storage. TheanalyticalmodelprovidesofestimatesCO 2 storageefciency,formationpressure proles,andCO 2 brineinterfacelocation.Theresultsfromtheanalyticalmodelwere comparedtothosefromasophisticatedandreliablenumericalmodelTOUGH 2 .The modelsshowedexcellentagreementwheninputconditionsappliedinbothweresimilar. Resultsfromsensitivitystudiesindicatethattheagreementbetweentheanalyticalmodel andTOUGH2stronglydependsonirreduciblebrinesaturation,gravityandontherelationshipbetweenrelativepermeabilityandbrinesaturation. Aseriesofnumericalexperimentshavebeenconductedtostudytheprosandconsof differentinjectionstrategiesforCO 2 storageinconnedsalineaquifers.Vertical,horizontal,andjointverticalandhorizontalinjectionwellswereconsidered.Simulationsresults showthathorizontalwellscouldbeutilizedtoimproveCO 2 storagecapacityandefciencyinconnedaquifersunderpressure-limitedconditionswithrelativepermeability ratiosgreaterthanorequalto 0 : 01 .Inaddition,jointwellsaremoreefcientthansingle verticalwellsandlessefcientthansinglehorizontalwellsforCO 2 storageinanisotropic aquifers. ix

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Chapter1 Introduction ThisdissertationaddressesissuesrelatedtostorageofcarbondioxideCO 2 indeep salineaquifers.Specialemphasesaregivento 1 analyticalmethodsforscreeningpotentialstoragesitesand 2 injectionstrategiestoenhanceCO 2 storage.Theserequire understandingofthephysicsofuidowinbrine-saturatedporousformationsandthebehaviorofinjectedCO 2 .IssuesconcerningCO 2 -inducedgeochemicalandgeomechanical effectsarebeyondthescopeofthiswork. ThischapterbeginswithabriefoverviewofgeologicsequestrationofCO 2 ,followedby descriptionsofthemotivationandresultingobjectivesofthiswork.Thechapterendswith asectiononthescopeandoutlineofthisdissertation. 1.1GeologicSequestrationofCO 2 GeologicsequestrationofCO 2 canbedenedastheisolationofCO 2 fromtheatmosphereforlongperiodsoftimeuptocenturiesormillenniaviainjectionintodeepconnedformationsBachu,2008.CO 2 isgenerallyseparatedfromanemissionstream,captured,andtransportedfromlargepointsourcestostoragesitespriortoinjection.The combinationoftheseproceduresCO 2 separation,capture,transportation,andinjectionis generallyreferredtoasCarbonCaptureandStorageCCS.CCShasbeenrecommended asamethodofreducinganthropogenicCO 2 emissionsandtherebymitigatingglobalclimatechangeKoideetal.,1992;Bachu,2000;Holloway,2001;Bruantetal.,2002;EnnisKingandPaterson,2002;PruessandGarc a,2002;BachuandAdams,2003;Whiteetal., 2003;IEA,2004;IPCC,2005.Examplesoflargepointsourcesincludefossil-fueled powerpowerplants,cementfactories,andreneriesIPCC,2005;Bachu,2008.Geologic analogs,likenaturalCO 2 reservoirs,serveasproofoftheviabilityofdeepgeologicformationstosequesterlargequantitiesofCO 2 oververylongperiodsBensonetal.,2000. CandidateformationsforCO 2 storageincludesalineaquifers,depletedoilreservoirs,and 1

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naturalgasreservoirsFalkowskietal.,2000;IPCC,2005;Kristianetal.,2005;NordbottenandCelia,2006;PruessandSpycher,2006.Deepconnedsalineaquifershavebeen proposedtohavethelargestcapacitytosequesterCO 2 thantheothergeologicformations becauseoftheiravailabilityworldwideandproximitytolocalizedlargepointsourceslike fossil-fueledpowerplants,cementfactoriesandoilreneriesIPCC,2005.Asaresult,the emergenceofCCShasmadethelocationofnewfossil-fueledpowerplantstobemorecriticalthanbeforeStanislaw,2008.ExamplesofcurrentCO 2 captureandstorageprojects includetheSleipnerprojectintheNorwegiansectoroftheNorthSea,theWeyburneldin Canada,theIn-SalahprojectinAlgeriaIPCC,2005,andtheSnhvitprojectinNorway Forward,2008a.Table1presentslistofcurrentfullscaleandpilotCO 2 storageprojects. Table1: ListofcurrentCO 2 storageprojects.FullscaleandpilotIPCC,2005; Forward,2008a;b;NETL,2008;Forward,2009;EstublierandLackner,2009. ProjectDepthRateWellFormationStart orcompanyLocationmMtons/yeartypetypedate SleipnerNorway8001.0horizontalsandstone1996 In-SalahAlgeria18701.2horizontalsandstone2004 Sn hvitNorway2600 z 0.7sandstone2007 KetzinGermany6000.03sandstone2008 Westunmineable2009 Consol'sVirginia3660.01horizontalcoalseamsorlater z beneathseabed Candidateformationsaregenerallyrequiredtosatisfythefollowingcriteria: 1.theformationmustbepermeable; 2.theformationmustbelocatedatadepthatwhichCO 2 issupercriticaltoenhance storativityandabateviscousowinstabilitiesviscousngeringGarc a,2003;Pruess etal.,2004; 3.theformationmustbeseparatedfromsurfaceandpotableundergroundwatersupplies byalow-permeabilityconningunit; 4.theformationshouldhaveadequatecapacitytostoresignicantquantitiesofCO 2 with minimalincreaseinpressure; 2

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5.themaximumpressurewithintheformationshouldnotexceed 90 %ofitslithostatic fracturingpressureBachuandAdams,2003toavoiddisintegrationoftheconning layers;and 6.theinjectedCO 2 plumemustnotextendtoanunacceptabledistance. AformationmaybeconsideredsuitableforCO 2 storageifithassufcientcapacityto accommodatesignicantlylargevolumesofCO 2 foraverylongperiodoftimemillennia tomillionsofyears.Candidaterepositoriesatdepthsgreaterthan 738 maregenerally preferablesincetheconditionsatsuchdepthsareabovethesupercriticaltemperatureand pressureofCO 2 i.e. 31 : 1 o Cand 73 : 8 bar,respectivelyBachu,2008.CO 2 issignicantlydenserundersupercriticalconditions > 800 kg/m 3 thanatstandardconditions 1 : 872 kg/m 3 Bachu,2003.Therefore,anincreaseinthemassofCO 2 storedperunit volumeofporousmediumisachievedundersupercriticalconditions.Theriskofcontaminationofpotablewateraquiferslocatedatshallowerdepthsisreducedsolongastheupper conninglayeroftheformationcaprockorsealisintact. 1.2Motivation Manygeoscientistsagreethattheadverseimpactsofanthropogenicactivitiesonglobal climatechangecanbeavoidedonlyifnetannualCO 2 emissionsaresignicantlyreduced morethan 50 %withinthiscenturyIPCC,2005;AGU,2007.CCShasbeenreportedto beaneffectivemethodofreducingCO 2 emissionsIPCC,2005;IEA,2004;Bruantetal., 2002;Ennis-KingandPaterson,2002;Pruessetal.,2001.ResearchattheElectricPower ResearchInstituteEPRIindicatesthatCO 2 emissionsintheUSelectricitysectorcan bereducedby 45 %throughaggressivedevelopmentanddeploymentofseveraladvanced technologiesbytheyear 2030 EPRI,2007b.Thesetechnologiesincludecarboncapture andstorageCCS,energyefciencyimprovements,renewableenergy,nuclearenergy, advancedcoalgeneration,plug-inhybridelectricvehicles,anddistributedenergyresources EPRI,2007b.Theneedforadvancementisimmediateandmustbeconductedinparallel inordertodeployafullportfolioofthetechnologies.CCSaccountsforabout 40 %of EPRI'sprojectedreductionsinCO 2 emissionintheUSelectricitysector,makingitthe biggestcontributorEPRI,2007b.FailuretosufcientlydemonstratetheviabilityofCCS couldbetheshowstopperforfutureuseofcoalEPRI,2007a.However,CCSdoesnot currentlydemonstratetheviabilitytooffersuchsignicantcontributionforvariousreasons includinglowstorageefciencyvanderMeer,1995;ObiandBlunt,2006;EPRI,2007b. 3

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Storageefciencyisdenedastheratiobetweentheactualinjectedvolumeofauidand themaximumstoragevolumeofarepositoryvanderMeer,1995. InjectionstrategiescurrentlyemployedtosequesterCO 2 insalineaquifersareexpected toachievestorageefcienciesbetween 2 and 6 %vanderMeer,1995;IPCC,2005.A conservativeestimateofglobalstoragecapacityofsalineaquifersisabout 1000 Gigatons GtonsofCO 2 IPCC,2005.Thus,ifweareabletoincreasethestorageefciencyfrom 6 %to 10 %,thiswillmeananadditional 40 billiontonsofCO 2 storagecapacity.This payoffisequivalenttoCO 2 emittedbyfty 1000 -MWcoal-redpowerplantsforaperiod of 60 yearsPruessetal.,2003.Furthermore,theadditionalstoragecapacitywillhelp buymoretimetoachievesignicantadvancesinthedevelopmentanddeploymentofless carbon-intensivetechnologiessuchasrenewableenergy,energyefcienttechnologies,and distributedenergyresources,whichguaranteethesustainabilityoffutureenergysupplies. Thiswillalsoaddmoretimetodevelopandredeveloppopulationcentersurbandesign andhumanconsumptionpatterns. 1.3Objectives Thelong-termgoalofthislineofresearchistodevelopCO 2 sequestrationindeepsaline aquifersasaviabletechnologytomitigateglobalclimatechange.Theoverallobjective ofthisdissertationistodevelopamethodologytomaximizeCO 2 storageindeepsaline aquifersviaimprovedrepositoryselectionandinjectionstrategies.Thecentralhypothesis ofthisprojectisthatacombinationofverticalandhorizontalinjectionwellswillincrease CO 2 storageinmoderatelyanisotropicformations.Therationaleforthisprojectisthat optimalinjectiontechniqueswillallowforefcientutilizationofrepositories,therebyprovidingasignicantavenueforreductionofCO 2 emissionoverlongperiodsoftime. Theoverallobjectiveofthisprojectisaccomplishedthroughachievementofthefour followingspecicgoals: 1.Developandvalidateaneasy-to-useanalyticalmodelforscreeningpotentialCO 2 repositoriesChapters 3 and 4 .Suchamodelcouldserveasascreeningtooltodetermineif candidaterepositoriesareworthfurtherinvestigation.Theworkinghypothesisofthis goalisthattheanalyticalmodelcansuitablydescribetheresponseofdeepconned aquiferstosteadyCO 2 injectionundercertainphysicalconditions. 2.Quantifyeffectsofhorizontalwelllengthonformationpressure,amountofdissolved CO 2 ,andstorageefciencyunderisotropicconditionsChapter 5 .Theworkinghy4

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pothesisofthisgoalisthatutilizationofhorizontalinjectionwellswillincreasethe amountofCO 2 storedperunitareaofaquiferascomparedtoverticalinjectionwells. 3.Quantifyeffectsofhorizontalwelllengthonformationpressure,amountofdissolved CO 2 ,andstorageefciencyunderanisotropicconditionsChapter 6 .Theworking hypothesisofthisgoalisthatthebenetsofutilizinghorizontalinjectionwellswillbe reducedinhighlyanisotropicformations. 4.QuantifytheeffectsofanisotropyratioonCO 2 storageefciency,amountofdissolved CO 2 ,andformationpressurewhenacombinationofhorizontalandverticalinjection wellsisemployedChapter 7 .Theworkinghypothesisofthisgoalisthatacombinationofverticalandhorizontalinjectionwellsismorebenecialthanasingleverticalor horizontalinjectionwellinanisotropicaquifers. Takentogether,thesefourspecicgoalswilladdressissuesrelatedtolocatingpotential repositoriesandwilltestthecentralhypothesisthatacombinationofverticalandhorizontalinjectionwellscanbeutilizedtoincreaseCO 2 storageinmoderatelyanisotropic formations. 1.4Overview Theinvestigationsinthisdissertationaredirectedtowardthephysicalprocessesthat occurduringCO 2 storageinbrine-saturatedaquifers.Consequently,theeffectsofCO 2 inducedgeochemicalreactionsandmechanicalstressarebeyondthescopeofthisstudy. Spatialvariationsintemperaturewithintheformationarealsoassumednegligibleisothermal.ItisalsoimportanttounderscorethatelddataonCO 2 injectioningeologicformationsarealmostunavailableorverydifculttoobtain.Asaresult,predictionsfrom establishednumericalsimulatorsareconsideredreliable.ExamplesofnumericalsimulatorsgenerallyemployedtopredictCO 2 plumeowdynamicsinporousformationsinclude TOUGH2/ECO2N,GEM,FLOTRAN,andEclipse 300 .Theadvantageofutilizinganalyticalornumericalmodelstostudyowdynamicsinporousmediaisthattheycansimulate uidinjectionand/orproductionatsignicantlylowercostsandtimesthaninactualeld operations.Inaddition,analyticalandnumericalformulationscanbecarriedoutmany timeswhileactualeldtestsaretypicallycarriedoutonceCoats,1992.Thenumerical simulatoremployedinthisstudyisTOUGH 2 .ResultsfromtheCodeIntercomparison ProjectPruessetal.,2004showTOUGH 2 toberobustandtohavethecapabilitiesof 5

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simulatingCO 2 storageingeologicformations.Thisissupportedbythegrowinguseof TOUGH 2 byresearcherswithinthecountryandworldwide 1 Thisdissertationiscanbeviewedtoconsistoffourparts.Therstpartconsistsofthis chapterandthenext.Chapter 2 givesanoverviewofpivotalphysicalprocessesthattake placeduringCO 2 storage.Italsoelucidatestheformulationandmethodsofsolvingmathematicalequationsthatdescribetheseprocesses.Thesecondpartconsistsoftwochapters 3 and 4 whichtogetherattempttodescribeCO 2 plumebehaviorinconned,homogeneous, salineaquifersusinganalyticalsolutions.Chapter 3 focusesonthederivationofanalyticalandsemi-analyticalequationsformulationsforestimatingCO 2 storageefciency. Chapter 4 proposesanalyticalequationsforestimatingpivotalparameterswhichcouldbe utilizedtoscreenpotentialCO 2 repositories,andcomparestheanalyticalresultstothose predictedbyTOUGH 2 numericalsimulator.Thethirdpartinvolvesthestudyofdifferent injectionstrategiesforimprovingCO 2 storageefciencyandsecurity.Itconsistsoffour chapters 5 8 .TherstandsecondchaptersofthissegmentstudytheeffectsofhorizontalwelllengthonCO 2 storageunderisotropicandanisotropicconditions,respectively. Thethirdchapterofthissegmentconsiderseffectsofutilizingacombinationofvertical andhorizontalwellsonCO 2 storageunderanisotropicconditions.Thelastchapterofthe thirdpartdiscusseseffectsofgravitysegregationbetweenCO 2 andbrineandpermeability anisotropyonchangesinnear-wellborepressureduringCO 2 injection.Thisdissertationis completedwithaconclusionchapter.Thechaptergivesgeneraldiscussionsonthendings inthesecondandthirdpartsandanoverallsummaryoftheresultsachievedinthisstudy. 1.5ReferencesCited AGU.AmericanGeophysicalUnion:Humanimpactsonclimate.Technicalreport,2007. S.Bachu.SequestrationofCO 2 ingeologicalmedia:Criteriaandapproachforsiteselectioninresponsetoclimatechange. EnergyConversionandManagement ,41:953, 2000. S.Bachu.ScreeningandrankingofsedimentarybasinsforsequestrationofCO 2 ingeologicalmedia. EnvironmentalGeology ,44:277,2003. S.Bachu.CO 2 storageingeologicalmedia:Role,means,status,andbarrierstodeployment. ProgressinEnergyandCombustionScience ,34:254,2008. 1 PersonalcommunicationwithKarstenPruess,LawrenceBerkeleyNationalLaboratory 6

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S.BachuandJ.J.Adams.SequestrationofCO 2 ingeologicalmediainresponsetoclimatechange:CapacityofdeepsalineaquiferstosequesterCO 2 insolution. Energy ConversionandManagement ,44:3151,2003. S.Benson,T.Dorchak,G.Jacobs,J.Ekmann,J.Bishop,andT.Grahame. Carbondioxide reuseandsequestration:Thestateofthearttoday.Energy2000:Stateoftheart BalabanInternationalScienceServices,L'Aquila,Italy,P.Cataniaedition,2000.ISBN 086689-05-56. R.Bruant,A.Guswa,M.Celia,andC.Peters.Safestorageofcarbondioxideindeepsaline aquifers. EnvironmentalScienceandTechnology ,36:240AA,June2002. K.Coats. Petroleunengineeringhandbook:Reservoirsimulation ,chapter48,page13 pages.SocietyofPetroleumEngineers,1992. J.Ennis-KingandL.Paterson.Engineringaspectsofgeologicalsequestrationofcarbon dioxide.volumeSPE-77809,SPEandCSIROPetroleum,2002.AsiaPacicOilandGas ConferenceandExhibition,Melbourne,Australia,October8. EPRI.Pathwaystosustainablepowerincarbon-constrainedfuture.Technicalreport,ElectricPowerResearchInstitute,2007a. EPRI.ThepowertoreduceCO 2 emissions:Thefullportfolio.Technicalreport,Electric PowerResearchInstitute,2007b. A.EstublierandA.Lackner.Long-termsimulationoftheSnhvitCO 2 storage. Energy Procedia ,1,2009. P.Falkowski,R.J.Scholes,E.Boyle,J.Canadell,D.Caneld,J.Elser,N.Gruber, K.Hibbard,P.Hogberg,S.Linder,F.T.Mackenzie,I.B.Moore,R.Y.Pedersen,T., S.Seitzinger,V.Smetacek,andW.Steffen.Theglobalcarboncycle:Atestofour knowledgeofearthasasystem. Science ,290:291,2000. K.Forward.StatoilhydrobeginsCO 2 injectionatSnhvit. CarbonCaptureJournal:TransportandStorgaeNews, ,page24,MayJune2008a.May/June,Issue3, www.carboncapturejournal.com. K.Forward.GermanybeginsCO 2 storageatKetzin. CarbonCaptureJournal: TransportandStorageNews, ,page25,JulyAugust2008b.July/August,Issue4, www.carboncapturejournal.com. K.Forward.CO 2 storagewithECBMstudybeginsinwestvirginia. CarbonCapture Journal:TransportandStorageNews ,page6,September2009.September,Issue11, www.carboncapturejournal.com. J.E.Garc a. Fluiddynamicsofcarbondioxidedisposalinsalineaquifers .Doctoraldissertation,UniversityofCalifornia,Berkeley,2003. 7

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S.Holloway.Storageoffossilfuel-derivedcarbondioxideseneaththesurfaceoftheearth. AnnualReviewofEnergyandtheEnvironment ,26:145,2001. IEA.ProspectsforCO 2 captureandstorage.Technicalreport,InternationalEnvironmental Agency,Paris,France,2004. IPCC.IPCCspecialreportoncarbondioxidecaptureandstorage.PreparedbyWorking GroupIIIoftheIntergovernmentalPanelonClimateChange[Metz,B.,Davidson,O., deConinck,H.C.,Loos,M.,andMeyer,L.A.eds.].Report,IntergovernmentalPanel onClimateChange,Cambridge,UnitedKingdomandNewYork,NY,USA,2005. H.Koide,Y.Tazaki,Y.Noguchi,S.Nakayama,M.Iijima,K.Ito,andY.Shindo.Subterraneancontainmentandlong-termstorageofcarbondioxideinunusedaquifersandin depletednatural-gasreservoirs. EnergyConversionandManagement ,33,1992. J.Kristian,A.Kovscek,andF.Orr.IncreasingCO 2 storageinoilrecovery. EnergyConversionandManagement ,46:293,2005. NETL.EnhancedcoalbedmethaneproductionwhilesequesteringCO 2 inunmineablecoal seams.Report,NationalEnergyTechnologyLaboratoryNETL,2008. J.NordbottenandM.Celia.Similaritysolutionsforuidinjectionintoconnedaquifers. JournalofFluidMechanics ,561:307,2006. O.ObiandM.Blunt.Streamline-basedsimulationofcarbondioxidestorage inaNorthSeaaquifer. WaterResourcesResearch ,42W03414:1,2006. doi:10.1029/2004WR003347. K.PruessandJ.Garc a.MultiphaseowdynamicsduringCO 2 disposalintosaline aquifers. EnvironmentalGeology ,42:282,2002. K.PruessandN.Spycher.ECO2NAnewTOUGH2uidpropertymoduleforstudiesof CO 2 storageinsalineaquifers.Berkeley,California,2006.LawrenceBerkeleyNational Laboratory. K.Pruess,C.Oldenburg,andG.Moridis.ProcessmodelingofCO 2 injectionintonatural gasreservoirsforcarbonsequestrationandenhancedgasrecovery. EnergyandFuels 15:293,2001. K.Pruess,T.Xu,J.Apps,andJ.E.Garc a.Numericalmodelingofaquiferdisposalof CO 2 SocietyofPetroleumEngineeringJournal ,8:49,2003. K.Pruess,J.E.Garc a,T.Kovscek,C.Oldenburg,J.Rutqvist,C.Steefel,andT.Xu.Code intercomparisonbuildscondenceinnumericalsimulationmodelsforgeologicdisposal ofCO 2 Energy ,29:1431,2004.doi:10.1016/j.energy.2004.03.077. 8

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J.A.Stanislaw.Climatechangeseverything:Thecomingrevolutionintheenergyindustry. JournalofPetroleumTechnologyJPT ,60:18,June2008. L.G.H.vanderMeer.TheCO 2 storageefciencyofaquifers. EnergyConversionand Management ,36:513,1995. C.White,B.Strazisar,E.Granite,J.Hoffman,andH.Pennline.SeparationandCapture ofCO 2 fromLargeStationarySourcesandSequestrationinGeologicalFormationsCoalbedsandDeepSalineAquifers. JournalofAirandWasteManagementAssociation 53,2003. 9

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Chapter2 Background TherehasbeenagrowinginterestinCO 2 injectionintodeepsalineformationsbecause oftheirpotentialtosequestersignicantlylargequantitiesofCO 2 .Thisinterestismarked byanumberofCO 2 injectionpilotprojectsRiddifordetal.,2003;IPCC,2005;Forward, 2008b;aasaresultofincreasedcommitmentofindustriesandgovernments,especiallyin NorthAmerica,Europe,andAustraliaForward,2008b;2009.However,theknowledge gaphinderingfull-scaledevelopmentanddeploymentofCO 2 sequestrationtechnologyis considerable.Understandingthephysicalandchemicalprocessesthattakeplaceduring theinjectionandpost-injectionphasesarepivotalprerequisitesinadvancingCO 2 sequestrationtechnology.TheobjectiveofthischapteristogiveanoverviewofimportantphysicalprocessesthattakeplaceduringCO 2 injectioninconnedgeologicformationsand mathematicalmethodsusedtosolvetheequationsthatdescribethem. Thischapterbeginswithasectionthatusesaconceptualmodeltodescribeimportant physicalprocessesthatoccurduringCO 2 injectionintoaconnedsalineaquifer.Italso introducesdifferentmechanismsthroughwhichCO 2 istrappedwithintheaquifer.Section2.2discussesdifferentorientationsforinjectionwellsandhowthoseorientationsmay inuenceCO 2 owpatternswithinaconnedaquifer.Section2.3givesanoverviewof themathematicalformulationoftwo-phaseowequationsthatdescribethephysicalprocessesthattakeplaceduringandafterCO 2 injection.Section2.4addressesthenumerical methodsemployedbyTOUGH 2 tosolvetheresultingmathematicalequationsformulated insection2.3.Section2.5discussespossiblenumericalerrorsassociatedwithnumericalmethodsemployedinsection2.4.ThevalidityoftheTOUGH 2 numericalsimulator isinvestigatedinsection2.6byconductingamassbalanceonasampleproblemofCO 2 injectionintoaconnedaquifer. 10

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2.1ConceptualModel Figure1showsaschematicofCO 2 injectionintoaconnedaquiferviaafullyperforated verticalwell.CO 2 isassumedtomigrateradiallyawayfromthewellNordbottenetal., 2005.ThisproblemissimilarinsettingtoaradialowproblemdescribedbyPruess andGarc a.InorderforCO 2 todisplacetheresidentbrine,itmustbeinjected atapressuregreaterthantheinitialpressureoftheaquiferinjectionpressure.AsCO 2 isinjectedintotheaquifer,itradiallydisplacesbrineawayfromthewellduetoviscous owwhilemovingupwardsduetobuoyancy.ThisisbecauseCO 2 islessviscousandless densethanbrineorwaterunderhightemperatureandhighpressurereservoirconditions BachuandAdams,2003.Asaresult,theCO 2 plumewilloverliebrinewithitsradial extentatthetop r max beinggreaterthanthatatthebottom r min oftheaquiferFigure 1Nordbottenetal.,2005;NordbottenandCelia,2006.Table2presentsestimatesofthe densitiesandviscositiesofCO 2 andbrineatdifferentdifferentgeothermalgradients,land surfacetemperatureanddepth 1000 mand 3000 mNordbottenetal.,2005. InFigure1, r min representstheminimumradialextentofaCO 2 plumeduringinjection, r max representsthemaximumradialextentoftheCO 2 plumeduringinjection, B represents theaquiferthickness,and b r;t representsthethicknessoftheCO 2 plumeasafunctionof spaceandtime.TheaquifershowninFigure1waspartitionedintothreedistinctregions namely:Region 1 ,Region 2 ,andRegion 3 .Region 1 ,whichrangesfromtheinjectionwell tor min ,isassumedtobesaturatedwithCO 2 .Region 2 ,whichrangesfrom r min to r max ,is assumedtoconsistofbothCO 2 andbrineseparatedbyasharpinterface.Lastly,Region 3 whichspansfrom r max tobeyond,isassumedtobefullysaturatedwithbrine.Theinterface betweenCO 2 andbrineshiftsawayfromtheinjectionwellasmoreCO 2 isinjectedinto theaquifer.Basedontheabove-mentionedassumptions,thethicknessofthegasplume atagiventime b r;t inFigure1isequaltothethicknessoftheconnedformation B at r min andzeroat r max .Theserelationshipswillbeemployedinthederivationof mathematicalexpressionsforestimating r min and r max inchapters 3 and 4 2.1.1StorageEfciency CO 2 storageefciencyisameasureofthefractionofavailableporousvolumethatis occupiedbyinjectedCO 2 .DuetodifferencesinviscosityanddensitybetweenCO 2 and brine,theshapeoftheCO 2 -brineinterfacewillassumeashapesimilartothatdepictedin Figure1Nordbottenetal.,2005;NordbottenandCelia,2006underconditionsofnegli11

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giblemasstransferbetweentheuidphases.Storageefciencyisdenedintheliterature astheratiobetweentheactualinjectedvolumeofauidandthemaximumstoragevolume ofarepositoryvanderMeer,1995.BasedonFigure1,CO 2 storageefciencycanbe denedastheratiobetweenthevolumeoccupiedbytheCO 2 plumeandthecylindrical volumeoftheaquiferwithradiusequivalentto r max whichisthevolumeavailableforgas storage.Thisismathematicallydescribedasfollows: s = V injected V aquifer = Q well t B r max 2 .1 where s , Q well ,and t ,arethestorageefciency,averageporosity,volumetricowrate, andinjectiontime,respectively. Detailsonthederivationofananalyticalexpressionforestimating s areaddressedin chapter 3 .TypicalestimatesofCO 2 storageefciencydescribedintheliteraturerange between 2 %and 6 %ObiandBlunt,2006;vanderMeer,1995. Figure1.: ConceptualmodeladaptedfromNordbottenetal.. 12

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Table2: DensityandviscosityofCO 2 andbrineincoldandwarmbasins.Temperaturegradientusedincoldandwarmbasinswere 25 C/kmand 45 C/km,respectively;thesurfacetemperatureincoldandwarmbasins usedwere 10 Cand 20 C,respectivelyNordbottenetal.,2005. Densitykg/m 3 ViscosityPa s Depthm CO 2 brine CO 2 brine Comment 1000 7141012 5.77 10 )]TJ/F17 7.9701 Tf 6.587 0 Td [(5 7.95 10 )]TJ/F17 7.9701 Tf 6.586 0 Td [(4 .58 10 )]TJ/F17 7.9701 Tf 6.587 0 Td [(3 cold 3000 733995 6.11 10 )]TJ/F17 7.9701 Tf 6.587 0 Td [(5 3.78 10 )]TJ/F17 7.9701 Tf 6.586 0 Td [(4 .44 10 )]TJ/F17 7.9701 Tf 6.587 0 Td [(4 basin 1000 266998 2.30 10 )]TJ/F17 7.9701 Tf 6.587 0 Td [(5 4.91 10 )]TJ/F17 7.9701 Tf 6.586 0 Td [(4 .83 10 )]TJ/F17 7.9701 Tf 6.587 0 Td [(4 warm 3000 479945 3.95 10 )]TJ/F17 7.9701 Tf 6.587 0 Td [(5 1.95 10 )]TJ/F17 7.9701 Tf 6.586 0 Td [(4 .12 10 )]TJ/F17 7.9701 Tf 6.587 0 Td [(4 basin 2.1.2FormationAnisotropy Theratiobetweentheverticalandhorizontalpermeabilitiesofaformationisthetermed anisotropyratio k vh ,i.e. k vh = k v k h .2 where k v and k h aretheaquifer'spermeabilitiesintheverticalanddirections,respectively. Ifthe k v and k h ofthesalineaquiferdepictedinFigure1areequal,itisconsidered isotropic.Ontheotherhand,anaquiferistermedanisotropicwhen k vh isdifferentfrom unity.Typicalvaluesofanisotropyratioforsedimentaryformationsmostlysandstoneand limestonegivenintheliteraturerangebetween 0 : 001 and 1 indeepsalineaquifersKumar etal.,2005;vanderMeer,1995.Onemayconsideraformationtobestronglyanisotropic when k vh < 0 : 01 ,andmoderatelyanisotropicwhen 0 : 01 k vh < 0 : 1 2.1.3TrappingMechanisms IfCO 2 andbrineareassumedimmiscibleasdepictedinFigure1,CO 2 willbestoredin theconnedaquiferasasupercriticaluidorgasdependingonthedepth.Consequently, thelengthoftimeitwillbeisolatedfromtheenvironmentwillstronglydependonthe integrityoftheconninglayers,especiallytheupperseal.Thetemperatureandpressure conditionsinsedimentarybasinsaregenerallysuitableforsupercriticalinjectionofCO 2 BachuandAdams,2003.ThesupercriticaltemperatureandpressureofCO 2 areabout 31 : 1 o Cand 7 : 38 MPa 73 : 8 bar,respectivelyVargaftik,1975;Vargaftiketal.,1996. Asignicantincreaseindensityfromabout 1 : 87 kg/m 3 atnormalconditionstoover 800 kg/m 3 undersupercriticalconditionsBachu,2003willbeachievedwhenCO 2 isinjected 13

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asasupercriticaluid.Asaresult,injectingCO 2 asasupercriticaluidwillincreasethe massofCO 2 storedperunitvolumeofanaquifer. Conversely,whenCO 2 andbrineareconsideredmiscible,interphasemasstransferbetweenCO 2 andbrinewilloccur,eventhoughbothuidsaresparinglysolublePruess andGarc a,2002.ThedissolutionofCO 2 intobrineisaveryimportantmechanismof trappingCO 2 becauseitservesasagatewayforCO 2 tobepermanentlysequesteredin carbonatemineralsviageochemicalreactionswithdivalentcationsinsolution. FourmajormechanismshavebeenidentiedbywhichCO 2 maybesequesteredinsaline aquifers.Theyincludephysicalhydrodynamic,structural,orstratigraphictrapping,residualtrapping,solubilitytrapping,andmineraltrappingBachuandAdams,2003;IPCC, 2005;OelkersandSchott,2005.Thesetrappingmechanismsdohavedifferenttimescale contributionstoCO 2 sequestrationFigure2.Physicaltrappingismostsignicantduring theinjectionphase.Contributionsfromresidualtrappingandsolubilitytrappingincrease overtimeaftertheinjectionphaseisover.Contributionfrommineraltrappingbecomes signicantonlyafterabout 1000 yearsIPCC,2005. 2.1.3.1PhysicalTrapping PhysicaltrappinginvolvesthestorageofCO 2 asagasorsupercriticaluidbelowlow permeabilityseals.PhysicaltrappingismostpredominantorimportantduringtheinjectionphaseofaCO 2 sequestrationprojectEnnis-KingandPaterson,2002.Thistrapping mechanismallowsforstorageofsignicantquantitiesofCO 2 .Verticalowoftheplume isinhibitedduetothepresenceofanimpermeablebarrieratthetopFriedmann,2007.As aresult,physicaltrappingishighlydependentontheintegrityoftheupperconninglayer IPCC,2005. 2.1.3.2ResidualTrapping ResidualtrappingreferstoresidualsaturationsofCO 2 trappedasbubblesofgasorsupercriticaluidsurroundedbybrineliquidphasewithintheporousmedium.Whenthe injectionwellisturnedoff,theowofCO 2 andbrinewillbecontrolledbybuoyancyforces asaresultoftheirdifferencesindensityDoughty,2007;Bachu,2008.AsaresultanupwardmovementoftheCO 2 plumewillbeinitiated.Consequently,asCO 2 non-wetting phasemovesupwards,brinewettingphasere-occupiestheporespacesthatwereoccupiedbyCO 2 .TheresidualsaturationofCO 2 leftbehindtherisingplumewillbetrappedby invadingbrineandisimmobilizedbyitsinterfacialtensionwithbrine.Thisphenomenon 14

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ispredominantatthetrailingedgeoftheCO 2 plumeandisreportedtobemoresignicant inthepost-injectionphaseBachu,2008. Figure2.: TimescalesofCO 2 trappingmechanismsadaptedfromIPCC 2.1.3.3SolubilityTrapping SolubilitytrappingreferstothedissolutionofCO 2 intobrinewithinaporousformation.Solubilitytrappingisaveryimportanttrappingmechanismbecauseitdiminishesor reversesbuoyancyeffectsfromrisingCO 2 IPCC,2005andalsomakesCO 2 available forgeochemicalreactionswithchemicalspeciesinsolutionbrine.TheamountofCO 2 storedthroughsolubilitytrappingcanbequantiedasadissolvedgasmassfraction X CO 2 insolutionandtotalmassofdissolvedgas M CO 2 ;aq asfollows: X CO 2 = nM CO 2 1000+ mM NaCl + nM CO 2 .3 15

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M CO 2 ;aq = ZZZ X CO 2 b dV .4 where n m M CO 2 M NaCl b ,and V arethemolalityofdissolvedCO 2 inbrine,molality ofdissolvedsalt,molarmassofCO 2 ,molarmassofsalt,brinedensityandporousvolume ofaquifer,respectively.Themolalityofachemicalspeciesinsolutionisgenerallydened asthenumberofmolesofthechemicalspeciesperkilogramofsolution. 2.1.3.4MineralTrapping MineraltrappinginvolvestheincorporationofCO 2 intothesolidphase.ThismechanismofCO 2 trappingisveryattractivebecauseitimmobilizestheformeronapermanent basisPruessetal.,2003.MineraltrappingtakesplacethroughprecipitationreactionsbetweenaqueousCO 2 mostlylikelyintheformofbicarbonate, HCO 3 )]TJ/F40 11.9552 Tf 7.085 -4.338 Td [(Bachu,2008and multivalentcationslike Ca 2+ Mg 2+ Mn 2+ Fe 2+ Sr 2+ ,and Ba 2+ informationbrine Pruessetal.,2003. 2.2VerticalvsHorizontalWells Foragivenformationwithahorizontalbeddingplane,awellisconsideredverticalif itisdrilledperpendicular 90 orhorizontalwhendrilledparallel 180 totheformation planeJoshi,1991.Aslantedwellwillbeatangle, ,between 0 and 90 i.e. 0 << 90 fromthebeddingplane.However,thescopeofthisstudyislimitedtoverticaland horizontalinjectionwells. GeologicstoragecanprovideasignicantreductioninCO 2 emissionsoverlongperiodsonlyifrepositoriesareutilizedefcientlybyimplementingbetterinjectionstrategies. However,CO 2 injectedviaverticalwellshasbeenreportedtooccupyabout 3 %ofthepore volumeavailableforstoragenumericalsimulationsvanderMeer,1995.Ontheother hand,researchrelatedtoCO 2 storageingeologicformationsusinghorizontalinjection wellsarefewe.g.Jikichetal.,2003;Ozahetal.,2005.ApracticalexampleofaCO 2 injectionviahorizontalwellsistheIn-SalahCO 2 storageproject.Theprojecthasthree long-reachhorizontalwellswithlengthsupto 1500 m.CO 2 isinjectedintoa 20 mthick sandstoneformationwithpermeabilityaslowas 5 mD 4 : 9 10 )]TJ/F17 7.9701 Tf 6.587 0 Td [(15 m 2 .Thetopseal oftheaquiferconsistsofamudstonelayerwithathicknessof 950 m.TheIn-Salahproject hasastoragecapacityofabout 1 : 2 milliontonsperannumRiddifordetal.,2003;IPCC, 16

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2005.OtherCO 2 captureandstorageprojectscurrentlyunderoperationincludetheSleipnerprojectintheNorwegiansectoroftheNorthSea,theWeyburneldinCanada,IPCC, 2005,andtheSnhvitprojectinNorwayForward,2008a. Horizontalwelltechnologyisextensivelyemployedintheoilandgasindustrytoincreasecrudeoilproduction.However,horizontalwellsareabout 1 : 4 to 3 timesmore expensivethanaverticalwellJoshi,1991.Asaresultthedecisiononwhichinjection strategytoimplementinaCO 2 captureandstorageprojectshouldconsiderthecostfactor. ThismayvaryfromonecandidateCO 2 repositorytoanother. 2.3MultiphaseFlowEquationsTOUGH2 SincethescopeofthisstudyislimitedtophysicalprocessesthatoccurduringCO 2 injectionintoaconnedsalineaquifer,onlytwophaseuidowCO 2 andbrinewillbe discussedinthissection.Asaresult,thesystemunderconsiderationconsistsofahomogeneousconnedaquifer,brine,andCO 2 .Theaquiferisconsideredtobelocatedatadepth ofatleast 800 m andinitiallysaturatedwithbrine.Aminimumdepthofapproximately 800 misreportedtobefavorableforinjectionofsupercriticalCO 2 Garc a,2003;Doughty, 2007;Marini,2007.ThethermophysicalpropertiesofCO 2 andbrinedensity,viscosity, andspecicenthalpywillvaryspatiallyduringandafterCO 2 injectionPruessetal.,1999; PruessandGarc a,2002;Pruessetal.,2003;2004;Pruess,2005.PhasechangeorinterphasemasstransferofCO 2 intotheaqueousphaseandwatervaporintothegaseousphase mayoccur,sincebothuidsaresparinglysoluble.However,thedissolutionofCO 2 into brineisadverselyaffectedbythesalinityofbrinePruessetal.,2003.Otherchemical speciesmaybepresentintheaqueousphasebrinei.e.dissolvedCO 2 andcationsand anionsfromdissolvedmineralslikecarbonates,silicates,andsulfatesMarini,2007. 2.3.1DevelopmentofFlowEquations TheowofuidsinporousmediaisgenerallydepictedusingDarcy'slawDarcy,1856 i.e. ~ F = ~ Q A = ~u = )]TJ/F19 11.9552 Tf 9.299 0 Td [(k r ~ P )]TJ/F19 11.9552 Tf 11.955 0 Td [(~g r ~ P = @P @x @P @y @P @z .5 17

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~u = )]TJ/F19 11.9552 Tf 10.771 8.088 Td [(k r ~ P )]TJ/F19 11.9552 Tf 11.955 0 Td [(~g ~g = : 0 ; 0 : 0 ; 9 : 81 T Inequation2.5 ~ F isthemassuxkg/s-m 2 ~ Q isthemassowratekg/s, A isthecrosssectionalaream 2 k istheintrinsicpermeabilitym 2 isuiddensitykg/m 3 isuid viscosityPa s, r ~ P ispressuredifferencePa, ~g isgravitym/s 2 ,and ~u istheDarcy velocitym/s. Equation2.5canalsobeextendedtoaccountforthepresenceofmultipleuidphasesas followsPruessetal.,1999;PruessandGarc a,2002: ~ F = ~u = )]TJ/F19 11.9552 Tf 9.298 0 Td [(k k r r ~ P )]TJ/F19 11.9552 Tf 11.955 0 Td [(~g ~ P = ~ P ref )]TJ/F19 11.9552 Tf 13.67 3.022 Td [(~ P cap .6 ~ P cap = ~ P gas )]TJ/F19 11.9552 Tf 13.67 3.022 Td [(~ P liq where representsauidphase, k r istherelativepermeabilityofauidphase ~ P is thepressureofuidphase ~ P ref isareferencepressure, ~ P cap isthecapillaryorsuction pressure, ~ P gas ispressureofgaseousphase,and ~ P liq ispressureofliquidphase. 2.3.2MassTransportandMassBalance Massistransportedwithinaporousmediumviaadvection,moleculardiffusionandhydrodynamicdispersion.Theadvectivemassuxofacomponent inauidphase is describedmathematicallyasfollowsPruessetal.,1999;PruessandGarc a,2002: ~ F adv = X X ~ F .7 Themasstransportofcomponent, ,inauidphaseviahydrodynamicdispersionand moleculardiffusionofauidphase, ,ismathematicallydescribedasfollowsdeMarsily, 1986;PruessandGarc a,2002: ~ F dis = )]TJ/F1 9.9626 Tf 11.291 9.963 Td [(X ~ D r X ~ D = D ;T ~ I + D ;L )]TJ/F19 11.9552 Tf 11.955 0 Td [(D ;T u 2 ~u ~u .8 18

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D ;L = )]TJ/F19 11.9552 Tf 9.299 0 Td [( 0 d + ;L ~u D ;T = )]TJ/F19 11.9552 Tf 9.299 0 Td [( 0 d + ;T ~u Inequations2.7and2.8 representsacomponentinauidphase ~ F adv istheadvective massuxofcomponent inalluidphases, X g isthemassfractionofcomponent in thegaseousphase, X l isthemassfractionofcomponent intheliquidphase, ~ F g isthe advectiveuxofthegaseousphase, ~ F l istheadvectiveuxoftheliquidphase, ~ F dis isthe diffusive-dispersiveuxofcomponent inalluidphases, isthedensityofuidphase ~ D ;T isthehydrodynamicdispersiontensor, X isthemassfractionofcomponent in uidphase D ;T isthetransversedispersioncoefcientperpendiculartodirectionof ow, D ;L isthelongitudinaldispersioncoefcientinthedirectionofow, ~ I isaunit tensor, istheaverageporosity, 0 isthetortuositycoefcientoftheporousmedium, is thetortuositycoefcientofuidphase dependentonuidphasesaturation S d is themoleculardiffusioncoefcientofcomponent inuidphase ;L isthelongitudinal dispersivity,and ;T isthetransversedispersivityPruessandGarc a,2002. Thecoefcientofhydrodynamicdispersion, D longitudinalandtransverse,accounts forcontributionsfrombothhydrodynamicdispersionandmoleculardiffusionBear,1972. D isfunctionofPecletnumber Pe Pe istheratiooftherateoftransportbyconvection hydrodynamicdispersiontotherateoftransportbymoleculardiffusionBear,1972. Moleculardiffusionpredominatesatsmallvaluesof Pe Pe< 0 : 4 Bear,1972i.e.,when rateoftransportbyconvectionadvectivevelocityissmallPruessetal.,1999.Forvalues of Pe rangingbetween 0 : 4 and 5 bothmoleculardiffusionandhydrodynamicdispersion areimportant.However,for Pe signicantlygreaterthan 5 moleculardiffusionbecomes lessimportantcomparedtohydrodynamicdispersionBear,1972. Thetotalmassuxofacomponent ~ F willbethesumoftheadvectiveanddiffusivedispersivemassuxesPruessandGarc a,2002i.e. ~ F = ~ F adv + ~ F dis .9 Amassbalanceacrossanarbitraryvolumeofconnedaquiferorporousmedium V ,can berepresentedasfollowsPruessetal.,1999;PruessandGarc a,2002: d dt Z V M dV = Z )]TJ/F19 11.9552 Tf 9.225 12.94 Td [(~ F ~nd )-222(+ Z V q dV .10 19

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Thelefthandsideofequation2.10istherateofchangeofmassofcomponent in V .Thersttermontherighthandsideofequation2.10isthemassuxofcomponent overthesurface )]TJ/F40 11.9552 Tf 7.314 0 Td [(.Lastly,thesecondtermontherighthandsideofequation2.10is themassuxintosourcesoroutsinksof V .Themassuxterminequation2.10can beconvertedtorepresentmassuxthroughthevolumeoftheaquiferusingGauss'or divergencetheoremasfollowsBearandBachmat,1991: Z )]TJ/F19 11.9552 Tf 9.226 12.94 Td [(~ F ~nd )-278(= )]TJ/F1 9.9626 Tf 11.291 14.059 Td [(Z V div ~ F dV .11 Substitutionofequation2.11intoequation2.10yieldsageneralequationformultiphase owinporousmediaPruessetal.,1999;PruessandGarc a,2002i.e. Z V d dt M + div ~ F # dV = Z V q dV .12 where M = S X M ismassofcomponent inallphases,and S issaturation ofuidphase Thetotalmassofcomponent inasystemoftwophases g;l isgivenbythefollowing Pruessetal.,1999;PruessandGarc a,2002: M = S g g X g + S l l X l # .13 2.4NumericalMethods TOUGH2employstheIntegralFiniteDifferenceIFDmethodNarasimhanandWitherspoon,1976andafullyimplicitrst-orderbackwardnitedifferencemethodtodiscretizeequation2.10inspaceandtimerespectivelyPruessandGarc a,2002.TheIFD methodwasselectedtodiscretizeinspacebecauseithasthecapabilityofrepresentingirregulargeologicfeaturesWuetal.,1999.Thespatiallydiscretizedformofeachtermin equation2.10isasfollowsPruessandGarc a,2002: Z V n M dV = V n M n .14 20

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Z )]TJ/F21 5.9776 Tf 4.505 -0.996 Td [(n ~ F ~nd )-278(= X m A nm F nm .15 Z V n q dV = V n q .16 where M n isaverageof M overasubdomain V n F nm istheaveragevalueoftheinwardor normalcomponentof ~ F overaportionofasurface A nm betweenvolumeelements V n and V m Substitutingequations2.14,2.15,and2.16intoequation2.10yieldthefollowing: V n dM dt = X m A nm F nm + V n q .17 Discretizingequation2.17implicityintimeusingthebackwardnitedifferencemethod andrearranginggivesthefollowing: M ;k +1 n )]TJ/F19 11.9552 Tf 11.955 0 Td [(M ;k n = t V n X m A nm F ;k +1 nm + V n q ;k +1 # .18 Equation2.18canbefurtherrearrangedasfollows: R ;k +1 n = M ;k +1 n )]TJ/F19 11.9552 Tf 11.955 0 Td [(M ;k n )]TJ/F15 11.9552 Tf 13.15 8.088 Td [( t V n X m A nm F ;k +1 nm + V n q ;k +1 # =0 .19 where R ;k +1 n representresidualsof equations.Equation2.19isasetof N nonlinear algebraicequationswhichcanonlybesolvednumerically.TOUGH 2 employstheNewtonRaphsoniterationmethodtosolveequation2.19PruessandGarc a,2002. Theiterationprocesscontinuesuntilapredenedconvergencecriteriaismetasfollows: R ;k +1 n M ;k +1 n .20 where isaverysmallnumberusually 10 )]TJ/F17 7.9701 Tf 6.587 0 Td [(5 orless. Thesetoflinearalgebraicequationsthatariseateachiterationsteparesolvedusing thepreconditionedconjugategradientmethodsMoridisandPruess,1998.Detailsonthe discretizationofequation2.10onatermbytermbasisisdescribedinPruessetal.; 21

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PruessandGarc a.Thedefaultvalueof inTOUGH2numericalsimulationsis 10 )]TJ/F17 7.9701 Tf 6.586 0 Td [(5 Pruessetal.,1999;PruessandGarc a,2002.However,thetotalnumberofiterationsrequiredtoachieveconvergencedependonthedominanceoftheleadingdiagonal coefcients,theiterativemethodemployed,initialsolutionvectorguess,andthespeciedconvergencecriterion.Anincreaseindominanceoftheleadingdiagonalcoefcients causesareductioninthenumberofiterationsrequiredtoachieveconvergence.Thecloser theinitialguessofthesolutionvectortotheactualsolutionvector,thelesserthenumberof iterationstoachieveconvergence.Onthecontrary,thesmallertheconvergencecriterionthe largerthenumberofrequirediterationsHoffman,2001;Coats,1992.Newton-Raphson iterationmethodandotheriterativemethodsarediscussedindetailinappliedmathematics textbookse.g.,Hoffman. 2.5NumericalErrors Numericalsolutionsapproximaterealsolutionsbyimplementingappropriateapproximationtechniques.Inthiscase,continuousspaceandtimevariablediscretizationare requiredtoapproximatetherealsolution.However,discretizationintroduceserrorsinthe processofapproximatingtherealsolutionofaproblemPruessetal.,1999;Pruessand Garc a,2002.Inotherwords,truncationerrorduetospatialandtimediscretizationis introducedbyreplacingthedifferentialequationsofthenumericalmodelbyintegralnite differenceapproximationsPruessandGarc a,2002andnitedifferenceapproximations Coats,1992,respectively.Round-offerrorisalsointroducedduringevaluationoftheintegralniteandnitedifferenceapproximationsofthedifferenceequationsbythecomputer. However,round-offerrorisnegligiblecomparedtotruncationerrorCoats,1992. Otherpotentialsourcesoferrorinnumericalsimulationsinclude:wrongassumptionsand/oromitteddescriptionofphenomenainthedifferentialformofamodeland insufcientdescriptionofrockand/oruidpropertiesCoats,1992.Theseformsoferrorarealsosignicantcomparedtoround-offerrors.Spatialandtimetruncationerrors canbeminimizedviaappropriatereductioningridblockandtimestepsizes,respectively. However,thereshouldbeabalancebetweenreducinggridblockortimestepsizeswith computermemorystorageandexecutiontime,sincetheseincreasewiththetotalnumber ofgridblocksandtime-stepsinanumericalsimulationCoats,1992;Hoffman,2001. Nonetheless,areductioningridblocksizesisnecessaryinregionswithinaformationto studydetaileduidowdynamics,forexamplethestudyofuidowinstabilitiesinthe vicinityofaninjectionwellPruessandGarc a,2002;Garc a,2003. 22

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Inmostcasesthemitigationoftimetruncationerrorishinderedbyeffectsofmodel stability,changesinowrate,andprintoutfrequenciesontime-stepsizeCoats,1992; Hoffman,2001.Somemodelsaresensitivetochangesintime-stepsizewhileothersare not.Generally,modelswhicharelesssensitivetochangesintime-stepsizehavelowtime truncationerrorsCoats,1992. Thespatialtruncationerrorsinnumericalmodelsemanatefromnumericaldispersion Ewingetal.,1983;CarrandChristie,1983andgrid-orientationeffectsToddetal.,1972; YanosikandMcCraken,1979.Grid-orientationeffectcanbedenedasafalsedependence ofsimulationresultsonamodel'sgridPruess,1992.ItiscausedbyacombinationofhydrodynamicinstabilityandanisotropicnumericaldiffusionBrandetal.,1991.However, grid-orientationeffectcanbesignicantlymitigatedbyemployinghigher-orderdifference methodsinordertoachieveisotropicnumericaldispersioninsimulatedresultsPruess, 1992.Numericaldispersionincreaseswithgridblocksizeassuchcanbemitigatedby reducinggridblocksizeEwingetal.,1983;CarrandChristie,1983,especiallynearthe injectionwellwheredetaileddescriptionofwellbehaviorisrequiredCoats,1992. 2.6MassBalance Amassbalanceanalysiswasconductedtovalidatetheselectednumericalsimulatorfor thisworkTable3.Thetestproblem 3 ofthecodeintercomparisonprojectPruessetal., 2004wasused.ItisabasicproblemofCO 2 injectionintoahomogeneous,isotropic, innite-acting,salineaquifer.Theaquiferis 100 mthickanditsdepthisintheorderof 1200 m.Theinitialpressure,temperatureandsalinityconditionsusedare 120 bar, 45 C, and 15 %byweight,respectively.CO 2 isuniformlyinjectedintotheaquiferataconstant rateof 100 kg/sandgravityandinertiaeffectsareassumednegligible.Theowofuid withintheaquiferisassumedtobe 1 -DradiallinesourcePruess,2005.TOUGH 2 was validatedbycomparingthetotalmasspresentintheaquifer M CO 2 ;T tothetotalmassof CO 2 injected M CO 2 ;inj asafunctionoftimeTable3. M CO 2 ;T isequivalenttothesumof themassofgaseousorsupercriticalCO 2 M CO 2 ;g andthemassofCO 2 dissolvedinbrine M CO 2 ;aq M CO 2 ;g and M CO 2 ;aq wereobtainedasoutputfromTOUGH 2 andaddedtoget M CO 2 ;T M CO 2 ;inj wascalculatedastheproductofthemassinjectionrateandtime. ResultsfromTable3showexcellentaccountabilityonamountofCO 2 injectedintothe aquiferbyTOUGH 2 .Therefore,TOUGH 2 canbeusedwithhighlevelofcondenceasa surrogateofelddataduetoscarcityofthelatter. 23

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Table3: CO 2 massbalanceontestproblem 3 ofthecodeintercomparison project. Timeyears M CO 2 ;inj kg M CO 2 ;T kgRelativeerror 00.00.00.0% 1 3 : 15 10 9 3 : 15 10 9 0 : 0 % 3 9 : 46 10 9 9 : 46 10 9 0 : 0 % 10 3 : 16 10 10 3 : 16 10 10 0 : 0 % 30 9 : 46 10 10 9 : 46 10 10 0 : 0 % 100 3 : 15 10 11 3 : 15 10 11 0 : 0 % Thesimulationsconductedhereinusedgridswith 10 layersintheverticaldirection.The validityoftheresultspredictedbythesimulationswastestedbycomparingitsresultsto thoseofsimulationswith 20 verticallayers.Thedifferencesbetweenpredictionsofthe maximumpressuresatthebottomandtoplayersfromthesimulationsusing 2 Dand 3 D meshgeometryarenegligiblelessthan 1 %relativeerror.SeeAppendixA. 2.7ReferencesCited S.Bachu.ScreeningandrankingofsedimentarybasinsforsequestrationofCO 2 ingeologicalmedia. EnvironmentalGeology ,44:277,2003. S.Bachu.CO 2 storageingeologicalmedia:Role,means,status,andbarrierstodeployment. ProgressinEnergyandCombustionScience ,34:254,2008. S.BachuandJ.J.Adams.SequestrationofCO 2 ingeologicalmediainresponsetoclimatechange:CapacityofdeepsalineaquiferstosequesterCO 2 insolution. Energy ConversionandManagement ,44:3151,2003. J.Bear. Dynmamicsofuidsinporousmedia .EnvironmentalScienceSeries.American ElsevierPublishingCompany,Inc.,NewYork,USA,1972.ISBN0-486-65675-6. J.BearandY.Bachmat. Introductiontomodelingoftransportphenomenainporousmedia volume4.KluwerAcademicPublishers,Dordrecht,TheNetherlands,1991.ISBN07923-0557-4. C.Brand,J.Heinemann,andK.Aziz.Thegridorientationeffectinreservoirsimulation. In EleventhSymposiumonReservoirSimulation ,numberSPE-21228,Anaheim,Carlifornia,USA,February1991.SocietyofPetroleumEngineers,SocietyofPetroleum Engineers. 24

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A.CarrandM.Christie.Controllingnumericaldiffusioninreservoirsimulationusing ux-correctedtransport.SPESymposiumonReservoirSimulation,SanFrancisco,California,1983. K.Coats. Petroleunengineeringhandbook:Reservoirsimulation ,chapter48,page13 pages.SocietyofPetroleumEngineers,1992. H.Darcy. LesfountainespubliquesdelavilledeDijon .Dalmont,Paris,1856. G.deMarsily. Quantitativehydrogeology .AcademicPress,Inc.,Orlando,FL,ParisSchool ofMines,Fontainebleau,January1986.OSTIID:6784827. C.Doughty.Modelinggeologicstorageofcarbondioxide:Comparisonofnon-hysteretic andhystereticcharacteristiccurves. EnergyConversion&Manangement ,48,2007. J.Ennis-KingandL.Paterson.Engineringaspectsofgeologicalsequestrationofcarbon dioxide.volumeSPE-77809,SPEandCSIROPetroleum,2002.AsiaPacicOilandGas ConferenceandExhibition,Melbourne,Australia,October8. R.Ewing,T.Russell,andM.Wheeler.Simulationofmiscibledisplacementusingmixed methodsandamodiedmethodofcharateristics.SPESymposiumonReservoirSimulation,SanFrancisco,California,1983. K.Forward.StatoilhydrobeginsCO 2 injectionatSnhvit. CarbonCaptureJournal:TransportandStorgaeNews, ,page24,MayJune2008a.May/June,Issue3, www.carboncapturejournal.com. K.Forward.GermanybeginsCO 2 storageatKetzin. CarbonCaptureJournal: TransportandStorageNews, ,page25,JulyAugust2008b.July/August,Issue4, www.carboncapturejournal.com. K.Forward.UKCCSexpertsmissiontoJapan. CarbonCaptureJournal:Projects andPolicyNews, ,pages13,JanuaryFebruary2009.January/February,Issue7, www.carboncapturejournal.com. J.Friedmann.Geologicalcarbondioxidesequestration. Elements ,3:197,June2007. CarbonManagementProgram,LawrenceLivermoreNationalLaboratory. J.E.Garc a. Fluiddynamicsofcarbondioxidedisposalinsalineaquifers .Doctoraldissertation,UniversityofCalifornia,Berkeley,2003. J.D.Hoffman. Numericalmethodsforengineersandscientists .MarcelHekkerInc.,New York,USA,2001.ISBN0-8247-0443-6. IPCC.IPCCspecialreportoncarbondioxidecaptureandstorage.PreparedbyWorking GroupIIIoftheIntergovernmentalPanelonClimateChange[Metz,B.,Davidson,O., deConinck,H.C.,Loos,M.,andMeyer,L.A.eds.].Report,IntergovernmentalPanel onClimateChange,Cambridge,UnitedKingdomandNewYork,NY,USA,2005. 25

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S.Jikich,W.Sams,G.Bromhal,G.Pope,N.Gupta,andD.Smith.Carbondioxideinjectivityinbrinereservoirsusinghorizontalwells.SecondAnnualConferenceonCarbon Sequestration,May5.Alexandria,VA,May2003. S.D.Joshi. Horizontalwelltechnology .PennWellBooks,Tulsa,Colorado,USA,1991. A.Kumar,R.Ozah,M.Noh,G.A.Pope,S.Bryant,K.Sepehrnoori,andL.W.Lake.ReservoirsimulationofCO 2 storageindeepsalineaquifers. SocietyofPetroleumEngineering Journal ,9SPE89343:336,September2005. L.Marini. Geologicalsequestrationofcarbondioxide:Thermodynamics,kinetics,and reactionpathmodeling .Elsevier,LaboratoryofGeochemistry,UniversityofGenova, Italy,rstedition,2007.ISBN0-444-52950-0. G.MoridisandK.Pruess.T2SOLV:AnenhancedpackageofsolversfortheTOUGH2 familyofreservoirsimulationcodes. Geothermics ,24:415,1998. T.NarasimhanandP.Witherspoon.Anintegratednitedifferencemethodforanalyzing uidowinporousmedia. WaterResourcesResearch ,12:57,1976. J.NordbottenandM.Celia.Similaritysolutionsforuidinjectionintoconnedaquifers. JournalofFluidMechanics ,561:307,2006. J.Nordbotten,M.Celia,andS.Bachu.InjectionandstorageofCO 2 indeepsalineaquifers: AnalyticalsolutionforCO 2 plumeevolutionduringinjection. TransportinPorousMedia ,58:339,2005. O.ObiandM.Blunt.Streamline-basedsimulationofcarbondioxidestorage inaNorthSeaaquifer. WaterResourcesResearch ,42W03414:1,2006. doi:10.1029/2004WR003347. E.H.OelkersandJ.Schott.GeochemicalaspectsofCO 2 sequestration. ChemicalGeology 217:183,2005. R.Ozah,G.Lakshminarasimhan,K.Sepehrnoori,andS.Bryant.Numericalsimulation ofthestorageofpureCO 2 andCO 2 -H 2 Sgasmixtureindeepsalineaquifers.In SPE AnnualTechnicalConferenceandExhibition ,SPE97255,pages1,Dallas,Texas, USA,2005.SocietyofPetroleumEngineers,SocietyofPetroleumEngineers. K.Pruess.AnalysisofowprocessesduringTCEinltrationinheterogeneoussoilsatthe SavannahRiversite,Aiken,SouthCarolina.ReportLBL-32418,UC-000,Lawrence BerkeleyNationalLaboratory,EarthScienceDivision,Berleley,California,1992.access date:January15,2009. K.Pruess. ECO2N:ATOUGH2uidpropertymoduleformixturesofwater,NaCl,and carbondioxide .LawrenceBerkeleyNationalLaboratory,Berkeley,California,2005. 26

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K.PruessandJ.Garc a.MultiphaseowdynamicsduringCO 2 disposalintosaline aquifers. EnvironmentalGeology ,42:282,2002. K.Pruess,C.Oldenburg,andG.Moridis.TOUGH2users'guide,version2.0.Manual LBNL-43134,LawrenceBerkeleyNationalLaboratory,Berleley,California,1999.accessdate:June10,2007. K.Pruess,T.Xu,J.Apps,andJ.E.Garc a.Numericalmodelingofaquiferdisposalof CO 2 SocietyofPetroleumEngineeringJournal ,8:49,2003. K.Pruess,J.E.Garc a,T.Kovscek,C.Oldenburg,J.Rutqvist,C.Steefel,andT.Xu.Code intercomparisonbuildscondenceinnumericalsimulationmodelsforgeologicdisposal ofCO 2 Energy ,29:1431,2004.doi:10.1016/j.energy.2004.03.077. T.Riddiford,C.Bishop,B.Taylor,andM.Smith.Acleanerdevelopment:TheIn-Salah gasproject,Algeria.In Proceedingsofthe6thInternationalConferenceonGreenhouse GasControlTechnologiesGHGT-6 ,pages601,Kyoto,Japan,October2003. M.Todd,P.O'Dell,andG.Harisaki.Methodsforincreasedaccuracyinnumericalreservoir simulators. SocietyofPetroleumEngineeringJournal,Trans.AIME ,253,1972. L.G.H.vanderMeer.TheCO 2 storageefciencyofaquifers. EnergyConversionand Management ,36:513,1995. N.Vargaftik. Tablesonthethermophysicalpropertiesofliquidsandgases .Wiley,New York,secondedition,1975. N.Vargaftik,Y.Vinogradov,andV.Yargin. Handbookofphysicalpropertiesofliquidsand gases .BegellHouse,NewYork,thirdedition,1996. Y.Wu,C.Haukwa,andG.Bodvarsson.Asite-scalemodelforuidandheatowinthe unsaturatedzoneofYuccamountain,Nevada. JournalofContaminantHydrology ,38 :185,1999. J.YanosikandT.McCraken.Anine-Point,nite-differencereservoirsimulatorforrealistic predictionofadversemobilityratiodisplacements. SocietyofPetroleumEngineering Journal,Trans.AIME ,267,1979. 27

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Chapter3 AnalyticalSolutionforEstimatingCO 2 StorageEfciency 2 3.1Abstract DuringinjectionofcarbondioxideCO 2 intodeepsalineaquifers,theavailablepore volumeoftheaquifermaybeusedinefciently,therebydecreasingtheeffectivecapacity oftherepositoryforCO 2 storage.Storageefciencyisthefractionoftheavailablepore spacethatisutilizedforCO 2 storage,or,inotherwords,itistheratiobetweenthevolume ofstoredCO 2 andthemaximumavailableporevolume.Inthischapter,Ideriveandpresent simpleanalyticalexpressionsforestimatingCO 2 storageefciencyunderthescenarioofa constant-rateinjectionofCO 2 intoaconned,homogeneous,isotropic,salineaquifer.The expressionsforstorageefciencyarederivedfrommodelsdevelopedpreviouslybyother researchersdescribingtheshapeoftheCO 2 -brineinterface.ThestorageefciencyofCO 2 isfoundtodependonthreedimensionlessgroups,namely:theresidualsaturationof brineafterdisplacementbyCO 2 ;theratioofCO 2 viscositytobrineviscosity;and adimensionlessgroupwhichIcallagravityfactorthatquantiestheimportanceof CO 2 buoyancyrelativetoCO 2 injectionrate.Thetheoreticalmaximumstorageefciency isequaltotheratiooftheCO 2 viscositytothebrineviscosity;thiswouldbeachieved inthecaseofnegligibleresidualbrinesaturationandnegligiblebuoyancyeffects.Storage efciencydecreasesasthegravityfactorincreases,becausethebuoyancyoftheCO 2 causes ittooccupyathinlayeratthetopoftheconnedformation,whileleavingthelowerpart oftheaquiferunder-utilized.Estimatesofstorageefciencyfrommysimpleanalytical expressionsareinreasonableagreementwithvaluescalculatedfromsimulationsperformed withmorecomplicatedmulti-phase-owsimulationsoftware.Therefore,Isuggestthatthe analyticalexpressionspresentedhereincouldbeusedasasimpleandrapidtooltoscreen thetechnicaloreconomicfeasibilityofaproposedCO 2 injectionscenario. 2 Okwen,R.T.,Stewart,M.,andCunningham,J.A.,, AcceptedonAugust27,2009:International JournalofGreenhouseGasControl 28

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3.2Introduction AmongthechallengesassociatedwithcarbondioxideCO 2 storageindeepsaline aquifersisestimatingthecapacityofacandidaterepositoryforCO 2 storagevanderMeer, 1995;Koppetal.,2009.BecausesupercriticalCO 2 isbothlessviscousandlessdense thanthebrinefoundinsalineaquifers,theinjectedCO 2 doesnotdisplaceresidentbrine inapistonorplug-owfashion.Instead,theCO 2 tendstorideoverthebrineasitis injected,formingalayerofCO 2 atthetopoftheconnedformationNordbottenetal., 2005.Thus,eveniftheoverallporevolumeofaconnedaquifercanbeestimatedaccurately,thefractionofthatvolumethatisavailableforCO 2 storageisnotlikelytobeknown apriori. StorageefciencycanbedenedastheratiobetweentheamountofCO 2 storedinan aquiferandthemaximumamountofCO 2 thatcouldtheoreticallybestoredinthesame aquifervolumevanderMeer,1995.PreviousestimatesofCO 2 storageefciencyhave oftenbeenbasedoncomplicatednumericalsimulationse.g.,vanderMeer;Obi andBluntthatcanbetime-consumingorcostlytoperform.Atpresent,asimple analyticalmethodforestimatingCO 2 storageefciencyislacking.Therefore,themain objectiveofthischapteristodevelopasimpleanalyticalequationforestimatingstorage efciencyduringCO 2 injection.Therationaleforthisstudyisthatafastandeasymethodof estimatingCO 2 storageefciencymayfacilitatethepredictionofthetotalamountofCO 2 agivenrepositorycansequester,and/ormayindicateifmoredetailednumericalmodeling orgeologicinvestigationiswarranted. 3.3ModelDevelopment 3.3.1ConceptualModel Inthischapter,weconsidertheinjectionofCO 2 ataconstantinjectionrateintoaconned,homogeneous,andisotropicsalineaquiferviaasingleverticalwell.Figure3isa cartoonillustratingsuchaninjectionscheme. Indevelopinganexpressionforthestorageefciency,Ialsomakethefollowingassumptionsorsimplications. 1.Theporousmediumishomogeneous,isotropic,inert,non-deformable,andinitially saturatedwithbrine; 2.Theradialextentoftheconnedaquiferisverylargecomparedtoitsthickness; 29

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3.Temperature,uiddensities,anduidviscositieswithintheaquifercanbeassumed constantoverbothspaceandtime; 4.Thegasandliquidphasesareimmiscible,i.e.,thereisasharpinterfacebetweenthe twouidsandwecanneglectinter-phasemasstransfer; 5.Theinjectionwellisperforatedacrosstheentirethicknessoftheaquifer,whichisa constantvalue B ; 6.CO 2 isinjectedataconstantvolumetricrate Q well ; 7.AsbrineisdisplacedbyinjectedCO 2 ,aresidualsaturationofbrine S lr isleftbehind theadvancingfrontofCO 2 ; 8.Thereisnegligiblediporinclineinthetopandbottomconningunits,i.e.,theseunits areparallelandeffectivelyhorizontal; 9.Flowintheformationispredominantlyhorizontal,whichmeansthatthepressuredistributionintheverticaldirectioncanbedescribedashydrostatic. Ofcourse,noactualgeologicformationwouldadheretoalloftheseassumedconditions.However,mostoftheassumptionsandsimplicationsarenotparticularlyrestrictive, andthereforetheanalysisthatfollowswouldbeexpectedtobeapproximatelyvalidata relativelylargenumberofpotentialCO 2 repositories.Itcanbenotedthatsimplications orassumptionssimilartothoselistedabovehavebeeninvokedpreviouslyinanumberof studieswhereCO 2 movementhasbeenmodeledanalyticallye.g.,Nordbottenetal.; NordbottenandCelia;Hesseetal.;2008;Juanesetal.. Underthisconceptualframework,theCO 2 plumemigratesradiallyfromtheinjection wellduringinjection,andthethickness b oftheregionoccupiedbyCO 2 isafunction oftime t andofradialdistance r fromtheinjectionwell.Theaquifercanthusbe partitionedintothreeregions,asshowninFigure3.Region 1 containsonlyCO 2 and residualbrine,andextendsfromtheinjectionwelltoaradius r min ,whichdenotesthe minimumradialdistanceoftheCO 2 -brineinterface.Thus,inregion1,thethicknessof theCO 2 layer, b r;t ,isequalto B ,thefullthicknessoftheaquifer.Region 2 contains CO 2 overlyingbrine,separatedbyasharpinterface.Inotherwords,region2istheportion oftheaquiferinwhichthethicknessoftheCO 2 layerobeys 0
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3 containssolelybrineandoccupiestheregionbeyond r max .Inthisregion,thereisnoCO 2 i.e., b r;t =0 Asstatedpreviously,thedenitionofstorageefciencyistheratiobetweentheamount ofCO 2 storedinanaquiferandthemaximumamountofCO 2 thatcouldtheoreticallybe storedinthesameaquifervolumevanderMeer,1995.Thus,forthescenariodepictedin Figure3,wemayestimatethestorageefciency accordingto = V injected V formation = Q well t B r max 2 .1 where istheporosityoftheformation. Figure3.: SchematicrepresentationofCO 2 injectionintoaconnedaquifer. ViaasingleverticalinjectionwellAdaptedfromNordbottenetal. Thestorageefciencymightbesignicantlylessthan 1 becausetheCO 2 ridesoverthe brine,leavingawastedaquifervolumethatremainslledwithbrine.Thepurposeofthis chapteristoderivesimpleexpressionsforestimating 31

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3.3.2MathematicalModel Nordbottenandco-workersNordbottenetal.,2005;NordbottenandCelia,2006have developedanalyticalexpressionsfortheshapeoftheCO 2 -brineinterfaceundertheconditionsandsimplicationsdescribedabove.FollowingNordbottenandco-workers,Ihere deneadimensionlessgroupthatquantiestheimportanceofCO 2 buoyancyrelativeto theCO 2 injectionrate: )-278(= 2 gk b B 2 Q well .2 where k istheintrinsicpermeabilityofthegeologicrepository, b isthemobilityofthe brineintheformationequaltotheinverseoftheviscosityofthebrine, g isthegravitationalaccelerationconstant,and isthedifferenceindensitybetweenthebrineandthe CO 2 When )]TJ/F40 11.9552 Tf 11.251 0 Td [(issmallenough,meaningthattheowofCO 2 isdominatedbytheinjection rateratherthanthebuoyancy,Nordbottenandco-workershaveshownthat r max = s Q well t B )]TJ/F19 11.9552 Tf 11.955 0 Td [(S lr .3 where istheratioofmobilitiesofthetwouids,i.e., = c = b = b = c ,wherethe subscript b denotesbrineandthesubscript c denotesCO 2 ,and isviscosity.Substituting equation.3intoequation.1yieldsthesimpleresultthat,when )]TJ/F40 11.9552 Tf 10.106 0 Td [(issufcientlysmall, = )]TJ/F19 11.9552 Tf 11.955 0 Td [(S lr c b = )]TJ/F19 11.9552 Tf 11.955 0 Td [(S lr 1 .4 Nordbottenandco-workersNordbottenetal.,2005;NordbottenandCelia,2006have arguedthattheeffectofgravitycanbeneglectedwhen )]TJ/F40 11.9552 Tf 10.303 0 Td [(islessthanabout 1 When )]TJ/F40 11.9552 Tf 10.159 0 Td [(islargerthanabout 0 : 5 or 1 ,thebuoyancyoftheCO 2 hasasignicanteffecton theshapeoftheCO 2 -brineinterface,andequations.3and.4arenotexpectedtobe valid.Inthatcase,Iproceedasfollows.AgainfollowingNordbottenandCelia,I non-dimensionalizethevariables r and t accordingto = r p k = Q well t 2 Bk )]TJ/F19 11.9552 Tf 11.955 0 Td [(S lr .5 andIalsodenethesimilarityvariable = 2 = 32

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Substitutingthesedenitionsintoequation.1producesthefollowing: = 2 )]TJ/F19 11.9552 Tf 11.955 0 Td [(S lr max .6 where max correspondstothenon-dimensionalizedvalueof r max Equation.6isasimpleexpressionforthestorageefciencyinthesalineaquifer. However,computationofthestorageefciencywithequation.6requiresustobeable toestimate max ,whichisnotsimple.Whenbuoyancyisnegligible,i.e.,when )]TJ/F40 11.9552 Tf 10.616 0 Td [(issufcientlysmall,then max =2 ,andwerecoverequation.4;butwhenbuoyancycannot beneglected,i.e.,when )]TJ/F40 11.9552 Tf 9.795 0 Td [(isgreaterthanabout 0 : 5 or 1 ,then max isacomplicatedfunction of )]TJ/F40 11.9552 Tf 9.769 0 Td [(andofthemobilityratio .AsdescribedbyNordbottenandCelia,computation of max whichtheycall 0 ;h requiressolutionofanonlinearordinarydifferentialequationsubjecttovolumebalanceconstraints.NordbottenandCeliashowcontoursof p max intheirFigure 3 c. Underrealisticconditions,Iwouldexpecttheviscosityofbrineinadeepsalineaquifer tobeabout 5 20 timestheviscosityofsupercriticalCO 2 Suekaneetal.,2005;Nordbotten etal.,2005.Therefore,Isolvedfor max fordifferentvaluesof between 5 and 20 ,and fordifferentvaluesof )]TJ/F40 11.9552 Tf 11.71 0 Td [(between 0 : 3 and 50 .Basedontheacquiredvaluesof max ,I determinedthat,for 5 20 and 0 : 5 )]TJ/F34 11.9552 Tf 11.241 0 Td [( 50 ,thefollowingequationisasuitable approximationto max max : 0324 )]TJ/F15 11.9552 Tf 11.955 0 Td [(0 : 0952)-222(+ : 1778 +5 : 9682)]TJ/F17 7.9701 Tf 35.279 4.936 Td [(1 = 2 +1 : 6962 )]TJ/F15 11.9552 Tf 11.955 0 Td [(3 : 0472 : .7 Thisempiricalequationyieldsestimatesof max thatareaccuratetowithin 10 %when 0 : 5 )]TJ/F34 11.9552 Tf 10.303 0 Td [( 1 andtobetterthan 5 %when 1 )]TJ/F34 11.9552 Tf 10.303 0 Td [( 50 Finally,Icanpresentthefollowingequationthatenablesmetoestimatethestorage efciencyofthesalineaquifer. )]TJ/F19 11.9552 Tf 11.955 0 Td [(S lr 1 = )]TJ/F19 11.9552 Tf 11.955 0 Td [(S lr c b 0 )]TJ/F19 11.9552 Tf 10.635 0 Td [(< 0 : 5 2 )]TJ/F19 11.9552 Tf 11.955 0 Td [(S lr : 0324 )]TJ/F15 11.9552 Tf 11.955 0 Td [(0 : 0952)-222(+ : 1778 +5 : 9682)]TJ/F17 7.9701 Tf 35.278 3.453 Td [(1 = 2 +1 : 6962 )]TJ/F15 11.9552 Tf 11.955 0 Td [(3 : 0472 0 : 5 )]TJ/F34 11.9552 Tf 10.635 0 Td [( 50 .8 33

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Theexpectedrangeofapplicabilityofequation.8is 5 20 and 0 )]TJ/F34 11.9552 Tf 10.156 0 Td [( 50 ,which spansarealisticrangeofconditionsthatmightbeencounteredinpractice. 3.4Results Itcanbeseenfromequation.8thatthestorageefciencydependsonthreedimensionlessgroups: S lr ,theresidualbrinesaturationfollowingdisplacementofbrinebyCO 2 ; ,theratioofbrineviscositytoCO 2 viscosity;and )]TJ/F40 11.9552 Tf 7.315 0 Td [(,adimensionlessgroupthatquanties theimportanceofCO 2 buoyancyrelativetoowrate.Inthissection,Iinvestigatefurther thedependenceofstorageefciencyoneachofthesevariables.Therstimportantpoint tonoticeisthatthetheoreticalupperlimitofstorageefciencybasedonasinglevertical injectionwell,asconsideredinthischapterisequaltotheratioofuidviscosities, max =1 = = c = b .Thiswouldbetheefciencywhenthereisnegligibleresidualbrinesaturation S lr 0 andtheeffectofgravityisalsonegligible )]TJ/F34 11.9552 Tf 10.047 0 Td [( 0 : 5 ,whichcorrespondstoa highinjectionrate.Aseither S lr or )]TJ/F40 11.9552 Tf 10.153 0 Td [(increases,thestorageefciencywilldecreasebelow itslimitingvalueof max = c = b .ConsideringatypicaldeepsalineaquiferPruess etal.,2004oftemperaturenear 45 C,pressurenear 120 bar 12 MPa,andsalinitynear 15 %,wewouldexpectsupercriticalCO 2 tohaveaviscosityofapproximately 5 : 0 10 )]TJ/F17 7.9701 Tf 6.587 0 Td [(5 Pa sMcHughandKrukonis,1986;Vesovicetal.,1990andbrinetohaveaviscosityof approximately 8 : 0 10 )]TJ/F17 7.9701 Tf 6.586 0 Td [(4 Pa sPalliserandMcKibbin,1998;AdamsandBachu,2002. Thisyieldsavalueof =16 ;theupperlimitofstorageefciencyinsuchaformation wouldbeabout 5 : 0 10 )]TJ/F17 7.9701 Tf 6.587 0 Td [(5 / 8 : 0 10 )]TJ/F17 7.9701 Tf 6.587 0 Td [(4 orabout 6 : 3 %. IftheCO 2 injectionrate Q well ishighenoughthatbuoyancyeffectscanbeneglected i.e., )]TJ/F19 11.9552 Tf 12.053 0 Td [(< 0 : 5 ,thenthestorageefciency dependsonlyonthemobilityratio and theresidualbrinesaturation S lr .Figure4showsthedependenceofstorageefciency onmobilityratioforthreedifferentvaluesof S lr underthecaseofnegligiblebuoyancy. Undertheseconditions,thepossiblerangeofstorageefcienciesisfromabout 3 %toabout 20 %.However,undermostrealisticaquiferconditions,wemightexpectaresidualbrine saturationofatleast 0 : 15 andamobilityratioofatleast 10 ;thuswemightexpectstorage efciencytoreachamaximumvalueofabout 8 : 5 %evenifbuoyancyeffectsarenegligible. AstheeffectofCO 2 buoyancyincreases )]TJ/F19 11.9552 Tf 11.693 0 Td [(> 0 : 5 ,thestorageefciencydecreases. ThisisbecausetheshapeoftheCO 2 plumeintheformationchanges.Buoyancydrives theCO 2 upwardssothatitoccupiesarelativelythinsectionatthetopoftheconned formation.ThustheCO 2 plumeisthinnerbutextendsfarther r max increases,andthereis morewastedvolumebelowtheCO 2 plume,resultinginadecreaseinstorageefciency. 34

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Figure4.: Storageefciency vsmobilityratio .Whentheeffectofgravityisnegligiblesmall )]TJ/F40 11.9552 Tf 7.314 0 Td [(. Figure5.: Storageefciency vs.gravityfactor )]TJ/F40 11.9552 Tf 7.314 0 Td [(.Thecurvesshownwere generatedassumingavalueofresidualbrinesaturation S lr =0 : 15 35

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Table4: Conditionsforarealisticinjectionscenario. Parameterorcondition Value Temperatureinaquifer C 45 Pressureinaquiferbar 120 Salinity 15% Aquiferthickness, B m 100 Aquiferpermeability, k m 2 10 )]TJ/F17 7.9701 Tf 6.586 0 Td [(13 Residualbrinesaturation, S lr 0.30 CO 2 injectionrate, Q kg/s 100 Figure5showsthedependenceofstorageefciencyonthegravityfactor )]TJ/F40 11.9552 Tf 10.029 0 Td [(fortherange 0 : 1 < )]TJ/F19 11.9552 Tf 11.175 0 Td [(< 100 .Notethattheequationfor wasdevelopedonlyfortherange )]TJ/F34 11.9552 Tf 11.176 0 Td [( 50 sotheremaybesomeerrorintheestimatesof intherange 50 < )]TJ/F34 11.9552 Tf 11.358 0 Td [( 100 .Figure5 considersdifferentvaluesofmobilityratio ,butwasgeneratedassumingasinglevalue of S lr equalto 0 : 15 .Asexpected,thegureshowsadecreaseinstorageefciencyas )]TJ/F40 11.9552 Tf -424.686 -17.928 Td [(increases.Intheextremecaseofahighmobilityratio =20 andahighgravityfactor )]TJ/F19 11.9552 Tf -424.686 -17.927 Td [(> 20 ,thestorageefciencyisexpectedtobelessthan 2 %. Finally,IconsideragainatypicalCO 2 injectionscenario.Conditionsforthisinjection scenarioaretakenfromanexampleproblemdescribedbyPruessandbyPruessand Spycher,andaresummarizedinTable4.Attheseconditions,theuidviscosities wouldbeapproximately b =8 : 0 10 )]TJ/F17 7.9701 Tf 6.586 0 Td [(4 Pa sand c =5 : 0 10 )]TJ/F17 7.9701 Tf 6.587 0 Td [(5 Pa s,asnotedpreviously.Also,theuiddensitieswouldbeapproximately b =1100 kg/m 3 McCutcheon etal.,1993and c =660 kg/m 3 BachuandAdams,2003.Theinjectionrateof 100 kg/s isequivalentto 0 : 15 m 3 /sassumingaCO 2 densityof 660 kg/m 3 .ACO 2 massinjection rateof 100 kg/sisequivalenttoCO 2 emissionsfroma 288 MWecoal-redpowerplant Hitchon,1996.Thus,thecalculatedvalueof )]TJ/F40 11.9552 Tf 11.425 0 Td [(accordingtoequation.2is 0 : 226 meaningthattheeffectofbuoyancyisessentiallynegligibleundertheseconditions.Therefore,theestimatedstorageefciencyforCO 2 injectionviaasingleverticalinjectionwell is,accordingtoequation.4or.8, =0 : 044=4 : 4 %. 3.5Discussion Itmustbenotedthatanumberofpotentiallyimportantfactorsarenotincludedinthis analysis.Forinstance:AsCO 2 isinjectedintotheaquifer,thepressureintheformation willincrease,whichwillinturncausethedensitiesandviscositiesoftheuidstochange. 36

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BothdensityandviscosityofsupercriticalCO 2 arerelativelystrongfunctionsofpressure near 45 Cand 120 bar.However,theanalysispresentedaboveassumesthatuidproperties areconstant,i.e.,donotchangeduringtheinjection.Itislikelythatarealaquiferwould exhibitheterogeneity,perhapsintheformoflayersorfaciesofdifferentpermeability,or perhapsintheformoffracturesthatcanactaspreferentialconduitsforuidow.Eitherof thesesituationswouldaltertheshapeoftheCO 2 plumefromthatshowninFigure3,with theresultthattheCO 2 storageefciencywouldalsobedifferentfromthatpredictedhere. Theanalysispresentedheredoesnotaccountfortheprocessofdry-out,inwhich residualbrinesaturationiseventuallyevaporatedbyinjectedCO 2 NordbottenandCelia, 2006;PruessandM uller,2009. Othercomplicatingfactorsnotconsideredinthisanalysisarealsocertaintoexist.However,thepurposeofthischapteristopresentarapid,simple,easy-to-usemethodforestimatingstorageefciencywithinareasonabledegreeofuncertainty.Tothatend,Iexpect thattheanalysispresentedhereinisacceptabledespitetheneglectofcertaincomplicating factors.Inote,forinstance,thattheestimatesof madeaboveapproximately 4 6 % fortypicalinjectionscenariosareinreasonableagreementwithestimatesmadebyother researchersusingsophisticatednumericalsimulationsoftwaree.g.,vanderMeer; ObiandBlunt.Thus,estimatesof madewithequation.8wouldlikelybe suitable,forinstance,inapreliminaryscreeningofthetechnicaloreconomicfeasibility ofaproposedCO 2 injectionproject.MorerobustpredictionsofCO 2 behavior,accounting forsomeorallofthefactorsmentionedabove,wouldrequirenumericalsimulationwitha multi-phaseowandtransportmodelsuchasTOUGHREACTXuetal.,2006. 3.6SummaryandConclusions Theobjectiveofthischapteristodevelopasimpleanalyticalequationforestimating storageefciencyduringCO 2 injection.BasedonanalyticalmodelsforCO 2 plumeshape developedpreviouslybyotherresearchersNordbottenetal.,2005;NordbottenandCelia, 2006,asimpleequationforthestorageefciency, ,wasderived.Thederivationincluded somesignicantassumptionsandsimplications,whichwillresultinsomeuncertaintyin estimatesof ;however,calculatedvaluesof arelikelytobesuitablefor,say,apreliminaryscreeningofthetechnicaloreconomicfeasibilityofaproposedCO 2 injectionproject. ApreliminaryestimateofCO 2 storageefciencymaybeused,forinstance,todetermine ifmoredetailednumericalmodelingorgeologicinvestigationarewarranted. 37

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ThestorageefciencyofCO 2 isfoundtodependonthreedimensionlessgroups,namely: S lr ,theresidualsaturationofbrineafterdisplacementbyCO 2 ; ,theratioofbrine viscositytoCO 2 viscosity;andadimensionlessgroup )]TJ/F40 11.9552 Tf 10.442 0 Td [(thatquantiestheimportance ofCO 2 buoyancyrelativetoCO 2 injectionrate.Dependenceofstorageefciencyonthe threedimensionlessgroupsisshowngraphicallyinFigures4and5.Thetheoreticalmaximumstorageefciencyis max =1 = = c = b ,whichwouldbeachievedinthecaseof negligibleresidualbrinesaturation S lr 0 andnegligiblebuoyancyeffects )]TJ/F19 11.9552 Tf 11.357 0 Td [(< 0 : 5 Storageefciencydecreasesas )]TJ/F40 11.9552 Tf 10.699 0 Td [(increases,becausethebuoyancyoftheCO 2 causesitto occupyathinlayeratthetopoftheconnedformation,whileleavingthelowerpartofthe aquiferunder-utilized. ItisworthnotingthatIestimatedlikelystorageefcienciesofonly 4 6 %underaset ofassumedbutrealisticconditions,andthattheseestimatesareevenslightlyhigherthan otherestimatesmadeusingnumericalmodelsvanderMeer,1995;ObiandBlunt,2006. Theselowstorageefcienciesareoneofthepotentialdrawbackstothetechnologyof geologicCO 2 sequestration.Ifstorageefcienciescouldberaisedtoevenashighas 10 %, itcoulddoubletheworldwidecapacityforCO 2 storageindeepsalineaquifers.Therefore, wesuggestinconclusionthatdevelopingstrategiesortechnologiesforincreasingCO 2 storageefciencyshouldbeasignicantpriorityduringourongoingdevelopmentofCO 2 sequestration. 3.7ReferencesCited J.AdamsandS.Bachu.Equationsofstateforbasingeouids:Algorithmreviewand intercomparisonforbrines. Geouids ,2,2002. S.BachuandJ.J.Adams.SequestrationofCO 2 ingeologicalmediainresponsetoclimatechange:CapacityofdeepsalineaquiferstosequesterCO 2 insolution. Energy ConversionandManagement ,44:3151,2003. M.Hesse,H.Tchelepi,B.Cantwell,F.Orr,Jr.,andJ.Friedmann.Gravitycurrentsin horizontalporouslayers:Transitionfromearlytolateself-similarity. J.FluidMech. 577:363,2007. M.Hesse,F.Orr,Jr.,andH.Tchelepi.Gravitycurrentswithresidualtrapping. J.Fluid Mech. ,611:36,2008. B.Hitchon. Aquiferdisposalofcarbondioxide .GeosciencePublishingLtd.,Sherwood Park,Alberta,Canada,1996. 38

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R.Juanes,C.MacMinn,andM.Szulczewski.ThefootprintoftheCO 2 plumeduring carbondioxidestorageinsalineaquifers:Storageefciencyforcapillarytrappingatthe basinscale. TransportinPorousMedia,inpress ,2009. A.Kopp,H.Class,andR.Helmig.InvestigationsonCO 2 storagecapacityinsaline aquifersPart 2 :Estimationofstoragecapacitycoefcients. InternationalJournalof GreenhouseGasControl ,3:277,2009. S.McCutcheon,J.Martin,andJ.Barnwell,T.O. WaterQuality.In:HandbookofHydrology .McGraw-Hill,NewYork,1993. M.McHughandV.Krukonis. SupercriticalFluidExtraction:PrinciplesandPractice ButterworthPublishers,Boston,1986. J.NordbottenandM.Celia.Similaritysolutionsforuidinjectionintoconnedaquifers. JournalofFluidMechanics ,561:307,2006. J.Nordbotten,M.Celia,andS.Bachu.InjectionandstorageofCO 2 indeepsalineaquifers: AnalyticalsolutionforCO 2 plumeevolutionduringinjection. TransportinPorousMedia ,58:339,2005. O.ObiandM.Blunt.Streamline-basedsimulationofcarbondioxidestorage inaNorthSeaaquifer. WaterResourcesResearch ,42W03414:1,2006. doi:10.1029/2004WR003347. C.PalliserandR.McKibbin.Amodelfordeepgeothermalbrines.III:Thermodynamic properties,enthalpyandviscosity. TransportinPorousMedia ,33,1998. K.Pruess. ECO2N:ATOUGH2uidpropertymoduleformixturesofwater,NaCl,and carbondioxide .LawrenceBerkeleyNationalLaboratory,Berkeley,California,2005. K.PruessandN.M uller.Formationdry-outfromCO 2 injectionintosalineaquifers: 1 : Effectsofsolidsprecipitationandtheirmitigation. WaterResourcesandResearch ,45 w03402:1,2009.doi:10.1029/2008WR007101. K.PruessandN.Spycher.ECO 2 N-AuidpropertymodulefortheTOUGH 2 codefor studiesofCO 2 storageinsalineaquifers. EnergyConversionandManagement ,48: 1761,2007.DOI:10.1016/j.enconman.2007.01.016. K.Pruess,J.E.Garc a,T.Kovscek,C.Oldenburg,J.Rutqvist,C.Steefel,andT.Xu.Code intercomparisonbuildscondenceinnumericalsimulationmodelsforgeologicdisposal ofCO 2 Energy ,29:1431,2004.doi:10.1016/j.energy.2004.03.077. T.Suekane,S.Soukawa,S.Iwatani,S.Tsushima,andS.Hirai.Behaviorofsupercritical CO 2 injectedintoporousmediacontainingwater. Energy ,30:2370,2005. 39

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L.G.H.vanderMeer.TheCO 2 storageefciencyofaquifers. EnergyConversionand Management ,36:513,1995. V.Vesovic,W.Wakeham,G.Olchowy,J.Sengers,J.Watson,andJ.Millat.Thetransport propertiesofcarbondioxide. J.Phys.Chem.Ref.Data ,19,1990. T.Xu,E.Sonnenthal,N.Spycher,andK.Pruess.TOUGHREACTAsimulationprogram fornon-isothermalmultiphasereactivegeochemicaltransportinvariablysaturatedgeologicmedia:ApplicationstogeothermalinjectivityandCO 2 geologicalsequestration. Computers & Geosciences ,32:145,2006. 40

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Chapter4 AnalyticalModelforScreeningPotentialCO 2 Repositories 4.1Abstract AssessingpotentialrepositoriesforsubsurfacesequestrationofcarbondioxideCO 2 usingnumericalmodelsiscomplicated,costly,andtimeconsuming,especiallyininstances wherethesuitabilityofamultitudeofgeologicformationsmustbeevaluated.Thischapter presentsascreeningtoolforassessingthesuitabilityofcandidaterepositoriesforsubsurfacesequestrationofcarbondioxideCO 2 ,usingasetofsimpleanalyticalequations model.IconsideredtheinjectionofCO 2 ataconstantrateintoaconnedsalineaquifer viaafullyperforatedverticalinjectionwell.ThevalidityoftheanalyticalmodelwasassessedviacomparisonwiththeTOUGH2numericalmodel.Themetricsusedincomparingthetwomodelsinclude:spatialvariationsinformationpressure,brinesaturation prole,andstorageefciency.WhentheinputconditionsandassumptionsinTOUGH 2 werechosentobesimilartothoseoftheanalyticalmodel,thetwomodelsshowedexcellent agreement.Theanalyticalmodelneglectscapillarypressureandthepressuredependence ofuidproperties.However,simulationsinTOUGH2indicatethatlittleerrorisintroduced bythesesimplications.SensitivitystudiesshowedthattheagreementbetweentheanalyticalmodelandTOUGH2dependsstronglyontheresidualbrinesaturation,gravity g ,andtherelationshipbetweenrelativepermeabilityandbrinesaturation k r S w Theresultsobtainedsuggestthattheanalyticalmodelisvalidwhen k r S w islinearor quasi-linearandwhentheirreduciblesaturationsofbrineiszeroorverysmall. 4.2Introduction Complexnumericalsimulators,likeTOUGH 2 /ECO 2 N,GEM,FLOTRAN,Eclipse 300 andCSIROPruessetal.,2004,arecurrentlyusedtostudyandpredictCO 2 plumebehaviorinconnedgeologicformations.Theoutputsfromthesesimulatorsincludeestimates 41

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ofthevaluesofpivotalparametersthatcanbeusedtodeterminethesuitabilityofgeologic formations.However,thesenumericalsimulatorsareexpensive,havesignicantlylong executiontimes,andrequirealargenumberofinputparameters.Therefore,ananalyticalmodelthatisrapidandusesfewerinputparameterstopredictpivotalparametersmay serveasacost-effectivesurrogatetonumericalsimulatorsforscreeningcandidaterepositoriespriortodetailedsite-specicfeasibilitystudiesanddesignofCO 2 injectionsystems. Nordbottenandco-workersNordbottenetal.,2005;NordbottenandCelia,2006previouslydevelopedanalyticalsolutionsmodelforpredictingCO 2 behaviorinconned aquifers.TheyconsideredCO 2 injectionviaaverticalwellintoaconnedsalineaquifer ofinniteradialextent.ThemodelpredictsthelocationoftheCO 2 -brineinterfaceand presentsapressurederivativei.e.,equation 7 inNordbottenandCelia.However,in itscurrentform,themodeldoesnotpredictpressurevariations.Themodelalsoignores capillarypressureeffectsandconsidersCO 2 andbrinetobeincompressibleandimmiscible witheachotheri.e.,nointer-phasemasstransfer.Anevaluationoftheanalyticalmodel isrequiredtoverifyiftheabove-mentionedassumptionsaretoolimiting. Theobjectivesofthischapterareto: 1.extendtheanalyticalmodeldevelopedbyNordbottenetal.andbyNordbotten andCeliatobeabletopredictpressurechangeswithintheformation 2.assessconditionsunderwhichthemodelcanbeconsideredvalid. Therationaleforthisstudyisthattheextended-analyticalmodelcanbeausefultoolfor screeningpotentialrepositoriesstoragesitesforCO 2 storage.Theextended-analytical modelwillalsofacilitatepredictionofpressurevariationswithintheaquifer,especiallyat theinjectionwell,wherepressureishighest. Equationsthatconstitutetheextended-analyticalmodelwerederivedbydeningamovingpressureboundaryDirichletcondition.Theconditionsunderwhichtheanalytical modelisvalidweredeterminedviacomparisonwithamoresophisticatednumericalmodel. Pivotalparametersmetricsusedincomparingbothmodelsincludethefollowing: 1.spatialvariationsofpressure P r;t withinaconnedformation; 2.thebrinesaturationprole S w t withinaconnedformation;and 3.temporalvariationinCO 2 storageefciency s t Theseparameterswereusedasmetricsforcomparingtheperformanceoftheanalytical modeltothatofthenumericalmodel. 42

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4.3ModelDevelopment 4.3.1ConceptualModel Thefollowingassumptionsweremadeinthedevelopmentoftheanalyticalmodel: 1.theporousmediumisinert,non-deformable,andinitiallysaturatedwithbrine; 2.theradialextentoftheconnedaquiferisinnitecomparedtoitsthickness; 3.changesintemperature,uiddensities,anduidviscositieswithintheformationare negligible; 4.thegasandliquidphasesareimmisciblenegligibleinter-phasemasstransfer; 5.capillaryforcesandhystereticeffectsarenegligible; 6.thegasplumemigratesradiallyfromtheinjectionwellduringinjectionandthethicknessoftheregionoccupiedbyCO 2 isafunctionoftimeandradialextent; 7.foragivenpointintime,thereexistsalocationwithintheformationsufcientlydistant fromtheinjectionwellwherethepressureisequivalenttoitsinitialvaluebackground pressure;and 8.thedipangleoftheaquiferiszeroornegligiblei.e.Aquiferisperfectlyhorizontal. Theassumptionofnointer-phasemasstransferbetweentheuidphasesimmiscible uidsmayberatherrigid.However,withthisassumption,theresultingequationscanbe easilysolvedbyhandorusingspreadsheet.Assumptionofconstantuidpropertiesinthe analyticalmodelmayintroduceerrornearthewellbore.However,thisapproximationis reasonablefortheremainderofanaquifersincepressurebuild-upduetouidinjection quicklydiminisheswithdistancefromthewellboreBachuetal.,2004.Aschematic representationofCO 2 injectionintoahomogeneousconnedaquiferisshowninFigure6. Toextendtheanalyticalmodel,theformationwaspartitionedintothreeregionsi.e., regions 1 2 ,and 3 Figure6.Region 1 containsonlyCO 2 ,andextendsfromtheinjection welltotheminimumradialdistanceoftheCO 2 -brineinterfacefromtheinjectionwell, r min .Region 2 containsCO 2 overlyingbrine,separatedbyasharpinterfaceandextends from r min tothemaximumradialdistanceoftheCO 2 -brineinterfacefromtheinjection well, r max .Lastly,region 3 containssolelybrineandoccupiestheregionbeyond r max 43

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Figure6.: SchematicrepresentationofCO 2 -brineinterfaceduringinjection. Intoaconnedaquiferviaasingleverticalwell.AdaptedfromNordbottenetal.. 4.3.2CurrentFormofAnalyticalModel TheanalyticalequationforestimatingtheCO 2 plumethicknessorlocationofCO 2 -brine interfacelocationderivedbyNordbottenetal.;NordbottenandCeliaisas follows: b 0 = 1 )]TJ/F15 11.9552 Tf 11.956 0 Td [(1 s 2 .1 where b 0 isthedimensionlessthicknessofthegasplume,i.e., b 0 = b r;t =B B isthe aquifer'sthickness[L], istheratiobetweenthemobilitiesofCO 2 andbrine,i.e., = c = w c isthemobilityofCO 2 [LTM )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ],and w isthemobilityofbrine[LTM )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 ]. Inequation.1 representsascalingvariablewhichismathematicallydenedas followsNordbottenandCelia,2006: 44

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= 2 .2 wherethevariables and arethedimensionlessradiusandtime,respectively,i.e. = r= p k and = Q well t= Bk )]TJ/F19 11.9552 Tf 12.418 0 Td [(S lr .Inaddition, r istheradiusfrominjectionwell [L]; k istheintrinsicpermeabilityoftheformation[L 2 ]; Q well isthevolumetricinjection rate[L 3 T )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ]; t isthetimeofinjection[T]; isaverageporosityoftheaquifer;and S lr istheresidualbrinesaturation; Adimensionalversionofequation4.1canbeobtainedbysubstitutingthe b 0 and whichisasfollows: b r;t = B )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 s Q well t )]TJ/F19 11.9552 Tf 11.956 0 Td [(S lr Br 2 )]TJ/F15 11.9552 Tf 11.956 0 Td [(1 # .3 Analyticalexpressionsforestimating r min and r max whengravityisignoredNordbotten etal.,2005,areasfollows: r min = s Q well t B )]TJ/F19 11.9552 Tf 11.956 0 Td [(S lr r max = s Q well t B )]TJ/F19 11.9552 Tf 11.955 0 Td [(S lr .4 ThepressurederivationderivedbyNordbottenandCeliaequation 7 isasfollows: @P @r =[ c h + w H )]TJ/F19 11.9552 Tf 11.955 0 Td [(h ] )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 c h @ gh @r )]TJ/F19 11.9552 Tf 13.151 8.088 Td [(Q well 2 rk # .5 Theterms h and H inequation.5areidenticalto b and B ,respectively,inequation.3. Withthisequation.5canbewrittenasfollows: @P @r = c b g @b @r )]TJ/F20 7.9701 Tf 13.151 5.137 Td [(Q well 2 rk [ c b + w B )]TJ/F19 11.9552 Tf 11.955 0 Td [(b ] .6 Atitscurrentform,equation.6requiresawelldenedDirichletboundarycondition inordertobesolvedanalytically.Inotherwords,thepressure, P mustbespeciedata locationrinordertosolveequation4.6. 45

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4.3.3DevelopmentofBoundaryConditiontoPredictFormationPressure Theanalyticalequationsthatconstitutethemodelweredevelopedbyextendingthe semi-analyticalequationsderivedbyNordbottenandCeliatoaccountforamoving boundaryconditionDirichletandtoalsoestimateCO 2 storageefciency.ADirichlet boundaryconditionisessentialindetermininganalyticalequationsforthepressurewithin theaquifer.Theboundaryconditionwasdenedbyderivinganequationforestimatingthe radialdistancefromtheinjectionwell R 1 atwhichtheformationpressureisequivalent toitsbackgroundorinitialpressure P init Analyticalequationsforpressurevariationswithintheconnedaquiferwereobtained byderivinganalyticalexpressionsforpressurechangesinregions 3 2 ,and 1 ofFigure 6,respectively.Theequationforpressurechangesinregion 3 wasrstderivedsinceitis dependentonamovingDirichletboundarydenedat R 1 [ L ]externalboundary.Again, R 1 istheradialdistancefromtheinjectionwellatwhichthepressurewithinanaquiferis approximatelyequivalenttoitsinitialorbackgroundpressure P init i.e., P r = R 1 = P init .However, R 1 isdifculttoestimatesinceitmoveswithtimemovingboundary. R 1 wasestimatedbyemployingtheCooper-JacobapproximationCooperandJacob, 1946oftheTheissolutionTheis,1935forpressurechangeinresponsetoinjectionand byaccountingforthepresenceofaseconduidphaseCO 2 inthiscase,whichextends fromtheinjectionwellto r max Figure6. R 1 = e )]TJ/F21 5.9776 Tf 7.782 3.752 Td [( 2 s 4 Tt S + r max .7 where 0 : 58 T ,and S areEuler'sconstant,formationtransmissivity[L 2 T )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 ],and formationstorativity[L],respectively. Therstandsecondtermsontheright-hand-sideofequation4.7areestimatesof R 1 usingTheissolutionandcorrectionduetothepresenceofaseconduidphase,respectivelyseederivationinAppendixB.Formationpressureat R 1 asafunctionoftime P r = R 1 = P init wasusedasthemovingDirichletboundaryconditioninpredicting thepressureresponseinregion 3 Figure6.Formationpressureat r max P r max t was employedasboundaryconditionbetweenregions 3 and 2 .Lastly,formationpressureat r min P r min t wasappliedasaboundaryconditionbetweenregions 2 and 1 Thefollowingequationsforpressureprolesinregions 1 2 ,and 3 wereobtainedsee derivationinappendix: 46

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P r;t = P init + 8 > > > > > > > > > > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > > > > > > > > > > : Q well 2 k w B ln R 1 r max +1 )]TJ/F17 7.9701 Tf 13.503 4.707 Td [(1 + 1 ln r min r !# region1 )]TJ/F17 7.9701 Tf 10.494 5.136 Td [( gB )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 2 )]TJ/F15 11.9552 Tf 11.955 0 Td [(ln )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 # Q well 2 k w B ln R 1 r max +1 )]TJ/F20 7.9701 Tf 20.654 4.707 Td [(r r max # region2 )]TJ/F17 7.9701 Tf 10.494 5.136 Td [( gB )]TJ/F17 7.9701 Tf 6.587 0 Td [(1 2 ln r r max + r max r )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 # Q well 2 k w B ln R 1 r !# region3 .8 where P r;t istheformationpressure[ML )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 T )]TJ/F17 7.9701 Tf 6.587 0 Td [(2 ];and P init istheinitialformation pressure[ML )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 T )]TJ/F17 7.9701 Tf 6.587 0 Td [(2 ]. Pressureattheinjectionwellcanbeestimatedbysubstituting r withthewellboreradius r well [L]inequation4.8region1.Inconditionswhere << )]TJ/F15 11.9552 Tf 12.039 0 Td [(1 negligiblebuoyancythethirdtermontherighthandsideofequation4.8regions 1 and 2 approaches zeroi.e., gB= )]TJ/F15 11.9552 Tf 12.492 0 Td [(1 2 0 .Thethirdtermontherighthandsideofequation.8 accountsforgravityeffect.Asaresulttheanalyticalmodeliscapableofestimatingpressureswhengravityisincludedturnedonandwhengravityisignored.Gravityisignored byeliminatingthethirdtermontherighthandsideofequation.8. 4.3.4BrineSaturationProle Inregion 3 ofFigure6,thethicknessoftheCO 2 -richphasegasplume, b r;t ,is consideredtobezerofunctiontheaquiferisassumedtobefullysaturatedwithbrineinthis region.Equation4.3wasassumedtoprovideagoodestimateof b r;t inregion 2 .Resultsfromtheliteratureindicatethatthisassumptionisvalidforvaluesofadimensionless gravityfactor )]TJ/F40 11.9552 Tf 7.314 0 Td [(lessthan 0 : 5 Nordbottenetal.,2005;NordbottenandCelia,2006. )]TJ/F40 11.9552 Tf -424.686 -17.928 Td [(quantiestheimportanceofCO 2 buoyancyrelativetotheCO 2 volumetricinjectionrate, i.e.; )-278(= 2 g w kB 2 Q well .9 47

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Lastly,inregion 1 b r;t wasassumedtobeequivalentto B ,becauseitissaturatedwith CO 2 .Theequationsemployedtoestimatebrinesaturationproleatagivenpointintime, S w r;t ,inregions 1 2 ,and 3 Figure6areasfollows: S w r;t = 8 > > > > > > > < > > > > > > > : S lr region1 1 : 0 )]TJ/F20 7.9701 Tf 13.151 5.579 Td [(b r;t B region2 1 : 0 region3 .10 4.4TestCasesforComparisontoTOUGH 2 TheanalyticalmodelwasappliedonaproblemsimilartoProblem 3 ofthecodeintercomparisonprojectPruessetal.,2004.TheprobleminvolvedCO 2 injectionintoa connedsalineaquiferviaafullyperforatedverticalwellFigure6ataconstantrate.Table5presentsthehydrogeologicparametersappliedinthemodel.TheCO 2 massinjection rateof 100 kg/semployedhereinisequivalenttoCO 2 emissionsfroma 288 MWecoalredpowerplantHitchon,1996.TheTOUGH 2 numericalsimulatorwasalsoappliedon theproblemanditsresultscomparedtothosefromtheanalyticalmodelinordertovalidate thelatter,basedonthemetrics. Table5: Aquiferpropertiesemployedinallsimulations. Physicalparameters Values Depthm 1200 Aquiferthicknessm 100 Formationbulkdensitykg/m 3 2600 Porecompressibilitym 2 /N 4 : 5 10 )]TJ/F17 7.9701 Tf 6.586 0 Td [(10 Rockcompressibilitym 2 /N 6 : 5 10 )]TJ/F17 7.9701 Tf 6.586 0 Td [(11 Initialpressureatbottomofformationbar 131 Temperature C 45 Averageporosity 0.12 Averagepermeabilitym 2 10 )]TJ/F17 7.9701 Tf 6.587 0 Td [(13 Gasinjectionratekg/s 100 TOUGH 2 isageneral-purposenumericalsimulationprogramformultiphaseowin porousandfracturedmedia,developedintheLawrenceBerkeleyNationalLaboratory,California,USAPruessetal.,1999.WhencoupledwiththeECO2Nuidpropertymodule, 48

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TOUGH2cansimulateCO 2 plumebehaviorindeepsalineaquifersPruessandSpycher, 2006.TOUGH 2 hasalsobeensuccessfullyusedinmodelingCO 2 injectioninheterogeneousformationsDoughtyandPruess,2004andtostudyCO 2 plumeowdynamics withintheUtsiraformationSleipnerProjectintheNorwegiansectoroftheNorthSea Garc a,2003;PruessandM uller,2009.Mostofall,acomparisonofTOUGH 2 with nineothersimulationtoolsbasedontheirperformanceoneighttestproblemsshowedgood agreementintheirpredictionsPruessetal.,2004.ThesefactorsqualifyTOUGH 2 asa reliableorviablenumericalmodel.Therefore,agreementinthepredictionsoftheanalyticalmodelandTOUGH 2 validatestheformer.Table6presentsthedifferentnumerical simulationsconductedtoevaluatethevalidityoftheanalyticalmodel. TheinputconditionsinSim1Aweresettomatchthesimplicationsinvokedintheanalyticalmodeli.e.constantuidproperties,negligiblecapillarypressure,andnointerphase masstransfer.TheuidpropertiesofCO 2 atallpressureswereassignedvaluesequalto theinitialconditionoftheformationSim1AinTable6.Thiswasachievedbyeditingthe CO2TABleinTOUGH 2 ,whichcontainstabulardataofCO 2 density,viscosityandspecicheatenthalpyatdifferenttemperaturesandpressuresAltunin,1975;Pruess,2005. Theuidpropertiesofbrinewereallowedtovarywithpressuresinceitissignicantlyless compressiblethanCO 2 .Theonlydifferencebetweentheinputconditionsintheanalytical modelandSim1Aisthatuidrelativepermeabilityisnotconsideredintheformerwhile alinearrelationshipbetweenuidrelativepermeability k r andbrineorliquidphasesaturation S w isappliedinthelatter.Therefore,comparisonoftheanalyticalmodelwith Sim1Awillrstdeterminewhethertheproposedboundaryconditionisacceptableandif theassumptionofnouidrelativepermeabilityimmiscibleuidsrelativetolinearuid relativepermeabilityisverylimiting.TheinputconditionsinSim1Baresimilartothose ofSim1Aexceptthattheconstantuidpropertiesassumptionwasrelaxed,theresidual brinesaturationvaluewasincreasedfrom 0 : 0 to 0 : 3 ,thebrinesalinitywasincreasedfrom 0 : 0 to 0 : 3 ,andnonlinearrelationshipbetweenbrinecapillarypressureandbrinesaturation, developedbyvanGenuchtenwasapplied.Therefore,thedifferencesintheinput conditionsbetweentheanalyticalmodelandSim1Bareinuidproperties,brinesalinity, andcapillarypressurefunction P cap .Acomparisonofthepredictionsoftheanalytical modelandSim1Bwillevaluatetheeffectsuidproperties,brinesalinityandmostespeciallybrinecapillarypressure. 49

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DifferencesintheinputconditionsofSim1CandSim1Bissolelyinuidrelativepermeabilityfunction.Thenonlinearrelationshipbetweentherelativepermeabilitiesofwater brineandgasCO 2 andbrinesaturationdevelopedbyvanGenuchtenandCorey ,respectively,wereappliedinSim1C.Asaresult,thedifferencesintheinputconditionsoftheanalyticalmodelandSim1CaresimilartothosebetweentheformerandSim 1B,exceptthatanonlinearrelativepermeabilityfunctionwasappliedinSim1C.Therefore, thevariableinvestigatedinthiscaseistherelativepermeabilityfunction k r .Comparison oftheresultspredictedbyanalyticalmodel,Sim1B,andSim1Cespeciallypressureand brinesaturationdistributionswillshowdifferencesbetweeneffectsofusinga;nouid relativepermeabilityanalyticalmodel,linearrelativepermeabilityfunctionSim1B, andnonlinearrelativepermeabilityfunctionSim1C. Table6: InputparametersandconditionsusedinTOUGH2simulations. VariablesSim1ASim1BSim1C FluidPropertiesConstantVaryVary Brinesalinity0.00.150.15 S lr 0.00.30.3 P cap 0.0nonlinearnonlinear k rw S w LinearLinearnonlinear y k rg S w LinearLinearnonlinear z m --0.457 g m/s 2 0.00.00.0 VariablesSim1DSim1ESim1F FluidPropertiesVaryVaryVary Brinesalinity0.150.150.15 S lr 0.30.30.3 P cap nonlinearnonlinear y nonlinear k rw S w Linearnonlinear y nonlinear k rg S w Linearnonlinear z nonlinear m -0.457 P cap :0.457, k r S w :1.0 g m/s 2 9.819.819.81 m = poresizedistributionindexvanGenuchten,1980 y vanGenuchten z Corey Sim1D,Sim1E,andSim1Fweredesignedtotestfortheeffectsofgravitybuoyancy atdifferentuidrelativepermeabilityfunctions k r .Sim1DandSim1EaresimplydifferentversionsSim1BandSim1C,respectively,withgravityincluded.Sim1Fissimilar toSim1Eexceptthataquasi-linearrelationshipbetween k r and S w wasappliedinthe Sim1F.Comparisonoftheresultspredictedbyanalyticalmodel,Sim1D,Sim1E,and 50

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Sim1Fwillevaluatetheimportanceofgravityeffectsfordifferentscenariosoftherelative permeabilityfunctions,i.e.,none,linear,nonlinear,andquasi-linearrelativepermeability functions.Thepredicted P r;t and S w r;t prolesfromtheanalyticalmodelandSim 1A,Sim1B,Sim1C,Sim1D,Sim1E,andSim1Fwereplottedasafunctionofasimilarity variable = r 2 =t i.e.partialdifferentialequationsin r and P aretransformedintoordinarydifferentialequationsin O'Sullivan,1981;DoughtyandPruess,1992.Thestorage efcienciesofthesimulationswasestimatedusingequations.4or.4dependingon thevalueof )]TJ/F40 11.9552 Tf 7.314 0 Td [(. 4.5ResultsandDiscussions ResultsobtainedfromboththeanalyticalmodelandTOUGH2predictedformationpressuretobehighestattheinjectionwellregion 1 andthelowestat r = R 1 region 3 .The predictedpressureprolesoftheanalyticalmodelreducedlogarithmicallyinregions 1 and 3 andlinearlyinregion 2 .Plotsofverticallyintegratedbrinesaturation S w r;t show brinesaturationtobezerooratresidualvalue S lr inregion 1 andincreasefartherfrom theinjectionwellandreachavalueof 1 : 0 at r max .Asmentionedearlier, r max isapresumedmaximumextentofCO 2 plumefromtheinjectionwell.Basedontherelationship describedinequation.6thebrinesaturationprole S w r;t fortheanalyticalmodelin regions 1 Figure6isconstant,i.e.,equalto S lr ,whilethe S w r;t proleinregion 1 of Sim1BSim1Farelessthan S lr .Thisisbecausetheanalyticalmodeldoesnotaccount forthedry-outofbrineinthevicinityoftheinjectionwellPruessandGarc a,2002; Fulleretal.,2006. 4.5.1ValidationofAnalyticalModel Inordertoassessifthepressureboundaryconditionappliedintheanalyticalmodelis acceptable,resultsfromtheanalyticalmodelwerecomparedtothosefromSim1ATable 6.Thisisbecausetheybothhavesimilarinputconditions.Acomparisonofthepredicted P r;t S w r;t proles,andstorageefciencies s oftheanalyticalmodelandSim1A showexcellentagreementFigure7aandbandTable7.Itmaybeconcludedthatthat analyticalmodelpredictsresultssimilartothosepredictedbyTOUGH 2 whentheinput parametersandphysicalconditionschoseninbothmodelsarethesame.Thisalsosuggests thattheboundaryconditionusedinsolvingthepressurederivativeequation.5or.6 isacceptable. 51

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Figure7.: ResultsobtainedfromanalyticalmodelandSim1A.Bothmodels havesimilarinputconditionst=10years;apressureprolesand bbrinesaturationproles. Table7: EstimatesofCO 2 storageefcienciesfromanalyticalmodeland TOUGH2.Inputconditionsinbothmodelsweresimilar. TimeyearsAnalyticalmodelSim1A 19.5%9.2% 109.5%9.6% 1009.5%9.7% 52

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Figure8.: Comparisonofpressureprolesfromanalyticalmodel.Whengravityisturnedonandoff t =10 years. Fromaconservativepointofview,higherestimatesofformationpressurearegenerally preferredoverlowerestimatesinordertoreducechancesofformationpressuresurpassingoverburdenpressure.Asaresultpressureprolespredictedbytheanalyticalmodel withgravityturnedonandoffwerecomparedtodeterminewhichwasgreater.Thepressureproles P r;t predictedbytheanalyticalmodelwithgravityorbuoyancyturnedon andoffindicatethatbuoyancyeffectcausestheformationpressuretodecreaseFigure8. Thepredictedpressureprolesoftheanalyticalmodelwithgravityignoredwasusedfor comparisonwithpressureprolesobtainedfromtheremainingnumericalsimulations. 4.5.2SensitivityAnalysis Sensitivityofthemetricstochangesinbrinecapillarypressure P cap ,uidrelative permeabilities k r ,andbuoyancywasanalyzedbasedonpredictionsfromthenumerical simulationsi.e.,Sim1BSim1F.Resultsfromthesensitivitystudieswerecomparedto thosefromtheanalyticalmodeltoassesswhenpredictionsfromtheanalyticalmodelare acceptableorvalid. 53

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4.5.2.1Effectof P cap FluidpropertiesinSim1Bweresettovarywithformationpressureandanonlinear capillarypressurefunction P cap S w wasapplied.Comparisonofthepredicted P r;t prolesfromtheanalyticalmodelandSim1Bshowedtheformerslightlylowerthanthe latterFigure9a.Agoodagreementinthepredicted S w r;t prolesoftheanalyticalmodelandSim1BwasalsoobtainedFigure9b,exceptthattheanalyticalmodel doesnotaccountforbrinedry-outinthevicinityofthewellboreasaresultofcontinuousinjectionofdryCO 2 PruessandGarc a,2002;Fulleretal.,2006.Thisindicates thatconsideringcapillarypressuretobenegligibleintheanalyticalmodelisanacceptable simplicationsinceitseffectonpressureandbrinesaturationproleisminimal. 4.5.2.2Effectof k r BothSim1BandSim1Cdifferedfromtheanalyticalmodelonthechoicesofuidpropertiesdensityandviscosityand P cap S w functionapplied.However,theinputconditions appliedinSim1CweresimilartothoseofSim1Bbutforthe k rw S w functionTable6. Thecontrastbetweenthepredicted P r;t prolesoftheanalyticalmodelandSim1Cwas noticeablysignicantthanthatwiththeformerandSim1BFigure9a.Similarly,the contrastinthe S w r;t prolesoftheanalyticalmodelandSim1Cwasworsethanthat betweentheformerandSim1BFigure9b.Inaddition,pressuresclosetotheinjectionwellinSim1CweresignicantlygreaterthanthatinSim1B.Itcanbeinferredthat thecontrastsinthepredicted P r;t prolesand S w r;t prolesbetweentheanalytical model,Sim1B,andSim1CinFigure9aandbareduetodisparitiesininputconditions appliedineach.SincethesoledifferenceintheinputconditionsappliedinSim1BandSim 1Cisinthedegreeofnonlinearityofthe k rw S w functionTable6,itcanbeconcluded thatrelativepermeabilityhasasignicantlylargereffectcomparedtocapillarityanduid propertiesonthepredictedformationpressureandbrineoruidsaturationdistributions whengravityisturnedoff. 4.5.2.3GravityorBuoyancyEffect TheeffectofgravityonCO 2 storagemetricswasinvestigatedusingresultsfromSim 1D,Sim1E,andSim1F.TheinputconditionsappliedinSim1DandSim1Earesimilarto thoseofSim1BandSim1C,respectively,exceptthatgravityisturnedoninSim1Dand Sim1E.Theaveragevalueof )]TJ/F40 11.9552 Tf 10.303 0 Td [(forSim1D,Sim1E,andSim1Fis 0 : 2 54

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Figure9.: Comparisonof P r;t and S w r;t proles.Betweenanalytical modelgravityignoredandSim1BSim1F,t= 10 years. 55

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)]TJ/F40 11.9552 Tf 10.26 0 Td [(inthesesimulationsaresimilarbecausethe Q appliedisconstantandchangesinuid densitiesandviscositiesmaybetoosmalltoacauseasignicantchangeinthevalueof )]TJ/F40 11.9552 Tf 7.314 0 Td [(.ThemajordifferencebetweentheinputconditionsinSim1DandSim1Eisthatthe k rw S w functionappliedintheformerislinearwhilethatofthelatterwasnonlinear. Comparisonofthepredicted P r;t prolesfromtheanalyticalmodelandSim1D showedgoodagreementFigure9c.Generally,thecontrastbetweenthe S w r;t prolesoftheanalyticalmodelandSim1DwassimilartothatbetweentheformerandSim1B Figure9bandd.Theagreementbetweenthepredicted P r;t and S w r;t proles oftheanalyticalmodelandSim1EwasworsethanthosebetweentheformerandSim1D Figure9candd,respectively. TheinputconditionsappliedinSim1FweresimilartothoseinSim1Eexceptthata quasi-linear k rw S w functionwasemployedintheformerTable6.ResultsinFigure9e andfshowgoodagreementbetweenthe P r;t and S w r;t prolesfromtheanalytical modelandSim1F. Thepredicted P r;t prolesinFigure9a,c,andefromTOUGH 2 showsignicant contrastsinpressureclosetotheinjectionwell P well t ,especiallybetweenSim1Cand Sim1E.SincetheinputconditionsinSim1CandSim1Edifferonlyingravity,itmay beconcludedthatthepressurewithintheaquiferreduceswhentheeffectofgravityforce actingontheformationuidsbuoyancyissignicant. Comparisonofthe S w r;t prolespredictedbytheanalyticalmodelandthenumerical simulationsconductedhereinFigure4.3b,d,andfindicatethattheanalyticalmodel predictconstantbrinesaturationsneartheinjectionwhilethenumericaldonot.Thisis becausetheassumptionofCO 2 andbrinetobeimmiscibleintheanalyticalmodelprevents itfromaccountingforinterphasemasstransferbetweentheCO 2 -richgasphaseand theliquidphasebrine.Onthecontrary,brinesaturationsneartheinjectionwellinthe numericalsimulationsareveryloworzerobecausetheyaccountforbrinedry-outbydry CO 2 PruessandGarc a,2002.Preliminarystudiesshowedthatthecontrastinthe S w r;t prolesoftheanalyticalmodelandthenumericalsimulationsnearthewellboredecreases with S lr .Thissuggestthattheanalyticalmodelgivebetterpredictionsofthe S w r;t prolesastheresidualbrinesaturationdiminishes S lr 0 : 0 .Itcanalsobeconcluded thattheassumptionofCO 2 andbrinebeingimmisciblemadeintheanalyticalmodellimits itscapabilitytogivegoodpredictionsofuidsaturationsCO 2 andbrineinthevicinityof theinjectionregion 1 ofFigure6astheirreduciblesaturationofbrineincreases. 56

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Table8: Estimatesof r max fromanalyticalmodelandTOUGH 2 simulations. 1Year10Years100Years Analyticalmodel1448458014482 Sim1B64420456471 Sim1C64420456471 Sim1D95531049878 Sim1E67522248079 Sim1F72526858756 4.5.2.4CO 2 PlumeExtent, r max ResultsinFigure9banddalsoindicatethatthegasplumeinSim1DandSim1E extendsfartherawayfromtheinjectionwellthaninSim1BandSim1C,respectively. ThisissupportedbytheresultspresentedinTable8,inwhichindicatethatvaluesof r max obtainedinSim1DandSim1EaregreaterthanthoseinSim1BandSim1C.Thisimplies thatgravityorbuoyancycausestheCO 2 plumetomigratefurtherawayfromtheinjection well.Predictionsof r max inSim1DandSim1FweregreaterthanthoseofSim1Ewhile thoseofSim1DweregreaterthanthoseofSim1FTable8.Predictedvaluesof r max fromtheanalyticalmodelwereobtainedusingequation4.4whilevaluesof r max fromthe numericalsimulationswereestimatedasthedistancebetweenthewellboreandtherstgrid blockatthetoplayeroftheaquiferwith S w r;t equaltozero.Itshouldbeunderscored thatanalyticalmodeldevelopedbyNordbottenandCeliaaccountsforgravitybut requiresanumericalsolution.Asaresult,gravitywasignoredinthisanalysis. ResultspresentedinTable8indicatethatCO 2 plumeextentfromtheinjectionwell r max decreasesasthedegreeofnonlinearityofthe k rw S w functionincreases.Itcan bededucedfromtheseanalysisthatbuoyancyenhanceslateralmigrationofthegasplume beneaththeupperconningbedofanaquifer.Conversely,capillaritypreventsoutwardmigrationofthegasplume,especiallywhentherelationshipbetweenuidrelativepermeabilitiesandbrinesaturationarenonlinear.Overall,theanalyticalmodelismoreconservative inestimating r max thanSim1BSim1F,whichisadvantageousfromregulativepointof view. 4.5.2.5StorageEfciency, s Equation3.8 )]TJ/F34 11.9552 Tf 12.473 0 Td [( 0 : 5 ofChapter 3 wasusedtoestimatetheCO 2 storageefciency s oftheanalyticalmodelwhilethoseofthenumericalsimulationswerenumerically 57

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determinedastheratioofaquiferporevolumeoccupiedbyinjectedCO 2 V injected andthe utilizedaquifervolume V formation ,i.e., s = V injected V formation .11 Itshouldbeunderscoredthat V formation consideredhereinistheporousvolumeofthe aquiferwithradiusequivalentto r max becauseitrepresentsaquifervolumethatisused-up forstorage. V formation isavailableforCO 2 storagebutitisnotfullyutilizedprincipally becauseofdisparitiesinthephysicalpropertiesofCO 2 andbrinee.g.viscosityanddensity asdescribedinthepreviouschapter. V injected wasestimatedastheproductofCO 2 mass injectionrate Q andinjectiontime t .Effortstominimizetruncationerrorsweremade byusingverysmallstepsinspace r .Table9presentsestimatesof s predictedbythe analyticalmodelandthenumericalsimulationsSim1BF.Theseresultssuggestthat the s oftheanalyticalarelowerthanthoseofthenumericalsimulations.Thisisbecause foragivenmassofinjectedCO 2 the r max predictedbytheformerisgreaterthanthoseof thenumericalsimulationsTable4.4. ResultsinTables8and9suggestaninverserelationshipbetween s and r max s decreasesas r max isincreased.Thereasonbeingthat,foraspeciedamountofCO 2 injected intoanaquifer, V formation increasesas r max isincreasedwhile V injected remainrelatively constant,therebyleadingtoacorrespondingdecreasein s .Forexample,theestimated valuesof s inSim1BandSim1Caresimilarbecausedifferencesintheirestimated r max areinsignicantTable4.4.Ontheother,estimatedvaluesof s inSim1Earegreaterthan thoseofSim1DandSim1Fbecausetheformerhasthesmallest r max valueTable4.4. Table9: Comparisonof s underdifferentphysicalconditions.At S lr =0 : 3 GravityoffGravityon TimeAnalyticalmodel Sim1BSim1C Sim1DSim1ESim1F 1year6.3% 15.9%16.3% 7.8%14.4%13.4% 10years6.3% 16.4%16.1% 7.4%14.0%10.0% 100years6.3% 16.4%16.0% 7.3%10.9%9.4% Takingnoteoftheinputconditionsappliedinthenumericalsimulations,theresults presentedinTable9suggestthatsimulationswithgravityignoredi.e.,Sim1BandSim 1Caremoreefcientthansimulationswithgravityturnedon.Thisismostprobably becausebuoyancyenhanceslateralmigrationofthegasplumeandasaresultcausesthe 58

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plumetospreadbeneaththeupperconningbedofanaquiferWeiretal.,1995;EnnisKingandPaterson,2002;Nordbottenetal.,2005.Consequently,numericalsimulations inwhichgravityeffectsaresignicant )]TJ/F34 11.9552 Tf 12.096 0 Td [( 0 : 5 tendtohavehigher r max valuesand subsequentlyhighvaluesof V formation whichcausesadecreasein s .Itcanalsobededuced fromTable9that s increasesastheexpressiondescribingtherelationshipbetweenuid relativepermeabilityandbrinesaturation k r s w changesfromalineartoanonlinear form.Thisisbecausethe s inSim1E,whichusedanonlinear k r s w function,isgreater thanthoseofSim1FandSim1Dwhichusedquasi-linearandlinear k r s w functions, respectively. 4.5.3Summary Sensitivityanalysesontheeffectofcapillarity,relativepermeabilityandbuoyancygravityonthemetricswereconductedtodetermineconditionsunderwhichtheanalytical modelisvalid.Overall,theabilityoftheanalyticalmodeldevelopedhereintopredict resultssimilartothoseofasophisticatednumericalsimulatorlikeTOUGH 2 improvesas thenumberofsimplicationsmadeinthelatterisincreased.Table10presentsrelative differencesinwellborepressuresovertime P well t betweentheanalyticalmodelandthe numericalsimulationsconductedherein.ExceptforSim1A,theanalyticalmodelunderpredictsthe P well t ofSim1BSim1F.Theseresultssuggestthatdifferencesin P well t aremostsignicantinSim1CandSim1E,whichusedanonlinearrelationshipbetween uidrelativepermeabilityandbrinesaturation. Theanalyticalmodelgenerallyunderestimatesthe s ofallthenumericalsimulations exceptSim1ATables8andTable9.However,the s predictedbytheanalyticalmodel areingoodagreementwithresultsreportedintheliteraturevanderMeer,1995;EnnisKingandPaterson,2002;ObiandBlunt,2006. Table10: Relativedifferencein P well t ataquiferbottom.Overallaverageis approximately 7 : 2 %. TimeyearsSim1ASim1BSim1CSim1DSim1ESim1F 10.30%-4.08%-21.38%-2.90%-18.50%-4.45% 30.28%-4.14%-21.41%-2.83%-14.36%-3.32% 100.26%-4.39%-21.50%-2.87%-9.84%-2.25% 300.25%-4.43%-21.61%-2.90%-7.23%-2.57% 1000.23%-4.53%-21.53%-2.94%-5.67%-2.50% 59

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Thesignicantdifferencesinthevaluesof s predictedbytheTOUGH2numericalsimulationsandthosereportedintheliteratureareprobablybecausethefollowingfactorswere notconsideredinthisstudy: 1.formationanisotropy; 2.formationheterogeneity;and 3.changesintemperaturewithinformation. Nevertheless,theestimatesof s fromthenumericalsimulationsweresuccessfullyemployedtoqualitativelyevaluatetheeffectsofcapillarity,relativepermeability,andgravity onformationpressure,CO 2 -brineinterfacelocation,maximumextentoftheCO 2 plume fromthewellboreandstorageefciencyduringCO 2 injection. Consideringthedifferencesintheinputconditionsappliedinthenumericalsimulations thefollowingimportantpointswereextractedfromananalysisoftheirresults: 1.formationpressurechangesarestronglydependentonbuoyancyandontherelationship betweenuidrelativepermeabilityandbrinesaturation,inconditionsofnegligible gravityeffectsFigure9; 2.theCO 2 plumeextentfromtheinjectionwellisalsodependentonbrinecapillarity, buoyancyandthedegreeofnonlinearityofthe k rw S w function;and 3.buoyancycausesCO 2 plumetomigrateupwardsandenhanceslateralmigrationofthe plumefartherfromtheinjectionwell. TheanalyticalmodeldevelopedhereincanbeutilizedbybothpolicymakersandCO 2 sequestrationprojectengineersinpermitapprovalsand/ordecidingontheviabilityofa givenrepositoryfromatechnologicalstandpoint.Foragivenaquiferofknownsurface area,thickness,porosity,depth,andaveragetemperature,locatednearafossil-fueledpower plant,regulatorscoulddraftpoliciesrelatedtothemaximumquantityofCO 2 toinjectin theformation.Also,themaximuminjectiontimecanbedeterminedbasedonestimates of r max P r;t atthetopandbottomofaformation,and s producedbytheanalytical model.Inaddition,CO 2 sequestrationprojectengineerscouldusethesameinformation todetermineifapotentialrepositorycanholdCO 2 emittedfromthepowerplantoverits lifetime.Thedistanceatwhichtherewillbeappreciableimpactoftheresultantpressure perturbations R 1 canalsobeestimated. 60

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Anadditionalinformationthatcanbeextractfromthepredictionsoftheanalyticalmodel ispressureattheinjection.ItisveryimportanttoknowinjectionpressureduringCO 2 injectioninordertomakesurethepressurewithintheformation,whichishighestatthe injectionwell,doesnotsurpasstheoverburdenpressure.Therebyavoidingriskofpossible formationfracturing. Simulationsconductedinthisstudydidnottakeintoconsiderationtheeffectsofformationheterogeneity,naturalbackgroundowgradient,aquiferdip,wellstimulation,and possiblegeochemicalreactionsbetweenCO 2 ,brine,andformationminerals. 4.6Conclusions Thischapterproposesananalyticalmodelthatusessignicantlyfewerinputparameters thanarerequiredbynumericalmodelstopredictthemetricsandpressureattheinjection well.ThesemetricscanbeutilizedasindicatorsindeterminingthesuitabilityofdeepgeologicsedimentaryformationsaspotentialCO 2 storagesites.Theanalyticalmodelalso requiresveryshortexecutiontimescomparedtocurrentnumericalsimulators.Sometheoreticalconclusionsthatmaybedrawnbasedonndingsinthisstudyincludethefollowing: 1.theanalyticalmodelandTOUGH 2 predictthesameformationpressureproles,brine saturationprolesandCO 2 storageefciencieswhensimilarinputconditionsandassumptionsareappliedinbothmodels; 2.relativepermeabilityhasthemostsignicanteffectonpredictionsofformationpressure changes,especiallywhengravityisignored; 3. s increaseswithnonlinearityoftherelativepermeabilityandcapillarypressurefunctionssincetheyimpedelateralmigrationofCO 2 plume;and 4.theanalyticalmodelcanbeconsideredconservativeinestimatingthemaximumradial extentofCO 2 plumeduringinjection. Theresultsobtainedinthisstudyvalidatethersthypothesisseechapter 1 thattheanalyticalmodelcansuitablydescribetheresponseofdeepconnedaquiferstosteadyCO 2 injectionundercertainphysicalconditions,whichinclude: 1.zeroorverysmallvaluesofirreduciblebrinesaturations S lr ;and 2.linearand/orquasi-linearrelationshipbetweenuidrelativepermeabilityandbrinesaturation. 61

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Thismodelcouldbeutilizedbybothregulators,CO 2 sequestrationprojectengineersand projectmanagerstofacilitatedecisionmakingrelatedtopermitting,suitabilityofpotential repositorysitesandlocationsofnewindustrialfacilities,whichemitlargequantitiesof carbondioxide. 4.7ReferencesCited V.Altunin.Thermophysicalpropertiesofcarbondioxide. PublishingHouseofStandards page551pages,1975. S.Bachu,J.Nordbotten,andM.Celia.Evaluationofthespreadofacidgasplumesinjected indeepsalineaquifersinwesternCanadaasananalogueforCO 2 injectionincontinental sedimentarybasins. ThePrincetonPapersatVancouver ,I.D.No.12,2004. H.CooperandC.Jacob.Ageneralizedgraphicalmethodforevaluatingformationconstants andsummerizingwelleldhistory. TransactionsoftheAmericanGeophysicalUnion 27:526,1946. A.Corey.Theinterrelationbetweengasandoilrelativepermeabilities. ProducersMonthly pages38,Noverber1954. C.DoughtyandK.Pruess.Asimilaritysolutionfortwo-phasewater,air,andheatow nearalinearheatsourceinaporousmedium. GeophysicalResearch ,97B2:1821, February1992. C.DoughtyandK.Pruess.ModelingsupercriticalCO 2 injectioninheterogeneousporous media. VadoseZoneJournal ,3:837,2004. J.Ennis-KingandL.Paterson.Engineringaspectsofgeologicalsequestrationofcarbon dioxide.volumeSPE-77809,SPEandCSIROPetroleum,2002.AsiaPacicOilandGas ConferenceandExhibition,Melbourne,Australia,October8. R.Fuller,J.Prevost,andM.Piri.Three-phaseequilibriumandpartitioningcalculationsfor sequstrationinsalineaquifers. JournalofGeophysicalResearch ,111B06207,2006. J.E.Garc a. Fluiddynamicsofcarbondioxidedisposalinsalineaquifers .Doctoraldissertation,UniversityofCalifornia,Berkeley,2003. B.Hitchon. Aquiferdisposalofcarbondioxide .GeosciencePublishingLtd.,Sherwood Park,Alberta,Canada,1996. J.NordbottenandM.Celia.Similaritysolutionsforuidinjectionintoconnedaquifers. JournalofFluidMechanics ,561:307,2006. 62

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J.Nordbotten,M.Celia,andS.Bachu.InjectionandstorageofCO 2 indeepsalineaquifers: AnalyticalsolutionforCO 2 plumeevolutionduringinjection. TransportinPorousMedia ,58:339,2005. O.ObiandM.Blunt.Streamline-basedsimulationofcarbondioxidestorage inaNorthSeaaquifer. WaterResourcesResearch ,42W03414:1,2006. doi:10.1029/2004WR003347. M.O'Sullivan.Asimilaritymethodforgeothermalwelltestanalysis. WaterResources Research ,17:390,1981. K.Pruess. ECO2N:ATOUGH2uidpropertymoduleformixturesofwater,NaCl,and carbondioxide .LawrenceBerkeleyNationalLaboratory,Berkeley,California,2005. K.PruessandJ.Garc a.MultiphaseowdynamicsduringCO 2 disposalintosaline aquifers. EnvironmentalGeology ,42:282,2002. K.PruessandN.M uller.Formationdry-outfromCO 2 injectionintosalineaquifers: 2 : Analyticalmodelforsaltprecipitation. WaterResourcesandResearch ,45w03403: 1,2009.doi:10.1029/2008WR007102. K.PruessandN.Spycher.ECO2NAnewTOUGH2uidpropertymoduleforstudiesof CO 2 storageinsalineaquifers.Berkeley,California,2006.LawrenceBerkeleyNational Laboratory. K.Pruess,C.Oldenburg,andG.Moridis.TOUGH2users'guide,version2.0.Manual LBNL-43134,LawrenceBerkeleyNationalLaboratory,Berleley,California,1999.accessdate:June10,2007. K.Pruess,J.E.Garc a,T.Kovscek,C.Oldenburg,J.Rutqvist,C.Steefel,andT.Xu.Code intercomparisonbuildscondenceinnumericalsimulationmodelsforgeologicdisposal ofCO 2 Energy ,29:1431,2004.doi:10.1016/j.energy.2004.03.077. C.V.Theis.Therelationbetweentheloweringofthepiezometricsurfaceandtherateand durationofdischargeofawellusinggroundwaterstorage. TransactionsoftheAmerican GeophysicalUnion ,2:519,1935. L.G.H.vanderMeer.TheCO 2 storageefciencyofaquifers. EnergyConversionand Management ,36:513,1995. M.T.vanGenuchten.Aclosed-formequationforpredictingthehydraulicconductivityof unsaturatedsoils. SoilSci.Soc.Am.J. ,44:892,1980. G.Weir,S.White,andW.Kissling.Reservoirstorageandcontainmentofgreenhouse gases. EnergyConversionandManagement ,36:531,1995. 63

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Chapter5 StorageofCO 2 inIsotropicAquifersviaHorizontalInjectionWells 5.1Abstract EffectsofwellorientationandlengthonthestorageofcarbondioxideCO 2 indeep salineaquiferswereevaluatedandquantiedbyconductingnumericalsimulationswith TOUGH 2 .SimulationsofCO 2 injectionintoconned,homogeneous,isotropic,saline aquiferswereconductedforbothverticalandhorizontalwells.Themetricsusedinquantifyingtheperformancesofdifferentstrategiesincludedchangesinpressurenearthewell, massofCO 2 dissolvedintobrine,fractionofinjectedCO 2 dissolvedintobrineandstorage efciency,allevaluatedoverasimulatedinjectionperiodof 50 years.Thesemetricswere quantiedasfunctionsofwelllengthandCO 2 injectionrate.Whenequalinjectionrates andwelllengthswerecompared,therewasnotasignicantdifferencebetweentheperformancesofhorizontalwellsandverticalwells.However,thelengthofahorizontalwell mayexceedthelengthofaverticalwellbecausethelengthofthehorizontalwellisnotconstrainedtotheverticalthicknessofthegeologicformation.Asthelengthofthehorizontal wellwasallowedtoincrease,thegeologicformationcouldreceiveasignicantlyhigher injectionrateofCO 2 withoutexceedingamaximumallowablepressure.Thisresultsina higherCO 2 storageefciencyintheformation,becausestorageefciencyincreaseswith injectionrate.TheseresultssuggestthathorizontalwellscouldbeutilizedtoimproveCO 2 storagecapacityinconnedaquifers,especiallyunderpressure-limitedconditions. 5.2Introduction DeepcutsincarbondioxideCO 2 emissionsfromanthropogenicsourceshavebeen proposedasameansofmitigatingrisksofadverseinterferencewithglobalclimateLaw andBachu,1996;Wigleyetal.,1996;Holloway,1997;IPCC,2005.CO 2 emittedintothe atmosphereprincipallyemanatesfromcombustionoffossilfuels,whichsupplyover 80 % 64

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ofglobalenergydemandsIPCC,2005.Asaresult,CO 2 concentrationsintheatmosphere haveincreasedfrompre-industriallevelsofabout 280 partspermillionppmto 380 ppm in 2005 IPCC,2007.SubsurfaceinjectionofCO 2 fromlargepointsourceshasbeen recommendedasapotentialstrategyforisolatingsignicantquantitiesofCO 2 fromthe atmospherePruessetal.,2001;Ennis-KingandPaterson,2002;Bruantetal.,2002;IEA, 2004;IPCC,2005PotentialdeepgeologicformationtypesforCO 2 sequestrationinclude abandonedoilandgaselds,unminablecoal-bedseams,andsalineaquifersBruantetal., 2002;IPCC,2005;KovscekandCakici,2005;Kristianetal.,2005;PruessandSpycher, 2006.Thelatterformationtypesalineaquifersisreportedtohavethelargeststorage capacityduetoitsworldwideavailabilityandlackofcompetitiveusesLawandBachu, 1996;Holloway,2001;PruessandGarc a,2002;BachuandAdams,2003;ObiandBlunt, 2006. PreviousworksonnumericalsimulationsofCO 2 injectionintoconnedsalineaquifers viafullyperforatedverticalwellsshowedtheCO 2 -rich`gas'phasetomigrateradially fromtheinjectionwell.Thegasphasewasalsoreportedtooverlieresidentbrineandrise untilitreachestheupperconninglayerofformationduetodifferencesindensityand viscositybetweenCO 2 andbrinevanderMeer,1993;LawandBachu,1996;Nordbotten etal.,2005.ThetendencyofCO 2 tosimultaneouslymigratelaterallyatafasterratethan brinewhilerisingtotheuppersectionofaformationhasanegativeeffectonthequantity ofCO 2 storedperunitvolumeofaquiferstorageefciency.Asaresult,theinjection strategyadoptedinaCO 2 storageprojectmusttakeintoconsiderationdifferencesinthe physicalpropertiesofCO 2 andresidentformationuidsinordertoenhancestorage. Theinjectionstrategiesconsideredinthisstudywerebasedonwellorientationandwell length.Theorientationofaninjectionwellcanbehorizontal,vertical,orslanted.The completedlengthofverticalwellsislimitedtotheaquifer'sthicknesswhilethoseofhorizontalwellscanbeaslongascurrenttechnologypermits.Horizontalwellscannowbe drilledtolengthsupto 9 11 kmDonnelly,2008. Researchintheoilandgasindustryhaveshownthataverticalwelldrainsacylindrical volumeofformationwhileahorizontalwelldrainsanellipsoidvolumeofformationJoshi, 1991.Asaresult,thelattergenerallyproduceslargervolumesofnaturalgasand/orcrude oilthantheformer.PreliminarynumericalsimulationsofCO 2 injectionviaverticaland horizontalwellssuggestthelattertobemoreefcientthantheformerbasedoninjectivity andstoragepotentialJikichetal.,2003;Ozahetal.,2005.However,theconditionsunder whichthesepredictionsarevalidareunknown. 65

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ThisstudyevaluatesandquantiestheeffectsofwellorientationandlengthonCO 2 storagepotentialofsalineaquifersunderisotropicconditions.Italsoaddressesconditionsunderwhichhorizontalinjectionwellsmaybetechnologicallymoreviablethantheir verticalcounterpartsforCO 2 storage.TheobjectivesofthischapterwereachievedviaconductingaseriesofnumericalsimulationsofCO 2 injectionviaverticalandhorizontalwells toquantifytheeffectsofwellorientationandlengthonCO 2 storage.Themetricsused toquantifyperformancesofthedifferentinjectionstrategiesincludethemaximumpressureneartheinjectionwell P w ,totalmassofCO 2 dissolvedinthebrineafter 50 years M CO 2 ;aq ,fractionofinjectedCO 2 intobrine f c ,andstorageefciency s .Comparison oftheresultsbasedonthemetricspredictthatCO 2 injectionviahorizontalwellsoflength greaterthantheverticalthicknessofanaquiferisamoreefcientinjectionstrategythan utilizingfullyperforatedverticalwells. Inordertoavoidrisksoffracturethepressurewithinaformationmustbelessthanits fracturingpressure.Thefracturingpressureofarockisdependentonitstensilestrength andthestressesonit.Thetensilestrengthofarockisalsodependentonitsstructure, compaction,andlevelofcementationMartinezetal.,1992.Anyinstanceofformation fracturingmayhampertheintegrityoftheupperconningbed,leadingtoescapeofCO 2 fromtherepository.Asaresult, P w couldserveasamaximumallowablepressurewithina repositoryinordertoavoidanyriskoffracturing. M CO 2 ;aq isameasureofthetotalmassofCO 2 dissolvedinresidentbrineasafunctionoftime.TheamountofdissolvedCO 2 inbrineishighlydependentonthevolume ofCO 2 plumeincontactwithresidentbrineOzahetal.,2005.However,themassfractionofdissolvedCO 2 X CO 2 isalsodependentonthesalinityofresidentbrineandformationtemperatureandpressurePruessandGarc a,2002;Spycheretal.,2003;Marini, 2007.Resultsfromthetechnicalliteratureindicatethat X CO 2 increaseswithpressurebut decreaseswithincreasingsalinityand/ortemperatureSpycheretal.,2003;Spycherand Pruess,2005.Nevertheless,dissolutionofCO 2 intobrineenhancesthesequestrationprocessinthatitreduceschancesofpossibleleakageofCO 2 ;itservesasagateway forinteractionofCO 2 withchemicalspeciesinsolution;anditmayeventuallyleadto formationofsecondaryprecipitatesXuetal.,2003;Kumaretal.,2005. 66

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5.3Approach AseriesofnumericalsimulationsofCO 2 injectionintoahomogeneous,isotropicconnedsalineaquifer,usingtheTOUGH 2 numericalsoftware,wasconductedbyvarying wellorientationandwelllength L w whilekeepingotherparametersconstantinorderto quantifytheeffectsofwelllengthonCO 2 storage.AdditionalTOUGH 2 numericalsimulationswerealsoconductedtostudytheeffectsofCO 2 injectionrate Q onthestorage performance.TheinputparametersappliedinallthesimulationsarepresentedinTable 11.Inallsimulations,therelationshipsdevelopedbyvanGenuchtenwereusedto describetheuidrelativepermeabilitiesandbrinecapillarypressure P cap asfunctionsof theliquidphasesaturation.An S lr valueof 0 : 0 intherelationshipbetween P cap andbrine saturationwasusedinorderfortheformertobeniteatallsaturationsPruess,1997.The dependenceofpermeabilityonporespacewasignoredorassumednegligible. Thecompletedportionsofverticalwellsextendedacrosstheverticalthicknessofthe aquiferwhilethoseofhorizontalwellswerevariedbetween 100 mand 3000 m.Thesimulationswereconductedusinga 3 Dgridofdimension 100 kmby 100 kmby 100 m,with theinjectionwellspositionedatthecenterverticalwelloratthebottomofthecentral portionoftheformationalongthex-axishorizontalwellsFigure10.Figure11also showsa 2 DschematicrepresentationofCO 2 injectionintoaconnedaquiferviaahorizontalwell.Horizontalwellswerepositionedatthebottomoftheaquifertomaximize thecontactbetweenCO 2 andtheaquifer,sincetheformerwillriseduetobuoyancy.The meshgridwasrenedclosetotheinjectionwellandattheupperportionoftheformationinordertocloselystudyuidowdynamicsintheseregions.Gridrenementwas concentratedaroundthecentralportionofthemesh,extendingupto 20 kilometersor 10 kilometersfromitscenter.ThiswaspredeterminedbyconductingtrialsimulationstoensurethattheCO 2 plumeextentinallsimulationswaswithintheabove-mentionedrange. Constantpressureswereimposedattheboundariesoftheformationbysettingverylarge volumefactors > 1 : 0 10 30 m 3 togridblocksattheboundaries.Asaresult,anyow intothegridblocksattheboundarieswillhavenegligibleimpactontheirpressures.CO 2 wascontinuouslyinjectedforupto 50 yearsinallsimulations.Resultsobtainedfromthe numericalsimulationswerecomparedandanalyzedbasedonthemetricslistedpreviously. Valuesofnear-wellborepressures P w andtotalmassofdissolvedCO 2 M CO 2 ;aq were obtaineddirectlyfromthesimulationresults.ThefractionofinjectedCO 2 dissolvedinto brine f c wascalculatedbydividing M CO 2 ;aq bythetotalmassofCO 2 injected,whichis aproductofthemassinjectionrate Q andtimeofcontinuousinjection t 67

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Table11: Hydrogeologicandnumericalparametersappliedinall simulations. ParameterValue Dimension L : W : H ,m 10 5 : 10 5 : 100 Gridblocks X : Y : Z 65 : 65 : 10 Aquiferdepthtop-bottom,m 1200 1300 Rockcompressibilityc,m 2 /N 4 : 5 10 )]TJ/F17 7.9701 Tf 6.586 0 Td [(10 Initialpressure P init ,bar 12 : 0 130 Temperature, C 45 : 0 Averageporosity 0 : 12 Averagepermeability k ,m 2 1 : 0 10 )]TJ/F17 7.9701 Tf 6.586 0 Td [(13 Residualbrinesaturation S lr 0 : 3 Residualgassaturation S gr 0 : 05 Figure10.: Schematicrepresentationofmeshgrid. 68

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Figure11.: SchematicrepresentationofCO 2 injectionviaahorizontalwell. Cross-sectionalview.AdaptedfromNordbottenetal.. TheCO 2 storageefciencies s ofthesimulationswereestimatedfromtheirgassaturation S g distributionswithintheconnedaquifer. s iscalculatedastheratiobetween volumeofCO 2 injected V inj andtheutilizedporousvolumeofaquifer V max V inj is calculatedastheproductof Q andinjectiontime t dividedbytheaveragedensityofCO 2 c;av .Weestimated V max basedontheCO 2 plumeshape.Dependingonthewellorientationandinjectiontime,theplumeextentinthe X and Y directionsmaybesimilaror different.Whentheplumeextentinthe X and Y directionsareequal,theplumeoccupies acylindricalvolumeoftheaquifer.Otherwise,theplumeoccupiesanellipsoidalvolume oftheaquiferwhentheplumeextentsinthe X and Y directionsaredifferent.Theformer isgenerallyencounteredinverticalwellsandthelatterinhorizontalwellsJoshi,1991. Themathematicalexpressionsforcalculatingcylindrical V max;c andellipsoidal V max;e plumevolumesareasfollows: V max;c = r max 2 B .1 V max;e = abB .2 69

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where istheaverageporosityoftheformation, r max istheradiusmaximumradialextent ofthecylindricalgasplume, a and b aretheequatorialradiioftheellipsoid-shapedgas plumealongthe X -and Y -axes,respectively. 5.4ResultsandDiscussions 5.4.1AnalysisoftheMetrics ResultsshowsaturationsofCO 2 -rich`gas'phase S g tobemaximumnearinjection wellsandvanishfarfromthewellsFigure12.Maximumvaluesof S g weregreaterin simulationsusingverticalinjectorsthanthoseusinghorizontalinjectorsFigure12aand b.ItcanbeviewedinFigure12aandbthat S g intheformerextendsfromtop tobottomofaquiferwhilethatofthesimulationusingahorizontalinjectorishighestat thelowersectionoftheaquifer.Thediametersofthegasplumeinallsimulationswere lessthan 20 kilometers,indicatingthattheplumedidnotmigratebeyondtheregionof high-resolutiongrid.Detailedanalysisoftheseresultsisdiscussedsubsequently. Resultsfromthesimulationsconductedhereinpredictpressurestobehighestatthe injectionwellandlowestattheboundariesoftheaquifers.ForspeciedCO 2 massinjection rate Q ,thepressuresinsimulationsusingverticalinjectorsweregenerallygreaterthan thoseusinghorizontalinjectorsFigure13aandb.Resultsfromthesimulationsalso predictincreasesinpressureasCO 2 massinjectionrate Q isincreased.Thisphenomenon wasmostpronouncedneartheinjectionwellsTable12.The Q valuesof 50 kg/s, 100 kg/s, and 200 kg/sappliedinthesimulationshereinareequivalenttoCO 2 emissionsfroma 144 MWe, 288 MWe,and 576 MWecoal-redpowerplant,respectivelyHitchon,1996. Foraxedwelllength,thetotalmassofCO 2 dissolvedinbrine M CO 2 ;aq increased withCO 2 massinjectionrate Q Table12.Thisisbecauseofacorrespondingincrease informationpressureasmoreCO 2 isinjectedperunitlengthofwell.Resultsreportedin previousstudiesonCO 2 solubilityinwateralsoindicatethattheamountofdissolvedCO 2 insolutionincreaseswithpressureKohlandNielsen,1997;SpycherandPruess,2005. However,thefractionoftheinjectedCO 2 thatdissolves f c slightlydecreasedas Q is decreased. TheCO 2 storageefciencies s estimatedfromthe S g prolesofthesimulationsindicatethat s alsoincreaseswith Q forxedwelllengthTable12.Similarobservations havebeenreportedinthetechnicalliteratureinwhichincreasesin s with Q werealso achievedvanderMeer,1995. 70

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Table12: Variationsof P w M CO 2 ;aq ,and s with Q at t equalto50 years. Injectionwell P w bar M CO 2 ;aq Mtons s % Q kg/s Q kg/s Q kg/s Orientation L w m 50100200 50100200 50100200 Vertical100 163195248 6.111.522.1 10.512.013.7 Horizontal100 164196247 6.111.521.4 10.512.013.5 Horizontal1000 159184230 5.810.920.9 9.712.314.7 Horizontal2000 158182225 5.810.920.9 9.712.714.4 Horizontal3000 157180222 5.910.920.9 10.012.615.2 Table13: Performancesofsimulationsusingverticalandhorizontal wells.Withequallength 100 mfor 50 yearsinjection. Well Qkg/s Metricsorientation 50100200 P w barvertical 163195248 horizontal 164196247 M CO 2 ;aq vertical 6.111.522.1 Mtonshorizontal 6.111.521.4 f c vertical 0.0770.0730.070 horizontal 0.0770.0730.068 s %vertical 10.512.013.7 horizontal 10.512.013.5 As Q decreases,gravitybecomesrelativelymoredominant.Thiscausesthegasplume CO 2 tooccupyathinbutbroadregionatthetopoftheformation,leadingtoadecrease in s TheresultspresentedinTable12alsoindicatethatforaspecied Q P w and M CO 2 ;aq generallydecreaseas L w isincreased,especiallyatsmallvaluesof Q .However,thiswas notthecasewith s forvaluesof Q greaterthan 50 kg/s.The s slightlyincreasedwith L w for Q equalto 100 and 200 kg/sbecausetheformergenerallyincreasesas Q isincreased vanderMeer,1995.Thechangesin Q M CO 2 ;aq and s as L w isincreased,atspecied valuesof P w willbeaddressedinthesubsequentsub-sectiononsensitivityanalysis. 5.4.2SensitivityAnalysis Theeffectsofinjectionwellorientationweredeterminedbycomparingtheperformances ofCO 2 injectionsimulationsusingaverticalwellandahorizontalwellofequallengthat aconstantmassinjectionrate Q 71

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Figure12.: S g spatialdistributionsafter 50 yearschapter5.CO 2 wascontinuouslyinjectedatarateof 100 kg=s .a S g distributionofvertical wellsimulation S g;max =0 : 962 ;b S g distributionofthehorizontalwellsimulation 2000 mlong S g;max =0 : 697 72

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Figure13.: P spatialdistributionsafter 50 years.CO 2 wascontinuouslyinjectedatarateof 100 kg=s .a P distributionofverticalwell simulation P w 191 bar;b P distributionofhorizontalwell simulation 2000 m P w 182 bar. 73

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ResultsinTable13indicatethatnosignicantdifferenceintheperformancesofboth simulationswasachieved.Therefore,itcanbeconcludedthatCO 2 injectionviaavertical wellorahorizontalwellofequallengthhavesimilarperformances.ResultsinTable13 alsosupporttheargumentsmadeintheprevioussubsectionthat M CO 2 ;aq and s increase withCO 2 massinjectionrate Q foraxedwelllength. Whenthelengthofthehorizontalwell L w wassystematicallyincreasedfrom 100 3000 mwhilekeeping Q constant, P w decreased.Itcanbededucedthat P w decreases withincreasingwelllengthduetoreductioninthemassofCO 2 injectedperunitwell length.Theaveragedensityofthegasphasealsodecreasedasaresult.Theseindicatethat additionalquantitiesofCO 2 canbeinjectedintotheaquiferwithoutexceedingalimiting pressureas L w isincreased. However,inordertoavoidriskofpossibleCO 2 leakage, P w mustnotsurpassthefracturingpressureoftheaquifer.Therefore,evaluatingtheperformancesofthesimulationsunder pressure-limitingconditionsiswarranted.Theperformancesofsimulationsusingvertical injectionwellsandhorizontalinjectionwellswereevaluatedandcomparedbyestimating amaximumCO 2 injectionrate Q max atspeciedmaximumpressureincreases P for differentwelllengths.Anempiricalrelationshipbetween P and Q max wasachievedby tting P w datapointsasfunctionsof Q ,withastraightlinepassingthroughtheorigin.The relationshipsweremadeat 50 yearsofCO 2 injection,whichroughlycorrespondstothe averagelifespanofheavy-dutyindustrialfacilitiesthatemitlargequantitiesofCO 2 .The resultinglinearequationsdepictingtherelationshipbetween P w and Q areasfollows: P =0 : 59 QL w =100 m vertical .3 P =0 : 59 QL w =100 m horizontal .4 P =0 : 50 QL w =1000 m horizontal .5 P =0 : 48 QL w =2000 m horizontal .6 P =0 : 46 QL w =3000 m horizontal .7 where P = P w )]TJ/F19 11.9552 Tf 11.955 0 Td [(P init and P init istheinitialpressure. Intheseequations, P and Q areinbarandkg/s,respectively.Theserelationshipswere determinedbyusingTOUGH 2 simulationresultstodeterminemaximumvaluesof P w at differentvaluesof Q .Resultsshowedexcellentagreementbetweenpressuresestimated usingtheaboveequationsandthosepredictedbyTOUGH 2 withrelativeerrorsoflessthan 2 %aspresentedinTable14. 74

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Table14: Comparisonofpressurespredicted.Usingequations.3.7and TOUGH 2 after 50 years. QWellWell PressurebarRelative kg/sOrientationlengthm AnalyticalTOUGH2error 170horizontal100 230.5230.9-0.2% 200vertical100 249.0248.50.2% 201horizontal1000 230.5229.90.3% 211horizontal2000 230.5229.90.3% 217horizontal3000 230.5229.10.6% 248horizontal2000 248.5245.01.4% 250vertical100 278.6275.51.1% 250horizontal1000 255.0251.11.5% 256horizontal3000 248.5244.41.7% Atagivenmaximumallowablepressure P max ,therequiredCO 2 massinjectionrate Q max usingverticalorhorizontalinjectionwellscanbeestimatedusingequations 3 7 basedonthewellorientationorlength.Table15presentresultsof Q max M CO 2 ;aq ,and s atdifferentwelllengthsforavalueof P max equalto 100 bar.Itcanbededucedfrom Table15thatatanyspecied P max ,themaximumallowableCO 2 massinjectionrate Q max increaseswithwelllengthandsubsequentlythestorageefciencies s M CO 2 ;aq alsoincreasedas Q wasincreasedbecausehorizontalwellsarereportedtosweepagreater cross-sectionalareaofaformationthanverticalwellsJoshi,1991.Thisalsoindicatesthat horizontalwellshavebetterverticalsweepthanverticalwellstherebyenhancingmixing betweenCO 2 andbrineastheformerrisestothetopoftheaquiferOzahetal.,2005. Despiteincreasesin s and M CO 2 ;aq withincreases Q ,thefractionofCO 2 dissolvedin brine f c slightlydecreasedas Q isincreasedTable15.Thismaybebecauseas Q increasesthereisadecreaseintheratioofCO 2 -brineinterfacialareainrelationtoCO 2 plumevolume. TheseindicatethathorizontalinjectionwellscanbeusedtoimprovetheCO 2 storage capacityofaconnedaquiferunderpressure-limitedconditions. Figure14showstheestimatedadditionalmassofCO 2 thatcanbestoredusinghorizontal injectionwellsofdifferentlengthsasopposedtoaverticalinjectionatdifferentvaluesof P max .TheresultsinFigure14indicatethattheadditionalmassofCO 2 thatcanbestored viahorizontalinjectorsincreaseswithwelllengthandthemaximumallowablepressure increase P max withinanaquifer. 75

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Table15: Q max M CO 2 ;aq ,and s atdifferentvaluesof L w .For P max =100 barandafter 50 yearsinjection. L w Q max M CO 2 ;aq f c s mkg/sMtons% 10017018.40.068613.0 100020121.00.066214.7 200021122.00.066015.1 300021722.60.066015.5 Forexample,at P max equalto 300 bar,anadditional 228 milliontonsMtonsof CO 2 canbestoredinaconnedaquiferusingahorizontalinjectoroflength 30 timesthe thicknessoftheaquifer.ThiscanaccommodateCO 2 emissionsfroma 1000 MWeelectric coal-redplantforover 20 yearsPruessetal.,2003.Itcanbeconcludedthatsignicantly largequantitiesofCO 2 couldbestoredusinglonghorizontalwellsatlittleornochangein pressureasreportedinpreviousworksbyJikichetal.andOzahetal.. Resultsfromsimulationsconductedhereinindicatethatadeclineinpressureasaresult ofwelllengthincrementatconstantinjectionratessubsequentlyleadstocorresponding reductionsintheaveragedensityandsolubilityofCO 2 .However,thepressuredecayalso leadstoreductionsintheamountofsolidsNaClinthisstudyprecipitatedandanincrease ininjectivity. Sensitivitystudiesontheeffectofinjectionrateontheowdynamicsandstorageof CO 2 indicatethatpressure,averagedensity,massofCO 2 dissolved,andstorageefciency generallyincreaseastheCO 2 massinjectionrateisincreased.Itcanbededucedfromthe resultspresentedinTable15thatthemassofCO 2 dissolvedinformationbrineincreases withCO 2 injectionrate.ResultsfromthesimulationsconductedhereinsuggestthatsubstantialquantitiesofadditionalCO 2 couldbesequesteredusinghorizontalwellsoflengths atleasttentimestheaquifer'sthickness.Basedontheresultsachievedinthisstudy,the appropriatehorizontalwellsoflengthrequiredtoimproveorenhanceCO 2 storagecapacity inanisotropicsalineaquifershouldbegreaterthan 1000 mi.e., 10 timesthethicknessof theaquiferconsideredherein.Thisisbecauseunderpressure-limitedconditions,aquifers usinghorizontalwellsoflength 1000 mormorecanstoreandsequesterlargerquantities ofCO 2 thanaquifersusingverticalinjectionwellsoflength 100 m.Inaddition,under pressure-limitingconditions,CO 2 injectionviahorizontalwellsismoreefcientsincethe maximumallowableinjectionrateincreaseswithwelllengthTable15. 76

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Figure14.: AdditionalmassofCO 2 thatcanbestored.Usinghorizontalinjectorsfor 50 years. Thisstudyaddressesonlythetechnicalfeasibilitiesofusingverticalandhorizontalwells forCO 2 sequestration.Economicandtechnicalaspectsrelatedtodrillingandcompletion ofhorizontalandverticalwellsarebeyondthescopeofthisstudy. 5.5Conclusions Thisstudywasconductedtoevaluateandquantifytheeffectsofwellorientationand welllengthonthestorageofCO 2 underisotropicconditions.Ourndingsshowhorizontal injectionwellstobeviableundercertainconditions.Underisotropicconditions,CO 2 storageefcienciesinsimulationsusinghorizontalinjectorsaregreaterthanthoseoftheir verticalcounterparts.Horizontalwellsoflengthsatleasttentimestheaquifer'sthickness couldbeusedtosignicantlyimprovethestoragecapacityofanaquiferunderpressurelimitedconditions.Thesendingssuggestthathorizontalinjectionwellscouldbeutilized tosignicantlyimproveCO 2 storagecapacitiesinconnedaquifers,underpressure-limited conditions. 77

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Thefollowingadditionalconclusionswerearrivedatbasedonanalysesoftheresults obtainedfromthesimulationsconductedinthisstudy: 1.ThepressureattheinjectionwelldecreaseswithwelllengthbutincreaseswithCO 2 injectionrate. 2.Pressuresatverticalinjectionwellsarehigherthanthoseoflonghorizontalwellsbecausecompletionlengthsoftheformerarelimitedtotheaquifer'sthickness. 3.TheaverageCO 2 densityincreaseswithinjectionratebutdecreaseswithincreasing welllength.CO 2 densitiesinsimulationsusinghorizontalinjectorsaregenerallylower thanthoseusingverticalinjectorsbecausepressuresencounteredintheformerare lowerthanthoseinthelatter. 4.TheCO 2 plumeinsimulationsusinglonghorizontalandverticalinjectionwellsare generallyellipsoidalandcylindricalinshape,respectively. ToenhanceCO 2 storage,theinjectionstrategyshouldaccountforthedifferencesin physicalpropertiesofCO 2 andtheresidentuidatconditionssuitablefordeepgeologic storage.Theeffectsofpermeabilityanisotropyor/andaquiferheterogeneitycoupledwith changesinwelllengthonCO 2 owdynamicsandstoragewillbeaddressedinsubsequent chapters. 5.6ReferencesCited S.BachuandJ.J.Adams.SequestrationofCO 2 ingeologicalmediainresponsetoclimatechange:CapacityofdeepsalineaquiferstosequesterCO 2 insolution. Energy ConversionandManagement ,44:3151,2003. R.Bruant,A.Guswa,M.Celia,andC.Peters.Safestorageofcarbondioxideindeepsaline aquifers. EnvironmentalScienceandTechnology ,36:240AA,June2002. J.Donnelly.Regionalupdate:Europe,ExxonNeftegas. JournalofPetroleumTechnology JPT ,60:10,May2008.Editotial. J.Ennis-KingandL.Paterson.Engineringaspectsofgeologicalsequestrationofcarbon dioxide.volumeSPE-77809,SPEandCSIROPetroleum,2002.AsiaPacicOilandGas ConferenceandExhibition,Melbourne,Australia,October8. B.Hitchon. Aquiferdisposalofcarbondioxide .GeosciencePublishingLtd.,Sherwood Park,Alberta,Canada,1996. 78

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S.Holloway.Anoverviewoftheundergrounddisposalofcarbondioxide. EnergyConversionandManagement ,38:193,1997. S.Holloway.Storageoffossilfuel-derivedcarbondioxideseneaththesurfaceoftheearth. AnnualReviewofEnergyandtheEnvironment ,26:145,2001. IEA.ProspectsforCO 2 captureandstorage.Technicalreport,InternationalEnvironmental Agency,Paris,France,2004. IPCC.IPCCspecialreportoncarbondioxidecaptureandstorage.PreparedbyWorking GroupIIIoftheIntergovernmentalPanelonClimateChange[Metz,B.,Davidson,O., deConinck,H.C.,Loos,M.,andMeyer,L.A.eds.].Report,IntergovernmentalPanel onClimateChange,Cambridge,UnitedKingdomandNewYork,NY,USA,2005. IPCC.Climatechange2007:Thephysicalsciencebasis.FourthAssessmentReport.Report,IntergovernmentalPanelonClimateChange,IPCCSecreteriat,Geneva,Switzerland,2007. S.Jikich,W.Sams,G.Bromhal,G.Pope,N.Gupta,andD.Smith.Carbondioxideinjectivityinbrinereservoirsusinghorizontalwells.SecondAnnualConferenceonCarbon Sequestration,May5.Alexandria,VA,May2003. S.D.Joshi. Horizontalwelltechnology .PennWellBooks,Tulsa,Colorado,USA,1991. A.KohlandR.Nielsen.Gaspurication.Technicalreport,GulfPubicationCompany, Houston,Texas,1997. A.KovscekandM.Cakici.Geologicstorageofcarbondioxideandenhancedoilrecovery: II.Co-optimizationofstorageandrecovery. EnergyConversionandManagement ,46: 1941,2005. J.Kristian,A.Kovscek,andF.Orr.IncreasingCO 2 storageinoilrecovery. EnergyConversionandManagement ,46:293,2005. A.Kumar,R.Ozah,M.Noh,G.A.Pope,S.Bryant,K.Sepehrnoori,andL.W.Lake.ReservoirsimulationofCO 2 storageindeepsalineaquifers. SocietyofPetroleumEngineering Journal ,9SPE89343:336,September2005. D.LawandS.Bachu.HydrogeologicalandnumericalanalysisofCO 2 disposalindeep aquifersintheAlbertasedimentarybasin. EnergyConversionsandManagement ,37 :1167,1996. L.Marini. Geologicalsequestrationofcarbondioxide:Thermodynamics,kinetics,and reactionpathmodeling .Elsevier,LaboratoryofGeochemistry,UniversityofGenova, Italy,rstedition,2007.ISBN0-444-52950-0. 79

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S.Martinez,R.Steanson,andA.Coulter. Petroleunengineeringhandbook:Formation fracturing ,chapter55,page12pp.SocietyofPetroleumEngineers,1992. J.Nordbotten,M.Celia,andS.Bachu.InjectionandstorageofCO 2 indeepsalineaquifers: AnalyticalsolutionforCO 2 plumeevolutionduringinjection. TransportinPorousMedia ,58:339,2005. O.ObiandM.Blunt.Streamline-basedsimulationofcarbondioxidestorage inaNorthSeaaquifer. WaterResourcesResearch ,42W03414:1,2006. doi:10.1029/2004WR003347. R.Ozah,G.Lakshminarasimhan,K.Sepehrnoori,andS.Bryant.Numericalsimulation ofthestorageofpureCO 2 andCO 2 -H 2 Sgasmixtureindeepsalineaquifers.In SPE AnnualTechnicalConferenceandExhibition ,SPE97255,pages1,Dallas,Texas, USA,2005.SocietyofPetroleumEngineers,SocietyofPetroleumEngineers. K.Pruess.Onvaporizingwaterowinhotsub-verticalrockfractures. TransportinPorous Media ,28:335,1997. K.PruessandJ.Garc a.MultiphaseowdynamicsduringCO 2 disposalintosaline aquifers. EnvironmentalGeology ,42:282,2002. K.PruessandN.Spycher.ECO2NAnewTOUGH2uidpropertymoduleforstudiesof CO 2 storageinsalineaquifers.Berkeley,California,2006.LawrenceBerkeleyNational Laboratory. K.Pruess,C.Oldenburg,andG.Moridis.ProcessmodelingofCO 2 injectionintonatural gasreservoirsforcarbonsequestrationandenhancedgasrecovery. EnergyandFuels 15:293,2001. K.Pruess,T.Xu,J.Apps,andJ.E.Garc a.Numericalmodelingofaquiferdisposalof CO 2 SocietyofPetroleumEngineeringJournal ,8:49,2003. N.SpycherandK.Pruess.CO 2 H 2 OmixturesinthegeologicalsequestrationofCO 2 .II. Partitioninginchloridebrinesat 12 to 100 o Candupto 600 bar. Geochim.Cosmochim. Acta ,69:3309,2005. N.Spycher,K.Pruess,andJ.Ennis-King.CO 2 H 2 OmixturesinthegeologicalsequestrationofCO 2 .I.Assessmentandcalculationofmutualsolubilitiesfrom 12 to 100 o Cand upto 600 bar. Geochim.Cosmochim.Acta ,67:3015,2003. L.G.H.vanderMeer.TheconditionslimitingCO 2 storageinaquifers. EnergyConversionsandManagement ,34,1993. L.G.H.vanderMeer.TheCO 2 storageefciencyofaquifers. EnergyConversionand Management ,36:513,1995. 80

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M.T.vanGenuchten.Aclosed-formequationforpredictingthehydraulicconductivityof unsaturatedsoils. SoilSci.Soc.Am.J. ,44:892,1980. T.Wigley,R.Richels,andJ.Edmonds.EconomicandenvironmentalchoicesinthestabilizationofatmosphericCO 2 concentrations. Nature ,379:240,1996. T.Xu,J.Apps,andK.Pruess.ReactivegeochemicaltransportsimulationtostudymineraltrappingforCO 2 disposalindeeparenaceousformations. JournalofGeophysical Research ,108B2,2071:ECV1,February2003.doi:10.1029/2002JB001979. 81

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Chapter6 StorageofCO 2 inAnisotropicAquifersviaHorizontalWells 6.1Abstract Thischapterinvestigatestheviabilityofhorizontalinjectionwellsfordeepgeologic storageofcarbondioxide.Numericalsimulationsofcarbondioxideintohomogeneous connedsalineaquiferswereconductedatdifferentvaluesofpermeabilityanisotropyratio PARandwelllength.Carbondioxidewascontinuouslyinjectedforup 50 yearsataxed rate.PARrepresentstheratiooftheverticaltothehorizontalpermeabilityofaformation. Themaximumpressureatthewellbore,totalmassofdissolvedcarbondioxide,wellinjectivityatthelocationofmaximumpressure,andstorageefciencywereusedasmetricsfor evaluatingtheperformancesofthesimulations.Carbondioxideinjectionvialonghorizontalinjectionwellswasfoundtobeaviabletechniqueforimprovingthestoragecapacities ofaquiferswithPARgreaterthanorequalto 0 : 01 .Conversely,verticalinjectionwellsare moreefcientforcarbondioxidestoragethanhorizontalinjectionwellsinaquiferswith permeabilityanisotropyratioequalto 0 : 001 .Inaddition,empiricalrelationshipsbetween themaximumpressureatthewellbore,massinjectionrateofcarbondioxide,andPARsuggestthathorizontalwellscanbeusedtosignicantlyincreasethecarbondioxidestorage capacityinanisotropicaquifersunderpressure-limitedconditionsascomparedtovertical wells. 6.2Introduction ThespatialdistributionoftheCO 2 plumewithinaconnedformationisreportedto highlydependonpermeabilityanisotropyKumaretal.,2005;PruessandM uller,2009. Permeabilityanisotropyratio k vh istheratiooftheverticaltothehorizontalpermeability i.e. k vh = k v =k h .Horizontalmovementoftheplumeisfavoredwhileverticalowisless signicantatlowvaluesof k vh Kumaretal.,2005.However,verticalmigrationofCO 2 82

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maybecomesignicantataveragetohigh k vh values.Valuesof k vh generallyusedinthe technicalliteraturerangefrom 0 : 001 to 1 : 0 e.g.,Pruessetal.;Guptaetal.; Kumaretal.;ObiandBlunt;PruessandM uller. Theobjectiveofthischapteristoevaluateandquantifytheeffectsorthebenetsof usinghorizontalinjectorsinstoringCO 2 inaconned,homogenous,anisotropicsaline aquifers.TOUGH 2 numericalsimulationswereconductedtoachievedthefollowing: 1.studytheeffectshorizontalinjectionwelllengthonCO 2 storagecapacityinanisotropic salineaquifers; 2.studyeffectsofpermeabilityanisotropyonCO 2 storagecapacity;and 3.testthehypothesisthatthebenetsofutilizinghorizontalinjectionwellsarereduced inhighlyanisotropicformations. Themetricsusedinquantifyingtheperformancesofthenumericalsimulationsincluded maximumpressureatthewell P w ,massofCO 2 dissolvedintobrine M CO 2 ;aq ,injectivity ,andstorageefciency s ,allevaluatedoverasimulatedinjectionperiodof 50 years. Thesemetricswerequantiedasfunctionsofwelllengthandpermeabilityanisotropyratio k vh 6.3Approach FivesetsofnumericalexperimentsofCO 2 injectionintoahomogeneous,anisotropic, connedsalineaquiferwereconducted.Eachsetconsistedofvenumericalsimulations; oneusingaverticalinjectorandfourutilizinghorizontalinjectorsoflengths 1000 m, 2000 m, 3000 m,and 4000 m,respectively.Aminimumhorizontallengthof 1000 mwasconsideredbasedonndingsinapreviousstudyChapter 5 whichindicatedthatsignicantly largerquantitiesofCO 2 canbestoredinisotropicconnedsalineaquifersusinghorizontal wellsoflengthatleasttentimestheaquifer'sthicknessasopposedtoutilizingverticalwells underpressure-limitedconditionsChapter 5 .Itshouldbeunderscoredthatthelengthor heightofaverticalwellislimitedtotheaquifer'sthickness. CO 2 wascontinuouslyinjectedfor 50 yearsviaverticalorhorizontalwells.Aninjection timeof 50 yearswasselectedbecauseitcoincideswiththelifespanofmostcoal-redpower plantsorheavy-dutyindustrialfacilitieslikeoilreneriesandcementfactories.Thesetsof numericalexperimentsdifferedinpermeabilityanisotropyratio k vh .The k vh valuesused inthisstudyrangedbetween 0 : 001 and 1 : 0 83

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Table16: Matrixofsimulationsthatwillbeconductedinphase3. Injectionwell Anisotropyratio, k vh OrientationL w m 0.0010.010.10.51.0 Vertical 100 Sim3A1Sim3B1Sim3C1Sim3D1Sim3E1 Horizontal1000 Sim3A2Sim3B2Sim3C2Sim3D2Sim3E2 Horizontal2000 Sim3A3Sim3B3Sim3C3Sim3D3Sim3E3 Horizontal3000 Sim3A4Sim3B4Sim3C4Sim3D4Sim3E4 Horizontal4000 Sim3A5Sim3B5Sim3C5Sim3D5Sim3E5 Basecasesimulations Table16presentsthedifferentsetsofnumericalexperimentsandthesimulationsconductedineachbasedonwelllengthandorientation.Foreachvalueof k vh ,asimulation usingaverticalinjectionwellwasusedasthebasecase. Thesimulationswereconductedusinga 3 Dgridsimilarindimensiontothatdescribed inchapter 5 .TheTOUGH2numericalsimulationsoftwarewasusedinconductingthesimulationsherein.DetailsonthedescriptionofTOUGH 2 andgoverningequationssolvedin TOUGH 2 ispresentedinPruessetal.,1999;PruessandGarc a,2002seeChapter 2 for adistilledversion.Table17presenttheinputconditionsappliedinthesimulationsconductedinthischapter.Equationsforrelativepermeabilitiesoftheliquidphase k lr andcapillarypressure P cap asfunctionsofuidsaturationsdevelopedbyvanGenuchten wereappliedinallsimulationsTable17.Therelativepermeabilityfunctiondevelopedby Coreywasusedtoestimatetherelativepermeabilityofthegasphase k gr InTable17, S lr S gr S l , P o ,and S ls denotetheresidualorirreducibleliquidsaturation,irreduciblegassaturation,liquidsaturation,poregeometryparametervanGenuchten, 1980,strengthcoefcient,andliquidsaturationatwhich P cap vanishesPruessandGarc a, 2002.Thevalueof S ls generallyusedinthetechnicalliteratureis 1 : 0 Ennis-KingandPaterson,2002;Pruessetal.,2003;Kumaretal.,2005;Ozahetal.,2005;PruessandM uller, 2009.TheCO 2 massinjectionrateof 100 kg/sappliedinthesimulationshereinisequivalenttoCO 2 emissionsfroma 288 MWecoal-redpowerplantHitchon,1996. Resultsfromthesimulationswithinandbetweenthesetsofnumericalexperimentswere comparedtodeterminetheeffectsofwelllength L w andpermeabilityanisotropy k vh onthemetricsi.e. P w M CO 2 ;T ,and s .Thevaluesof P w and M CO 2 ;aq weredirectly obtainedfromthesimulationresults. s wascalculatedastheratiobetweenvolumeofCO 2 injected V inj andtheutilizedporousvolumeofaquifer V max .Theapproachormethod usedincalculating V inj and V max hereinaresimilartothosedescribedinchapter 5 .Again, 84

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injectivity isthemassinjectionrateperunitthicknessperunitpressurechangebetween theinjectionwellandtheaquiferLawandBachu,1996.Inotherwords,itmeasures theeasewithwhichauidcanbeinjectedintoageologicformationperunitheightor thicknessoftheformationKovscek,2002;IPCC,2005.Injectivity ismathematically denedasfollowsDake,1978;LawandBachu,1996: = Q B P .1 where Q isthemassowratekg/s, B istheformationthicknessm,and P P w )]TJ/F19 11.9552 Tf 10.313 0 Td [(P init isthedifferencebetweenpressureatthewellanditsinitialpressure. The P w datafromthenumericalsimulationswerettedasfunctionsof Q and k vh witha straightlinepassingthroughtheorigintoobtainedempiricalrelationshipsbetweenpressure changesneartheinjectionwell P Q ,and k vh forverticalwellsandhorizontalwells. Therelationshipsweremadeat 50 yearsofCO 2 injection,whichroughlycorrespondsto theaveragelifespanofheavy-dutyindustrialfacilitiesthatemitlargequantitiesofCO 2 Thefollowingdimensionlessparameterswereusedtoevaluatetheeffectsofwelllength and k vh onthemetrics: = L w B .2 = P h w )]TJ/F19 11.9552 Tf 11.955 0 Td [(P v w P v w .3 = M h CO 2 ;aq )]TJ/F19 11.9552 Tf 11.956 0 Td [(M v CO 2 ;aq M v CO 2 ;aq .4 = h s )]TJ/F19 11.9552 Tf 11.955 0 Td [(" v s v s .5 = h )]TJ/F19 11.9552 Tf 11.955 0 Td [( v v .6 85

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Table17: Inputparametersappliedinallsimulationschapter6. ParameterValue DimensionL W Hm10 5 10 5 100 Gridblocks X : Y : Z 65 65 10 Depthtopbottom D ,m1200 Porecompressibility, c ,m 2 /N4.5 10 )]TJ/F17 7.9701 Tf 6.587 0 Td [(10 Initialpressuretop:bottom P init ,MPa12.0:13.1 Temperature T C45.0 Averageporosity, 0.12 Averagepermeability k ,m 2 1.0 10 )]TJ/F17 7.9701 Tf 6.587 0 Td [(13 Permeabilityanisotropyratio k vh 0.001.0 Massinjectionrate Q ,kg/s100 Injectiontime t ,years50 Relativepermeability Brine } k rl = p S f 1 )]TJ/F15 11.9552 Tf 11.955 0 Td [( )]TJ/F15 11.9552 Tf 11.955 0 Td [([ S ] 1 g 2 S = S l )]TJ/F20 7.9701 Tf 6.586 0 Td [(S lr 1 )]TJ/F20 7.9701 Tf 6.587 0 Td [(S lr Residualbrinesaturation S lr =0 : 3 Exponent =0 : 457 GasCO 2 ~ k rg = )]TJ/F15 11.9552 Tf 13.952 3.022 Td [(^ S 2 )]TJ/F15 11.9552 Tf 13.952 3.022 Td [(^ S 2 ^ S = S l )]TJ/F20 7.9701 Tf 6.586 0 Td [(S lr 1 )]TJ/F20 7.9701 Tf 6.587 0 Td [(S lr )]TJ/F20 7.9701 Tf 6.586 0 Td [(S gr Residualgassaturation S gr =0 : 05 Capillarypressure } P cap = )]TJ/F19 11.9552 Tf 9.299 0 Td [(P o [ S ] )]TJ/F18 5.9776 Tf 8.155 3.258 Td [(1 )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 1 )]TJ/F20 7.9701 Tf 6.586 0 Td [( S = S l )]TJ/F20 7.9701 Tf 6.587 0 Td [(S lr S ls )]TJ/F20 7.9701 Tf 6.587 0 Td [(S lr Residualbrinesaturation S lr =0 : 0 Strengthcoefcientbar P o =1 : 0 10 7 Exponent =0 : 457 } vanGenuchten ~ Corey where P h w and P v w aremaximumpressuresatthehorizontalandverticalwells, M h CO 2 ;aq and M v CO 2 ;aq arethetotalmassesofdissolvedCO 2 forsimulationsusinghorizontalandvertical wells, h s and v s aretheCO 2 storageefcienciesforsimulationswithhorizontalandvertical injectionwells,and h and v areinjectivitiesofsimulationsusinghorizontalandvertical injectionwells,respectively. 86

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6.4ResultsandDiscussions 6.4.1AnalysisoftheMetrics ResultsfromthesimulationsconductedhereinshowCO 2 plumetotakelongertimesto reachtheupperconninglayeras k vh isreduced,forsimulationsusinghorizontalinjectors.ThetimeafterwhichtheCO 2 plumehitstheupperconninglayeralsoincreases withthelengthofhorizontalinjectionwell.TheCO 2 -richgasphasesaturations S g weregreatestatthebottomsectionoftheaquiferforsimulationsusinghorizontalinjectors. However,themassfractionofCO 2 dissolvedinformationbrine X CO 2 wasloweratthe bottomoftheaquifer,intheregionnearthehorizontalwell.Thisisbecausethisregionis closesttotheCO 2 sourcehorizontalwell.Signicantdifferencebetweenthedensitiesof CO 2 andresidentbrinecausesacountercurrentowasCO 2 risesduetobuoyancywhile CO 2 -saturated-brinesinkstothebottomoftheaquiferOzahetal.,2005. Tables18and19presentvaluesof P w M CO 2 ;aq ,and ,respectively,after 50 yearsof continuousCO 2 injectionviaverticalandhorizontalinjectorsat k vh equalto 0 : 001 0 : 01 0 : 1 0 : 5 ,and 1 : 0 .Theresultspresentedintheabove-mentionedtablesindicatethatfora speciedvalueof Q k k h ,and L w : 1. P w decreasesas k vh isincreasedfrom 0 : 001 to 1 : 0 .Thisisbecauseas k vh 1 : 0 k v increasesandresistancetouidowintheverticaldirectionreduces. 2. M CO 2 ;aq alsodecreasesas k vh isincreasedbecauseofacorrespondingdropin P w ThisisinaccordancewithndingsinthetechnicalliteraturewhichindicatethatCO 2 solubility M CO 2 ;aq increaseswithpressureSpycheretal.,2003;SpycherandPruess, 2005. 3. increaseswithincreasing k vh duetoacorrespondingdecreasein P w atthexed valueof Q .Thisisinagreementwithequation6.1whichdepictaninverserelationship between and P 4. s increasesas k vh isdecreased.Thismaybebecausethegasplumemigratesmore slowlyinverticaldirectionas k vh decreases.Asaresult,italsotakesalongertime toreachtheupperconningbedpriortoformingathinlayer,therebyminimizingthe under-utilizedporousvolumeoftheaquifer. 87

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Figure15.: S g spatialdistributionsafter 50 yearschapter6.CO 2 wascontinuouslyinjectedatarateof 100 kg=s k vh =0 : 01 .averticalwell simulation S g;max =0 : 954 ;bhorizontalwellsimulation 3000 mlong S g;max =0 : 931 88

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Figure16.: X CO 2 spatialdistributionsafter 50 years.CO 2 wascontinuously injectedatarateof 100 kg=s k vh =0 : 001 .averticalwellsimulation X CO 2 =0 : 0288 ;bhorizontalwellsimulation 3000 m X CO 2 =0 : 0288 89

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6.4.2SensitivityAnalysis Analysesoftheresultsfromthesimulationsconductedhereinbasedonthedimensionlessparametersdenedinequations6.2.6arepresentedinFigure17.Figure17show dimensionlessplotsof , ,and asfunctionsof k vh and Resultsshowed togenerallydecreasewithincreasing asaresultofreductioninmass ofCO 2 injectedperunitwelllengthFigure17a.ItcanalsobededucedfromFigure 17athat increasesas k vh decreases.TheseindicatethatpressuresnearCO 2 injection wellsdiminishwithincreasingwelllengthbutincreaseas k vh isdecreasedorasvertical permeabilityisreduced.ThisisinagreementwiththepressuredatapresentedinTable18. Theobservedincreaseinpressureneartheinjectorswithdecreasingvaluesof k vh ismost probablybecauseofincreasedresistancetouidowintheverticaldirectionlowvertical permeabilityBachuetal.,1994;Kumaretal.,2005. Changesin asafunctionof areverysmallFigure17b.However,thevariation of asafunctionof k vh didnotfollowauniformtrend. at k vh equalto 1 wasthelowest followedbythatatthe k vh valueof 0 : 5 .However,valuesof at k vh equalto 0 : 01 was highest,followedbythoseat k vh equalto 0 : 1 and 0 : 001 respectively.Since represents therelativechangein M CO 2 ;aq inusingahorizontalinjectorasopposetoverticalinjector, itcanbeinferredfromFigure17bthatthemostfavorablegainorchangein M CO 2 ;aq was achievedat k vh equalto 0 : 01 ResultsinFigure17cshow toincreasewith and k vh .Thisindicatesthatinjectivity increaseswithwelllengthbutdeclinewithdecreasing k vh .Similarresultsonthevariabilityof asafunctionof k vh havebeenreportedinthetechnicalliteratureJikichetal., 2003;Ozahetal.,2005.ThisanalogyisinagreementwiththeresultspresentedinFigure 17ainwhich declinedwithincreasing and k vh ,sincepressurechangeswithinthe aquiferisinverselyproportionaltoinjectivitywhen Q and B areconstant. Thevariabilityof asafunctionof wasminimalFigure17d.However,values of at k vh equalto 0 : 001 wasnegativewhilethoseof k vh equalto 0 : 01 0 : 1 0 : 5 ,and 1 : 0 werepositivebutlessthan 20 %.Thegreatestvaluesof wereobtainedat k vh equalto 0 : 1 followedby 0 : 01 0 : 5 and 1 : 0 respectively.Theseindicatethattherelativegainin s using horizontalwellsratherthanverticalwelltoinjectCO 2 inconnedaquifersisgreatestat k vh equalto 0 : 1 andleastat 0 : 001 InFigure17bvaluesof arepositiveonlyfor k vh equal 0 : 01 followedbythoseof k vh equalto 0 : 1 ,whichisjustbelowthezeromark.Thevaluesof fortheremainingvalues of k vh ,i.e., 0 : 001 0 : 5 ,and 1 : 0 ,aremorenegativethanthoseof k vh equalto 0 : 1 .Valuesof 90

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for k vh equalto 0 : 01 and 0 : 1 inFigure17baregreaterthanzerowhilethosefor k vh equalto 0 : 001 0 : 5 ,and 1 : 0 arenegativeespeciallyat k vh equalto 0 : 001 .Foragivenvalue of ,apositive signiesthatmoremassofCO 2 dissolvesinbrinewheninjectedvia horizontalwellsthanverticalwellsandapositive indicatesthathorizontalwellsare moreefcientthanverticalwellsandviceversa.Therefore,theresultsinFigure17b anddsuggestthatlonghorizontalinjectorsi.e., 10 aremoreefcientthanvertical injectorsforCO 2 storageinconnedaquiferswith k vh 0 : 01 Table18: Variationsof P w and M CO 2 ;aq with k vh at t equalto 50 years. Injectionwell P w bar Orientation L w m k vh :0.0010.010.10.51.0 Vertical100 235229205195193 Horizontal1000 245227198186184 Horizontal2000 236222194184182 Horizontal3000 231218192182180 Horizontal4000 226216189181179 M CO 2 ;aq Mtons Orientation L w m k vh :0.0010.010.10.51.0 Vertical100 20.920.315.512.211.5 Horizontal1000 20.520.215.311.710.9 Horizontal2000 20.520.415.411.810.9 Horizontal3000 20.620.615.411.810.9 Horizontal4000 20.720.615.511.811.0 TheresultspresentedinTables18and19indicatethatatvaluesof k vh equalto 0 : 001 theusageofverticalinjectorstostoreCO 2 maybeamoreviableinjectionstrategythan usinghorizontalinjectors.Thisisbecauseat k vh equalto 0 : 001 thesimulationusinga verticalinjectorhasacomparativelylow P w andgreatervaluesof M CO 2 ;aq and s thanthe simulationsusinghorizontalinjectionwells. Resultsintable18indicatethat M CO 2 ;aq increasesas k vh isdecreased.Thisindicates thatvariationsinverticalpermeabilityhasasignicantimpactonsolubilityofCO 2 during injectionphaseasreportedbyEnnis-KingandPaterson.Resultsof s atdifferent valuesof k vh presentedinTable19showthatthenegativevaluesof obtainedat k vh equal to 0 : 001 Figure17disbecause h s )]TJ/F19 11.9552 Tf 11.955 0 Td [(" v s equation.6isnegative. 91

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Figure17.: Graphsof , ,and against .Atdifferentvaluesofpermeabilityanisotropyratio Q =100 kg/s. 92

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Table19: Variationsof and s with k vh at t equalto 50 years. Injectionwell tons/d/m/bar Orientation L w m k vh :0.0010.010.10.51.0 Vertical100 0.830.871.161.331.38 Horizontal1000 0.820.891.291.551.62 Horizontal2000 0.820.941.361.621.69 Horizontal3000 0.860.981.411.681.74 Horizontal4000 0.901.021.471.721.78 s Orientation L w m k vh :0.0010.010.10.51.0 Vertical100 35.0%19.6%14.1%12.0%12.0% Horizontal1000 21.3%21.5%15.7%13.2%12.8% Horizontal2000 21.3%21.6%15.7%12.7%12.7% Horizontal3000 19.6%21.8%16.5%13.2%12.6% Horizontal4000 21.5%21.8%16.0%13.5%12.1% Table20: Valuesof P barfordifferentvaluesof k vh and L w at 50 years. Q =100kg/s. InjectionwellAnisotropyratio, k vh OrientationL w m 0.0010.010.10.51.0 Vertical100 10499756562 Horizontal1000 11497675653 Horizontal2000 10591635351 Horizontal3000 10088615149 Horizontal4000 9585595048 6.4.3EmpiricalRelationshipsBetween P Q ,and k vh Table20showsthevaluesof P for k vh equalto 0 : 001 0 : 01 0 : 1 and 1 : 0 P at k vh equalto 1 : 0 isequivalenttochangesinpressureunderisotropicconditionsaddressedin Chapter 5 .Forthepurposeofclarity,let P iso and P aniso represent P inanisotropic andanisotropicaquifer,respectively.Wedenedanewparameter P 0 astheratiobetween P aniso and P iso asfollows: P 0 = P aniso P iso .7 93

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Table21: Valuesof P 0 fordifferentvaluesof k vh and L w at 50 years. InjectionwellAnisotropyratio, k vh OrientationL w m 0.0010.010.10.5 Vertical100 1.671.581.201.04 Horizontal1000 2.151.821.261.05 Horizontal2000 2.071.801.251.04 Horizontal3000 2.031.781.231.04 Horizontal4000 1.981.761.221.03 Valuesof P 0 atdifferent k vh andwelllengths L w arepresentedinTable21.Theempiricalrelationshipsbetween P 0 and k vh fordifferentwelllengthsandorientationswere obtainedbyttingthedatapresentinTable21.Theresultinglogarithmicequationsdescribingtherelationshipbetween P and k vh areasfollows: P 0 = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 24519log k vh +1 R 2 =0 : 96 L w =100 m vertical .8 P 0 = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 38370log k vh +1 R 2 =0 : 98 L w =1000 m horizontal .9 P 0 = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 36324log k vh +1 R 2 =0 : 97 L w =2000 m horizontal .10 P 0 = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 35133log k vh +1 R 2 =0 : 97 L w =3000 m horizontal .11 P 0 = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 33792log k vh +1 R 2 =0 : 96 L w =4000 m horizontal .12 Equations.8.12depictchangesin P 0 asafunctionof k vh inaverticalinjection wellandhorizontalinjectionwellsoflengths 1000 m, 2000 m, 3000 m,and 4000 m,respectively,forvaluesof Q equalto 100 kg/s.Toestimate P aniso atvaluesof Q differentfrom 100 kg/s,theempiricalrelationshipsbetween P iso and Q obtainedinChapter 5 equations.3.7werecombinedaccordinglywithequations.8.12toobtainthe followinggeneralizeempiricalrelationshipbetween P 0 P iso P aniso Q ,and k vh see appendixfordetailedderivation: 94

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P 0 = P aniso P iso = B log k vh +1 .13 P aniso = A Q B log k vh +1 .14 P iso = A Q whereA and B arecoefcientsatdifferentvaluesof Table22. Table22: ValuesofcoefcientsA andB asfunctionsof A B 1 0.5911-0.24519 10 0.4967-0.38370 20 0.4753-0.36324 30 0.4602-0.35133 40 0.4566-0.34904 Thevalidityofequation6.14wasveriedbycomparingitspredictionstothoseof TOUGH 2 simulationsatdifferentvaluesof Q and k vh Table23.ResultsinTable23 showexcellentagreementbetweenpressuresestimatedusingequation.14andthose predictedbyTOUGH 2 withrelativeerrorswithin 4 %.Thevalidityoftheseequations wastestedforvaluesof Q rangingfrom 50 to 255 kg/sand k vh rangingfrom 0 : 001 to 1 : 0 Equation.14canbeusedtogetroughestimatesofthemaximumpressureduringCO 2 injectioninconnedsalineformations. Inpressure-limitedscenarios,equation.14canalsobeusedtoestimatethemaximum allowableCO 2 massinjectionrate Q max inananisotropicformation,for 50 yearsof continuousCO 2 injection,i.e., Q max = P aniso;max A [ B log k vh +1] .15 where P aniso;max isthemaximumchangeinpressurewithinananisotropicconned aquifer. Figure18showvariationsin Q max asafunctionof L w atdifferentvaluesof k vh ,for P aniso equalto 200 bar.Figure19alsoshowvariationsin Q max asafunctionof k vh at differentvaluesof L w ,for P aniso equalto 200 bar. 95

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Table23: Valuesof P fordifferentvaluesof k vh andwelllengthat 50 years. InjectionwellParameters P w bar OrientationL w m Q k vh AnalyticalTOUGH 2 Relativeerror Vertical100 500.001 182186 -2.29% Horizontal1000 1000.01 219227 -3.84% Horizontal2000 2480.1 291282 3.32% Horizontal3000 2560.5 261251 4.00% Horizontal4000 2000.001 312307 1.41% ResultsinFigure18indicatethat Q max increasesas L w isincreased.Theresultsin Figure19suggestthatforaspeciedvalueof P aniso;max Q max increasesasasthethe aquiferbecomesmoreisotropici.e. k vh 1 : 0 Figure18.: Q max asafunctionof L w and k vh for P aniso equalto 200 bar. t = 50 years. Forexample,for P aniso;max equalto 200 bar,the Q max usinga 4000 mlonghorizontal wellinahighlyanisotropicaquiferwitha k vh valueof 0 : 001 isabout 221 kg/sasopposed to 195 kg/susingaverticalwell 100 mFigure18.Ontheotherhand,the Q max usinga 4000 mlonghorizontalwellinalessanisotropicaquiferwith k vh equalto 0 : 5 isabout 409 kg/swhilethatforusingaverticalwellis 315 kg/s. 96

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Figure19.: Q max asafunctionof k vh for P aniso equalto 200 bar. t =50 years. Thisindicatesthattheaquiferwith k vh equalto 0 : 001 couldstoreanadditional 26 Mtons ofCO 2 whiletheotheraquiferwith k vh equalto 0 : 5 couldstoreadditional 95 Mtonsof CO 2 usinga 4000 mlonghorizontalwellafter 50 yearsofcontinuousinjection. 26 Mtons and 95 MtonsofCO 2 isequivalenttoCO 2 emissionsfroma 1000 MWecoal-redpower forover 2 and 9 years,respectively.Resultsfromthisexamplesuggestthat k vh hasamore signicanteffectonanaquifersstoragecapacitythanhorizontalwelllength. Itshouldbeunderscoredthatequations.8.15arevalidonlyforthespecied valuesof k and usedinthisstudy.Thisisbecauseformationpressuredependsstrongly ontheabove-mentionedhydrogeologicparameters,especiallytheformationpermeability k .However,theycanbeemployedtocarryoutqualitativeanalysestodeterminethebest injectionstrategyforCO 2 storagetoapplyonacasebycasebasis. 97

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6.5Conclusions TheutilizationofhorizontalinjectionwellstoboostertheCO 2 storagecapacityof anisotropicaquiferswasevaluatedbyconductingaseriesofnumericalsimulations.The simulationswereconductedatdifferentwelllengthsandpermeabilityanisotropy.The performancesofthenumericalsimulationswerecomparedtodeterminethebenetsand limitationsofusinghorizontalinjectionwellsasaviableCO 2 injectionstrategybasedon ametrics,whichinclude:maximumpressureneartheinjectionwell,massofCO 2 dissolvedinbrine,injectivity,andstorageefciency.Resultsobtainedfromthesimulations suggestthatforaspeciedCO 2 massinjectionrate,welllength,andaveragepermeability inthehorizontaldirection,thepressurenearaninjectionwelldecreasesasthepermeability anisotropyratioisincreased.Inaddition,thedeclineinnearwellborepressurealsocauses thetotalamountofCO 2 dissolvedinbrinetodecrease.Thenearwellborepressurealso decreasedasthelengthoftheinjectionwellisincreasedduetoacorrespondingdeclinein themassofCO 2 injectedperunitwelllength. AnalysesoftheresultsusingagroupofdimensionlessparameterssuggestthatCO 2 storageviahorizontalinjectionwellscouldbeaviableinjectionstrategyinenhancingstorage capacityinformationsoraquiferswithpermeabilityanisotropyratiorangingbetween 0 : 01 and 1 : 0 .VerticalinjectionwellswerefoundtobemoreefcientthanhorizontalinjectionwellsforCO 2 storageinconnedaquiferswithpermeabilityanisotropyratiolessthan 0 : 01 i.e. k vh equalto 0 : 001 .Thisconformswiththehypothesisthatbenetsofutilizing horizontalinjectionwellsreducesinhighlyanisotropicformationse.g., k vh equalto 0 : 001 Empiricalrelationshipsbetweenchangesinnearwellborepressure,CO 2 massinjection rateandpermeabilityanisotropyratioafter 50 yearsindicatethatunderpressure-limited conditions,horizontalinjectionwellscanbeusedtosignicantlyincreaseCO 2 storage capacityofaquifersandminimizedriskofCO 2 leakage. 6.6ReferencesCited S.Bachu,W.Gunter,andE.Perkins.AquiferdisposalofCO 2 :Hydrodynamicandtrapping. EnergyConversionandManagement ,35,1994. A.Corey.Theinterrelationbetweengasandoilrelativepermeabilities. ProducersMonthly pages38,Noverber1954. L.Dake. Fundamentalsofreservoirengineering ,volume8.ElsevierScienticPublishing, Amsterdam,2edition,1978.ISBN0-444-41667-6. 98

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J.Ennis-KingandL.Paterson.Engineringaspectsofgeologicalsequestrationofcarbon dioxide.volumeSPE-77809,SPEandCSIROPetroleum,2002.AsiaPacicOilandGas ConferenceandExhibition,Melbourne,Australia,October8. N.Gupta,B.Sass,S.Chattopadhyay,J.Sminchak,P.Wang,andT.Espie.Geologicstorage ofCO 2 fromreningandchemicalfacilitiesintheMidwesternUS. Energy ,29:1599 1609,2004. B.Hitchon. Aquiferdisposalofcarbondioxide .GeosciencePublishingLtd.,Sherwood Park,Alberta,Canada,1996. IPCC.IPCCspecialreportoncarbondioxidecaptureandstorage.PreparedbyWorking GroupIIIoftheIntergovernmentalPanelonClimateChange[Metz,B.,Davidson,O., deConinck,H.C.,Loos,M.,andMeyer,L.A.eds.].Report,IntergovernmentalPanel onClimateChange,Cambridge,UnitedKingdomandNewYork,NY,USA,2005. S.Jikich,W.Sams,G.Bromhal,G.Pope,N.Gupta,andD.Smith.Carbondioxideinjectivityinbrinereservoirsusinghorizontalwells.SecondAnnualConferenceonCarbon Sequestration,May5.Alexandria,VA,May2003. A.Kovscek.ScreeningcriteriaforCO 2 storageinoilreservoirs. PetroleumScienceand Technology ,20:841,2002. A.Kumar,R.Ozah,M.Noh,G.A.Pope,S.Bryant,K.Sepehrnoori,andL.W.Lake.ReservoirsimulationofCO 2 storageindeepsalineaquifers. SocietyofPetroleumEngineering Journal ,9SPE89343:336,September2005. D.LawandS.Bachu.HydrogeologicalandnumericalanalysisofCO 2 disposalindeep aquifersintheAlbertasedimentarybasin. EnergyConversionsandManagement ,37 :1167,1996. O.ObiandM.Blunt.Streamline-basedsimulationofcarbondioxidestorage inaNorthSeaaquifer. WaterResourcesResearch ,42W03414:1,2006. doi:10.1029/2004WR003347. R.Ozah,G.Lakshminarasimhan,K.Sepehrnoori,andS.Bryant.Numericalsimulation ofthestorageofpureCO 2 andCO 2 -H 2 Sgasmixtureindeepsalineaquifers.In SPE AnnualTechnicalConferenceandExhibition ,SPE97255,pages1,Dallas,Texas, USA,2005.SocietyofPetroleumEngineers,SocietyofPetroleumEngineers. K.PruessandJ.Garc a.MultiphaseowdynamicsduringCO 2 disposalintosaline aquifers. EnvironmentalGeology ,42:282,2002. K.PruessandN.M uller.Formationdry-outfromCO 2 injectionintosalineaquifers: 1 : Effectsofsolidsprecipitationandtheirmitigation. WaterResourcesandResearch ,45 w03402:1,2009.doi:10.1029/2008WR007101. 99

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K.Pruess,C.Oldenburg,andG.Moridis.TOUGH2users'guide,version2.0.Manual LBNL-43134,LawrenceBerkeleyNationalLaboratory,Berleley,California,1999.accessdate:June10,2007. K.Pruess,T.Xu,J.Apps,andJ.E.Garc a.Numericalmodelingofaquiferdisposalof CO 2 SocietyofPetroleumEngineeringJournal ,8:49,2003. N.SpycherandK.Pruess.CO 2 H 2 OmixturesinthegeologicalsequestrationofCO 2 .II. Partitioninginchloridebrinesat 12 to 100 o Candupto 600 bar. Geochim.Cosmochim. Acta ,69:3309,2005. N.Spycher,K.Pruess,andJ.Ennis-King.CO 2 H 2 OmixturesinthegeologicalsequestrationofCO 2 .I.Assessmentandcalculationofmutualsolubilitiesfrom 12 to 100 o Cand upto 600 bar. Geochim.Cosmochim.Acta ,67:3015,2003. M.T.vanGenuchten.Aclosed-formequationforpredictingthehydraulicconductivityof unsaturatedsoils. SoilSci.Soc.Am.J. ,44:892,1980. 100

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Chapter7 StorageofCO 2 inAnisotropicAquifersviaJointInjectionWells 7.1Abstract NumericalsimulationsofcarbondioxideCO 2 injectioninconnedsalineaquifers wereconductedtoevaluatethebenetsofusingacombinationofverticalandhorizontalwellsjointwellforgeologicstorage.Thisasachievedbydevelopinganalytical relationshipstodeterminethedistributionofCO 2 betweentheverticalandhorizontalsegmentsofajointinjectionwellandhowitaffectsthestoragecapacityofananisotropic aquiferandcomparetheperformancesofthenumericalsimulationsofCO 2 injection viaajoint,vertical,andhorizontalinjectiontodetermineconditionsunderwhichjointwells areefcientthanverticalorhorizontalwells.Themetricsusedtoevaluateperformances ofthenumericalsimulationsinclude;maximumpressureattheinjectionwell,totalmass ofCO 2 dissolvedinbrine,andstorageefciency.ItwasfoundthatmoreCO 2 distributes tothehorizontalsegmentofjointwellinlessanisotropicaquifersandasthelengthofthe horizontalsegmentincreases.Underpressure-limitedconditions,simulationswithmostof theinjectedCO 2 distributedtothehorizontalsegmentofthejointaremoreefcientthan thoseinwhichmostoftheCO 2 ischanneledintotheaquiferviatheverticalsegment.A Comparisonoftheperformancesofthejoint,vertical,andhorizontalinjectionwellssuggestthatjointwellsaremoreefcientthanverticalwellsandlessefcientthanhorizontal wellsinanisotropicconnedaquifers. 7.2Introduction ThestorageofcarbondioxideCO 2 incandidateconnedaquifersrequiresdrillingof wells.Thewellscanbevertical,horizontal,orslanted.Basedonlessonslearnedfrom previousstudies,thechoiceofwellorientationdependsonthehydrogeologicpropertiesof aquifers,especiallytheirpermeabilitiesandtoalesserextentonthephysicalpropertiesof 101

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CO 2 relativetothoseoftheresidentuidseeChapters6.Instronglyanisotropicaquifers withpermeabilityanisotropyratio k vh equalto 0 : 001 orless,theuseofverticalinjection wellsforCO 2 storageisfavored. k vh istheratiooftheverticaltothehorizontalpermeabilityofaformation.Conversely,whenthe k vh ofanaquiferisequalto 0 : 01 orgreater, longhorizontalinjectionwellsarepreferableforCO 2 storage.Itshouldbeunderscored thatundereldconditions,verticalwellsaremoreeasytodrillthanhorizontalwells.This isbecauseindrillingthelatter,theformerisdrilledpriortodrillingatanangleparallel tothebeddingoftheaquifer.Inaddition,undereldconditionsthehorizontalsectionor segmentofawellishardlyparalleltothebeddingofanaquiferJoshi,1991. Whenonlythehorizontalsegmentofthedrilledwelliscompletedorperforated,CO 2 willentertheformationviathatsectionofthewell,andthewelltermedahorizontalwell. Ontheotherhand,iftheentiresectionofthewelllocatedwithintheaquiferiscompleted, CO 2 willentertheformationviaboththeverticalandhorizontalsegmentsofthewell. Thisistermedajointinjectionwell.Figure20showsaschematicrepresentationofCO 2 injectionintoaconnedsalineaquiferviaajointinjectionwell.However,anunderstanding ofhowCO 2 willbedistributedwithinajointwellandtheeffectsitmayhaveonthestorage capacityofananisotropicaquiferiswarranted. Figure20.: A 2 DschematicrepresentationofCO 2 injection.Intoaconned aquiferviaajointwell. 102

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Thischapterevaluatesthebenetsofusingajointverticalandhorizontal`joint'injectionwellforCO 2 storageinananisotropic,homogeneous,connedaquiferviaachievementofthefollowingsub-objectives: 1.estimatethedistributionofinjectedCO 2 alongajointwell; 2.studyeffectsofCO 2 distributionbetweentheverticalandhorizontalsegmentsofajoint injectionwellonstorageinananisotropicaquifer;and 3.testthehypothesisthatacombinationofverticalandhorizontalinjectionwellsjoint wellismorebenecialthanasingleverticalorhorizontalinjectionwellinanisotropic aquifers. ThedistributionofCO 2 betweentheverticalandhorizontalsegmentsofajointwellwas estimatedbasedonthelengthsofthesegments,permeabilityanisotropyratio k vh ,and theCO 2 massinjectionrate Q .Themetricsusedinevaluatingthebenetsofutilizing ajointinjectionwellforCO 2 storageinclude:maximumpressureatthewellbore P w totalmassofCO 2 dissolvedinbrine M CO 2 ;aq ,andstorageefciency s .EffectsofCO 2 distributionalongthesegmentsofajointinjectionwellonthemetricswerestudiedvia numericalsimulations.Resultsfromthesimulationswerealsousedtodetermineconditions underwhichusageofjointinjectionwellscouldbebenecialinenhancingCO 2 storage. 7.3Approach 7.3.1CO 2 DistributionBetweenInjectionWellSegments Asnotedabove,thedistributionofinjectedCO 2 betweentheverticalandhorizontal segmentsofajointwellwasassumedtodependontheCO 2 massinjectionrate Q ,permeabilityanisotropyratio k vh ,andlengthsofthesegmentsi.e.lengthsofverticalwell L v andhorizontalwell L h .Let I vh ,referredhereinasCO 2 massinjectionratio,representtheratioofthemassinjectionrateoftheverticalsegment Q v tothemassinjection rateofthehorizontalsegment Q h ofajointinjectionwelli.e. I vh = Q v Q h .1 Inanisotropicaquifer, I vh canbeassumedtobeequivalenttheratioofthelengthofthe verticaltothehorizontalsegmentsofajointwelli.e., 103

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I vh = I v = h = L v L h .2 Inananisotropicaquifer, Q h willbestronglydependenton k v and L h while Q v willbe afunctionof k h and L v .Therefore,Imakethefollowingassumptions: I vh = Q v Q h L v k h L h k v = L v L h k vh = L v =L h I vh .3 where L v L h ,and k vh aretheverticalwelllength,horizontalwelllength,andpermeability anisotropyratio,i.e., k vh = k v =k h ,respectively. Thisindicatesthattheinjectionrateofthehorizontalsegmentincreasesas L h and k vh increase.ExpressionsforCO 2 massinjectionratesinthevertical Q v andhorizontal Q h segmentsofthejointwellareasfollowsfromequation7.1andfromrealizingthat Q = Q v + Q h : Q v = QI vh 1+ I vh .4 Q h = Q 1+ I vh .5 where Q isthetotalCO 2 massinjectionrate. Therefore,foraspecied Q L v L h ,and k vh I vh andsubsequently Q v and Q h canbe estimatedusingequations7.3,7.4,and7.5,respectively. 7.3.2DescriptionofSimulations EightnumericalsimulationsofCO 2 injectionintoadeepsalineaquiferviaajointwell wereconductedforaperiodof 50 yearsTable24.ThesimulationspresentedinTable 24canbeclassiedintotwogroupsbasedonthevalueof k vh used,i.e., k vh equalto 0 : 1 and 0 : 01 .Ineachgroupofnumericalsimulations, Q and L v wereheldconstantat 200 kg/s and 100 m,respectively,while L h wasvariedfrom 1000 mto 4000 m.Equations7.3,7.4, and7.5wereusedtoestimate I vh Q v and Q h ,respectively.Thevaluesof Q v and Q h were subsequentlyusedasinputsinthenumericalsimulations. 104

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Table24: Simulationmatrix Q = 200 kg/s. Case L v m L h m k vh I vh Q v kg/s Q h kg/s 110010000.101.00100.00100.00 210020000.100.5066.67133.33 310030000.100.3349.62150.38 410040000.100.2540.00160.00 510010000.0110.00181.8218.18 610020000.015.00166.6733.33 710030000.013.33153.8146.19 810040000.012.50142.8657.14 TheinputconditionsappliedinthesimulationsconductedhereinarepresentedinTable 25.InTable25, S lr S gr S l , P o ,and S ls denotetheirreducibleliquidsaturation,irreduciblegassaturation,liquidsaturation,poregeometryparameter,strengthcoefcient,and liquidsaturationatwhich P cap vanishesPruessandGarc a,2002.Thevalueof S ls generallyusedinthetechnicalliteratureis 1 : 0 e.g.,Ennis-KingandPaterson;Pruess etal.;Kumaretal.;Ozahetal.;PruessandM uller.Thevalue of S lr inestimationofcapillarypressure P cap wassetto 0 : 0 toavoidunphysicalbehavior ofthevanGenuchtenfunctioninwhichas k lr 0 P cap Pruess,1997;Pruessand Garc a,2002.Lastly,thedependenceofpermeabilityonporositywasignoredorassumed negligible. Thesimulationswereconductedusinga 3 Dgridsimilarindimensiontothatdescribed chapter 5 .TheTOUGH 2 numericalsimulationsoftwarewasusedinconductingsimulationsinthisstudy.DetailsonthedescriptionofTOUGH 2 andgoverningequationssolved inTOUGH 2 arepresentedbyPruessetal.andbyPruessandGarc a,see Chapter 2 foradistilledversion.Theperformancesofthedifferentinjectionscenarios wereevaluatedbasedonthemetrics P w M CO 2 ;aq ,and s todeterminetheeffectsof k vh onCO 2 storagewhenajointwellisusedforCO 2 injectionintoaconnedaquifer. Thehypothesisstatedinsection 7 : 1 wastestedbyconductingTwoadditionaljointinjectionwellsimulationswithinputconditionssimilartothoseofcase 2 I vh =0 : 5 andcase 6 I vh =5 ofTable24exceptthataCO 2 massinjection Q wasusedinbothsimulations. Theperformancesofthetwojointwellsimulationswerecomparedtothoseoftwosingle verticalwellandtwosinglehorizontalwellsimulationstothehypothesisthatacombinationofverticalandhorizontalinjectionwellsjointwellismorebenecialthanasingle verticalorhorizontalinjectionwellinanisotropicaquifers. 105

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Table25: Inputconditionsappliedinallsimulationschapter7. ParameterValue DimensionL:W:Hm 10 5 : 10 5 : 100 Gridblocks X : Y : Z 65:65:10 Depthtopbottom, D ,m1200 Porecompressibility, c ,m 2 /N4.5 10 )]TJ/F17 7.9701 Tf 6.586 0 Td [(10 Initialpressure, P init ,topbottom,MPa12.0.1 Temperature, T C45.0 Averageporosity, 0 : 12 Averagepermeability, k ,m 2 1.0 10 )]TJ/F17 7.9701 Tf 6.586 0 Td [(13 Permeabilityanisotropyratio, k vh 0.01.1 Injectiontime, t ,years50 Relativepermeability Brine:vanGenuchten k rl = p S f 1 )]TJ/F15 11.9552 Tf 11.955 0 Td [( )]TJ/F15 11.9552 Tf 11.955 0 Td [([ S ] 1 g 2 S = S l )]TJ/F20 7.9701 Tf 6.586 0 Td [(S lr 1 )]TJ/F20 7.9701 Tf 6.586 0 Td [(S lr Residualbrinesaturation S lr =0 : 3 Exponent =0 : 457 GasCO 2 :Corey k rg = )]TJ/F15 11.9552 Tf 13.952 3.022 Td [(^ S 2 )]TJ/F15 11.9552 Tf 13.952 3.022 Td [(^ S 2 ^ S = S l )]TJ/F20 7.9701 Tf 6.587 0 Td [(S lr 1 )]TJ/F20 7.9701 Tf 6.586 0 Td [(S lr )]TJ/F20 7.9701 Tf 6.587 0 Td [(S gr Residualgassaturation S gr =0 : 05 Capillarypressure:vanGenuchten P cap = )]TJ/F19 11.9552 Tf 9.299 0 Td [(P o [ S ] )]TJ/F18 5.9776 Tf 8.155 3.259 Td [(1 )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 1 )]TJ/F20 7.9701 Tf 6.586 0 Td [( S = S l )]TJ/F20 7.9701 Tf 6.586 0 Td [(S lr S ls )]TJ/F20 7.9701 Tf 6.586 0 Td [(S lr Residualbrinesaturation S lr =0 : 0 Strengthcoefcientbar P o =1 : 96 10 4 Exponent =0 : 457 7.4ResultsandDiscussion TOUGH 2 numericalsimulationsofCO 2 injectionintoajointwellwithaverticalsegmentofconstantlengthandalongerhorizontalsegmentofvaryinglengths,wereconducted toevaluatethebenetsofusingajointinjectionwellforCO 2 storage. Pressureswithintheaquiferwerehighestattheinjectionwellandlowestatitsouter boundaries.Inthisstudy I vh withvalues 1 : 0 wereconsideredlowwhilethosewith values 2 : 5 wereconsideredhigh.Insimulationswithlow I vh ,pressuresweregreatest alongthehorizontalsegmentofthejointinjectionwells.Ontheotherhand,pressureswere greatestatthebottomoftheverticalsegmentsofjointwellsinsimulationswithhighvalues of I vh .Thisisbecauseinsimulationshavinglowvaluesof I vh mostoftheCO 2 isinjected viathehorizontalsegmentofthejointwellwhilemostoftheCO 2 injectedintheaquifer passesthroughtheverticalsegmentofthejointwellforsimulationshavinghigh I vh values. 106

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TheCO 2 -rich`gas'phasesaturations S g predictedbythesimulationsweregreatest nearinjectionwells.Thediametersofthegasplumeinallsimulationswerelessthan 20 kilometers,indicatingthattheplumedidnotmigratebeyondtheregionofhigh-resolution grid.Maximumvaluesof S g weregreaterinsimulationswithhighvaluesof I vh thanin thosewithlower I vh valuesFigure21aandb.ItcanbeviewedinFigure21aand bthatthe Sg insimulationswithhighvaluesof I vh extendfromthetoptothebottomof aquifer.Ontheotherhand,the S g insimulationswithlowvaluesof I vh arehighestatthe lowerportionoftheaquifer. 7.4.1AnalysisoftheMetrics Resultsshow P w M CO 2 ;aq ,and s togenerallyincreasewith I vh Figure22.Resultsin Figure22aindicatethat P w increaseswith I vh .Thisimpliesthatformationpressuresare lowwhenmoreCO 2 isinjectedviathehorizontalsegmentofajointwellandviceversa. Aswasexpected, P w atthebottomoftheformationwashigherthanatthetop.However, thedifferencebetween P w atthebottomandtopoftheformationincreasedas I vh was increased. TwoimportantphenomenacanbeidentiedfromFigure22b.First, M CO 2 ;aq atlow andhighvaluesof I vh i.e. I vh 1 : 0 and I vh 2 : 5 ,respectively.The M CO 2 ;aq in simulationswithhigh I vh weregreaterthanthoseofsimulationswithlow I vh Figure22 b.However,the M CO 2 ;aq foragiven k vh wasrelativelyconstant. Secondly, s slightlyincreasedwithincreasing I vh ,i.e., s isgreaterinsimulationsor situationswheremostoftheCO 2 isinjectedviatheverticalsegmentofthejointwell. However,thisconclusionisvalidinsituationswherethereisnolimitationonthemaximum pressurewithinaformation.Underpressure-limitedconditions,theaboveconclusionis nottruebecause P w fromsimulationswithhighvaluesof I vh aregreaterthanthosefrom simulationswithlow I vh valuesFigure23a. Ataspeciedvalueof P w themaximumallowablemassinjectionrate Q max insimulationswithlow I vh isgreaterthanthoseinsimulationswithhigh I vh values.Asaresult, s intheformerwillbeatleastequaltoorgreaterthanthoseofthelatter,because s increases withCO 2 massinjectionratevanderMeer,1995. 107

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Figure21.: Gassaturationdistribution t =50 yearschapter7.a I vh equal to 0 : 25 P max equalto 242 bar,andplumeextentsalong X and Y axesare 16731 mand 13385 m,respectively;b I vh equalto 10 P max equalto 318 bar,andplumeextentsalong X and Y axesare 13385 mand 13385 m,respectively. 108

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7.4.2SensitivityAnalysis 7.4.2.1Injectivity Theinjectivitiesatthebottomoftheaquiferforsimulationsconductedhereinafter 50 yearsofcontinuousinjectionwerecomparedtodeterminewhichsimulationcanaccommodatethegreatestquantityofCO 2 .Injectivity isdenedasthemassinjectionrateper unitthicknessperunitpressurechangebetweentheinjectionwellandtheaquiferLawand Bachu,1996.Itrepresentsameasureoftheeasewithwhichauidcanbeinjectedintoa geologicformationperunitheightorthicknessofaformationoraquiferKovscek,2002; IPCC,2005.Thisimpliesthatas isreduced,theadditionalquantityofCO 2 arepository canaccommodatedecreases.Injectivity ismathematicallydenedasfollowsDake, 1978;LawandBachu,1996: = Q B P .6 where Q isthemassowratekg/s, B istheformationthicknessm,and P isthe differencebetweenthepressureatthewellandtheinitialpressureoftheaquiferatthe well'slocation,i.e., P = P w )]TJ/F19 11.9552 Tf 11.955 0 Td [(P init ResultsinFigure23indicatethat decreasesas I vh isincreased.Thismaybebecause wellborepressuresaresignicantlyhigherforhighthanlowvaluesof I vh Figure22. Basedonequation7.6,ahighvalueof P w leadstoadecreasein .Thisalsosupportsthe suggestionthatthemaximumallowablemassinjectionrate Q max insimulationshaving lowvaluesof I vh willbegreaterthanthoseofsimulationshavinghighvaluesof I vh ,under pressure-limitedconditions. 7.4.2.2ComparisonofWellPerformances NumericalsimulationsofCO 2 intoananisotropicconnedaquiferviavertical,horizontal,andjointinjectionwellswereconductedtoevaluatetheperformancesoftheinjection wellsbasedonthemetricssoastoverifythehypothesisinsection7.2.Anaquiferof similardimensionandinputconditionsasdescribedinTable25wasusedinallthreesimulations.Thelengthofthesingleverticalwellsimulationswas 100 mandthelengththe singlehorizontalwellsimulationswas 2000 m.CO 2 wascontinuouslyinjectedatarateof 100 kg/sforaperiodof 50 years.ResultsfromthesimulationsarepresentedinTable26. 109

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Figure22.: Effectsof I vh onona P w ,b M CO 2 ;aq ,andc s .After 50 years ofcontinuousinjection. 110

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Figure23.: atbottomofwellboreasafunctionof I vh t =50 years. TheresultsinTable26suggestthatthejointinjectionwellperformsbetterthanthe verticalinjectionwellbutislessefcientthanthehorizontalinjectionwell,especially underhighlyanisotropic k vh =0 : 01 conditions.Thisindicatesthatthehypothesisthata combinationofverticalandhorizontalinjectionwellsjointwellismorebenecialthan asingleverticalorhorizontalinjectionwellinanisotropicaquiferssection7.2isnot valid.However,itcanberephrasedbystatingthat,ajointinjectionwellcanstoreagreater quantityofCO 2 andismoreefcientthanasingleverticalinjectionwellinanisotropic aquiferswithpermeabilityanisotropyratiogreaterthanorequalto 0 : 01 BasedontheassumptionsImadeinequations.2.5,agreaterproportionofinjectedCO 2 entersanaquiferviatheverticalsegmentofajointwellasthevaluesof k vh and L h declinei.e., I vh > 1 .Ontheother,mostoftheinjectedCO 2 entersanaquiferthrough thehorizontalsegmentofajointwellas k vh and L h increasei.e., I vh < 1 .Underpressurelimitedconditionssimulationswithlow I vh willstoremoremassofCO 2 thanthosewith high I vh .Thisisbecausetheinjectivities oftheformeraregreaterthanthoseofthe latterasdepictedinFigure23.Therefore,moreCO 2 canbeinjectedintoanaquiferifa greaterportionofthegasenterstheformationviathehorizontalsegmentoftheformation. Thisconclusionisvalidfor k vh rangingfrom 0 : 01 0 : 1 ,inclusive. 111

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Table26: ComparisonofperformancesofCO 2 injectionstrategies.Viajoint, vertical,andhorizontalinjectionwells Q =100 kg/s. Welltype k vh L h m L v m P w bar M CO 2 ;aq Mtons s Joint0.12000100195.115.715.4% Vertical0.1100205.315.514.1% Horizontal0.12000194.215.415.7% Joint0.012000100226.420.518.8% Vertical0.01100229.320.319.6% Horizontal0.012000222.120.421.6% 7.5Conclusions TheobjectivesofthischapteraretoestimatethedistributionofCO 2 betweenthe verticalandhorizontalsegmentsofajointinjectionwell,studyeffectsofCO 2 distributionbetweentheverticalandhorizontalsegmentsofajointinjectionwellonstorageinan anisotropicaquifer,andtestthehypothesisthatacombinationofverticalandhorizontal injectionwellsjointwellismorebenecialthanasingleverticalorhorizontalinjection wellinanisotropicaquifers. TheassumptionsmadehereinsuggestthattheCO 2 massinjectionratio I vh isafunction ofthepermeabilityanisotropyratio k vh andthelengthsofthevertical L v andhorizontal L h segmentsofajointwell.Accordingtotheassumedrelationshipbetween I vh k vh L v and L h ,mostoftheinjectedCO 2 enterstheaquiferviathehorizontalsegmentwhenCO 2 massinjectionratio I vh islessthanorequalto 1 : 0 .Conversely,mostoftheinjectedCO 2 enterstheaquiferviatheverticalsegmentofthejointwellwhenCO 2 massinjectionratiois greaterthan 1 : 0 .Under-pressurelimitedconditions,simulationswithCO 2 massinjection ratioslessthanorequalto 1 : 0 havethepotentialofstoringmoremassofCO 2 thanthose withCO 2 massinjectionratiogreaterthan 1 : 0 becausetheformerhavegreaterinjectivities. Comparisonoftheperformancesofsimulationsusingaverticalinjection,ahorizontal injectionandajointinjectionwellsuggestthatjointinjectionwellscanstoreagreater quantityofCO 2 andismoreefcientthansingleverticalinjectionwellsforstoragein connedaquiferswithpermeabilityanisotropyratiogreaterthanorequalto 0 : 01 112

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7.6ReferencesCited A.Corey.Theinterrelationbetweengasandoilrelativepermeabilities. ProducersMonthly pages38,Noverber1954. L.Dake. Fundamentalsofreservoirengineering ,volume8.ElsevierScienticPublishing, Amsterdam,2edition,1978.ISBN0-444-41667-6. J.Ennis-KingandL.Paterson.Engineringaspectsofgeologicalsequestrationofcarbon dioxide.volumeSPE-77809,SPEandCSIROPetroleum,2002.AsiaPacicOilandGas ConferenceandExhibition,Melbourne,Australia,October8. IPCC.IPCCspecialreportoncarbondioxidecaptureandstorage.PreparedbyWorking GroupIIIoftheIntergovernmentalPanelonClimateChange[Metz,B.,Davidson,O., deConinck,H.C.,Loos,M.,andMeyer,L.A.eds.].Report,IntergovernmentalPanel onClimateChange,Cambridge,UnitedKingdomandNewYork,NY,USA,2005. S.D.Joshi. Horizontalwelltechnology .PennWellBooks,Tulsa,Colorado,USA,1991. A.Kovscek.ScreeningcriteriaforCO 2 storageinoilreservoirs. PetroleumScienceand Technology ,20:841,2002. A.Kumar,R.Ozah,M.Noh,G.A.Pope,S.Bryant,K.Sepehrnoori,andL.W.Lake.ReservoirsimulationofCO 2 storageindeepsalineaquifers. SocietyofPetroleumEngineering Journal ,9SPE89343:336,September2005. D.LawandS.Bachu.HydrogeologicalandnumericalanalysisofCO 2 disposalindeep aquifersintheAlbertasedimentarybasin. EnergyConversionsandManagement ,37 :1167,1996. R.Ozah,G.Lakshminarasimhan,K.Sepehrnoori,andS.Bryant.Numericalsimulation ofthestorageofpureCO 2 andCO 2 -H 2 Sgasmixtureindeepsalineaquifers.In SPE AnnualTechnicalConferenceandExhibition ,SPE97255,pages1,Dallas,Texas, USA,2005.SocietyofPetroleumEngineers,SocietyofPetroleumEngineers. K.Pruess.Onvaporizingwaterowinhotsub-verticalrockfractures. TransportinPorous Media ,28:335,1997. K.PruessandJ.Garc a.MultiphaseowdynamicsduringCO 2 disposalintosaline aquifers. EnvironmentalGeology ,42:282,2002. K.PruessandN.M uller.Formationdry-outfromCO 2 injectionintosalineaquifers: 1 : Effectsofsolidsprecipitationandtheirmitigation. WaterResourcesandResearch ,45 w03402:1,2009.doi:10.1029/2008WR007101. 113

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K.Pruess,C.Oldenburg,andG.Moridis.TOUGH2users'guide,version2.0.Manual LBNL-43134,LawrenceBerkeleyNationalLaboratory,Berleley,California,1999.accessdate:June10,2007. K.Pruess,T.Xu,J.Apps,andJ.E.Garc a.Numericalmodelingofaquiferdisposalof CO 2 SocietyofPetroleumEngineeringJournal ,8:49,2003. L.G.H.vanderMeer.TheCO 2 storageefciencyofaquifers. EnergyConversionand Management ,36:513,1995. M.T.vanGenuchten.Aclosed-formequationforpredictingthehydraulicconductivityof unsaturatedsoils. SoilSci.Soc.Am.J. ,44:892,1980. 114

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Chapter8 TemporalVariationsinNear-wellborePressuresDuringCO 2 Injection 8.1Abstract NumericalsimulationsofCO 2 injectioninhomogeneousconnedsalineaquiferswere conductedtostudytemporalvariationsinnear-wellborepressures.Themajorphysicalfactorsaffectingnear-wellborepressureconsideredinthisstudyinclude:densitydifference betweenCO 2 andbrine,permeabilityanisotropy,andinjectionrate.Effectofuiddensity differencewasinvestigatedbycomparingresultsfromsimulationsofCO 2 injectiontoresultsofwaterinjectioninaconnedaquifer.Contributionsfrompermeabilityanisotropy, aquiferthickness,andinjectionratewerestudiedbyconductingnumericalsimulationsof CO 2 injectionatdifferentpermeabilityanisotropyratioandaquiferthickness,respectively. Permeabilityanisotropyratioistheratiooftheverticalpermeabilitytothehorizontalpermeability.Resultsshowtemporalvariationsinnear-wellborepressurestobestronglydependentonpermeabilityanisotropyandthedifferenceindensitybetweenCO 2 andbrine. PressuresinthevicinityofthewellborearenotexpectedtodeclineovertimeasCO 2 or wateruidisinjectedintotheaquifer.PressuresneartheinjectionwellwerefoundtodeclinemoreovertimeasCO 2 injectionrateisincreased.Findingsofthisstudysuggestthat reductionsinnear-wellborepressuresovertimeduringCO 2 injectioninisotropicconned aquifersareasaresultofgravitysegregationbetweenthelessdenseCO 2 -richgasphase andbrine.Sensitivityanalysesalsosuggestthatthetemporalvariationsinnear-wellbore pressuresdependstronglyonpermeabilityanisotropyandthecontrastindensitybetween CO 2 andbrine.Nearwellborepressuresdidnotdeclineovertimewhentheratioofthe verticaltothehorizontalpermeabilityisverysmall 0 : 001 duetoincreaseinresistanceto uidowintheverticaldirection. 115

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8.2Introduction DuringcarbondioxideCO 2 injectioninconnedformations,theintegrityoftheseals, especiallytheupperconningbed,ispivotalinminimizingriskofpotentialleakageinto potablewateraquifersandsubsequentlytheatmosphere.CO 2 leakagefromtargetedstorageformationsduringtheinjectionphasecouldbefromexistingfractures,leakagesat thewellboredueimproperinstallation,abandonedwellorinducedfracturingNordbotten etal.,2004.InducedfracturingreferstofracturingofaformationduetoexcessiveincreaseinuidpressureviainjectionMartinezetal.,1992.AssumingtherisksofCO 2 leakagefromallpossiblecausesexceptinducedfracturingtobenegligible,thetemporal variationsinthemaximumpressurewithinanaquiferisveryimportantindeterminingthe likelihoodoffracturingaformationduringinjection.Sinceformationpressuresarehighestatinjectionwellsthestudyoftemporalvariationsinpressurenearinjectionwellsis warranted. PreviousstudieshaveindicatedthatformationfracturingiscausedbyuidpressureexceedingtheoverburdenpressureoftheformationDake,1978;Martinezetal.,1992.Overburdenpressure P overburden isthesumofuidpressure P fluid andgrainpressure P grain i.e., P overburden = P fluid + P grain .1 GrainpressureisthepressureactingbetweenrockgrainswithinaformationDake, 1978.Asuidpressureincreases,thegrainpressuredecreasesandviceversa.Whenthe grainpressureiszero,theuidpressurebecomesequivalenttotheoverburdenpressureand furtherincreaseinuidpressurewillinitiateformationfracturingMartinezetal.,1992. InjectionofCO 2 intoaconnedformationwillcausepressureincreasesespeciallycloseto thewellwhereitismaximum.Aruleofthumbgenerallyemployedisthatthemaximum uidpressureshouldnotexceed 90 %oftheoverburdenpressureinordertoavoidriskof formationfractureBachuandAdams,2003. SimulationsofcontinuousCO 2 injectionintoahomogeneousconnedsalineaquifer viaverticalwellsusinga 1 -Dradialgeometrypredictincreasesinnear-wellborepressures overtime P w t Pruessetal.,2004.However,asimilarsimulationusing 2 Dradial geometryr,zpredictadeclinein P w t withtime.Themajordifferencebetweenthe above-mentionedsimulationsisthattheformerneglectsgravitysegregationasaresultof thedifferenceindensitybetweenbrineandCO 2 Pruessetal.,2004whilethelatterdoes 116

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not.Asaresultonemaybetemptedtoconcludethatthedifferencesinthenear-wellbore pressureprolesbetweenthetwosimulationsisduetogravitysegregationorbuoyancy. However,vericationofwhycontinuousinjectionofCO 2 intoaconnedsalineaquifer doesnotleadtopressurebuild-upovertimeasencounteredinundergroundwastewater injectionHickeyandVecchioli,1986,forexample,iswarranted. Thischapterinvestigatestemporalvariationsinnear-wellborepressuresduringCO 2 injectioninconnedaquifersofinniteradialextents.Aseriesofnumericalexperiments wereconductedtoachievethefollowing: 1.testthehypothesisthatthedeclineinnear-wellborepressuresduringCO 2 injectionin isotropicconnedaquifersisprincipallyduetocontrastindensitybetweenCO 2 -rich gasandresidentbrine,referredtoasgravitysegregationphaseseparation;and 2.studytheeffectsofverticalpermeability,aquiferthickness,andCO 2 injectionrateon changesinnear-wellborepressuresovertime. Thehypothesiswasvalidatedbycomparingpredictednear-wellborepressuresfromnumericalsimulationsofCO 2 injectiontothosefromsimulationsofwaterinjectioninsaline aquiferswithsimilarinputconditions.Effectsofpermeabilityanisotropyandmassinjectionrateonnear-wellborepressurewerestudiedbyconductingnumericalsimulations ofcontinuousCO 2 injectionatdifferentvaluesof k vh andaquiferthickness,respectively. Resultsobtainedpredictthattemporalvariationsinnear-wellborepressurearestrongly dependonthedifferenceindensitybetweenCO 2 andbrine'densitydifference'andon formationanisotropy. 8.3Background ThetendencyofinjectedCO 2 tomigrateupwardsinconnedaquifersunderreservoir conditionshasbeenattributedtothecontrastindensitybetweenCO 2 -richgasphase andformationbrineArtsetal.,2004;TorpandDale,2004;Nordbottenetal.,2005.The effectsofgravitysegregationorbuoyancyonCO 2 sweepefciency,storagecapacity,solubilityinbrineanduidowdynamicswithinaconnedaquiferhavebeenextensively addressedinthetechnicalliteraturevanderMeer,1995;1996;Ennis-KingandPaterson, 2002;BachuandAdams,2003;Nordbottenetal.,2005;IPCC,2005;Ozahetal.,2005; NordbottenandCelia,2006;Doughty,2007;Friedmann,2007;Bachu,2008.However, theeffectsofgravitysegregationphaseseparationontemporalvariationsofformation pressurenearinjectionwellshavenotbeenfullyaddressed. 117

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GravitysegregationbetweenCO 2 andbrineisreportedtobemorepronouncedwithincreasingtemperaturebecauseCO 2 densityisfurtherreducedathightemperatures,thereby increasingthecontrastindensitybetweenCO 2 andbrine.Consequently,theCO 2 bubble willrapidlymoveupwardstothetopoftheaquiferKumaretal.,2005andaccumulate beneaththeupperconningbedortopsealEnnis-KingandPaterson,2001;2002.However,spatialvariationsintemperaturewereconsiderednegligiblebecausethesimulations conductedhereinwereatconstanttemperatureisothermal. ThelengthoftimeaCO 2 bubbleatthebottomofanaquifercantaketoreachthetop increaseswithdecreasingverticalpermeabilityandviceversaKumaretal.,2005.This indicatesthatgravitysegregationbetweenCO 2 andbrinereducesasverticalpermeability isdecreased.LowverticalpermeabilitiesalsoinhibittheCO 2 -saturatedbrineattheCO 2 brineinterfacefromsinktothebottomoftheaquifervanderMeer,1996;Kumaretal., 2005.Inaddition,themagnitudeofgravitysegregationbetweenCO 2 andbrineisalso dependentonthepressuregradientbetweenthetopandbottomoftheaquifer.Asaresult, thepressuregradientintheverticaldirectionincreaseswiththethicknessofanaquifer. 8.4Approach TheTOUGH 2 general-purposenumericalsimulatorPruessetal.,1999;Pruessand Garc a,2002;Pruess,2004becauseofitswidespreadusagebymanyresearchgroups worldwidetosolveCO 2 geologicalsequestrationproblemsWeiretal.,1995;McPherson andLichtner,2001;Ennis-KingandPaterson,2002;Pruessetal.,2003. ThehydrogeologicparametersusedinthesimulationsarelistedinTable27.Thesymbols S lr S gr S l , P o ,and S ls inTable27,denotetheresidualliquidsaturation,residualgassaturation,liquidphasesaturation,poregeometryparameter,strengthcoefcient vanGenuchten,1980,andliquidphasesaturationatwhich P cap vanishesPruessand Garc a,2002.Thevalueof S lr inestimationofcapillarypressure P cap wassetto 0 : 0 to avoidunphysicalbehaviorofthevanGenuchten;M ulleretal.functioninwhichas k lr )167(! 0 P cap )167(! Pruess,1997;PruessandGarc a,2002.Detailedexplanation oftherationaletouseazeroresidualliquidphasesaturationinestimatingcapillarypressureisgivenbyPruess.Thetubes-in-seriesmodeldevelopedbyVermaandPruess wasusedtoaccountforpermeabilityreductionduetosaltNaClprecipitation. )]TJ/F20 7.9701 Tf 7.314 -1.793 Td [(L representsfractionallengthofporebodiesVermaandPruessand r isthefraction oftheoriginalporosityatwhichpermeabilityisreducedtozeroVermaandPruess,1988; PruessandM uller,2009. )]TJ/F20 7.9701 Tf 7.314 -1.793 Td [(L and r werebothassignedavalueof 0 : 8 inallsimulations, 118

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similartowhatwasemployedincodeintercomparisonproblem 3 Pruessetal.,2004.A CO 2 massinjectionrateof 100 kg/swasappliedinallsimulations.Thisisequivalentto CO 2 emissionsfroma 288 MWecoal-redpowerplantHitchon,1996. Table27: Inputparametersappliedinallsimulationschapter8. ParameterValue DimensionR H m 10 5 100 Gridblocks X : Z 435 20 Wellboreradius m r =0 : 3 Depthtop-bottom m D =1200 1300 Porecompressibility Pa )]TJ/F17 7.9701 Tf 6.586 0 Td [(1 c =4 : 5 10 )]TJ/F17 7.9701 Tf 6.586 0 Td [(10 Initialpressuretop:bottom MPa P init 12 : 0 : 13 : 1 Temperature C T =45 : 0 Averageporosity =0 : 12 Averagehorizontalpermeabilitym 2 k =1 : 0 10 )]TJ/F17 7.9701 Tf 6.587 0 Td [(13 Permeabilityanisotropyratio k vh =0 : 001 )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 : 0 Injectiontimeyears t =50 Relativepermeability Brine:vanGenuchten k rl = p S f 1 )]TJ/F15 11.9552 Tf 11.955 0 Td [( )]TJ/F15 11.9552 Tf 11.955 0 Td [([ S ] 1 g 2 S = S l )]TJ/F20 7.9701 Tf 6.587 0 Td [(S lr 1 )]TJ/F20 7.9701 Tf 6.587 0 Td [(S lr Residualbrinesaturation S lr =0 : 3 Exponent =0 : 457 GasCO 2 :Corey k rg = )]TJ/F15 11.9552 Tf 13.952 3.022 Td [(^ S 2 )]TJ/F15 11.9552 Tf 13.952 3.022 Td [(^ S 2 ^ S = S l )]TJ/F20 7.9701 Tf 6.586 0 Td [(S lr 1 )]TJ/F20 7.9701 Tf 6.587 0 Td [(S lr )]TJ/F20 7.9701 Tf 6.586 0 Td [(S gr Residualgassaturation S gr =0 : 05 Capillarypressure:vanGenuchten P cap = )]TJ/F19 11.9552 Tf 9.299 0 Td [(P o [ S ] )]TJ/F18 5.9776 Tf 8.155 3.258 Td [(1 )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 1 )]TJ/F20 7.9701 Tf 6.586 0 Td [( S = S l )]TJ/F20 7.9701 Tf 6.587 0 Td [(S lr S ls )]TJ/F20 7.9701 Tf 6.587 0 Td [(S lr Residualbrinesaturation S lr =0 : 0 Strengthcoefcientbar P o =1 : 96 10 4 Exponent =0 : 457 Thehypothesisofthisworkwastestedbyconductingtwonumericalsimulationswith similaraquiferdimensionsandinputconditionsbutwithdifferentinjectantsunderisotropic conditions.CO 2 andwaterwereseparatelyusedineachsimulationandtheirtemporal changesinnear-wellborepressures P w t forperiodsupto 200 yearswerecompared. Waterwaschosenasanalternateinjectantbecausethedifferencebetweenitsdensityand thatofbrineissignicantlysmallcomparedtoCO 2 .ThesimulationusingCO 2 asthe injectantwasconsideredasthebasecasesimulationinthisstudy. 119

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Effectsofverticalpermeabilityon P w t duringCO 2 injectionwereinvestigatedbyconductingthreeadditionalnumericalexperimentswhichdifferedfromthebasecasesimulationsbythevalueof k vh applied.The k vh valuesusedwere 0 : 1 0 : 01 ,and 0 : 001 k vh is theratiooftheverticaltothehorizontalpermeabilityofanaquifer.Resultsof P w t for allthreesimulationsplusthebasecasesimulation k vh =1 : 0 werecomparedtodetermine theeffectofverticalpermeabilityonchangesinnear-wellborepressuresovertime.Lastly, theeffectofCO 2 massinjectionrate Q on P w t wasstudiedbyconductingtwonumericalsimulationssimilartothebasecasesimulationexceptforaquiferthickness.Thiswas achievedbychangingthevaluesof B 25 mand 50 m,respectivelywhilekeepingthe Q constanttherebyincreasingthemassofinjectedCO 2 perunitthicknessofaquifer.Resultsfromthesesimulationsandthebasecasesimulationswerecomparedtodeterminethe effectsofCO 2 massinjectionrateonchangesinnear-wellborepressuresovertime P w t 8.5ResultsandDiscussions 8.5.1DensityEffect Effectofthecontrastinuiddensityontemporalvariationsinpressureclosetotheinjectionwell P w t wasinvestigatedbycomparingresultsofCO 2 andwaterinjectioninto aconnedsalineaquifer.Bothsimulationspredictedapressurejumpatthebeginningof injectionbutpredicteddifferentpressurehistoriesovertime.Figure24aandbshow pressurechangesneartheinjectionwell P w t overtimeatthetopandbottomofthe aquifer,respectively. P w t increasedovertimeinthesimulationusingwaterasinjectant. Ontheotherhand,theCO 2 injectionsimulationpredictedaninitialjumpin P w t followed byadeclineforupto 30 yearsafterwhichitstabilizesandincreasesthereafter t> 100 years.Sincetheonlydifferenceintheinputconditionsofbothsimulationswastheirinjectants,itcanbededucedthatthedifferenceinthe P w t proledepictedinFigure24aand bisduetodifferencesbetweenthephysicalpropertiesofCO 2 ,water,andbrine.However,thedifferencesinthephysicalpropertiesofwaterandbrineviscosityanddensity arenegligiblecomparedtothatbetweenCO 2 andbrine.Thus,thedropin P w t atearly timesofCO 2 injectioncanbeattributedtodifferencesindensityandviscositybetween CO 2 andbrine.AsimilarstudyofCO 2 injectionintoaconnedaquiferofinniteradial extentinwhichgravitywasconsiderednegligible 1 D radialmeshshowed P w t toincreaseovertimePruessandGarc a,2002;Pruessetal.,2004,indicatingthatdifference inviscositybetweenCO 2 andbrinehasanegligiblecontribution.Therefore,thedecline 120

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in P w t predictedatearlytimes < 30 yearsofCO 2 injectionintoahomogeneousand isotropicconnedsalineaquiferisduetodensitydifferencebetweenCO 2 andbrine.This validatesthehypothesisstatedinsection8.2. 8.5.2EffectofVerticalPermeability Theeffectofverticalpermeabilityon P w t duringCO 2 injectionwasinvestigatedby comparing P w t prolesfromsimulationswithdifferentvaluesofpermeabilityanisotropy ratio k vh asafunctionoftime.Valuesof k vh usedinsimulationsrangedbetween 0 : 001 and 1 : 0 .Asmallvalueof k vh indicatesthatanaquifer'sverticalpermeability k v issmall comparedtoitspermeabilityinthehorizontaldirection k h .When k vh isverysmall,uids intheaquiferwillpreferentiallyowinthehorizontaldirection.ResultsinFigure25a andbshow P w t todecreaseovertimeforsimulationsthatused k vh valuesof 1 : 0 and 0 : 1 withthegradientoftheformerbeingsteeper. P w t initiallyincreasedatearlytimesand subsequentlydeclinedforthesimulationthatuseda k vh valueof 0 : 01 .Onlythesimulation with k vh equalto 0 : 001 predictedvaluesof P w t thatincreasedmonotonicallyovertime. Theseindicatethatthebuoyancyeffectdecreasesas k v isreduced. Apossiblecauseoftheunusualtrendin P w t obtainedinthesimulationwith k vh equal to 0 : 01 waslookeduponbystudyingtheCO 2 bubblemigrationovertime.Figure26show CO 2 bubbledistributionatselectedtimesforup 100 years.Thisguredepictsapistonlikeowatearlytimes 1 and 10 yearsduringwhichgravityeffectisnegligible.Atlarge timese.g. 30 years,whentheCO 2 -brineinterfaceisfarfromtheinjectionwell,gravity segregationbecomessignicant,afterwhichatongueorthinlayerofCO 2 bubblebegins todevelopbeneaththeupperconningbedFigure26candd.Inaddition,gravity segregationbetweenCO 2 -saturatedbrineandbrine,attheCO 2 -brineinterfacevander Meer,1996isalsodominantduringthisperiod.Theseareagreementwithndingsof Ennis-KingandPatersonthatgravitysegregationissignicantfarfromtheinjection well. 8.5.3EffectofCO 2 MassInjectionRate Q Reducingtheaquiferthickness B whilekeepingtheinjectionrate Q constantincreasesthequantityofCO 2 injectedperunitaquiferthicknessorwelllength.When B is reducedbyafactorof 2 or 4 Q=B isdoubledorquadruple,respectively.Itshouldbeunderscoredthat Q=B isinverselyproportionaltothegravityfactor )]TJ/F40 11.9552 Tf 7.314 0 Td [(discussedinchapters 3 and 4 121

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Figure24.: Effectofdensityonnear-wellborepressures.Asafunctionof time.atopandbbottom Q =100 kg/s. 122

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Figure25.: Effectof k v onnear-wellborepressures.Asafunctionoftime.a topandbbottom Q =100 kg/s. 123

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Figure26.: Gassaturationdistributionovertimeat k vh equalto 0 : 01 .a 1 year,b 10 years,c 30 years,andd 100 years. Thenumericalsimulationsinwhichthethicknessoftheaquiferwasreducedbyafactoroftwoandfourpredicted P w t toincreaseinmagnitudewithincreasingCO 2 mass injectionrateperunitthicknessofaquifer Q=B .However,changesin P w t overtime followedatrendsimilartothatofthebasecasesimulation.Inaddition,therateofdecline in P w t increaseswith Q=B ormassinjectionperunitlengthofinjectionwellFigure27 aandb.Therefore,itcanbeconcludedthatincreasingCO 2 injectionrateintensies theeffectofgravitysegregationon P w t inisotropicformations. TherstthreesimulationslistedinTable28andFigure24aandbdemonstratethat theinitialdeclineinpressureinthevicinityoftheinjectionwellisduetodifferenceindensitybetweenCO 2 andbrinebuoyancyandtherebyvalidatingthehypothesisofthisstudy. Cases 4 6 inTable28andFigure25aandbalsodemonstratethattemporalchangesin near-wellborepressuresstronglydependon k vh .Thedependenceofnear-wellborepressure onbuoyancyovertimediminishesaspermeabilityanisotropyratiodecreasesuntilacritical pointisreachedwherebuoyancyeffectsbecomenegligible.Forthesimulationsconducted hereinthecriticalpointisreachedata k vh valueof 0 : 001 124

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Figure27.: Effectof Q perunitwelllengthonnear-wellborepressures.Asa functionoftime.atopandbbottom Q =100 kg/s. 125

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Buoyancyandpermeabilityanisotropycanbeviewedtocompeteovercontroloftemporalchangesinnear-wellborepressureduringCO 2 injection.However,buoyancywill eventuallypredominateCO 2 plumemigrationfarfromtheinjectionwellEnnis-Kingand Paterson,2002especiallyinaquifershavingmoderatelylowpermeabilityanisotropyi.e. k vh valueof 0 : 01 inthisstudy. Table28: Sensitivityof P w onhydrogeologicparameters Q =100 kg=s CaseFluidBm k vh VariationResults 1CO 2 1001.01D P w increasedmonotonically | 2CO 2 1001.02D P w declinedatearlytimes x 3H 2 O1001.0density P w increasedmonotonically 4CO 2 1000.1 k vh P w declinedatearlytimes 5CO 2 1000.01 k vh P w declinedatearlytimes 6CO 2 1000.001 k vh P w increasedmonotonically 7CO 2 501.0Thickness P w declinedatearlytimes 8CO 2 251.0Thickness P w declinedatearlytimes | Pruessetal. basecasesimulation x atleast 20 yearst20 Toconrmthatincreasesinnear-wellborepressuresovertimeinhighlyanisotropic aquifers k vh =0 : 001 isduetoacorrespondingincreaseintheresistancetouidow intheverticaldirectionandnotasaresultofthedry-outeffectPruessandGarc a,2002; Garc a,2003,weconductedcontrolsimulationsinwhichpermeabilityandporosityreductionsduetosaltprecipitationareignored.Thesesimulationswereconductedfor k vh equal to 0 : 001 and 1 : 0 .Resultsofthenear-wellborepressures P w atthebottomoftheaquifer forupto 100 yearsarepresentedinTables29and30. Table29: P w t barasafunctionofpermeabilityreduction k vh =1 : 0 .Atthebottomoftheformation. Permeabilityreduction Timeyears ConsideredNotconsideredDifference 1 94.191.03.1 3 93.980.53.4 10 74.771.03.7 30 70.366.24.1 100 69.865.34.5 126

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Table30: P w t barasafunctionpermeabilityreduction k vh = 0 : 001 .Atthebottomoftheformation. Permeabilityreduction Timeyears ConsideredNotconsideredDifference 1 234.3231.23.1 3 235.3231.83.5 10 236.3232.43.9 30 237.3233.14.2 100 239.5234.84.7 ResultsinTables29and30showpressurestobeslightlygreaterinsimulationsthat accountforpermeabilityreductionsduetosaltprecipitationdry-outeffectthaninthose whichneglectedpermeabilityreductions.Thesesuggestthattheeffectpermeabilityreductionsduetosaltprecipitationinthevicinityofthewellbore,mayhaveonthetemporal variationsinnear-wellborepressureisnegligiblecomparedtopermeabilityanisotropy.The salinityusedinthesimulationsconductedhereinis 15 %.Pressureincreasesduetosalt precipitationmayincreaseathighervaluesofbrinesalinityasitisthecaseinPruessand M uller,where 25 %brinesalinitywasemployed. 8.5.4Mechanism AcartoonshowingthemajorforcesactingonaCO 2 bubbleinthevicinityofawellboreispresentedinFigure28.Thismechanismisbasedonresultsobtainedinthisstudy. Figure28depictsCO 2 injectionintoaconnedsalineaquiferinitiallysaturatedwithbrine. Theextractregion-of-interestfromthegureshowsaCO 2 bubblewithdensity c and anaqueousphasewithdensity w c isconsideredtobesignicantlylessthan w .Brine capillaryforceswereconsiderednegligiblecomparedtoviscousandbuoyancyforcesduringCO 2 injectionsinceitseffectsaresmallatlargespatialscalesNordbottenetal.,2009. ThemajorforcesactingontheCO 2 bubble ~ F includeviscousforce, ~ F v ,andbuoyancy force, ~ F b ~ F v canberesolvedincartesiancoordinatesinto F v x F v y ,and F v z ,representing the X Y ,and Z components,respectively.Themagnitudeof ~ F b iszerointhe X and Y directionsbutnegativeinthe Z directionbecausegravitysegregationbetweenCO 2 andbrine willcausetheformertomoveupwardsagainstdirectionofgravity.Therefore,thetotal forceactingontheCO 2 bubble, ~ F ,canbemathematicallydescribedasfollows: 127

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~ F =[ F v x ;F v y ; F v z )]TJ/F19 11.9552 Tf 11.955 0 Td [(F b z ] .2 Itcanbededucedfromequation.2thatthemagnitudeoftheresultantortotalforce actingontheCO 2 bubble, j ~ F j ,increasesas F b z 0 anddiminishesas ~ F b ~ F v .However, underconditionsatwhichCO 2 isinjectedindeepgeologicformationsboth ~ F b and ~ F v have beenreportedtobeimportantEnnis-KingandPaterson,2002;Nordbottenetal.,2005. Factorsaffecting ~ F b thatwereconsideredinthisworkinclude:verticalpermeabilityor anisotropyratio,densitydifference,andmassinjectionrateperunitaquiferthickness. Figure28.: ProposedmechanismdepictingmajorforcesactingonaCO 2 bubble.AdaptedfromNordbottenetal.. 8.6Conclusions NumericalsimulationsofCO 2 injectionintoahomogeneousconnedsalineaquifer wereconductedtoinvestigatetherootcauseorcausesofchangesinnear-wellborepressuresovertime.ResultsfromthesimulationssuggestthattemporalchangesinnearwellborepressureduringCO 2 injectioninisotropicaquifersareduetocontrastindensitybetweenCO 2 andbrine.Inaddition,temporalchangesinnear-wellborepressuresin anisotropicaquiferswerefoundtostronglydependonpermeabilityanisotropyandgravity segregation. 128

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ThedifferenceindensitybetweenCO 2 andbrinebuoyancyaffectsmultiphaseowdynamicsinaquifersaswellaschangesinpressureinthevicinityoftheinjectionwell.Buoyancyeffectwasfoundtodiminishwithdecreasingpermeabilityanisotropyratioorvertical permeability.Inisotropicsalineaquifers,temporalvariationsinnear-wellborepressures ishighlydependentonbuoyancy.However,itsdependencyonbuoyancydecreasesin anisotropicaquifersandeventuallyvanisheswhenacriticalpermeabilityanisotropyratio isreachedafterwhichviscousowpredominates.Basedonresultsfromthesimulations conductedherein,acriticalpermeabilityanisotropyratioof 0 : 001 .ThismaynotbeauniversalvaluesincecriticalpermeabilityanisotropyratiomayvarywithCO 2 massinjection rate,aquiferthicknessandmostimportantlytheabsolutepermeabilityofanaquifer. 8.7ReferencesCited R.Arts,O.Eiken,A.Chadwick,P.Zweigel,L.vanderMeer,andB.Zniszner.Monotoring ofCO 2 injectedatSleipnerusingtime-lapseseismicdata. Energy ,29:1383,2004. S.Bachu.CO 2 storageingeologicalmedia:Role,means,status,andbarrierstodeployment. ProgressinEnergyandCombustionScience ,34:254,2008. S.BachuandJ.J.Adams.SequestrationofCO 2 ingeologicalmediainresponsetoclimatechange:CapacityofdeepsalineaquiferstosequesterCO 2 insolution. Energy ConversionandManagement ,44:3151,2003. A.Corey.Theinterrelationbetweengasandoilrelativepermeabilities. ProducersMonthly pages38,Noverber1954. L.Dake. Fundamentalsofreservoirengineering ,volume8.ElsevierScienticPublishing, Amsterdam,2edition,1978.ISBN0-444-41667-6. C.Doughty.Modelinggeologicstorageofcarbondioxide:Comparisonofnon-hysteretic andhystereticcharacteristiccurves. EnergyConversion&Manangement ,48,2007. J.Ennis-KingandL.Paterson.Reservoirengineringissuesinthegeologicaldisposalof carbondioxide.pages290,CSIRO,Melbourne,Australia,2001.Proceedingsofthe InternationalConferenceonGreenhouseGasControlTechnologies. J.Ennis-KingandL.Paterson.Engineringaspectsofgeologicalsequestrationofcarbon dioxide.volumeSPE-77809,SPEandCSIROPetroleum,2002.AsiaPacicOilandGas ConferenceandExhibition,Melbourne,Australia,October8. J.Friedmann.Geologicalcarbondioxidesequestration. Elements ,3:197,June2007. CarbonManagementProgram,LawrenceLivermoreNationalLaboratory. 129

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J.E.Garc a. Fluiddynamicsofcarbondioxidedisposalinsalineaquifers .Doctoraldissertation,UniversityofCalifornia,Berkeley,2003. J.HickeyandJ.Vecchioli.Subsurfaceinjectionofliquidwasteswithemphasisoninjection practicesinFlorida.paper2281,U.S.GeologicalSurvey,U.S.GeologicalSurveyWaterSupply,1986. B.Hitchon. Aquiferdisposalofcarbondioxide .GeosciencePublishingLtd.,Sherwood Park,Alberta,Canada,1996. IPCC.IPCCspecialreportoncarbondioxidecaptureandstorage.PreparedbyWorking GroupIIIoftheIntergovernmentalPanelonClimateChange[Metz,B.,Davidson,O., deConinck,H.C.,Loos,M.,andMeyer,L.A.eds.].Report,IntergovernmentalPanel onClimateChange,Cambridge,UnitedKingdomandNewYork,NY,USA,2005. A.Kumar,R.Ozah,M.Noh,G.A.Pope,S.Bryant,K.Sepehrnoori,andL.W.Lake.ReservoirsimulationofCO 2 storageindeepsalineaquifers. SocietyofPetroleumEngineering Journal ,9SPE89343:336,September2005. S.Martinez,R.Steanson,andA.Coulter. Petroleunengineeringhandbook:Formation fracturing ,chapter55,page12pp.SocietyofPetroleumEngineers,1992. B.McPhersonandP.Lichtner.CO 2 sequestrationindeepsalineaquifers.Washington, D.C.,U.S.A.,2001.FirstNationalConferenceinCarbonSequestration. N.M uller,R.Qi,E.Mackie,K.Pruess,andJ.Blunt.CO 2 injectionimpairmentdueto haliteprecipitation. J.NordbottenandM.Celia.Similaritysolutionsforuidinjectionintoconnedaquifers. JournalofFluidMechanics ,561:307,2006. J.Nordbotten,M.Celia,andS.Bachu.InjectionandstorageofCO 2 indeepsalineaquifers: AnalyticalsolutionforCO 2 plumeevolutionduringinjection. TransportinPorousMedia ,58:339,2005. J.Nordbotten,D.Kavetski,M.Celia,andS.Bachu.ModelforCO 2 leakageincludingmultiplegeologicallayersandmultipleleakywells. EnvironmentalScienceandTechnology 43:743,2009. J.M.Nordbotten,M.A.Celia,andS.Bachu.Analyticalsolutionsforleakageratesthorugh abandonedwells. WaterResourcesResearch ,40,2004.W04204. R.Ozah,G.Lakshminarasimhan,K.Sepehrnoori,andS.Bryant.Numericalsimulation ofthestorageofpureCO 2 andCO 2 -H 2 Sgasmixtureindeepsalineaquifers.In SPE AnnualTechnicalConferenceandExhibition ,SPE97255,pages1,Dallas,Texas, USA,2005.SocietyofPetroleumEngineers,SocietyofPetroleumEngineers. 130

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K.Pruess.Onvaporizingwaterowinhotsub-verticalrockfractures. TransportinPorous Media ,28:335,1997. K.Pruess.TheTOUGH 2 code-Afamiliyofsimulationtoolsformultiphaseowand transportprocessesinpermeablemedia. VadoseZoneJournal ,3:738,2004. K.PruessandJ.Garc a.MultiphaseowdynamicsduringCO 2 disposalintosaline aquifers. EnvironmentalGeology ,42:282,2002. K.PruessandN.M uller.Formationdry-outfromCO 2 injectionintosalineaquifers: 1 : Effectsofsolidsprecipitationandtheirmitigation. WaterResourcesandResearch ,45 w03402:1,2009.doi:10.1029/2008WR007101. K.Pruess,C.Oldenburg,andG.Moridis.TOUGH2users'guide,version2.0.Manual LBNL-43134,LawrenceBerkeleyNationalLaboratory,Berleley,California,1999.accessdate:June10,2007. K.Pruess,T.Xu,J.Apps,andJ.E.Garc a.Numericalmodelingofaquiferdisposalof CO 2 SocietyofPetroleumEngineeringJournal ,8:49,2003. K.Pruess,J.E.Garc a,T.Kovscek,C.Oldenburg,J.Rutqvist,C.Steefel,andT.Xu.Code intercomparisonbuildscondenceinnumericalsimulationmodelsforgeologicdisposal ofCO 2 Energy ,29:1431,2004.doi:10.1016/j.energy.2004.03.077. T.TorpandJ.Dale.DemonstratingstorageofCO 2 ingeologicalreservoirs:TheSleipner andSACSprojects. Energy ,29,2004. L.G.H.vanderMeer.TheCO 2 storageefciencyofaquifers. EnergyConversionand Management ,36:513,1995. L.G.H.vanderMeer.ComputermodellingofundergroundCO 2 storage. EnergyConversionandManagement ,37:1155,1996. M.T.vanGenuchten.Aclosed-formequationforpredictingthehydraulicconductivityof unsaturatedsoils. SoilSci.Soc.Am.J. ,44:892,1980. A.VermaandK.Pruess.Thermohydrologicconditionsandsilicaredistributionnearhighlevelnuclearwastesemplacedinsaturatedgeologicalformations. JournalofGeophysicalResearchs ,93B2:1159,1988. G.Weir,S.White,andW.Kissling.Reservoirstorageandcontainmentofgreenhouse gases. EnergyConversionandManagement ,36:531,1995. 131

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Chapter9 Conclusions ThisdissertationexploresbothanalyticalmethodsforevaluatingtheviabilityofpotentialCO 2 repositoriesandinjectionstrategiesforenhancingstoragecapacity.Injection strategiesforimprovingCO 2 storagewereevaluatedvianumericalexperimentsusingthe TOUGH 2 general-purposenumericalsimulator.Thisworkwasmotivatedbytheneedto developandarapidandeasy-to-useanalyticalmodelthatcanbeutilizedtoscreen potentialCO 2 repositories;andtechniquesforenhancingCO 2 storagecapacityand security,especiallyunderpressure-limitedconditions. Therstpartofthisworkchapters 1 and 2 givesabriefintroductiontoCO 2 sequestrationingeologicformationsandbackgroundknowledgeonconceptsandtheoriesgenerally employedtodescribethebehaviorofCO 2 indeepgeologicformations,withemphasison thephysicalprocessesthatoccurduringCO 2 injectionandnumericalmethodsforsolving equationsthatdepicttheprocesses. ThesecondpartpresentsasetofanalyticalequationsforestimatingCO 2 storageefciencychapter 3 ,brinesaturationprole,andpressureprolechapter 4 duringCO 2 injectionintoanisotropic,homogeneous,connedaquifer.Theseequationswereconsideredtoconstituteanextended-analyticalmodelcapableofestimatingthefollowing: 1.pressurevariationswithinanaquifer; 2.pressureattheinjectionwell; 3.variationsinbrinesaturationwithinanaquifer; 4.radialextentofCO 2 plume;and 5.storageefciency. EstimatesofCO 2 storageefciencyfromtheanalyticalmodelareingoodagreement withvaluescalculatedfrommulti-phase-ownumericalsimulators.Sensitivityanalyses 132

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indicatethattheanalyticalmodelisconsideredavalidandeasy-to-usescreeningtoolfor assessingsuitabilityofpotentialCO 2 repositories,whentherelationshipbetweenuidrelativepermeabilityandbrinesaturationislinearorslightlynonlinearandwhentheirreduciblebrinesaturationoftheformationissufcientlylow. Inthethirdpartdifferentinjectiontechniqueswereevaluatedvianumericalsimulations basedontheircapabilitiestoenhanceCO 2 storagecapacityandsecurityinconnedsaline aquifers.Simulationresultssuggestthatunderisotropicconditionschapter5,thedifferencebetweentheperformancesofaverticalwellandahorizontalwellofsamelengthis negligible.However,horizontalwellstendtoout-performverticalwellsunderpressurelimitedconditionsastheirlengthswereincreased,sincethelengthofthelatterisconstrainedtotheaquifer'sthickness.Thus,signicantlylargequantitiesmassofCO 2 can bestoredinahomogeneous,isotropicaquiferusinglonghorizontalwellscomparedto verticalwells,underpressure-limitedconditions. Chapter 6 investigatesthebenetsofusinghorizontalinjectionwellstostoreCO 2 in anisotropicsalineaquifers.Thevariablesinvestigatedinthischapterwerehorizontalwell lengthandpermeabilityanisotropyratio.AnalysesoftheresultsfromnumericalsimulationsconductedthereinsuggestthatCO 2 storageviahorizontalinjectionwellscould beaviableinjectionstrategyinenhancingstoragecapacityinaquiferswithpermeability anisotropyratiorangingbetween 0 : 01 and 1 : 0 .Inaddition,inpressure-constrainedsituations,horizontalinjectionwellscanbeusedtoincreasetheCO 2 storagecapacityofaquifers andalsominimizeriskofCO 2 leakage. Inchapter 7 thebenetsofusingajointverticalandhorizontalwellforCO 2 storage inananisotropicaquiferwasevaluated;sincetheverticalwellisindirectlydrilledpriorto drillinginthelateraldirectionofaformation,inpractice.Thendingsinthischaptersuggestthatjointwellsaremorebenecialthanverticalwellsbutlessefcientthanhorizontal wellsforCO 2 injectionintoananisotropic,connedaquifer. Overall,resultsfromthesimulationsconductedinchapters 5 6 ,and 7 suggestthatlong horizontalinjectionwellsorjointwellswithlonghorizontalsegmentswellsareviablefor CO 2 storageinaquiferswithpermeabilityanisotropyratiosgreaterthanorequalto 0 : 01 VerticalinjectionwellsaremoreefcientforCO 2 storageinaquiferswithpermeability anisotropyratioslessthan 0 : 01 .AdditionalstudiesonthechangesinpressureattheinjectionwellduringCO 2 injectionchapter 8 suggestthatnear-wellborepressuresdecrease overtimeinisotropicaquifersduetocontrastindensitybetweenCO 2 andbrinegravity segregation. 133

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However,gravitysegregationbecomeslesssignicantasthepermeabilityanisotropy ratiooftheaquiferdecreasesduetoincreasedresistancetoverticalow. Thefollowingtopicsarerecommendedforfuturestudies: 1.CO 2 injectioninmulti-layeranisotropicaquifersusingacasestudy. 2.UsingmultiplehorizontalwellsforCO 2 storageindeepgeologicformations. 3.InjectingmixturesofCO 2 andbrineasatechniquetominimizegravitysegregation. 4.Effectsofbrinesalinityonnear-wellborepressuresatdifferentscenariosof k vh and Q 5.CO 2 -inducedgeochemicalandgeomechanicaleffects. 134

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Nomenclature Subscriptsandsuperscripts uidphasegas,liquid componentinauidphase Variables )]TJ/F40 11.9552 Tf 35.616 0 Td [(gravityfactor mobilityratio Euler'sconstant 0.58 averageporosity dimensionlessradius dimensionlesstime max dimensionless r max A cross-sectionalaream 2 ;L longitudinaldispersivity ;T transversedispersivity matrixcompressibility B thicknessofconnedaquifer b r;t thicknessorheightofCO 2 plume b 0 dimensionlessthicknessofgasplume, b 0 = b r;t =B uidcompressibility D ;T transversedispersioncoefcientperpendiculartodirectionofow D ;L longitudinaldispersioncoefcientinthedirectionofow d moleculardiffusioncoefcientofcomponent inuidphase s CO 2 storageefciency 135

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f c massfractionofinjectedCO 2 thatisdissolvedinbrine F nm averagevalueoftheinwardornormalcomponentof ~ F overaportionofasurface A nm betweenvolumeelements V n and V m h hydraulichead h init initialhydraulichead I vh CO 2 massinjectionratio, I vh = I v =I h k intrinsicpermeability k v permeabilityinverticaldirection k h permeabilityinhorizontaldirection k vh permeabilityanisotropyratio, k vh = k v =k h K hydraulicconductivity k r relativepermeabilityofuidphase L w lengthofinjectionwell L h lengthofhorizontalsegmentofajointwell L v lengthofverticalsegmentofajointwell mobilityofuidphase uidviscosity m molalityofdissolvedsalt M CO 2 molarmassofCO 2 M NaCl molarmassofsalt M CO 2 ;aq totalmassofdissolvedCO 2 M n averageof M overasubdomain V n n molalityofdissolvedCO 2 inbrine P r;t pressure P init initialpressure P cap brinecapillarypressure Q well massinjectionrate Q v CO 2 massinjectionrateoftheverticalsegmentofajointwell Q h CO 2 massinjectionrateofthehorizontalsegmentofajointwell r radialdistancefrominjectionwell 136

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r well injectionwellradius r min minimumradialextentofgasplume r max maximumradialextentofgasplume uiddensity b brinedensity densityofuidphase R 1 radialdistancefrominjectionwellatwhich P r;t = P init S lr irreduciblesaturationofliquidphase S gr irreduciblesaturationofgasphase S w saturationofliquidphase S storativity S s Speciccapacity S saturationofuidphase t time T transmissivity densityofuidphase 0 tortuositycoefcientoftheporousmedium tortuositycoefcientofuidphase u dimensionlessparameter V volume W u wellfunction X CO 2 massfractionofdissolvedCO 2 X massfractionofcomponent inuidphase X g massfractionofcomponent inthegaseousphase X l massfractionofcomponent intheliquidphase X massfractionofcomponent inuidphase X g massfractionofcomponent inthegaseousphase X l massfractionofcomponent intheliquidphase wellinjectivity 137

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Vectors ~ D ;T hydrodynamicdispersiontensor ~ F g advectiveuxofthegaseousphase ~ F l advectiveuxoftheliquidphase ~ F dis diffusive-dispersiveuxofcomponent inalluidphases ~ F adv advectivemassuxofcomponent inalluidphases ~g accelerationduetogravity ~ I unittensor r ~ P pressuredifference ~ Q isthemassowrate ~u Darcyvelocity 138

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Appendices 139

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AppendixA:ValidationofGridMesh Table31: Comparisonof P w barbetween 10 and 20 layer 2 Dmeshgrids.At Q = 100 kg/smeshradius =10 6 m. BottomlayerToplayer Timeyears 10layers20layersRel.error 10layers20layersRel.error 1 218.2216.80.7% 210.7209.20.7% 10 198.7197.60.6% 191.4190.30.6% 30 194.0193.40.3% 186.9186.10.4% 50 192.8192.30.2% 185.7185.20.3% Table32: Comparisonof P w barbetween 10 and 20 layer 3 Dmeshgrids.At Q = 100 kg/smeshlengthorwidth =10 5 m. BottomlayerToplayer Timeyears 10layers20layersRel.error 10layers20layersRel.error 1 228.5228.30.1% 220.4220.20.1% 10 203.3202.60.4% 195.7195.00.4% 30 197.2195.80.7% 189.7188.30.7% 50 193.1191.30.9% 185.6183.90.9% 140

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AppendixB:DerivationofFormationPressureEquations FromFigure6ofchapter 4 ,pressurechangesatthewellboreandwithintheaquiferor formationcanbeestimatedbyanalyzingfromthesinglephaseregionRegion 3 towards thewellbore. B.1:Region 3 Boundaries: r max and r< : 12 Tt=S 1 = 2 or u = r 2 S = Tt < 0 : 03 Range: r max r R 1 Theboundaryconditioninthisregionisthatatasufcientlyfardistancefromtheinjectionwell R 1 ,theformationpressureisequivalenttoitsbackgroundpressure.Since thisregionisasingle-phaseregionwithnopresenceofCO 2 ,theTheisanalyticalsolution isvalidinthisregion.TheTheisanalyticalsolutionforinjectionofauidintoaconned homogeneousaquiferisgivenbytheexpression, h )]TJ/F19 11.9552 Tf 11.955 0 Td [(h init = Q well 4 T W u However, T = kgB= = k= singlephase = w and W u = )]TJ/F19 11.9552 Tf 9.299 0 Td [( )]TJ/F15 11.9552 Tf 11.23 0 Td [(ln u forvery smallvaluesof u .Substitutingtheaboveexpressionsintoequationgives; g h )]TJ/F19 11.9552 Tf 11.955 0 Td [(h init = Q well 4 B k [ )]TJ/F19 11.9552 Tf 9.298 0 Td [( )]TJ/F15 11.9552 Tf 11.955 0 Td [(ln u ] Rearranging P r;t )]TJ/F19 11.9552 Tf 11.955 0 Td [(P init = Q well 4 k w B [ )]TJ/F19 11.9552 Tf 9.299 0 Td [( )]TJ/F15 11.9552 Tf 11.956 0 Td [(ln u ]= Q well 2 k w B )]TJ/F19 11.9552 Tf 13.151 8.087 Td [( 2 )]TJ/F15 11.9552 Tf 11.955 0 Td [(ln u 1 = 2 # Substitutingtheexpressionfor u intoequationandrearranginggives, P r;t = P init + Q well 2 k w B ln q 4 Tt=S r )]TJ/F19 11.9552 Tf 13.151 8.088 Td [( 2 # Let d = q 4 Tt S exp )]TJ/F20 7.9701 Tf 10.494 5.136 Td [( 2 ,sothatequationcanbesimpliedintothefollowing, P r;t = P init + Q well 2 k w B ln d r 141

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AppendixBContinued However,theTheissolutionisonlyvalidforsingle-phaseuidowinporousmedia.To accountforasecondphasewithinaconnedformationCO 2 orgaseousphaseinregions 1 and 2 ,thevalueofthemaximumradialextentofthegasplume, r max ,isaddedto d i.e. R 1 = r max + d .SubstitutingthisexpressionintoA6yieldsthefollowing, P r;t = P init + Q well 2 k w B ln R 1 r r max servesasboundarybetweenregion 3 andregion 2 .At r max formationpressurein bothregionsareequalboundarycondition.Substituting r max intoequationyieldsthe following: P r;t = P init + Q well 2 k w B ln R 1 r max B.2:Region 2 Boundaries: r min and r max Range: r min r r max Fromequation 7 inNordbottenetal. @P @r = c h @ gh @r )]TJ/F20 7.9701 Tf 13.15 5.137 Td [(Q well 2 rk c h + w H )]TJ/F19 11.9552 Tf 11.955 0 Td [(h Letting b = h and B = H andassumingconstantuidpropertiesandgravityyieldthe followingequation: @P @r = c b g @ b @r )]TJ/F20 7.9701 Tf 13.151 5.137 Td [(Q well 2 rk c b + w B )]TJ/F19 11.9552 Tf 11.955 0 Td [(b ThedenominatorontheR.H.S.ofequationandcanrearrangedasfollows, c b + w B )]TJ/F19 11.9552 Tf 11.955 0 Td [(b = w [ )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 b + B ] where = c = w 142

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AppendixBContinued Substitutingequationintoequationgives, @P @r = b g @ b @r )]TJ/F20 7.9701 Tf 17.16 5.136 Td [(Q well 2 rk w )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 b + B DividingthenumeratoranddenominatoroftheR.H.S.ofequationby r yieldsthe followingequation, @P @r = grb @ b @r )]TJ/F20 7.9701 Tf 15.131 5.136 Td [(Q well 2 k w r [ )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 b + B ] AssumingthatequationderivedbyNordbottenetal.isvalid,itcanrearrange andsubstitutedintoequation12asfollows, b r;t = B )]TJ/F15 11.9552 Tf 11.956 0 Td [(1 s Q well t )]TJ/F19 11.9552 Tf 11.956 0 Td [(S lr Br 2 )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 = B )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 r max r )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 Rearrangingequation r [ )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 b + B ]= B Q well t )]TJ/F19 11.9552 Tf 11.955 0 Td [(S lr B 1 = 2 = Br max Differentiatingequationyieldsthefollowingequation, @b r;t @r t = B )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 )]TJ/F19 11.9552 Tf 13.151 8.088 Td [(r max r 2 # Multiplyingequationandequationyields, b r;t @b r;t @r t = B )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 r max r )]TJ/F15 11.9552 Tf 11.956 0 Td [(1 B )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 )]TJ/F19 11.9552 Tf 13.151 8.088 Td [(r max r 2 # = B )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 2 r max 1 r 2 )]TJ/F19 11.9552 Tf 13.151 8.088 Td [(r max r 3 # Substitutingequationsandintoequationandrearranginggivesthefollowingequation, dP dr = gB )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 2 1 r )]TJ/F19 11.9552 Tf 13.151 8.088 Td [(r max r 2 )]TJ/F19 11.9552 Tf 21.797 8.088 Td [(Q well 2 k w B 1 r max 143

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AppendixBContinued Integratingequationgives P r;t = )]TJ/F19 11.9552 Tf 19.141 8.088 Td [(Q well 2 k w B r r max + gB )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 2 ln r + r max r + C Theexpressionfortheintegrationconstant, C wasobtainedbyapplyingequation7as boundaryconditionbetweenregion 2 andregion 3 .Theresultingexpressionfor C isas follows, C = P init + Q well 2 k w B ln R 1 r max +1 # )]TJ/F15 11.9552 Tf 14.64 8.088 Td [( gB )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 2 ln r max +1 Substitutingequationintoequationgivestheequationforformationpressurein region 2 ,whichisasfollows, P r;t = P init + Q well 2 k w B ln R 1 r max +1 )]TJ/F19 11.9552 Tf 21.615 8.088 Td [(r r max # + gB )]TJ/F15 11.9552 Tf 11.956 0 Td [(1 2 ln r r max + r max r )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 # r min servesasboundarybetweenregion 2 andregion 1 .At r min formationpressurein bothregionsareequalboundarycondition.Substituting r min intoequationgives; P r;t = P init + Q well 2 k w B ln R 1 r max +1 )]TJ/F19 11.9552 Tf 13.772 8.088 Td [(r min r max # + gB )]TJ/F15 11.9552 Tf 11.956 0 Td [(1 2 ln r min r max + r max r min )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 # B.3:Region 1 Boundaries: r well and r min Range: r well r r min AsshowninFigure1,region1ispredominantly occupiedbythegaseousphaseassumptioni.e. b r;t B .Withthisassumption,equationcanbesimpliedintothefollowing: @P @r = c B g @ B @r )]TJ/F20 7.9701 Tf 13.151 5.137 Td [(Q well 2 rk c B + w B )]TJ/F19 11.9552 Tf 11.955 0 Td [(B = )]TJ/F19 11.9552 Tf 10.494 8.088 Td [(Q well 2 rk 1 c B = )]TJ/F19 11.9552 Tf 19.141 8.088 Td [(Q well 2 k w B 1 r 144

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AppendixBContinued Integratingequationyieldsthefollowing P r;t = )]TJ/F19 11.9552 Tf 19.14 8.088 Td [(Q well 2 k w B 1 ln r + C 1 Theexpressionfortheintegrationconstant, C 1 wasobtainedbyapplyingequation21as boundaryconditionbetweenregion 1 andregion 2 .Theresultingexpressionfor C 1 isas follows, C 1 = P init + Q well 2 k w B ln R 1 r max +1 )]TJ/F19 11.9552 Tf 13.772 8.087 Td [(r min r max + 1 ln r min # + gB )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 2 ln r min r max + r max r min )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 # Substitutingequationintoequationandrearrangingtermswillgivetheequation forformationpressureinregion 1 ,whichisasfollows, P r;t = P init + Q well 2 k w B ln R 1 r max +1 )]TJ/F19 11.9552 Tf 13.772 8.088 Td [(r min r max + 1 ln r min r !# + gB )]TJ/F15 11.9552 Tf 11.956 0 Td [(1 2 ln r min r max + r max r min )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 # But r min r max = 1 and r max r min = Thissimpliesequationasfollows, P r;t = P init + Q well 2 k w B ln R 1 r max +1 )]TJ/F15 11.9552 Tf 13.638 8.088 Td [(1 + 1 ln r min r !# + gB )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 2 )]TJ/F15 11.9552 Tf 11.955 0 Td [(ln )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 # Thepressureattheinjectionwellisestimatedbysubstituting r inequationwith r well asfollows, 145

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AppendixBContinued P r;t = P init + Q well 2 k w B ln R 1 r max +1 )]TJ/F15 11.9552 Tf 13.638 8.088 Td [(1 + 1 ln r min r well !# + gB )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 2 )]TJ/F15 11.9552 Tf 11.955 0 Td [(ln )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 # B.4:Summary Thesignof g inequations18through27isnegativebecausebuoyancyeffectcauses CO 2 plumetoriseupwardsagainstdirectionofgravity.Asaresultthesignoftheterm containingthegravityparameterinequations,,,andbecomenegative. Therefore,thepressureequationsforregions 1 2 ,and 3 areasfollows: Region 1 : P r;t = P init + Q well 2 k w B ln R 1 r max +1 )]TJ/F15 11.9552 Tf 13.639 8.088 Td [(1 + 1 ln r min r !# )]TJ/F40 11.9552 Tf 52.309 0 Td [( gB )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 2 )]TJ/F15 11.9552 Tf 11.955 0 Td [(ln )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 # Region 2 : P r;t = P init + Q well 2 k w B ln R 1 r max +1 )]TJ/F19 11.9552 Tf 21.615 8.088 Td [(r r max # )]TJ/F40 11.9552 Tf 82.873 0 Td [( gB )]TJ/F15 11.9552 Tf 11.956 0 Td [(1 2 ln r r max + r max r )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 # Region 3 : P r;t = P init + Q well 2 k w B ln R 1 r !# 146

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AppendixBContinued Lastly,equationforpressureattheinjectionisafollows: P r;t = P init + Q well 2 k w B ln R 1 r max +1 )]TJ/F15 11.9552 Tf 13.639 8.088 Td [(1 + 1 ln r min r well !# )]TJ/F40 11.9552 Tf 52.309 0 Td [( gB )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 2 )]TJ/F15 11.9552 Tf 11.955 0 Td [(ln )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 # 147

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AppendixC:FortranCodeforAnalyticalModel PROGRAManalytical_model !===================================================== !Thisprogramestimatespivotalparametersthatcanbe !usedtoscreenpotentialstoragesitesforcarbon !dioxidesequestration. !Thismodelpredictsthebehaviorofcarbondioxidein !confinedsalineaquifersduringinjection. !Pivotalparameterspredictedbythemodelincludethe !following: !Pressureatinjectionwellasafunctionoftime !Minimumplumeextentatbottomofaquifer !Maximumplumeextentatthetopofaconfined !aquifer !CO2-brineinterfacelocationasafunctionoftime !PressureasafunctionofspaceandtimePr,t !CO2storageefficiencyasafunctionoftime. !======================================================= !Definitionofparameters !r=radiusfrominjectionwellinm !t_s=times !t=timeinyears !B=thicknessofformation !phi=averageporosity !d=depthattopofformation !temp=temperatureindegreeCelsius !rho_c=densityofcarbondioxideinkg/m !rho_w=densityofbrineinkg/m !delta_rho=rho_w-rho_c !mu_c=viscosityofcarbondioxideinPa.s !mu_w=viscosityofbrineinPa.s !lambda_c=mobilityofcarbondioxideinPa.s-1 !lambda_w=mobilityofbrineinPa.s-1 !lambda=mobilityratiolambda_c/lambda_w !b=thicknessofgasplume !b_prime=b/B,dimensionlessthicknessofgasplume !r_prime=dimensionlessradius !V_inj=carbondioxideinjectionrateinkg/s !Q_well=carbondioxideinjectionrateinm/s !Q=carbondioxideinjectionrateinm/year 148

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AppendixCContinued !gamma=Euler'sconstant.5772157 !alpha=rockcompressibility.5e-11Pa-1 !beta=porecompressibility.5e-10Pa-1 !R_inf=radialdistanceatwhichformationpressure !isequivalenttoitsinitialpressure !P_init=initialpressureinPa !P=pressureatthebottomlayerofaformation !inPa !P_well=pressureatthebottomportionofwell !Gamm=dimensionlessgravityfactor !delta_r=spatialstepintheradialdirection !delta-z=spatialstepinthez-diection !ss=specificstorativity[-] !s=storativityinm !Tr=transmissivitym/s !V_p=availableporevolume !r_min=minimumradialextentofgasplumeinm !r_max=maximumradialextentofgasplumeinm !S_r=residualbrinesaturation !epsilon_s=storageefficiency !g=accelerationduetogravity.81m/s !pi=constant !k=intrinsicpermeabilitym !K_w=conductivityofbrine=rho_w g k/mu_wm/year !V_waste=wastedaquifervolume !Rm=Radialextentofformationm !Sim=similarityvariabler/tm/s !tau=dimensionlesstimeeq.5inchapter3 !eta=dimensionlessradiuseq.5inchapter3 !chi=eta eta/tau !chi_max=maximumvalueofchi USEinput_data IMPLICITNONE OPENUNIT=6,FILE='RO_MODEL.DAT',STATUS='REPLACE' WRITE, '' WRITE, '&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& &&&&&&&&&&&&&&&& 149

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AppendixCContinued &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& &&&&&&&&' WRITE, '& &' WRITE,4 4FORMATX,'&THISANALYTICALMODELDEPICTSCARBON DIOXIDEPLUMEBEHAVIORINAHOMOGENEOUS, ISOTROPIC,AND&'/4X,& '&CONFINEDAQUIFER.ITISANEXTENSIONOFTHE SEMI-ANALYTICALEQUATIONDERIVEDBYNORDBOTTEN &'/4X,& '&ETAL.,2006.THISMODELCANBE EMPLOYEDTOSCREENPOTENTIALREPOSITORIESFOR GEOLOGIC&'/4X,&' &SEQUESTRATIONOFCARBONDIOXIDE. &' WRITE, '& &' WRITE,5 5FORMATX,"& THISMODELWASDEVELOPEDINTHEDEPARTMENTOFCIVIL ANDENVIRONMENTALENGINEERINGATTHE &"/4X& &"&UNIVERSITYOFSOUTHFLORIDA. &"/4X& &"&DATE:NOVEMBER30,2008 &"/4X& &" &AUTHORS: ROLANDT.OKWENANDJEFFREYA.CUNNINGHAM &" WRITE, &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&' WRITE, '' WRITE, '' WRITE, @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@& @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@' WRITE, "@ 150

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AppendixCContinued THEFOLLOWINGASSUMPTIONSWEREMADEINTHISMODEL:& @" WRITE, "@CONSTANTINJECTIONRATE @" WRITE, "@ CONSTANTTEMPERATUREISOTHERMALCONDITION& @" WRITE, "@ NEGLIGIBLECAPILLARYEFFECT& @" WRITE, "@ NOINTERPHASEMASSTRANSFERBETWEENCO2& ANDBRINE@" WRITE, "@ CONSTANTFLUIDPROPERTIESDENSITYAND& VISCOSITY@" WRITE, @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@& @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@' WRITE, '' !Readinputparameters PRINT ,"Enterthicknessofaquiferinmeters" !B=100.0 READ ,B IFB<0.0THEN PRINT ,"Thethicknessshouldbeapositivenumber" STOP ELSE CONTINUE ENDIF PRINT ,"Enterradialextentofaquiferinmeters& Shouldbegreaterthanthickness" !Rm=100000.0 READ ,Rm IFRm
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AppendixCContinued STOP ELSE CONTINUE ENDIF PRINT "Entervalueofresidualbrinesaturation, between0.0and1.0"!S_r=0.3 READ ,S_r IFS<0.0THEN PRINT ,"S_rshouldbegreaterthanorequalto0.0" STOP ELSE CONTINUE ENDIF PRINT "Entervalueofaverageporositybetween0.0and1.0" READ ,phi !phi=0.12 IFphi<=0.0THEN PRINT ,"Thisformationisimpervious" STOP ELSEIFphi>1.0THEN PRINT ,"Theporosityisunrealistic" STOP ELSE CONTINUE ENDIF PRINT "Entervalueforintrinsicpermeabilityinm" !READ ,k k=1.0e-13 IFk<=0.0THEN PRINT ,"Thisformationisimpervious" STOP ELSE CONTINUE ENDIF 152

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AppendixCContinued !PRINT ,"Enterdepthofaquifertop" READ ,d !d=1200.0 IFd<=0.0THEN d=absd ELSE CONTINUE ENDIF PRINT "EnteraverageformationtemperatureindegreeCelsius" READ ,temp !temp=45.0 PRINT "Enteraveragedensitykg/mofcarbondioxideand viscosityPa.sofcarbondioxide" READ ,rho_c,mu_c !rho_c=700.48 !mu_c=5.0e-5 IFrho_c<=0.0.OR.mu_c<=0.0THEN PRINT ,"Error!!Valuesmustbepositive" STOP ELSE CONTINUE ENDIF lambda_c=1.0/mu_c PRINT "Enteraveragedensitykg/mandviscosityPa.s ofbrine" READ ,rho_w,mu_w !rho_w=1176.00 !mu_w=8.0e-4 IFrho_w<=0.0.OR.mu_w<=0.0THEN PRINT ,"Error!!Valuesmustbepositive" STOP ELSE CONTINUE ENDIF 153

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AppendixCContinued !CalculatedensitydifferencebetweenbrineandCO2 delta_rho=rho_w-rho_c !Calculatemobilityofbrine lambda_w=1.0/mu_w !MobilityratiobetweenCO2andbrine lambda=lambda_c/lambda_w !lambda=10.0 PRINT ,"Mobilityratio=",lambda !Calculatetransmissivityofbrine Tr=k_crho_w,mu_w,g,k B!unitsm/year PRINT ,"Transmissivity=",Tr !Calculatestorativityofbrine S=ssrho_w,g,phi B!Unitm PRINT ,"Storativity=",S PRINT "Entercarbondioxideinjectionrateinkg/s" READ ,V_inj !V_inj=100.0 !convertCO2injectionratefrommass/stovolume/s Q_well=V_inj/rho_c !convertinjectionratefromvolume/sectovolume/year Q=Q_well 60.0 60.0 24.0 365.0 PRINT "Howmanypointsintimedoyouwishtoevaluate?" READ ,num !num=4 !PRINT "Enternumberofdesireddatapointsinradialaxis?" !READ ,n n=400 !Calculatepivotalparameters !calculateGravityfactorGamm !Gamm=6.0 Gamm=2.0 pi delta_rho g lambda_w k B B/Q_well PRINT ,"GravityFactor=",Gamm 154

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AppendixCContinued !Approach:makethefluidsPropsubroutinemoregeneral. !distinguishbetweencasesofgravityofforonbased !onthevalueorexpressionofBig_lambda IFGamm<0.5THEN !Assumption:GravityfactorGamm=0andtheLagrange !MultiplierBig_lambda=lambda-1/ lambda !Big_lambda=lambda-1.0/.0 lambda CALLgravity_offlambda,Q,Q_well,phi,S_r,B,pi,gamma,mu_c& ,mu_w,S,Tr,V_p,Rm,g,delta_rho,k,lambda_w,P,d,rho_w,n,& num,Gamm ELSEIFGamm>=0.2THEN PRINT'A',"Thisproblemrequiresinclusionofgravity" CALLgravity_onlambda,Q,Q_well,phi,S_r,B,pi,gamma,mu_c& ,mu_w,S,Tr,V_p,Rm,g,delta_rho,k,lambda_w,P,d,rho_w,n,& num,Gamm,Big_lambda !CONTINUE!STOP ENDIF ENDPROGRAManalytical_model !%%%%%%%%%%%%%%%%%%%%%%MODULEinputdata%%%%%%%%%%%%% MODULEinput_data IMPLICITNONE !Variablesdeclaration INTEGER::max_iter,err1,n,num!i,j, REAL,EXTERNAL::f REAL::start1,start2,tolerance,root REAL,PARAMETER::gamma=0.5772157,pi=3.1415926,g=9.81 REAL::B,t_s,t,phi,d,temp,rho_c,rho_w,mu_c,mu_w,V_inj,& S_r,k,Rm,chi_max REAL,EXTERNAL::k_c,ss REAL::Q_well,Q,lambda_c,lambda_w,lambda,Tr,S,Gamm,& delta_rho,b_r,P REAL::r_max,r_min,V_p,R_inf,epsilon_s,V_waste,Big_lambda ENDMODULEinput_data 155

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AppendixCContinued !%%%%%%%%%%%%%%%%SUBROUTINEgravity_off%%%%%%%%%%%%%%% SUBROUTINEgravity_offlambda,Q,Q_well,phi,S_r,B,pi,& gamma,mu_c,mu_w,S,Tr,V_p,Rm,g,delta_rho,k,lambda_w,& P,d,rho_w,n,num,Gamm IMPLICITNONE !Dummyargument REAL,INTENTOUT::V_p,P REAL,INTENTIN::lambda,Q,phi,S_r,B,pi,gamma,mu_c,& mu_w,S,Tr,Rm,delta_rho,g,k,lambda_w,Q_well,d,rho_w INTEGER,INTENTIN::n,num REAL::u,r,B_eff!=0.3!allinmeters REAL::S_w,S_eff,points,t,delta_r,Gamm,P_init,P1,P2,& P3,Sim,t_s,b_r,r_min,r_max,epsilon_s,R_inf INTEGER::i,j !Calculateinitialpressure P_init=rho_w g d+B !P_init=1.3079e7 u=lambda-1.0 !Looptoreadtimeandcalculatecorresponding !parametersatapointintime delta_r=1.0 S_eff=1.0-S_r OUTER:DOi=1,num IFi==1THEN PRINT ,"Pleaseenterthefirstpointintime& inyears:time" READ ,t ElSEIFi>1.AND.i
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AppendixCContinued !Calculatetimeinseconds t_s=t 60.0 60.0 24.0 365.0 !Calculater_min,r_maxatthistime r_min=sqrtQ t/pi/lambda/B/phi/S_eff r_max=sqrtlambda Q t/pi/B/phi/S_eff V_p=pi r_max r_max B epsilon_s=100.0 mu_c S_eff/mu_w !V_waste=.0-epsilon_s/100.0 V_p R_inf=exp-gamma 0.5 sqrt.0 Tr t/S+r_max !100FORMATA,F6.0,1X,A,4X,A,F6.2,A,4X,A,F6.2,A PRINT"x'Timeinyears=',F6.2",t PRINT"x'r_mininmeters=',F10.2",r_min PRINT"x'r_maxinmeters',F10.2",r_max PRINT"x'storageefficiencyin%=',F6.2",epsilon_s PRINT"x'R_inf=',F12.2",R_inf !PRINT101,"CO2storageefficiencyat",t,"years:",,"%" WRITEUNIT=6,FMT=98"Time=",t,"years",& "r_min=",r_min,"m","r_max=",r_max,"m" 98FORMATx,A,F10.2,A,3x,A,F10.2,A,3x,A,F10.2,A WRITEUNIT=6,FMT=99"Storageeffciency",epsilon_s,"%",& "R_inf",R_inf,"m" 99FORMATx,A,F6.2,A,3x,A,F12.2,A WRITE, '' WRITE, '=========================================& =====================================================& ====' WRITEUNIT=6,FMT=102"rm","br,tm","Pr,tPa",& "r/tm/s","Sw" 102FORMATx,A,12x,A,10x,A,11x,A,12x,A WRITE, '=========================================& =====================================================& ====' !WRITE, '' !PRINT102,"r","br,t","Pr,t" INNER:DOj=1,n !createradialpoints 157

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AppendixCContinued IFj<11THEN r=FLOATj 0.3 ELSEIFj<=20THEN r=FLOATj/5.0 3.0 ELSEIFj<=30THEN r=FLOATj 2.0 ELSEIFj<=40THEN r=FLOATj 5.0 ELSEIFj<=60THEN r=FLOATj 10.0 ELSEIFj<=70THEN r=FLOATj 20.0 ELSEIFj<=80THEN r=FLOATj 40.0 ELSEIFj<=90THEN r=FLOATj 100.0 ELSEIFj<=100THEN r=FLOATj 200.0 ELSE r=FLOATj 500.0 ENDIF !Calculatesimilarityvariable Sim=r r/t_s !EstimateCO2plumethicknesscalculation b_r=B/u sqrtlambda Q t/pi/phi/S_eff/B/r/r-1.0 B_eff=B S_eff IFb_r>=BTHEN b_r=B! S_eff S_w=S_r ELSEIFb_r>=B_effTHEN b_r=b_r! S_eff S_w=S_r ELSEIFb_r<=0.0THEN b_r=0.0 S_w=1.0 ELSE!IFr>r_min.AND.r
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AppendixCContinued !Pressurecalculation P1=P_init+Q_well/2.0/pi/k/lambda_w/B & logR_inf/r_max& +1.0-.0/lambda+.0/lambda & logr_min/r P2=P_init+Q_well/2.0/pi/k/lambda_w/B & logR_inf/r_max& +1.0-r/r_max P3=P_init+Q_well/2.0/pi/k/lambda_w/B & logR_inf/r IFr=r_min.AND.r=r_max.AND.r=R_infTHEN P=P_init!!Boundaryconditionatr=R_inf ENDIF !Printresults !WRITE, '' WRITEUNIT=6,FMT=104r,b_r,P,Sim,S_w 104FORMATx,F15.2,6x,F15.6,6x,E15.6,6x,E15.6,6x,& F12.4 !WRITE, '' !PRINT104,r,b_r,P ENDDOINNER WRITE, '=========================================& =====& ====================================================' ENDDOOUTER ENDSUBROUTINEgravity_off 159

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AppendixCContinued !%%%%%%%%%%%%%%%%%%%%%%SUBROUTINEgravity_on%%%%%%%%%% SUBROUTINEgravity_onlambda,Q,Q_well,phi,S_r,B,pi,& gamma,mu_c,& mu_w,S,Tr,V_p,Rm,g,delta_rho,k,lambda_w,P,d,rho_w,& n,num,Gamm,Big_lambda IMPLICITNONE !Dummyargument REAL,INTENTOUT::V_p,P REAL,INTENTIN::lambda,Q,Q_well,phi,S_r,B,pi,gamma,& mu_c,mu_w,& S,Tr,Rm,delta_rho,g,k,lambda_w REAL,INTENTIN::Gamm,d,rho_w,Big_lambda INTEGER,INTENTIN::n,num REAL::r!allinmeters REAL::S_w,B_eff,points,t,delta_r,P_init,P1,P2,P3,Sim,& t_s,b_r,r_min,r_max,epsilon_s,R_inf INTEGER::i,j,option !Localvariable REAL::b_prime,u,db,S_eff,g1,g2,chi_max,tau,eta,r_max1,& rmax_diff,r_min1,rmin_diff !Calculateinitialpressure P_init=rho_w g d+B !P_init=1.31e7 S_eff=1.0-S_r B_eff=B S_eff !Calculatechi_maxusingequation7ofChapter3 chi_max=.0324 lambda-0.0952 Gamm+& .1778 lambda+5.9682& Gamm ** 0.5+1.6962 lambda-3.0472 PRINT ,"chi_max=",chi_max db=B/n u=lambda-1.0 PRINT ,"Doyouwanttoincludegravityeffects& inyourpressurecalculations?" PRINT ,"Note:Calculationswithgravityturned& 160

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AppendixCContinued onpredictlowerpressures" PRINT ,"Enter1forexclusionofgravityor2& forinclusionofgravityinpressurecalculations" READ ,option !Looptoreadtimeandcalculatecorresponding !parametersatthepointintime OUTER:DOi=1,num IFi==1THEN PRINT ,"Pleaseenterthefirstpointintimein& years:time" READ ,t !Calculatetimeinseconds !t_s=t 60.0 60.0 24.0 365.25 ElSEIFi>1.AND.i
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AppendixCContinued r=FLOATj 0.3 ELSEIFj<=20THEN r=FLOATj/5.0 3.0 ELSEIFj<=30THEN r=FLOATj 2.0 ELSEIFj<=40THEN r=FLOATj 5.0 ELSEIFj<=60THEN r=FLOATj 10.0 ELSEIFj<=70THEN r=FLOATj 20.0 ELSEIFj<=80THEN r=FLOATj 40.0 ELSEIFj<=90THEN r=FLOATj 100.0 ELSEIFj<=100THEN r=FLOATj 200.0 ELSE r=FLOATj 500.0 ENDIF !Calculatesimilarityvariable Sim=r r/t_s !Pressurecalculation P1=P_init+Q_well/2.0/pi/k/lambda_w/B & logR_inf/r_max+& 1.0-.0/lambda+.0/lambda logr_min/r P2=P_init+Q_well/2.0/pi/k/lambda_w/B & logR_inf/r_max+& 1.0-r/r_max P3=P_init+Q_well/2.0/pi/k/lambda_w/B & logR_inf/r !Print ,"Pressureinregion1;gexcluded:",P1 IFr>=R_infTHEN P=P_init!!Boundaryconditionatr=R_inf 163

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AppendixCContinued ELSEIFr>=r_maxTHEN P=P3!region3 !ELSEIFr==r_maxTHEN !P=P3!Boundaryconditionatr=r_max ELSEIFr>=r_min.AND.r0.0THEN !region1andboundaryconditionatr=r_min P=P1 ENDIF !Printresults WRITEUNIT=6,FMT=104r,Sim,P 104FORMATx,F16.4,6x,E12.6,6x,E15.8 !PRINT104,r,b_r,P ENDDOINNER !!!Option2!++++++++++++++++++++++++++++++++++++++++ Print ,"Option2selected" CASE WRITEUNIT=6,FMT=1021"Youchoosetheoptionof& estimatingpressurewithgravityturnedon." WRITE, '' WRITE, '========================================& ==========================' WRITEUNIT=6,FMT=1012"rm","r/tm/s","Pr,tPa" 1012FORMATx,A,9x,A,7x,A WRITE, '===========================================& =======================' WRITE, '' 1021FORMATx,A INNER1:DOj=1,n !createradialpoints IFj<11THEN r=FLOATj 0.3 ELSEIFj<=20THEN r=FLOATj/5.0 3.0 ELSEIFj<=30THEN 164

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AppendixCContinued r=FLOATj 2.0 ELSEIFj<=40THEN r=FLOATj 5.0 ELSEIFj<=60THEN r=FLOATj 10.0 ELSEIFj<=70THEN r=FLOATj 20.0 ELSEIFj<=80THEN r=FLOATj 40.0 ELSEIFj<=90THEN r=FLOATj 100.0 ELSEIFj<=100THEN r=FLOATj 200.0 ELSE r=FLOATj 500.0 ENDIF !Calculatesimilarityvariable Sim=r r/t_s g1=delta_rho g lambda B/u/u & Lambda-loglambda-1.0 g2=delta_rho g lambda B/u u logr/r_max+& r_max/r-1.0 !Print ,"Gravityinregion1:",g1 !Print ,"Gravityinregion1:",g2 !Pressurecalculation P1=P_init+Q_well/2.0/pi/k/lambda_w/B & logR_inf/r_max+& 1.0-.0/lambda+.0/lambda logr_min/r-g1 P2=P_init+Q_well/2.0/pi/k/lambda_w/B & logR_inf/r_max+1.0-r/r_max-g2 P3=P_init+Q_well/2.0/pi/k/lambda_w/B & logR_inf/r !Print ,"Pressureinregion1:",P1 IFr>=R_infTHEN P=P_init!!Boundaryconditionatr=R_inf ELSEIFr>=r_maxTHEN P=P3!region3 165

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AppendixCContinued !ELSEIFr==r_maxTHEN !P=P3!Boundaryconditionatr=r_max ELSEIFr>=r_min.AND.r0.0THEN !region1andboundaryconditionatr=r_min P=P1 ENDIF !Printresults !WRITE, '' WRITEUNIT=6,FMT=114r,Sim,P 114FORMATx,F16.4,6x,E12.6,6x,E15.8 !WRITE, '' ENDDOINNER1 ENDSELECT!IF !CalculationofCO2-brineinterfacelocation WRITE, '' WRITE, '========================================& ====================================================& ===================' WRITEUNIT=6,FMT=111"rm","r/tm/s",& "br,tm","Sw" 111FORMATx,A,9x,A,8x,A,15x,A WRITE, '===========================================& =======================================================& =============' INNER2:DOj=1,n !createradialpoints IFj<11THEN r=FLOATj 0.3 ELSEIFj<=20THEN r=FLOATj/5.0 3.0 166

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AppendixCContinued ELSEIFj<=30THEN r=FLOATj 2.0 ELSEIFj<=40THEN r=FLOATj 5.0 ELSEIFj<=60THEN r=FLOATj 10.0 ELSEIFj<=70THEN r=FLOATj 20.0 ELSEIFj<=80THEN r=FLOATj 40.0 ELSEIFj<=90THEN r=FLOATj 100.0 ELSEIFj<=100THEN r=FLOATj 200.0 ELSE r=FLOATj 500.0 ENDIF !Calculatesimilarityvariable Sim=r r/t_s IFb_r>=BTHEN b_r=B! S_eff S_w=S_r ELSEIFb_r>=B_effTHEN b_r=b_r! S_eff S_w=S_r ELSEIFb_r<=0.0THEN b_r=0.0 S_w=1.0 ELSE!IFr>r_min.AND.r
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AppendixCContinued ==================================================& ========================' ENDDOOUTER ENDSUBROUTINEgravity_on !%%%%%%%%%%%%%%%%FUNCTIONss%%%%%%%%%%%%%%%%%%%%% REALFUNCTIONssrho_w,g,phi !Functiontocalculatethestorativityofbrine !Dummyargumentdeclaration REAL,INTENTIN::rho_w,g,phi !Declarationoflocalvariables REAL,PARAMETER::alpha=6.5e-11,beta=4.5e-10 !calculatess ss=rho_w g phi beta+alpha ENDFUNCTIONss !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% !%%%%%%%%%%%%%%%%%%%%%%FUNCTIONk_c%%%%%%%%%%%%%%% REALFUNCTIONk_crho_w,mu_w,g,k !Functiontocalculatetheconductivityofbrine !Dummyargumentdeclaration REAL,INTENTIN::rho_w,mu_w,g,k !calculateconductivityinm/year k_c=rho_w g k/mu_w 60.0 60.0 24.0 365.25 ENDFUNCTIONk_c !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 168

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AppendixD:EmpiricalRelationshipsBetween P Q ,and k vh Ageneralequationdepictingtherelationshipbetween P and Q foranisotropicaquifer isasfollows: P = P w )]TJ/F19 11.9552 Tf 11.955 0 Td [(P init = A Q where A representaconstantandalsovarywithwellorientationorlength.Values A for thevariouswelltypesandlengthusedinthisstudyarepresentedinTable33. Table33: Valuesof A for equalto 1 40 A R 2 1 0.59110.99 10 0.49670.99 20 0.47530.99 30 0.46020.99 40 0.45660.99 Equationestimatespressurechangesnearhorizontalinjectionwellsoflengthsup to 3000 minisotropicconnedaquifers.Theequationforestimatingtheratioofthe near-wellborepressuresinananisotropicaquifers P aniso tothatofanisotropicaquifer P iso asfunctionsof k vh passingthroughtheorigincanbegenerallydescribedasfollows: P 0 = P aniso P iso = B log k vh +1 Where B areconstantsfordifferentvaluesof aspresentedinTable34. Table34: Valuesof B for equalto 1 40 B R 2 1 -0.245190.96 10 -0.383700.98 20 -0.363240.97 30 -0.351330.97 40 -0.337920.96 169

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AppendixDContinued Equationcanberearrangedasfollows: P aniso = P iso [ B log k vh +1] Substitutingequationintoequationgivesanequationforestimating P aniso as afunctionof Q and k vh whichisasfollows: P aniso = A Q [ B log k vh +1] Foragivenmaximumchangeinpressurewithinananisotropicconnedformation P aniso;max ,themaximumallowableCO 2 massinjectionrate Q max canbeestimated byrearrangingequationasfollows: Q max = P aniso;max A [ B log k vh +1] 170

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AbouttheAuthor RolandT.Okwenwasin 1974 inCameroon.HeobtainedhisBSinChemistryfrom theUniversityofBuea,Cameroon,in 1997 .HelaterrelocatedtoDenmarkwherehe studiedEnvironmentalManagementatAalborgUniversityfromSeptember 2001 toJune 2002 .HelaterenrolledintheTechnicalUniversityofDenmarkinSeptember 2002 andcompletedtheMSprograminPetroleumEngineeringinDecember 2004 .Roland enrolledattheUniversityofSouthFloridaUSFinSpringof 2006 asagraduatestudent intheDepartmentofCivil&EnvironmentalEngineering.WhileatUSF,Rolandserved intheUniversity'sGraduateCouncilasastudentrepresentativefrom2007.He wasactivelyinresearchbothwithintheUniversityandwiththeindustrialsector.He receivedtheAlfredP.SloanMinorityPh.D.Scholarship,NSF-RISEFellowship,USFDSSFellowshipandworkedasaresearchassistantforanexternallyfundedresearch grant.agoodnumberofscholarshipsandresearchsponsorshipsbothwithinUSFand fromexternalsources.HeattendedconferencesandseminarswithinUSAandabroadin whichhepresentedsomeofhisresearchwork.AftergraduationfromUSF,Rolandplans toworkasaPost-doctoralfellowattheSchlumbergerCambridgeResearchCenter,in Cambridge,England.