Mathematical Models for Under-Deposit Corrosion in Aerated and De-Aerated Solutions

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Mathematical Models for Under-Deposit Corrosion in Aerated and De-Aerated Solutions
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english
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Chang, Ya-Chiao
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University of Florida
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Doctorate ( Ph.D.)
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University of Florida
Degree Disciplines:
Chemical Engineering
Committee Chair:
ORAZEM,MARK E
Committee Co-Chair:
CHAUHAN,ANUJ
Committee Members:
ZIEGLER,KIRK JEREMY
VU,LOC QUOC

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Subjects / Keywords:
co2 -- corrosion -- modeling -- o2 -- under-deposit
Chemical Engineering -- Dissertations, Academic -- UF
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Chemical Engineering thesis, Ph.D.
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theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
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Abstract:
A 2-D axi-symmetrictime-dependent mathematical model was developed to investigate conditions underwhich the onset of under-deposit corrosion occurs. Model development ispresented sequentially. The systems considered included steels in both aeratedwater and de-aerated electrolyte containing CO2. One unique featureof this work was that, the presence of anodic and cathodic regions was notassumed a priori, but was rather the result of numerical simulations, whichrevealed galvanic coupling caused by the differential aeration cells. Incontrast to models presented in the literature, the conservation equation foreach ionic species was employed in this work rather than Laplace's equation.Two geometries were considered. An one-quarter-ellipse geometry was used todescribe a water droplet placed on the bare metal surface; whereas, atwo-quarter-ellipse geometry was used to represent a predefined depositsurrounded by a bulk solution. Solutions containing O2 and CO2were calculated in both geometries. Two types of precipitates are discussed inthe models containing O2. The precipitate Fe(OH)2 wasassumed to be less protective and to inhibit both anodic and cathodicreactions; whereas, Fe(OH)3 was assumed to be protective and topassivate only the iron dissolution reaction. The species FeCO3 wasassumed to be the precipitate in the system containing CO2, whichinvolved additional homogeneous and cathodic reactions. The results weresensitive to both mesh size and time step size. For the two-quarter-ellipsegeometry models, the area ratio of the covered region to the bare metal surfacewas found to be important since it influences the location and rate of anodicand cathodic reactions. A systematic study was performed to identify the propermodeling parameters. The mathematical model included coupled, time-dependent,nonlinear, convective diffusion equations for ionic species; localelectroneutrality; homogeneous reactions; formation of primary precipitates;and anodic and cathodic reactions written explicitly in terms of localconcentration and potential driving forces. It provides a framework formodeling systems involving homogeneous and heterogeneous reactions and, withsimple modifications, can apply to different conditions. The results showedunder-deposit corrosion occurs and can lead to more serious problems under someconditions.
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Includes vita.
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by Ya-Chiao Chang.
Thesis:
Thesis (Ph.D.)--University of Florida, 2013.
Local:
Adviser: ORAZEM,MARK E.
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Co-adviser: CHAUHAN,ANUJ.

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MATHEMATICALMODELSFORUNDER-DEPOSITCORROSIONINAERATEDANDDE-AERATEDSOLUTIONSByYA-CHIAOCHANGADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2013

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c2013Ya-ChiaoChang 2

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Tomyparentsandmyhusband 3

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ACKNOWLEDGMENTS Ithankmyadvisor,ProfessorMarkE.Orazem,forhisexpertise,guidance,andsupportinthiswork.Hehasshownmenotonlyhowtoimprovemyabilitiesinresearch,buthowtoimprovemyabilitiesasapersonwithhisunmatchedpatience.IwouldliketothankRichardWoollamofBPAmericaforhisinvolvementinsponsoringthisproject.IalsothankmycommitteemembersProfessorAnujChauhan,ProfessorLocVu-Quoc,andProfessorKirkZiegler.Iwouldliketothankallofthestudentsandpost-docwhohaveworkedinProfessorOrazem'sgroupduringmytimeatUniversityofFlorida.Finally,Iwouldliketothankmyhusband,myparents,mybrother,andmygrandfatherfortheirloveandencouragementduringmystudies. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 7 LISTOFFIGURES ..................................... 8 ABSTRACT ......................................... 14 CHAPTER 1INTRODUCTION ................................... 16 2LITERATUREREVIEW ............................... 20 2.1LocalizedandUnder-DepositCorrosion ................... 20 2.2DifferentialCell ................................. 21 2.3CorrosioninPresenceofCarbonDioxide .................. 22 2.4ReviewofMechanisticModels ........................ 24 2.4.1ElectrochemicalModels ........................ 24 2.4.2Transport-BasedElectrochemical ................... 25 2.4.3Thermodynamically-BasedElectrochemical ............. 27 3NUMERICALAPPROACH ............................. 29 3.1ProblemDescription .............................. 29 3.1.1AeratedSolution(O2) ......................... 30 3.1.2De-aeratedSolution(CO2) ....................... 31 3.2SimulatedGeometries ............................. 32 3.2.1DropletModel .............................. 32 3.2.2DepositModel .............................. 34 3.3TheMathematicalModelDevelopment .................... 35 3.3.1AeratedSolution(O2) ......................... 36 3.3.1.1ElectrochemicalReactions ................. 36 3.3.1.2ConservationEquationsandChemicalReactions .... 37 3.3.1.3Active-PassiveTransition .................. 39 3.3.2De-AeratedSolution(CO2) ...................... 41 3.3.2.1ElectrochemicalReactions ................. 42 3.3.2.2ConservationEquationsandChemicalReactions .... 43 3.3.2.3Active-PassiveTransition .................. 46 4RESULTSANDDISCUSSIONS .......................... 49 4.1AeratedModel-O2 ............................... 49 4.1.1Active-PassiveTransition ........................ 50 4.1.2TheEffectofPrecipitation ....................... 53 5

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4.1.2.1Less-ProtectivePrecipitates(Fe(OH)2) .......... 55 4.1.2.2ProtectivePrecipitates(Fe(OH)3) .............. 59 4.1.3OtherInuences ............................ 63 4.1.3.1ComparisonbetweenAnalyticSolutionsandNumericalSolutions ........................... 63 4.1.3.2DropSize ........................... 66 4.1.3.3DropEccentricity ....................... 67 4.1.3.4MeshDensity ......................... 68 4.1.3.5DepositModel-InuenceofUncoveredRegion ..... 69 4.2De-aeratedModel-CO2 ............................ 69 4.2.1TheComparisonsbetweenMechanismsProposedbyRemitaandNordsveen ................................ 72 4.2.2PassivationBehavior .......................... 77 4.2.2.1CO2DropletModel ...................... 77 4.2.2.2CO2DepositModel ..................... 79 4.2.3TheInuenceofTimeStep ...................... 81 4.2.4TheInuenceofMeshSize ...................... 83 5OVERVIEWOFUNDER-DEPOSITCORROSIONMODEL ........... 89 6CONCLUSIONS ................................... 91 7SUGGESTIONSFORFUTUREWORK ...................... 94 7.12-DAxi-Symmetricto3-D ........................... 94 7.22-DLow-ReynoldsNumberk-"TurbulenceModel .............. 94 7.33-DLow-ReynoldsNumberk-"TurbulenceModel .............. 96 7.4MovingBoundary ................................ 96 7.5MoreCorrosiveConditions .......................... 97 REFERENCES ....................................... 99 BIOGRAPHICALSKETCH ................................ 105 6

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LISTOFTABLES Table page 1-1ComparisonofpredictionmodelsforCO2/H2Scorrosion. ............ 19 2-1FactorsinuencingcorrosioninCO2containingenvironments. ......... 23 4-1Parametersforthesimulationsinvolvinganodicreactionsthatareactive-passivecontrolled. .............................. 50 4-2ParametersfortheO2simulationsinone-quarterellipsegeometry. ....... 51 4-3ParametersfortheO2simulationsintwo-quarterellipsegeometry. ....... 52 4-4Errorsfordifferentmeshdensityandtimestep. .................. 67 4-5ParametersforthesimulationsinCO2DepositmodelwiththemechanismproposedbyRemita. ................................. 73 4-6ParametersforthesimulationsinCO2DropletmodelwiththemechanismproposedbyNordsveen. ............................... 75 4-7ParametersforthesimulationsinCO2DepositmodelwiththemechanismproposedbyNordsveen. ............................... 76 4-8DifferencesforthesimulationsinCO2DropletmodelwithdifferentmeshsizebyRemita. ...................................... 84 7

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LISTOFFIGURES Figure page 2-1Mixedpotentialanalysisforthedifferentialaerationcell. ............. 21 3-1Thecoordinatesr,,andusedinthecalculations. ............... 33 3-2Schematicrepresentationsofmodels. ....................... 33 3-3TheconcentrationdistributionofO2alongthemetalsurface. .......... 35 4-1Calculatedpolarizationcurvesshowinganodicandcathodiccurrentdensitiesforthemodel. .................................... 53 4-2Resultscalculatedforthefunctionmodel. .................... 54 4-3Calculatedpolarizationcurvesshowinganodicandcathodiccurrentdensitiesatr=0forthedepositmodel. ............................ 54 4-4Surface-averagedcurrentdensitycalculatedforthedepositmodelatr=0asafunctionofappliedpotential. ........................... 55 4-5RadialdistributionscalculatedfortheEvans'dropmodelwithtimeasaparameter. ...................................... 56 4-6ConcentrationdistributionsofoxygenofthedropletmodelforthesystemcontainingO2. .................................... 57 4-7APourbaixdiagramforironanditsvariousspeciesat25C. ........... 58 4-8RadialdistributionsofpHcalculatedfortheEvans'dropmodel. ......... 59 4-9Radialdistributionsofcalculatedforthedepositmodelwithtimeasaparameter. ...................................... 60 4-10Representationsofpotentialandcurrentdistributions. .............. 61 4-11PotentialdistributionsfortheresultspresentedinFigure 4-9 .......... 61 4-12Radialdistributionsoffractionalsurfacecoveragecalculatedforthedepositmodelwithtimeasaparameter. .......................... 62 4-13Potentialdistributionsalongtheelectrodesurface. ................ 63 4-14Radialdistributionsofcalculatedforthedepositmodelwithtimeasaparameter. ...................................... 64 4-15Radialdistributionsoffractionalsurfacecoveragecalculatedforthedepositmodelwithtimeasaparameter. .......................... 65 4-16Concentrationprolesforunsteady-statediffusionequation. ........... 67 8

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4-17Cathodicpolarizationcurveforoxygenreductionwithdropradiusasaparameter. ...................................... 68 4-18Cathodicpolarizationcurveforoxygenreductionwithdropshapeasaparameter. ...................................... 69 4-19Cathodicandanodicpolarizationcurveswithmeshdensityasaparameter. .. 70 4-20SchematicrepresentationoftheDepositmodel. ................. 70 4-21Calculatedpotentialdistributionsalongelectrodesurfaceatthetimeofmaximumpotentialvariationwithrs=rbasaparameter. .............. 71 4-22Thedistributionofcurrentdensityfordifferentmechanisms. ........... 74 4-23Thepotentialdistributionfordifferentmechanisms. ................ 74 4-24Thedistributionsofcurrentdensityfordifferentmechanisms. .......... 77 4-25Radialdistributionsofcalculatedtotalcurrentdensityand. ........... 78 4-26Potentialdistributionforthefalsecolorrepresentationandstreamlinerepresentationofcurrentdensity. .................... 80 4-27ThepHdistributionasafunctionoftimecalculatedfortheCO2Dropletmodel. 81 4-28RadialdistributionsofcalculatedtotalcurrentdensityattheelectrodesurfacewithtimeasaparameterfortheCO2Depositmodel. ............... 82 4-29RadialdistributionsofcalculatedsurfacecoverageattheelectrodesurfacewithtimeasaparameterfortheCO2Depositmodel. ............... 82 4-30Potentialdistributionalongelectrodesurfacewithtimeasaparametercalculatedforthedepositssurroundedbybulksolutions. ............. 83 4-31Potentialdistributionforthefalsecolorrepresentationandstreamlinerepresentationofcurrentdensityatt=560s. ................... 84 4-32Radialdistributionsofcalculatedattheelectrodesurfacewithtimestepasaparameter. ..................................... 85 4-33Radialdistributionsofcalculatedtotalcurrentdensity. .............. 86 4-34Radialdistributionsoftotalcurrentdensityattheelectrodesurface. ....... 86 4-35Distributionsofmeshdensity. ............................ 87 4-36Radialdistributionsofcalculatedattheelectrodesurfacewithmaximummeshelementsizeasaparameter. ......................... 88 7-1Schematicrepresentationsofthechannelowmodel. .............. 95 9

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7-2Schematicrepresentationsofconcentrationproleinturbulentow. ...... 96 7-3Schematicrepresentationsofthechannelowmodelwithanewboundarycondition. ....................................... 97 10

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LISTOFSYMBOLS aractivityofthereactingspeciesAsurfacearea,m2A1constantusedfortheEddydiffusivitytermtodescribetheturbulentowA2constantusedfortheEddydiffusivitytermtodescribetheturbulentowApconstantusedfortheactive-passivetransitionbaanodiccoefcient,V)]TJ /F3 7.97 Tf 6.59 0 Td[(1bccathodiccoefcient,V)]TJ /F3 7.97 Tf 6.59 0 Td[(1cimolarconcentrationofspeciesi,mol/literci,refbulkconcentrationofspeciesi,mol/litercrmolarconcentrationforreactants,mol/litercpmolarconcentrationforproducts,mol/literDidiffusioncoefcientforspeciesi,cm2/sDi,coveredeffectivediffusioncoefcientofspeciesiinthecoveredregion,cm2/sDi,bulkeffectivediffusioncoefcientofspeciesiinthebulkregion,cm2/sD(t)iposition-depend,cm2/sEaactivationenergy,VEppotentialatwhichtheactive-passivetransitionoccurs,VFFaraday'sconstant,96487C/equivHiHenry'sconstanticurrentdensity,mA/cm2 11

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i0exchangecurrentdensity,mA/cm2iaanodiccurrentdensity,mA/cm2iccathodiccurrentdensity,mA/cm2ictchargetransfercurrentdensity,mA/cm2ikkineticallycontrolledcurrentdensity,mA/cm2ilimmass-transfer-limitedcurrentdensity,mA/cm2ippassivecurrentdensity,mA/cm2krateconstantforelectrochemicalreactionthatexcludestheexponentialdependenceonpotentialkfrateconstantinforwardreactionkbrateconstantinbackwardreactionkjrateconstantoftheformationofscalejKsp,isolubilityproductofsaltiKwdissociationconstantforwater,mol2/kg2KsolkineticconstantforthedissolvedrateofCO2Kidissociationconstantforwater,mol2/kg2Niuxofspeciesi,mol/cm2sPCO2carbondioxidepartialpressure,barRuniversalgasconstant,8.3143J/molKRirateofreaction,mol/cm2srradialcoordinate,mTtemperature,Kttime,sUiequilibriumpotentialforagivenreaction,V 12

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vvelocity,cm/sVinterfacialpotentialunderequilibriumconditionsforagivenreactionzichargeassociatedwithspeciesiz+dimensionlessdistancefromthemetalsurfaceTafelslope,V/decadeofcurrent)]TJ /F1 11.955 Tf 28.35 0 Td[(surfaceconcentrationofspeciesfractionalsurfacecoveragethickness,cmporosity"erroroverpotentialforagivenreaction,Vradialcoordinateconductivityparameterthatcontrolsthesteepnessofthepotentialchangecorrespondingtotheactive-passivetransitionkinematicviscosity,cm2/spotential-dependentweightingfactoruiddensity,g/cm3sprecipitatesdensity,g/cm3owallshearstress,N/cm2radialcoordinatepotential,V0potentialoftheelectrolyteadjacenttotheworkingelectrode,Vmelectrodepotential,V 13

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyMATHEMATICALMODELSFORUNDER-DEPOSITCORROSIONINAERATEDANDDE-AERATEDSOLUTIONSByYa-ChiaoChangDecember2013Chair:MarkE.OrazemMajor:ChemicalEngineeringA2-Daxi-symmetrictime-dependentmathematicalmodelwasdevelopedtoinvestigateconditionsunderwhichtheonsetofunder-depositcorrosionoccurs.Modeldevelopmentispresentedsequentially.Thesystemsconsideredincludedsteelsinbothaeratedwaterandde-aeratedelectrolytecontainingCO2.Oneuniquefeatureofthisworkwasthat,thepresenceofanodicandcathodicregionswasnotassumedapriori,butwasrathertheresultofnumericalsimulations,whichrevealedgalvaniccouplingcausedbythedifferentialaerationcells.Incontrasttomodelspresentedintheliterature,theconservationequationforeachionicspecieswasemployedinthisworkratherthanLaplace'sequation.Twogeometrieswereconsidered.Anone-quarter-ellipsegeometrywasusedtodescribeawaterdropletplacedonthebaremetalsurface;whereas,atwo-quarter-ellipsegeometrywasusedtorepresentapredeneddepositsurroundedbyabulksolution.SolutionscontainingO2andCO2werecalculatedinbothgeometries.TwotypesofprecipitatesarediscussedinthemodelscontainingO2.TheprecipitateFe(OH)2wasassumedtobelessprotectiveandtoinhibitbothanodicandcathodicreactions;whereas,Fe(OH)3wasassumedtobeprotectiveandtopassivateonlytheirondissolutionreaction.ThespeciesFeCO3wasassumedtobetheprecipitateinthesystemcontainingCO2,whichinvolvedadditionalhomogeneousandcathodicreactions.Theresultsweresensitivetobothmeshsizeandtimestepsize.Forthe 14

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two-quarter-ellipsegeometrymodels,thearearatioofthecoveredregiontothebaremetalsurfacewasfoundtobeimportantsinceitinuencesthelocationandrateofanodicandcathodicreactions.Asystematicstudywasperformedtoidentifythepropermodelingparameters.Themathematicalmodelincludedcoupled,time-dependent,nonlinear,convectivediffusionequationsforionicspecies;localelectroneutrality;homogeneousreactions;formationofprimaryprecipitates;andanodicandcathodicreactionswrittenexplicitlyintermsoflocalconcentrationandpotentialdrivingforces.Itprovidesaframeworkformodelingsystemsinvolvinghomogeneousandheterogeneousreactionsand,withsimplemodications,canapplytodifferentconditions.Theresultsshowedunder-depositcorrosionoccursandcanleadtomoreseriousproblemsundersomeconditions. 15

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CHAPTER1INTRODUCTIONOnAugust192000,a30-inch-diameternaturalgaspipelinerupturednearCarlsbd,NewMexico.Twelveliveswereclaimedbytheexplosionandre.Thesignicantreductioninpipewallthicknessresultedfrominternalcorrosioncausedthisaccident.ThisndingwasconrmedbytheNationalTransportationSafetyBoard[ 1 ].ThereportpointedoutthatthecombinationofmicrobiallmsandcontaminantssuchasO2,CO2,H2S,andchloridesinitiatedtheinternalcorrosion.Catastrophicincidentsduetointernalcorrosioninoilandgasindustryarenotrare.IntheUnitedStates,thetotalannualcostofcorrosion-relatedincidentsingasandoilindustryisfrom471to875million[ 2 ].Thecontroltechniquestopreventinternalcorrosionhavenotbeenimprovedsince1970s.Thecurrentexaminationinvolvesrunninganinstrumentedpigthroughthepipeusingultrasoundtechniquestomeasurewallthickness[ 3 4 ].However,thesecannotpreventtheincidentmentionedabovebecauseitisdifculttoidentifyandrepairdamagecoveredwithcorrosiveproducts.Therefore,itisimportanttobuildamathematicmodeltopredictthecorrosionanddenealimitationtotheuseofsteelpipelines.Therecognitionoftheinternalcorrosionproblembeginsin1940sandthemodelshavebeendevelopedsincethemid1970s.Thesemodelscanbeclassiedasempirical,semi-empirical,andmechanical,asshowninTable 1-1 .Bothempiricalandsemi-empiricalmodelscanprovideaccurateprediction,butthesemodelsrequirecomplicatedcorrectionfactorswhennewoperatingparametersareconsidered,therebylimitingtheapplicabilityofthemodel.Mostmodelsfocusontheuniformcorrosiononmetalsurfacetoreducethecomplexityofcalculation;however,localizedcorrosioniscommonlyobserved.Under-depositcorrosionisatypeoflocalizedcorrosionthatcanleadtoacatastrophicconsequenceduetothelackofpredictability.Inordertoimprovepresentmodels,acomputationalmodelwasdevelopedthataccounts 16

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fortheinitialunder-depositenvironment,mechanismsoftheformationofdifferentialcell,thestructureofprotectivelm,andchemicalreactionsassociatedwithO2andCO2.Under-depositcorrosioncontainingcorrosivespeciescanleadtomoreserioustypesofcorrosion.Themechanismfortheonsetoflocalizedcorrosionhasbeenstudiedbymanyindustrialandacademicresearchgroups.CORMED[ 5 ],Norsok[ 5 ],anddeWaards[ 6 ]builtempiricalandsemi-empiricalmodelsthatcanprovideaccurateinterpolationpredictionforcorrosionrate;however,morecomplicatedcorrectionfactorsarerequiredtoaccountforsituationswhereextrapolationorpredictionfails.MechanisticmodelsdevelopedbyGray[ 7 ],Nesic[ 8 9 ],andAnderko[ 10 ]arebasedonfundamentaltheories,buttheassumptionofpredenedanodicandcathodicregionsintroduceserrorsinthepredictedcorrosionrates.Inthiswork,inordertoconstructamodelprovidingmoreinformationofthecorrosionmechanisms,thepresenceofanodicandcathodicregionswasdeterminedbylocalpotentialdistributioncausedbytheformationofdifferentialaerationcells.Theobjectofthisworkistopresenta2-Daxi-symmetrictime-dependantmathematicalmodelinvestigatingconditionsunderwhichtheonsetofunder-depositcorrosionoccursinaeratedandde-aeratedmedia.Theactive-passivetransitionsofmetalslikeironwasassumedtobetheconsequenceofformationofprecipitate.Theuiddynamicwasalsotakenintoaccountbyusingtheeddydiffusivity.Themodeldevelopmentwillbeintroducedsequentiallyinthiswork.Incontrasttopreviousmodels,thelocationofanodicandcathodicregionswasnotassumedapriori,butwasrathertheresultofthenumericalsimulation.Thismodelalsoincludesthegalvaniccouplingeffectresultedfromtheformationofprecipitates.TheconservationequationforeachionicspecieswasemployedinthisworkratherthanLaplace'sequation.Thepresentstudysimulatesthecorrosionprocessbyusingfundamentalphysicalandelectrochemicallawswhichprovidingaframeworkofunderstandingtheconcentrationvariationofreactingspeciesinthesolution.Theadvantageofthismodelisitcanbeadaptedtoothertypes 17

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ofcorrosionwithsimplemodications.MorecomplicatedreactionsinvolvingseveralreactionspeciessuchasH2SandHS)]TJ /F1 11.955 Tf 7.08 -4.34 Td[(,morecorrosiveenvironmentcontainingCl)]TJ /F1 11.955 Tf 7.09 -4.34 Td[(,andothergeometriescanbeaddressedinfuturework. 18

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Table1-1. ComparisonofpredictionmodelsforCO2/H2Scorrosion. ModeltypeFeaturesExample EmpiricalprovidesaccurateinterpolationpredictionCORMED[ 5 ]1980sextrapolationpredictionfailedNorsok[ 5 ]1990sparametersarebest-tSemi-empiricalprovidesgoodinterpolationpredictiondeWaards[ 5 6 ]1975extrapolationpredictionmaybeincorrectsomeparametershavephysicalmeaningswhileothersarebest-tMechanisticprovidegoodextrapolationasinterpolationpredictionElectrochemicalstrongtheoreticalbackgroundGray[ 7 ]1989Transport-basedNesic[ 9 11 ]1996,2001Thermodynamic-basedAnderko[ 10 ]1998 19

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CHAPTER2LITERATUREREVIEWThebasicconceptofunder-depositcorrosionisintroducedinsequenceasfollows,includingthemechanismoflocalizedcorrosion,propertiesofdifferentialcells,andtheinuenceofCO2andH2Sunderhumidiedcondition.Finally,areviewofmechanisticmodelsproposedinthepastdecadesispresented. 2.1LocalizedandUnder-DepositCorrosionInternalcorrosioncanbecategorizedintotwotypes.Oneisuniformcorrosionwhichiseasytoforeseeandcanberepairedbeforeanincidentoccurs.Anotherislocalizedcorrosionsuchaspitting,stresscorrosioncracking,crevicecorrosion,erosion,and...etcUnder-depositcorrosionisatypeoflocalizedcorrosionandwillbediscussedinthiswork.Acommoncauseofrupturedoilandgaspipelinesisunder-depositcorrosionwhichisatypeoflocalizedcorrosion.Itishardtoobservebecausethepitorcreviceisoftenburiedundersandsorcorrosiveproducts.Onceitisdetected,surfacedamageisalreadysignicant.Theonsetofunder-depositcorrosionisgenerallyexplainedbytheimperfectionofcorrosionproductsonametalsurface.Theimperfectionmostlyisassociatedwiththebreakdownoftheprotectivescaleresultedfromtheuidow[ 12 14 ].Oncethemetalpotentialachievesacriticalvalue,thelocalizedcorrosionisinitiatedandleadstomoreseriousproblemssuchaspittingcorrosion[ 15 17 ].Atthesametime,theelectrochemistryandthetransportprocessonthemetalsurfacebegintodifferfromthebulksystem[ 18 ].Manyattemptshavebeenmadetodevelopasmall-scale,inexpensive,andefcientmethodtosimulatetheenvironmentinpipelines[ 19 21 ].Modelsforinitiationoflocalizedcorrosionarebasedonconceptsassociatedwithtransportofspeciesthroughthepassivelmandintheoccludedregion.Alkireetal.[ 22 ]developedasimplemodelneglectingelectromigrationandconsideringthetransportoftheneutralbinaryelectrolytes.AlkireandSiitarirevealedthatpotentialand 20

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concentrationdistributionscouldbealteredbyintroducingacathodicreactioninsidethepit[ 23 ].Under-depositcorrosion,ontheotherhand,hasbeenassociatedwithformationofdifferentialcells. 2.2DifferentialCellDifferentialcellsrepresentatypeofconcentrationcellsinwhichelectrochemicalreactionsaredrivenbyconcentrationdifferencesofspeciesbetweentwometalsortwopointsonthesamemetalsurface.Theprecipitationlayeractsasabarriertoreactivespeciesandleadstodifferentreactionratesbecauseofthenon-uniformsurface.Intheoilandgasindustry,waterreductionandirondissolutionarethecommonredoxreactions.Whenthesurfacecoveredwithcorrosiveproductsoraclusterofmicrobesleadstooxygendepletions,theanodicreactionrateincreases.Ontheotherhand,thecathodicreactiondominatesonthesurfacewithoutprecipitationlayers.Differentialaerationcellsareintroducedasanexampleofdifferentialcellinthefollowing.ThissituationisseeninFigure 2-1A wherethecontributionsofoxygenreductionand A BFigure2-1. Mixedpotentialanalysisforthedifferentialaerationcell:A)undertheassumptionofuniformelectrolytecompositionsandcurrentdistributionsB)withapassivatedcathode. 21

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corrosionreactionsaregivenassolidlines.Manymetalslikeiron,chromium,nickel,titaniumandtheiralloysdemonstrateanactive-passivetransition,whichisinuencedbytheelectrolytepH.ThecorrespondingdiagramisgiveninFigure 2-1B .Twocorrosionlinesaredrawn,onefortheacidicelectrolyteandtheotherforthealkalineelectrolyte.Thesubstantialdifferenceofcorrosionratebetweenanodeandcathodeexpressesanaccelerationofcorrosionbythedifferentialaerationeffect.Evans[ 24 ]demonstratedawaterdropletexperimentshowingtheeffectacceleratesthecorrosionnearawaterlineonametalsurface.Otherfactorssuchasarestrictedaccessofinhibitorsandretentionofcorrosivespeciescanalsoincreasetheunder-depositcorrosionrate[ 25 26 ].Alkireetal.[ 27 ]developedamodeltocalculatecurrentdistributionsonametalsubjectedtodifferentialaerationcorrosion.LaQue[ 28 29 ]showedthatcopperdiskscorrodedalongtheperipherywheretheowwasturbulentandtherateoftransportofoxygenwashigher.Conversely,theirondisksspinningundersameconditionscorrodedatthecenterwheretheowwaslaminaranddeceleratedtransportofoxygen.Theactive-passivetransitionandthedistributionofcorrosionratearerelatedtotheelectrodesize,oxygenconcentration,andsolutionconductivity[ 30 31 ].Goodagreementwasobtainedbetweencalculationsandexperimentalobservations[ 28 29 ].OrazemandMiller[ 32 ]proposedthatoscillationofcurrentnearthepassivationpotentialresultsfromtheformationofsaltlms. 2.3CorrosioninPresenceofCarbonDioxideTheenvironmentcaninuencetherateofunder-depositcorrosion,especiallyCO2andH2Sinamoisturizedcondition.ThehistoryofstudyingcorrosioninCO2containingenvironmentcanbetracedbackto1940swhenthiswasrstfoundingasandsweet-oilwells.Asrecognized,carbonicacidismorecorrosivethanacompletelydissociatedacidatthesamecondition(pHvalue)[ 6 ].Thecauseshavebeeninvestigatedextensivelybymanyacademicandindustrialgroupsoverthepastdecades[ 7 33 35 ].Dependingontheinuence,thefactorscanbesortedintothreecategories,medium-related, 22

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Table2-1. FactorsinuencingcorrosioninCO2containingenvironments[ 34 36 ]. Medium-relatedMaterial-relatedInterface-related CO2partialpressureO2contentAlloycompositionTemperaturepHvalueFe2+concentrationMicrostructureFluidowrateSourgas(H2S)BrinecompositionMultiphaseowOrganicacid(HAc)CrudeOilSurfacelmsWaterwetting materials-related,andinterface-related[ 36 ].TheseparametersarelistedinTable 2-1 .Thesefactorsareallinterconnectedandhaveadirectorindirectimpactonmechanisms.Forexample,thepartialpressureofCO2directlyaffectsthepHvalueofthemedium,whichcanaltermechanisms.AthigherpHvalueorhighertemperature,almofironcarbonateismorelikelytoform,protectingthemetalsurfaceandaffectingthecorrosionrateindirectly[ 8 ].Similarly,theprecipitationratevariesaccordingtouidowbychangingthedegreeofwater-wettingonametalsurface.ThepresenceofH2SplaysansignicantroleintheCO2containingcorrosionbecauseitincreasesthecorrosionpotentialtoaregionwherelocalizedbreakdownandpittingcorrosioncouldoccur.Theeffectiscomplexduetotheco-existenceoftwocompetitiveproducts,FeCO3andFeS[ 37 ].CorrosioncontainingH2Shasbeenstudiedsince1950s.ItcanacceleratethecorrosionratebygivingoutadditionalH+ionsordeceleratethecorrosionratebyformingathinprotectivelm[ 6 38 39 ].Onthecontrary,severalstudiesshowedthatasconcentrationofH2Slessthan500ppmatpH(<5),thereisnoprecipitationlayeronametalsurface.Aftertheconcentrationexceedsacriticalvalue,thecorrosionratedecreases[ 40 41 ].Moreover,theeffectduetotemperaturechangeismoresignicantthantheconcentrationgradientofH2S[ 41 ].Thecorrosionbehaviorofsteelinthepresenceofcarbondioxideandaceticacidhavebeenstudied[ 42 ].TheeffectoftheexistenceofCH3COOHcanbeobservedatelevatedtemperaturesandtheundissociatedformofaceticacidcanleadtoanincreasingcorrosionrate. 23

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Generally,localdefectsformadifferenceofcorrosionactivitiesandarecommonlybelievedtoserveastheinitiator.Amicroturbulenceowisintroducedbyanunevenscaleonametal.Whenhydrodynamicforcesreachacriticalvalueknownaswallshearstresses,aruptureoftheprotectivescalestarts.ThestudyofcorrosioninapresenceofCO2andH2Sinvolvesacombinationofalltheabovefactors. 2.4ReviewofMechanisticModelsTheelaborationofmechanisticmodelsrequirestrongphysicalandchemicalfoundations.Themechanisticmodelshavebeenclassiedintothreecategories,electrochemical,transport-basedelectrochemical,andthermodynamically-basedelectrochemical. 2.4.1ElectrochemicalModelsThecorrosionrateisaffectedbyredoxreactionswhichincludeanodicdissolutionofthemetalandcathodicreactionssuchasevolutionofhydrogenorreductionofoxygen.Sinceironisamajorcomponentinpipelines,themostcommonanodicreactionisirondissolutiongivenby[ 43 44 ] Fe!Fe2++2e)]TJ /F1 11.955 Tf 169 -4.93 Td[((2)Oneofthecathodicreactionsishydrogenevolution.Thehydrogencanbeevolveddirectlyfromwater[ 45 ],carbonicacid[ 9 ],andaceticacid[ 42 ]asdescribedbelow H2O+e)]TJ /F2 11.955 Tf 10.41 -4.94 Td[(!1 2H2(g)+OH)]TJ /F1 11.955 Tf 142.43 -4.94 Td[((2) H2CO3+e)]TJ /F2 11.955 Tf 10.41 -4.93 Td[(!1 2H2(g)+HCO)]TJ /F3 7.97 Tf 0 -7.97 Td[(3(2)and HAc+e)]TJ /F2 11.955 Tf 10.41 -4.94 Td[(!1 2H2(g)+Ac)]TJ /F1 11.955 Tf 144.85 -4.94 Td[((2)Thecurrentofindividualreactionscanbeformulatedas 1 ik=1 ik,ct+1 ik,lim(2) 24

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wherethesubscriptkrepresentsthekthreaction,ik,ctischarge-transfercurrent,andik,limismasstransfer-limitedcurrent.Forthechargetransfersteps,ict,aandict,ccanbeexpressedby ict,a=i0,a10=ba(2)and ict,c=)]TJ /F5 11.955 Tf 9.29 0 Td[(i0,c10)]TJ /F13 7.97 Tf 6.59 0 Td[(=bc(2)respectively,whereisoverpotential,i0isexchangecurrentdensity,andbisTafelslopeforeachreaction.Thereisnolimitingcurrentforirondissolutionandwaterreductionbecausetheunlimitedquantityofironinthemetalandwatermolecularinbulksolution.Fortheaceticacidreduction,thecurrentislimitedbythediffusionofreactingspeciestothemetalsurface.Becauseofthespecicpropertyofcarbonicacid,thedehydrationdegreeofcarbonicacidshouldbeincorporated[ 46 ].Afteralltheparametersarespecied,thecorrosionpotentialandcurrentdensitycanbesolvedthroughthechargebalanceatsteadystate Xik=0(2)Thecorrosionratecanthereforebecalculatedfromtheanodiccurrentdensity. 2.4.2Transport-BasedElectrochemicalIntheelectrochemicalmodel,thetransportprocessissimpliedbyassumingalineardistributionofconcentrationthroughastagnantboundarylayer.However,thecorrosionbehaviorchangeswhenalayerisformed.Therefore,thetransportofreactingspeciesthroughthelayerofcorrosiveproductsshouldbeincorporatedtoderiveamorepracticalmodel[ 47 48 ].Thedrivingforceofspeciesinanaqueoussolutioncanbeclassiedbythreesources:convectionifaspeciesismovingwiththeuidvelocityv,diffusionifthereisadifferenceinconcentrationrci,andmigrationifaspecieshaschargeziandisundera 25

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potentialgradientr.Theuxofaspeciesicanbeexpressedby Ni=)]TJ /F5 11.955 Tf 15.28 8.09 Td[(F RTziDicir)]TJ /F5 11.955 Tf 11.95 0 Td[(Dirci+civ(2)Therelationshipbetweencurrentandchargedspeciesis i=FXiziNi(2)Eachspeciesisconservedandcanbewrittenasacombinationequationofhomogeneouschemicalreactionsandtheuxofspecies. @ci @t=rNi+Ri(2)Riisthesourceofispeciesresultingfromhomogeneousreactionsandcanbeexpressedas Ri=kfYrcr)]TJ /F5 11.955 Tf 11.95 0 Td[(kbYpcp(2)wherekfandkbaretherateconstantsforforwardandbackwardreactions,andcrandcparetheconcentrationforreactantsandproducts,respectively.InaCO2containingsolution,thehomogeneousreactionscouldbehydrationofCO2,dissociationofwaterandotherorganicacids,andtheformationofprotectivelm[ 49 ].Foranaqueoussolutioncontainingnsolutes,therearenexpressionsintheformofEquation 2 .Theelectroneutralityequation nXizici=0(2)isneededtocalculatetheelectricalpotential.ThemigrationterminEquation 2 isnegligibleiftheelectrolyteissupportedbyaninertionicspecies[ 50 ].Themassconservationforthespeciesinbulksolutioncanbepresentedby[ 47 51 ] @(ci) @t=@ @x1.5(Di+D(t)i)@ci @x+Ri(2) 26

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whereD(t)iisaposition-dependentturbulenteddydiffusivityandisvolumetricporosityofthelm.Theelectrochemicalreactionsarecoupledtothetransportequationsthroughtheboundaryconditions.Thecorrosionratecanbeobtainedaftertheconcentrationproleissolved. 2.4.3Thermodynamically-BasedElectrochemicalThetwomechanisticmodelsdescribedabovearerestrictedtoanidealsolution.Thethermodynamicsofsolutionsisaddedtoincludetheeffectofinteractionsamongsolutes.Itiscapableofcalculatingtheequilibriaofliquidphase,oilphase,andseveralsolidphasesinamulti-componentsystem[ 10 52 ].Theconcentrationofreactingspeciesinthepreviouselectrochemicalreactionsisreplacedbyactivityai.Theexchangecurrentdensitycanbeformulatedas i0,k=i0,kYramranH2O(2)wherei0istheconcentration-independentpart,andmandnarethereactionordersrelatedtotheactivitiesofthereactingspeciesandwater.Ifthelmisformed,aprecipitationrateshouldbeconsideredandisgivenby[ 52 53 ] Rj=kj,fYi)]TJ /F8 7.97 Tf 6.78 5.52 Td[(nii(2)wherekj,frepresentstherateconstantoftheformationofscalej,)]TJ /F8 7.97 Tf 6.78 -1.79 Td[(iisthesurfaceconcentrationofspeciesiwhichisresponsiblefortheprecipitationreaction,andniisthereactionorder.Sincetheanodicdissolutionandcathodicreactionsareassumedtotakeplaceonlyontheuncoveredregion,thepartialcurrentisintroducedasafunctionofsurfacecoverageby[ 53 ] i0=i 1)]TJ /F15 11.955 Tf 11.96 11.36 Td[(Xjj!(2)wherejisthefractionofthesurfacecoveredbyscalej. 27

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Thiscalculationcanachievegoodagreementwithexperimentalresultsoveracertainrangeoftemperature,however,itneglectstheinuenceoflocalizedcorrosionresultingfromthepartiallycoveredmetal.Therefore,thissimpliedmodelshouldbeextendedtopredictcorrosioninsidepipelinesinoilandgasindustry. 28

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CHAPTER3NUMERICALAPPROACHUnder-depositcorrosionisatypeoflocalizedcorrosionthatcanleadtoacatastrophicconsequenceingasandoilindustry.ManymodelsforcorrosioninuidscontainingCO2havebeendeveloped[ 5 10 ].Mostempiricalandsemi-empiricalmodelscanprovideaccurateinterpolationpredictionforcorrosionrate;however,morecomplicatedcorrectionfactorsarerequiredtoaccountforsituationswhereextrapolationorpredictionfails.Othermodelsbasedonmechanisticmodelspre-denedtheanodicandcathodicregionsandmay,therefore,introduceserrorsinthepredictedcorrosionrate.Inthiswork,inordertoconstructamodelprovidingmoreinformationofthecorrosionmechanisms,thepresenceofanodicandcathodicregionswasdeterminedbylocalpotentialdistributioncausedbytheformationofdifferentialcells.Theobjectofthisworkistopresenta2-Daxi-symmetricmathematicalmodelthatcanbeusedtoinvestigateconditionsunderwhichtheonsetofunder-depositcorrosionoccursinbothaerated(containingdissolvedO2)andde-aerated(containingdissolvedCO2)media.Modeldevelopmentispresentedsequentially.Incontrasttopreviousmodels,thelocationofanodicandcathodicregionswasnotassumedapriori,butwasrathertheresultofthenumericalsimulation.Thepresentstudysimulatesthecorrosionprocessbyusingfundamentalphysicalandelectrochemicallawswhichprovidingaframeworkofunderstandingtheconcentrationvariationofreactingspeciesinthesolution.Theadvantageofthismodelisitcanbeadaptedtoothertypesofcorrosionwithsimplemodications.MorecomplicatedreactionsinvolvingseveralreactionspeciessuchasHS)]TJ /F1 11.955 Tf 10.4 -4.34 Td[(andH2Scanbeaddressedinfuturework. 3.1ProblemDescriptionManyattemptshavebeenmadetoproposeamechanismforthelocalizedcorrosionresultingfromthebreakdownofscalesonametalsurfaceforthesolutionscontainingO2andCO2.However,severalessentialpropertiesofunder-depositcorrosionsuch 29

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astheformationofconcentrationcellsandthetransportofreactingspeciesthroughadiffusionbarrierhavebeenneglected.Inaddition,atransientanalysisisrequiredtopredictthetimeframeforcorrosionfailure. 3.1.1AeratedSolution(O2)Generally,oxygenhashighafnitytoformastableoxidelayer(normallymicrometersthick),whichprovidesinertnesstocorrosiveenvironment.However,theprotectionagainstthecorrosivemediacanbedestroyedbythechemicalorphysicalheterogeneityatthesurfacesuchasacrackoradefect.Oncethecriticalacidicationandthecorrosionpotentialarereached,localizedcorrosionisinitiated.Metaldissolutionpromotesthegrowthofpitswithoxygenreductionoutsidethepit.Sandsandprecipitationsformedinthebulksolutioncanbetransportedbytheuidsinpipelinesanddepositonthemetalsurface.Underthedeposit,iftheoxygenconcentrationbecomessignicantlylessthanthatinthebulk,differentialaeration(orconcentration)cellsaregenerated.Inthiswork,thecorrosionrateisproportionaltothedifferencebetweentheoxygencontentinunder-depositareaandbulksystem.Therefore,understandingthediffusionprocessinthediffusionbarrierisagoodstartingpointforstudyingtheunder-depositcorrosionsincethediffusionofreactingspeciesthroughaporousdepositlayerhasagreateffectonthelocalizedcorrosionbeneathdeposit.Modeldevelopmenttookplacethroughasequenceofmodelsofincreasingcomplexities.Tounderstandtheconcentrationvariationofoxygenontheelectrodesurface,oxygendiffusiontoametalsurfaceinawaterdropletwasmodeled.Metaldissolutioncanoccurintheregionunderdepositwhereoxygenisdepleted.Oxygenreductiontakesplaceintheoxygen-richarea.Theanodicandcathodicregionareformedduetothelocalenvironmentaldifferences.TwotypesofprecipitateswereassumedtobeforminthesolutionscontainingdissolvedO2:Fe(OH)2wasassumedtobetheprimaryprecipitateandlessprotectiveandtheotheroneisFe(OH)3whichwasassumedtobeprotective.Tomodelthediffusionprocessthroughadiffusionbarrier 30

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suchasaporouslayer,alayerofloosely-packedsandscanbeemployedinsteadofthewaterdroplet.Inordertoconstructageneralmodelwhichcanprovideanmoreaccuratepredictionoftheunder-depositcorrosionrate,differentenvironment,typesofdeposit,andreactionsinvolvingseveralreactionspeciessuchasCO2,HCO)]TJ /F3 7.97 Tf 0 -7.97 Td[(3,andCO2)]TJ /F3 7.97 Tf -4.43 -7.97 Td[(3weretakenintoaccountinthede-aeratedmedia. 3.1.2De-aeratedSolution(CO2)Inpipelines,sandsandprecipitationsformedinthebulksolutioncanbetransportedbytheuidsanddepositonthemetalsurface.Under-depositcorrosionmodelinaeratedsolutionprovidesusaframeworktostudyconditioncontaingCO2andtheapproachesusedinO2modelswereimplementedintotheCO2models.UnderthedepositinasolutioncontainingCO2,iftheCO2concentrationbecomessignicantlylessthanthatinthebulk,concentrationcellsaregenerated.Thedissociationproduct(i.e.,CO)]TJ /F3 7.97 Tf 6.59 0 Td[(23)hashighafnitytoformastablecarbonatelayer,whichprovidesinertnesstocorrosiveenvironment.However,theunevendistributionofthedepositionofcorrosionproductscouldformanotherconcentrationcellandenhancecorrosionrate.Modeldevelopmenttakesplacethroughasequenceofstepsofincreasingcomplexities.Forsolutionscontainingdissolvedcarbondioxide,itcomprisesCO2,HCO)]TJ /F3 7.97 Tf 0 -7.97 Td[(3,CO2)]TJ /F3 7.97 Tf -4.43 -7.97 Td[(3,H+,andOH)]TJ /F1 11.955 Tf 7.09 -4.33 Td[(.Achangeofacidityistheconsequenceofthedissociationofcarbonicacid.TheratesofdissociationsarealsodependantonthevalueofpH;therefore,acorrectedpredictionoflocalpHvalueisimportant.IncomparisonwithstrongacidsolutionsatthesamepH,thecorrosionrateisenhancedinde-aeratedsolutionscontainingdissolvedCO2[ 34 ].Alargenumberofmechanismsofthedissociationofcarbonicacidhavebeenproposed[ 6 7 9 34 54 57 ].Twomechanismswerestudiedinthiswork.Nordsveen[ 47 ]consideredthepresenceofH2CO3anditscontributiontothecathodicreactionbyincludingthehydrationreactionofCO2.ThedirectreductionofH2CO3andH+arebothconsideredinthecathodicreactionsoftheCO2models.ThehydrationofCO2andtwodissociationstepsofH2CO3are 31

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alsoconsidered.TounderstandtheconcentrationvariationofH+ontheelectrodesurfaceandthetwodissociationstepsofH2CO3,CO2diffusiontoametalsurfaceinawaterdropletwasmodeled.Remitaetal.[ 58 ]assumedthereactionrateoftherstdeprotonationreactionisfastenoughtoignoretheexistenceofH2CO3andonlyhydrogenevolutionwasconsideredinthecathodicreaction.MetaldissolutionwaspreferredintheregionunderdepositwhereH2CO3andH+weredepleted.UntilenoughFe2+wasgeneratedandreactedwithCO2)]TJ /F3 7.97 Tf -4.44 -7.98 Td[(3toformFeCO3,(s)inthecenter.Tomodelthediffusionprocessthroughadiffusionbarriersuchasaporouslayer,alayerofloosely-packedsandssurroundedbyabulksolutionwasemployedinsteadofasinglewaterdroplet. 3.2SimulatedGeometriesAnite-elementmethod( COMSOLMultiphysics )wasusedtosolvetheequationsgoverningthissystem.Thecoordinatesr,,andareshowninFigure 3-1 .Undertheassumptionofaxialsymmetry,anone-quarter-ellipsegeometrywasusedtorepresentawaterdropletsaturatedwithairandplacedonthemetalsurfaceasshowninFigure 3-2A [ 24 ].Ageometryconsistingoftwoconcentricquarter-ellipseswasusedtorepresentthedepositssurroundedbyabulksolution,asisshowninFigure 3-2B 3.2.1DropletModelAsarststeptowarddevelopmentofamodelforunder-depositcorrosioninsidepipelines,amodelisbeingdevelopedtosimulatetheEvan'sdrop.AschematicpresentationofthedropletonametalsurfaceisshowninFigure 3-2A .Undertheassumptionofaxiallysymmetry,aquarter-ellipsegeometrycouldbeusedtoreducethenumberofnodesneededtorepresentthedroplet.Thelocalpotentialdistributioncangiverisetoformationofdistinctcathodicandanodicregionsonthemetalsurface.Thelengthofthediffusionpathforoxygenorcarbondioxidefromtheair-waterinterfaceto 32

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Figure3-1. Thecoordinatesr,,andusedinthecalculations. A BFigure3-2. Schematicrepresentationsof:A)awaterdropletonametalsurface;andB)depositssurroundedbybulksolutions. 33

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metalsurfacevariesalongtheradiusofthemetalcoveredbythedroplet,thuscreatingalocalpotentialdistribution. 3.2.2DepositModelThedropletmodelisextended.Thescaleisenlargedtosimulateadefectresultedfromthecorrosivedepositsandsandsinsideapipeline.Thegeometrycomprisingtwoconcentricquarter-ellipseswasusedtorepresentthedepositssurroundedbyabulksolution,asshowninFigure 3-2B .Thecoveredareaistreatedasaporousmedium,andtheeffectivediffusioncoefcientofspeciesDi,coveredwasexpressedbytheBruggemanapproximation[ 50 59 ] Di,covered=1.5Di(3)whereistheporosityvolumefraction.Inthebulkregion,theeddydiffusivitytermD(t)iwasusedtoaccountfortheinuenceofturbulenceonmasstransfer[ 47 51 ]. Di,bulk=Di+D(t)i(3)Thecorrespondingexpressionsfortheeddydiffusivityare D(t)i =8>>>>><>>>>>:4A1z+3)]TJ /F6 11.955 Tf 11.95 0 Td[(5A2z+4 1)]TJ /F6 11.955 Tf 11.95 0 Td[(4A1z+3+5A2z+4forz+20z+ 2.5)]TJ /F6 11.955 Tf 11.95 0 Td[(1forz+>20(3)whereisthekinematicviscosityandz+=p 0=isthedimensionlessdistancefromthemetalsurface.Thewallshearstress0wasassignedavalueof0.16Painthiswork.ItisbelowthecriticalvaluethattheinitiationoflocalizedcorrosionatcarbonsteelisindependentofowunderCO2corrosioncondition[ 60 ].Thedissolvedgaswasassumedtodiffusefromthetopofthedroplet.Theconcentrationdistributionofthedissolvedgaswasdependentonthediffusivitydifferencesbetweenthedeposit(Di,covered)andthebulkregion(D(t)i).Theconcentrationgradientforreactingspecies(O2)alongthemetalsurfacedecreasesduetotheturbulentow,asshowninFigure 3-3 34

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Thebluecurvesrepresenttheconcentrationdistributioninlaminarowandtheblack Figure3-3. TheconcentrationdistributionofO2alongthemetalsurface.Thebluecurvesrepresenttheconditionswithlaminarowandtheblackonesrepresenttheconditionswithturbulentow. onesarefortheturbulentconditions. 3.3TheMathematicalModelDevelopmentBothDropletandDepositmodelswereperformedatappliedpotentialsandcorrosionpotential(open-circuitcondition).Intherst,thecorrosionreactionisrepresentedbyactive-passivetransitionbehaviorswithappliespotentialsinpolarizationcurves.Aftershowingthepolarizationcurvesbyapplyinganouterpotential,theinducedcathodicandanodicregionsundertheopen-circuitconditionarepresented.Thenetcurrentiszerobyassumingtheanodicandcathodicreactionsreachequilibriumstatewhichmeanstheanodicandcathodicreactionratesareequal.Themodelscalculatedfortheopen-circuitpotentialwereexpendedbyaddingtimevariable.Theaeratedsolutionwasactedasthesteppingstonefortheunder-depositmodeland 35

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thede-aeratedsolutioncanbecalculatedbyreplacingthereactingspeciesandthehomogeneousreactions.Bothaeratedandde-aeratedsolutionswerecalculatedundertwosimulatedgeometries(DropletandDepositmodels).Themodeldevelopmentcanbeclassiedintothreecategories:electrochemicalreactions,conservationequationsandchemicalreactions,andactive-passivetransitioninbothaeratedandde-aeratedsolutions. 3.3.1AeratedSolution(O2)Thedissolvedgasvariedfortheaeratedandde-aeratedsolutions,therefore,cathodicreactionswereassumeddifferentlyforeachsolution.Onlyoxygenwasinvolvedinthecathodicreactionfortheaeratedsolution.Waterdissociationandformationofferroushydroxideweretreatedashomogeneousreactionsinthismodel;whereastheformationofferrichydroxidewasassumedtohaveacontributioninanodicreactions. 3.3.1.1ElectrochemicalReactionsThecathodicreactionwasassumedtobethereductionofoxygen O2+2H2O+4e)]TJ /F2 11.955 Tf 10.41 -4.94 Td[(!4OH)]TJ /F1 11.955 Tf 142.54 -4.94 Td[((3)Thecorrespondingcurrentdensitycanbeexpressedas iO2,k=)]TJ /F5 11.955 Tf 9.3 0 Td[(i0,O2[cO2(0)]exp)]TJ /F6 11.955 Tf 10.49 8.09 Td[(2.303 O2(m)]TJ /F6 11.955 Tf 11.95 0 Td[(0)(3)whereO2istheTafelslopefortheoxygenreductionreaction.ThecurrentdensityiO2isafunctionofboththelocalpotentialdrivingforce(m)]TJ /F6 11.955 Tf 12.28 0 Td[(0)andtheconcentrationofoxygenattheelectrodesurfacecO2(0).Theequilibriumpotentialforoxygenreduction(UO2)wasincludedinthevalueoftheexchangecurrentdensity.Sinceironisamajorcomponentinpipelinesteel,theanodicreactionwasassumedtobeirondissolution,givenby[ 43 44 ] Fe!Fe2++2e)]TJ /F1 11.955 Tf 169 -4.93 Td[((3) 36

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Theanodicreactionshowingtheactivetopassivetransitionwasassumedtobetheconsequenceoftheformationofcorrosiveproducts.Intheabsenceoflmsassociatedwithcorrosionproducts,thekineticcurrentdensityikO2,Fewasgivenby ikO2,Fe=(i0O2,Fe)exp"2.303 FeO2(m)]TJ /F6 11.955 Tf 11.95 0 Td[(0)#(3)wheretheequilibriumpotentialforirondissolution(UFe)wasincludedinthevalueoftheexchangecurrentdensity.Passivationwasincludedinthekineticexpressionbyallowingthefractionalsurfacecoverageofcorrosiveproductstoweightthecontributionsofthepassiveandactivecurrentdensities.Thus, iFe=(1)]TJ /F4 11.955 Tf 11.95 0 Td[()ik,Fe+()ip,Fe(3)whereip,Feisthevalueofthepassivecurrentdensity.ThevalueofwasdeterminedfromthereactionsconsideredinSection 3.3.1.3 3.3.1.2ConservationEquationsandChemicalReactionsThemodelaccountedforconservationofionicspeciesanddissolvedoxygen,i.e., @ci @t=rNi+Ri(3)whereRiisthenetrateofproductionofspeciesibyhomogeneousreactions.Ricanbeexpressedas Ri=kfYrcr(r,,t))]TJ /F5 11.955 Tf 11.95 0 Td[(kbYpcp(r,,t)(3)wherekfandkbaretherateconstantsforforwardandbackwardreactions,andcrandcparetheconcentrationsforreactantsandproducts.ThehomogeneousreactionsconsideredindissolvedO2solutionsincludedthedissociationofwater H2OH++OH)]TJ ET BT /F1 11.955 Tf 433.45 -609.97 Td[((3) 37

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Therateofproductionwasexpressedby RH+=ROH)]TJ /F6 11.955 Tf 10.07 -.3 Td[(=kb(Kw)]TJ /F5 11.955 Tf 11.95 0 Td[(cH+cOH)]TJ /F6 11.955 Tf 6.75 -.3 Td[()(3)whereKwisthedissociationconstantforwater.Theformationoftheferroushydroxideprecipitateswasassumedtofollow Fe2++2OH)]TJ /F17 11.955 Tf 17.05 -5.15 Td[(Fe(OH)2(s) (3) Thereactionratewasexpressedas RFe(OH)2=8>>>><>>>>:0ifFe(OH)20kFe(OH)2[cFe(OH)2(cOH)2])]TJ /F6 11.955 Tf 11.95 0 Td[(Ksp,Fe(OH)2ifFe(OH)2>0(3)whereKsp,Fe(OH)2isthesolubility-productconstant.Undertheassumptionthatconvectioncanbeneglected,theconcentrationofdissolvedoxygeninsidethedepositfollowed @cO2 @t=r2cO2(3)Theuxofspeciesiwasexpressedby Ni=)]TJ /F6 11.955 Tf 16.07 8.08 Td[(F RTziDicir)]TJ /F5 11.955 Tf 11.96 0 Td[(Dirci(3)Theconvectiontermwasnotemployedinthiswork.Withinthedeposit,thevelocitywasassumedtobeequaltozero;whereas,outsidethedeposit,diffusionwasassumedtobeenhancedbyturbulentow,asisdescribedlater.Thepotentialdistributionwasassumedtobegovernedby r(r)+FXizir(Dirci)=0(3)Equation 3 revertstoLaplace'sequationunderassumptionofauniformconductivityandintheabsenceofconcentrationgradients. 38

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3.3.1.3Active-PassiveTransitionExperimentalpolarizationcurvesformaterialsshowingactive-passivetransitionsoftenshow,inaddition,theappearanceofanapparentmass-transfer-limitedcurrentplateau.Thisplateaumaybeassociatedwithdepositionoflms.Therststepwasapplyinganarticialfunctiontodescribeactive-passivetransitions.Inageneralcasewhereanelectrochemicalreactionislimitedbytheniterateoftransportofreactingspeciestothereactionsurface,thecurrentmaybeformulatedas 1 iFe=1 ik,Fe+1 ilim,Fe(3)whereilimisthemass-transfer-limitedcurrentdensityandthekineticcurrentdensity,ik,isthekineticcurrentdensityasshowninEquation 3 .Passivationwasincludedinthekineticexpressionbyassigningapotential-dependentweightingfactortopassiveandactivecurrentdensities.Thus, iFe=(1)]TJ /F4 11.955 Tf 11.95 0 Td[()i0,Fe24exp2.303 Fe(m)]TJ /F6 11.955 Tf 11.95 0 Td[(0)]TJ /F5 11.955 Tf 11.95 0 Td[(UFe) 1+i0,Fe ilim,Feexp2.303 Fe(m)]TJ /F6 11.955 Tf 11.96 0 Td[(0)]TJ /F5 11.955 Tf 11.96 0 Td[(UFe)35+()ipO2,Fe(3)whereipO2,Feisthevalueofthepassivecurrentdensity,and =exp((m)]TJ /F6 11.955 Tf 11.96 0 Td[(0)]TJ /F5 11.955 Tf 11.96 0 Td[(Ep)) 1+exp((m)]TJ /F6 11.955 Tf 11.95 0 Td[(0)]TJ /F5 11.955 Tf 11.95 0 Td[(Ep))(3)isthepotential-dependentweightingfactor.InEquation 3 ,theparametercontrolsthesteepnessofthepotentialchangecorrespondingtotheactive-passivetransitionandEpisthepotentialatwhichthetransitionoccurs.Therelationshipbetweencurrentdensityandchargedspeciesisgivenby i=FXiziNi(3)Atthemetalsurface,theuxesofFe2+andOH)]TJ /F1 11.955 Tf 10.41 -4.34 Td[(canbewrittenas NFe2+j=90o=iFe(0) F(3) 39

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and NOH)]TJ /F2 11.955 Tf 6.76 -.3 Td[(j=90o=)]TJ /F5 11.955 Tf 10.49 8.08 Td[(iO2(0) F(3)Thefunctionshowsthemass-transfer-limitedcurrentplateauandtheresultsareshowninChapter 4 .Therefore,asimilarapproachwasemployedtocorrelatetheformationofprecipitatesandthetransitions.Theactive-passivationtransitionwasassumedtoberesultedfromtheformationofprecipitatesinthefollowingcalculation.Thesurfacecoverageofprecipitates()istheratioofthesurfaceareaofdepositedprecipitatestothesurfaceareaofmetalsurfaceandcanbeexpressedas Fe(OH)2=AFe(OH)2 Ametalsurface=cFe(OH)2Vmesh=(s,Fe(OH)2) Amesh(3)whereVmeshandAmesharethevolumeandsurfacearea,respectively,ofthedeformedmeshdirectlyabovethemetalsurface,s,Fe(OH)2isthedensityofprecipitatedFe(OH)2,andisthemonolayerthickness.ThesurfacecoveragewasemployedtocalculatethepassivecurrentdensityassociatedwiththeformationofFe(OH)2.Forirondissolution,theanodiccurrentdensitywasmodiedfollowing iFeO2=8>>>><>>>>:(1)]TJ /F4 11.955 Tf 11.96 0 Td[(Fe(OH)2)ikO2,Fe+(Fe(OH)2)ipO2,FeifFe(OH)21ipO2,FeifFe(OH)2>1(3)whereipO2,Fe,theexchangecurrentdensityforirondissolutionatthemetal-precipitateinterface,isextremelysmallascomparedtoi0O2,Feforirondissolutionatthemetalsurface.Thesurfacecoverage()actsasthesameasthefunctioninEquation 3 .Asimilarapproachwasemployedfortheoxygenreductionreactionwiththeexceptionthatthereactiononthepassivelayersurfacewaslessinhibitedtoaccountforthesemiconductivenatureoftheprecipitates.Theoxygenreductioncouldstilloccurontheprecipitatesandtheirondissolutionwasassumedtobepassivated.Thecathodic 40

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currentdensitywasexpressedas iO2=8>>>><>>>>:)]TJ /F15 11.955 Tf 11.29 9.68 Td[((1)]TJ /F4 11.955 Tf 11.96 0 Td[(Fe(OH)2)iO2,k+(Fe(OH)2)ioxide,O2ifFe(OH)21)]TJ /F5 11.955 Tf 9.3 0 Td[(ioxide,O2ifFe(OH)2>1(3)whereioxide,O2=(ip0O2,Fe)exp2.303 FeO2(m)]TJ /F6 11.955 Tf 11.95 0 Td[(0),thepassivecurrentdensityforoxygenreductionatprecipitate-solutioninterface.Theferrousionscanfurtherreactwithhydrogenionsandoxygentoproduceferricions,andtheferricionsreactswithhydroxideionstoproduceferricoxide.Thenetreactioncanbewrittenas Fe(OH)2+OH)]TJ /F17 11.955 Tf 17.05 -4.94 Td[(Fe(OH)3(s)+e)]TJ ET BT /F1 11.955 Tf 433.45 -260.98 Td[((3) Thecurrentdensitywasexpressedas iFe(OH)3 F=ka(cOH)]TJ /F6 11.955 Tf 6.75 -.3 Td[()exp2.303 Fe3+)]TJ /F6 11.955 Tf 5.48 -9.68 Td[(m)]TJ /F6 11.955 Tf 11.96 0 Td[(0)]TJ /F6 11.955 Tf 11.96 0 Td[(UFe(OH)3 (3) ThesurfacecoverageresultedfromtheformationofFe(OH)3canbecalculatedbyusingEquation 3 .TheinuenceofFe(OH)3ontheanodicreactioncanbedescribedasfollows iFeO2=8>>>><>>>>:(1)]TJ /F4 11.955 Tf 11.96 0 Td[(Fe(OH)3)ikO2,Fe+(Fe(OH)3)ipO2,FeifFe(OH)31ipO2,FeifFe(OH)3>1(3) 3.3.2De-AeratedSolution(CO2)TwomechanismswerestudiedinthesolutionscontainingdissolvedCO2:OnewasproposedbyRemita,itwasundertheassumptionthattherstdissociationstepofH2CO3wasfastenoughtoignoretheexistenceofH2CO3.Onlyhydrogenevolutioncontributedinthecathodicreaction[ 58 ].AnothermechanismwasproposedbyNordsveen[ 47 ],thepresenceofH2CO3andbothhydrogenevolutionsdirectlyfrom 41

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hydrogenionsandH2CO3wereallincluded.Waterdissociation,hydrationofcarbondioxide,twodissociationstepsofcarbonicacid,andformationofferrouscarbonateweretreatedashomogeneousreactionsinthismodel. 3.3.2.1ElectrochemicalReactionsThemaincathodicreactionswereassumedtobethehydrogenevolutionfromH+onlyinthemechanismproposedbyRemita[ 58 ]. 2H++2e)]TJ /F2 11.955 Tf 10.4 -4.93 Td[(!H2(3)Thecorrespondingcurrentdensityofindividualcathodicreactioncanbeexpressedas iR,H2=)]TJ /F5 11.955 Tf 9.3 0 Td[(iR0,H2[cH+(0)]0.5exp)]TJ /F6 11.955 Tf 10.49 8.09 Td[(2.303 H2(m)]TJ /F6 11.955 Tf 11.95 0 Td[(0)(3)wherecH2istheTafelslopeforthehydrogenevolutionreactionfromH+.ThecurrentdensityiR,H2isafunctionofboththelocalpotentialdrivingforce(m)]TJ /F6 11.955 Tf 12.88 0 Td[(0)andtheconcentrationofhydrogenionsattheelectrodesurfacecH+(0).ThemaincathodicreactionswereassumedtobethehydrogenevolutionfromH+andH2CO3inthemechanismproposedbyNordsveen[ 47 ]. 2H2CO3+2e)]TJ /F2 11.955 Tf 10.4 -4.94 Td[(!H2+2HCO)]TJ /F3 7.97 Tf 0 -7.97 Td[(3(3)Thecorrespondingcurrentdensityofindividualcathodicreactioncanbeexpressedas iN,H2=iN0,H2cH+(0) cH+,ref0.5"10(m)]TJ /F9 5.978 Tf 5.75 0 Td[(0)]TJ /F9 5.978 Tf 5.75 0 Td[(UH2,ref) bH2)]TJ /F6 11.955 Tf 11.95 0 Td[(10)]TJ /F6 11.955 Tf 5.76 -1.66 Td[((m)]TJ /F9 5.978 Tf 5.76 0 Td[(0)]TJ /F9 5.978 Tf 5.75 0 Td[(UH2,ref) bH2#(3)wherebH2isthecoefcientforthehydrogenevolutionreactionfromH+.ThecurrentdensityiN,H2isafunctionofboththelocalpotentialdrivingforce(m)]TJ /F6 11.955 Tf 12.87 0 Td[(0)andtheconcentrationofhydrogenionsattheelectrodesurfacecH+(0). iH2CO3=i0,H2CO3hcH+(0) cH+,refi)]TJ /F3 7.97 Tf 6.59 0 Td[(0.5hcH2CO3(0) cH2CO3,refi"10(m)]TJ /F9 5.978 Tf 5.75 0 Td[(0)]TJ /F9 5.978 Tf 5.76 0 Td[(UH2CO3,ref) bH2CO3)]TJ /F6 11.955 Tf 11.96 0 Td[(10)]TJ /F6 11.955 Tf 5.75 -1.66 Td[((m)]TJ /F9 5.978 Tf 5.76 0 Td[(0)]TJ /F9 5.978 Tf 5.76 0 Td[(UH2CO3,ref) bH2CO3#(3) 42

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wherebH2CO3istheTafelslopeforthehydrogenevolutionreactionfromH2CO3.ThecurrentdensityiH2CO3isafunctionofboththelocalpotentialdrivingforce(m)]TJ /F6 11.955 Tf 12.11 0 Td[(0)andtheconcentrationofcarbonicacidattheelectrodesurfacecH2CO3(0).InthedissolvedCO2solution,irondissolutionwasassumedtobetheanodicreactionandcanbeexpressedinEquation 3 [ 43 44 ].TheanodicreactionshowingtheactivetopassivetransitionwasassumedtobetheconsequenceoftheformationofFeCO3.Intheabsenceoflmsassociatedwithcorrosionproducts,thekineticcurrentdensityikwasgivenby ikCO2,Fe=i0CO2,Fe"10(m)]TJ /F9 5.978 Tf 5.75 0 Td[(0)]TJ /F9 5.978 Tf 5.75 0 Td[(EFe2+,ref) bFe2+)]TJ /F6 11.955 Tf 11.96 0 Td[(10)]TJ /F6 11.955 Tf 5.75 -1.66 Td[((m)]TJ /F9 5.978 Tf 5.76 0 Td[(0)]TJ /F9 5.978 Tf 5.75 0 Td[(EFe2+,ref) bFe2+#(3)Passivationwasconsideredinthekineticexpressionbyincludingthefractionalsurfacecoverageofcorrosiveproductstoweightthecontributionsofthepassiveandactivecurrentdensities.Thus,Equation 3 canalsobeapplied.ThevalueofwasdeterminedfromtheformationofferrouscarbonateandwillbeshowninSection 3.3.2.3 3.3.2.2ConservationEquationsandChemicalReactionsThehomogeneousreactionsconsideredinthepresentmodelincludedthedissociationofwater,asdescribedinEquation 3 andEquation 3 .ForthemechanismsproposedbyRemita,thehomogeneousreactionsinvolvingCO2,HCO)]TJ /F3 7.97 Tf 0 -7.97 Td[(3,andCO2)]TJ /F3 7.97 Tf -4.43 -7.97 Td[(3areasfollows CO2(g)CO2 (3) Theconcentrationofdissolvedcarbondioxidewasexpressedby cCO2(aq)bulk=HCO2PCO2(3) 43

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whereHCO2istheHenry'sconstantforCO2andPCO2isthepartialpressureofCO2inthegasphase. H2O+CO2(aq)HCO3)]TJ /F6 11.955 Tf 9.75 -5.15 Td[(+H+ (3) Therateofproductionwasexpressedby RHCO)]TJ /F9 5.978 Tf 0 -6.19 Td[(3=)]TJ /F5 11.955 Tf 9.3 0 Td[(RCO2(aq)=k1cCO2(aq))]TJ /F5 11.955 Tf 11.96 0 Td[(k)]TJ /F3 7.97 Tf 6.58 0 Td[(1cH+cHCO)]TJ /F9 5.978 Tf 0 -6.19 Td[(3(3)wherek1andk)]TJ /F3 7.97 Tf 6.59 0 Td[(1arethekineticconstants. HCO3)]TJ /F17 11.955 Tf 17.05 -5.15 Td[(CO32)]TJ /F6 11.955 Tf 9.74 -5.15 Td[(+H+ (3) Therateofproductionwasexpressedby RCO2)]TJ /F9 5.978 Tf -3.32 -6.19 Td[(3=k2cHCO)]TJ /F9 5.978 Tf 0 -6.18 Td[(3)]TJ /F5 11.955 Tf 11.96 0 Td[(k)]TJ /F3 7.97 Tf 6.58 0 Td[(2cH+cCO2)]TJ /F9 5.978 Tf -3.33 -6.19 Td[(3(3)wherek2andk)]TJ /F3 7.97 Tf 6.59 0 Td[(2arethekineticconstants.TherateofproductionforH+wasexpressedby RH+=RHCO)]TJ /F9 5.978 Tf 0 -6.19 Td[(3+RCO2)]TJ /F9 5.978 Tf -3.33 -6.19 Td[(3(3)ForthemechanismsforhydrationcarbondioxideandthedissociationofH2CO3intheaqueoussolution,themechanismisproposedbyNordsveen[ 47 ]assumedthedissociationisatwo-stepsequenceasfollowing CO2(g)CO2 (3) Theconcentrationofdissolvedcarbondioxidewasexpressedby cCO2(aq)bulk=KsolPCO2(3)whereKsolisthekineticconstantsforthedissolvedrate. H2O+CO2(aq)H2CO3 (3) 44

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H2CO3H++HCO3)]TJ ET BT /F1 11.955 Tf 433.45 -11.96 Td[((3) Therateofproductionwasexpressedby RH2CO3=)]TJ /F5 11.955 Tf 9.3 0 Td[(kf,cacH2CO3+kb,cacH+cHCO)]TJ /F9 5.978 Tf 0 -6.19 Td[(3(3)wherekf,caandkb,caaretherateconstants. HCO)]TJ /F3 7.97 Tf 0 -8.1 Td[(3CO2)]TJ /F3 7.97 Tf -4.43 -8.1 Td[(3+H+ (3) Allthespeciescanbeexpressbyusingamatrixformasfollows[ 47 ]: 0BBBBBBB@RH2CO3RH+RHCO)]TJ /F9 5.978 Tf 0 -6.19 Td[(3RCO2)]TJ /F9 5.978 Tf -3.33 -6.18 Td[(31CCCCCCCA=0BBBBBBB@)]TJ /F6 11.955 Tf 9.3 0 Td[(10111)]TJ /F6 11.955 Tf 9.3 0 Td[(1011CCCCCCCA0B@kf,cacH2CO3)]TJ /F5 11.955 Tf 11.95 0 Td[(kb,cacH+cHCO)]TJ /F9 5.978 Tf 0 -6.18 Td[(3kf,bicHCO)]TJ /F9 5.978 Tf 0 -6.19 Td[(3)]TJ /F5 11.955 Tf 11.96 0 Td[(kb,bicH+cCO2)]TJ /F9 5.978 Tf -3.33 -6.19 Td[(31CA(3)ThetwodissociationreactionsarerelativelyslowcomparedwiththehydrationofCO2andthereforetheequilibriumstatescouldbeassumed.H2CO3wasdeterminedbythediffusionofCO2andhydrationreactionwhileHCO)]TJ /F3 7.97 Tf 0 -7.98 Td[(3,CO2)]TJ /F3 7.97 Tf -4.43 -7.98 Td[(3,H+,andOH)]TJ /F1 11.955 Tf 10.41 -4.34 Td[(aresatisedwiththeequilibriumstatesofwaterdissociationanddissociationofcarbonicacid.Thereactingspeciesi(i=HCO)]TJ /F3 7.97 Tf 0 -7.97 Td[(3,CO2)]TJ /F3 7.97 Tf -4.43 -7.97 Td[(3,H+,andOH)]TJ /F1 11.955 Tf 7.09 -4.34 Td[()isgovernedbythediffusionequationwithappliedboundaryconditions.Inordertoforcetheequilibriumconditionsbeingsatised,thefeedbackloopconceptwasappliedtoeliminatethediscrepancyasfollows. Extrawa=Kw)]TJ /F5 11.955 Tf 11.95 0 Td[(cOH)]TJ /F5 11.955 Tf 6.75 -.3 Td[(cH+(3) Extraca=KcacH2CO3)]TJ /F5 11.955 Tf 11.95 0 Td[(cHCO)]TJ /F9 5.978 Tf 0 -6.18 Td[(3cH+(3) Extrabi=KbicHCO)]TJ /F9 5.978 Tf 0 -6.19 Td[(3)]TJ /F5 11.955 Tf 11.95 0 Td[(cCO2)]TJ /F9 5.978 Tf -3.32 -6.19 Td[(3cH+(3) 45

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Thenewvariables,Extrawa,Extraca,andExtrabiwereincorporatedintodiffusionequationsasareactionratethatconsumesadditionalspeciesandgeneratesmorefordepletion.Themechanismoftheironcarbonateprecipitationwasassumedtofollow Fe(s)+2H2CO3,(aq)Fe2++H2,(g)+2HCO)]TJ /F3 7.97 Tf 0 -8.72 Td[(3,(aq)ifS1Fe2++CO2)]TJ /F3 7.97 Tf -4.43 -7.97 Td[(3FeCO3,(s)ifS>1(3)whereS=cFe2+cCO2)]TJ /F9 5.978 Tf -3.32 -5.92 Td[(3 Ksp,FeCO3ThereactionratewasexpressedasafunctionofSasfollowing RFeCO3=8>>>><>>>>:0ifS1Apexp()]TJ /F3 7.97 Tf 6.59 0 Td[(Ea RT)(A V)Ksp,FeCO3(S)]TJ /F6 11.955 Tf 11.95 0 Td[(1)ifS>1(3)whereApisaconstant,Eaistheactivationenergy,Risuniversalgasconstant,Aisthemetalsurfacearea,Visthesolutionvolume,andKsp,FeCO3isthesolubility-productconstant.Undertheassumptionthatconvectioncanbeneglected,theconcentrationofdissolvedcarbondioxideinsidethedepositfollowed @cCO2 @t=r2cCO2(3)TheuxofspeciesiwasexpressedbyEquation 3 ThepotentialdistributionwasassumedtobegovernedbyEquation 3 3.3.2.3Active-PassiveTransitionAtthemetalsurface,theuxofFe2+canbeexpressedbyEquation 3 ;whereastheuxesofH+,H2CO3,andHCO)]TJ /F3 7.97 Tf 0 -7.97 Td[(3canbewrittenas NH+j=90o=)]TJ /F5 11.955 Tf 10.49 8.09 Td[(iH2(0) F(3) 46

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NH2CO3j=90o=)]TJ /F5 11.955 Tf 10.49 8.08 Td[(iH2CO3(0) F(3)and NHCO)]TJ /F9 5.978 Tf 0 -6.18 Td[(3j=90o=iH2CO3(0) F(3)Thesurfacecoverage()istheratioofthesurfaceareaofdepositedprecipitatestothesurfaceareaofmetalsurfaceandcanbeexpressedas FeCO3=AFeCO3 Ametalsurface=cFeCO3Vmesh=(s,FeCO3) Amesh(3)wheres,FeCO3isthedensityofprecipitateFeCO3.ThesurfacecoveragewasemployedtocalculatethepassivecurrentdensityduetotheformationofFeCO3.Forirondissolution,theanodiccurrentdensitywasusingthesameapproachasdescribedinEquation 3 .Asimilarapproachwasemployedforthehydrogenreductionreactionswiththeexceptionthatthereactiononthepassivelayersurfacewaslessinhibitedtoaccountforthesemiconductivenatureoftheprecipitates.Thecathodiccurrentdensitywasexpressedas ic=iH2+iH2CO3(3) iH2CO2=8>>>><>>>>:)]TJ /F6 11.955 Tf 11.29 -.17 Td[([(1)]TJ /F4 11.955 Tf 11.96 0 Td[(FeCO3)iH2+(FeCO3)ip,H2]ifFeCO31ip,H2ifFeCO3>1(3)where ip,H2=ip0,H2cH+(0) cH+,ref0.5"10(m)]TJ /F9 5.978 Tf 5.76 0 Td[(0)]TJ /F9 5.978 Tf 5.76 0 Td[(EH2,ref) bH2)]TJ /F6 11.955 Tf 11.96 0 Td[(10)]TJ /F6 11.955 Tf 5.75 -1.67 Td[((m)]TJ /F9 5.978 Tf 5.76 0 Td[(0)]TJ /F9 5.978 Tf 5.76 0 Td[(EH2,ref) bH2#(3) 47

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thepassivecurrentdensityforhydrogenevolutionfromH+atprecipitate-solutioninterface. iH2CO3CO2=8>>>><>>>>:)]TJ /F6 11.955 Tf 11.29 -.17 Td[([(1)]TJ /F4 11.955 Tf 11.95 0 Td[(FeCO3)iH2CO3+FeCO3ip,H2CO3]ifFeCO31ip,H2CO3ifFeCO3>1(3)where ip,H2CO3=ip0,H2CO3hcH+(0) cH+,refi)]TJ /F3 7.97 Tf 6.59 0 Td[(0.5hcH2CO3(0) cH2CO3,refi"10(m)]TJ /F9 5.978 Tf 5.75 0 Td[(0)]TJ /F9 5.978 Tf 5.76 0 Td[(EH2CO3,ref) bH2CO3)]TJ /F6 11.955 Tf 11.96 0 Td[(10)]TJ /F6 11.955 Tf 5.75 -1.67 Td[((m)]TJ /F9 5.978 Tf 5.76 0 Td[(0)]TJ /F9 5.978 Tf 5.76 0 Td[(EH2CO3,ref) bH2CO3#(3)thepassivecurrentdensityforhydrogenevolutionfromH2CO3atprecipitate-solutioninterface. 48

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CHAPTER4RESULTSANDDISCUSSIONSTheresultsforsystemscontainingO2andCO2aresequentiallypresentedinthefollowing. 4.1AeratedModel-O2Thecorrosionrateisstronglydependentonthepresenceandpropertiesofsurfacelmsandassociatedchemicalandelectrochemicalreactions.Inthepresentwork,ironwasusedasthereactingspeciesasitistheprinciplematerialusedingasandoilpipelines.Iron,chromium,nickel,titaniumandtheiralloysalsodemonstrateactive-passivetransitions,whichinthispaperwasassumedtobetheconsequenceofthepresenceofthecorrosiveproducts.Undercertainconditions,thesurfaceunderthedropcanexperiencebothactiveandpassivebehavior.Toexploresimultaneousactiveandpassivebehavior,parameterswerechosentoallowtheopen-circuitpotentialdistributiononthemetalsurfacetoencompasstheregionbetweenpassiveandactivebehavior.Theopen-circuitpotentialisthepotentialatwhichthereisnocurrentandtheequilibriumpotentialofacorrodingsystem.TheparametersusedinthecalculationsarepresentedinTable 4-1 4-2 ,and 4-3 .Fortheone-quarter-ellipsegeometry(seeO2Evans'DropinTable 4-2 ),theshiftofpassivatedareacanbeillustratedbychangesofthetotalcurrentdensity.ThelocalpHdifferencescanonlybeobservedwhenFe(OH)2reactsfurtherwithOH)]TJ /F1 11.955 Tf 10.41 -4.34 Td[(toformFe(OH)3.Thetwo-concentric-quarter-ellipsegeometry(seeO2DepositinTable 4-3 )wasusedtoevaluateunder-depositcorrosionandtheinuencesofboththeformationofprecipitatesandthesurroundingturbulentow[ 28 29 ].Theresultsarepresentedintermsoftwosetsofcalculations.TheparametersmarkedLessActiveinTable 4-3 leadtoacorrosionproductthatstillallowsirondissolutionandoxygenreductionreact;whereas,theparametersmarkedPassiveinTable 4-3 leadtoacorrosionproductthatstronglyinhibitsanodicreaction.Theresultswereusedtostudytheinuenceofthe 49

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protectivenessandpropertiesofprecipitates.Otherinuentialfactors,suchasmeshsize,dropeccentricity,dropsize...etcwillbediscussedinSection 4.1.3 Table4-1. Parametersforthesimulationsinvolvinganodicreactionsthatareactive-passivecontrolledwithfunction. Active-Passive(function) i0,O21.0010)]TJ /F3 7.97 Tf 6.59 0 Td[(3A/cm2DO21.9710)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/s5.5010)]TJ /F3 7.97 Tf 6.59 0 Td[(4S/mcO2(r0)0.284mol/m3UO20.401VO20.09V/decadei0,Fe1.0010)]TJ /F3 7.97 Tf 6.59 0 Td[(3A/cm2Fe0.01V/decadeUFe)]TJ /F6 11.955 Tf 9.3 0 Td[(0.44VEp0.1Vip,Fe5.0010)]TJ /F3 7.97 Tf 6.59 0 Td[(5A/cm2ilim7.0010)]TJ /F3 7.97 Tf 6.59 0 Td[(1A/cm2550 4.1.1Active-PassiveTransitionCalculatedlocalanodicandcathodiccurrentdensitiesfortheactive-passivecontrolledinvolvingfunctionareshowninFigure 4-1 .Figure 4-2A showstheconcentrationdistributionofoxygenalongthemetalsurfacewithappliedpotentialastheparameter.ThepotentialdistributionatthemaximumconcentrationgradientwasplottedinFigure 4-2B andthecathodicreactionisdominatedattheperipherywhiletheanodicreactionispreferredatthecenter.Forthemodelsassumingthepassivationresultedfromtheformationofprecipitate,themass-transfer-limitedplateauisalsoshowninFigure 4-3 asfunctionsofelectrodepotentialforthedepositmodelatapositionr=0.Theanodicreactionshowsanactive-passivetransitioninwhichtheactivecorrosionisreplacedbypassivebehaviorastheelectrodepotentialincreases.Theresultingsurface-averagedcurrentispresentedinFigure 4-4 asindividualpointscorrespondingtoeachappliedpotential.TheroleoflmformationinpassivationisevidentinFigure 4-5 inwhichdistributionsofcurrentdensity(Figure 4-5A )andsurfacecoverage(Figure 50

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Table4-2. ParametersfortheO2simulationsinone-quarterellipsegeometryinvolvingsurfacecoverage. O2Evans'Drop(one-quarterellipseasshowninFigure 3-2A ) i0,O27.010)]TJ /F3 7.97 Tf 6.58 0 Td[(7A/cm2DO21.9710)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/scO2(1)0.284mol/m3O20.12V/decadeioxide,O27.010)]TJ /F3 7.97 Tf 6.58 0 Td[(7A/cm2i0,Fe1.0010)]TJ /F3 7.97 Tf 6.59 0 Td[(8A/cm2DFe2+7.2010)]TJ /F3 7.97 Tf 6.59 0 Td[(6cm2/sFe0.06V/decadeip,Fe1.0010)]TJ /F3 7.97 Tf 6.59 0 Td[(12A/cm24.4210)]TJ /F3 7.97 Tf 6.59 0 Td[(4S/mDH+9.3110)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sDOH)]TJ /F6 11.955 Tf 18.71 -.3 Td[(5.2610)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sDNO)]TJ /F9 5.978 Tf 0 -6.18 Td[(31.9010)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sDK+1.9810)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/skb,H2O500Kw1.0010)]TJ /F3 7.97 Tf 6.59 0 Td[(8mol2/m6Ksp,Fe(OH)24.8710)]TJ /F3 7.97 Tf 6.59 0 Td[(60.2(1.5)Vmesh7.2010)]TJ /F3 7.97 Tf 6.59 0 Td[(6cm3/s3.4g/cm37.010)]TJ /F3 7.97 Tf 6.58 0 Td[(9mAmesh7.2010)]TJ /F3 7.97 Tf 6.59 0 Td[(6cm2/sKsp,Fe(OH)36.310)]TJ /F3 7.97 Tf 6.58 0 Td[(38 4-5B )arepresentedatdifferenttimesfortheEvans'dropmodel.Atshorttimes,duetothegreateraccessibilityofoxygenatthewater-airinterface,thecathodicreactiondominatedattheperipheryofthedroplet.ConcentrationofO2att=10swasplottedinFigure 4-6 ,whichshowsO2isabundantintheperipheryregionanddecientatthecenter.Ferrousionsareproducedbytheanodicreactionandreactwithhydroxideionsproducedbythecathodicreactiontoformferroushydroxides.Fe(OH)2furtherreactswiththeexcessOH)]TJ /F1 11.955 Tf 10.41 -4.34 Td[(toformferrichydroxides,whichisaaninsolubleironhydroxidecomplexandcouldslowlydehydratetoformrust.ThePourbaixdiagrampresentedinFigure 4-7 showsthatFe(OH)3isthemajorprecipitateunderthegivenconditions.The 51

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Table4-3. ParametersfortheO2simulationsintwo-quarterellipsegeometryinvolvingsurfacecoverage.. O2Deposit(two-quarterellipseFigure 3-2B )LessActivePassive i0,O21.010)]TJ /F3 7.97 Tf 6.59 0 Td[(4A/cm23.3810)]TJ /F3 7.97 Tf 6.59 0 Td[(8A/cm2DO21.9710)]TJ /F3 7.97 Tf 6.58 0 Td[(5cm2/s1.9710)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/scO2(1)0.284mol/m30.284mol/m3O20.2V/decade0.2V/decadeioxide,O27.010)]TJ /F3 7.97 Tf 6.59 0 Td[(5A/cm22.6310)]TJ /F3 7.97 Tf 6.59 0 Td[(10A/cm2i0,Fe5.010)]TJ /F3 7.97 Tf 6.59 0 Td[(10A/cm21.010)]TJ /F3 7.97 Tf 6.59 0 Td[(9A/cm2DFe2+7.2010)]TJ /F3 7.97 Tf 6.58 0 Td[(6cm2/s7.2010)]TJ /F3 7.97 Tf 6.59 0 Td[(6cm2/sFe0.5V/decade0.5V/decadeip,Fe4.9610)]TJ /F3 7.97 Tf 6.58 0 Td[(11A/cm22.5410)]TJ /F3 7.97 Tf 6.59 0 Td[(15A/cm24.4210)]TJ /F3 7.97 Tf 6.58 0 Td[(4S/m4.4210)]TJ /F3 7.97 Tf 6.59 0 Td[(4S/mDH+9.3110)]TJ /F3 7.97 Tf 6.58 0 Td[(5cm2/s9.3110)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sDOH)]TJ /F6 11.955 Tf 18.71 -.29 Td[(5.2610)]TJ /F3 7.97 Tf 6.58 0 Td[(5cm2/s5.2610)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sDNO)]TJ /F9 5.978 Tf 0 -6.19 Td[(31.9010)]TJ /F3 7.97 Tf 6.58 0 Td[(5cm2/s1.9010)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sDK+1.9810)]TJ /F3 7.97 Tf 6.58 0 Td[(5cm2/s1.9810)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/skb,H2O500500Kw1.0010)]TJ /F3 7.97 Tf 6.58 0 Td[(8mol2/m61.0010)]TJ /F3 7.97 Tf 6.59 0 Td[(8mol2/m6Ksp,Fe(OH)24.8710)]TJ /F3 7.97 Tf 6.58 0 Td[(64.8710)]TJ /F3 7.97 Tf 6.59 0 Td[(60.2(1.5)0.2(1.5)Vmesh7.2010)]TJ /F3 7.97 Tf 6.58 0 Td[(6cm3/s7.2010)]TJ /F3 7.97 Tf 6.59 0 Td[(6cm3/s3.4g/cm33.4g/cm37.010)]TJ /F3 7.97 Tf 6.59 0 Td[(9m7.010)]TJ /F3 7.97 Tf 6.59 0 Td[(9mAmesh7.2010)]TJ /F3 7.97 Tf 6.58 0 Td[(6cm2/s7.2010)]TJ /F3 7.97 Tf 6.59 0 Td[(6cm2/sKsp,Fe(OH)36.310)]TJ /F3 7.97 Tf 6.59 0 Td[(386.310)]TJ /F3 7.97 Tf 6.59 0 Td[(381.0510)]TJ /F3 7.97 Tf 6.58 0 Td[(6m2/s1.0510)]TJ /F3 7.97 Tf 6.59 0 Td[(6m2/sA11.097210)]TJ /F3 7.97 Tf 6.59 0 Td[(41.097210)]TJ /F3 7.97 Tf 6.59 0 Td[(4A23.29510)]TJ /F3 7.97 Tf 6.59 0 Td[(63.29510)]TJ /F3 7.97 Tf 6.58 0 Td[(6 alkaliregionprevailsattheedgeareaastheresultsofcathodicreactionpredominatingatperipherywhenthecentershowsacidityastheconsequenceoftheformationofprecipitates,asshowninFigure 4-8 .TheformationofFe(OH)3canbeindicatedbythesurfacecoveragewhichisshowninFigure 4-5B .Astimeincreases,thesurfacecoverageexceededthefullcoveragevalue,i.e.,=1,startingfromtheperipheryandextendingtothecenteruntilthesurfacewasallcoveredwithprecipitates.TheanodicreactionwasinhibitedbytheformationofFe(OH)3,butthecathodicreactionwasstill 52

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Figure4-1. Calculatedpolarizationcurvesshowinganodicandcathodiccurrentdensitiesforthemodelsimulatingtheactive-passivetransitionwithfunction. active.Theactive-passivetransitionwas,therefore,aconsequenceoftheformationofprecipitates. 4.1.2TheEffectofPrecipitationAlltypesofprecipitatesformedundertheconditionsthatironimmersedindissolvedO2solutionsareshowninFigure 4-7 .Theactive-passivetransitionswasassumedtobeaconsequenceoftheformationofFe(OH)2andFe(OH)3.Fe(OH)2wasassumedtobeformedascolloidalgelonthemetalsurfaceandfurtherreactswithOH)]TJ /F1 11.955 Tf 10.4 -4.34 Td[(toformsolidFe(OH)3depositingonthesurface.Therefore,theformationofferroushydroxideresultsinless-protectiveprecipitatesandtheanodicreactionwaspartiallyinhibitedbyit.InSection 4.1.2.2 ,Fe(OH)3passivatesthereactingsurfaceasitdepositsonthemetalsurface. 53

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A BFigure4-2. Resultscalculatedforthemodelsimulatingtheactive-passivetransitionwithfunction:A)radialdistributionsofO2alongthemetalsurfacewithappliedpotentialastheparameter;andB)falsecolorrepresentationofpotentialforthemaximumconcentrationgradientofO2. Figure4-3. Calculatedpolarizationcurvesshowinganodicandcathodiccurrentdensitiesatr=0forthedepositmodel. 54

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Figure4-4. Surface-averagedcurrentdensitycalculatedforthedepositmodelatr=0asafunctionofappliedpotential. 4.1.2.1Less-ProtectivePrecipitates(Fe(OH)2)Inthiscalculation,thepassivationwasassumedtoresultfromtheless-protectiveprecipitates,Fe(OH)2.Fe(OH)3accumulatesontopofFe(OH)2and,therefore,doesnotplayapartinpassivation.TheinuenceofturbulentowcanbeobservedinFigure 4-9A .Att=92s,theconcentrationofoxygenattheelectrodesurfaceapproachedzero.Attimest>92s,thetransportofoxygentothereactingsurfaceintheregionwithturbulentowwasgreaterthaninthecoveredregion.Asaconsequence,thecathodicreactionwasfavorableinthesurroundingarea,whiletheanodicreactiondominatedinthecenter.TheshiftfromactivetopassivebehaviorwasobservedastheresultofthedevelopmentofprecipitateswhichisshowninFigure 4-9B .Figure 4-10B representsthetotalcurrentdensitydistributionafterwholemetalsurfaceiscoveredwithprecipitates. 55

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A BFigure4-5. RadialdistributionscalculatedfortheEvans'dropmodelwithtimeasaparameter:A)totalcurrentdensity;andB)fractionalsurfacecoverage. 56

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Figure4-6. ThefalsecolorrepresentationofconcentrationdistributionsofoxygenforthedropletmodelcontainingO2att=10s. ThecorrespondingchangesofpotentialdistributionarepresentedinFigure 4-11 .Themaximumpotentialdifferenceof0.1Vwasobtainedwhentheouterregionwascompletelycoveredwithprecipitates(t=96s).Theprecipitatescontinuedtoaccumulateonthemetalsurface,andthecorrosionremainedactiveunderthepredenedcoveredregionasaresultofthedifferentialoxygenationcelldrivenbythesurroundingturbulentow.Thestabilityoflmsintheexposureofirontoaeratedwateratroomtemperaturemaybeinuencedbythesolubilityofferroushydroxide.Asthelmgrewandreducedtherateofcorrosion,theexchangeofuidwiththebulksolutioncausedtheconcentrationsofFe2+andOH)]TJ /F1 11.955 Tf 10.4 -4.34 Td[(tofallbelowthesuper-saturatedvalue,thusfavoringdissolutionofthelm.ThedissolutionrateofFe(OH)2wasassumedtobedependantonthesolution 57

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Figure4-7. APourbaixdiagramforironanditsvariousspeciesat25C.ThediagramsweregeneratedbyCorrosionAnalyzer1.3Revision1.3.33byOLISystemsInc. composition,temperature,andpressure.Twodifferentvaluesofsolubilityproductwereusedinthispaper.Whitman[ 61 ]calculatedthesolubilityproductofFe(OH)2tobe8.710)]TJ /F3 7.97 Tf 6.59 0 Td[(14intheferrous-ionconcentrationin20%potassiumhydroxidesolution.AvalueofFe(OH)2=8.010)]TJ /F3 7.97 Tf 6.59 0 Td[(16wasobtainedbyLeussing[ 62 ]atatemperatureof25C.TheimpactofthesolubilityproductvaluecanbeshowninFigure 4-12 inwhichfractionalsurfacecoveragecalculatedforthedepositmodelispresentedasafunctionofradialpositionwithtimeasaparameter.Thelmdissolvedforthesolubilityproductof8.710)]TJ /F3 7.97 Tf 6.58 0 Td[(14,butremainedintactforKsp=8.010)]TJ /F3 7.97 Tf 6.59 0 Td[(16.CarefulexaminationofFigure 4-12B showsaslightthinningatr=1mm.Forthiscondition,theanodicreactionoccurredneartheintersectionofpredenedporousmediumandbulksolution.ThepotentialandcurrentdistributionsareplottedinFigure 4-13A and 4-13B 58

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Figure4-8. RadialdistributionsofpHcalculatedfortheEvans'dropmodel. 4.1.2.2ProtectivePrecipitates(Fe(OH)3)FerroushydroxidescanreactfurtherwiththeexcessOH)]TJ /F1 11.955 Tf 7.08 -4.34 Td[(,producingthesecondaryprecipitates,ferrichydroxides.Ferroushydroxidewasassumedtobeintheformofacolloidalgelthatdidnotpassivatethemetalsurface.Onlyferrichydroxideswasassumedtocompletelyshieldtheactivemetalsurface.Thecathodicreactionwaspreferredinthesurroundingarea,whiletheanodicreactionwasfavoredinthecenter,asshowninFigure 4-14 .Asaconsequenceofprotectiveprecipitates,thecorrosionratedecreasedafterthemetalsurfacewasfully-covered.However,fortheprotectivecase,theinuenceofsolubilityproductvalueisnotsignicant.Whenthesecondaryprecipitates(Fe(OH)3)isthesourceofpassivation,thechangeofsolubilityproductonlyaffectedthetimeframeforbuildingupdeposits,asshowninFigure 4-15 .TheprecipitatesaccumulatefasterwhenthesolubilityproductissmallerasshowninFigure 4-15B 59

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A BFigure4-9. Radialdistributionsofcalculatedforthedepositmodelwithtimeasaparameter:A)totalcurrentdensityandB)fractionalsurfacecoverage. 60

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A BFigure4-10. Representationsof:A)potentialdistributionalongtheelectrodesurfacewithtimeasaparameter;B)totalcurrentdensitydistributionalongtheelectrodesurfaceatt=1600scalculatedforthedepositmodel. A BFigure4-11. PotentialdistributionsfortheresultspresentedinFigure 4-9 :A)potentialalongtheelectrodesurfacewithtimeasaparameter;B)falsecolorrepresentationofpotentialfort=96swithsuperimposedcurrentlines. 61

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A BFigure4-12. Radialdistributionsoffractionalsurfacecoveragecalculatedforthedepositmodelwithtimeasaparameter:A)Ksp,Fe(OH)2=8.710)]TJ /F3 7.97 Tf 6.58 0 Td[(14;andB)Ksp,Fe(OH)2=8.010)]TJ /F3 7.97 Tf 6.59 0 Td[(16. 62

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A BFigure4-13. Potentialdistributions:A)alongtheelectrodesurfaceatt=72000sB)forthefalsecolorrepresentationandstreamlinerepresentationofcurrentdensityatt=72000scalculatedforthedepositmodel. 4.1.3OtherInuencesTheconcentrationgradientofdissolvedgasisthedrivingforceofthegalvaniccouplingreactions.TheconcentrationdistributionofO2inthesolutionisrelevantwiththedistancebetweenthewater-airinterfaceandthemetalsurface.Thesizeandtheshapeofthedropletwerediscussedintherstapproach,whichisthemodelapplyingfunctiontosimulatetheactive-passivetransitions.Themeshqualityisalsodiscussedsincenermeshresultsinmoreaccuratesolutionsandrequiresmoretimeandcosts.Asthedevelopmentofmodelprogresses,thearearatioofcoveredregionandthebaremetalsurfacefortheDepositmodelalsoplaysanimportantroleandtheresultswillbeshown. 4.1.3.1ComparisonbetweenAnalyticSolutionsandNumericalSolutionsTheperformanceofthenumericallycomputationalmethodisevaluatedbyusingabenchmark.Inthiscase,calculationsofatemperatureproleforunsteady-stateheatconductionwasused. 63

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A BFigure4-14. Radialdistributionsofcalculatedforthedepositmodelwithtimeasaparameter:A)totalcurrentdensityandB)fractionalsurfacecoverage. 64

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A BFigure4-15. Radialdistributionsoffractionalsurfacecoveragecalculatedforthedepositmodelwithtimeasaparameter:A)Ksp,Fe(OH)3=6.310)]TJ /F3 7.97 Tf 6.58 0 Td[(36;andB)Ksp,Fe(OH)3=6.310)]TJ /F3 7.97 Tf 6.59 0 Td[(38. Assumingtheconvectioncanbeneglectedandthetimevariableisconsidered,theconcentrationofdissolvedoxygencanbeexpressedastheconservationequationinanone-dimensionalformas @cO2 @t=DO2r2cO2(4)Thetemperatureforheatconductioncanbedescribedby @T @t=r2T(4)TheanalyticsolutionsforbothEquation 4 andEquation 4 canbeobtainedbyusingthesameapproach.Therefore,theoxygenconcentrationprolefordiffusionequation 65

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issimilartothetemperatureproleforheatconduction.Section 4.1.3.1 providesacomparisonbetweentheconcentrationproleforunsteady-statediffusionequationusingthenite-elementpackage(COMSOLMulti-physics)withthoseusingananalyticmethod.TheiterationprocedureintheanalyticsolutionwasconductedinMATLABsoftware.Arectangulargeometrywasusedastheslab,andtheentiredomainwasgovernedbydiffusionequationgivenasEquation 4 .Aty=b,theconcentrationsweresetatsaturatedconcentrationc1.Bothanalyticandnumericaldatawereanalyzedbydimensionlessvariables.Asolidslaboccupyingthespacebetweeny=)]TJ /F5 11.955 Tf 9.3 0 Td[(bandy=+bwasinitiallyatconcentrationc0.Attimet=0thesurfacesaty=baresuddenlyraisedtoc1andmaintainedthatvalue[ 63 ].GoverningequationisgivenbyEquation 4 .TheslabremainsatT0att=0.Fort>0,concentrationraisestoT1aty=b.Fourimportantmethodsareusedtosolveunsteady-statediffusionproblemsanalytically:combinationofvariables,separationofvariables,sinusoidalresponse,andLaplacetransform.Theanalyticsolutionofconcentrationcanbewrittenasafunctionofyininniteseriesgivenby c1)]TJ /F5 11.955 Tf 11.95 0 Td[(c c1)]TJ /F5 11.955 Tf 11.96 0 Td[(c0=21Xn=0()]TJ /F6 11.955 Tf 9.29 0 Td[(1)n (n+1 2)exp[)]TJ /F6 11.955 Tf 9.3 0 Td[((n+1 2)22t b2]cos(n+1 2)y b(4)TheconcentrationprolewascalculatedbyiterativemethodsinMATLABasshowninFigure 4-16A ;whereas,theconcentrationproleforunsteady-statediffutioninasphereofradiusaisalsocalculatedandpresentedinFigure 4-16B .Itindicatesthedifferencebetweentheanalyticandnumericalsolutionsissmall.TheerrorsdenedastherelativepercentagedifferencebetweenthemagnitudecalculatedbytheanalyticsolutionandthatbythenumericalsolutioninCOMSOL.Table 4-4 demonstratesthetrendoftheerrordecreasingwithsmallertimestepsandhighermeshdensity. 4.1.3.2DropSizeAsdiscussedinSection 4.1.3.2 ,thecathodicreactionislimitedbymasstransferofoxygen.Thediffusionofoxygenisaffectedbythesizeofthewaterdropletbecausethe 66

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A BFigure4-16. Concentrationprolesforunsteady-statediffusion.Theinitialconcentrationoftheslabisc0,andc1istheconcentrationimposesatthesurfacesfortimet>0.A)foraslabofnitethickness2b;andB)inasphereofradiusa. Table4-4. Errorsfordifferentmeshdensityandtimestep. CoarseMeshwith1sTimeStep(%)FinerMeshwith1msTimeStep(%) =0.0108.780.210.0413.740.210.116.120.040.220.530.150.489.620.330.609.282.45161.110.55 dropsizecontrolsthedistancebetweenthewater-airinterfaceandthemetalsurface.AsshowninFigure 4-17 ,themass-transfer-limitedcurrentdensityincreaseswithdecreasingdropradius.Themass-transfer-limitedplateauismoreapparentwhenthedropletsizeislarger;therefore,1mmwasusedfortheradiusofthedroplet. 4.1.3.3DropEccentricityTheshapeofdropletalsoaffectsthediffusion-limitedcurrentdensity.Astheshapeofthedropletbecomesmoreelliptical,thevariationinconcentrationofoxygenalongtheelectrodesurfaceisreducedandtheaveragemass-transfer-limitedcurrentdensityofoxygenisincreased.TheeffectisillustratedinFigure 4-18 ,whichillustratesthat 67

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Figure4-17. Cathodicpolarizationcurveforoxygenreductionwithdropradiusasaparameter. limitingdiffusioncurrentrisesasthedropletbecomesmoreelliptical.Theeccentricity1wasappliedinthefollowingmodelsinordertoobtainlargeconcentrationgradientofdissolvedgas. 4.1.3.4MeshDensityAnermeshdensityprovidesmoreaccurateresults,butrequiresmorecalculationtime.Asthenumberofelementsinthemeshisdoubledandthesizeofelementsattheperipheralisreduced,concentrationpolarizationcurveshifts.CathodicandanodicpolarizationcurvesarepresentedinFigure 4-19 withmeshdensityasaparameter.Theanodicreactionisunaffectedbythechangeinmeshdensity;whereas,thecathodicreactionisinuencedathighercurrentdensities,wheretheinuenceofmasstransferismoreapparent.Anermeshisneededtomodeltheregionsalongtheelectrodesurfaceandatthemetal-liquid-airinterfacewheretheoxygenconcentrationgradients 68

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Figure4-18. Cathodicpolarizationcurveforoxygenreductionwithdropshapeasaparameter. arelargest.Possiblesourcesoftheerrorsincludethemeshdensityandthechosentimestep.Finermeshmightberequired 4.1.3.5DepositModel-InuenceofUncoveredRegionTheratiooftheradiuscoveredbythedepositstotheouterbulksolutionregionradius(rs=rb)asshowninFigure 4-20 wasstudiedsinceitcouldbeaninuentialfactorfortheinitiationofpitting.AsillustratedinFigure 4-21 ,thepotentialvariationdependedstronglyonrs=rb.Alargepotentialvariationatlargevaluesofrs=rbasshowninFigure 4-11A mayresultinpittingand,thus,under-depositcorrosion. 4.2De-aeratedModel-CO2TheobjectiveofSection 4.2 istoextendtheaeratedunder-depositcorrosionmodeltothecaseofde-aeratedconditionscontainingdissolvedCO2.ItemploysthesameapproachastheO2modeltodealwiththeconcentrationgradientofionicspecies, 69

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Figure4-19. Cathodicandanodicpolarizationcurveswithmeshdensityasaparameter. Figure4-20. SchematicrepresentationoftheDepositmodel. 70

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Figure4-21. Calculatedpotentialdistributionsalongelectrodesurfaceatthetimeofmaximumpotentialvariationwithrs=rbasaparameter. morecomplexhomogeneousandheterogeneousreactions,andtheturbulentowbehaviorinthede-aeratedbulkregion.ForcorrosionintheconditioncontainingCO2,thedeprotonationofcarbonicspeciesplaysanimportantrole.Themechanismofdissociationofcarbonicspecieshasbeenstudiedsince1975andlargenumberofmechanismshavebeenproposed.Inthiswork,twomechanismsofthehydrationanddissociationofCO2wereemployedandstudied.OnewasproposedbyRemita[ 58 ],whichassumedthattherstdissociationstepofH2CO3wasfastenoughtoignoretheexistenceofH2CO3.HydrogenevolutionevolveddirectlyfromH+wasassumedtobetheonlycontributionofthecathodicreaction.ThemodeladoptedbythemechanismproposedbyRemita[ 58 ]isreferredasRemita'sModelinthefollowingcontents.AnothermechanismwasproposedbyNordsveen[ 47 ],whichincreasedthecomplexityofthismodelbyinvolvingthehydrationofCO2,twodissociationstepsofH2CO3,andcathodicreactionswereassumedtobethehydrogenevolutionevolvedfrombothH+andH2CO2. 71

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ThemodeladoptedbythemechanismproposedbyNordsveen[ 47 ]isreferredasNordsveen'sModelinthefollowingcontents.ThesolutioncontainingdissolvedCO2showsthat,withsmallmodications,theunder-depositmodelcanbeadaptedtootherconditionsbyaddingorremovingspeciesandreactions.Undercertainconditions,themetalsurfaceunderthedissolvedCO2solutionscanexperiencebothactiveandpassivebehaviorcausedbyFeCO3.Toexploretheseconditions,parametersweretakenfromthevaluesRemita[ 58 ]andNordsveen[ 47 ]usedtoallowtheopen-circuitpotentialdistributiononthemetalsurfacetoencompasstheregionbetweenpassiveandactivebehavior.TheparametersusedinthecalculationsarepresentedinTable 4-5 ,Table 4-6 ,and 4-7 .ModelsforsolutionscontainingdissolvedCO2involvingmorecomplicatedreactionsthanthesolutionscontainingdissolvedO2;therefore,stabilityissuewasobserved.Asmallertimestepandnermeshsizeweresuggestedtoobtainmorestableresults. 4.2.1TheComparisonsbetweenMechanismsProposedbyRemitaandNordsveenTwocorrosionmechanismsforthesolutioncontainingdissolvedCO2wereemployedandcomparedintheone-quarter-ellipsegeometry.ThemechanismproposedbyRemitawasundertheassumptionthattheexistenceofH2CO3canbeneglectedandonlythehydrogenevolutiondirectlyfromH+playsaroleinthecathodicreaction.NordsveentooktheexistenceofH2CO3intoaccountandassumedthathydrogenevolvedfrombothH+andH2CO3.ThemechanismproposedbyNordsveendescribedtherateconstantsasafunctionoftemperature,pressure,andthecompositionofasolution.Inthecontrary,forthemechanismproposedbyRemita,therateconstantsaretheexperimentalresultsat25Cand1atm.Inthiswork,bothmodelswerecalculatedat25Cand1atmtocomparetheresults.Ittook40timeslongerfortheNordsveen'smodeltoobtainthesamesurfacecoverageofFeCO3comparedwiththeRemita'smodel. 72

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Table4-5. ParametersforthesimulationsinCO2DepositmodelwiththemechanismproposedbyRemita. CO2DropletModel(one-quarterellipseFigure 3-2A ) i0,H24.010)]TJ /F3 7.97 Tf 6.58 0 Td[(3A/cm2H20.07V/decadei0,Fe3.8910)]TJ /F3 7.97 Tf 6.59 0 Td[(3A/cm2bFe2+0.06V/decadeip,Fe1.0010)]TJ /F3 7.97 Tf 6.59 0 Td[(16A/cm2DH+9.3110)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sDOH)]TJ /F6 11.955 Tf 18.71 -.3 Td[(5.2610)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sDFe2+0.7210)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sDO21.9710)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sDNO)]TJ /F9 5.978 Tf 0 -6.19 Td[(31.9010)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sDK+1.9810)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sDCO21.9610)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sDHCO)]TJ /F9 5.978 Tf 0 -6.19 Td[(31.0510)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sDCO2)]TJ /F9 5.978 Tf -3.32 -6.18 Td[(39.2010)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sKw9.0210)]TJ /F3 7.97 Tf 6.59 0 Td[(9mol2/m6Kca1.7810)]TJ /F3 7.97 Tf 6.59 0 Td[(1mol/m3Kbi4.9410)]TJ /F3 7.97 Tf 6.59 0 Td[(8mol/m3HCO23.310)]TJ /F3 7.97 Tf 6.58 0 Td[(5mol/cm3barT298.15KR8.3143J/molKcCO2(0)PCO2HCO2mol/m3cHCO)]TJ /F9 5.978 Tf 0 -6.18 Td[(3(0)0.113mol/m3cCO2)]TJ /F9 5.978 Tf -3.32 -6.19 Td[(3(0)4.710)]TJ /F3 7.97 Tf 6.58 0 Td[(8mol/m3cH+(0)0.142mol/m3cOH)]TJ /F6 11.955 Tf 6.76 -.3 Td[((0)7.0410)]TJ /F3 7.97 Tf 6.59 0 Td[(8mol/m3cFe2+(0)0mol/m3Ksp,FeCO31.510)]TJ /F3 7.97 Tf 6.58 0 Td[(11PCO21bar ForthemechanismwithouttheexistenceofH2CO3,thetotalcurrentdensityalongthemetalsurfaceaftertheformationofprecipitatewereshowninFigure 4-22A .ThecalculatedtotalcurrentdensitybasedonthemechanismsproposedbyNordsveenwereplottedinFigure 4-22B .ThecorrespondingpotentialwereplottedinFigure 4-23 whichindicatesthatthecorrosionoccurredinthewholecoveredregionforbothmechanisms.Thecathodicreactionwasfavoredintheregionclosetowhere 73

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A BFigure4-22. Thedistributionoftotalcurrentdensityatt=470sforthemechanismsA)proposedbyRemitaB)proposedbyNordsveenoftheCO2Depositmodel. A BFigure4-23. Thepotentialdistributionsatt=470sforthemechanismsA)proposedbyRemitaB)proposedbyNordsveenoftheCO2Depositmodel. 74

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Table4-6. ParametersforthesimulationsinCO2DropletmodelwiththemechanismproposedbyNordsveen. CO2DropletModel(one-quarterellipseFigure 3-2A ) i0,H25.010)]TJ /F3 7.97 Tf 6.59 0 Td[(6A/cm2T298.15Ki0,H2CO36.010)]TJ /F3 7.97 Tf 6.59 0 Td[(6A/cm2R8.3143J/molKcH+,ref0.1mol/m3s3.9g/cm3cH2CO3,ref0.1mol/m37.010)]TJ /F3 7.97 Tf 6.58 0 Td[(9mbH20.12V/decadecCO2(0)PCO2KsolbH2CO30.2V/decadecH2CO3(0)0.08215mol/m3EH2,ref0.12V/decadecHCO)]TJ /F9 5.978 Tf 0 -6.19 Td[(3(0)0.12102mol/m3EH2CO3,ref0.2VcCO2)]TJ /F9 5.978 Tf -3.32 -6.18 Td[(3(0)4.944910)]TJ /F3 7.97 Tf 6.58 0 Td[(8mol/m3i0,Fe110)]TJ /F3 7.97 Tf 6.59 0 Td[(4A/cm2cH+(0)0.12102mol/m3bFe2+0.04V/decadecOH)]TJ /F6 11.955 Tf 6.76 -.3 Td[((0)7.45110)]TJ /F3 7.97 Tf 6.59 0 Td[(8mol/m3EFe2+ref)]TJ /F6 11.955 Tf 9.3 0 Td[(0.44VcFe2+(0)0mol/m3ip,Fe1.0010)]TJ /F3 7.97 Tf 6.59 0 Td[(1A/cm2Ksp,FeCO31.2910)]TJ /F3 7.97 Tf 6.59 0 Td[(11DH+9.3110)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sAp1.771012DOH)]TJ /F6 11.955 Tf 18.71 -.3 Td[(5.2610)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sEa64.9KJ/molDFe2+0.7210)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sPCO21105PaDO21.9710)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sionic0DNO)]TJ /F9 5.978 Tf 0 -6.19 Td[(31.9010)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sKsol0.031841DK+1.9810)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sDCO21.9610)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sDH2CO32.0010)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sDHCO)]TJ /F9 5.978 Tf 0 -6.18 Td[(31.0510)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sDCO2)]TJ /F9 5.978 Tf -3.32 -6.19 Td[(39.2010)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sKw9.0210)]TJ /F3 7.97 Tf 6.59 0 Td[(9mol2/m6Khy2.5810)]TJ /F3 7.97 Tf 6.59 0 Td[(3Kca1.7810)]TJ /F3 7.97 Tf 6.59 0 Td[(1mol/m3Kbi4.9410)]TJ /F3 7.97 Tf 6.59 0 Td[(8mol/m3khy,f2.6010)]TJ /F3 7.97 Tf 6.59 0 Td[(2/skhy,b10.08/s thecorrosionoccurredforthemechanismproposedbyRemita;whilethewholeoutersurfaceactedasacathodeforthemechanismproposedbyNordsveen.ThecathodiccurrentdensitiesofthehydrogenevolutionfromH2CO3andH+wereplottedinFigure 4-24 .Figure 4-24B indicatesthesignicantcontributionofhydrogenevolutionfromH2CO3incathodicreactions.TheparametersappliedinRemita'smodelwerebasedonexperimentsconductedatroomtemperatureandpressure;whilemostof 75

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Table4-7. ParametersforthesimulationsinCO2DepositmodelwiththemechanismproposedbyNordsveen. CO2DepositModel(two-quarterellipseFigure 3-2B ) i0,H25.010)]TJ /F3 7.97 Tf 6.59 0 Td[(6A/cm2T298.15Ki0,H2CO36.010)]TJ /F3 7.97 Tf 6.59 0 Td[(6A/cm2R8.3143J/molKcH+,ref0.1mol/m3s3.9g/cm3cH2CO3,ref0.1mol/m37.010)]TJ /F3 7.97 Tf 6.58 0 Td[(9mbH20.12V/decadecCO2(0)PCO2KsolbH2CO30.2V/decadecH2CO3(0)0.08215mol/m3EH2,ref0.12V/decadecHCO)]TJ /F9 5.978 Tf 0 -6.19 Td[(3(0)0.12102mol/m3EH2CO3,ref0.2VcCO2)]TJ /F9 5.978 Tf -3.32 -6.18 Td[(3(0)4.944910)]TJ /F3 7.97 Tf 6.58 0 Td[(8mol/m3i0,Fe110)]TJ /F3 7.97 Tf 6.59 0 Td[(4A/cm2cH+(0)0.12102mol/m3bFe2+0.04V/decadecOH)]TJ /F6 11.955 Tf 6.76 -.3 Td[((0)7.45110)]TJ /F3 7.97 Tf 6.59 0 Td[(8mol/m3EFe2+ref)]TJ /F6 11.955 Tf 9.3 0 Td[(0.44VcFe2+(0)0mol/m3ip,Fe1.0010)]TJ /F3 7.97 Tf 6.59 0 Td[(1A/cm2Ksp,FeCO31.2910)]TJ /F3 7.97 Tf 6.59 0 Td[(11DH+9.3110)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sAp1.771012DOH)]TJ /F6 11.955 Tf 18.71 -.3 Td[(5.2610)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sEa64.9KJ/molDFe2+0.7210)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sPCO21105PaDO21.9710)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sionic0DNO)]TJ /F9 5.978 Tf 0 -6.19 Td[(31.9010)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sKsol0.031841DK+1.9810)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/s0.2(1.5)DCO21.9610)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/s1.0510)]TJ /F3 7.97 Tf 6.59 0 Td[(6m2/sDH2CO32.0010)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sA11.097210)]TJ /F3 7.97 Tf 6.58 0 Td[(4DHCO)]TJ /F9 5.978 Tf 0 -6.19 Td[(31.0510)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sA23.29510)]TJ /F3 7.97 Tf 6.59 0 Td[(6DCO2)]TJ /F9 5.978 Tf -3.32 -6.18 Td[(39.2010)]TJ /F3 7.97 Tf 6.59 0 Td[(5cm2/sKw9.0210)]TJ /F3 7.97 Tf 6.59 0 Td[(9mol2/m6Khy2.5810)]TJ /F3 7.97 Tf 6.59 0 Td[(3Kca1.7810)]TJ /F3 7.97 Tf 6.59 0 Td[(1mol/m3Kbi4.9410)]TJ /F3 7.97 Tf 6.59 0 Td[(8mol/m3khy,f2.6010)]TJ /F3 7.97 Tf 6.59 0 Td[(2/skhy,b10.08/s theparametersintheNordsveen'smechanismwereobtainedfromexperimentswithtemperaturesfrom40Cto60C.ItrepresentsthattheexistenceofH2CO3isnotnegligibleforhightemperatureandthemechanismproposedbyNordsveenhasthelimitationoftemperaturerange.However,protectiveironcarbonateorironcarbidelmsusuallyareobservedunderhighertemperatureandpressure.ThemechanismproposedbyNordsveencanprovidemoreappropriateapproachtostudythecorrosionwith 76

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A BFigure4-24. Thedistributionsofcurrentdensityatt=470sforthemechanismsA)proposedbyRemitaB)proposedbyNordsveenoftheCO2Depositmodel.ch4 theformationofprecipitates.Therefore,themechanismproposedbyNordsveenwasemployedinthetwo-concentric-quarter-ellipsegeometrytostudythegalvaniccouplingeffectresultedfromtheformationofprecipitates. 4.2.2PassivationBehaviorTheresultswerepresentedintermsoftwosetsofcalculations.Fortheone-quarter-ellipsegeometry(CO2DropletinTable 4-6 ),theshiftofpassivatedareacanbeillustratedinthechangesofthetotalcurrentdensity.Thetwo-concentric-quarter-ellipsegeometry(CO2DepositinTable 4-7 )wasappliedtoevaluateunder-depositcorrosionandtheinuencesofboththeformationofprecipitatesandthesurroundedturbulentow.TheprecipitatesstartedtoformfromthecenterandaccumulatedtowardstotheperipherybecausethelackofCO2)]TJ /F3 7.97 Tf -4.43 -7.98 Td[(3inthesolution.TheconcentrationofFe2+isthecriteriaintheformationofFeCO3.ThepHvalueabovethemetalsurfacewaspresentedtoshowtheabilityofpredictinglocalconcentrationofionicspeciesinbothDropletandDepositmodels. 4.2.2.1CO2DropletModelTheroleoflmpassivationisevidentinFigure 4-25 inwhichdistributionofcurrent 77

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A BFigure4-25. RadialdistributionsofcalculatedA)totalcurrentdensityandB)surfacecoverage()attheelectrodesurfacewithtimeasaparameterfortheCO2Dropletmodel. 78

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density(Figure 4-25A )andsurfacecoverage(Figure 4-25B )werepresentedatdifferenttimesfortheCO2Dropletmodel.Atshorttimes,duetothegreateraccessibilitytocarbondioxides,thecathodicreactiondominatesattheperipheryofthedroplet.Ferrousionswereassumedtobeproducedbytheanodicreactionandreactwithcarbonateionsproducedbythedissociationreactionsofcarbonicacidtoformferrouscarbonate.TheformationofFeCO3canbeindicatedbythesurfacecoveragewhichisshowninFigure 4-25B .Astimeincreases,thesurfacecoverageapproachesthefullcoveragevalue(=1).Theprecipitatesdepositedfromthecenterandextendedtotheperipheryregionuntilthesystemreachesequilibrium.TheprecipitateFeCO3wasassumedtobeprotectiveandtopassivateonlytheirondissolutionreaction.Ferrousionsarethecriteriaofformingferrouscarbonatesincecarbonateionsarelimitedbytheslowhydrationofcarbondioxides.Theactive-passivetransitionwasassumedtobeaconsequenceoftheformationofprecipitates.Whenthesystemreachestheequilibriumstate,corrosionoccursatthecoveredregionclosetotheboundaryofoccludedandthebulksolutionregion.ThecorrespondingchangesofpotentialdistributionwereplottedinFigure 4-26 .Theprecipitatesactastheprotectivelmonthemetalsurfaceandshieldthereactingsurface.ThepHvaluedecreasesaftertheformationofFeCO3sincetheconsumptionofCO2)]TJ /F3 7.97 Tf -4.44 -7.97 Td[(3prompttheformationofH+.ThepHvaluerightabovethesurfacewasplottedinFigure 4-27 withtimeasaparameterandindicatesalargechangeinashortperiodoftime(0.1sto130s).Smallertimestepandnermeshwereexpectedtobeemployedtounderstandtherelationshipofthetwocathodicreaction(Equation 3 andEquation 3 ),twodissociationstepsofH2CO3,andhydrationofCO2. 4.2.2.2CO2DepositModelTheinuenceofturbulentowcanbeobservedinFigure 4-28 .Thesurroundedturbulentowenhancedthecathodicreactionintheouterregion;therefore,thecorrosionunderthecoveredregionbecamemoresevere.Aftertheexistingcarbondioxidewasallconsumed,thediffusedcarbondioxidebroughttothereactingsurface 79

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Figure4-26. Potentialdistributionforthefalsecolorrepresentationandstreamlinerepresentationofcurrentdensityatt=1000scalculatedfortheCO2Dropletmodel. intheturbulentowwasfasterthantheoneinthecoveredregion.Asaconsequence,thecathodicreactionwasfavorableinthesurroundingareawhiletheanodicreactiondominatedinthecenter.ThepassivationbehaviorwasobservedastheresultoftheformationofprecipitateswhichisshowninFigure 4-29 and 4-30 .Ironcarbonateswasassumedtobesemi-conductiveinthiscalculationandtopassivateonlytheirondissolutionreaction.ThecorrespondingchangesofpotentialdistributionwereplottedinFigure 4-30 .Themaximumpotentialdifferencewasobtainedattheinitiationofprecipitationwiththemaximumanodiccurrentdensity.Itprovidessufcientferrousandcarbonateionsforprecipitation.ThepotentialdistributionplottedinFigure 4-31 whenthecoveredregionreachesthemaximumsurfacecoverage.Theprecipitatescontinuesaccumulatingonthemetalsurfaceandthecorrosionremainsactiveunderthe 80

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Figure4-27. ThepHdistributionasafunctionoftimecalculatedfortheCO2Dropletmodel. predenedcoveredregionduetothecarbondioxidesgradientdrivenbythesurroundingturbulentow. 4.2.3TheInuenceofTimeStepMorecomplicatedhomogeneousreactionsandcathodicreactionwereinvolvedintheCO2model,suchasthehydrationofCO2,thetwodissociatestepsofH2CO3,andtwocathodicreactions(thereductionofH+andH2CO3).TheratesofeachreactionvarywidelyandmoreiterationswererequiredfortheCO2modelcomparedwiththeO2model.Thehydrationreactionwasassumedtobemuchslowercomparedwiththedissociationreactions.AlargechangeofpHwasobservedwithashortperiodoftime(0.1sto130sinFigure 4-27 )asthereactionprogresses.Differentcathodicreactionwaspreferredatdifferentstageofreaction;therefore,timestepplaysanimportantroleintheCO2modelinordertoobtainmorecorrectandstableresultsasshowninFigure 81

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Figure4-28. RadialdistributionsofcalculatedtotalcurrentdensityattheelectrodesurfacewithtimeasaparameterfortheCO2Depositmodel. Figure4-29. RadialdistributionsofcalculatedsurfacecoverageattheelectrodesurfacewithtimeasaparameterfortheCO2Depositmodel. 82

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Figure4-30. Potentialdistributionalongelectrodesurfacewithtimeasaparametercalculatedforthedepositssurroundedbybulksolutions. 4-32 .Thesmallertimestepnotonlyimprovetheroughnessoftheresultsbutalsothevalueofit.Smallertimestepwasrequiredinmorecomplicatedmodeltoobtainmoreaccurateresults. 4.2.4TheInuenceofMeshSizeThespikesandroughnessoftheresultswereobservedinbothDropletandDepositmodel.TheresultsobtainedfromtheDropletmodelwasimprovedbyusingsmallertimestep,however,theresultsobtainedfromDepositmodelcannotbeimprovedbyapplyingsmallertimestep.ThegeometrywasmorecomplicatedfortheDepositmodelcomparedwiththeDropletmodel;therefore,usingnermeshwasexpectedtoobtainamoreaccurateresults.FortheDropletmodel,singularityproblemscouldoccurattheperiphery.ThedistributionoftotalcurrentdensityalongthemetalsurfacewithmeshsizeastheparameterwasplottedinFigure 4-33 .Itshowsthecalculatedresultschangedwithdifferentmeshsize,especiallyfortheregionfairlyclosetothewater-airinterface. 83

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Figure4-31. Potentialdistributionforthefalsecolorrepresentationandstreamlinerepresentationofcurrentdensityatt=560scalculatedforthedepositssurroundedbybulksolutions. Table4-8. DifferencesforthesimulationsinCO2DropletmodelwithdifferentmeshsizebyRemita. MaximumMeshSize=m410)]TJ /F3 7.97 Tf 6.59 0 Td[(5110)]TJ /F3 7.97 Tf 6.59 0 Td[(5110)]TJ /F3 7.97 Tf 6.59 0 Td[(6110)]TJ /F3 7.97 Tf 6.58 0 Td[(7110)]TJ /F3 7.97 Tf 6.59 0 Td[(8 "fromEquation 4 6.0710)]TJ /F3 7.97 Tf 6.59 0 Td[(12.9810)]TJ /F3 7.97 Tf 6.58 0 Td[(21.4210)]TJ /F3 7.97 Tf 6.59 0 Td[(26.6510)]TJ /F3 7.97 Tf 6.58 0 Td[(40 ThecomparisonofdifferentmeshsizecanbecalculatedbyusingEquation 4 asfollows "=(Rr0irefrdrd))]TJ /F6 11.955 Tf 11.96 0 Td[((Rr0irdrd) Rr0irefrdrdforiandiref>0(4)whereirefisthetotalcurrentdensitycalculatedbyusingthe410)]TJ /F3 7.97 Tf 6.59 0 Td[(8/masthemaximummeshsizewhichwasalsousedinthefollowingcalculations.TheresultswerepresentedinTable 4-8 .FinermeshattheperipherywasemployedintheDepositmodel,butitdidnotimprovethequalityoftheresultsaftertheformationofprecipitatesasshowninFigure 4-34 .Theroughnessofthecurveswasstillobservedaftertheformationofprecipitatesinthecoveredregion.Theresultswasnotchangedbyusing 84

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Figure4-32. RadialdistributionsofcalculatedsurfacecoverageattheelectrodesurfacewithtimestepasaparameterfortheCO2Dropletmodel. 85

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A BFigure4-33. RadialdistributionsofcalculatedA)totalcurrentdensityandB)thetotalcurrentdensityneartheperipheryregionattheelectrodesurfacewithtimeasaparameterfortheCO2Dropletmodel. Figure4-34. RadialdistributionsofcalculatedtotalcurrentdensityattheelectrodesurfacewithmaximummeshelementsizeasaparameterfortheCO2Dropletmodel. 86

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Figure4-35. SchematicrepresentationofthedistributionsofmeshdensityfortheDepositmodel. nermesh.However,theroughnessoftheresultscanbeimprovedbyusingsmallertimestepasshowninFigure 4-32 .FortheDepositmodel,theroughnessofthecurvescannotberesolvedbyusingsmallertimestepsize.SingularityproblemscouldoccuratboththeperipheryandtheinterfaceofinneroccludedandtheouterbulkregionfortheDepositmodel.Sincetheroughnessappearedaftertheformationofprecipitates,nermeshsizerightabovethemetalsurfacewasalsoemployedasshowninFigure 4-35 .However,employingnermeshdidnotimprovetheroughnessofthecurves.ItchangestheresultssincethesurfacecoveragesincethecurrentdensitieswerecouplingwiththeformationofFeCO3.Figure 4-36 representsthedistributionofsurfacecoveragewithmaximummeshelementsizeasaparameter. 87

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Figure4-36. RadialdistributionsofcalculatedsurfacecoverageattheelectrodesurfacewithmaximummeshelementsizeasaparameterfortheCO2Dropletmodel. 88

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CHAPTER5OVERVIEWOFUNDER-DEPOSITCORROSIONMODELTheunder-depositmodelcanbecategorizedintoDropletandDepositmodelbythephysicalconguration.BothDropletandDepositmodelswerestudiedinaerated(O2)andde-aerated(CO2)media.TheDropletmodelinvolvedacomplicatedcouplingofnonuniformmasstransfer,potentialdistributions,andtheactive-passivetransitionswhichwasassumedtoberesultedfromtheformationofprecipitates.ThesolutionscontainingdissolvedO2wasusedasthesteppingstonetondtheappropriateparameters,geometries,andmeshqualities.Thepolarizationcurveswereplottedrsttodemonstratetheactive-passivetransitionswithaseriesofappliedpotentialatsteady-statecalculations.Theimportanceofdropletsizeandshapeandthemeshqualitywasaddressedinthesteady-statecalculations.Theconcentrationdistributionsofthedissolvedgasvaryalongthemetalsurfacesincethediffusionpathwasdifferentbetweentheperipheryandthecenter.Thisvariationbuildupaconcentrationgradientandprovidesthedrivingforceforthereactions.Maximumeccentricitywasusedtoshowthedifferentialconcentrationcellbehavior.Areasonablemeshsizewasappliedtoobtaincorrectresultswithoutcostingsignicantcalculationtime.Finermeshmightberequiredwhenthecomplexityofthemodelincreasesinthemodeldevelopment,especiallyforthesolutionscontainingdissolvedCO2.Atimevariablewasintroducedtostudythedistributionofreactingspeciesatopen-circuitpotential.Astimeincreases,theprecipitatesaccumulatedonthemetalsurfaceanddistributeddifferentlyduetothemechanismoftheinvolvedreactions.Inthepresenceofactive-passivebehavior,thecenterofthedropcanremainactivewhiletheelectrodeneartheedgeofthedroppassivatesresultedfromtheformationofFe(OH)2andFe(OH)3fortheO2model.FortheCO2model,theprecipitatesstartedtoforminthecentersincetheinsufcientconcentrationofCO2)]TJ /F3 7.97 Tf -4.44 -7.97 Td[(3resultedfromthedissociationstepsofHCO)]TJ /F3 7.97 Tf 0 -7.97 Td[(3andH2CO3. 89

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TheDepositmodelisanextensionoftheDropletmodel.Thescalewasenlargedtosimulateanoccludedregionresultedfromthecorrosivedepositsandsandsinsideapipeline.Theinnerellipseactsasanoccludedregionandissurroundedbyabulksystem(outerellipse).Thecoveredareawastreatedasaporousmedium,andtheeffectivediffusioncoefcientofspeciescouldbeexpressedbytheBruggemanapproximation.Thesurroundingbulksolutionwasassumedtobeaturbulentowandcouldbedescribedbyaddingtheeddydiffusivityterm.Thecathodicreactionwaspreferredintheoutersurfacesincetheturbulentowhelpedbringthedissolvedgasontometalsurface;therefore,enhancedtheirondissolutionintheoccludedregion.TheO2modelisthesteppingstonetoconstructtheunder-depositcorrosionmodelandtheCO2modelshowsthecapabilityofimplementingthecurrentmodelstructuretodifferentenvironments.TwomechanismsproposedbyRemitaandNordsveenwerestudiedforthesolutioncontainingdissolvedCO2.ThemechanismproposedbyNordsveenwasemployedsinceitshowsthecorrosionoccurringunderthedeposits.TheCO2modelinvolvesmorecomplexhomogeneousreactionsandelectrochemicalreactions.ThedissolvedO2providesadirectsourceforoxygenreductionintheO2model;whilethehydrationanddissociationreactionswererequiredtoprovideH2CO3andH+forcathodicreactioninCO2model.SmallertimestepwasrequiredinsteadofnermeshsincetheCO2involvesmorechemicalreactionandhavedifferentreactionrates.Withsomemodications,thisunder-depositmodelcanappliedtodifferentconditions,suchassolutionscontainingH2SorbothCO2andH2S.Theformationofprecipitatesandthelocalconcentrationvaluescanbecalculatedifalltherequiredparametersaregiven. 90

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CHAPTER6CONCLUSIONSThisworkprovidesaframeworktostudylocalizedcorrosioninaeratedandde-aeratedsolutions.Unliketoothermodels[ 20 47 ],alocalizedcorrosionandthegalvaniceffectresultedfromtheformationofprecipitateswerestudiedinthiswork.Theregionofanodicandcathodicbehaviorwasnotassumedapriori.Theactive-passivetransitionwastreatedasaresultofdepositionoflmscomposingofcorrosionproducts.Timevariablewasintroducedtostudytheformationandlocaldistributionofprecipitates.Theionicspecieswascalculatedbyusingconservationequationsbut,rather,byusingLaplace'sequation.Therefore,thelocalconcentrations(pH),currentdensity(corrosionrate),andthepropertiesofprecipitatescanallbestudiedandcorrelatedsimultaneously.However,nermeshandsmallertimestepareexpectedtoberequiredtosolveforconditionsathighertemperatureandpressuretostudythegalvaniccouplingeffectresultedfromtheprotectiveprecipitates.Thisworkstudiesinteractionsamongchemicalreactions,electrochemicalreactions,depositionoflms,andmasstransport.ThemodeldevelopmentwassequentiallypresentedinChapter 3 .Thesystemcontainingdissolvedoxygenwasstudiedtobuildabasicstructurefortheunder-depositmodel.AsimilarapproachwithmorecomplexhomogeneousreactionswereappliedforsystemcontainingdissolvedCO2.TwogeometrieswereusedinsystemcontainingO2andCO2tostudytheformationofprecipitatesonthebaremetalsurfaceandtheactualuideffectonthemetalsurfacewiththepreexistingdeposits.Theone-ellipsegeometry,alsocalledDropletmodelinthiswork,wasemployedtostudythedifferentialconcentrationcellsresultedfromtheconcentrationgradientofdissolvedgasduetothediffusionpathdifferences.Thetwo-ellipsegeometry,alsocalledDepositmodelinthiswork,wasusedtosimulatethepipeowandstudytheeffectoftheturbulentowonthecathodicreactions. 91

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DifferentialconcentrationcellswereshowntobeformedinboththeDropletmodelandthemodelofapredeneddepositsurroundedbytheturbulentow.Thedifferencesofthediffusionbehaviorsinadjacentareascreatedtwodistinctenvironmentsandcausedgalvaniccoupling.Calculationsforaseriesofappliedpotentialatsteady-statewereperformedtoshowtheactive-passivetransitions.Inthepresenceofactive-passivebehavior,theanodiccurrentshowsthetransitioncurve;whereas,thecathodiccurrentdisplaysthemass-transfer-limitedplateau.Time-dependentcalculationsatthecorrosionpotential(open-circuitcondition)wereperformedtostudytheformationofprecipitatesandthelocalconcentrationsandcurrentdensity.FortheDropletmodelofbothconditionscontainingO2andCO2,thecathodicreactionsarepreferredatperipheryregionandcorrosionoccursatthecenterduetotheaccessibilityofdissolvedgases.However,thedistributionofprecipitatefortheO2andCO2modelsaredifferent.ForDropletmodelcontainingO2,thecenterofthedropcanremainactivewhiletheelectrodeneartheedgeofthedroppassivatesbytheaccumulationofFe(OH)2.ThespeciesFe2+andOH)]TJ /F1 11.955 Tf 10.41 -4.33 Td[(reachthesolubilityproductvaluenearthecathodicreactiondominatedregionsinceOH)]TJ /F1 11.955 Tf 10.41 -4.34 Td[(istheproductofoxygendissociation.FortheDropletmodelcontainingCO2,thespeciesFeCO3begantoaccumulateintheanodicreactiondominatedareabecausecarbonateisaproductofhomogenousreaction.ForthedepositmodelcontainingO2,itshowsa0.1/Vpotentialdropresultedfromthesurroundingturbulentowandthepredeneddepositregion.Thecorrosionoccurredunderthepredeneddeposit.Turbulentowenhancesthecathodicreactionsinthebulkregionbecauseitbringsthereactingspeciestothemetalsurface.Pittingpotentialmaybeobservedifmorecorrosiveconditionsaregivenandthereforeunder-depositcorrosionmaybeoneoftheconditionsfortheinitiationofpitting.FortheDepositmodelcontainingCO2,unstableresultswereobtainedsinceitinvolvesmorecomplicatedreactionsandsingularityproblemsduetotheboundaryconditionsandthewaterchemistry.Moreaccurateresultscanbeobtainedwithnermeshandsmallertime 92

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step,butbothrequirelongcalculationtimeandlargecostofmemory.Conrmingthemeshsizeandtimestepissuggestedtobetherststepifanychangesaremadeinthemodels.Finermeshattheboundariesandsmallertimestepsforsystemsinvolvingmorecomplexreactionsarealsosuggested.Themaximumeccentricityofthedropletwassuggestedtobeusedtoobtainthemaximumconcentrationgradientofdissolvedgasesinthistypeofwork.FortheDepositmodel,thearearatioofpredeneddepositregiontothebulkregionisimportant.Thelargerratiocangeneratelargerpotentialdropandcanleadustomoreseriouscorrosion. 93

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CHAPTER7SUGGESTIONSFORFUTUREWORKThemodelstructureofthepresentworkareusedtoproposeadditionalstepsforthecontinuationofthisproject.SolutionscontainingCO2canleadtomoreseverecorrosionproblem;therefore,theextensionoftheCO2modelisproposedinChapter 7 .TheCO2DropletandCO2Depositmodelsareproposedtoextendbyusing3-Dcoordinatesinsteadof2-Daxi-symmetriccoordinates.Turbulentowissuggestedtobecalculatedinthechannelowmodeltostudythecorrosionwithmorerealisticowdynamics,suchasthelow-Reynoldsnumberk-"turbulencemodelinCOMSOLMultiphysics.Anewboundaryconditionaresuggestedtobeincludedtosimulatehowdefectexpandwiththecalculatedcorrosionrate.Morecorrosiveconditionscontainingmorereactingspeciesaresuggestedtoalsobestudied. 7.12-DAxi-Symmetricto3-DTheCO2DropletandCO2Depositmodelsareproposedtoextendfroma2-Daxi-symmetriccoordinatestoa3-DcoordinatesinCOMSOLMultiphysics.Ahemi-ellipsoidissuggestedtobeusedinthiscalculationandtheresultscanbecomparedwiththe2-Daxi-symmetriccoordinatesresults.Non-symmetricgeometrycanalsobecalculated,therelationshipbetweentheshapeandtheonsetoftheformationofprecipitatescanbediscussed.Thismodelcanprovideaframeworkforthechannelowmodelin3-D. 7.22-DLow-ReynoldsNumberk-"TurbulenceModelThephysicalcongurationofthepreviousmodelissuggestedtobemodiedtosimulatetheowdynamicsinthepipelinesmoreaccurately.TheschematicdiagramofthechannelowmodelisshowninFigure 7-1 .A2-Dcoordinatecanbeusedastherststeptovalidatethephysics.Aturbulencemodelwhichyieldsmoreaccurateresultsfortheowclosetothewallturbulentowcanbeappliedinthisstage.Masstransferboundarylayerisoftenembeddedinsidemomentumboundarylayerforwatersystem. 94

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Figure7-1. Schematicrepresentationsofthechannelowmodel. Inordertoavoidthenumericaldifcultiesinthemomentumboundarylayer,therstgridpointofthecalculationisalwaysplacedfarawayfromwheremajorconcentrationgradientoccurs.Theestimatedvaluefortheconcentrationgradientatwallislessthantheactualvalue.Thewalluxofreactingspeciesbasedontheboundarylayersolutionis Nwall)]TJ /F5 11.955 Tf 21.92 0 Td[(DCb)]TJ /F5 11.955 Tf 11.96 0 Td[(Cs dx2(7)andtheactualvalueshouldbedescribedas Nwall)]TJ /F5 11.955 Tf 21.92 0 Td[(DCb)]TJ /F5 11.955 Tf 11.96 0 Td[(Cs dx1(7)wheredx1anddx2canberepresentedinFigure 7-2 .Thelow-Reynoldsnumberk)]TJ /F4 11.955 Tf 9.3 0 Td[(modeliscapableofcalculatingmasstransferwithproperlysolvingmomentumtransportandthecalculationgridpointcanbeplaceascloseaspossibletothewallsurface.Thebuild-inmodelTheowrecirculationexistsinsidethepredeneddefect(thedarkblueregioninFigure 7-1 )andtheturbulentbehaviorcanbedescribedbyapplyingthelow-Reynoldsnumberk-"modelbuiltinCOMSOLMultiphysics.ConcentrationcellsformedduetotheformationofprecipitationwhereCO2isdepleted,whileotherplacesarenot. 95

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Figure7-2. Schematicrepresentationsofconcentrationproleinturbulentow. 7.33-DLow-ReynoldsNumberk-"TurbulenceModelThe2-Dchannelowmodelisproposedtobeextendedtoa3-Dchannelowmodel.Themetalsurfaceinthepredeneddefectregionactsasananodeandthecathodicreactionsaredominatedonthemetalsurfaceoftherestofthepipeline.Theratioofthesizeofthepredeneddefecttotheradiusandlengthofthepipelineplaysanimportroleinthismodel. 7.4MovingBoundaryTheabovemodelisproposedtobeextendedbyreplacingthepredenedsemi-circledefectwithdifferentshapeofthedefectandalsoemploythemovingboundaryconditionstostudythedefectexpansionwithcalculatedcorrosionrate.Thecorrosionratedependsontheanodiccurrentdensityandcanbeappliedontheboundaryofdefecttopredictthepropagationofcorrosiondamage.Figure 7-3 showsthepredeneddefectregionandtheexpansionofitwhenthemovingboundaryconditionappliedtothemetalsurface.Theresultsareexpectedtobeabletopredictthe 96

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Figure7-3. Schematicrepresentationsofthechannelowmodelwithmovingboundaryconditionsonthepredeneddefect. sizeofthedefectastimeincreasesandcanbecomparedwiththeexperimentalresults.ThechangesinpHcanbeexpectedinthiscalculations. 7.5MoreCorrosiveConditionsMorecorrosiveconditionsareproposedtobetakenintoaccount,suchassolutionscontainingCl)]TJ /F1 11.955 Tf 7.08 -4.34 Td[(,H2S,andHS)]TJ /F1 11.955 Tf 7.08 -4.34 Td[(.Theexistenceofchlorideionscouldleadustostudythepitinitiationmechanismandtheprogressioncorrosion.Pittingcorrosioncouldbetheconsequenceoftheprotectivelmbreakdown,whichcanberesultedfromthewaterchemistry.DecientO2orCO2andtheexistenceofchloridesmayenhancethebreakdownofthepassivelmandpitpropagation.Hydrogensuldecanbemorecorrosivetostainlesssteelbecausenotonlytheeffectofincreasingaciditybutalsotheexistenceofotherlocalizedcorrosionmechanismi.e.,SuldeStressCracking(SSC).At25C,twokineticsoftheprecipitationreactionbetweenferrousionsanddissolvedsuldewereproposedbyRickard[ 64 ].Therstreactioncanbeexpressedby Fe2++H2S=FeS(s)+2H+(7)andtheothercompetingreactioncanberepresentedby Fe2++2HS)]TJ /F6 11.955 Tf 10.4 -4.94 Td[(=Fe(HS)2(s)(7) Fe(HS)2(s)=FeS(s)+H2S(7) 97

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ThemechanismoftheformationofFeSathighertemperaturewasdiscussedinotherplaces[ 65 66 ]. 98

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[66] H.Tokuda,D.Kuchar,N.Mihara,M.Kubota,H.Matsuda,andT.Fukuta,StudyonreactionkineticsandselectiveprecipitationofCu,Zn,NiandSnwithfH2Sginsingle-metalandmulti-metalsystems,Chemosphere,73(2008)14481452. 104

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BIOGRAPHICALSKETCH Ya-Chiao(Jo)ChanggraduatedfromtheNationalTaiwanUniversitywithaBachelorofSciencedegreeinchemicalengineeringin2008.SheenteredgraduateschoolinAugustof2008attheUniversityofFlorida.In2009,JopursuedherdoctorateinchemicalengineeringandjoinedProfessorMarkOrazemsresearchgroupwhichspecializesinelectrochemicalengineering.Inthesummerof2013,JohadaninternshipinBPAmerica.ThisinternshipallowedJotoapplyherunder-depositcorrosionmodelstoothersystemswhichisanextensiontoherdoctoralresearch.DuringhertimeattheUniversityofFlorida,JowasmarriedtoTe-YuKaoin2013.ShereceivedherPh.D.fromtheUniversityofFloridainthefallof2013. 105