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KP-TR-018-NP, Revision 2, Postulated Event Analysis Methodology
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KP-NRC-2302-002 Postulated Event Analysis Methodology, KP-TR-018-NP (Non-proprietary)

KPTR018NP

KairosPowerLLC 707W.TowerAve SuiteA Alameda,CA94501

Postulated Event Methodology

TechnicalReport

RevisionNo.2 DocumentDate:February2023

NonProprietary

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COPYRIGHTNotice ThisdocumentisthepropertyofKairosPowerLLC(KairosPower)andwaspreparedinsupportofthe developmentoftheKPFluorideSaltCooledHighTemperatureReactor(KPFHR)design.Otherthanby theNRCanditscontractorsaspartofregulatoryreviewsoftheKPFHRdesign,thecontenthereinmay notbereproduced,disclosed,orused,withoutpriorwrittenapprovalofKairosPower.

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Rev DescriptionofChange Date 0

InitialIssuance September2021 1

RevisionupdatesSections3.2,3.4,4.1,and4.5,Tables32, 44,and45,andAppendixAtoaddressfeedbackfromNRC audit.

September2022 2

RevisionupdatesSection3.4andTable32toaddress feedbackfromNRCaudit.

February2023

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4of98 ExecutiveSummary Thisreportdescribesthepostulatedeventsandthemethodologythat,whenusedtoevaluateevents withinthedesignbasis,ensurestherearesufficientdesignfeaturesavailabletomitigatetheireffects andkeepthepotentialconsequencesboundedbythemaximumhypotheticalaccident(MHA).

Figuresofmeritarederivedforthepostulatedeventstoprovidesurrogatemetricswhichdemonstrate thattheresultingdoseisboundedbythedoseconsequencesoftheMHAanalysis.Acceptancecriteria forthesefiguresofmeritrepresentdesignlimitsthatensuretheMHAisbounding.

Theevaluationmodelsusedtoanalyzethepostulatedeventsaredescribedaswellastheassociated verificationandvalidationplans.Samplepostulatedeventanalysesareprovidedinappendixasan illustrationofthemethodsdescribedinthisreport.

TheMHAissummarizedinthisreportonlytoprovidecontextforthederivationoffiguresofmeritfor postulatedeventsthatwhenevaluatedensurethatthedoseisboundedbyanMHAwithacceptable doseconsequences.

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5of98 TableofContents PostulatedEventMethodology....................................................................................................................1 1

Introduction........................................................................................................................8 1.1 DesignFeatures...........................................................................................................................8 1.1.1 DesignBackground..................................................................................................................8 1.1.2 KeyDesignFeaturesoftheKPFHR.........................................................................................8 1.2 RegulatoryBackground...............................................................................................................9 2

MaximumHypotheticalAccidentSummary.....................................................................11 2.1 MaximumHypotheticalAccidentNarrative..............................................................................11 2.2 MaximumHypotheticalAccidentTemperatureCurve..............................................................11 2.3 ConservativeReleaseModels....................................................................................................11 2.4 Results.......................................................................................................................................17 3

CapabilityofEvaluationModels.......................................................................................18 3.1 OverviewofEvaluationModelsforPostulatedEvents.............................................................18 3.2 EvaluationModelApplicability..................................................................................................18 3.2.1 PostulatedEventCategoriesandDurationofEvaluation.....................................................18 3.2.2 PostulatedEvents..................................................................................................................18 3.2.3 EvaluationModelsUsedtoAnalyzePostulatedEvents........................................................26 3.3 PhenomenaIdentificationandRankingTables.........................................................................26 3.4 FiguresofMerit.........................................................................................................................27 3.4.1 DoseAcceptanceCriteria......................................................................................................27 3.4.2 PostulatedEventFiguresofMerit.........................................................................................28 4

EvaluationModels............................................................................................................32 4.1 SystemsAnalysis........................................................................................................................32 4.1.1 KPSAMCodeDescription.....................................................................................................32 4.1.2 KPSAMVerificationandValidationPlan..............................................................................35 4.1.3 PlantKPSAMModel.............................................................................................................35 4.2 FuelPerformance......................................................................................................................36 4.3 Neutronics.................................................................................................................................38 4.4 StructuralAnalysis.....................................................................................................................38 4.5 EventSpecificMethods.............................................................................................................38 4.5.1 SaltSpills................................................................................................................................38 4.5.2 InsertionofExcessReactivity................................................................................................42 4.5.3 LossofForcedCirculation.....................................................................................................43 4.5.4 PebbleHandlingandStorageSystemMalfunction...............................................................45 5

Conclusions.......................................................................................................................51 6

References........................................................................................................................52 Table21:PrescriptiveMaximumHypotheticalAccidentTemperatures...................................................54 Table31:AnalyzedPostulatedEventsandAppliedEvaluationModels....................................................55 Table32:DerivedFiguresofMeritandAcceptanceCriteriaforPostulatedEvents.................................56 Table41:KPSAMModelsandFieldEquations.........................................................................................58 Table42:SampleKPSAMInputComponentsbyNodalType...................................................................59 Table43:KPFHRTRISOfuelspecificationforasmanufacturedcontaminationanddefectfractions.....60 Table44:InputParametersConsideredforPostulatedEvents................................................................61 Figure11:ElementsofEvaluationModelDevelopmentandAssessmentProcess...................................63 Figure21:PrescriptiveMHATemperatures..............................................................................................64

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6of98 Figure41:SAMCodeStructure.................................................................................................................65 Figure42:KPSAMSampleNodalDiagramoftheHermesReactor..........................................................66 APPENDIXA.

SampleTransientResults..................................................................................................67

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7of98 ListofAcronyms

C/HM carbontoheavymetalatomratio DHRS decayheatremovalsystem EAB exclusionareaboundary EMDAP evaluationmodeldevelopmentandassessmentprocess HRR heatrejectionradiator LPZ lowpopulationzone LWR lightwaterreactors MAR radioactivematerialatriskforrelease MHA maximumhypotheticalaccident MHTGR ModularHighTemperatureGasCooledReactor MOOSE MultiphysicsObjectOrientedSimulationEnvironment PHSS pebblehandlingandstoragesystem PIRT Phenomenaidentificationandrankingtable PSP primarysaltpump RCSS reactivitycontrolandshutdownsystem RF releasefraction RG regulatoryguide SSCs structures,systems,andcomponents TRISO tristructuralisotropic

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INTRODUCTION Thisreportdetailsthepostulatedeventsthatmustbeconsideredandthetransientmethodologythat, whenusedtoevaluateeventswithinthedesignbasis,ensurestherearesufficientdesignfeatures availabletomitigatetheeffectsandkeepthepotentialconsequencesboundedbythemaximum hypotheticalaccident(MHA).ConsistentwiththeguidanceinNUREG1537,GuidelinesforPreparing andReviewingApplicationsfortheLicensingofNonPowerReactors,anMHAisusedtodemonstrate thattheradiologicalconsequencesfromaboundingeventresultinacceptabledoselevels.

Eventswithinthedesignbasisarereferredtoaspostulatedevents.Allpostulatedeventsmustbe consideredtoensuretherearesufficientdesignfeaturesavailabletomitigatetheeffectsandkeepthe potentialconsequencesboundedbytheMHA,consistentwiththerequirementsin10CFR50.34(a).

AnMHAissummarizedinSection2onlytoprovidecontextforthederivationoffiguresofmeritfor postulatedeventsthatfunctionassurrogatesfordose.TheMHAthatdemonstratesdosecompliancefor thedesignisprovidedinthelicensingapplication.AnMHAisaneventwithhypotheticalconditions designedtoresultinareleaseofradionuclidesfromthefuel.Thehypotheticalfuelrelease,alongwith hypotheticalconditionsthatresultinthereleaseofotherradioactivematerialatriskforrelease(MAR) containedintheprimarysystem,resultsinareasonablyboundingdoseatthesiteboundary.TheMHA doseisreasonablyboundingbecauseitisbasedonnonphysicalconditionsthatarebeyondthedesign basis.ThisreportdetailsthederivationoffiguresofmeritfromtheMHAconditions,butthefinal numbersfortheacceptancecriteriaarebasedontheMHApresentedinthelicensingapplication.

1.1 DESIGNFEATURES 1.1.1 DesignBackground ThistechnicalreportprovidestransientmethodsbasedonaKPFHRdesign.Keydesignfeaturesare providedinthissectionwhichareconsideredinherenttotheKPFHRtechnology.Theseprovidethe basistosupportthesafetyreviewofthetransientmethodology.

TheKPFHRisaU.S.developedGenerationIVadvancedreactortechnology.Inthelastdecade,U.S.

nationallaboratoriesanduniversitieshavedevelopedpreconceptualFluorideSaltCooledHigh TemperatureReactor(FHR)designswithdifferentfuelgeometries,coreconfigurations,heattransport systemconfigurations,powercycles,andpowerlevels.Morerecently,UniversityofCaliforniaat BerkeleydevelopedtheMark1pebblebedFHR,incorporatinglessonslearnedfromtheprevious decadeofFHRpreconceptualdesigns(Reference1).KairosPowerhasbuiltonthefoundationlaidby DepartmentofEnergysponsoreduniversityIntegratedResearchProjectstodeveloptheKPFHR.

AdditionaldesigndescriptioninformationforKPFHRpowerreactortechnologyisprovidedinthe DesignOverviewoftheKairosPowerFluorideSaltCooled,HighTemperatureReactor(KPFHR)

TechnicalReport(Reference2).

1.1.2 KeyDesignFeaturesoftheKPFHR TheKPFHRisahightemperaturereactorwithmoltenfluoridesaltcoolantoperatingatnear atmosphericpressure.ThefuelintheKPFHRisbasedontheTriStructuralIsotropic(TRISO)high temperaturecarbonaceousmatrixcoatedparticlefuelinapebblefuelelementdevelopedforhigh temperaturegascooledreactors.Coatingsontheparticlefuelprovideretentionofradionuclides.The reactorcoolantisachemicallystablemoltenfluoridesaltmixture,27LiF:BeF2(Flibewithenrichmentof the7Liisotope)whichalsoprovidesretentionofradionuclidesthatescapefromanyfueldefects.A

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9of98 primarycoolantloopcirculatesthereactorcoolantusingpumpsandtransferstheheatviaaheat exchanger.Thedesignincludesdecayheatremovalcapabilityforbothnormalconditionsandaccident conditions.Passivedecayheatremoval,alongwithnaturalcirculationinthereactorvessel,isusedto removedecayheatinresponsetoapostulatedevent.TheKPFHRdoesnotrelyonelectricalpowerto achieveandmaintainsafeshutdownfordesignbasisaccidents.

TheKPFHRdesignreliesonafunctionalcontainmentapproachsimilartotheModularHigh TemperatureGasCooledReactor(MHTGR)insteadofthetypicallightwaterreactor(LWR)lowleakage, pressureretainingcontainmentstructure.TheKPFHRfunctionalcontainmentsafetydesignobjectiveis tomeet10CFR50.34(10CFR52.79)offsitedoserequirementsattheplant'sexclusionareaboundary (EAB)withmargin.AfunctionalcontainmentisdefinedinRG1.232,DevelopingPrincipalDesign CriteriaforNonLightWaterReactorsasa"barrier,orsetofbarrierstakentogether,thateffectively limitthephysicaltransportandreleaseofradionuclidestotheenvironmentacrossafullrangeofnormal operatingconditions,anticipatedoperationaloccurrences,andaccidentconditions.RG1.232includes anexampledesigncriterionforthefunctionalcontainment(MHTGRCriterion16).AsalsostatedinRG 1.232,theNuclearRegulatoryCommissionhasreviewedthefunctionalcontainmentconceptandfound itgenerallyacceptable,providedthatappropriateperformancerequirementsandcriteriaare developed.TheNuclearRegulatoryCommissionstaffhasdevelopedaproposedmethodologyfor establishingfunctionalcontainmentperformancecriteriafornonLWRs,whichispresentedinSECY18 0096,FunctionalContainmentPerformanceCriteriaforNonLightWaterReactors.ThisSECYhasbeen approvedbytheCommission.

ThefunctionalcontainmentapproachfortheKPFHRistocontrolradionuclidesprimarilyattheirsource withinthecoatedfuelparticleundernormaloperationsandaccidentconditionswithoutrequiringactive designfeaturesoroperatoractions.TheKPFHRdesignreliesprimarilyonthemultiplebarrierswithin theTRISOfuelparticlestoensurethatthedoseatthesiteboundaryasaconsequenceofpostulated accidentsmeetsregulatorylimits.However,intheKPFHRasopposedtotheMHTGR,themoltensalt coolantservesasadistinctadditionalbarrierprovidingretentionofradionuclidesthatescapethefuel particleandfuelpebblebarriers.Thisadditionalretentionisakeyfeatureoftheenhancedsafetyand reducedsourcetermintheKPFHR.

1.2 REGULATORYBACKGROUND Applicantsforanonpowerreactorconstructionpermitmustprepareapreliminarysafetyanalysis reportinaccordancewiththeregulationsin10CFR50.34(a)(1)(i)and10CFR50.34(a)(2)through10CFR 50.34(a)(8).Thedoserequirementsforanonpowerreactorarespecifiedin10CFR100(referencedby 10CFR50.34(a)(1)(i)).Specifically,10CFR100.11setsthedoselimitsforsitingatest(nonpower) reactor.ConsistentwiththeguidanceinNUREG1537,anMHAisusedtodemonstratethatthe radiologicalconsequencesfromaboundingeventresultinacceptabledoselevels.Theboundingnature oftheMHAalsoprovidesthepreliminaryanalysisofthefacilityanddeterminationofthemarginof safetyduringtransientconditionsrequiredby10CFR50.34(a)(4).

Thefinalanalysisofthefacilityanddeterminationofthemarginofsafetyduringtransientconditionsis deferredtothefinalsafetyanalysisreport.Deferringthefinalsafetyanalysisisconsistentwiththe expectationsin10CFR50.35(a)(2)becausethefinaldesigndetailsandthetechnicalinformationneeded tocompleteafinalsafetyanalysis,suchasvalidationtesting,willnotbesubmitteduntiltheoperating licenseapplicationstage.Tosupportafindingthattheremainingportionsofthesafetyanalysiscan reasonablybelefttothefinalsafetyanalysisreport,thetransientmethodologyisprovidedinthis technicalreport,alongwithsamplecalculationsforeachcategoryofpostulatedeventtoillustratethe

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10of98 methodsandpotentialmarginsinthefinalsafetyanalysis.However,thesamplecalculationsarefor illustrationpurposesonlybecauseKairosPowerisnotrequestingCommissionapprovalofthesafetyof anydesignfeatureorspecificationintheconstructionpermitapplication,aspermittedby10CFR 50.35(b).Theverificationandvalidationplanforcodesusedinthesafetyanalysisevaluationarealso providedinthisreport,consistentwiththeexpectationin10CFR50.35(a)(3)and10CFR50.35(a)(4).

ThetransientmethodologypresentedinthisreportisconsistentwiththeNUREG1537objectivesfor informationonpostulatedeventswiththeexceptionofguidanceforrejectionofapotentialevent.

ThepotentialeventinitiatorspreventedbydesignareprovidedinthePreliminarySafetyAnalysis Report.TheobjectiveslistedinNUREG1537are:

Ensurethatenougheventshavebeenconsideredtoincludeanyaccidentwithsignificantradiological consequences.Rejectionofapotentialeventshouldbejustifiedinthediscussions.

Categorizetheinitiatingeventsandscenariosbytypeandlikelihoodofoccurrencesothatonlythe limitingcasesineachgroupmustbequantitativelyanalyzed.

Developandapplyconsistent,specificacceptancecriteriafortheconsequencesofeachpostulated event.

Thedevelopmentofevaluationmodels(EMs)forsafetyanalysisisconsistentwiththeapplicable portionsoftheevaluationmodeldevelopmentandassessmentprocess(EMDAP)describedinRG1.203, TransientandAccidentAnalysisMethods.AsummaryoftheEMDAPisprovidedinFigure11.This reportfollowstheprocessforElements1and3.Elements2and4willbeprovidedinafuturelicensing submittaltosupportafinalsafetyanalysisreport.

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MAXIMUMHYPOTHETICALACCIDENT

SUMMARY

2.1 MAXIMUMHYPOTHETICALACCIDENTNARRATIVE Thereactoristrippedduetoanunspecifiedtransient.Pretransientdiffusionofradionuclidesfromthe fuelkernelsarehypotheticallyandconservativelynotmodeledtomaximizeavailablefuelinventory release.Theaccidentisdetectedbythereactorprotectionsystem,andthesafetyfunctionsforreactor shutdownanddecayheatremovalareassumedtobefulfilled.However,thethermalfluidresponseis notdirectlymodeled.Hypotheticaltemperaturecurvesareusedtoboundexpectedsystem temperaturesandthusconservativelydriveradionuclidemovementthroughthecreditedbarriers:

RadionuclidesdiffusefromallTRISOcohorts(e.g.,intact,failedSiC,exposedkernels).Thisfuel releaseishypotheticalgiventhesteadystatediffusionassumptions.

Tritiumdesorbsfrominvesselgraphiteandsteel.

RadionuclidesevaporateanddegasfromtheFlibedrivenbynaturalconvectiveforcesinthecover gas.

Nongaseousradionuclides(i.e.,SaltsolubleFluorides,NobleMetals,andOxides)evaporatefrom theFlibefreesurfaceinthereactorvessel.

Gaseousradionuclides,includingtritium,bypasstheFlibe.

Airborneradionuclidesareconservativelyassumedtobypassthecovergasspaceanddirectlyenterthe facilityair.Radionuclidesthathavebeenmobilizedinthefacilityairarethentransportedbydispersion tothesiteboundaryonthebasisofconservativeanalysiswithunfilteredgroundlevelreleases.

2.2 MAXIMUMHYPOTHETICALACCIDENTTEMPERATURECURVE AtimetemperatureplotoftheprescribedMHAsystemtemperaturesisshowninFigure21andTable 21.Thistemperatureprofileboundstheexpectedreleasefromfuel,Flibe,andstructuraltemperatures forpostulatedevents.

2.3 CONSERVATIVERELEASEMODELS ThecalculationofthedoseconsequencesoftheMHAusesthesourcetermmethodsfordesignbasis accidentspresentedinReference3.Thissectionprovidesahighlevelsummaryofthemethodsused andtheinputstothecalculation.

TheevaluationoftheMHAdoseconsequencesfirstidentifiesandaccountsforthesourcesofMARand thebarrierstorelease.Eachbarrieristhenevaluatedforareleasefractiontoprovidedose consequencesattheexclusionareaandlowpopulationzoneboundaries.

ThefoursourcesofMARandtheassociatedbarrierstoreleaseintheMHA:

TRISOfuelinthereactorcore o Barriers:TRISOlayers,Flibe,andgasspace Circulatingactivity o Barriers:Flibeandgasspace StructuralMAR

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12of98 o TritiumretainedbygraphiteandinFlibe Barriers:Graphitegrains(fornonFlibetritium)andgasspace o Argon41retainedinclosedgraphitepores Barriers:Graphiteporesandgasspace ThereareseveralnonphysicalconditionsthatarehypothesizedtoensureaboundingMHA:

Pretransientdiffusionofradionuclidesfromthefuelinthereactorcoreisneglected:This conservatismisachievedintheevaluationbyassumingthatthefullradionuclideinventoryofthe fuelisavailableforreleaseattheinitiationoftheMHA.Thecirculatingactivityisstillassumedtobe atanupperboundlevel.Therefore,anyMARoriginatinginthefuelthatcontributestothe circulatingactivityiseffectivelydoublecounted.

Hypotheticaltemperaturehistoriesareappliedtothetransient:thehypotheticaltemperature historiesappliedtotheMHAisprovidedinFigure21.Thesetemperaturessetanupperlimitforthe figureofmerittemperaturesinthepostulatedevents.

ThegasspaceisnotcreditedforconfinementoftheradionuclidesthatreleasefromtheFlibefree surface:radionuclidetransportinthegasspacebarrierismodeledusingtheconservativebuilding transportandoffsitedispersionmethodsdescribedinReference3.

Conservative,unfiltered,groundlevelreleases:thegasspacetransportevaluationassumesa conservativeleakagerateforthereactorbuildingthatreleasestheentirevolumewithina2hour windowasthebuildingisassumedtonotbeaconfinementstructure.Thedispersionevaluation assumesnoradionuclidesarefilteredafterthebuildingtransportisevaluatedtoavoidtakingcredit foranyradionuclidefilteringthatcouldoccurintheheating,ventilation,andairconditioning system.

Initialtritiuminventoriesarecalculatedforanassumed50MWthcorethatoperatesata100%

capacityfactorovertenyears.TheHermesreactorisexpectedtooperateatlowerpowerswitha lowercapacityfactor.Loweroperatingpowersresultinalowertritiumproductionrateandlower capacityfactorsallowforthegraphitegrainstoexperiencetimeperiodsoftritiumdesorption insteadofsorption.

Aboundingvesselvoidfractionof0.1isassumedtofacilitatethereleaseoflowvolatilityspeciesin thevesselviabubbleburst.

QuantificationofMARSources ThefuelMARconsistsofradionuclidesproducedbynormaloperation.ASerpent2evaluationprovides thefuelinventory.ThefuelMARisassumedtotransportintheradionuclidegroupsdescribedin Reference3.

AboundingvalueofcirculatingactivityisassumedforFlibeMARintheanalysis.TheFlibeMARis assumedtotransportinthegroupsdescribedinReference3.

Thequantityofretainedtritiumisconservativelyboundwithingraphiteandstructuresover10yearsof operation.ThetritiumTspeciationissimplifiedtofullytritiumfluorideforanoxidizingsalt.Afully moleculartritiumcaseforareducingsaltiscalculated,butthefullytritiumfluoridecaseisusedbecause itleadstoahighergraphiteinventoryandhighertotalreleaseoftritium.Thetritiumfluorideisassumed

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13of98 toberetainedbythegraphite,butdoesnotpermeate,anditsevolutiontooffgasisneglected.The tritiumfluoridedistributionisdeterminedbymasstransferinFlibe,wherethegraphiteistreatedasa perfectabsorber.Distributionfractionstoeachregionarecalculatedbymasstransfercoefficient multipliedbythesurfacearea.Themasstransfercoefficientsarecalculatedbythecorrelationsin Reference3.Oncethetransientbegins,theconcentrationoftritiumintheFlibeisreducedtozeroand thustheconcentrationgradientreverses,movingtritiumoutofgrainsandbackintotheFlibe.Tritium releasefractionsarecalculatedusinganumericalsolutiontodiffusionequations.Thetritiumtransport throughgraphiteporesisassumedtobeinstantaneous,andgraphitegrainsareexposedtothesame tritiumuptakeconditions.Strongtritiumtrappingsitesareneglectedtoboundreleasefractions.

TheAr41buildupandreleasemodelspredictthediffusionofargoncovergasintographiteclosedpores whicharethenactivatedinthecoreandreflectorregions.GraphiteusedfortheHermesreflectoras wellascarbonmatrixusedforfuelandmoderatorpebblesareporousmaterials.Smallentrancepore sizesofthegraphitepreventsaltintrusionintothebulkmaterial,andthevolumeofporesisavailable foroccupancybyagas.Theclosedporousvolumeofgraphiteandcarbonmatrixisoccupiedbythe covergasforthereactor.CovergasalsodiffusesthroughtheFlibeandentersgraphiteclosedpores duringreactoroperationssinceargoncovergashassmall,butnonzerosolubilityinFlibe.Theinventory ofAr41isassumedtobepuffreleaseddirectlyintothegasspace.

RadionuclideTransportinFuel ThegroupedfuelMARdiffusesthroughtheTRISOlayers,drivenbythehypotheticaltemperaturehistory inFigure21.AsdiscussedinReference3,thetransportofmobileradionuclidesthroughtheTRISOfuel particleismodeledbyFickslawsofdiffusion.

Nofurthergenerationofradionuclidesoccursafterthereactortrip.Additionally,noradioactivedecayis modeledinthemassdiffusionequations.TheshorttimeapproximationoftheBoothsolutionisusedto determinethefractionalreleaseofradionuclidesfromthekernelforconditionswhere0.155(no power,nofurthergenerationofnuclides)(Reference4):

6 3

(1)

where, RF(T)=releasefractionofradionuclidesuptotimet=T

=reduceddiffusioncoefficient=DT/a2(unitless) a=radiusofequivalentsphere(m)

D=diffusivitycoefficientoftherepresentativeradionuclide(m2/s),consistentwiththevaluesin Reference3.

t=time(s)

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14of98 Forconditionswhere0.155andradioactivedecayareignored,thelongtimeapproximationfor releasefractionforthekernelismodeledas(Reference5):

1 6

(2)

Theshorttimeapproximationforfractionalreleaseofacoatinglayeris(Reference6):

241

.1 61 125 66 (3)

where, RF(T)=releasefractionofradionuclidesuptotimet=T

=ratiooflayerthicknesstotheinnerradiusofthelayer(unitless)

reduceddiffusioncoefficient

(unitless)

D=diffusivityofthediffusingspeciesinthediffusingmedium(m2/s),consistentwiththevalues inReference3.

t=time(s) d=thicknessofthecoatinglayer(m)

Thisshorttimeapproximationisappliedtoconditionswhere0.2.When0.2,thefollowinglong timeapproximationequationisusedtocalculatethefractionalreleaseforacoatinglayer(Reference6):

1 1 2

(4)

RadionuclidediffusionthroughTRISOlayersisemployedforfuelreleaseassumingnodepletionofthe radionuclideinventoryduetooperationtime.Inthisboundingmodel,radionuclidesareassumedto continuouslychallengeeachbarrierindependentofquantityofradionuclidesactuallychallenginga barrieratanygiventime.Forexample,radionuclidesthatreachtheouterpyrolyticcarbon(OPyC)layer atdayfiveofthesimulationwouldinstantlybereleasedfromtheOPyClayerwithafractionequivalent toradionuclidesthathavebeendiffusingthroughthebarriersincetheinitiationofthetransient.The releasefraction(RF)ofcompromisedlayersisconservativelysetto1.0.

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(5)

StructuralMARTransportfromStructuralMaterials ThetritiumisreleasedfromthesysteminthefollowingbatcheswhichroughlycorrespondstotheX/Q dispersionbins:

1)

PuffreleaseoftritiuminboththeFlibeandpebblecarbonmatrix,duetothehigh diffusivitiesattheprescribedpebblecarbonmatrixtemperatures,atthebeginning ofthetransient

2)

Aboundingdiffusionmodelestimatesthefractionoftritiumthattransportsoutof reflectorgraphitegrainsfrom:

i. 0to10min ii. 10minto2hours iii. 2hoursto8hours iv. 8hoursto14hours

v. 14hoursto24hours

3)

Remainingtritiuminthesystemtransportsoutofthesystembyanassumedpuff release24hoursintothetransient AllAr41predictedtobecontainedwithingraphitestructuresattheinitiationofthetransientispuff releasedintothegasspace.

TransportofMARfromFlibetotheGasSpace ThetworeleasemechanismsforMARinthecirculatingFlibearebubbleburstfromentrainedcovergas inthevesselcoolantandevaporationdrivenbytheMHAtemperaturecurve.Bubbleburstoccursbefore transientdiffusioncanoccurfromthefuelintotheFlibe,butevaporationmobilizesbothcirculating activityandMARthathasdiffusedfromthefuelintotheFlibe.

Foratwophaseflow,thevoidfractionoftheflowisdesignatedby.Thevolumetricflowrateofgas

, isrelatedtothetwophasemassflowrateofFlibe, bythefollowingexpression:

1 (6)

Theaerosolgenerationrate,isobtainedthroughthevolumetricratio(theratioofthevolumeof particlesgeneratedbyasinglebubbleburstingtothevolumeofthebubble)as:

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1 (7)

Theboundingvalueof=2.1x106ischosenfortheFlibeargonsystem.

Forconservatism,nodepositionisassumedduringtheaerosolgenerationprocess.Thetotalmassof aerosolisgivenby:

1 (8) where,isthemassoftwophaseFlibe.Thus,theaerosolreleasefractionfrombubbleburstis calculatedusing:

1 (9)

Thereleaseratesforgasesandhighvolatilitynoblemetalsinthecirculatingactivityareconservatively boundedbyinstantaneous(orpuff)releasesatthebeginningofthetransient.Otherradionuclides releasefromtheFlibeataratedeterminedbythegeneralevaporationlaw,asdescribedinReference3.

Conservativemasstransfercoefficientsthatneglectliquidsidemasstransferresistanceareused.

TheradionuclidesevaporatedfromtheFlibefreesurfaceareseparatedintothefollowingrelease inventories:

1)

PuffreleaseofdissolvednoblegasesandbubbleburstFlibeaerosolsatthe beginningofthetransient;

2)

Onelinearreleaseforevaporationofradionuclidesoverthefirst10min temperatureintervalcorrespondingtoprereactortripfueltemperature;

3)

Onelinearreleaseforevaporationofradionuclidesoverthenext110min temperatureinterval;

4)

Onelinearreleaseforevaporationofradionuclidesoverthe70hourrelease interval;

5)

Onelinearreleaseperdayforthenextsevendaysforthereactorcooldownperiod; and

6)

Onefinallinearreleaseoverthe20days.

GasSpace Thegasspacetransportevaluationisdividedintotwomodels:buildingtransportandatmospheric dispersion.ThemethodologyforDesignBasisAccidentsinReference3isusedtoevaluatethegasspace transport.Sitespecific

valuesareusedasinputtothedispersionmodeling.

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17of98 2.4 RESULTS TheMHAsummarizedinthisreportresultsindosesthatarewellbelowthe10CFR100limitsfornon powerreactorsitingandbelowtheEnvironmentalProtectionAgencyGuidelineguidanceforprotection actions.Acceptancecriteriaforfiguresofmeritthataresurrogatesforradionuclidereleasesforthe variouspostulatedeventcategoriesarederivedfromtheMHAconditionstoensurethatpostulated eventsareboundedbytheMHAasdiscussedinSection3.4.

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CAPABILITYOFEVALUATIONMODELS 3.1 OVERVIEWOFEVALUATIONMODELSFORPOSTULATEDEVENTS ThesafetyanalysisofpostulatedeventsrequirestheuseofseveralEMs.Thissectiondescribesthe capabilityoftheevaluationmodelsbyprovidingthelistofpostulatedeventsthattheEMsareusedto analyze,theimportantphenomenathatmustbecapturedbytheEMs,andthefiguresofmeritthat mustbeevaluatedbytheEMs.

3.2 EVALUATIONMODELAPPLICABILITY 3.2.1 PostulatedEventCategoriesandDurationofEvaluation Thepostulatedeventsincludeanypotentialupsettoplantoperations,withintheplantdesignbasis,that causesanunplannedtransienttooccur.Theeffectsofpostulatedeventsaremitigatedbydesign features.Anyeventexcluded(preventedbydesign)mustbedescribedinthelicensingapplication.

ConsistentwithNUREG1537,thepostulatedeventswithsimilarcharacteristicsandmodeling approachesaregroupedintocategories.Thepostulatedeventsaregroupedintothefollowing categories:

SaltSpills InsertionofExcessReactivity IncreaseinHeatRemoval LossofForcedCirculation(LossofNormalElectricalPowereventsareboundedbythiseventgroup)

InternalHazardEvents ExternalHazardEvents PebbleHandlingandStorageSystemMalfunction RadioactiveReleasefromaSubsystemorComponent GeneralChallengestoNormalOperation Thelimitingeventforeachcategoryisanalyzedfromtheeventinitiationuntiltheplantreachesasafe state.Thesafestateisdefinedforeachcategoryofeventsasapointwherethetransientfiguresof merithavestabilizedinasafecondition.Foranyeventsthatoccurwhenfuelisloadedinthecore,the plantmustbeinasafeshutdowncondition,wherethecontrolandshutdownelementsinsertto shutdownthereactorandmaintainlongtermreactivitycontrol,andthedecayheatisremovedeither throughparasiticheatlosses,orbythedecayheatremovalsystem.Thedecayheatremovalsystem (DHRS)isalwaysonwhentheanticipatedreactordecayheatloadisgreaterthanparasiticheat loss.Similartootherpassivereactordesigns,Hermesreliesonpassiveheatremovalthatdoesnot requireoperatorinterventiontomitigatetheheatupeffectsofpostulatedevents.Therefore,the transientmethodsforeachcategoryofpostulatedeventrequirethatananalysisshowstheevent reachesandmaintainsasafestateforatleast72hoursfollowingtheinitiationofthetransient.Thetime duringwhichthedecayheatremovalsystemisreliedupontomitigatetheheatupeffectsofaneventis referredtoasthemissiontime.

3.2.2 PostulatedEvents

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19of98 Thissectionprovidesanarrativedescriptionofeachpostulatedeventcategory.Ineachcategory,the narrativeisaccompaniedbytheeventspecificcharacteristicsthatdefineasafestate,andthefiguresof meritthatthedesignisevaluatedagainsttoensurethelimitingpostulatedeventforthecategory remainsboundedbytheMHA.Thegeneralnarrativeforeachpostulatedeventcategoryisprovidedin thissectiontoprovidecontextforthefiguresofmerit.Theeventspecificdetailsandanalysismethods areprovidedinSection4.5.

3.2.2.1 SaltSpills Ahypotheticaldoubleendedguillotinebreakintheprimarysaltpipingduringnormaloperation causesFlibetospillfromtheprimaryheattransportsystem.Saltspillsaredetecteddirectlyorindirectly bythereactorprotectionsystem,whichinitiatescontrolandshutdownelementsinsertion,fulfillingthe reactivitycontrolfunction.Theprimarycoolantpumptripandantisiphonfeaturesoftheprimary systemlimittheamountofspilledFlibe.Thereactordecayheatremovalsystemlimitsreactor temperatureandfulfillsthedecayheatremovalfunction.Inthereactor,airthatentersthereactor systemfromthebreakreactswithFlibetoformvolatileproductsandoxidizesunsubmergedstructural graphiteandpebblecarbonmatrixofunsubmergedpebbles.Afractionoftheradionuclidesthatare normallycirculatingintheFlibearereleasedintothefacilityairwhenaerosolsaregeneratedfromthe saltthatexitsthepipe.TheFlibespillsontothereactorcellfloorandformsapool.Thereactorcellfloor isassumedtobedesignedtoprecludeFlibeconcretereactions.Additionalradionuclidesinthespilled FlibearereleasedthroughevaporationuntilthetopsurfaceoftheFlibepoolissolidified.

Asafestateisestablishedwhen:

Thecoreissubcriticalandlongtermreactivitycontrolisassured.

Thedecayheatisbeingremovedandlongtermcoolingisassured,wherefiguresofmerit temperaturesaresteadilydecreasingduringthemissiontimeofthedecayheatremovalsystem.

FlibetemperatureinsidethereactorvesselremainsabovetheFlibefreezingtemperature.

FlibestopsspillingoutofthebreakandtheresultingFlibepoolfreezes.

Thisnarrativecapturesthelimitingeventofthispostulatedeventcategory.Othereventsgroupedinthis categoryinclude:

Spuriousdrainingandsmallerleaksfromtheprimaryheattransportsystem LeaksfromotherFlibecontainingsystemsandcomponents(e.g.,inventorymanagementsystem fill/draintank,inventorymanagementsystempiping,chemistrycontrolsystempiping,heat rejectionradiator[HRR]tube)

Leaksuptothehypotheticaldoubleendedguillotineprimarysaltpipingbreaksize MechanicalimpactorcollisioneventsinvolvingFlibecontainingstructures,systems,and components(SSCs)(exceptthevessel)

Thepipebreakonthehotlegisassumedtobethelimitingscenario.However,theeventspecific methodsinSection4.5describeaspectrumofbreaksizesandscenariosisanalyzedtoconfirmthe boundingsaltspillevent.Thebreaksizesandlocationsdeterminetheamountofmechanicalaerosol generatedbythespilledFlibejet.Afterthepipebreakisdetectedbythereactorprotectionsystemand tripsthereactor,theresponseofthecoreissimilarforotherbreaksizes.

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20of98 ForpipebreakscenariosinotherFlibecontainingSSCs(exceptthevessel)notconnectedtothereactor, thecoredoesnotexperienceatransientfromreactortrip.

Inordertoensurethatthedesignfeaturesmitigatingasaltspilleventaresufficienttokeepthe consequencesboundedbytheMHA,thefollowingkeyfiguresofmeritmustbeevaluated:

PeakTRISOtemperaturetolimitdiffusionofradionuclides TRISOfailureprobabilitytolimitincrementalTRISOlayerfailures PeakFlibecovergasinterfacialtemperaturetolimitevaporationmasstransferofradionuclides Peakvesselandcorebarreltemperaturestopreventvesselfailureandmaintainlongtermcooling AerosolsgeneratedbyreleasedFlibetolimitthematerialsatriskreleased VolatileproductsformedfromthechemicalreactionbetweenFlibeandair,Flibeandstainlesssteel, andFlibeandinsulationtolimitthematerialsatriskreleased Masslossofstructuralgraphiteduetooxidationtolimittritiumrelease Masslossofpebblecarbonmatrixduetooxidationtolimittritiumreleaseandpreventadditional releaseofmaterialsatrisk Peaktemperatureofstructuralgraphitetolimitthetritiumrelease Peaktemperatureofpebblecarbonmatrixtolimittheamountoftritiumrelease 3.2.2.2 InsertionofExcessReactivity Acontrolsystemerrororoperatorerrorcausesacontinuouswithdrawalofthehighestworthcontrol elementatmaximumreactivitycontrolandshutdownsystem(RCSS)drivespeed.Thereactivity insertionisdetectedbythereactorprotectionsystemwhichinitiatescontrolandshutdownelements insertion,fulfillingthereactivitycontrolfunction.Thereactordecayheatremovalsystemlimitsreactor temperatureandfulfillstheheatremovalfunction.

Asafestateisestablishedwhen:

Thecoreissubcriticalandlongtermreactivitycontrolisassured.

Thedecayheatisbeingremovedandlongtermcoolingisassured,wherefiguresofmerit temperaturesaresteadilydecreasingduringthemissiontimeofthedecayheatremovalsystem.

FlibetemperatureinsidethereactorvesselremainsabovetheFlibefreezingtemperature.

Thisnarrativecapturesthelimitingeventofthispostulatedeventcategory.Othereventsgroupedinthis categoryinclude:

Reactivityinsertioneventscausedbyfuelloadingerror(e.g.,errorsinrateoffreshfuelinjection, incorrectorderoffuelinsertion)

Reactivityinsertioneventswithconcurrentpumptrip Reactivityinsertioneventswithnormalheatrejectionavailable Localphenomenaleadingtorampinsertionofreactivity Changeinreactivityduetoshiftingofgraphitereflectorblocks

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21of98 Ventingofgasbubblesaccumulatedintheactivecore Localphenomenaleadingtostepinsertionofreactivity Localnegativereactivityanomaly(e.g.,inadvertentsingleelementinsertion,covergasinjection)

Reactivityinsertioneventsduringstartup Thecontrolelementwithdrawalatmaximumspeed,describedabove,isassumedtobethelimiting eventofthiscategory.However,theamountandrateofreactivityinsertionfromothergroupedevents underinsertionofexcessreactivity(e.g.,duringthepebbleloadingerrorevent,ventingofaccumulated gasbubblesintheactivecore)iscomparedwiththosefromthecontrolelementwithdrawalevents.

Additionally,thereactivityinsertionduetoIncreaseinHeatRemovaleventsanddesignbasisseismic event,respectively,iscomparedtothereactivityinsertionofcontrolelementwithdrawalevents.

Inordertoensurethatthedesignfeaturesmitigatingareactivityinsertioneventaresufficienttokeep theconsequencesboundedbytheMHA,thefollowingkeyfiguresofmeritmustbeevaluated:

PeakTRISOtemperaturetolimitdiffusionofradionuclides TRISOfailureprobabilitytolimitincrementalTRISOlayerfailures PeakFlibecovergasinterfacialtemperaturetolimitevaporationmasstransferofradionuclides Peakvesselandcorebarreltemperaturestopreventvesselfailureandmaintainlongtermcooling Peaktemperatureofstructuralgraphitetolimitthetritiumrelease Peaktemperatureofpebblecarbonmatrixtolimittheamountoftritiumrelease 3.2.2.3 IncreaseinHeatRemoval Theprimarycoolantpumpoverspeeds,causingasurgeinsertionofcoldFlibeintothecore.Theeventis detectedbythereactorprotectionsystem,whichinitiatescontrolandshutdownelementsinsertion, fulfillingthereactivitycontrolfunction.Thereactorprotectionsystemalsotripstheprimarycoolant pump.Thereactordecayheatremovalsystemlimitsreactortemperatureandfulfillstheheatremoval function.

Asafestateisestablishedwhen:

Thecoreissubcriticalandlongtermreactivitycontrolisassured.

Thedecayheatisbeingremovedandlongtermcoolingisassured,wherefigureofmerit temperaturesaresteadilydecreasingduringthemissiontimeofthedecayheatremovalsystem.

FlibetemperatureinsidethereactorvesselremainsabovetheFlibefreezingtemperature.

Thisnarrativecapturesthelimitingeventofthispostulatedeventcategory.Othereventsgroupedinthis categoryinclude:

Increaseinheatremovalduetooverspeedofheatrejectionblower Increaseinheatremovalduringlowpoweroperation Theincreaseinheatremovaleventsaredemonstratedtobeboundedbytheinsertionofexcess reactivitypostulatedevent.

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22of98 Inordertoensurethatthedesignfeaturesmitigatinganincreaseinheatremovaleventaresufficientto keeptheconsequencesboundedbytheMHA,thefollowingkeyfiguresofmeritmustbeevaluated:

PeakTRISOtemperaturetolimitdiffusionofradionuclides TRISOfailureprobabilitytolimitincrementalTRISOlayerfailures PeakFlibecovergasinterfacialtemperaturetolimitevaporationmasstransferofradionuclides Peakvesselandcorebarreltemperaturestopreventvesselfailureandmaintainlongtermcooling Peaktemperatureofstructuralgraphitetolimitthetritiumrelease Peaktemperatureofpebblecarbonmatrixtolimittheamountoftritiumrelease 3.2.2.4 LossofForcedCirculation Thefailureoftheprimarysaltpumpresultsinthelossofforcedcirculation.Thereducedflowis detecteddirectlyorindirectlybythereactorprotectionsystem,whichinitiatescontrolandshutdown elementsinsertion,fulfillingthereactivitycontrolfunction.Thereactordecayheatremovalsystem limitsreactortemperatureandfulfillstheheatremovalfunction.

Asafestateisestablishedwhen:

Thecoreissubcriticalandlongtermreactivitycontrolisassured.

Thedecayheatisbeingremovedandlongtermcoolingisassured,wherefiguresofmerit temperaturesaresteadilydecreasingduringthemissiontimeofthedecayheatremovalsystem.

FlibetemperatureinsidethereactorvesselremainsabovetheFlibefreezingtemperature.

Thisnarrativecapturesthelimitingeventofthispostulatedeventcategory.Othereventsgroupedinthis categoryincludelossofforcedcirculationdueto:

Blockageofflowpathexternaltothereactorvesselintheprimaryheattransportsystem, Spuriouspumptripsignal Pumpseizure Shaftfracture Bearingfailure Pumpcontrolsystemerrors Supplybreakerspuriousopening Lossofnetpositivesuctionhead(e.g.,pumpoverspeed,lowlevel)

Lossofnormalelectricalpower Flibefreezinginsideheatrejectionradiatortubes Lossofnormalheatsink Therearetwoboundingeventswithinthiseventcategorytoevaluatethelongtermpassivecooling performance.Oneistoboundtheoverheatingconsequence,andanotheristoboundthedowncomer freezingconsequence.Twoscenariosareconsideredforthesetwoboundingevents:

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23of98 Thefirsteventscenario(overheating)considersthelimitingcasetoanalyzethepeakvesselandcore barreltemperaturestopreventvesselfailureandmaintaincoolablegeometry.Themostlimiting reactoroperationpowerandoperatinghistoryareassumed.

Thesecondscenario(longtermovercooling)aimatthereactorperformanceevaluationintermsof coolantfreezepreventionatdowncomer.Aspectrumofreactordecayheatlevelsandoperating powerlevelsareanalyzedforthispurpose.

Fortheoverheatingboundingevent,thelossofforcedcirculationduetolossofnormalelectricalpower isboundedbytheprimarysaltpumpfailurescenario.Thelossofpowertothereactivitycontroland shutdownsystemmechanismsresultsinreleaseandinsertionofthecontrolandshutdownelements.As such,thereactorpowerisreducedfastercomparedtootherlossofforcedcirculationscenarioswhere thereactortripsonareactortripsignal.Forthelongtermovercoolingboundingevent,thelossof normalelectricalpowereventboundsotherlossofcirculationscenariossincethiseventhastheleast storedenergy.

Inordertoensurethatthedesignfeaturesmitigatingalossofforcedcirculationeventaresufficientto keeptheconsequencesboundedbytheMHA,thefollowingkeyfiguresofmeritmustbeevaluated:

PeakTRISOtemperaturetolimitdiffusionofradionuclides TRISOfailureprobabilitytolimitincrementalTRISOlayerfailures PeakFlibecovergasinterfacialtemperaturetolimitevaporationmasstransferofradionuclides Peakvesselandcorebarreltemperaturestopreventvesselfailureandmaintainlongtermcooling Peaktemperatureofstructuralgraphitetolimitthetritiumrelease Peaktemperatureofpebblecarbonmatrixtolimittheamountoftritiumrelease Theonlyfigureofmeritforthelongtermovercoolingscenariois:

Minimumreactorvesselinnersurfacetemperaturetopreventpartialfreezingwithindowncomer 3.2.2.5 PebbleHandlingandStorageSystemMalfunction Therearethreetypesofeventsinthiseventcategory:pebblehandlingandstoragesystem(PHSS) break,lossofPHSScooling,andgrindingofapebbleinthepebblehandlingmachine.However,theloss ofPHSScoolingisaneventmitigatedthroughdesignofpebblestoragesystem,andthegrindingof pebblemitigatedthroughthedesignofpebbleextractionmachine.Theconsequencesofthesetwo eventsareexpectedtobelimitedbythedesignspecificationswhichareboundedbyMHAconsequence.

Therefore,thePHSSbreakeventistheassumedlimitingeventtobeanalyzedforthiscategory.

Thepebblehandlingandstoragesystemtransferlinebreakswhenpebblesaregettingremovedfrom thecore,resultinginspillingofthepebbleswithinthetransferlineintothereactorcell.Thisconditionis detecteddirectlyorindirectlybythereactorprotectionsystem,whichtripsthepebblehandlingand storagesystemtostoppebblemovement.Forthespilledpebbles,thereactivitycontrolfunctionis fulfilledbythelowfissileinventoryofpebbles,whichprecludescriticalitysafetyconcerns,whileheat transfermechanismswithintheroomfulfillstheheatremovalfunction.Thestructuralintegrityofthe pebblesmaintainstheconfinementfunction.Forthepebblesremaininginthepebblehandlingand storagesystem,thereactivitycontrol,heatremovalandconfinementfunctionscontinuetobefulfilled bythesystemdesignresultinginasafeandstablestate.TheheatupofthepebblesinthePHSS

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24of98 mobilizestheFlibeaccumulatedonthepiping.AiringressintothePHSSandreactorcovergasregion occursthroughthebreak.

Asafestateisestablishedwhen:

Themovementofpebblesoutsideofthecorehasstoppedandcriticalitysafetyisassured.

Decayheatisbeingremovedfrompebblesoutsideofthecoreandlongtermcoolingisassured, wherefigureofmerittemperaturesaresteadilydecreasing.

ThisnarrativecapturesthelimitingPHSSbreakeventofthispostulatedeventcategory.OtherPHSS breakeventsgroupedinthiscategoryinclude:

Atransferlinebreakwhenpebblesaregettinginsertedintoemptycore Atransferlinebreakwhenpebblesaregettinginsertedintothecoreatpower Atransferlinebreakwhenpebblesaregettingtransferredtostoragecanisters Amishandlingoffueloutsidethereactor(e.g.,containmentbox,atthematerialbalanceareasand keymeasurepoints)

ThePHSSbreakeventwhenpebblesareextractedfromthecoreisconsideredboundingamongthe groupedeventsbecausethespilledpebbleshavehighertemperaturesandburnups,therefore,the highestdecayheatandMARloadingcomparedtoothereventsinthegroup.

InordertoensurethatthedesignfeaturesmitigatingaPHSSbreakeventaresufficienttokeepthe consequencesboundedbytheMHA,thefollowingkeyfiguresofmeritmustbeevaluated:

PeakTRISOtemperatureexvesseltolimitdiffusionofradionuclides MobilizedFlibeandgraphitedustreleased PeakTRISOtemperatureinvesseltolimitdiffusionofradionuclides TRISOfailureprobabilitytolimitincrementalTRISOlayerfailures PeakFlibecovergasinterfacialtemperaturetolimitevaporationmasstransferofradionuclides Peakvesselandcorebarreltemperaturestopreventvesselfailureandmaintainlongtermcooling Masslossofpebblecarbonmatrixduetooxidationtolimittritiumreleaseandpreventadditional releaseofmaterialsatrisk Masslossofstructuralgraphiteduetooxidationtolimittritiumrelease Peaktemperatureofstructuralgraphitetolimitthetritiumrelease Peaktemperatureofpebblecarbonmatrixtolimittheamountoftritiumrelease 3.2.2.6 RadioactiveReleasefromaSubsystemorComponent Anexternalhazardeventcausesafailureofcomponentsnotprotectedfromthehazardtofailand releaseMARstoredinthesesystems.Thesesystemsinclude:

Tritiummanagementsystem Inertgassystem

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25of98 Chemistrycontrolsystem Inventorymanagementsystem Thisnarrativecapturesthelimitingeventofthispostulatedeventcategory.Othereventsgroupedinthis categoryinclude:

Individualboundarybreachesorleaksfromanyoftheabovesystemsduetointernalhazardsor randomfailure RadioactivereleasefromSSCs(e.g.,residualFlibeintheprimarysaltpump(PSP),dustinPHSS piping)isolatedformaintenance Thekeyfigureofmeritforthiseventis:

Amountofmaterialsatriskreleased Thelimitingeventforthiscategoryisassumedtobeaseismiceventthatresultsinthefailureofall systemsorcomponentsnotqualifiedtomaintainstructuralintegrityinasafetyshutdownearthquake.

TheamountofMARinthesesystemsisassumedtobelimitedtoanupperboundlimitsuchthat thetotalamountofmaterialsatriskreleasedisboundedbytheamountreleasedduringthe MHA.Therefore,noadditionaltransientanalysisisneeded.

3.2.2.7 NotUsed 3.2.2.8 InternalandExternalHazards TheinternalhazardeventsintheHermesdesignbasisinclude:

Internalfire Internalwaterflood TheexternalhazardeventsintheHermesdesignbasisinclude:

Seismicevent Highwindevent Toxicrelease MechanicalimpactorcollisionwithSSCs Externalflood Thereactorcanbeshutdownmanually(e.g.,duringatoxicrelease)orautomatically(e.g.,waterflood causingalossofelectricalpower).Thedecayheatremovalsystemperformsitsfunctiontolimitreactor temperatureandfulfilltheheatremovalfunction.

Thekeyfiguresofmeritforinternalandexternalhazardeventsare TheSSCsassociatedwithengineeredsafetyfeaturesareavailabletomitigatetheevents.

TheamountofmaterialsatriskinSSCsnotprotectedfromthehazardarelimited.

Engineeredsafetyfeaturescontainedwithinareasprotectedfromorabletowithstandtheintensityof thehazardloadingforhazardeventsinitiatedoutsidethoseareas(e.g.,fire)maintaintheircapabilityto bringtheplanttoasafestatefollowingapostulatedevent.TheSSCswithinthoseareasaredesignedto

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26of98 withstandanupperboundhazardloadingintensityassociatedwiththearea(e.g.,SSCscanwithstandan upperboundheatloadandtheassociatedareaisequippedwithfiredetectionandsuppressionsystems tolimittheheatload).

ForSSCsnotprotectedwithsuchanarea,theamountofmaterialsatriskareassumedtobelimitedto anupperboundlimitsuchthattheamountofmaterialsatriskreleasedisboundedbytheamount releasedduringtheMHA.

Duringaseismicevent,thepackingfractionofthepebblebedwouldincreaseduetoshakingofthe pebblebed,andthegraphitereflectorblockswouldshift.Thisresultsinanincreaseinreactivity,causing anincreaseinfueltemperature.Theincreaseinreactivityduetoincreaseinpackingfractionofthe pebblebedandmaximumdisplacementofgraphitereflectorblocksduringaseismiceventisbounded bytheinsertionofexcessreactivityeventwherethecontrolelementisinadvertentlywithdrawn.

IncreaseinpackingfractioninthecoreisequivalenttoremovalofFlibewhichisanegativereactivity impact.Theoverallcarbontoheavymetalatomratio(C/HM)staysfairlyconstantwithinthecore.

However,ontheperipheryofthebedclosetothereflector,theC/HMishigherthanthebeditself.This causesasituationwherethereductioninthatC/HMbringsaboutapositivereactivityinsertioninthe core.Neutronicsmodelswithvariouspackingfractions(latticemodels)isusedtodemonstratethatthe impactsaresmall.

MechanicalaerosolscouldalsobegeneratedduetosplashingofFlibeinthereactorduringaseismic event.Theamountofaerosolsgeneratedduringaseismiceventisboundedbytheamountofaerosols generatedbythesaltspilleventwhereapipebreaks.

3.2.2.9 GeneralChallengestoNormalOperation Ageneralchallengetonormaloperationoccursthatrequiresanautomaticormanualshutdownofthe plant.Thedisturbanceisdetecteddirectlyorindirectlybythereactorprotectionsystem,whichinitiates controlandshutdownelementsinsertion,fulfillingthereactivitycontrolfunction.Thereactordecay heatremovalsystemperformsitsfunctiontolimitreactortemperatureandfulfilltheheatremoval function.

Groupedeventsincludespurioustripsduetocontrolsystemanomalies,operatorerrorsandequipment failures.Thiseventgroupalsoincludesscenarioswhereoperatorschoosetomanuallyshutdownthe plant.Alsoincludedarefaultsinthereactivitycontrolandshutdownsystem,electricalsystem,heat rejectionsystem,andotherplantsystemsthatwouldchallengenormaloperations.

Thisgroupalsocontainsinertgassystemdisturbances,andinstrumentationandcontrol(I&C)faults.

ThiseventgroupisboundedbytheLossofForcedCirculationpostulatedevent.

3.2.3 EvaluationModelsUsedtoAnalyzePostulatedEvents Table31providesthelistofpostulatedeventcategories,andtheEMusedtoanalyzethem.Notall postulatedeventsgroupedinthecategoriesareexplicitlyanalyzedwiththeEMsdescribedinthis report.Section4.5describestheeventspecificanalysismethodology,whichinsomecasesprovidesthe justificationforapostulatedeventorapostulatedeventcategorybeingboundedbyamorelimiting postulatedevent.

3.3 PHENOMENAIDENTIFICATIONANDRANKINGTABLES ThePhenomenaIdentificationandRankingTable(PIRT)processisanintegralpartoftheEvaluation ModelDevelopmentandAssessmentProcesslaidoutinRG1.203.APIRTreliesonexpertjudgmentto

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27of98 identifyandrankkeyphenomenaforaspecificsystemundergoingaspecifictimephaseofaspecific transient.ThePIRTprocessgeneratesaprioritizedlistofkeyphenomenathatneedtobecharacterized andmodeledtopredictresponsetospecifictransients.Italsorankstheknowledgelevelforeachkey phenomenonforeachcomponent,thusidentifyingcriticalgapsintheunderstandingofspecific phenomena.

KairosPowerhasperformedaseriesofPIRTsforKPFHRs.ThelistofPIRTsrelevanttothedevelopment ofsafetyanalysisEMs,whichleveragedifferentsetsofpanelexperts,include:

ThermalfluidsPIRT RadiologicalsourcetermPIRT(SummaryprovidedinReference3)

FuelElementPIRT(SummaryprovidedinReference7)

NeutronicsPIRT(SummaryprovidedinReference8)

HightemperaturestructuralmaterialsPIRT(SummaryprovidedinReference9)

ThethermalfluidsPIRTwasperformedtoidentifykeythermalhydraulicsphenomenaimportantto safety,prioritizethermalhydraulicstestsandEMdevelopment.ThePIRThelpsinformwhichareasof theEMsrequireexistingdataortestingtovalidate.Ultimately,thePIRTisatoolthathelpsinformthe safetyanalysismethodologydevelopmentandassessmentofoverallevaluationmodeladequacy.

KeyphenomenarelevanttoHermespostulatedeventsthatwereidentifiedashavingahighimportance tosafetyandalowknowledgelevelforpostulatedeventsaresummarizedinthefollowinglist,andwill beaddressedwithmodeldevelopmentor/andvalidationtests:

((

))

3.4 FIGURESOFMERIT 3.4.1 DoseAcceptanceCriteria ThedoseconsequencesoftheMHAdemonstratetheacceptabilityofthedesignwhencomparedto regulatorydoselimits.Therearenodoselimitsdefinedin10CFR50foranonpowerreactor;10CFR 100definesdoselimitsapplicabletoanonpowerreactor.Thedoselimitsin10CFR100.11requirethat anapplicantforanonpowerreactorevaluatedoseattheEABandthelowpopulationzone(LPZ)as follows:

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28of98 EAB:AnindividuallocatedontheEABfortwohoursimmediatelyfollowingonsetofthepostulated fissionproductreleasewouldnotreceiveatotalradiationdosetothewholebodyinexcessof25 remoratotalradiationdoseinexcessof300remtothethyroidfromiodineexposure.

LPZ:AnindividuallocatedontheouterboundaryoftheLPZwhoisexposedtotheradioactivecloud resultingfromtheMHA(duringtheentireperiodofitspassage)wouldnotreceiveatotalradiation dosetothewholebodyinexcessof25remoratotalradiationdoseinexcessof300remtothe thyroidfromiodineexposure.

TheMHAdescribedinSection2resultsinaboundingdoseconsequenceforaKPFHRwithdesign featuresdescribedinSection1thataresignificantlylowerthanthosespecifiedin10CFR100.11.

Specifically,theMHAresultsinawholebodydoseatthesiteboundarythatislessthan1rem.

3.4.2 PostulatedEventFiguresofMerit ThreemethodsareavailabletoensureanddemonstrateapostulatedeventisboundedbytheMHA:(1) directdosecalculationforallreleasepathways,(2)usingfiguresofmeritassurrogatefordose,and(3) usingbothdirectdosecalculationforsomereleasepathwaysandfiguresofmeritforotherpathways.

Directdosecalculationisthemoststraightforwardmethod;however,itrequirescomplexanalysis.

Figuresofmeritmethodcansignificantlyreduceanalysiscostsincethedoseofthesamerelease pathwaycanbeboundedbyoneboundingcase.

Figuresofmeritforthepostulatedeventmustbedemonstratedtomeetacceptancecriteriaderived fromtheMHAconditions.Thefiguresofmeritforeachpostulatedeventaredevelopedbasedonthe releasepathwaysofradionuclidesduringtheevent.Theacceptancecriteriaforfiguresofmeritare developedtoensuretheradionuclidereleasesfromthepostulatedeventsthroughthesamepathways astheMHAarelessthanthosefromtheMHA.Therefore,iftheacceptancecriteriaforallfiguresof meritforapostulatedeventaremet,thedoseofthepostulatedeventisboundedbytheMHA.

ForthepostulatedeventswithadditionalreleasepathwaysthatdonotexistintheMHA,thethird methodisused.Thismethodhasthreesteps:

1.

Boundingdosesarecalculatedforeachreleasepathway;boundingdoseforeachrelease pathwayisthenusedtoderiveacceptancecriteriaforfiguresofmeritaccordingtothe boundingreleasepathwayconditionsforthepostulatedevent.

2.

Foreachspecificpostulatedevent,iffiguresofmeritfortheinvolvedreleasepathways meetacceptancecriteria,thecorrespondingboundingdosevaluesforthepathwayscanbe usedinsteadofdirectdoseanalysis.Directdoseanalysisforcertainreleasepathwayscan alsobeperformed.

3.

Allthedosevaluesforeachreleasepathwayforthepostulatedeventaresummedto comparewiththeMHAtotalreleasedose.Thetotaldoseforthepostulatedeventmustbe lowerthantheMHAdose.

Asanexample,forthefiguresofmeritmethod(i.e.,secondmethod),duringacoretransient, radionuclidesdiffusethroughtheTRISOfuellayersasafunctionoftemperature.Radionuclides inFlibeevaporatefromtheFlibecovergasinterfaceasafunctionoftemperature.Tritiumdesorbsfrom thegraphiteandpebblecarbonmatrix.Therefore,thepeakTRISOtemperaturetime,peakFlibecover gasinterfacialtemperature,peakgraphitetemperatureandpeakpebblecarbonmatrixtemperature profilesduringtheeventarefiguresofmeritforapostulatedeventthatinvolvesthecore.Additionally, TRISOfailureprobabilityisalsoafigureofmerittolimitincrementalfuelfailuretoanegligiblelevel

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29of98 duringthetransient;peakvesselandcorebarreltemperaturesarekeyfigureofmerittoensurethe reactorvesselperformsitssafetyfunction.

Thefiguresofmeritusedforsystemscodeanalysis(KPSAM)areasurrogatefordemonstratingthat consequencesareboundedbyMHAdoses,orformaintainingacoolablegeometry.However,ifdoseis thefigureofmeritforanevent(i.e.,adoseanalysisisperformedfortheevent),thenthosesurrogate figuresofmeritfordosedonotneedtomeetacceptancecriteria,becausethedoseacceptancecriterion isbeingexplicitlyevaluated.Likewise,whenafigureofmerithasbeenanalyzedseparatelyforbounding conditions(e.g.,astructuralanalysisofthevesselisperformedseparatelyfromthesystemsanalysis) thenthatfigureofmeritdoesnotneedtobeanalyzedinthesystemscodetomeetanacceptance criterion.

ThefiguresofmeritandassociatedacceptancecriteriaareprovidedinTable32.Theapplicableevent(s) arethosethatareexpectedtoprovidethelimitingcaseforagivenfigureofmerit.

3.4.2.1 PeakTRISOTemperatureTime Thereleasepathwayforfuelisdiffusionalreleaseasafunctionoftemperature.Duringapostulated event,peakTRISOtemperatureisboundedbytemperaturetimecurvederivedfromtheassumedMHA fueltemperaturetimecurvetolimitdiffusionofradionuclidestolessthantheamountduringtheMHA.

BoundingtemperaturetimecurvederivedfromtheassumedMHAtemperaturetimecurvecanbe basedonintegratedeffectsondose.

3.4.2.2 TRISOFailureProbability BasedonTRISOfuelqualificationeffortsasdescribedin(Reference26),itisexpectedthatduringa postulatedevent,incrementalfailureofTRISOfuelislimitedtoanegligiblelevelifthepeaktemperature isbelow1600°C.FailureprobabilityofTRISOfuelcanincreaseduetooverpressureintheTRISO particles,whichisafunctiontemperature.ThefailureprobabilityofTRISOfuelisevaluatedusingthe methodologydescribedinSection4.2.

3.4.2.3 PeakFlibecovergasinterfacialtemperatures RadionuclidereleasefromFlibeisthroughevaporation.Duringapostulatedevent,peakFlibecovergas interfacialtemperatureisboundedbytemperaturetimecurvederivedfromtheassumedMHAFlibe covergasinterfacialtemperaturetimecurvetolimitevaporationmasstransferofradionuclidestoless thantheamountduringtheMHA.BoundingtemperaturetimecurvederivedfromtheassumedMHA temperaturetimecurvecanbebasedonintegratedeffectsondose.

3.4.2.4 Peakvesselandcorebarreltemperature Topreventvesselfailureandmaintainlongtermcoolingduringapostulatedevent,thepeakvesseland corebarreltemperaturesmustbelessthanboth(a)amaximumallowabletemperaturederivedtolimit excessivecreepdeformationanddamageaccumulationand(b)750°C.Themaximumallowable temperatureiscalculatedsothatthecreepstraininducedbyprimarymembranestresseswithinthe vesselandthecorebarreldoesnotexceed1%attheendofreactorlife.Itsderivationreliesonthe followingassumptions:

AllregionsofthevesselandcorebarrelincontactwithFlibeareexposedtotemperatureslower thanorequalto650°Cforthehotoperatingtimeofthevesselandtemperatureslowerthanor equaltothevesselandcorebarrelpeaktemperaturesforamaximumdurationof360hours(15 days).

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30of98 Themaximumprimarystressesundergonebythevesselandcorebarrelcanbeboundedbya maximumstressvaluederivedasdescribedintheevaluationmodelforstructuralintegrity.

3.4.2.5 Minimumreactorvesselinnersurfacetemperature ToensurethattheFlibetemperaturewithinthevesselremainsabovetheFlibefreezingtemperaturefor atleast72hours,alowerlimitonthereactorvesselinnersurfacetemperatureisconservativelysetto theFlibefreezingtemperature.

3.4.2.6 Airbornereleasefractionofspilled/splashedFlibe Duringasaltspillevent,aerosolscanbegeneratedthroughjetbreakup,andspillingandsplashing.The airbornereleasefractionsduetoaerosolizationmustbelimitedsothatthedoseconsequencesofthe saltspilleventsareboundedbytheMHA.

3.4.2.7 VolatileproductsfromFlibechemicalreactions Flibecouldbeexposedtoairduringasaltspillevent.ThekeyreleasepathwayofradionuclidefromFlibe isthroughevaporation,whichisafunctionofvaporpressureoftheradionuclidespecies.WhenFlibeis exposedtoair,theFlibeairchemicalreactiondoesnotresultinexcessivereactivevaporizationwhich wouldformradionuclidechemicalspeciesthathaveahighervaporpressurethanthosealreadyexistsin Flibecirculatingactivity.ItisexpectedthatafewspecificRNchemicalspecieswillhaveahighervapor pressureafterreactingwithairthanthoseinthecirculatingactivity.However,thosespeciesare expectedtobepresentatverylowconcentrationsandtheresultingdifferenceinevaporationratewill beofminimalsignificance.Forexample,CsFdissolvedinFlibedoesnotreactwithairtoformahighly volatilecesiumhydroxide.Assuch,Flibeairreactiondoesnotresultinsignificantadditionalreleaseof radionuclidesfromFlibethroughevaporation.

ThereactorcellfloorisassumedtobedesignedtoprecludeFlibeconcretereaction.WhenFlibeis spilled,ithasthepotentialtocomeincontactwithstainlesssteelandinsulationmaterial.Flibe interactionswithstainlesssteelandinsulationdonotresultinformationofradionuclidechemical speciesthathaveahighervaporpressurethanthosealreadyexistsinFlibecirculatingactivity.

Therefore,FlibestainlesssteelandFlibeinsulationreactionsintheHermesdesignbasisdonotresultin additionalreleaseofradionuclidesfromFlibethroughevaporation.

Duringasaltspillevent,Flibeisnotexposedtowater,andthereforenoFlibewaterreactionneedtobe considered.However,ifacommoncausefailure(e.g.,seismic)causesawatercontainingSSCandFlibe containingSSCtofailconcurrently,theamountofwaterthatFlibecouldbeexposedtoisassumedtobe limitedtoanupperboundlimitbydesign.Wheninteractingwiththisupperboundamountofwater, Fliberedoxpotentialisstillmaintainedwithintheboundsofsaltchemistryconditionsdefinedforthe evaporationmodel;therefore,doesnotresultinadditionalreleaseofradionuclidesfromFlibethrough evaporation.

3.4.2.8 Masslossofstructuralgraphiteandpebblecarbonmatrix PebblesandstructuralgraphitenotsubmergedinFlibecanoxidizewhenexposedtoair.Ifthemassloss ofthepebblecarbonmatrixdoesnotextendtothefueledzone,tritiumreleaseistheonlyadditional MARreleasepathwaytobeconsideredwhenfuelpebbleoxidizes.Tritiumispuffreleasedfromoxidized pebblecarbonmatrixandoxidizedstructuralgraphite.IntheMHAanalysis,theassumedtemperature forpebblecarbonmatrixissohighthatallavailabletritiumiseffectivelypuffreleasedfromthepebble carbonmatrix.TheportionofstructuralgraphiteunsubmergedinFlibeissmall.Theinventoryoftritium puffreleased(insteadofasafunctionoftemperature)fromoxidizationofstructuralgraphitenot

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31of98 submergedinFlibeisaccommodatedbythefollowinginherentconservatisminthetreatmentoftritium intheMHA:

Conservativeinventoryoftritiumavailableforrelease Conservativelyhighassumedtemperatureofpebbles Moderatorpebblesassumedtohavethesametemperatureasfuelpebbles 3.4.2.9 Peakstructuralgraphitetemperature Tritiumisreleasefromstructuralgraphiteasafunctionoftemperature.Duringapostulatedevent,the peakstructuralgraphitetemperatureisboundedbytemperaturetimecurvesderivedfromtheassumed MHAstructuralgraphitetemperaturetimecurvetolimittritiumreleasetotheamountduringtheMHA.

BoundingtemperaturetimecurvederivedfromtheassumedMHAtemperaturetimecurvecanbe basedonintegratedeffectsondose.

3.4.2.10 Peakpebblecarbonmatrixtemperature Tritiumisreleasedfrompebblecarbonmatrixasafunctionoftemperature.Duringapostulatedevent, thepeakpebblecarbonmatrixtemperatureisboundedbytemperaturetimecurvesderivedfromthe assumedMHApeakpebblecarbonmatrixtemperaturetimecurvetolimittritiumreleasetotheamount duringtheMHA.BoundingtemperaturetimecurvederivedfromtheassumedMHAtemperaturetime curvecanbebasedonintegratedeffectsondose.

3.4.2.11 Amountofmaterialsatriskreleased DuringaPHSSbreak,additionalmaterialsatriskcanbereleasedthroughgraphitedustandmobilized Flibeinthesystem.AsthesearenotreleasepathwaysintheMHA,theequivalentdoseofthese materialsatriskreleasedislimitedtobelowaderivedlimittoensurethesereleasepathwaysdonot causetheconsequenceofthispostulatedeventtoexceedthoseoftheMHA.

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32of98 4

EVALUATIONMODELS 4.1 SYSTEMSANALYSIS 4.1.1 KPSAMCodeDescription TheSystemAnalysisModulecode,alsoknownasSAM,wasdevelopedbytheU.S.DepartmentofEnergy andArgonneNationalLaboratoryasagenericsystemlevelsafetyanalysistoolforadvancednonLWRs.

Thecodesolvestightlycoupledphysicalphenomenaincludingfissionreaction,heattransfer,andfluid dynamicsinreactorstructures,systems,andcomponents.

KairosPowerhasdevelopedandmaintainedaKPFHRspecificcodebasedonSAMwiththecapabilities ofSAMcalledKPSAM.

KPSAMisdirectlybuiltontheMultiphysicsObjectOrientedSimulationEnvironment(MOOSE) frameworkatshowninFigure41whichhandlesmostofthenumericalmethods,outputprocessingand mostoftheinputprocessing.MOOSEanditsbasepackageslikeLibMeshandPETScareopensource softwarethusthemajordevelopmentfromSAMtoKPSAMincludesadescriptionofthephysicsand systemcomponentbehaviors,handlingspecificnumericalmethodssuchascontinuousFiniteElement Methodstabilizingmethods,andaddingspecificfunctionsforthesystemscode.

KPSAM,likeSAMusessimplifiedthermalhydraulicmodelstorepresentthemajorphysicalcomponents anddescribemajorphysicalprocessessuchasfluidflowandheattransfer.Themaintypesof componentsinSAMarelistedbelow.

Basicgeometriccomponentsdescribingindividual1D/2Dfluidorsoliddomains 0Dcomponentsforsettingboundaryconditionsfor1Dfluiddomains 0Dcomponentsforconnecting1Dcomponents Assemblycomponentsthatareconstitutedbycombiningdifferentbasicgeometriccomponentsor 0Dconnectingcomponents Nongeometriccomponentsforphysicsintegration,controlandtripsystems,orspecial1Dmodels suchasthepointkineticmodel 4.1.1.1 PhysicalModelsandEquations KPSAM,likeSAMhastwotypesofphysicsmodels:fieldequationsandclosuremodels.Fieldequations aresolvedtodeterminethetransportofthequantitiesofinterestin0D,1D,or2Ddomains.The singlephaseflowfieldequationsinKPSAMshowninEquation10include1Dmass,momentum,and energyconservationsalongtheflowdirection.

0

ll 2

(10)

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33of98

where,

=coolantdensity u=velocity T=coolanttemperature t=time s=theaxialcoordinateinflowdirection p=pressure gg cos

=anglebetweentheflowdirectionandgravityvector g=thegravityconstant.

f=frictioncoefficient D=equivalenthydraulicdiameter c=thespecificheat q=theconvectionheatfluxfromsolidsurface PandA=heatedperimeterandcrosssectionalareaofthecoolantchannelrespectively.

TheprimaryvariablesforthesinglephaseflowmodelinKPSAMarethepressure,velocity,and temperature.

Heatstructuresmodeltheheatconductioninsidethesolidsandpermitthemodelingofheattransferat theinterfacesbetweensolidandfluidcomponents.Heatstructuresarerepresentedby1Dor2Dheat conductioninCartesianorcylindricalcoordinates.Onedimensionalsphericalheatconductionmodelis alsodevelopedforpebblebedsimulation.Temperaturedependentthermalconductivitiesand volumetricheatcapacitiescanbeprovidedintabularorfunctionalformfromusersupplieddata,or directlyprovidedbythecodeandaccessedthroughgivenmaterialnames.Themodelingcapabilitiesof heatstructurescanbeusedtopredictthetemperaturedistributionsinsolidcomponentssuchasfuel pinsorplates,heatexchangertubes,andpipeandvesselwalls,aswellastocalculatetheheatflux conditionsforfluidcomponents.Thethermalconductioninsidethesolidstructuresisgovernedbythe heatconductionequation.

KPSAMincludesaTRISOparticleaveragetemperaturemodelassociatedwithpebblebedcorechannel componentmodel.ThefuelpebbleofKPFHRdesignhasafuelannuluslayerbetweenthecentrallow densitycoreandouterfuelfreeshell.TRISOmodelinKPSAMsimulatestemperaturesofthefuelkernel, buffer,andcover(theIPyC,SiC,andOPyClumpedtogether),inadditiontotheaveragetemperaturein fuelannuluswhichismodeledbyheatstructuremodel.

Special0Dmodelscanbetakenas0Dfieldequations.The3Dfieldequationsareintegratedoverthe domainandthepartialdifferentialequationsbecomeordinarydifferentialequations.Thespatial integrationprocessneedsspecialspatialprofileassumptions.Thespecial0DmodelsinKPSAMinclude

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34of98 thevolumebranch,valve,pump,tank,pointkineticmodels,thermalradiation,andgapconductance models.

Thewidelyusedpointkineticsequationsmodelformultiplegroupsofdelayedneutronprecursorswas implementedinKPSAMwithfullyimplicittimeschemeoptionsavailableupto5thorderaccuracy.The decayheatpowercanbecalculatedfromtheuserprovideddecaycurve,ortheANSI/ANS5.12005 standardmethod.Whichevermethodisused,uncertaintyfactorswillbeappliedtoensureitis conservative.Forthepredictivedecayheatmodel,thefissilematerialfissionfractionsincludeU235,U 238,Pu239,andPu241andareprovidedbythereactorcoredesigncalculation.Thefissionratiosof fissilematerialsareprovidedforvariousstagesofoperation(buildup).Asensitivityfactorcanalsobe appliedtothedecayheatfractioninordertoconservativelyaccountforuncertaintiesindecayheat.

Closurerelationsarecorrelationsandequationsthathelptomodelthetermsinthefieldequationsby providingcodecapabilitytomodelandscaleparticularprocesses.Typicalclosuremodelsincludewall frictionfactorandformlossmodelsfordifferentflowgeometries,convectiveheattransfercorrelations fordifferentheattransfersurfacesandpumpperformancecurves.Forexample,theKerntechnischer Ausschuss(KTA)correlation(Reference27)wasusedforpebblebedpressuredropcalculationsinthe sampletransientKPSAManalysis.Fluidandsolidproperties,includingequationsofstatearealso neededtoclosethefieldequations.ThefluidstobesimulatedincludeFlibe,intermediatesalt,water, simulantoil,air,andargongas.

Table41summarizesthemodelsandthefieldequationsusedbyKPSAM.

4.1.1.2 ControlSystemDescription TheSAMcontrolsystemisusedtoperformtheevaluationofalgebraicandsimpleordinarydifferential equations;thetripsystemisusedtoperformtheevaluationoflogicalstatements.Thefundamental approximationmadeinthedesignofcontrol/tripsystemisthattheexecutionofcontrol/tripsystemis decoupledfromtheotherpartsofthehydraulicsystems.Themainexecutionofindividualcontrol/trip unitsissetattheendofeachtimestep.

4.1.1.3 NumericalMethods SAMusesacontinuousfiniteelementmethodsformulationforthespatialdiscretizationofthe1Dor2 Dfieldequations.ThedetaileddiscretizationforbothtimeandspaceismanagedbyMOOSE,withthe codeformulatedsuchthatthenumericalmethodordersarecontrolledthroughuserinputs.Forfluid models,aspatialstabilizationmethodisrequiredtosuppresscheckerboardtypespatialoscillationsthat manifestwhensolvingadvectiondominatedproblemsusingcontinuousfiniteelementmethods.The StreamLineUpwind/PetrovGalerkinandthePressureStabilizing/PetrovGalerkinschemeare implementedinSAMtoresolvethenumericalinstabilityissues(Reference10).

ThephysicsinSAMisintegratedintoasinglefullycouplednonlinearequationsystem.Thediscretized nonlinearequationsystemissolvedusingapreconditionedJacobianFreeNewtonKrylovmethod.The combinationoftheJacobianFreeNewtonKrylovnonlinearsolverandhighordernumericalmethodsfor bothtimeandspaceenablesthecapabilitytominimizenumericalerrors.

4.1.1.4 QualityAssuranceandConfigurationControl Thesoftwarequalityassuranceplanisdesignedtoprovideaframeworkforsolvingcomputational engineeringproblems.Thesoftwarequalityassuranceplanincludesrolesandresponsibilitiesforthe softwaredeveloper,reviewer,tester,anduseraswellasdocumentationandsoftwarereview requirements.Thesoftwarequalityassuranceplanalsodescribesconfigurationmanagement,change

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35of98 control,auditrequirements,softwareengineeringmethods,standards,practices,conventions,and metricstobeused,thecontrolofsupportsoftware,trainingandrecordsthataretobecollected, maintained,andretained.

4.1.2 KPSAMVerificationandValidationPlan KPSAMwillbeverifiedandvalidatedpriortothefinalsafetyanalysis.

TheKPSAMverificationprocessconfirmsthesoftwarefunctionsasdesigned(i.e.,softwareverification);

andthattheequationsarecorrectlysolvedbythecode(i.e.,numericalverification.)Inasystemscode, softwareverificationisthroughregressiontestscoveringthecomponents,boundaryconditions, functionsforsteadystate,restart,etc.

TheKPSAMvalidationcomparessimulationresultsagainstexperimentaldata.Unittestcoverssimple testdataandisusedtovalidatefluidandsolidpropertiesandheattransferandwallfriction correlations.Separateeffectstestvalidationcoverstheimportantthermalhydraulicphenomena relevantduringaccidentconditions,asidentifiedbythePIRT.Integratedeffectstestvalidationcovers scaledintegraltestsatsystemlevelorplantlevel,oftenatdifferentscalestoavoidscalingdistortion.

Reactortestsprovidemoredirectevidencethatthesystemscodecanaccuratelysimulatetransient responses.Thethermalhydraulicandreactorphysicsstronglycoupledunprotectedeventscanonlybe performedwithatestreactor.

TheassessmentoftheKPSAMEMadequacyincludestheevaluationofclosurerelationsandthe integratedEMadequacytoquantifyuncertainties.

4.1.3 PlantKPSAMModel AsamplebaseKPSAMmodelisprovidedforeventsthatrequireasystemsanalysis.Thisbasemodelcan bemodifiedaccordingtothespecificmodelingneedsforeachevent.Itisprovidedhereasanexample ofanacceptablemodelforusewiththeHermestransientmethodology.

TheKPSAMmodelincludesupperandlowerplena,asubdividedcorebasedonflowareaand correspondinglysubdividedreflector,downcomer,vessel,andcoolingpanelsections.Asetofprimary pipingisincludedinthemodelmakingupthehotandcoldlegsofthereactorandincludesmodelsfora pumpandaPHX.Nonfuel/PHXheatstructuresinthemodelare2Dinordertomodelaxialheat transfer.Thereactorpowerismodeledusingapointkineticsanddecayheatmodel.Thetemperature profilewithinthepebbleismodelledbya1DconductionmodelwithaspecialmodelforTRISOparticles withinthefuellayeroffuelpebbles.

Areflectorbypasschannelismodeledtocapturetheeffectofflowfromthelowerplenumbypassing thecoreinfavoroftheflowpaththroughthereflector.Theareaofthisbypasschannelissetsuchthat anassumedconservativefractionoftheflowmakesitswaydirectlyfromthelowerplenumtotheupper plenum.Abypassflowpathcontainingafluidicdiode,isalsoincludedinthemodeltoredirectthe coolantintheupperplenumdownintothedowncomer,duringnaturalcirculationmode.

ThePHXisutilizedduringsteadystatetorejectheatfromthesystemandcontrolthelowerplenum temperature.ThesecondarysideofthePHXisdefinedbytimedependentboundaryconditions.

Similarly,theDHRSismodeledbyradiativelycouplingvesselheatstructuresandcoolingpanelheat structuresandplacingatemperatureboundaryconditionontheoutsidewallofthecoolingpanels.The instrumentandcontrolsystemismodeledbytheKPSAMtripandcontrolsystem.ThesampleKPSAM

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36of98 nodaldiagramisdepictedinFigure42.Table42summarizesKPSAMcomponentsusedforeachregion inthesamplenodaldiagram.

NotethatthePHXisreplacedwiththeHRRintheHermesdesign.ThePHXintheKPSAMmodelwillalso bereplacedwithHRR.

Ahotchannelfactormethodconservativelyenvelopesthemaximumbulkcoolanttemperatureinthe coreforfuelperformanceanalysis:

(11)

where,

=conservativemaximumcoolanttemperature

=lowerplenumcoolanttemperature

=calculatedpeakcoolanttemperature

=directflowhotchannelfactor

=directpowerhotchannelfactor Inthishighlysimplifiedmethod,itisassumedthatanythingthatcouldskewthereactorpowerprofileor coolantdistributionwithinthecorehappensincoincidence.Themethodismadefurtherconservative byscalingthegradientbetweentheKPSAMcalculatedpeakcoolanttemperatureandthelowerplenum temperatureinsteadoftakingthecoolanttemperaturetobeatthenodewithmaximumfuel temperature.

Thedirectpowerhotchannelfactor(e.g.,1.3)accountsforradialpeakinganduncertaintiesinthe neutroniccalculations.Powermeasurementuncertaintyishandledexplicitlybybiasingthereactor powerinthemodel.Thedirectflowhotchannelfactor(e.g.,1.2)andisintendedtotakeintoaccount anykindofbulkflowmaldistributionfromsourcessuchaspumpintakeplacementthatcouldbepresent inthecore.Itisnotnecessarytoderiveasubfactorforflowbypassingthecoreandtravelingthrough thereflectorbecausethisismodeledexplicitly.

Onceareactortripisinitiatedandthecontrolandshutdownelementsstarttoinsert,thereactorpower transientismainlyaffectedbythenegativereactivityinsertionbythecontrolandshutdownelements insertion.Thepositiondependentcontrolandshutdownelementworthisdeterminedbynuclearcore analysisandisappliedinthesafetyanalysiswithaddeduncertainties.Themostlimitingminimum controlsystemworthisused,consideringthereactorcorefuelcycle,whichisassumedtobethe equilibriumcore.Theelementinsertionspeedisconservativelyapplied,aswell.

4.2 FUELPERFORMANCE ThecodeKPBISONisusedtomodelfuelperformanceusingthemethodologydescribedinReference7.

TheevaluationmodelforpostulatedeventsusesKPBISONwithaconservativeapproachtoassessthe pretransientfuelfailureprobabilityandradionuclidereleaseduringnormaloperationtoinformthe stateofthefuelateventinitiation.Themodelingofthenormaloperationphasereliesontwobounding trajectories(i.e.,physicalpathsfollowedbythefuelpebblesinthecorealongwhichtheyaccumulate burnupandfastfluence)toensureconservativepretransientfuelfailureprobabilitiesandfission productreleasefractions:

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37of98 AlowtemperaturetrajectoryisusedtocomputetheprobabilityoffailureoftheSiClayerbyIPyC cracking.

Ahightemperaturesteadystatetrajectoryisusedtocomputetheprobabilityofpretransient failureoftheTRISOparticlebyoverpressureandoftheSiClayerbychemicalattackandthe fractionalreleaseofradionuclides.

Thetwotrajectoriesbothfollowtheirradiationhistorythatachievesdischargeburnupandmaximum fastfluenceoftheHermesfuelandusetheminimumcoldleginletandmaximumcorehotchannel outlettemperaturesasbaselinetemperaturestocalculateconservativeisothermalpebblesurface temperaturesbasedonpebblecoolantheattransferandpotentiallocalconditions(e.g.,pebblepebble contact,etc.).Theseisothermaltemperaturesareusedtocalculatethelowandhighfueltemperatures appliedtotheTRISOparticlesforthecalculationofthepretransientfailureprobabilitiesand radionuclidereleasefractions.

ModelingofthenormaloperationphaseisincludedinthemethodologybecauseTRISOparticlesare morelikelytofailduringnormaloperationandinservicefailuresmustbeaccountedforinadditionto manufacturingdefects.Additionally,radionuclidestransportedthroughoutthecoatinglayersduringthe normaloperationphaseare,ingeneral,morereadilyavailabletobereleasedduringtransients.

Thepostulatedeventsaremodeledattheendofthenormaloperationphasetomaximizethe probabilityofpretransientIPyCcracking,thefissiongasinventorythatbuildsupinternalpressure,and thetimedependentpalladiumpenetration.Attheinitiationoftheevents,inservicefailuresfromthe normaloperationphaseareaddedtomanufacturingdefects(Table43).Incrementalfailuresfromthe transientphasearethencalculatedbyKPBISON,usingthepowerandtemperatureprofilesofthe transient.

ThecorrespondingradionuclidereleasefractionsarecalculatedforthevariousTRISOparticlecohorts (e.g.,intact,defective,orfailed)andcombinedwiththerelativefractionsofeachofthesecohortsto provideanoverallradionuclidereleasefromthefuel.

TheTRISOfuelpretransientfailuremodescanleadtofivedifferentmechanicalstatesfortheTRISO particles:

Intact CrackedIPyC CrackedIPyC+failedSiC(fromIPyCcrackingleadingtoSiCfailure)

FailedSiC(fromPdpenetration)

FailedTRISO(allcoatinglayersfailedfrominternaloverpressure)

Inaddition,TRISOparticlescanhavedefectivelayersfrommanufacturing.Fivecompromisedstates resultfromparticlesbeingeitherdefectiveorfailed.Intactparticlesaddasixthpossiblestate.Thesesix statesareeachassociatedwithaprobabilityofoccurrence:

Intact(1dIdSdOdT)x(1fIfISfSfT)

CompromisedIPyCdI+(1dIdSdOdT)xfI CompromisedIPyC+SiC(1dIdSdOdT)xfIS

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38of98 CompromisedSiCdS+(1dIdSdOdT)xfS CompromisedOPyCdO CompromisedTRISOdT+(1dIdSdOdT)xfT WheredI,dS,dO,anddTarethedefectivefractionsoftheIPyClayer,SiClayer,OPyClayer,andTRISO particle(i.e.,exposedkernel),respectively,whilefI(crackedIPyC),fIS(crackedIPyC+failedSiC),fS(failed SiC),andfT(failedTRISO)aretheinservicefailurefractionsfortheTRISOfuelfailuremodes.

Radionuclidereleaseiscalculatedforeachoftheintactandfivecompromisedstatesandtheoverall radionuclidereleasefromthepopulationofTRISOparticlesisobtainedbyweightingtheresulting releasefractionsbytheprobabilitiesofoccurrenceofthesestates.Disperseduraniumisassumedtobe fullyreleasedfromtheTRISOparticlesanditscontributionisaddedtothereleasefromtheintactand compromisedparticles.

TheverificationandvalidationplansfortheKPBISONcodearesummarizedinReference7.

4.3 NEUTRONICS TheSerpent2codeisusedforneutronicscalculations.TheStarCCM+codeisusedforbothdiscrete elementmodelingofthepebbleflowandporousmediaapproximationforthermalhydraulicsfeedback.

Thedescriptionofthesetoolsandmodelsalongwithvalidation,verification,anduncertaintiesare presentedinReference8.

4.4 STRUCTURALANALYSIS ThematerialsqualificationplanforhightemperaturemetallicmaterialsisprovidedinReference9.The materialsqualificationplanforgraphitematerialsisprovidedinReference11.Thesequalificationplans informthefiguresofmeritforthereactorvesselandinternalsdescribedinthisreport.Thestructural analysisofthematerialsunderpostulatedeventconditionswillbeperformedpriortosubmittalofan OperatingLicenseApplication.

4.5 EVENTSPECIFICMETHODS Thissectionprovidestheeventspecificmethodsthatusetheevaluationmodelswithconservative inputstoanalyzethetransientsdiscussedinSection3.Keymodeluncertaintiesandinitialconditionsare conservativelyappliedtothemethodstoensurefiguresofmeritareconservativelypredicted.

ParameterrangesconsideredforalleventsareprovidedinTable44.Sampleresultsforthepostulated eventcategoriesareprovidedinAppendixAtoillustratethetransientmethodologies.

4.5.1 SaltSpills ThesaltspilleventcategoryisdescribedinSection3.2.2.Theanalysisoftheboundingsaltspilleventis composedofthefollowingmodels:

Singlephasebreakflowmodel-themassflowratewithtimethroughthebreakandthefinalupper plenumfreesurfacelevelarethetwomajormodelingresults.Twophaseflowduetogas entrainmentispreventedthroughtheprimarypumpdesign.Twomodelingoptionsareavailable:(a)

KPSAMmodelbasedontheslightmodificationofthebaselineplantmodeltoincludethesingle phasebreakflowmodel;and(b)aconservativeanalyticalmodel Longtermperformanceofpassivedecayheatremovalmodel-thisissimilarasthemodelusedfor lossofforcedcirculationoverheatingboundingcasebutwithreducedfreesurfacelevel.

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39of98 Radioactivesourcetermreleasemodelstoestimatetheboundingtotalreleasefromtheevent.Two majorsourcetermmodelsarerequired:

o Aerosolgenerationrateandamountduetosinglephasecoolantjet.

o FissionproductevaporationratesandamountfromthespilledFlibepoolandfromtheinvessel Flibefreesurface.

Airingressionandgraphiteoxidationmodels-generalgasflowmodelisavailableinKPSAM;aKPSAM inputmodelisusedtoperformtheanalysis:

o General gas flow model including buoyancy driven counter current flow limits the oxygen concentrationinthecovergasspace.

o Graphiteoxidationmodelprovidesboundinggraphitedensityreductionrate.

o AspecialKPSAMinputmodelwillcapturethemajorcomponentsinvolvingairingressionand graphiteoxidationmodels.

Acceptancecriteria-thethirdmethoddiscussedinSection3.4,usingbothdirectdosecalculationfor some release pathways and figures of merit for other pathways, is used to demonstrate that this postulatedeventisboundedbytheMHA.

4.5.1.1 InitialConditions Theinitialconditionsforthelimitingscenariomustbeprovidedandjustified.Thelimitingscenariois assumedtooccurwhenthereactorisoperatingatfullpowerandoperatingpressureandhasbeen operatinglongenoughforthefueltocontainfissionproductsatequilibriumconcentrations.Therefore, themaximumpossibledecayheatisavailableatthestartoftheevent.Althoughthehypothetical doubleendedguillotinehotlegbreakattheHRRinletisconsideredtheboundingcase,theentire spectrumofbreaksizesandlocationmustbeconsideredtoconfirmthatthedoubleendedguillotine breakisbounding.

TheinitialconditionsfortheamountanddistributionofMARimmediatelybeforethebreakmustbe determinedtocalculateasourcetermforthisevent.AsthiseventdoesnotinvolvethePHSS,theMAR inPHSSisexcludedfromtheanalysis.TheinitialMARdistributionissummarizedbelow:

FuelPebbleMAR ThemajorityoftheMARiscontainedbytheTRISOparticlesinthefuelpebblesinthecore.The inventoryofMARinthefuelisestablishedthroughcodeanalysisusingSerpent2.Thedefectratioof TRISOparticles,theadditionalinservicefailureoftheparticles,andthefractionofheavymetal contaminationarespecifiedthroughfuelqualificationrequirements(Reference12).

FlibeinMARinthePrimarySystem AconservativeamountofMARintheFlibeisassumedinthecirculatingactivityinthecoolant.Note theremayexistsmallamountofgraphitedustwhichissuspendedwithintheFlibe.Thedustbehavesas getterandabsorberoftritium.Thechemistrycontrolsystemensurestheloadingofgraphitedustis withinacceptablebounds.

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40of98 GraphiteandMetalStructuresMAR Onlytritiumisconsideredtobeabsorbedbygraphiteandmetalstructuresbasedonexistingknowledge.

Theamountoftritiumingraphiteandmetalstructureisestimatedwiththesameconservativeapproach asintheMHA.

CoverGasMAR AconservativeamountofMARintheargoncovergasisassumedtoaccountfortheactivityofthecover gassystem.

4.5.1.2 TransientAnalysisMethods VolumeofSpilledFlibe ToevaluatereleaseofMARtothebuildingairspaceandeventuallytotheenvironmentair,theamount ofFlibethatcanbespilledisdetermined.Acoolantleveltripsignalfromthereactorprotectionsystem iscreditedtotripthepump.Oncethepumpistripped,itcoastsdownuntilthepumpflowratedropsto almostzero.Atthispoint,avacuumbreakerisactivatedtoallowairtoenterthehighpointofthehot legpreventingsyphoningtheFlibeinthevessel.Anothersimilarvacuumbreaklocatedinthecoldleg alsoallowsairtoenterthehighpointofthecoldlegtoo.ThevolumeoftheFlibethatisspilledoutof thebreakisevaluatedas:

(12) whereisthevolumeofFlibeinthecoldlegbetweentheelevationofcoldlegnozzleandthe elevationofthebreak,isthetotalvolumeoftheFlibeinthehotleg,andistheaccumulative volumepumpedoutfromthetimeofpumptriptothefullycoastdowncondition.Assumethepump volumetricflowfollowsacoastdowncurvegivenby

(13) whereandarepumpvolumetricflowandtheflowatnormaloperation,isacharacteristic pumpcoastdowntime,equals// ln2,where/isthetimewhenthepumpvolumetricflowis reducedbyhalf.Thetotalvolumepumpedoutduringthecoastdowntimeisthengivenby

/

2 (14)

Therefore,forgivenvalueof/andhotlegandvesselgeometries,thevolumeofthespilledFlibecan bedeterminedthroughEquation12.Note:Equation12assumesthatislessthanthevolumefrom thelowlowsetpointleveltothepumpsuction.Ifthecumulativevolumeislargerthanthevolume fromthelowlowsetpointleveltothepumpsuctionlevel,shouldbeusedtoreplacein Equation12,becauseinthisconditionthepumpsuctionisexposedbeforethepumpfullycoastsdown.

Themethodstoevaluatethereleasesfromthefuelpebbles,remainingFlibe,graphiteandmetal structuresinthevesselisidenticaltothatofMHA,withthefollowingexceptions:

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41of98 TheconcentrationsofMARremaininginthevesselaregivenbycirculatingactivityalone,whilethe concentrationinMHAisthesumofthecirculatingactivityandtheconcentrationsduetoadditional fuelreleaseassumedinMHAevent.

TemperaturesofFlibe,fuelandstructuresinthiseventareevaluatedwithKPSAMbasedon conservativeassumptionsofdecayheatremovalcapabilitiesandotherboundaryconditions,while thetemperaturesinMHAeventfollowaboundingtemperatureversustimecurve.

InstantaneousReleasefromSpilledFlibe Theinstantaneousreleaseisthephaserightafterthebreak,whenthedischargedFlibeformsajet.The releaseisdominatedbytwomechanismsthatgenerateaerosols:jetbreakup,andsplashingandspilling whenFlibefallsontotheground.

WhenFlibeisdischargedfromthevesseltothebuilding,itformsacoherentjetbeforeitbreaksupinto droplets.Ifthefallingheightfromthebreaklocationtothegroundisshorterthanthebreakup distance,thejetisnotexpectedtobreakupandminimumamountofaerosolisgenerated.For conservatism,itisassumedthejetisalwaysbrokenupnomatterhowshortthefallingheightis.Most dropletsfromthejetbreakaretoolargetobeconsideredasaerosolparticlesbecausetheydeposit quicklyunderthegravity.However,asmallfractionofthedropletsissmallenoughtobesuspendedin theairandtransportedasaerosols.Toestimatethisfractionoftheaerosols,theSauterMeanDiameter whichistheaveragediameterbasedontheratiooftotalvolumeandtotalsurfacearea,isevaluated firstthroughanequationbyEpstein(Reference13)whichisbasedonanevenearlierderivationby Mayer(Reference14):

36.4

(15) whereislosscoefficientofthebreakandisthepressuredifferencebetweenthevesselandthe buildingair.AssumethedropletsfollowaRosinRammlersizedistribution(Reference15)andthe fractionofaerosolparticlescanbeobtainedthroughthecumulativefractionofthesizedistribution belowamaximumdiameterof50 (Reference16).Themaximumdiameterischosentobe consistentwiththeaerosolmodelinMELCORcode.Themassofaerosolgeneratedthroughthejet breakisthenobtainedfromtheproductoftotalspilledmassofFlibeandthefractionofaerosols.

AerosolscanalsobegeneratedwhenthejetordropletsfromthebrokenjetfallintoaFlibepool accumulatedonthegroundofreactorcell.WhenthejethitsthesurfaceoftheFlibepool,itentrainsair withitandformsbubblesinalayeradjacenttothesurfaceoftheFlibe.Bubbleburstingproducesvery fineaerosolparticles.Theamountofairentrainedbythejetanddropletsisbasedonanempirical expressiondevelopedbyBin(Reference17)as

0.04

(16) whereandarevolumetricflowratesoftheentrainedairandFlibeflow,Histhefallingheight, andisFroudenumberoftheFlibeflow.Volumetricrateofaerosolsgeneratedthroughthebubble burstingisconservativelyboundedbyalinearexpression(Reference18)

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42of98 (17) whereEisanentrainmentcoefficient.AconservativelyhighvalueofEis2.1E6(Reference19).The aerosolgenerationduetothespillingandsplashingisthenobtainedthroughtheFlibespillingrateand Equations16and17.

MARreleaseassociatedwiththeaerosolgenerationisevaluatedthroughtheaerosolamountandthe concentrationofMARinthespilledFlibe.

EvaporativeReleasefromSpilledFlibe TheevaporativereleaseisthephasewhenthedischargeoftheFlibefromthevesselendsandthe spilledFlibecompletesspreadingonthereactorcellfloor.SmallamountofFlibeislikelytospreadonlya fractionofthereactorcellfloorareabeforeitiscompletelysolidified.ItisnotamajorconcernforMAR releaseforpartiallyspreadingFlibebecauseitfreezesquickly.Moreconcernislargeamountofspilled Flibewhichspreadstheentireareaofthereactorcellfloor.Inthiscase,aFlibepoolisexpectedtoform withadepthofmoltenFlibe.Thebottomofthepoolcontactswithsteellinerwhichisplacedtoprevent Flibeconcreteinteraction.Thetopofthepooltransfersheattoairthroughconvectionandto surroundingstructuresthroughradiation.NowaterandnowatersourcesarepresentwheretheFlibe spreads,andFlibewaterinteractionisexcluded.

MARreleasefromtheFlibepoolisdominatedbyevaporationoverthetopsurfaceofthepool.It continuesuntilthetopsurfaceissolidified.ToevaluatetheamountofMARreleased,Flibe temperaturesareevaluatedfirst.TheFlibetemperatureisbasedonenergybalanceofthepool.Forthe downwardheattransfer,alayerofsolidifiedFlibeisexpectedbetweentheliquidFlibeandtheliner.A 1Dmovingboundaryequationneedstobesolvedforthetemperatureprofilewithinthesolidifiedlayer, andgrowth(orshrinkage)ofthelayer.TheboundaryconditionattheinterfacebetweentheliquidFlibe andthesolidifiedlayerisdeterminedbyGlobeDropkincorrelation(Reference20).Theboundary conditionattheinterfacebetweenthesolidifiedlayerandtheunderneathlinerisgivenbygap conductancebetweenthesolidifiedlayerandtheliner,orthroughcontinuityconditionsoftemperature andheatfluxifnogapisassumed.TheheattransferbetweentheliquidFlibetothetopsurfaceis determinedbyGlobeDropkincorrelationagain,andtheheattransferontheairsideisbasedon McAdamscorrelation(Reference21)fornaturalconvectionandradiationwithalowtemperatureheat structure.TheseheattransfertermsarecombinedtodeterminetheenergychangeoftheliquidFlibe duetoheattransferandsolidificationatthebottom,andeventuallythetemperaturesoftheliquidFlibe andatthetopsurface.

Oncethetemperaturesaredetermined,evaporationratesareassessedwiththesamemethodasthe MHAforMAR.Theevaporationrateandintegralreleaseamountareevaluateduntilthetemperatureof thetopsurfaceislowerthantheFlibemeltingtemperature.

4.5.2 InsertionofExcessReactivity ThelimitinginsertionofexcessreactivityisdescribedinSection3.2.2.Theanalysisofthelimitingevent inthiscategory(acontrolelementwithdrawal)includesasystemsanalysiswithconservativeneutronics andfuelperformanceinput.

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43of98 4.5.2.1 InitialConditions Theinitialconditionsofthetransientarebiasedtoensureaconservativeevaluationofthefiguresof merit.Thelimitingcontrolrodwithdrawalscenarioisassumedtoinitiatefromthehighestpossible reactorpowerbecausethehigherpowerprovidesthehighestheatinputtochallengetheidentified figuresofmerit.However,sensitivitiesmustbeperformedtoensurethatreactivityinsertionsfrom lowerpowerlevelsdonotunexpectedlychallengeafigureofmerit.Apoweruncertaintyisappliedto reactorpowertobiasthepowerhigh.

4.5.2.2 TransientAnalysisMethods Thereactivityinsertiontransientinvolvesachangeincorereactivitythataddsheattoprimarysystem.

Therefore,theeventanalysisrequiresinformationfromthesystemscode,fuelperformance,and neutronicsEMs.Thesystemscode,KPSAManalyzestheeventprogressionwithinputsfromthe neutronicsEMandprovidesinputstothefuelperformanceEM.

Thenuclearfissionpowerprofilewithinthepebblebedisaffectedbytheneutronfluxdistributioninthe coreregionandthefuelburnupstatusofthepebbles.Thecurrentapproachtomodelingcorepower densityisanaxiallyresolvedradiallyaveragedmethodanddoesnotexplicitlyaccountforradialpower peakinginthecore.Theradialpowerprofileanditseffectonthecoolantandfueltemperaturearenot explicitlymodeled;therefore,localpeakcoolantandfueltemperaturesarenotfullyresolved.Thehot channelfactormethodologydescribedinSection4.1accountsforbothpowerpeakingandthe possibilityofflowbeingpoorlydistributedinthecore.

Inordertoensureaconservativeevaluationofthelimitingreactivityinsertionevent,thefollowing conservatismsareappliedtomodelinputs:

Highestworthcontrolelementisassumedtobewithdrawn.

o Thelimitingreactivityinsertionrateisdeterminedfromthelimitingreactivityrodworthper lengthfromneutronicsEM,combinedwiththemaximumcontrolelementwithdrawalspeed.

o Arangeofreactivityinsertionrates,uptoandincludingthemaximumreactivityinsertionrate, areanalyzedinthefinalsafetyanalysis.

o Atfullpowerandhotzeropower,theinitialcontrolelementpositionisassumedtobefully insertedinthereactorcore.

o Aconservativetreatmentisappliedtoaddresstheimpactofadynamicchangeinpowershape associatedwiththecontrolelementmovement.

Leastnegativereactivityfeedbackcoefficientsareusedtominimizethepowersuppressioneffectby thenegativereactivityfeedbackinpreliminarysafetyanalysis.

Mostnegativereactivityfeedbackcoefficientsarealsobeappliedandanalyzedtoinvestigatethe effectofdelayedreactortripinthefinalsafetyanalysis.

Thiseventisalsoidentifiedasoneoftheboundingfuelperformancecasesandmustbeanalyzedwith theKPBISONusingthemethodologydescribedinSection4.2.

4.5.3 LossofForcedCirculation ThelimitinglossofforcedcirculationscenarioisdescribedinSection3.2.2.Theanalysisofthelimiting eventinthiscategoryincludesasystemsanalysiswithconservativeneutronicsinput.

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44of98 4.5.3.1 InitialConditions Theinitialconditionsofthetransientarebiasedtoensureaconservativeevaluationofthefiguresof merit.Thelimitinglossofforcedcirculationscenarioisassumedtoinitiatefromthehighestpossible reactorpowerbecausethehigherpowerprovidesthehighestheatinputtochallengetheidentified figuresofmerit.However,sensitivitiesmustbeperformedtoensurethatlossofforcedcirculation eventsfromlowerpowerlevelsdonotunexpectedlychallengeafigureofmerit.

4.5.3.2 TransientAnalysisMethods Theimportantthermalandhydraulicphenomenaduringthetransientincludetheflowfriction(negative head)atthepump,heattransferbetweenthecoolantandvariousinterfacingstructuressuchaspebble, reactorvesselwallandinternals.Becausetheforcedcirculationislost,thefluidfrictionthroughthe coolantloop,includingthereactorcore,ismoreimportantthanothereventswhereforcedflowis maintained.

KPSAMisusedtoanalyzetheeventprogressionwithinputsfromtheneutronicsEMandprovides inputstothestructuralintegrityEM.Uponalossofforcedcirculation,thereactorexperiencesan immediateincreaseinthefuel(pebble)temperaturebecauseofthereducedheattransfertothe coolant.ThecoolanttemperaturealsorisesbecauseheatremovalfromthereactorcoretotheHRRis reducedandeventuallystops.Theincreasedtemperatureofthecoolantcouldchallengetheintegrityof reactorvesselandcorebarrelstructures.

Thenuclearfissionpowerprofilewithinthepebblebedisaffectedbytheneutronfluxdistributioninthe coreregionandthefuelburnupstatusofthepebbles.Thecurrentapproachtomodelingcorepower densityisanaxiallyresolvedradiallyaveragedmethodanddoesnotexplicitlyaccountforradialpower peakinginthecore.Theradialpowerprofileanditseffectonthecoolantandfueltemperaturesarenot explicitlymodeled;therefore,localpeakcoolantandfueltemperaturesarenotfullyresolved.Thehot channelfactormethodologydescribedinSection4.1accountsforbothpowerpeakingandthe possibilityofflowbeingpoorlydistributedinthecore.

TheKPSAMbasemodeldescribedinSection4.1isusedtoanalyzealossofforcedcirculationevent withthefollowingmodifications:

Typically,theinteractionbetweenthefluidsystemandpump,duringthetransient,ismodeledusing headandtorquecurvesofthepump.Forthelossofforcedcirculationanalysis,thecoolantflow responseismodeledwithoutthedetailedpumpcharacteristics,byconservativelyassumingthe pumpheadafterthetransientstarts.Sincethepumprotorisassumedtostopinstantly,thepump torqueinformationisnotneeded.

Thereactivityfeedbackeffectonpowerisminimizedforconservativecalculationbyusingleast negativereactivitycoefficientvaluestominimizetheeffectofpowerreductionfromtheinitial temperatureincreasebythereducedcoolantflow.

TheuncertaintiesinmaterialpropertiesoftheFlibecoolantandvesselstructuresareaddressed conservatively.Thethermalmassofthematerialisreducedsuchthatthetemperaturesoffueland vesselstructurearepredictedhigher.Thereactivityfeedbackeffectismodeledinsuchawaythat theincreasedtemperaturesofthefuel,coolant,andstructure(graphite)donotoverestimatethe negativefeedbackeffect.

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45of98 Reactorprotectionsystemsetpointandtimedelay:Reactorprotectionsystemsignalsinitiatethe reactorshutdownelementtodropintothereactorcorebyagravity.Thesetpointdetectionand signaldelaybetweenthesystemareconservativelyappliedintheanalysis.

Headprovidedbythepumpisreducedtozerooninitiationoftheeventinordertomodelkey aspectsofpumpseizure.

4.5.4 PebbleHandlingandStorageSystemMalfunction ThelimitingPHSSmalfunctioneventisdescribedinSection3.2.2.Theanalysisofthelimitingeventin thiscategoryincludesaneventspecificevaluationmodeldescribedinthissection.

4.5.4.1 InitialConditions TheinitialconditionsoftheeventarebiasedtoensurethemaximumamountofMARisreleased.The MARindifferentbarriers(regions)attheinitialconditionneedstobeidentifiedandquantifiedsothat transientreleasesofMARcanbeevaluated.

FuelPebbleSpillDuringPHSSTransferLineBreak:

DuetothecontinuousrefuelingstrategyusedbytheKPFHR,fuelpebblesinthepebbletransferlines areeithertransportedfromthecoretothePHSSorsentbacktothecorefromthePHSS.Asdescribedin theeventscenarioinSection3.2.2,itisassumedthelongesttransportlinebreakscausingpebblesto spillfromtheline.Inaddition,adelaytimeisassumedbetweenthepebblespillingandthetripofthe pebbleextractionmachine.Thenumberofpebblesthatcanbespilledoutofthebreakisbasedonthree designparameters:thelengthofthetransportline,thespeedofpebblesmovingintheline,and therefuelingrate:

(18) whereinEquation18isthedelaytime.Conservatively,thespilledpebblesareassumedtohave thehighestburnupandthelargestamountofMARamongthepebbles.

GraphiteDustAccumulatedinthePHSS:

TheamountofgraphitedustaccumulatedinthePHSSisbasedonanestimatedmaximumdust generationrateduringnormaloperation.TheconcentrationofMARinthedustisassumedtobe identicaltotheMARinthegraphitematrixofthepebbleswiththehighestburnupandloadingofMAR.

However,creditistakenforradionuclidedecayduringnormaloperation.Foraradionuclideindexedby i,theamountofthegivenradionuclideinthegraphitedustisevaluatedthroughthesolutionofthe followingequation:

(19) where,isthedustgenerationrate,,istheconcentrationoftheradionuclideinthegraphite matrix,andisthedecayconstantoftheradionuclide.

FlibeAccumulatedinthePHSS:

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46of98 AcertainamountofFlibeisexpectedtobeaccumulatedinthePHSSduetocarryingoverbypebbles.It isexpectedthattheFlibesolidifiesinthePHSSduetoitslowtemperaturecomparedtoinsidethe reactorvessel.TheMARintheaccumulatedFlibeisbasedontheassumedconservativecirculating activityofradionuclidesinFlibeduringnormaloperation.

ArgonGasinthePHSS:

ItisassumedtheamountofMARinargongasinthePHSSissmallenoughthatitcanbetreatedasde minimisforMARrelease.Theamountisboundedbytheassumedconservativecirculatingactivityof radionuclidesincovergasduringnormaloperation.

FuelPebbles,Flibe,Graphite,MetalStructures,andCoverGasintheVessel ItisconservativelyassumedthatwhenthePHSSbreaks,thevesselisnotisolatedandMARinthevessel canbereleasedthroughthebreak.TheMARinvesseldistributesinbarriersincludingfuelpebblesinthe core,Flibe,graphiteandmetallicstructures,aswellascovergas.TheamountofMARisboundedbythe MARassumedinthesaltspillevent.

4.5.4.2 TransientAnalysisMethods TheobjectiveoftheanalysisofthePHSSbreakeventistoevaluatekeyfiguresofmeritfortheevent,so thatthedoseconsequencecanbeassessedanddemonstratedasbeingboundedbytheconsequenceof theMHA.

TheevaluationisperformedwithacombinationofanalysesusingSerpent2andKPBISON.Serpent2is usedtocalculatedecaypowerandquantitiesofMAR,includingtritiuminventoriesinfuelandFlibe,and KPBISONisusedtocalculatetheamountofMARheldupingraphiteandtheinitialMARdistributionin TRISOparticlesandthegraphitematrix.Theamountoftritiumabsorbedbyfuelpebbles,graphiteand metalstructuresisdeterminedwiththesameapproachastheMHAandisboundedforradionuclidesin theFlibeandcovergasduringnormaloperatingconditions.

UpondeterminingtheinitialconditionsofMARasdescribedabove,quantitativeanalysesaremadefor barriersthatareidentifiedthroughthequalitativeanalysisprocess.

ThenumberoffuelpebblesthatcanbespilledisobtainedthroughEquation18.Theinitialtemperature, decaypowerandMARconcentrationsinthegraphitematrixareassumedtobeconservativelyhighfor thespilledpebbles.

Whenapebbletransferlinebreaks,transportingpebblesforextractionorinsertion,pebblesintheline canspilloutofthebreakandfallonthefloorofthebuilding.Thespilledpebbles,sincethe temperaturesarehigh,canreactwiththeairinthebuildingtogenerateheatandtransferheattothe surroundingcoolairthroughnaturalconvectionandthermalradiation.Theheatremovalratethrough naturalconvectionandradiationmustbehigherthanthesumofdecayheatandchemicalreactionheat inorderforthepebblestobecooledandoxidationreducedtodeminimis.However,beforethepebble reachesafinalstablecondition,somemassofthepebbleislostduetooxidationandtheMARholdup associatedwiththelostmassreleasedintothebuildingair.Theobjectiveofthepebbleoxidationmodel istoevaluatethefractionofthemasslossandMARreleaseuntilthepebblereachesastablecondition.

Twomajorassumptionsaremadeinthedevelopmentofthepebbleoxidationmodel:

Eachpebblecanbeconsideredseparatelyfromotherpebblesforheattransferandoxidation becausepebblesareunlikelytopileuponthefloortoformapebblebed.

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47of98 TheMARreleasedfromapebbleisproportionaltothemasslossofthepebble.

TheoxidationofgraphiteisassumedtobeintheregimeIwhereoxygeninfiltrationoccurscausing volumetricoxidationinthepebbles.Theoxidationregimeassumptionisjustifiablebecauseofthe transitiontemperaturefromthekineticscontrolledoxidation(regimeI)tothekineticsandmass transfercontrolledoxidation(regimeII).Testresultsonagraphitesamplesimilartothegraphiteusedin Hermes,indicatethetransitiontemperatureisashighas700°C,butthehighesttemperatureofspilled pebblesislessthan700°C.

Forconservatism,thespilledpebblesareassumedtohavethesamedecayheat,initialtemperature,and MARholdupconcentration,whicharesettoconservativelyhighvaluestoboundtheconsequenceof pebbleoxidation.Theconductionequationofaspherewithinternalheatgenerationissolvedtoobtain thetemperatureprofileinasinglepebble.Convectiveandradiationboundaryconditionsareassumed ontheoutersurfaceofthepebble,givenby

(20) whereispebbletemperature,ispebbleradius,ispebblethermalconductivity,isthepebbles heattransfercoefficient,isthegastemperature,andaretheeffectiveemissivitybetweentwo graybodiesandtheStefanBoltzmannconstant,isthetemperatureoftheheatstructurewith radiationheatexchangewiththepebble.Thevolumetricheatgenerationrateinthepebbleisthesum ofdecayheatandthechemicalreactionheatrates,

(21) andthevolumetricoxidationheatgenerationrateisevaluatedbasedonmassrateofoxidationas:

(22) whereisthemassoxidationrateinunitsof

, isthegraphitedensityinunitof

, and is theenthalpychangeofoxidationreactioninunitsof/.Notethenegativesignintheequationof "isbecauseanegativevalueof indicatesanexothermalreaction.Forconservativism,the highestenthalpychangeof32.792MJ/kg(Reference22)amongalloxidationreactionsbetweencarbon andoxygenisused,whichisthechangeforthereactiongeneratingcarbondioxide.Theoxidationrateis afunctionoftemperatureinthepebble.Theoxidationratecorrelationsvaryinliteraturebecausethe typesofgraphiteandpropertiesaredifferent.Here,thecorrelationbyZhouet.al.(Reference28)for regimeIoxidationisproposedfortheanalysisbecausethegraphitesampleinthisliteratureissimilarto thetypeofgraphitethatisusedforpebblesofHermes.

0.7194 10./

(23) where,theunitofthetemperatureTisKelvinandtheunitoftheoxidationrateis1/s.Solutionofthe energyequationleadstotimedependenttemperatureandoxidationrate.Thetotalmasslossofthe graphiteisobtainedthroughtheintegraloftheoxidationrate:

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48of98 4,

(24)

AnestimateofthereleaseofMARwhichisoriginallyheldupinthegraphitematrixofthespilled pebblescanbemadeaccordingtothemassloss.TheactivitiesofholdupMARinthegraphitematrix areestimatedbasedonreleaseofMARfromdefectiveTRISOparticlesinthepebble,includingthose withdefectiveSiClayers,exposedkernels,andheavymetalcontamination.Suchanestimateis conservativebecauseitdoesnotcreditretentionofradioisotopesbythedefectiveparticles,butinstead assumesalltheMARintheseparticlesarereleasedandheldbythegraphitematrixinthepebble.By usingthisassumption,theactivitiesofMARinthegraphitematrixaregivenby (25) where,subscriptiistheindexoftheradioisotopeofMAR,A,istheactivityoftheisotopeinthe pebble,andfisthefractionofthedefectiveparticlesincludingthosewithdefectiveSiClayers, exposedkernels,andheavymetalcontamination.TheMARisassumedtobeuniformlydistributedin thegraphitematrixduetothelargediffusioncoefficient.SincethereleasedMARisassumedtobe proportionaltothemasslossofthepebble,thereleasedMARactivitiescanbeevaluatedas

(26) wheresubscriptiistheindexoftheradioisotopeofMAR, isthenumberofspilledpebbles,and isthemassofthegraphitematrixinapebble.

GraphiteDustAccumulatedinthePHSS:

GraphitedustisgeneratedandaccumulatedinPHSSduringnormaloperationduetopebblewear.Dust particlescanbehavelikegettersforMAR.WhenthePHSSbreaks,thedustcanberesuspendedand expelledfromthePHSStobuildingbytheleakagegasflowresultinginanincreaseinradioactivityinthe buildinggasspace.Theobjectiveofthegraphitedustresuspensionmodelistoassesstheamountofthe resuspendeddustandestimatetheMARreleasesduetoresuspension.

ThedustgenerationrateisdeterminedinordertoestimatethemassandactivitiesofdustinthePHSS.

Therateisbasedonanupperboundestimateofthespecificwearrateofpebblesslidingonthesurface ofstainlesssteel.Thespecificwearrate,inunitsof

,istherateofmasslossofpebblesdueto wearingunderunitnormalforceandslidingdistance.ForPHSS,thenormalforceofapebbleisthe weightofthepebble,assumingthereisnoothermechanicalforceexertedonitduringthepebble transferandinspection.Anupperboundslidingdistance canbeestimatedsincethedetailed designofPHSShasnotbeencompleted.Themassgenerationrateisthengivenby:

(27) whereisthemassofthepebble,gisthegravityaccelerationrate,andu,isthenumberof pebblesextractedpersecondinunitsof

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49of98 AmajorassumptionofthegraphitedustresuspensionmodelisthattheMARconcentrationinthe graphitedustequalstheconcentrationinthegraphitematrixwherethedustisgenerated.However, creditistakenfordecayingofradionuclidesduringnormaloperation.Theassumptionisconservative becausetheMARconcentrationingraphitematrixhasbeenestimatedconservatively,asdescribed above.Basedonthisassumption,theactivitiesofMARinthegraphitedustcanbedeterminedthrough thefollowingequation:

(28) where m andA, aremassofgraphitematrixinapebble,andtheactivityoftheradioisotope inthematrix,and isthedecayconstant. f intheequationrepresentsthefractionofthefuel pebblesinthecoreregion,becausetherearelargenumberofgraphitepebblesintheHermescorethat moderateneutrons.Therefore,apebblethatisextractedfromthecoreregionhasaprobabilitylessthan onebeingthefuelpebble,andonlythedustgeneratedbyfuelpebblescontributestotheactivityofMAR inthegraphitedust.SolutionofEquation28leadstoaformulationoftheactivityofdustasthefunction ofoperatingtime t ofthereactor:

,1

(29)

TheresuspensionmodelinMELCOR(Reference23)isusedforthedustresuspensionevaluationand assumesinstantaneousresuspensionbasedonthehighestleakagegasvelocity.Themodelwasderived throughtheconsiderationofbalancebetweentheaerodynamicliftforceandtheadherenceforce.It evaluatesacutoffdiameteroftheresuspendeddustparticles,abovewhichallthedustparticles originallydepositedonthesurfaceofthestructuresareresuspended.Thecutoffdiameterisafunction oftheroughness,inmicrons,andtheshearstressexertedbythegasflowgivenby 1

2 (30) where,istheFanningfrictionfactor,isthegasdensityanduisthegasvelocity.Thegasvelocity canbedeterminedthroughanexpression(Reference24)forcompressibleisentropicflowdrivenby pressuredifference.

Ifthecutoffdiameterisgreaterthanorequalto50,theresuspendeddustparticlesarenot consideredaerosolsbecausethesizeistoolargeforairborneparticles,i.e.,theparticlesareexpectedto bedepositedquicklyoncereleasedfromthePHSS.Otherwise,thefractionalreleaseofthegraphitedust isevaluatedwithanassumedsizedistributionofdustparticles.Alognormaldistributionofthe depositedparticlesisassumedbyFriedlander(Reference25)andthedistributionwaslaterusedby MELCORforcomparisonwiththeSTORMexperimentshowingreasonableagreement.

1 2

2 (31)

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50of98 where,istheparticlediameter,isthedistributionfunctionofparticlenumberdensities(i.e.,

isthefractionofthenumberofparticleswithdiameter),lnisthemeanofthelog normaldistribution,isthegeometricmeandiameter,lnisthestandarddeviationofthe distribution,andisthegeometricstandarddeviation.Forthelognormaldistribution,thegeometric meandiameterandstandarddeviationsofthedepositeddustparticlesneedtobeprovidedasinput.

Theresuspendedfractionofthedustparticlesisdeterminedasthefractionofthedustparticles withdiameterslargerthanthecutoffdiameterbutsmallerthantheupperlimitdiameterofaerosol particles50,i.e.,

(32) where, isthecutoffliftdiameter, 50 istheupperlimitoftheaerosolparticles,and isthethirdmomentofthenumberdistribution.InsertingthelognormaldistributionofEquation31into Equation32resultsinananalyticalformulationoftheresuspensionmassfraction:

2

2 (33) where, iserrorfunction,and 3. TheMARintheresuspendeddustparticlesisassumed tobereleasedasaerosolspromptlyforconservativism.

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CONCLUSIONS Thispostulatedeventsandtransientmethodologydescribedinthisreportmeettheobjectives describedinNUREG1537(exceptfortherejectionofpotentialevents,whichmustbedescribedinthe PreliminarySafetyAnalysisReport).Acomprehensivelistofeventcategoriesisdescribedtoensurethat enougheventshavebeenconsideredtoincludeanyeventthatcouldresultinsignificantradiological consequences.Theinitiatingeventsandscenariosarecategorizedbytypeandalimitingcaseforeach categoryisdescribed.Consistentandspecificacceptancecriteriafortheconsequencesofeach postulatedeventareprovided.

Themethodsdescribedinthisreportareusedtoevaluateeventswithinthedesignbasistoensurethere aresufficientdesignfeaturesavailabletomitigatetheeffectsandkeepthepotentialconsequences boundedbytheMHAdescribedinthisreport.

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REFERENCES

1. UniversityofCaliforniaBerkeleyNuclearEngineering.2015.FluorideSaltCooledHighTemperature Reactor.[ONLINE]Availableat:http://fhr.nuc.berkeley.edu.(AccessedJuly9,2021).

2. KairosPower,LLC,DesignOverviewofKairosPowerFluorideSaltCooled,HighTemperatureReactor.

KPTR001,Revision1.February2020.

3. KairosPower,LLC,KPFHRMechanisticSourceTermMethodologyTopicalReport.KPTR012PA.

May2022.

4. MELCORFissionProductReleaseModelforHTGRs,SAND20100800CSandiaNational Laboratories,2010.

5. B.J.Lewis,D.Evens,F.C.Iglesias,andY.Liu,ModellingofShortLivedFissionProductRelease BehaviorDuringAnnealingConditions,JournalofNuclearMaterials,vol.238,pp.183-188,1996.

6. HighTemperatureGasCooledReactorFuelsandMaterials,InternationalAtomicEnergyAgency, Vienna,IAEATECDOC1645,2010.

7. KairosPower,LLC,KPFHRFuelPerformanceMethodologyTopicalReport.KPTR010PA.May2022.

8. KairosPower,LLC,CoreDesignandAnalysisMethodologyTechnicalReport.KPTR017,Revision1.

September2022.

9. KairosPower,LLC,MetallicMaterialsQualificationfortheKairosPowerFluorideSaltCooledHigh TemperatureReactorTopicalReport.KPTR013,Revision4.September2022.

10. L.Cheng,A.Hanson,D.Diamond,J.Xu,J.Carew,D.Rorer,PhysicsandSafetyAnalysisfortheNIST ResearchReactor,BNLNIST0803,Rev.1,March2004.

11. KairosPower,LLC,GraphiteMaterialQualificationfortheKairosPowerFluorideSaltCooledHigh TemperatureReactorTopicalReport.KPTR014,Revision4.September2022.

12. KairosPower,LLC,FuelQualificationMethodologyTopicalReport.KPTR011P,Revision2.July 2022.

13. M.Epstein,FlibeAerosolSourceTerms:ModelingRecommendations.MemoofFauske&Associates, October23,2019.

14. E.Mayer,TheoryofLiquidAtomizationinHighVelocityGasStreams,ARSJournal31,pp.17831785, 1961.

15. A.H.Lefebvre,andV.G.McDonell,AtomizationandSprays,2ndEdition,CRCPress,2017.

16. MELCORComputerCodeManualsVol.1:PrimerandUsersGuideVersion2.2.95412017,Section 3.1.5,SAND20170455O,SandiaNationalLaboratories,January2017.

17. A.K.Bin,GasEntrainmentbyPlungingLiquidJets,ChemicalEngineeringScience,Vol.48,No.21, pp.3585~3630,1993.

18. T.Ginsberg,Aerosolgenerationbyliquidbreakupresultingfromspargingofmoltenpoolsof coriumbygasesreleasedduringcore/concreteinteractions,NuclearScienceandEngineering,vol.

89,no.1,pp.36~48,1985.

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19. M.Epstein,andM.Plys,PredictionofAerosolSourceTermsforDoseSiteFacilityApplications, ProceedingsofEFCOGSafetyAnalysisWorkingGroup,AprilMay2006.

20. S.Globe,andD.Dropkin,NaturalConvectionHeatTransferinLiquidsConfinedbyTwoHorizontal PlatesandHeatedfromBelow,J.HeatTransfer,Vol81,No.1,pp.2428,February1959.

21. W.McAdams,HeatTransmission,3rdEdition,McGrawHill,NewYork,p.180,1954.

22. K.Jafarpur,Yovanovich,M.M.,LaminarFreeConvectiveHeatTransferfromIsothermalSpheres:a NewAnalyticalMethod,Int.J.HeatMassTransfer,Vol35,No.9,pp.21952201,1992.

23. M.F.Young,LiftoffModelforMELCOR,SAND20156119,SandiaNationalLab,2015.

24. S.Levy,TwoPhaseFlowinComplexSystems,1stEdition,WileyInterscience,August1999.

25. S.K.Friedlander,Smoke,Dust,andHaze:FundamentalsofAerosolDynamics,2ndEd.,Oxford UniversityPress,2000.

26. ElectricPowerResearchInstitute,UraniumOxycarbide(UCO)TristructuralIsotropic(TRISO)Coated ParticleFuelPerformance,TopicalReportEPRIAR(NP)A,3002019978,November2020.

27. GeschftsstelledesKerntechnischenAusschusses,NuclearSafetyCommissionofGermany(KTA).

SafetyStandardLossofpressurethroughfrictioninpebblebedcores.KTA3102.31987;Issue 3/81.

28. X.Zhou,et.al.,OxidationBehaviorofMatrixGraphiteandItsEffectonCompressiveStrength, ScienceandTechnologyofNuclearInstallations,Vol.2017.

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54of98 Table21:PrescriptiveMaximumHypotheticalAccidentTemperatures

StartTime (Days)

EndTime (Days)

Duration (Days)

FlibeFreeSurfaceand StructuralGraphite Temperatures(K)

Kernel,SiC,andPyCand PebbleCarbonMatrix Temperatures(K) 0.00 0.01 0.01 1,000 1,423 0.01 0.08 0.08 1,000 1,089 0.08 3.00 2.92 1,089 1,089 3.00 4.00 1.00 1,059 1,059 4.00 5.00 1.00 1,029 1,029 5.00 6.00 1.00 999 999 6.00 7.00 1.00 969 969 7.00 8.00 1.00 939 939 8.00 9.00 1.00 909 909 9.00 10.00 1.00 879 879 10.00 30.00 20.00 859 859

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55of98 Table31:AnalyzedPostulatedEventsandAppliedEvaluationModels

Event KPSAM KPBISON NonsoftwarebasedSpecialEM SaltSpills Airingressandgraphite oxidationmodelsalong withlongtermpassive coolinginputmodel Notused Coolantleakingmodel;Single phasejetaerosolgeneration model;SpilledFlibepoolheat transfermodel Insertionof ExcessReactivity Systemsmodel; Pointkineticsequations model Usedasoneof thefuel performance boundingcases N/A IncreaseinHeat Removal Notused Notused Asimplemodeltoshowthatthe maximumequivalentreactivity insertionduetoincreaseinheat removalcanbeboundedbythe InsertionofExcessReactivity event.

LossofForced Circulation Systemsmodelsforboth overheatingandlong termovercooling boundingcases Theoverheating caseusedasone ofthefuel performance boundingcases N/A PebbleHandling andStorage System Malfunction Break Notused Notused Pebbleheattransferand oxidationmodel;graphitedust resuspensionmodel;sourceterm releasemodel

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56of98 Table32:DerivedFiguresofMeritandAcceptanceCriteriaforPostulatedEvents

FigureofMerit AcceptanceCriterion ApplicableEvents PeakTRISOtemperaturetime Generallyboundedbytemperature timecurvesderivedfromthe assumedMHAfueltemperature timecurve SaltSpills,Reactivity Insertion,IncreaseinHeat Removal,LossofForced Circulation,PHSSbreak, Seismic TRISOfailureprobability NegligibleTRISOfuelfailure probability SaltSpills,Reactivity Insertion,IncreaseinHeat Removal,LossofForced Circulation,PHSSbreak PeakFlibecovergasinterfacial temperature Generallyboundedbytemperature timecurvesderivedfromthe assumedMHAFlibecovergas interfacialtemperaturetimecurve

SaltSpills,Reactivity Insertion,IncreaseinHeat Removal,LossofForced Circulation,PHSSbreak Peakvesselandcorebarrel temperatures Boundedbyboththemaximum allowabletemperaturederivedto limitexcessivecreepdeformation anddamageaccumulationandby 750°C(highestvesseldesign temperature)

SaltSpills,Reactivity Insertion,IncreaseinHeat Removal,LossofForced Circulation,PHSSbreak Minimumreactorvesselinner surfacetemperature AboveFlibemeltingtemperature LossofForcedCirculation (overcooling)

Airbornereleasefractionof spilled/splashedFlibe Belowairbornereleasefraction limitderivedtoboundtotalreleases ofthepostulatedeventtolessthan theMHA SaltSpills,Seismic Volatileproductformationfrom Flibeairreaction Negligibleamountofadditional volatileproductsformed SaltSpills,PHSSbreak Volatileproductformation fromFlibechemicalreactionwith water,concrete,and/or constructionmaterials(e.g.,

insulation,steel)

Negligibleamountofadditional volatileproductsformed SaltSpill Masslossofpebblecarbon matrixduetooxidation Masslossdoesnotextendintothe fueledzone SaltSpills,PHSSbreak Masslossofstructuralgraphite duetooxidation BoundedbytheMHArelease SaltSpills,PHSSbreak Peakstructuralgraphite temperaturetime Generallyboundedbytemperature timecurvesderivedfromthe assumedMHAstructuralgraphite temperaturetimecurve SaltSpills,Reactivity Insertion,IncreaseinHeat Removal,LossofForced Circulation,PHSSbreak Peakpebblecarbonmatrix temperaturetime Generallyboundedbytemperature timecurvesderivedfromthe SaltSpills,Reactivity Insertion,IncreaseinHeat

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57of98 FigureofMerit AcceptanceCriterion ApplicableEvents assumedMHApebblecarbonmatrix temperaturetimecurve

Removal,LossofForced Circulation,PHSSbreak PeakTRISOtemperaturetimeex vessel Generallyboundedbytemperature timecurvesderivedfromthe assumedMHAfueltemperature timecurve PHSSbreak Amountofmaterialsatrisk released Lessthanlimitderivedtobound totalreleasesofthepostulated eventtolessthantheMHA PHSSbreak

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58of98 Table41:KPSAMModelsandFieldEquations

ModelName Field Description Dimension Singlephaseflow

Mass, momentum,and energy 1Dfluidflowwithwallfrictionandheat transfer.Theflowmodelissinglephase (liquidorgas)withtheprimaryvariables beingpressure,velocity,andtemperature.

1D Heatconduction Energy Heatconductionmodelforplate,cylindrical, orsphericalgeometrieswithtemperatureas primaryvariable.Canbecoupledto0D/1D fluidvolumessuchaspipes.Maycoupleto othersurfacesbythermalradiationorgap conductancemodel.

1D/2D

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59of98 Table42:SampleKPSAMInputComponentsbyNodalType

ComponentNumber KPSAMType Description C01C14 PebbleBedCoreChannel Fueling(C01),Divergence(C02C04),Activecorecylinder portion(C05C06),Convergence(C07C12),Defueling (C13C14)

F01F10 PBOneDFluidComponent Bypass(F01),Divergence(F02F04),andConvergence (F05F10)multipipes T01 Tank Pumpbowlswithfreesurface,covergas,andvesseltop head F11 PBOneDFluidComponent Primarypumpdrawline P01 PBPump PrimarySaltPump F12F13 PBOneDFluidComponent HotLegPipes HX01 PBHeatExchanger PHX F14F15 PBOneDFluidComponent ColdLegPipes F16F17 PBOneDFluidComponent Downcomer(split)

F1830 PBOneDFluidComponent Downcomer E01 PBTDJ PHXSecondaryInletBC E02 PBTDV PHXSecondaryOutletBC B01B29 PBBranch Junctionconnectingflowchannels VB01VB02 PBVolumeBranch Lowerplenum(VB01),fluidicdiode(VB02)

R01R14,S01S23 PBCoupledHeatStructure Reflectorstructure(R01R14),coolingpanels(S01S09),

vessel(S10S23)

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60of98 Table43:KPFHRTRISOfuelspecificationforasmanufacturedcontaminationanddefectfractions

Property SpecifiedFraction Disperseduraniumfraction 1.0x105 Exposedkernelfraction 5.0x105 DefectiveSiCcoatingfraction 1.0x104 DefectiveIPyCfraction 1.0x104 DefectiveOPyCfraction 1.0x102

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61of98 Table44:InputParametersConsideredforPostulatedEvents

Parameter Value Rationale Reactorinitialpower Rangeofvaluesuptoand includingmaximumpowerlevel includinguncertainty Rangesofpowerlevelsanalyzed Coolantaveragetemperature Rangeovercontrollerdeadband andmeasurementuncertainty Limitingvaluemaybeevent dependent Systempressure Nominalforalleventsexcept forsaltspill Theeffectofthesystem pressureisinsignificantforall eventsexceptforsaltspill events Powerdistribution Axial+radialpowerdistribution forpeakingfactor

Bothfreshcoreandequilibrium coreareconsideredaslimiting conditions Mostlimitingpowerdistribution isconsidered Shutdownmargin Considersmostreactive shutdownrodisunavailable Providemarginformalfunctions Shutdownrodinsertiontime Conservativeshutdownrod insertiontimesassumed Delaystheshutdownofthe reactor Reactivitycoefficients Valuesassumedonanevent specificbasisandaccountfor uncertainty Limitingvaluesmaybeevent dependent DHRSCapacity Minimumandmaximum performanceassumedonan eventspecificbasis

Minimumperformanceassumes lossofatrainofDHRSand minimumperformance requirements

Maximumperformance assumesfullcapacityofDHRS plusuncertainty MinimumDHRSperformanceis expectedtobeboundingfor heatupevents

MaximumDHRSperformanceis expectedtobeboundingfor overcoolingevents Decayheat Minimumandmaximumvalues assumedonaneventspecific basis Maximizingdecayheatis expectedtobeboundingfor heatupevents

Minimizingdecayheatis expectedtobeboundingfor overcoolingevents

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Parameter Value Rationale Materialproperties Rangedwithinuncertainties Uncertaintyinmaterial propertiesforcoolantand structurestreatedonanevent specificbasis ReactorProtectionSystem analyticallimits Actuationon:

HighReactorPower HighFluxRate HighCoolantTemperature LowLevel Analyticallimitsprovidemargin tosafetylimits

Measurementuncertainty appliedtosetpointsarederived fromanalyticallimits ReactorProtectionSystem actuationdelay Conservativedelaytimes applied Delayreactortrip PlantControlSystems Potentialeventmitigation capabilitiesoftheplantcontrol systemsarenotcredited

Suitablyconservativetreatment ofrelevantplantcontrol featuresisappliedinthesafety analysis Plantcontrolsystemsarenot safetyrelated

Potentiallyadverse performanceofplantcontrol systemsneedstobeconsidered

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63of98 Figure11:ElementsofEvaluationModelDevelopmentandAssessmentProcess

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64of98 Figure21:PrescriptiveMHATemperatures

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65of98 Figure41:SAMCodeStructure

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66of98 Figure42:KPSAMSampleNodalDiagramoftheHermesReactor

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67of98 APPENDIXA.

SAMPLETRANSIENTRESULTS A.1 InsertionofExcessReactivity EventDescription Acontrolelementwith3.02$reactivityworthisassumedtobewithdrawncompletelyover100seconds.

Therateofreactivityinsertiondependsonaworthcurveandtheprogressionoftherodwithdrawal.

Whenthepowerlevelexceedsthetripsetpoint,16.8$ofreactivityisinsertedtothecoreover10 secondsaccordingtoanelementworthcurve.After10seconds,thisreactivityismaintained,simulating thetotalassumedelementworth.Theassumptionsmadearesummarizedasbelowandinitial conditionsareprovidedinTableA11.

Powertripsetpoint=120%

Upperplenumtemperaturetripsetpoint=958.1K(665°C+3%)

Powertripdelaytime=2s Temperaturetripdelaytime=2s Elementinsertiondelayaftertrip=2s Timetofullyinsertrodsaftertrip=10s Elementworth=16.8$

Primarysaltpumphalvingtime=2s Intermediatevelocityhalvingtime=1s KPSAManalysisresults Thetransientisinitiatedat0secondswiththestartofreactivityinsertion.Priortoareactortrip,this positivereactivityinsertioniscounteractedinpartbynegativeDoppler,moderator,andcoolant feedbackrespectivelyinorderofmagnitude.Soonafterreactortripisinitiated,thetotalchangein reactivityofthesystembecomesnegativeandremainssodespitethecontinuationofthereactivity insertion,asshowninFigureA11.

Whenthereactortripisinitiated,thePSPistrippedaswell,causingadecreaseinflowratethroughout thesystem.Thishasnotableimpactsonheattransferthroughoutthesystemduringtheentire simulation,asthiswillcharacterizesflowbehaviorinthecoreduringearlierstagesofthetransientand facilitatethetransitiontonaturalcirculationinthelongterm.

KPSAMConclusions Areactivityinsertionof3.02$over100secondswasassumedtosimulateanuncontrolledcontrol elementwithdrawal.Thereactoristrippedbyahighfluxprotectionsignal(120%)at9secondsafterthe

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68of98 eventinitiation.FigureA12showskeypredictedtemperaturesrelativetothetemperatureusedinthe MHAanalysis.ThetemperaturerisesintheTRISOandfuelmatrixwereobserved,withverylittlechange intheFlibetemperature.Theresultingtemperatures,withtheexceptionofreflectortemperatures,are withintheacceptancelevel,withsignificantmargins.Theshortdeviation(i.e.,ontheorderofafew minutes)ofthereflectortemperatureslightlyabovetheMHAtemperatureisacceptableduetothe timeattemperaturenatureofdiffusionoftritiumoutofgraphitegrains.

FuelPerformanceAnalysis ThepowerandtemperatureprofileswereusedasinputstoKPBISON.Thetransientismodeledatthe endofanormaloperationphasethatprovidestheadequatestateoftheTRISOfuelparticles(e.g.,

failurefractions,fissionproductdistribution,fissiongasinventory,etc.).

ThenormaloperationphaseismodeledusingtheirradiationconditionsshowninTableA12.

TableA12showsthefailureprobabilitiescalculatedbyKPBISONwithintheMonteCarlocalculation schemefortheTRISOfailuremodesfornormaloperationandreactivityinsertionevent.Theresultsin TableA12indicatethatthetemperatureduringnormaloperationandtransientisnothighenoughto challengetheTRISOfuelwithoverpressureorPdattack.Furthermore,TableA13showsthatthe reactivityinsertioneventdoesnotleadtoanysignificantincrementalfailure.

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69of98 TableA11:InitialconditionsforInsertionofExcessReactivityAssumedBoundingEvent

Parameter InitialCondition Rationale Reactorinitial power 102%

Assumedpowermeasurementuncertainty Coolantaverage temperature Nominal+3%°C Controllerdeadbandandmeasurement uncertainties Systempressure Nominal Theeffectofthesystempressureisinsignificant Powerdistribution Axial+radialpower distributionforpeaking factor

Bothfreshcore,and equilibriumcoreare consideredaslimiting conditions Mostlimitingpowerdistributionisconsidered

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70of98 TableA12:95%ConfidenceLevelUpperLimitonInServiceFailureFractionsforNormalOperation andReactivityInsertionPostulatedEvent

FailureProbability Normal Operation NormalOperation+

ReactivityInsertion ProbabilityofIPyCcracking 9.75x101 9.75x101 ProbabilityofSiCfailure Contributionduetopalladiumpenetration ContributionduetoIPyCcracking 2.26x103 3.00x106 2.26x103 2.26x103 3.00x106 2.26x103 ProbabilityofTRISOfailure 3.00x106 3.00x106

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71of98 TableA13:CompromisedFractionsforNormalOperationandReactivityInsertionPostulatedEvent

ReleaseFraction NormalOperation NormalOperation+

ReactivityInsertion Intact 2.25x102 2.25x102 CompromisedIPyC 9.65x101 9.65x101 CompromisedIPyC+SiC 2.24x103 2.24x103 CompromisedSiC 1.03x104 1.03x104 CompromisedOPyC 1.00x102 1.00x102 CompromisedIPyC+SiC+OPyC 5.30x105 5.30x105

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72of98 FigureA11:ReactivityInsertionandReactivityFeedbackAfterFullRodWithdrawal

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73of98 FigureA12:FiguresofMeritDuringandAfterReactivityInsertion

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74of98 A.2 IncreaseinHeatRemoval EventDescription Anincreaseinheatremovalmayinsertpositivereactivityintothesystem.Inordertodemonstratethat thiseventisboundedbyreactivityinsertionscomingfromtheRCSS,aconservativepromptjump reactivityinsertionisusedtoapproximatetheeffectsofanincreaseinheatremoval.

InherentsourcesofreactivityfeedbackinthesystemincludetheDoppler(comingfromthefuel),

moderator(nonfuelportionsofpebbles),reflectorandcoolant.Sinceanyincreaseinreactivity(and power)fromanincreaseinheatremovalfirstoccursduetothereductionincoolanttemperatureitis conservativetoassumethatboththefuelandmoderatorfeedbackonlyactstoresistthischange.Thus, itisconservativetoneglectthereactivityfeedbackassociatedwithfuelandmoderatorheating.Asa result,theonlytwocomponentsofreactivityfeedbackthatneedtobeconsideredarecoolantand reflectorfeedback.Thereflectorfeedbackisdelayedrelativetootherfeedbackmechanismsbutcanin somestatesinsertpositivereactivityintothesystemasitcoolsdown.Thus,anextralayerof conservatismisaddedbyprescribingthatthereflectorandcoolantbothexperiencethesame simultaneousreductionintemperaturefromtheincreaseinheatremoval.Additionally,yetanother layerofconservatismisappliedbyassumingthatboththecoolantandreflectorfeedbackcoefficients areattheirmostnegativeacrosstemperaturerangesconsidered.Asummaryoftheparametersusedto drivethepromptjumpapproximationareprovidedbelow:

Delayedneutronfraction=6.08768E3 Coolantreactivityfeedbackcoefficient=1.95pcm/°C Reflectorreactivityfeedbackcoefficient=1.25pcm/°C Thepromptjumpapproximationfornormalizedreactorpowerafterastepinsertionofreactivityis providedintheequationbelowwhereisareactivityfeedbackcoefficient,isthedelayedneutron fractionandTistheimposeinstantaneousreductionincoolantandreflectortemperature.

Pnorm 1 T T

AnalysisResults FigureA21showstheresultofapplyingtheequationabovetoarangeofinstantaneousreflectorand coolanttemperaturereductions.InFigureA21itisshownthatboththereflectorandthecoolantwould needtobereducedinstantaneouslyby~40°Cinordertoapproachtheoverpowerseenfromthecontrol rodwithdrawal.Suchalargeglobalreductionincoretemperaturewouldrequireamassiveand sustainedincreaseinheatremoval.ConsideringtheconservatismsofneglectingmoderatorandDoppler feedback,theimpossibilityofinstantaneouslyreducingthetemperatureofthecoresentireFlibeand reflectorvolumetosuchanextentthatitwouldcauseanoverpowerlikewhatcouldoccurinarod withdrawalevent,andtherealitythatthesymptomsofexcessiveheatremovalareeasilydetectable; reactivityinsertionsoriginatingfromtheRCSSboundthosecausedbyanincreaseinheatremoval.

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75of98 FigureA21:NormalizedReactorPowervsInstantaneousAverageFuelandCoolingTemperatureDrop

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76of98 A.3 SaltSpill EventDescription TheeventisdescribedinSections3.2.2and4.5withTablesA31andA32providingkeyinput parametersandthepropertiesofFlibeandairbasedonthespilledFlibetemperatureandbuildingair temperature.

Whenthelargepipebreakeventoccurs,theliquidthroughthehotlegisdrivenbythePSPtodischarge atahighvelocity.TheFlibeinthecoldleg,however,isexpectedtodrainundergravityatalowvelocity outofthebreak.Thedifferenceinthespeedsaffectsaerosolgenerationratesbecauseahighervelocity jetproducessmallersizeparticlesandthusconvertsalargerfractionofthedischargedliquidmassinto aerosols.ItisassumedthatboththeFlibejetsthroughthehotandcoldlegsaredischargedatthesame pumpdrivenvelocityandproduceidenticalfractionalamountofaerosol.

LiquidFlibedrivenbythePSPisacceleratedwhenthebreakoccursbecauseofsuddendecreaseofthe downstreampressure.Theflowvelocityincreasesuntilitreachestherunoffvelocityatwhichthepump headisreducedtozero.Therefore,therunoffvelocityofPSPcanbeconsideredasaboundingvelocity forthevelocityofFlibeoutofthebreak.However,therunoffvelocityisspecifictoaparticularpump rotationalspeed.Whenthebreakoccurs,notonlytheflowvelocitybutalsothepumpspeedincreases.

Theflowvelocityatthepumpoutletrequiresadetailedpumpdynamicmodel.Toavoidthecomplexity associatedwiththedynamicpumpmodel,therunoffvelocityisused.Forthisapproach,theflow velocityisevaluatedwiththeBernoulliequationbasedonnormaloperationpumpheadandgravity headbetweenthepumpoutlet.

AnalysisResults Aerosolgenerationrateduetosinglephasejetbreakupandspillingisevaluatedbasedonthe methodologyinsection4.5.TableA33listscalculatedvaluesbasedonparametersprovidedinTables A31andA32.UsingthevaluesprovidedinTableA33,thetotalcumulativeaerosolmassproduced duringthepostulateddoubleendedguillotinePHTSpipebreakeventisthesumofthemassthrough singlephaseandtwophaseflow:

,,0.0685 WhenlargeamountsofFlibeisspilledfromtheprimarysystem,itisexpectedtospreadonthefloor and,whenthespreadingends,formsaFlibepool.Thereleaselastsuntilthetemperatureonthetop surfacedropstotheFlibemeltingpointandasolidcruststartstoform.Oncethecrustisformed,the evaporationprocessislimitedbydiffusionthroughthecrustandexpectedtobenegligible.Therefore,a keyvariablefortheevaporativereleasefromaFlibepoolisthetopsurfacetemperaturehistorybefore itdropstotheFlibemeltingpoint.

ThetemperatureofaFlibepoolisstronglydependentonthespreadingareaanddepth.Thereactorcell designisassumedtohaveaflatfloorareaofmorethan200.However,thespreadingareaofthe Flibemaybelessthantheflatfloorareaduetoseveralfactors:

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77of98 ThespreadingofFlibemaybelimitedbytheareaofdripcatchpanifused.Theareaofthedrip panwouldbesmallerthantheflatfloorarea.

ThespreadingofFlibemaybeincomplete(withoutcoveringtheentireareaofthereactorcellor drippan)becauseoffreezingatthebottomandformationofcrustonthespreadingfront.

Flibemayflowandaccumulateatcertainlowerareainthereactorcellifthereactorcellin realityhasaslope.

==

Conclusions:==

Materialatriskisreleasedthroughfourpaths:evaporationfromthevesselandspilledFlibe,tritium degassinganddesorption,mechanicalaerosolization,andoxidationofexposedstructuregraphiteand pebblesforthepipebreakevent.Conservativeassumptionswereusedintheanalysisabovetoevaluate dosesanddemonstratethatthepipebreakeventisboundedbytheMHAintermsofdose consequences.

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78of98 TableA31:KeyInputParameters

Parameters Value DelaytimetotriggerthereactortripandPSPtripsignals(seconds) 10 PSPcoastdownhalfflowtime(seconds) 2 PSPnormaloperationvolumetricflow(m3/s) 0.177 PSPnormaloperationpumphead(Pa) 1.5E5 Flibevolumeinsidehotleg(m3) 1.23 Flibevolumeinsidecoldlegs(m3) 1.13 Flibevolumeinthepumpbowlfromnormaloperationleveltopumpsuction(m3) 0.33 Breakdiameter(m) 0.254 Elevationdifferencebetweenthebreakandpumpoutlet(m) 10 Heightofthebreakcenterlinerelativetothefloor(m) 1 SpilledFlibetemperature(°C) 650 Buildingairtemperature(°C) 100 Buildingairpressure(Pa) 1E5

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79of98 TableA32:PropertiesofSpilledFlibeandBuildingAir

Properties Value DensityofFlibe,f(kg/m3) 1960 DynamicViscosityofFlibe,f(Pas) 6.781E3 SurfaceTensionofFlibe,f(N/m) 0.185 DensityofAirinBuilding,g(kg/m3) 0.378

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80of98 TableA33:CalculatedValuesfortheSaltSpillEvent

CalculatedParameter Value VolumeofliquidpumpedoutbyPSPbeforecoastdown,Vcoast(m3) 2.28 VolumeofspilledFlibe,Vspill(m3) 2.69 MassofspilledFlibe,mspill(kg) 5272 Flowvelocity,vjet(m/s) 18.7 SauterMeanDiameter(m) 3.63E3 Fractionofaerosolizationthroughjetbreakup,fa,jet 1.234E5 Fractionofaerosolizationthroughspillingandsplashing,fa,spill 5.89E7 Cumulativemassofaerosolsgeneratedbysinglephasejet,ma,1p(kg) 0.0682 Cumulativemassofaerosolsgeneratedthroughtwophaseflow,ma,2p(kg) 3.64E4

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81of98 A.4 LossofForcedCirculation EventDescription Thepurposeofthiseventistodetermineifthereactorisadequatelydesignedforlongtermheatup events.Assuch,oneofthekeyassumptionsisthatonly75%ofDHRScapacityisavailable.Thelossof forcedcirculationoverheatingboundingeventappliedtotheplantmodelisinitiatedbymanually trippingthepumpandreducingtheheadtozeronearlyinstantaneously.Thecompletelossofflow definesthebeginningofthetransientandoccursconcurrentlywithalossofintermediatecoolantflow.

Intermediatecoolantflowisnotlikelytobelostduringalossofforcedcirculationeventbutisimposed inthisanalysistodemonstratethatintermediatecoolantflowisnotneededtoprotecttheplantduring alossofforcedcirculationevent.Duringthistransient,itisexpectedthatthelargereductionincoolant flowthroughthecoreregionresultsinasignificantriseintemperatureacrossthecore.Therisein temperatureeventuallycausesthereactortotrip,leadingtoalongtermcoolingtransientandthesafe shutdownconditionofthereactor.Initialconditionsfortheoverheatinglossofforcedcirculation assumedboundingeventareprovidedinTableA41.Asetofassumptionskeytothisanalysisarelisted inTableA44.

Thelossofforcedcirculationtransientwasrunoverthecourseof72hoursofsimulationtime.During thetransient,theupperplenumtemperatureexceedsthetripsetpointafter23seconds,withrod insertionfollowingatripdelay.Priortotherodinsertion,powerisreducedbyreactivityfeedbackasthe coreheatsup,afterwardsthestronginsertionofnegativereactivityfromtherodinsertionbringsthe reactorpowerdowntodecayheatlevels.FigureA41showskeypredictedtemperaturesrelativetothe temperatureusedintheMHAanalysis.

Thecompromisedfractionsforthesixstatesareobtainedfromthedefectandinservicefailure fractionsinTable43(seeSection4.2)andTableA45.TheseareshowninTableA46,assumingthe upperspecificationorboundingvalues.

LossofForcedCirculationOverheating AlossofforcedcirculationtransientbiasedforoverheatingwasperformedusingKPSAM.Inthis simulation,itwasdemonstratedthatdecayheatremovalthroughtheDHRScancompensatefortheloss oftheintermediatesaltflowtoachievestablecoolingafterthefaststageofthetransient.

TheTRISOtemperatureprofileisboundedbytheMHAcurve,whichdemonstratesthatthediffusional releaseofradionuclidesfromfuelisboundedbytheMHA.TheFlibecovergasinterfacialtemperature profileisboundedbytheMHAcurve,whichdemonstratesthatthereleasefromFlibethrough evaporationisalsoboundedbytheMHA.

ThegraphitereflectorandfuelpebbletemperatureprofilesareboundedbytheMHAcurves,which demonstratesthatthetritiumreleaseisboundedbytheMHA.Itisshownthattemperaturesstaybelow thosedefinedbytheMHAexceptfortheupperplenumandreflector/graphitetemperatures.TheMHA releaseanalysisisconservative.TheMHAmarginismaintainedsincedeviationsareminimalandof shortduration(asscaledrelativetothecorrespondingX/Qwindowassociatedwiththedeviation)due totheconservativeevaporativeboundaryconditionsintheMHA(i.e.,aggressivetemperaturegradients drivingnaturalcirculation)andtimesassociatedwiththosetemperaturescorrespondingintheMHA

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82of98 (i.e.,evaporationanddiffusionaretimeattemperaturereleasemechanisms).Freezingdoesnotoccur inthiseventandthatthevesselremainsbelowthedefinedtemperaturelimit.

ThepowerandtemperatureprofileswereusedasinputstoKPBISON.Thetransientismodeledatthe endofanormaloperationphasethatprovidestheadequatestateoftheTRISOfuelparticles(e.g.,

failurefractions,fissionproductdistribution,fissiongasinventory,etc.).Thenormaloperationphaseis modeledusingtheirradiationconditionsshowninTableA43.

ThefailureprobabilitiesassociatedwiththepotentialfailuremodeslistedinSection4.2wereobtained byaMonteCarlosimulationof106samples.Note:thesamplesizewaschosentooptimizecomputing time.FromtheMonteCarlosimulationresults,upperlimitsonthefailureprobabilitiesassociatedwith eachfailuremodesareobtainedata95%confidencelevelusingtheCopperPearsonexactmethod.

TheselimitsarereportedinTableA45forthenormaloperationandlossofforcedcirculation postulatedevent.

TheresultsinTableA45indicatethatthetemperaturesduringnormaloperationandthetransientare nothighenoughtochallengetheTRISOfuelwithoverpressureorPdattack.Inparticular,theupperlimit onTRISOfailurebyoverpressureisonlyafewpercent(6%)oftheasmanufacturedexposedkernel fractionof5.0x105.Furthermore,TableA45showsthattheTRISOfuelismorelikelytofailduring normaloperationandthatthelossofforcedcirculationeventdoesnotleadtoanysignificant incrementalfailure.Becauseoftheconservativeassumptionsusedtosetupthelowandhigh temperaturetrajectories,thecalculatedfailureprobabilitiesarealsoconservativeandrepresentupper limitsforexpectedfailureprobabilities.

LossofForcedCirculationOvercooling Whiletheoverheatingversionofthiseventisdesignedtochallengethemargintomaximum temperatures,theovercoolingscenarioisdesignedtochallengethemargintominimumtemperatures.

InthiscasethelimitingminimumtemperatureistakenasthepointatwhichFlibefreezes.Inorderto conservativelyprecludefreezing,theminimumvesselinnersurfacetemperatureistakenasabounding surrogatefortheminimumFlibetemperature.Theeventisinitiatedbymanuallyinitiatingacontrolrod insertion,primarypumptripandintermediateflowtripatt=0.Theprimarypumpandintermediate flowareallowedtocoastdownnormally.Additionally,theDHRSismodeledat100%capacity.Initial conditionsforthelossofforcedcirculationovercoolingeventareprovidedinTableA42.Asetofkey assumptionsfortheexamplecalculationisprovidedinTableA44.

Theexamplecalculationofacooldownbiasedlossofforcedcirculationtransientwasrunoverthe courseof72hoursofsimulationtime.FigureA42showskeypredictedtemperaturesrelativetothe temperatureusedintheMHAanalysis.TemperaturespredictedbytheKPSAMmodelarebelowthe temperaturesdefinedbytheMHAandfreezingdoesnotoccurwithin72hours.

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83of98 TableA41:InitialConditionsforLossofForcedCirculationOverheatingAssumedBoundingEvent

Parameter InitialCondition Rationale Reactorinitial power 102%

Assumedpowermeasurementuncertainty Coolantaverage temperature Nominal+3%°C Controllerdeadbandandmeasurementuncertainties Systempressure Nominal Theeffectofthesystempressureisinsignificant Powerdistribution Axial+radialpower distributionfor peakingfactor

Bothfreshcore,and equilibriumcoreare consideredaslimiting conditions Mostlimitingpowerdistributionisconsidered DHRScapacity 75%

AssumeoneDHRStrainisoutofoperation Heatstructureheat capacity 75%

Accountforanyuncertaintyrelatedtotheheat capacityofsolidmaterialsinthemodel Flibeheatcapacity 95%

AccountforuncertaintyintheheatcapacityofFlibe Reactivity coefficient magnitude 75%

Reducedtoconservativelybiastheimpactofreactivity feedbackpriortoreactortrip

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84of98 TableA42:InitialConditionsforLossofForcedCirculationOvercoolingAssumedBoundingEvent

Parameter InitialCondition Rationale Reactorinitial power 98%

Assumedpowermeasurementuncertainty Minimizedstoredenergy

Coolantaverage temperature Nominal3%°C Controllerdeadbandandmeasurementuncertainties Systempressure Nominal Theeffectofthesystempressureisinsignificant Powerdistribution Axial+radialpower distributionfor peakingfactor

Bothfreshcore,and equilibriumcoreare consideredaslimiting conditions Mostlimitingpowerdistributionisconsidered DHRScapacity 100%

FullcapacityofDHRS Heatstructureheat capacity 75%

Accountforanyuncertaintyrelatedtotheheat capacityofsolidmaterialsinthemodel Minimizesstoredenergyandacceleratescooldown Flibeheatcapacity 95%

AccountforuncertaintyintheheatcapacityofFlibe Minimizesstoredenergyandacceleratescooldown Reactivity coefficient magnitude Nominal Reactortripinitiatedimmediatelyfollowingevent initiation

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85of98 TableA43:IrradiationConditionsforSimulatedNormalOperationofHermes

Parameter Value Irradiationlength(EFPD) 300 Powerdensity(fission/m3s 5.7x1019 Burnup(%FIMA) 6.0 Fastflux(n/m2s,E>0.1MeV) 7.7x1017 Fastfluence(n/m2s,E>0.1MeV) 2.0x1025

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86of98 TableA44:InputsforLossofForcedCirculationPostulatedEvents

LossofForcedCirculation-Overheating LossofForcedCirculationOvercooling Parameter Value Parameter Value Temperaturetripdelaytime(s) 2 Timetofullyinsertrodsaftertrip(s) 10 Elementinsertiondelayaftertrip(s) 2

Timetofullyinsertrodsaftertrip(s) 10 Tripdelayaftereventinitiation(µs) 20 Tripworth($ofreactivity) 16.8 Tripworth($ofreactivity) 16.8 Primarysaltpumphalvingtime(pump seizureapproximation)(s) 0.01 Primarysaltpumphalvingtime(s) 2 Intermediatevelocityhalvingtime(s) 1 Intermediatevelocityhalvingtime(s) 1 DHRScapacity(%)

75 DHRScapacity(%)

100

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87of98 TableA45:95%ConfidenceLevelUpperLimitsonInServiceFailureFractionsforNormalOperation andLossofForcedCirculationPostulatedEvents

FailureProbability NormalOperation NormalOperation+

LossofForced Circulation IPyCCracking 9.75x101 9.75x101 SiCFailure Contributionduetopalladiumpenetration ContributionduetoIPyCcracking 2.26x103 3.00x106 2.26x103 2.26x103 3.00x106 2.26x103 TRISOFailure 3.00x106 3.00x106

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88of98 TableA46:CompromisedFractionsforNormalOperationandLossofForcedCirculationPostulated Event

ReleaseFraction NormalOperation NormalOperation+Lossof ForcedCirculation Intact 2.25x102 2.25x102 CompromisedIPyC 9.65x101 9.65x101 CompromisedIPyC+SiC 2.24x103 2.24x103 CompromisedSiC 1.03x104 1.03x104 CompromisedOPyC 1.00x102 1.00x102 CompromisedIPyC+SiC+OPyC 5.30x105 5.30x105

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89of98 FigureA41:FiguresofMerit-Overheating

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90of98 FigureA42:FiguresofMerit-Overcooling

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91of98 A.5 PebbleHandlingandStorageSystemMalfunctionEvent EventDescription:

ThePHSSbreakeventisdescribedinSection3.2.2andSection4.5.Itiscausedbyahypotheticaldouble endedbreakinthepipeintheoffheadconveyancesystemthattransferspebblesfromthepebble extractionmechanismtothepebbleprocessing/inspectionsystem.Thesequenceofeventsincludes:

ThebreakleadstoapebblespillfromthetransferlineonthefloorofthePHSShotcell.

TheisolationvalvebetweenthePHSSandthevesselisconservativelyassumedtoopen.The breakinthetransferringlinethuscreatesapathforthegasinthePHSSandvesseltoleakinto thePHSShotcell.

Thereactorprotectionsystemdetectsthebreakandtriggersareactortripsignal.RCSS elementsareinsertedintothecoretoshutdownthereactor.

ThedecayheatisremovedbytheDHRS.

TheheatupofthepebblesinthePHSSsystemmobilizestheFlibeaccumulatedonthepiping.

AiringressintothePHSSandreactorcovergasregionoccursthroughthebreak.

EventAnalyzed:

ConservativeinputparametersarelistedinTableA51.Theinitialtemperatureofspilledpebblesisvery conservativebecauseitisequaltotheFlibetemperatureintheupperplenumofthecoreduringnormal operation.Thepebbletemperaturesinthetransferlineareexpectedtobelowerduetoheatlosstothe covergasandsurroundingstructureswhentheyareextractedfromthecore.

Thedecayheatgenerationrateof42Wisabout2%ofthenormaloperatingpowerperpebble,whichis equivalenttothepowerapproximately15minutesafterapebbleisextractedfromtheactivecore.Itis alsoconservativesincepebblesareexpectedtobeinthenonactivezoneformuchlongerthan15 minutesbeforetheyareextractedbythepebbleextractionmechanism.

ThegastemperatureinthePHSShotcellisusedtodemonstratethemethodology.Initialpressureinthe PHSSisestimatedbasedonthedesignobjectivetokeepthePHSSandreactorupperheadonlyslightly abovetheatmosphericpressure.Theoverpressureforthisestimateisabout500Pa.

TheslidingdistanceofpebblesinthePHSSisusedtocalculatethedustaccumulationinthesystemand isanestimateformethodologydemonstration.Thespecificwearrateofpebblesisanassumedvalue representativeoftheupperboundofthewearratefromthetestresultsofpebblesslidingonstainless steelplate.Thepebbleextractionspeedisevaluatedbasedonthecoredesigndatawhichconcludesa totalof35,000pebblesinthecoreandtheaverageresidencetimeof225daysduringwhichit experiencessixpasses(extractions).

AnalysisResults:

InordertoevaluatethereleaseofMARandassociateddoseconsequenceduetospilledpebbleand resuspendedgraphitedust,theMARholdupinthepebblegraphitematrixwasevaluatedfirst.As describedinsection4.5,aboundingestimateismadeassuming100%oftheMARindefectiveTRISO particlesisreleasedtothegraphitematrixinthepebble.MARinthegraphitematrixdistributes

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92of98 uniformlyduetothelargediffusioncoefficientsinthematrix.TheMARactivityconcentration(inunitof Ci/kggraphite)inthegraphitematrixisthenobtainedthroughtheinventoryofMARholdupinthe graphitematrixdividedbythemassofthegraphitematrix.TableA52liststheactivitiesforselected elementsandtotalactivitiesinthegraphitematrixforthehighestburnuppebble.

ThemassofdustinthePHSSisdeterminedbytheproductofthedustaccumulationrateandthetimeat operation.TheMARinthedustcanbeevaluatedbasedontheMARholdupinthepebblegraphite matrix,assumingthesameconcentrationofMARinthedustandthepebblegraphitematrix,whenthe dustisgenerated.However,creditistakenforradioactiveisotopedecaysincedustaccumulationoccurs overmanyyears.Creditisalsotakenfortheextractionofnonfuelpebblesfromthecoreregionaswell.

Itisexpectedthatabout35%ofthepebblesinthecorearegraphitepebbleswhichdonotcontainMAR.

ThetotalactivityforMARinthedustafteranoperatingtimeof10yearsisabout0.2Ci.

OxidationofaspilledpebblewasalsosimulatedwiththemethodologyinSection4.5andevaluatesthe temperatureinthepebblebasedon1Dconductionsolutionofaspherewithinternalheatgeneration.

Theboundaryconditionofthepebbleisnaturalconvectionandradiation.Thesimulationtimewas 400s.FigureA51andFigureA52showgraphiteoxidationrateandmasslossinthepebble.

Themasslossafter400secondsisabout3.3E5kg,whichisabout0.077%ofthemassofthegraphite matrixinthepebbletherefore,thereleasefractionofMARis0.077%forthespilledpebbles.FromTable A52,thetotalactivitiesofMARheldupinthegraphitematrixofonepebbleis20.15Ci.Theactivityof MARreleasedthroughpebbleoxidationof30pebbleswasdeterminedas0.47Ci,throughtherelease fractionandtheactivityinthegraphitematrix.

FigureA53showsthetemperatureontheoutersurfaceofthepebble.After400seconds,the temperatureattheoutersurfaceislessthan400°Cwhichisgenerallyconsideredthetemperature belowwhichthegraphiteoxidationrateisinsignificant.Thetemperatureinthedeeperregionofthe pebbleishigherthanthetemperatureontheoutersurfacebecauseofdecayheatandoxidationheat generation.However,FigureA51showsthattheoxidationrateisverysmallafter400seconds, indicatingeventhetemperaturesindeeperregionofthepebblearelowenoughforoxidation termination.Theresultsindicatethepebbleiscoolablewithin400seconds.

ThefractionofthedustparticlesthatareresuspendedasaerosolsduringaPHSSlinebreakisafunction ofgasvelocityinthelocationwherethedustisdeposited.Forconservatism,thedustparticlesare assumedtoaccumulateinthepebbletransferlineandareadjacenttothebreaklocation.Thedust particlesintheselocations,eveniftheyareresuspended,aresubjecttodepositingmechanismssuchas inertialimpactandturbulentdepositionthatremovethemfromthegasspacealongthepathtothe breaklocation.

Resuspensionfractionofgraphitedustparticlesisevaluatedwiththemethodologyinsection4.5.The fractiondependsonthegasvelocityinthetransferlinewhichisontheotherhanddependsontheratio ofthebreakareaandthecrosssectionalareaofthepebbletransferline.Thegasvelocityinthepebble transferlineiscloseto28m/sforthearearatioof1,whichrepresentsthedoubleendedbreak condition.Oncethegasvelocityisdetermined,thecriticalliftoffdiameterofdustparticlescanbe evaluated.Thecriticalliftoffdiameterislargerthan50mforarearatiolessthan0.2,indicatingthe sizesofresuspendedparticlesaretoolargetobeconsideredasaerosols.Themassfractioniszerofor arearatiolessthan0.2asexpected.However,itincreasesrapidlyforlargerbreakarea.Itbecomes

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93of98 97.9%forthedoubleendedbreakcondition.Thisindicatesthatthereleasefractionofthedustparticles inPHSSisalmost100%foralargebreak.FromTableA52,thetotalactivitiesinthedustinPHSSare about0.2Ciforanassumed10yearsofoperationofHermes.Fortheresuspensionfractionof97.9%,

theactivitiesreleasedduetoresuspensionare0.196Ci.

Materialsatriskarereleasedthroughthreepaths,i.e.,dustresuspension,oxidationofspilledpebbles andexposedpebblesinsidePHSS,andevaporationsfromtheFlibepoolinthevesselthroughthebreak, forPHSSbreakevent.DosesareevaluatedtodemonstratethatthePHSSbreakeventisboundedbythe MHAintermsofeventconsequences.TheapproachtoevaluatedoseconsequencesofPHSSbreak eventutilizethegasspacetransportmethodologyfordesignbasisaccidentsinReference3.

Keyassumptionsofthedoseconsequenceanalysisaresummarizedbelow:

Ar41thatisheldupinclosedgraphiteporesisconservativelyreleasedinapuffattimezero.

Releasesfromdustresuspensionandspilledpebbleoxidationoccurattimezerofor conservatism.

HighvolatilitynoblemetalsanddissolvedgasesintheFlibeareconservativelypuffreleasedat timezero.

Flibepoolinthevesselhasavoidfractionof1%whichisconsideredasaboundingestimateof gasentrainedbyRCPduringnormaloperation.Aerosolgenerationduetobubbleburstingwhen RCPtripsisconsideredthroughaconservativeaerosolgenerationefficiency.Theaerosols generatedthroughbubbleburstingareconservativelyreleasedinapuffattimezero.

TheradiologicalconsequencesfromthiseventarelessthantheMHAbecause:

InvesselpostulatedeventevaporativereleasesaremuchlowerthantheMHAduetoless severeinvesselevaporativeconditionsappliedtothepostulatedeventanalysissuchasan overallshortercumulativetimeathighcovergas/Flibeinterfacialtemperaturesandlesssevere naturalcirculationmasstransferconditions.

Thetritiumreleasesrates,evengivenaggressivetritiumreleasesfromoxidizedgraphite,willbe lowerthantheMHAbecausetheincoregraphitewillhavesignificantlylowerspatial temperaturedistributionsofincorepebblecarbonmatrixandgraphitereflectortemperatures.

FuelreleaseswillbereducedinthepostulatedeventanalysisbecausetheoverallinitialTRISO inventorieswereinflatedduetoahypotheticallyassumedundiffusedTRISOinitialconditionsin theMHA.Asaresult,lowerpostulatedeventinitialconditionscoupledwithreducedtimeat temperaturesasadrivingforcetodiffusethoseinventoriesoutofthefuelwillresultinlower fuelreleases.

==

Conclusions:==

TheseconservatismsintheMHA,whentakentogether,provideenoughdosemargintoaccommodate theadditionalreleaseofoxidizedgraphiteMARanddustresuspensionmodeledintheproceeding sectionsandboundthereleasesofMARforthePHSSbreakevent.

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94of98 TableA51:KeyInputParametersforPebbleHandlingandStorageSystemMalfunctionEvent

InputParameter Value FractionofdefectiveTRISOparticlesinapebble 0.0022 Numberofspilledpebbles 30 Massofgraphitematrixinapebble(kg) 0.0583 Massofpebble(kg) 0.0428 Initialtemperatureofspilledpebbles(K) 923 Decayheatperpebble(W) 42 GastemperatureinthePHSShotcell(K) 373 InitialpressureinPHSS(Pa) 1.018x105 Diameterofpebbletransferline(m) 0.254 SlidingdistanceofpebblesinPHSS(m) 10 Specificwearrate(g/Nm) 15 Pebbleextractionspeed(s1) 0.0108 Geometricmeandiameterofgraphitedustparticles(m) 10 Geometricstandarddeviationofgraphitedustparticles 1.5 Pebbleradius(m) 0.02 Pebbleaveragedensity(kg/m3) 1740 TRISOparticlepackingfraction(fuelregionofpebble)(%)

36.8 AverageTRISOparticledensity(kg/m3) 3000 Graphitedustaccumulationrate(kg/s) 9.27x1010

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95of98 TableA52:TotalActivitiesandActivitiesforSelectedElementsinGraphiteMatrixinPebbleswith HighestBurnup

Element Activity(Ci)

ActivityConcentration(Ci/kggraphite)

Cs 0.890 20.78 I

1.256 29.33 Sr 1.162 27.14 Te 0.887 20.72 Total 20.15 470.6

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96of98 FigureA51:GraphiteOxidationRate

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97of98 FigureA52:MassLossofGraphiteMatrixandReleaseFractionofMAR

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98of98 FigureA53:TemperatureoftheOuterSurfaceofthePebble

ML23055A676

Text

SUMMARY

reduceddiffusioncoefficient

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