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KP-TR-018-NP, Revision 2, Postulated Event Analysis Methodology
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Enclosure 3 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

PostulatedEventAnalysisMethodology

NonProprietary DocNumber Rev EffectiveDate KPTR018NP 2 February2023

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, September2022 44,and45,andAppendixAtoaddressfeedbackfromNRC audit.

2 RevisionupdatesSection3.4andTable32toaddress February2023 feedbackfromNRCaudit.

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

Figuresofmeritarederivedforthepostulatedeventstoprovidesurrogatemetricswhichdemonstrate thattheresultingdoseisboundedbythedoseconsequencesoftheMHAanalysis.Acceptancecriteria forthesefiguresofmeritrepresentdesignlimitsthatensuretheMHAisbounding.

Theevaluationmodelsusedtoanalyzethepostulatedeventsaredescribedaswellastheassociated verificationandvalidationplans.Samplepostulatedeventanalysesareprovidedinappendixasan illustrationofthemethodsdescribedinthisreport.

TheMHAissummarizedinthisreportonlytoprovidecontextforthederivationoffiguresofmeritfor postulatedeventsthatwhenevaluatedensurethatthedoseisboundedbyanMHAwithacceptable doseconsequences.

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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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Figure41:SAMCodeStructure.................................................................................................................65 Figure42:KPSAMSampleNodalDiagramoftheHermesReactor..........................................................66 APPENDIXA. SampleTransientResults..................................................................................................67

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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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1 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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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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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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2 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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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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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 determinethefractionalreleaseofradionuclidesfromthekernelforconditionswhere 0.155(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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Forconditionswhere 0.155andradioactivedecayareignored,thelongtimeapproximationfor releasefractionforthekernelismodeledas(Reference5):

1 6 (2)

Theshorttimeapproximationforfractionalreleaseofacoatinglayeris(Reference6):

241. 1 61 12 5 6 6 (3)

where,

RF(T)=releasefractionofradionuclidesuptotimet=T

=ratiooflayerthicknesstotheinnerradiusofthelayer(unitless)

=reduceddiffusioncoefficient= (unitless)

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

t=time(s)

d=thicknessofthecoatinglayer(m)

Thisshorttimeapproximationisappliedtoconditionswhere 0.2.When 0.2,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:

,, (6) 1

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.Sitespecificvaluesareusedasinputtothedispersionmodeling.

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

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3 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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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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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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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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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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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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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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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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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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identifyandrankkeyphenomenaforaspecificsystemundergoing aspecifictimephaseofaspecific transient.ThePIRTprocessgeneratesaprioritized listofkeyphenomenathatneedtobecharacterized andmodeledtopredictresponsetospecifictransients.Italsorankstheknowledgelevel for eachkey phenomenonforeachcomponent,thusidentifyingcriticalgapsintheunderstandingofspecific phenomena.

Kairos Powerhasperformed aseriesofPIRTsforKPFHRs. ThelistofPIRTsrelevanttothedevelopment ofsafetyanalysisEMs,whichleveragedifferentsetsofpanelexperts,include:

ThermalfluidsPIRT Radiological sourcetermPIRT(Summaryprovidedin Reference3)

FuelElementPIRT(SummaryprovidedinReference7)

NeutronicsPIRT(Summaryprovidedin Reference8)

Hightemperature structuralmaterialsPIRT(SummaryprovidedinReference9)

Thethermal fluidsPIRTwasperformedtoidentifykeythermal hydraulicsphenomenaimportantto safety,prioritizethermalhydraulicstests andEMdevelopment.ThePIRThelpsinformwhichareas of theEMsrequireexistingdataortestingtovalidate.Ultimately,thePIRTisatoolthathelpsinformthe safetyanalysismethodologydevelopmentandassessmentofoverallevaluationmodeladequacy.

Key phenomenarelevanttoHermespostulatedeventsthatwereidentified as having ahighimportance tosafetyandalow knowledgelevelforpostulatedeventsaresummarizedin thefollowinglist,andwill be addressed withmodeldevelopmentor/andvalidation tests:

((

))

3.4 FIGURES OFMERIT 3.4.1 DoseAcceptanceCriteria ThedoseconsequencesoftheMHAdemonstrate theacceptabilityofthedesign whencomparedto regulatory doselimits.Therearenodoselimitsdefinedin10 CFR50 foranonpower reactor;10 CFR 100definesdoselimitsapplicabletoanonpower reactor.Thedoselimitsin 10CFR100.11requirethat anapplicantforanonpower reactor evaluatedoseattheEABandthelow populationzone(LPZ)as follows:

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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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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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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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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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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

l l (10) 2

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where,

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

=anglebetweentheflowdirectionandgravityvector g=thegravityconstant.

f=frictioncoefficient D =equivalenthydraulicdiameter c =thespecificheat q=theconvectionheatfluxfromsolidsurface

P andA=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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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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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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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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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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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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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.

Acceptance criteria - the third method discussed in Section 3.4, using both direct dose calculation for 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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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)

where isthevolumeofFlibeinthecoldlegbetweentheelevationofcoldlegnozzleandthe elevationofthebreak, isthetotalvolumeoftheFlibeinthehotleg,and istheaccumulative volumepumpedoutfromthetimeofpumptriptothefullycoastdowncondition.Assumethepump volumetricflowfollowsacoastdowncurvegivenby

(13)

whereand arepumpvolumetricflowandtheflowatnormaloperation, isacharacteristic pumpcoastdowntime,equals / /ln2,where / isthetimewhenthepumpvolumetricflowis reducedbyhalf.Thetotalvolumepumpedoutduringthecoastdowntimeisthengivenby

/ (14) 2

Therefore,forgivenvalueof / andhotlegandvesselgeometries,thevolumeofthespilledFlibecan bedeterminedthroughEquation12.Note:Equation12assumesthat islessthanthevolumefrom thelowlowsetpointleveltothepumpsuction.Ifthecumulativevolumeislargerthanthevolume fromthelowlowsetpointleveltothepumpsuctionlevel, shouldbeusedtoreplace in Equation12,becauseinthisconditionthepumpsuctionisexposedbeforethepumpfullycoastsdown.

Themethodstoevaluatethereleasesfromthefuelpebbles,remainingFlibe,graphiteandmetal structuresinthevesselisidenticaltothatofMHA,withthefollowingexceptions:

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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)

where islosscoefficientofthebreakandisthepressuredifferencebetweenthevesselandthe 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)

where and arevolumetricflowratesoftheentrainedairandFlibeflow,Histhefallingheight, and isFroudenumberoftheFlibeflow.Volumetricrateofaerosolsgeneratedthroughthebubble burstingisconservativelyboundedbyalinearexpression(Reference18)

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(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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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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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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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)

where in Equation18 is the delay time. Conservatively, the spilled pebbles are assumed to have thehighestburnupandthelargestamountofMARamongthepebbles.

GraphiteDustAccumulatedinthePHSS:

TheamountofgraphitedustaccumulatedinthePHSSisbasedonanestimatedmaximumdust generationrateduringnormaloperation.TheconcentrationofMARinthedustisassumedtobe identicaltotheMARinthegraphitematrixofthepebbleswiththehighestburnupandloadingofMAR.

However,creditistakenforradionuclidedecayduringnormaloperation.Foraradionuclideindexedby i,theamountofthegivenradionuclideinthegraphitedustisevaluatedthroughthesolutionofthe followingequation:

, (19)

where, isthedustgenerationrate,,istheconcentrationoftheradionuclideinthegraphite matrix,andisthedecayconstantoftheradionuclide.

FlibeAccumulatedinthePHSS:

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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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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)

where isthemassoxidationrateinunitsof, 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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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)

where subscript i is the index of the radioisotope of MAR, is the number of spilled pebbles, 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)

where isthemassofthepebble,gisthegravityaccelerationrate,andu,isthenumberof pebblesextractedpersecondinunitsof.

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

,, (28)

where m andA, aremassofgraphitematrixinapebble,andtheactivityoftheradioisotope in the matrix, and is the decay constant. f in the equation represents the fraction of the fuel pebbles in the core region, because there are large number of graphite pebbles in the Hermes core that moderateneutrons.Therefore,apebblethatisextractedfromthecoreregionhasaprobabilitylessthan onebeingthefuelpebble,andonlythedustgeneratedbyfuelpebblescontributestotheactivityofMAR inthegraphitedust.SolutionofEquation28leadstoaformulationoftheactivityofdustasthefunction ofoperatingtime t ofthereactor:

(29)

,, 1

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

1 (30) 2

where, istheFanningfrictionfactor, isthegasdensityandu isthegasvelocity.Thegasvelocity canbedeterminedthroughanexpression(Reference24)forcompressibleisentropicflowdrivenby pressuredifference.

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

1 (31) 2 2

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where,istheparticlediameter,isthedistributionfunctionofparticlenumberdensities(i.e.,

isthefractionofthenumberofparticleswithdiameter ), ln isthemeanofthelog normaldistribution, isthegeometricmeandiameter, ln isthestandarddeviationofthe distribution,and isthegeometricstandarddeviation.Forthelognormaldistribution,thegeometric meandiameterandstandarddeviationsofthedepositeddustparticlesneedtobeprovidedasinput.

Theresuspendedfractionofthedustparticlesisdeterminedasthefractionofthedustparticles withdiameterslargerthanthecutoffdiameterbutsmallerthantheupperlimitdiameterofaerosol particles 50,i.e.,

(32)

where, is the cutoff lift diameter, 50 is the upper limit of the aerosol particles, and isthethirdmomentofthenumberdistribution.InsertingthelognormaldistributionofEquation31into Equation32resultsinananalyticalformulationoftheresuspensionmassfraction:

2 2 2 (33)

where, is error function, and 3. The MAR in the resuspended dust particles is assumed tobereleasedasaerosolspromptlyforconservativism.

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5 CONCLUSIONS

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

Themethodsdescribedinthisreportareusedtoevaluateeventswithinthedesignbasistoensurethere aresufficientdesignfeaturesavailabletomitigatetheeffectsandkeepthepotentialconsequences boundedbytheMHAdescribedinthisreport.

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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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Table21:PrescriptiveMaximumHypotheticalAccidentTemperatures

StartTime EndTime Duration FlibeFreeSurfaceand Kernel,SiC,andPyCand (Days) (Days) (Days) StructuralGraphite PebbleCarbonMatrix Temperatures(K) 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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Table31:AnalyzedPostulatedEventsandAppliedEvaluationModels

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

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

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Table32:DerivedFiguresofMeritandAcceptanceCriteriaforPostulatedEvents

FigureofMerit AcceptanceCriterion ApplicableEvents PeakTRISOtemperaturetime GenerallyboundedbytemperatureSaltSpills,Reactivity timecurvesderivedfromthe Insertion,IncreaseinHeat assumedMHAfueltemperature Removal,LossofForced timecurve Circulation,PHSSbreak, Seismic TRISOfailureprobability NegligibleTRISOfuelfailureSaltSpills,Reactivity probability Insertion,IncreaseinHeat Removal,LossofForced Circulation,PHSSbreak PeakFlibecovergasinterfacial Generallyboundedbytemperature SaltSpills,Reactivity temperature timecurvesderivedfromthe Insertion,IncreaseinHeat assumedMHAFlibecovergas Removal,LossofForced interfacialtemperaturetimecurve Circulation,PHSSbreak Peakvesselandcorebarrel Boundedbyboththemaximum SaltSpills,Reactivity temperatures allowabletemperaturederivedto Insertion,IncreaseinHeat limitexcessivecreepdeformation Removal,LossofForced anddamageaccumulationandby Circulation,PHSSbreak 750°C(highestvesseldesign temperature)

Minimumreactorvesselinner AboveFlibemeltingtemperature LossofForcedCirculation surfacetemperature (overcooling)

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

insulation,steel)

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

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FigureofMerit AcceptanceCriterion ApplicableEvents assumedMHApebblecarbonmatrix Removal,LossofForced temperaturetimecurve Circulation,PHSSbreak PeakTRISOtemperaturetimeex Generallyboundedbytemperature PHSSbreak vessel timecurvesderivedfromthe assumedMHAfueltemperature timecurve Amountofmaterialsatrisk Lessthanlimitderivedtobound PHSSbreak released totalreleasesofthepostulated eventtolessthantheMHA

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Table41:KPSAMModelsandFieldEquations

ModelName Field Description Dimension Singlephaseflow Mass, 1Dfluidflowwithwallfrictionandheat 1D momentum,and transfer.Theflowmodelissinglephase energy (liquidorgas)withtheprimaryvariables beingpressure,velocity,andtemperature.

Heatconduction Energy Heatconductionmodelforplate,cylindrical,1D/2D orsphericalgeometrieswithtemperatureas primaryvariable.Canbecoupledto0D/1D fluidvolumessuchaspipes.Maycoupleto othersurfacesbythermalradiationorgap conductancemodel.

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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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Table43:KPFHRTRISOfuelspecificationforasmanufacturedcontaminationanddefectfractions

Property SpecifiedFraction

Disperseduraniumfraction1.0x105

Exposedkernelfraction5.0x105

DefectiveSiCcoatingfraction1.0x104

DefectiveIPyCfraction1.0x104

DefectiveOPyCfraction1.0x102

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Table44:InputParametersConsideredforPostulatedEvents

Parameter Value Rationale Reactorinitialpower RangeofvaluesuptoandRangesofpowerlevelsanalyzed includingmaximumpowerlevel includinguncertainty Coolantaveragetemperature Rangeovercontrollerdeadband Limitingvaluemaybeevent andmeasurementuncertainty dependent Systempressure NominalforalleventsexceptTheeffectofthesystem forsaltspill pressureisinsignificantforall eventsexceptforsaltspill events Powerdistribution Axial+radialpowerdistributionMostlimitingpowerdistribution forpeakingfactor isconsidered

Bothfreshcoreandequilibrium coreareconsideredaslimiting conditions Shutdownmargin ConsidersmostreactiveProvidemarginformalfunctions shutdownrodisunavailable Shutdownrodinsertiontime Conservativeshutdownrod Delaystheshutdownofthe insertiontimesassumed reactor Reactivitycoefficients ValuesassumedonaneventLimitingvaluesmaybeevent specificbasisandaccountfor dependent uncertainty DHRSCapacity MinimumandmaximumMinimumDHRSperformanceis performanceassumedonan expectedtobeboundingfor eventspecificbasis heatupevents

Minimumperformanceassumes MaximumDHRSperformanceis lossofatrainofDHRSand expectedtobeboundingfor minimumperformance overcoolingevents requirements

Maximumperformance assumesfullcapacityofDHRS plusuncertainty Decayheat MinimumandmaximumvaluesMaximizingdecayheatis assumedonaneventspecific expectedtobeboundingfor basis heatupevents

Minimizingdecayheatis expectedtobeboundingfor overcoolingevents

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Parameter Value Rationale Materialproperties Rangedwithinuncertainties Uncertaintyinmaterial propertiesforcoolantand structurestreatedonanevent specificbasis ReactorProtectionSystem Actuationon: Analyticallimitsprovidemargin analyticallimits HighReactorPower tosafetylimits HighFluxRate HighCoolantTemperature Measurementuncertainty LowLevel appliedtosetpointsarederived fromanalyticallimits ReactorProtectionSystem Conservativedelaytimes Delayreactortrip actuationdelay applied PlantControlSystems PotentialeventmitigationPlantcontrolsystemsarenot capabilitiesoftheplantcontrol safetyrelated systemsarenotcredited Potentiallyadverse Suitablyconservativetreatment performanceofplantcontrol ofrelevantplantcontrol systemsneedstobeconsidered featuresisappliedinthesafety analysis

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Figure11:ElementsofEvaluationModelDevelopmentandAssessmentProcess

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Figure21:PrescriptiveMHATemperatures

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Figure41:SAMCodeStructure

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Figure42:KPSAMSampleNodalDiagramoftheHermesReactor

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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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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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TableA11:InitialconditionsforInsertionofExcessReactivityAssumedBoundingEvent

Parameter InitialCondition Rationale Reactorinitial 102% Assumedpowermeasurementuncertainty power Coolantaverage Nominal+3%°C Controllerdeadbandandmeasurement temperature uncertainties Systempressure Nominal Theeffectofthesystempressureisinsignificant Powerdistribution Axial+radialpower Mostlimitingpowerdistributionisconsidered distributionforpeaking factor

Bothfreshcore,and equilibriumcoreare consideredaslimiting conditions

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TableA12:95%ConfidenceLevelUpperLimitonInServiceFailureFractionsforNormalOperation andReactivityInsertionPostulatedEvent

FailureProbability Normal NormalOperation+

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

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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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FigureA11:ReactivityInsertionandReactivityFeedbackAfterFullRodWithdrawal

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FigureA12:FiguresofMeritDuringandAfterReactivityInsertion

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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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FigureA21:NormalizedReactorPowervsInstantaneousAverageFuelandCoolingTemperatureDrop

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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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ThespreadingofFlibemaybelimitedbytheareaofdripcatchpanifused.Theareaofthedrip panwouldbesmallerthantheflatfloorarea.

ThespreadingofFlibemaybeincomplete(withoutcoveringtheentireareaofthereactorcellor drippan)becauseoffreezingatthebottomandformationofcrustonthespreadingfront.

Flibemayflowandaccumulateatcertainlowerareainthereactorcellifthereactorcellin realityhasaslope.

==

Conclusions:==

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

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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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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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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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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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(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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TableA41:InitialConditionsforLossofForcedCirculationOverheatingAssumedBoundingEvent

Parameter InitialCondition Rationale Reactorinitial 102% Assumedpowermeasurementuncertainty power Coolantaverage Nominal+3%°C Controllerdeadbandandmeasurementuncertainties temperature Systempressure Nominal Theeffectofthesystempressureisinsignificant Powerdistribution Axial+radialpower Mostlimitingpowerdistributionisconsidered distributionfor peakingfactor

Bothfreshcore,and equilibriumcoreare consideredaslimiting conditions DHRScapacity 75% AssumeoneDHRStrainisoutofoperation Heatstructureheat 75% Accountforanyuncertaintyrelatedtotheheat capacity capacityofsolidmaterialsinthemodel Flibeheatcapacity 95% AccountforuncertaintyintheheatcapacityofFlibe Reactivity 75% Reducedtoconservativelybiastheimpactofreactivity coefficient feedbackpriortoreactortrip magnitude

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TableA42:InitialConditionsforLossofForcedCirculationOvercoolingAssumedBoundingEvent

Parameter InitialCondition Rationale Reactorinitial 98% Assumedpowermeasurementuncertainty power Minimizedstoredenergy

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

Bothfreshcore,and equilibriumcoreare consideredaslimiting conditions DHRScapacity 100% FullcapacityofDHRS Heatstructureheat 75% Accountforanyuncertaintyrelatedtotheheat capacity capacityofsolidmaterialsinthemodel Minimizesstoredenergyandacceleratescooldown Flibeheatcapacity 95% AccountforuncertaintyintheheatcapacityofFlibe Minimizesstoredenergyandacceleratescooldown Reactivity Nominal Reactortripinitiatedimmediatelyfollowingevent coefficient initiation magnitude

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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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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 0.01 Primarysaltpumphalvingtime(s) 2 seizureapproximation)(s)

Intermediatevelocityhalvingtime(s) 1 Intermediatevelocityhalvingtime(s) 1 DHRScapacity(%) 75 DHRScapacity(%) 100

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TableA45:95%ConfidenceLevelUpperLimitsonInServiceFailureFractionsforNormalOperation andLossofForcedCirculationPostulatedEvents

FailureProbability NormalOperation NormalOperation+

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

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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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FigureA41:FiguresofMerit-Overheating

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FigureA42:FiguresofMerit-Overcooling

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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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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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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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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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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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FigureA51:GraphiteOxidationRate

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FigureA52:MassLossofGraphiteMatrixandReleaseFractionofMAR

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FigureA53:TemperatureoftheOuterSurfaceofthePebble

ML23055A676

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