ML111890408
| ML111890408 | |
| Person / Time | |
|---|---|
| Site: | South Texas  |
| Issue date: | 07/06/2011 |
| From: | Kreslyon Fleming, Lydell B KNF Consulting Services, Risk Management, Scandpower |
| To: | Balwant Singal Plant Licensing Branch IV |
| Singal, B K, NRR/DORL, 301-415-301 | |
| Shared Package | |
| ML111890371 | List: |
| References | |
| TAC ME5358, GSI-191, TAC ME5359 | |
| Download: ML111890408 (34) | |
Text
Development of LOCA Initiating Event Frequencies for South Texas Project GSI-191 (Draft Report)
Developed for South Texas Project Electric Generating Station by Karl N. Fleming KNF Consulting Services LLC and Bengt O. Y. Lydell July 2011
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Table of Contents 1.
SummaryofLOCAQuantificationProcedure.......................................................................................4 2.
ExampleApplicationofLOCAFrequencyMethodology.......................................................................6 2.1.
FailureDataQuery........................................................................................................................6 2.2.
ComponentPopulationExposure................................................................................................7 2.3.
DamageMechanismSusceptibility.............................................................................................10 2.4.
FailureRateBayesUpdates.......................................................................................................10 2.5.
FailureRateSynthesis.................................................................................................................14 2.6.
ConditionalRuptureModeProbabilityModel............................................................................14 2.6.1.
UseofNUREG1829Data....................................................................................................14 2.6.2.
ModelforDerivingConditionalProbabilitiesfromRuptureFrequencies..........................17 2.6.3.
IncorporationofEpistemicUncertaintiesfromNUREG1829............................................20 2.6.4.
BayesUpdateoftheConditionalProbabilityDistributions...............................................28 2.7.
LOCAFrequenciesAssociatedwithSurgeLineWelds................................................................29 2.7.1.
BaseCaseResults................................................................................................................29 2.7.2.
InfluenceofNDEInspectionsonLocationSpecificLOCAFrequencies...............................30 2.8.
LOCAFrequencySummary..........................................................................................................32 3.
References..........................................................................................................................................33
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Figures
Figure21EventTreeModeltoRepresentUncertaintyinSurgeLineBJWeldExposureforThermal Fatigue........................................................................................................................................................12 Figure22Category1LOCAFrequenciesforPWRPipingSystemsat25YearsofPlantOperation (ReproducedfromFigureL.13inNUREG1829).........................................................................................16 Figure23BenchmarkingLognormalDistributionstoLydellBaseCaseResults-HPIInjectionLine........18 Figure24BenchmarkingLognormalDistributionstoLydellBaseCaseResults-RCSSurgeLine.............19 Figure25BenchmarkingLognormalDistributionstoLydellBaseCaseResults-RCSHotLeg.................19 Figure26DefinitionofTargetBoundsforHPIInjectionLineLOCAFrequencies......................................21 Figure27CalibrationofConditionalProbabilityModeltoMatchTargetsforHPIInjectionLine.............22 Figure28DefinitionofTargetBoundsforRCSSurgeLineLOCAFrequencies..........................................23 Figure29CalibrationofConditionalProbabilityModeltoMatchTargetsforRCSSurgeLine.................24 Figure210DefinitionofTargetBoundsforRCSHotLegLOCAFrequencies.............................................25 Figure211CalibrationofConditionalProbabilityModeltoMatchTargetsforRCSHotLeg....................25 Figure212ComparisonofConditionalProbabilityModelsforHPIInjectionline.....................................27 Figure213ComparisonofConditionalProbabilityModelsforRCSSurgeLine........................................27 Figure214ComparisonofConditionalProbabilityModelsforRCSHotLeg.............................................28 Figure215ComparisonofSurgeLineLOCAFrequencieswithDifferentDamageMechanismInputs.....30 Figure216ComparisonofWeldFailureRatesDeterminedbyMarkovModelforDifferentReliability IntegrityManagementApproaches............................................................................................................32 Tables Table21ResultsofClass1FailureDataQuerybySystemandComponent...............................................7 Table22ResultsofClass1FailureDataQuerybyFailureMechanism.......................................................8 Table23DefinitionofFailureMechanisms.................................................................................................9 Table24ServiceExperiencebyWestinghouseReactorType.....................................................................9 Table25PlantDataUsedtoEstimateSurgeLineWeldPopulation..........................................................10 Table26SusceptibilityFractionsforSurgeLineWelds.............................................................................11 Table27ParametersofBayesUpdatesforWeldFailureRateCases.......................................................13 Table28TotalFailureRatesforSurgeLineWelds....................................................................................14 Table29NUREG1829andSTPPRALOCACategories...............................................................................15 Table210LognormalDistributionsforConditionalLOCACategoryProbabilitiesthatMatchBengt LydellsBaseCaseResults...........................................................................................................................20 Table211STPConditionalProbabilityModelsDerivedFromTargetLOCAFrequencies.........................26 Table212ResultsofBayesUpdateofConditionalLOCAProbabilities....................................................29 Table213UnconditionalLOCAFrequenciesforSurgeLineWelds...........................................................31
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- 1. Summary of LOCA Quantification Procedure ThetechnicalapproachtoestimatingLOCAinitiatingeventfrequenciesisframedaroundthemodel expressedbyEquations(1)and(2)forestimatingthefrequencyofaLOCAofagivensize.Theparameter xistreatedasadiscretevariablerepresentingdifferentbreaksizerangessuchasthoseusedinNUREG 1829todescribethe6LOCAcategories.Hencextakesonvalues:{1,2,3,4,5,6}tocorrespondwiththe LOCAcategoriesdefinedinNUREG1829[1].Forthetimebeing,weshallusetheNUREG1829 categorieswiththeunderstandingthatthesemayberedefinedlaterifnecessary.
i ix i
x m
LOCA F
)
(
(1) ik ik x
k ik ix jx I
F R
P
)
(
(2) where:
)
(
x LOCA F
FrequencyofLOCAofsizex,perreactorcalendaryear,subjectto epistemicuncertaintycalculatedviaMonteCarlo
i m
Numberofpipeweldsoftypei;eachtypedeterminedbypipesize, weldtype,applicabledamagemechanisms,andinspectionstatus (leaktestandNDE);nouncertainty
ix
Frequencyofruptureofcomponenttypeiwithbreaksizex,subject toepistemicuncertaintycalculatedviaMonteCarlo
ik
Failurerateperweldyearforpipecomponenttypeiduetofailure mechanismk,subjecttoepistemicuncertaintydeterminedbyRIISI BayesmethodandEq.(3)
)
(
ik x F R
P Conditionalprobabilityofruptureofsizexgivenfailureofpipe componenttypeiduetodamagemechanismk,subjecttoepistemic uncertaintydeterminedviaexpertelicitation(NUREG1829)
ik I
Integritymanagementfactorforweldtypeiandfailuremechanismk, subjecttoepistemicuncertaintydeterminedbyMonteCarloand Markovmodel
Forapointestimateofthefailureratefortypeiandfailuremechanismk:
i i
ik ik ik ik ik T
N f
n n
(3)
where:
ik n
Numberoffailuresinpipecomponent(i.e.,weld)typeiduetofailure mechanismk;verylittleepistemicuncertainty
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ik
Componentexposurepopulationforweldsoftypeisusceptibleto failuremechanismk,subjecttoepistemicuncertaintydeterminedby expertopinion
ikf Estimateofthefractionofthecomponentexposurepopulationfor weldtypeithatissusceptibletofailuremechanismk,subjectto epistemicuncertainty,estimatedfromresultsofRIISIforpopulation ofplantsandexpertopinion
i N
Estimateoftheaveragenumberofpipeweldsoftypeiperreactorin theapplicablereactoryearsexposureforthedatacollection,subject toepistemicuncertainty,estimatedfromresultsofRIISIfor populationofplantsandexpertopinion
iT Totalnumberofreactoryearsexposureforthedatacollectionfor componenttypei;littleornouncertainty
ForaBayesEstimate,apriorisupdatedusingnikandikwithaPoissonlikelihoodfunction.
Thekeyinputsthatareneededtoprovidethepipefailurerateinformationinclude:
Identificationofwhichlocationswillbeinvestigatedfordebrisformationandthegroupingsof locationsthatwillbeperformedtosupporttheriskevaluation.
Countsofpipefailuresinapplicablenuclearindustrypipingsystems,essentiallyallthefailure datainASMEClass1and2pipingsystemsinPWRsinU.S.serviceexperienceandapplicable internationalplantswithsimilardesignsandintegritymanagementprograms-fromPIPExp database.[2]
Pipeexposureestimates-quantityofpipeandpipeweldsandthereactoryearsofservice experiencethatproducedthefailurecountsidentifiedabove.Theseestimatesarebasedon informationcontainedinthePIPExpdatabaseaswellastheinformationavailableinrisk informedinserviceinspectionsubmittalstotheNRC,whichincludeanenumerationofweld countsindifferentcategoriesandtheresultsofdamagemechanismevaluations.
Estimatesofthefractionsofpipingsystemcomponentsintheservicedatathataresusceptible todifferentdamagemechanisms.TheseestimatesarebasedonNUREG1829andsupporting computerfilesthatprovideinformationonepistemicuncertaintyaboutpiperupture frequenciesvs.breaksizefordifferentpressureboundarycomponents STPRIISIevaluationreportandsupportingcalculationsprovidinginformationonapplicable damagemechanismsforeachweldandadefinitionofwhichweldsareselectedforNDE.
ResultsofinspectionreportsandotherevidenceofanypipefailureordegradationatSTPthat mayinfluencetheplantspecificfailurerates,aswellastheinformationneededtoestimate exposuredata.
TheintegritymanagementfactorIikofEquation(2)isquantifiedusingtheMarkovmodelforPiping ReliabilitythatwasdevelopedtosupporttheEPRIRIISIprojects.
Themethodologyoutlinedaboveandthemethodsanddatabasesthathavebeendevelopedto implementthisapproachwereoriginallydevelopedtosupporttheEPRIRIISImethodologythathas
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beenimplementedformanyoftheexistingNRClicensedplantsandseveralforeignplants.Thepartof thismethodologythatisrelevanttoestimatingLOCAfrequenciesisdescribedindetailinReference[3]
andhasbeenrecentlyappliedinEPRIsponsoredprojectstodeveloppipingsystemfailureratesforuse ininternalfloodingandhighenergylinebreakPRAs,asdocumentedinReferences[4]and[5].The originalEPRIstudythatwasresponsiblefordevelopingtheMarkovmodelandBayesmethodfor estimatingpipefailureratesandrupturefrequencieswasdocumentedinEPRITR110161[6],andan earlyversionofthepipefailureratedatabaseforbothconditionalandunconditionalpipefailurerates waspublishedinEPRITR111880[7].Anindependentreviewofthesereportswascarriedoutbythe UniversityofMaryland,whichvalidatedthemethodologythatwasdevelopedinthesereports.These methodsanddatawerethenusedaspartoftheEPRIRIISItechnicalapproachasdescribedintheEPRI RIISITopicalReport[9].TheNRCapprovedthesemethodsanddataforuseinappliedRIISIevaluations asdocumentedintheSafetyEvaluationReport[10].TheNRCSERwassupportedbyanindependent reviewoftheBayesfailureratemethodandtheMarkovmodelbyLosAlamosNationalLaboratory[11],
whichprovidesasecondindependentreviewofthemethodology,includingavalidationoftheMarkov modelsolutions.
TheapplicationoftheMarkovmodelrequiresthedevelopmentofrathercomplexclosedformsolutions tothedifferentialequationssupportingtheMarkovmodel,whichwereoriginallydevelopedinTR 110161andarealsopublishedinReference[12].Usingtheseclosedformsolutions,itisstraightforward toquantifytheuncertaintiesintheresultinginspectionfactorsusingMonteCarlosimulationmethods viaMicrosoftExcel'andOracleCrystalBall',whichistheapproachbeingusedinthisSTPGSI191 evaluation.
- 2. Example of Applying LOCA Frequency Methodology Inthissection,theLOCAfrequencymethodologythatisbeingusedfortheSTPGSI191projectis describedusingsomeexamplesandsomeofthepreliminaryresults.Theexamplespresentedhereare chosentodescribethevariousdataanalysesandmodelingassumptionsthatwillbeusedbasedon someearlyandpreliminaryresultsthataresubjecttochangepriortotheactualNRCsubmittal.The purposeistoprovidetheNRCwithabetterunderstandingoftheapproachandtohelpidentify potentialreviewissues.
2.1. Failure Data Query ThefailuredataquerywasperformedonWestinghouseandFramatomePWRplantoperating experiencefrom1970through2010andincludedASMEClass1pipingsystems.Thisgenerallyincludes reactorcoolantsystem(RCS)pipingandsystemsthatinterfacewiththeRCSinsidetheisolationvalves thatnormallyseparatetheRCSfrominterfacingASMEClass2piping.Interfacingsystemsincludethe emergencycorecooling,residualheatremoval,chemicalvolumeandcontrolsystem,andvariousother systemsincludingRPVheadventsandinstrumentationlines.Thepreliminaryresultsofthedataquery areshowninTable21brokendownbykeycomponentsalongthepressureboundaryandTable22by failuremechanism.Becauseroughlyhalfofthecurrentfleetofoperatingplantsweredesignedandbuilt
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priortothedevelopmentofASMEnuclearpipingcodes,muchofthispipewasoriginallydesignedto B31.1designcodes,andthenlaterinspectionandISIrequirementsforClass1pipingwereretrofitted intotheseplants.Sofromadesignandmaterialsperspective,theLOCAsensitivepipingactuallyreflects amixtureofB31.1andClass1pipe.
Table21ResultsofClass1FailureDataQuerybySystemandComponent SYSTEM Nominal PipeSize (NPS)
PipeFailuresbyMode(1),(2),(3)
Total Crack Full Crack Part Small Leak Leak Large Leak CVC 1"
7 1
6
2"ø4" 7
1 6
SafetyInjection 1"
2 2
4"ø10" 6
3 1
1 1
PressurizerSample 2"
5 4
1
PressurizerPORV 4"ø10" 2
2
PressurizerSPRAY 1"
4 1
2 1
4"ø10" 3
2 1
PressurizerSRV 4"ø10" 7
6 1
PressurizerSurge 14" 3
3
RCS 2"
76 4
10 53 4
5 RCSColdLeg 32" 4
4
RCSHotLeg 32" 6
5 1
RHR 1"
6 6
RHR 4"ø10" 1
1
RCHotLegS/G Inlet 32" 19 19
S/GSystem 2"
8 2
2 4
TOTALS
166 12 59 83 6
6 Notes (1) Queryaccountsfor3914reactoryearsbasedondateofinitialcriticalityfrom1970-2010.
(2) Failureisdefinedasanyeventthatrequiredrepairorreplacementofdamagedcomponent.
(3) Smallleakshaveleakflows<<1gpm;Leaks<1gpm;LargeLeaks<10gpm.
2.2. Component Population Exposure Pipecomponentexposureisevaluatedinthecurrentanalysisintermsofpipeweldsinthedataquery.
Thisisestimatedfromacombinationofthereactoryearsofserviceexperienceandanestimateofthe totalnumberofweldsperplant.Inprinciple,thenumberofweldsperplantisknownbutisseldomin thepublicdomain.Inaddition,thereisusuallysignificantplanttoplantvariabilityinthenumberof weldsfordifferentcomponents,oneexceptionbeingthenumberofcoolantloopsorpressurizers.To addressthis,thecomponentexposure,e.g.,totalweldyearsofexperienceresponsiblefortheidentified failures,istreatedasanuncertainparameterinfailureratedevelopment.Inaddition,tosupportthe estimationoffailure
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Table22ResultsofClass1FailureDataQuerybyFailureMechanism System Event Type NPS Failure Count by Failure Mechanism Totals C-F D&C ECSCC Fret.
IGSCC LC-FAT PWSCC OVLD TF TGSCC TAE V-F CVC Crack 1"
1 1
2" ø 4" 1
1 Leak 1"
6 1
5 2" ø 4" 6
1 5
Safety Injection Crack 4" ø 10" 3
1 2
Leak 1"
2 2
4" ø 10" 3
3 Prz-Sample/Instr.
Crack 2"
5 1
2 2
Prz-PORV Crack 4" ø 10" 2
2 Prz-SPRAY Crack 1"
1 1
Crack 4" ø 10" 2
2 Leak 1"
3 1
1 1
Leak 4" ø 10" 1
1 Prz-SRV Crack 4" ø 10" 6
1 5
Leak 4" ø 10" 1
1 Prz-Surge Crack 14" 3
3 RCS Crack 2"
14 1
3 3
2 1
4 Leak 2"
62 1
12 2
1 1
2 2
8 33 RCS Cold Leg Crack 32" 4
3 1
RCS Hot Leg Crack 32" 5
5 Leak 32" 1
1 RHR Crack 4" ø 10" 1
1 RHR Leak 1"
6 1
1 4
S/G Inlet Crack 32" 19 1
18 S/G System Leak 1"
1 1
Crack 1"
2 1
1 Crack 1" < ø 4" 2
2 Leak 1"
3 1
1 1
TOTALS 166 1
23 7
4 3
2 48 1
9 11 1
56
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Table23DefinitionofFailureMechanisms ID Description Comment CF CorrosionFatigue
D&C Design&ConstructionFlaws Mayormaynotpropagatethroughwall ECSCC ExternalChlorideInduced SCC Primarilyaconcernwithsmallborelines IGSCC IntergranularSCC Stagnantlocationswithhighresidualstresses LCFAT LowCycleFatigue
PWSCC PrimaryWaterSCC Nibasemetallocationsonly OVLD Overload Mechanicallyinducedtensileloading TF ThermalFatigue
TGSCC TransgranularSCC
TAE ThermalAgingEmbrittlement Hightemp/pressurelocationsonly VF VibrationFatigue
ratesfromdifferentdamagemechanisms,itisnecessarytoestimatethefractionofthepopulationthat issusceptibletoagivendamagemechanism,whichisalsouncertain.Resultsofpublishedreportson RiskInformedInServiceInspectionevaluationsareusefulsourcestosampletoprovidebothweldcount andfractionsusceptibleestimates.
ThereactoryearsofserviceexperiencebyreactortyperesponsibleforthefailuresinTable21and22 arelistedinTable24.
Table24ServiceExperiencebyWestinghouseReactorType WE Type Rx Reactor-Calendar Years Initial Grid Connection Initial Criticality 2-Loop 570.1 581.4 3-Loop 2052.6 2096.1 4-Loop 1193.9 1236.5 Total 3816.6 3914.0
Oneofthekeystepsintheanalysisistomakeuseofinsightsfromtheserviceexperiencetobreakdown theClass1weldpopulationintohomogenousclassesforthepurposeoffailureratedevelopment.Asan example,considerthepressurizersurgelineforwhichthreecomponentfailuresarelistedinTable21.
Therearethreedistinctclassesofweldsinthepressurizersurgeline:asingleBFweld,abimetallicweld thatconnectsthesurgelinetothepressurizernozzle,twobranchconnectionweldsthatconnectthe surgelinetooneofthehotlegs,andsomenumberofBJweldsthatlinksurgelinepipetopipe connectionsbetweenthebranchconnectionandpressurizer.Table25depictsinformationusedto estimateweldcountsforthepressurizersurgeline.Asseeninthistable,thereissignificantvariability fromplanttoplantinthenumberofBJwelds.
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Table25PlantDataUsedtoEstimateSurgeLineWeldPopulation
Plant
PWR Type WeldPopulation(1)
BFWelds InlineBJWelds BranchConnection toHotLeg Braidwood1 4Loop 1
8 2
Braidwood2 4Loop 1
7 2
Byron1 4Loop 1
6 2
Byron2 4Loop 1
6 2
Kewaunee 2Loop 1
6 2
Koeberg1 3Loop 1
5 2
Koeberg2 3Loop 1
5 2
STP1 4Loop 1
8 2
STP2 4Loop 1
8 2
V.C.Summer 3Loop 1
10 2
Note (1) KewauneesurgelineisNPS10;remainingplantsareNPS14to16.
2.3. Damage Mechanism Susceptibility Damagemechanismsusceptibilityisassessedbasedoninsightsfromserviceexperienceandtheresults ofRIISIevaluationsonClass1pipingsystems,whichhavebeencompletedformostUSPWRplants.The bimetallicBFweldsareinherentlysusceptibletoPWSCCbecausetheyarebasedonNibasedalloys.The branchconnectionweldsareinherentlysusceptibletothermalfatigue.SomeoftheBJweldsarealso susceptibletothermalfatigue,andalloftheClass1weldsaresubjecttothepossibilitytodesignand constructiondefects.Asummaryofthedamagemechanismsusceptibilityforthesurgelineweldsis showninTable26.ThesusceptibilityandweldcountsoftheBJweldsareuncertain.TheLOCA frequencymethodologyusedinthisstudyandsummarizedinSection2.1usesatechniquedevelopedin theEPRIRIISIProgram[9],inwhichthefailureratesaredevelopedfordiscretecombinationsof estimatesofweldpopulationanddamagemechanismsusceptibility,whichisillustratedinFigure21.
2.4. Failure Rate Bayes Updates ThenextstepintheLOCAfrequencyquantificationprocedureistoperformBayesupdatesforeach component/damagemechanism/populationexposureestimatethatsupportsthecalculation.The priordistributionsusedinthisassessmentarebasedonthosethatweredevelopedinReference[7]for useintheEPRIRIISIevaluationsthatfollowedthemethodologyintheEPRIRIISITopicalReport[9],
whichwasreviewedbytheNRCandLANLasdocumentedinReferences[10]and[11].Theevidencefor theupdatesisbasedon3failuresofBFsurgelineweldsduetoPWSCC,and0failuresforeitherthe branchconnectionorBJweldsforthesurgeline.Theparametersofthepriorandupdateddistributions forallthecasesneededtosupportthesurgelineweldsarelistedinTable27.
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Table26SusceptibilityFractionsforSurgeLineWelds System Location Confidence Level WeldSusceptibilityFractions CF D&C ECSCC Fretting IGSCC PWSCC TF TGSCC TAE VF
Pressurizer SurgeLine
BF(1)
Low N/A 1
N/A N/A N/A 1
N/A N/A N/A N/A Medium N/A 1
N/A N/A N/A 1
N/A N/A N/A N/A High N/A 1
N/A N/A N/A 1
N/A N/A N/A N/A
BJ Low N/A 1
N/A N/A N/A N/A 0.01 N/A N/A N/A Medium N/A 1
N/A N/A N/A N/A 0.05 N/A N/A N/A High N/A 1
N/A N/A N/A N/A 0.25 N/A N/A N/A RCHL Branch Connection Low N/A 1
N/A N/A N/A N/A 1
N/A N/A N/A Medium N/A 1
N/A N/A N/A N/A 1
N/A N/A N/A High N/A 1
N/A N/A N/A N/A 1
N/A N/A N/A Note(1)ThesusceptibilityofBFweldstoPWSCCcanbeeffectivelymitigated byapplicationofweldoverlays.
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Figure21EventTreeModeltoRepresentUncertaintyinSurgeLineBJWeldExposureforThermalFatigue
Welds/Rx 6.9 Rx-yrs 3914 Base Exposure 27006.6 Weld Count Uncertainty Fraction of B-J Welds Susceptible to Thermal Fatigue Exposure Case Probability Exposure Multiplier p=.25 0.0625 0.5 13,503 weld-yrs High (.25 x Base) p=.25 p=.50 0.125 0.1 2,701 weld-yrs High (2 X Base)
Medium (.05 x Base) p=.25 0.0625 0.02 540 weld-yrs Low (.01 x Base) p=.25 0.125 0.25 6,752 weld-yrs High (.25 x Base) p=.50 p=.50 0.25 0.05 1,350 weld-yrs Medium (1.0 X Base)
Medium (.05 x Base) p=.25 0.125 0.01 270 weld-yrs Low (.01 x Base) p=.25 0.0625 0.125 3,376 weld-yrs High (.25 x Base) p=.25 p=.50 0.125 0.025 675 weld-yrs Low (0.5 X Base)
Medium (.05 x Base) p=.25 0.0625 0.005 135 weld-yrs Low (.01 x Base)
Exposure
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Table27ParametersofBayesUpdatesforWeldFailureRateCases WeldType andDM(3)
Weld Count Case DM Susceptibility Case PriorDistribution(1)
Evidence(2)
BayesPosteriorDistribution(1)
Type Median RF Failures Exposure Mean 5th 50th 95th RF SurgeBFSC Base Base Lognormal 8.48E07 100 3
3914 5.62E04 1.23E04 4.83E04 1.27E03 3.2 SurgeBFDC Base Base Lognormal 5.46E08 100 0
3914 1.41E06 5.41E10 5.33E08 4.77E06 93.9 SurgeBCTF Base Base Lognormal 2.66E07 100 0
7828 3.25E06 2.53E09 2.34E07 1.47E05 76.1 SurgeBCDC Base Base Lognormal 5.46E08 100 0
7828 1.17E06 5.37E10 5.24E08 4.37E06 90.1 SurgeBJTF Low Low Lognormal 2.66E07 100 0
135 9.75E06 2.66E09 2.65E07 2.58E05 98.5 Medium Lognormal 2.66E07 100 0
675 7.17E06 2.64E09 2.61E07 2.36E05 94.6 High Lognormal 2.66E07 100 0
3376 4.48E06 2.59E09 2.48E07 1.85E05 84.5 Medium Low Lognormal 2.66E07 100 0
270 8.70E06 2.65E09 2.64E07 2.51E05 97.4 Medium Lognormal 2.66E07 100 0
1350 5.98E06 2.62E09 2.57E07 2.18E05 91.2 High Lognormal 2.66E07 100 0
6752 3.46E06 2.54E09 2.37E07 1.54E05 77.7 High Low Lognormal 2.66E07 100 0
540 7.55E06 2.64E09 2.62E07 2.41E05 95.4 Medium Lognormal 2.66E07 100 0
2701 4.83E06 2.60E09 2.51E07 1.94E05 86.4 High Lognormal 2.66E07 100 0
13503 2.58E06 2.47E09 2.22E07 1.21E05 69.8 SurgeBJDC Low Base Lognormal 5.46E08 100 0
13503 9.83E07 5.33E10 5.14E08 3.96E06 86.2 Medium Base Lognormal 5.46E08 100 0
27007 7.66E07 5.25E10 4.94E08 3.34E06 79.8 High Base Lognormal 5.46E08 100 0
54013 5.77E07 5.12E10 4.65E08 2.67E06 72.2 Notes (1) Failureratesinunitsoffailuresperweldyear.
(2) Exposureinunitsofweldyears.
(3) SC=stresscorrosioncracking;TF=thermalfatigue;DC=designandconstructiondefects;BF=BFweld;BC=branchconnectionweld;BJ=BJweld.
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2.5. Failure Rate Synthesis ThetotalweldfailureratesarecalculatedusingaMonteCarloposteriorweightingtechniqueto combinethedistributionsfromthedifferentweldcountanddamagemechanismsusceptibility hypothesesandthensummingthecontributionsfromdifferentdamagemechanisms.ForBJwelds,the failurerateforthermalfatiguewasdevelopedbyMonteCarlosamplingfromadiscretedistribution definedbyFigure21todeterminewhichofthelognormaldistributionsforBJTFfromTable27touse forthattrial.Repeatingthisprocessovermanytrials(100,000trialsusedforthecurrentexamples) yieldsasingledistributionfortheBJweldfailurerateduetothermalfatiguewhichincorporatesa probabilisticallyweightedcontributionfromeachsupportingweldcounthypothesis.FortheBJweld failurerateduetodesignandconstructiondefects,only3casesarerequiredtomodeluncertaintyinthe weldcountsbecauseallweldsareassumedtobesusceptibletoD&C.ThenthetotalfailurerateforBJ weldsiscalculatedbysummingthecontributionsfromTFandD&C.FortheBFweldsandbranch connectionwelds,thereisnosignificantuncertaintyforweldcountsorDMsusceptibility.Therefore,its necessaryonlytosumtherandomsamplesfromtheDMdistributionstocomputethetotalcomponent failureratesfortheseweldtypes.
Table28TotalFailureRatesforSurgeLineWelds WeldType FailureRateperWeldYear Mean 5%tile 50%tile 95%tile BF 5.62E04 1.38E04 4.37E04 1.40E03 BranchConnection 4.54E06 9.64E09 2.88E07 1.17E05 BJ 6.29E06 9.78E09 3.26E07 1.57E05
2.6. Conditional Rupture Mode Probability Model ThissectionillustrateshowweplantouseinformationfromNUREG1829asinputtodevelopthe conditionalruptureprobabilitymodelsforselectedcomponents.Thismaterialisstillunderreviewandis subjecttochangeinthefinalsubmittal.WeplantoreviewthesupportinginformationfromNUREG 1829thatwasrecentlymadeavailablebytheNRC,andwemaymodifyourapproachafterwehave completedourevaluationofthatsupportinginformation.Importantly,ourapproachincludesastepto calculatethetotalLOCAinitiatingeventfrequenciesfromallthemodeledlocationsandtoperforma sanitychecktoensurethattheresultsobtainedfromthisbottomupprocessyieldsreasonable results.Inadditionweplantocomparetheaggregatedresultsfromourapproachwiththeaggregated LOCAfrequenciesinNUREG1829andotherrelevantsourcesandidentifyatechnicalbasisforthe acceptingtheresultsofsuchcomparisons.
2.6.1. Use of NUREG1829 Data TheexpertelicitationthatwasperformedanddocumentedinNUREG1829[1]providedestimatesof thefrequenciesforlossofcoolantaccidentsbasedonasetofLOCAcategoriesselectedtospanthe breaksizesandleakratesthatarenormallymodeledinPWRandBWRPRAs.Theestimatesprovidedin NUREG1829includedbothpipefailuresandnonpipefailures.However,inthisexampleonlythepipe failurepartisconsidered.LOCAscausedbynonpipefailureswillbeaddressedin2012.TheLOCA
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categoriesforPWRsusedinNUREG1829aresummarizedinTable29.SincethelargestpipesinaPWR reactorcoolantsystem,whichcorrespondtothecoldlegpiping,areontheorderof31nominalpipe size(NPS),theNUREG1829LOCAcategoriesdonotincludeadoubleendedguillotinebreak(DEGB).The effectivebreaksizeofacoldlegpipeof31NPSwouldbeabout44.
TheapproachtousinginformationinNUREG1829todevelopestimatesoftheconditionalprobabilityof piperupturesisbasedonthefollowingobservationsandinformationpresentedinthatdocument.
Basecaseresultsarepresentedinthereportforthreewelldefinedpipingcomponentsfor PWRs,namely,hotlegpiping,pressurizersurgelinepiping,andhighpressureinjectionpiping, whichcomprisepartoftheASMEClass1pressureboundary.Foreachcomponent,therewere fourdifferentandindependentestimatesprovidedforeachapplicableLOCAcategory,twoof whichwerebasedonastatisticalanalysisofservicedataandsimplemodelssimilartothosethat willbeusedintheSTPGSI191evaluation,andtwobasedonprobabilisticfracturemechanics analyses.Thesebasecaseresultswereprovidedasinputtotheexperts,andsomeexpertschose tousethesebasecaseresultsasanchorsfortheirrespectiveinputs.Thebasecaseresultsare summarizedinSection4ofNUREG1829aswellasinthesupportingappendices.
Table29NUREG1829andSTPPRALOCACategories LOCA Category STPPRACategory Effective BreakSize (in.)
FlowRate (gpm) 1 SmallLOCA(1) 0.5 100 2
MediumLOCA(1) 1.5 1,500 3
LargeLOCA 3
5,000 4
6.75 25,000 5
14 100,000 6
31.5 500,000 Note(1)ThebreakpointbetweenSmallandMediumLOCAintheSTPPRAandmost PWRPRAsisactually2.
Aspartoftheelicitation,mostoftheexpertsprovidedinputtotheestimationofLOCA frequenciesforspecificcomponentsinthereactorcoolantsystempressureboundary,including thecomponentsthatwereevaluatedinthebasecaseresultsaswellasessentiallyallthemajor componentsontheClass1pressureboundary.Selectedcomponentlevelresultsofthis elicitationarefoundinAppendixLofNUREG1829.ForPWRs,theseresultsarepresentedfor LOCACategories1,3,and5.AnexampleoftheformofthisinformationforLOCACategory1is showninFigure22.Thereisalsocomponentlevelexpertelicitationinformationpresentedin thisappendixforhotlegpipingforLOCACategory6.TheNUREG1829supportinginformation thatwasjustrecentlyreleasedhasadditionalinformationoncomponentlevelLOCAestimates forLOCAfrequenciesthatwehavenotyetbeenabletoanalyze.
IntheevaluationofservicedatathatwasperformedinsupportofNUREG1829,whichincludes thebasecaseanalysesperformedbyBillGalleanandBengtLydell,noneofthereviewedservice
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datainvolvedtheoccurrenceofaLOCAofanyofthe6LOCAcategories.Theservicedatawe havecollectedinTable21and22forthesesystems,atotalof166pipefailures,includeflaws, cracks,andrathersmallleaks,butnoleaksofthemagnitudethatwouldclassifyasasmallLOCA, whichcorrespondstoLOCACategory1.Thepiperupturemodelsusedinthebasecasestudies ofLydellandGalleanandtheoneusedinthisstudy,assumesthateachpipefailureisa precursortoaLOCA.Eachofthesemodelsstartswithanestimateofthefailurerate,which includesallpipefailuresrequiringrepairorreplacement.Thebridgebetweenthefailurerates, whichareestimatedusingservicedata,andthemoresignificantpipefailuresproducingLOCAs, isthemodelfortheconditionalprobabilityofabreakofagivensizegivenapipefailure.
Anotherwaytolookatthismodelisthatpipefailuresareassumedtorepresentchallengesto thesystemanduponeachchallenge,thereisaprobabilityofexperiencingabreakofagiven size.Byconsideringallthepossibilitiesfordifferentbreaksizes,alltheLOCAfrequency categoriescanbequantified.
Usingtheaboveinformationandinsights,ourapproachtousinginformationfromNUREG1829isto convertinformationthatwaspresentedintheformofLOCAfrequenciesvs.LOCAcategoryto conditionalprobabilitiesvs.breaksize.ThisapproachisappliedtothethreePWRcomponentsthatwere includedinthebasecaseresultsaswellasinAppendixLnamely,theRCShotleg,theRCSsurgeline, andtheHPIinjectionline.ThesespanarepresentativerangeofnominalpipesizesinthePWRClass1 pressureboundaryof30,14,and3.75,respectively.
Figure22Category1LOCAFrequenciesforPWRPipingSystemsat25YearsofPlantOperation (ReproducedfromFigureL.13inNUREG1829)
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2.6.2. Model for Deriving Conditional Probabilities from Rupture Frequencies Themodelusedtoconvertinformationonunconditionalrupturefrequenciestoconditionalfailure probabilitiesmakesuseofthebasecaseresultsofLydellforeachofthethreeselectedPWR components(hotleg,surgeline,HPinjectionline)andthefollowingequation:
)
(
)
(
F R
P m
LOCA F
j l
l l
j
(4)
Where:
)
(
j LOCA F
UnconditionalfrequencyofLOCACategoryjduetopipefailuresin selectedcomponent,perreactorcalendaryear
l m
Numberofpipeweldsoftypelinselectedcomponenthavingthe samefailurerate
l Failurerateperweldyearforpipeweldtype lwithintheselected componentinLydellsbasecaseanalysisfromAppendixDinNUREG 1829
)
(
F R
P j
ConditionalprobabilityofLOCACategoryjgivenfailureinselected component
Eachterminthismodelissubjecttoepistemicuncertainty,whichistobeestimated.Therefore,the approachistousethismodelandthebasecaseanalysisofthefailureratesfromLydelltoderive epistemicuncertaintiesontheconditionalprobabilityofpiperuptureineachLOCAcategorythat producesthesamedistributionofunconditionalLOCAcategoryfrequenciesaspresentedinAppendixL.
Thisapproachmakesuseoftherebeingatechnicalbasisforthefailurerateestimatesfromservicedata andawellreviewedandextensivelyappliedBayesuncertaintyanalysismethod,andtheseestimates werepartoftheinformationthatotherexpertsusedtoanchortheirinputs.Sincetherehavebeenno Category1,2,3,4,or5LOCAs,theexpertelicitationresultsofalltheexpertsconstituteakindof extrapolationoftheexistingservicedata.Therefore,ourapproachsimplyassumesthatthevariabilityin theexpertelicitationinputsforLOCAfrequencyrepresentstheepistemicuncertaintyintheLOCA frequencyforeachcomponent.Thisepistemicuncertaintyisthenassumedtoresultfromthe combinationoftheepistemicuncertaintyinthefailurerateandtheepistemicuncertaintyinthe conditionalprobabilityofeachLOCAcategory.
ThismodelissimilartobutsomewhatsimplifiedincomparisontotheLydellbasecaseanalysisin AppendixDofNUREG1829.LydellsbasecaseanalysisusesdifferentconditionalLOCAcategory probabilitiesfordifferentloadingconditionsandthencombinesthemtoproducehisbasecaseresults.
So,beforeincorporatingtheexpertelicitationresultsintothismodel,weshallderiveanequivalent conditionalprobabilitymodelusingEquation(4)thatattemptstoreproducetheLydellbasecaseresults inordertobenchmarkthismodelagainsttheslightlydifferentmodelusedintheLydellbasecase results.ThenweshalladjusttheepistemicuncertaintiesintheconditionalprobabilityofaLOCAina mannerthatmatchestargetLOCAfrequenciesthataresettoincorporatethevariabilityamongexperts estimatesinNUREG1829.
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UsingthesameMicrosoftExcel'andOracleCrystalBall'filesthatLydellusedtodevelophisbasecase results,thesimplifiedmodelofEquation(4)wasappliedtothesamefailurerateestimatesthatLydell derivedanddocumentedinAppendixDofNUREG1829,assumingalognormaldistributionforthe conditionalLOCAcategoryprobabilityforeachcomponent.Thisresultedinlognormalparametersthat essentiallyreproduceLydellsAppendixDresults,asshowninFigures23,24,and25,fortheHPI injectionline,RCSsurgeline,andRCShotleg,respectively.Themethodusedtoobtainthesewastofirst developnewoutputparametersthatcalculatetheequivalentconditionalprobabilitiesandthento adjusttheresultingdistributionsbytrialanderroruntilagoodmatchwasdetermined.Theparameters oftheselognormaldistributionsareshowninTable22.Thefigurescomparingthebasecaseresults fromNUREG1829withtheresultsobtainedusingtheequivalentlognormaldistributionsindicate excellentagreement.TheunderlyinglognormaldistributionparametersfortheconditionalLOCA probabilitiesinTable210arereasonable.Itisnotedthattheconditionalprobabilityofagivenbreak sizeisinverselyproportionaltopipesize.
Figure23BenchmarkingLognormalDistributionstoLydellBaseCaseResults-HPIInjectionLine
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Figure24BenchmarkingLognormalDistributionstoLydellBaseCaseResults-RCSSurgeLine
Figure25BenchmarkingLognormalDistributionstoLydellBaseCaseResults-RCSHotLeg
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Table210LognormalDistributionsforConditionalLOCACategoryProbabilitiesthatMatchLydells BaseCaseResults Component LOCA Category BreakSize (in.)
Median Mean Range Factor 5%tile 95%tile RCSHL 1
.5 7.86E4 2.16E3 10.4 7.56E5 8.16E3 2
1.5 5.10E5 1.56E4 11.7 4.38E6 5.94E4 3
3 2.01E5 6.06E5 11.6 1.73E6 2.31E4 4
6.76 7.42E6 2.29E5 11.8 6.29E7 8.75E5 5
14 2.74E6 8.43E6 11.8 2.33E7 3.23E5 6
31.5 1.32E6 4.06E6 11.8 1.12E7 1.56E5 RCSSurge Line 1
.5 5.12E3 6.99E3 3.67 1.40E3 1.87E2 2
1.5 4.02E4 6.06E4 4.44 9.06E5 1.78E3 3
3 1.59E4 2.43E4 4.53 3.51E5 7.23E4 4
6.76 5.80E5 9.03E5 4.70 1.23E5 2.73E4 5
14 2.28E5 3.44E5 4.43 5.15E5 1.01E4 HPI 1
.5 7.68E3 1.06E2 3.72 2.06E3 2.86E2 2
1.5 1.04E3 1.57E3 4.44 2.35E4 4.64E3 3
3 4.10E4 6.26E4 4.54 9.03E5 1.86E3
2.6.3. Incorporation of Epistemic Uncertainties from NUREG1829 Thenextstepistoadjustthelognormaldistributionstoreflectthevariabilityofexpertopinion regardingthefrequencyofeachLOCAcategory,basedontheinformationinAppendixLofNUREG1829 andsupportinginformationavailableontheNRCwebsitethatprovidestheresultsofindividualexperts estimatesofLOCAfrequenciesforspecificcomponents.Thisprocessbeginsbysuperimposingthe extrememaximumandminimumvaluesfromtheboxandwhiskerplotsonLOCAfrequenciesvs.LOCA category(andhence,breaksize)inAppendixLofNUREG1829forthethreePWRcomponentsanalyzed intheLydellbasecaseanalysisandcomparingtheseextremevaluestotheLydellbasecaseresults.Then atarget95%tilelineandatarget5%tilelinearedrawnonaloglogplotofthecorrespondingLOCA frequencyvs.breaksizecurve,inordertocapturetheAppendixLresultsoftheexpertelicitation.The conditionalprobabilityvs.breaksizemodelthatwasoriginallydevelopedtobenchmarktheLydellbase caseresultsisthenadjustedsothattherevisedLOCAfrequencyvs.breaksizemodelapproximatesthe targets.TheapplicationofthisapproachtotheHPIinjectionlinesisshowninFigure26andFigure27.
TheformerfigureshowshowtheresultsoftheexpertelicitationinAppendixLcomparetotheLydell basecaseresultsandhowtheAppendixLresultsforLOCACategories1and3areusedtoconstructthe targetdistributionsforthiscomponent.Thelatterfigureshowshowthetargetvalueswereusedto benchmarktheconditionalprobabilitymodelsforthiscomponent.
Morerecently,NRChasmadeavailablemoredetailedinformationontheexpertestimatesofLOCA frequenciesforindividualcomponentsthatcoversmoreLOCAsizesthancoveredintheplotsinNUREG 1829AppendixL.Atotalof9expertsoutthetotal12panelistsprovidedinformationatthislevel.Using thisinformation,ananalysiswasperformedinwhicheachexpertsinputwastreatedasalognormal distributionandaposteriorweightingprocedurewasappliedtosynthesizethe9expertinputsintoa compositeuncertaintydistributiongivingeachexpertequalweight.The95%tileand5%tilesfromthis
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compositedistributionwerethenusedinlieuofthevaluesreadofftheboxandwhiskerplotsin AppendixLofNUREG1829,andthisprovidedamorecomplete,moreaccurate,andappropriately probabilisticallyweightedcharacterizationoftheNUREG1829inputtoselectionoftargetLOCA frequencies.Thisistheapproachthatisadoptedfortheremainingstepsoftheanalysisforall components.
Figure26DefinitionofTargetBoundsforHPIInjectionLineLOCAFrequencies Thiscasewasrathersimplebecausetheexpertinputforthiscomponentagreeswellwiththeresultsof theLydellbenchmark,andAppendixLincludesresultsforonlytwoLOCAcategories,whichmakesit easytodefinealineonaloglogplot.Thisfigureshowsthatconditionalruptureprobabilitiesthatmeet thetargetsinFigure25,whencombinedwiththeLydellHPIleakfrequencies,willencompassthe resultsoftheexpertelicitation.Inthenextupdate,theHPImodelwillbecalibratedusingtheexperts compositedistributionapproachdescribedaboveinlieuofAppendixLinformation.
TheapplicationoftheexpertscompositedistributionproceduretotheRCSsurgelineisshownin Figures28and29.Figure28comparestheelicitationresultsintheformofthe95%tileand5%tileof theexpertscompositedistributionforthiscomponentwiththeLydellbasecaseresultsandalso presentstheproposedtargetsfortheconditionalruptureprobabilitymodel.
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Figure27CalibrationofConditionalProbabilityModeltoMatchTargetsforHPIInjectionLine AlsoshowninFigure28arethe95%tileand5%tileofthesurgelinefailureratedistributionwhichwas usedintheLydellBaseCaseresults.Inthiscase,thereahugevariabilityintheelicitationresultsforthe surgeline,afullsixordersofmagnitudebetweenthemaximumandminimumforLOCAcategories1 and3,andsevenordersforCategory5.Thetargetsforthe5thpercentileforthiscomponentarebased onthelowerboundresultsfromtheelicitation,causingastraightlineontheloglogplotonFigure28.
Whenselectingthe95thpercentileforthiscomponent,itwasnotedexpertscompositeestimatesare unreasonablyhigh,astheyproduce,whencombinedwiththeLydellestimatesoftheunderlying componentfailurerates,conditionalruptureprobabilitiesgreaterthanone.Inotherwords,theexperts attheextremehighendproducehigherestimatesofLOCAfrequencies,whichhaveneveroccurred, thanestimatesoftheunderlyingfailureratesprovidedintheLydellbasecaseresults,whicharewell supportedbyserviceexperiencedata.Thedataquerypresentedpreviouslyincludes166pipefailures experiencedovernearly4,000reactoryearsofservicedatawithnoleaksexceedingabout10gpm,much smallerthanthehighleakratesoftheseLOCAcategories.Thefailureratesincludeanyeventsinwhich repairorreplacementoftheweldwasrequired,yetnoneoftheexperiencedfailuresinvolvedsignificant leakageandcertainlynoLOCAsinCategories1,2,3,4,or5.Aswillbeshownbelow,thetarget95th percentileselectedforthesurgeline,whilesetsomewhatlowerthantheupperboundvaluesfromthe expertscompositedistribution,stillyieldsveryhighconditionalruptureprobabilities.
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Figure28DefinitionofTargetBoundsforRCSSurgeLineLOCAFrequencies TheapplicationofthisprocedurefortheRCShotlegisshowninFigures29and210.InFigure29,the targetsforthe95%tilesand5%tilesaresettocapturetherangeofresultsfromtheexpertelicitation whileassumingastraightlineonaloglogplotofLOCAfrequencyvs.breaksize.Theanchorpointfor LOCACategory1istakenas10%ofthe95%tileofthesurgelinefailureratedistributionoftheLydell BaseCaseanalysis.ThischaracterizationoftheupperboundtargetLOCAfrequenciesyields,aswillbe shownbelow,veryhighconditionalprobabilityofLOCAvalues.
TheanalysisfortheRCShotlegcomponentisshowninFigures210and211usingthegraphical procedureappliedabovetothehotleg.Thisanalysiswillbereplacedbytheexpertscomposite approachinthenextrevisiontothisreport.
Thenetresultofthisbenchmarkingwasthederivationoftheconditionalprobabilitymodelforthese selectedcomponents,whoseresultsareshowninTable211.Becauseoftheratherhighupperbound LOCAfrequenciesembodiedinthetargetsthatwerestronglyinfluencedbytheupperboundvalues fromtheexpertelicitation,andtheassumptionoflognormaldistributionsfortheconditionalrupture probabilityateachLOCAsize,thelognormaldistributionshadtobetruncatedat1.0,otherwisea significantpartoftheuppertailofthedistributionswouldexceed1.0,especiallyfortheRCSsurgeline andRCShotlegmodels.Asaresult,thepropertiesofthetruncateddistributions,suchasmedians,
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means,andpercentiles,aredifferentfromthoseoftheunderlyinglognormaldistributionspriorto truncation.
Acomparisonoftheconditionalprobabilitiesthatweredevelopedfortheseexamplesagainstthe conditionalprobabilitiesthatarelinkedtotheLydellbasecaseanalysisisshowninFigures211,212, and213fortheHPIinjectionline,RCSsurgeline,andRCShotleg,respectively.Asexpected,theseplots trackverycloselythepreviousplotsfortheLOCAfrequenciesvs.breaksizebecausebothsetsofplots usethesamefailureratemodel.However,thisverifiesthattheresultsareinternallyconsistent.
Figure29CalibrationofConditionalProbabilityModeltoMatchTargetsforRCSSurgeLine
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Figure210DefinitionofTargetBoundsforRCSHotLegLOCAFrequencies
Figure211CalibrationofConditionalProbabilityModeltoMatchTargetsforRCSHotLeg
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Table211STPConditionalProbabilityModelsDerivedfromTargetLOCAFrequencies Component LOCA Category Break Size(in.)
DistributionInputParameters TruncatedDistributionParameters Type Median
[Note(1)]
Range Factor Median Mean 5th Percentile 95th Percentile
RCSHot Leg 1
.5 Lognormal truncated at1.0 1.39E04 7.40E+01 1.40E04 3.35E03 1.90E06 1.01E02 2
1.5 2.49E05 1.20E+02 2.48E05 1.29E03 2.05E07 2.99E03 3
3 8.65E06 1.63E+02 8.60E06 7.99E04 5.30E08 1.45E03 4
6.76 2.43E06 2.38E+02 2.43E06 4.32E04 1.06E08 5.73E04 5
14 8.10E07 3.23E+02 7.90E07 2.86E04 2.46E09 2.62E04 6
31.5 2.20E07 4.56E+02 2.19E07 1.46E04 4.97E10 9.92E05
RCSSurge Line 1
.5 3.33E02 5.60E+01 2.59E02 1.05E01 5.38E04 5.36E01 2
1.5 4.12E03 5.48E+01 3.97E03 3.46E02 7.41E05 1.76E01 3
3 1.36E03 6.80E+01 1.34E03 1.85E02 1.99E05 8.24E02 4
6.76 3.90E04 8.96E+01 3.88E04 9.09E03 4.34E06 3.32E02 5
14 1.30E04 1.19E+02 1.34E04 5.16E03 1.12E06 1.55E02
HPILine 1
.5 5.85E03 1.52E+01 5.78E03 2.15E02 3.77E04 8.88E02 2
1.5 1.20E03 1.91E+01 1.18E03 5.87E03 6.34E05 2.30E02 3
3 4.56E04 2.21E+01 4.59E04 2.61E03 2.07E05 1.01E02 Note(1)ThesearemedianstospecifytheinputdistributiontoCrystalBall'priortotruncation;themedianofthetruncateddistributionis generallydifferentfollowingtruncation.
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Figure212ComparisonofConditionalProbabilityModelsforHPIInjectionline
Figure213ComparisonofConditionalProbabilityModelsforRCSSurgeLine
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Figure214ComparisonofConditionalProbabilityModelsforRCSHotLeg
2.6.4. Bayes Update of the Conditional Probability Distributions Theconditionalprobabilitymodeldevelopedintheprevioussectionisusedasthebasisforaprior distributionwhichwethenupdatewiththeevidencefromtheservicedatawhichisnolossofcoolant accidentsoutof3surgelineweldfailures.Weareinvestigatingwhethertoconsiderpoolingthedata overalargerdatasetforthispurpose,butforthetimebeingwetaketheconservativeapproachof limitingourselvesintheBayesupdatetotheSurgelineweldexperience.Inthenextupdatetothis reportwewillconsiderpoolingthedataforsimilarcomponentsforthepurposeofcharacterizingthe evidencefortheseconditionalruptureprobabilities.Thetruncatedlognormaldistributionsdescribedin Table211wereusedaspriordistributionsandthenupdatedwith0Category1,2,3,4,or5LOCAsout of3observedfailures.TheresultsaresummarizedinTable212.Itisnotedthateventhoughthe evidenceisratherweak,the95%tilesoftheposteriordistributionsaresignificantlyreduced.Thisinturn influencesthemeansofthedistributionstoasignificantdegree.Hencethisprocedurewasimportantto apply.
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Table212ResultsofBayesUpdateofConditionalLOCAProbabilities LOCA Category Break Size(in.)
Distribution Type(1)
DistributionParameters(2)
Mean 5%tile 50%tile 95%tile Range Factor(3) 1 0.5 Prior TruncatedLognormal 1.05E01 5.38E04 2.59E02 5.36E01 53.6 Posterior LognormalBinomial 4.43E02 4.11E04 1.45E02 1.95E01 21.8 2
1.5 Prior TruncatedLognormal 3.46E02 7.41E05 3.97E03 1.76E01 48.8 Posterior LognormalBinomial 1.75E02 6.75E05 3.17E03 8.45E02 35.4 3
3 Prior TruncatedLognormal 1.85E02 1.99E05 1.34E03 8.24E02 64.3 Posterior LognormalBinomial 1.00E02 1.88E05 1.17E03 4.79E02 50.5 4
6.76 Prior TruncatedLognormal 9.09E03 4.34E06 3.88E04 3.32E02 87.5 Posterior LognormalBinomial 5.27E03 4.22E06 3.60E04 2.33E02 74.3 5
14 Prior TruncatedLognormal 5.16E03 1.12E06 1.34E04 1.55E02 117 Posterior LognormalBinomial 3.10E03 1.11E06 1.28E04 1.21E02 105 Notes (1) Priorlognormaldistributionstruncatedat1.0.
(2) ValuesformeansandpercentilesrepresentconditionalprobabilityofLOCAcategorygivenpipefailure.
(3) RangeFactor=SQRT(95%tile/5%tile)
2.7. LOCA Frequencies Associated with Surge Line Welds 2.7.1. Base Case Results TheapplicationofthismethodologytoSTPisaworkinprogress.Thissectionillustratestheapproachby developingasetofbasecaseresultsaswellassomesensitivitycasesbasedonsomeassumptionsabout STPinputs.
TheunconditionalfrequenciesofLOCAsasafunctionofbreaksizewereobtainedbyMonteCarlo uncertaintypropagationofthefailureratedistributionsandtheconditionalprobabilityofbreaksize distributionsusingtheresultsoftheprevioussectionsandEquation(2).Theresultsforeachweldand forthetotalsurgelineLOCAfrequencyareshowninTable213.Theseresultsarebasedontheinput datathatwereassumed,whichincludetheassumptionsregardingsusceptibilitytodamage mechanisms.TheresultsforBFwelds,forexample,areheavilyinfluencedbytheinherentsensitivityto PWSCC.Ifthisdamagemechanismismitigated,forexample,byapplicationofweldoverlays,these weldswouldentaillessfrequentfailureandfewerdesignandconstructiondefects.TheSTPBFwelds haveinfactbeenrepairedusingweldoverlays.TheseresultsalsodonotreflecttheresultsoftheSTPRI ISIevaluation,whichincludedaweldbyweldevaluationofdamagemechanisms.ThesusceptibilityofB Jweldstothermalfatigueisassessedinthebasecaseresultsbasedongenericdata.Ifthermalfatigue andanyotherdamagemechanismstotheBJweldswereruledout,thefailureratesofthesewelds wouldbedeterminedsolelybydesignandconstructiondefects.Asasensitivitycase,thetotalLOCA frequencieswerereevaluatedtoreflectPWSCCmitigationbyweldoverlayandanassumptionthatno BJweldsaresusceptibletothermalfatigue.AcomparisonofthemeansurgelineLOCAfrequenciesfor thebasecaseandthissensitivitycaseareshowninFigure215,whichshowstheinfluenceofdamage
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mechanismsensitivityassumptions.Inthesubmittal,anSTPspecificevaluationofdamagemechanisms willbeincorporatedintotheseresults.
Figure215ComparisonofSurgeLineLOCAFrequencieswithDifferentDamageMechanismInputs 2.7.2. Influence of NDE Inspections on LocationSpecific LOCA Frequencies Alltheresultspresenteduptothispointhaveincludedtheeffectsofpipinginspectionsandintegrity managementprogramsonlyimplicitly,inthatthefailureratedataandinputstotheexpertelicitationof NUREG1829thatformthebasisforourconditionalprobabilityoftheLOCAmodelhavebeenbasedon averagenuclearpowerplantservicedata.Theseaverages,benefitedfromreliabilityintegrity managementprogramsincludingtestingandmonitoringforleaksaswellasnondestructive examinationsthatareperformedinthevariousISIprogramsonanaveragebasis.Inderivinglocation specificLOCAfrequenciesforSTP,theactualstatusofeachweldasbeingeitherincludedorexcluded fromtheNDEprogramwillbetakenintoaccountusingtheMarkovmodeldevelopedforthispurposein theEPRIRIISIprogram.Thedetailsofthisapplicationwillbedocumentedinthesubmittal.Anexample ofthekindofchangesinLOCAfrequenciesthatcanresultfromlocationbylocationchangesinthepipe inspectionandleakmonitoringprogramisshowninFigure216foranRCSweldsubjecttostress corrosioncracking[13].Asseeninthisfigure,thefrequencyofapipebreakmaychangebymorethan anorderofmagnitude,duetochangesinthereliabilityintegritymanagementprogram,allotherfactors beingequal.
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Table213UnconditionalLOCAFrequenciesforSurgeLineWelds WeldType Parameter DistributionParameters RF(2)
Mean 5%tile 50%tile 95%tile BF FailureRate 5.61E04 1.37E04 4.38E04 1.40E03 3.2 Category1 2.13E05 1.44E07 3.81E06 9.35E05 25.5 Category2 1.03E05 2.44E08 1.01E06 4.26E05 41.7 Category3 6.71E06 6.94E09 4.10E07 2.38E05 58.6 Category4 3.67E06 1.55E09 1.36E07 1.16E05 86.6 Category5 2.22E06 4.27E10 5.05E08 5.95E06 118.0 Branch Connection FailureRate 4.16E06 9.75E09 2.91E07 1.17E05 34.7 Category1 1.43E07 2.65E11 2.58E09 2.87E07 104.1 Category2 8.14E08 5.02E12 6.87E10 1.12E07 149.3 Category3 4.35E08 1.51E12 2.81E10 5.73E08 194.9 Category4 2.87E08 3.68E13 9.32E11 2.55E08 263.1 Category5 1.45E08 1.06E13 3.45E11 1.23E08 339.4 BJ FailureRate 2.03E07 2.66E11 2.86E09 3.74E07 118.6 Category1 4.38E08 1.12E12 2.68E10 6.33E08 238.3 Category2 2.13E08 2.34E13 7.40E11 2.38E08 319.0 Category3 1.49E08 7.21E14 2.98E11 1.15E08 398.5 Category4 8.68E09 1.85E14 9.77E12 4.92E09 515.9 Category5 2.07E09 1.26E13 2.23E11 3.84E09 175.0 BaseCase TotalSurge Line(1)
FailureRate 5.71E04 1.37E04 4.39E04 1.42E03 3.2 Category1 2.19E05 1.44E07 3.81E06 9.45E05 25.6 Category2 1.06E05 2.45E08 1.02E06 4.29E05 41.9 Category3 6.90E06 6.94E09 4.11E07 2.40E05 58.8 Category4 3.79E06 1.55E09 1.36E07 1.17E05 86.9 Category5 2.26E06 4.28E10 5.07E08 6.00E06 118.4 CasewithBF weldoverlay andnoTF Susceptibility forBJwelds FailureRate 1.50E05 2.37E08 9.77E07 5.13E05 46.5 Category1 4.39E07 5.35E11 5.45E09 7.25E07 116.4 Category2 3.04E07 1.01E11 1.46E09 3.02E07 172.9 Category3 1.90E07 3.04E12 6.01E10 1.68E07 235.3 Category4 1.46E07 7.41E13 2.02E10 8.45E08 337.8 Category5 8.73E08 2.17E13 8.12E11 5.29E08 493.6 Notes (1) Totalsurgelineresultsarebasedon1BFweld,2BCwelds,and6.9BJwelds.
(2) RF=SQRT(95%tile/5%tile)
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Figure216ComparisonofWeldFailureRatesDeterminedbyMarkovModelforDifferentReliability IntegrityManagementApproaches
2.8. LOCA Frequency Summary ThetechnicalapproachtoestimationofLOCAfrequenciesfortheSTPGSI191projecthasbeen describedinthissection,withsomepreliminaryresultsforeachstep.Threecategoriesofweldsinthe pressurizersurgelinehavebeenselectedtoillustratemostofthestepsoftheapproach.Whenallthe componentsintheSTPClass1pressureboundaryarecompleted,theresultswillbecombinedto determinetheLOCAinitiatingeventfrequenciesforthePRAmodel,andthelocationspecificresultswill beprovidedtotheCasaGrandemodeltodeterminethephenomenologicalimpactsassociatedwith debrisformation.Thespecificcapabilitiesthathavebeendemonstratedinclude:
ThecapabilitytoestimateLOCAfrequenciesasafunctionofbreaksizeateachlocation.
ThecapabilitytoutilizeinformationfromNUREG1829tocharacterizeepistemicuncertainty associatedwithLOCAfrequencies.
AmethodthatincorporatesviaBayesuncertaintyanalysistheservicedataonpipefailuresand componentexposures.
Afullquantificationofepistemicuncertaintiesassociatedwithestimatingtheinputparameters inthemodelequations.
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Thecapabilitytoquantifytheimpactsofinformationondegradationmechanismsusceptibility ateachlocation,basedoninsightsfromservicedataandresultsofRIISIevaluation.
Thecapabilitytoadjusttheresultstoaccountforlocationbylocationdifferencesinthe reliabilityinspectionprogramforleakmonitoringandNDE.
Thesubmittalwillincludeamorecompleteapplicationofthismethodologyaswellasfurther justificationforsupportingassumptionsandinputdata.
Asnotedearlier,thequantitativeinformationpresentedisbasedonaworkinprogressandissubjectto changeastheprojectunfolds.Allresultsarepreliminaryandarepresentedprimarilytodescribehow theanalyseswillbeperformed.
- 3. References
[1] Tregoning,R.,L.Abramson,andP.Scott,EstimatingLossofCoolantAccident(LOCA)
FrequenciesThroughtheElicitationProcess,NUREG1829,U.S.NuclearRegulatoryCommission, Washington,DC,April2008.
[2] Lydell,B.O.Y.,PIPExp/PIPE2010:MonthlySummaryofDatabaseContent(Statusasof31Mar 2010),RSATechnologies,Fallbrook,CA.Monthlysummaryreportshavebeenissuedsince January1999.
[3] Fleming,K.N.andB.O.Y.Lydell,DatabaseDevelopmentandUncertaintyTreatmentfor EstimatingPipeFailureRatesandRuptureFrequencies,ReliabilityEngineeringandSystem Safety,86:227-246,2004.
[4] PipeRuptureFrequenciesforInternalFloodingPRAs,Revision1.EPRI,PaloAlto,CA:2006.
1013141.
[5] PipeRuptureFrequenciesforInternalFloodingPRAs,Revision2.EPRI,PaloAlto,CA:2010.
1021086.
[6] PipingSystemReliabilityandFailureRateEstimationModelsforUseinRiskInformedInService InspectionApplications.EPRI,PaloAlto,CA:1998.TR110161.
[7] PipingSystemFailureRatesandRuptureFrequenciesforUseinRiskInformedInService InspectionApplications.EPRI,PaloAlto,CA:1999.TR111880.
[8] Mosleh,A.andF.Groen,TechnicalReviewoftheMethodologyofEPRITR110161,University ofMarylandreportforEPRI,publishedasanAppendixtoEPRITR110161(Reference[6]).
[9] RevisedRiskInformedInServiceInspectionProcedure.EPRI,PaloAlto,CA:1999.TR112657, Rev.BA.
[10] U.S.NuclearRegulatoryCommission,SafetyEvaluationReportRelatedtoRevisedRiskInformed InServiceInspectionEvaluationProcedure:EPRITR112657,Rev.B,July1999,Washington,DC, 1999.PublishedasaforwardtoTR112657(Reference[9]).
[11] Martz,H.,Final(Revised)ReviewoftheEPRIProposedMarkovModeling/BayesianUpdating MethodologyforUseinRiskInformedInServiceInspectionofPipinginCommercialNuclear PowerPlants,LosAlamosNationalLaboratory,June1999.TSA1/99164.
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[12] Fleming,K.N.,MarkovModelsforEvaluatingRiskInformedInServiceInspectionStrategiesfor NuclearPowerPlantPipingSystems,ReliabilityEngineeringandSystemSafety,83(1):27-45, 2004.
[13] Fleming,K.N.etal.,TreatmentofPassiveComponentReliabilityinRiskInformedSafety MarginCharacterization-FiscalYear2010StatusReport,reportpreparedbyPacificNorthwest NationalLaboratoryfortheU.S.DepartmentofEnergy,September2010.
[14] U.S.NuclearRegulatoryCommission,SupportinginformationforNUREG1829(Reference[1])
onIndividualExpertsEstimatesofLOCAfrequenciesforspecificcomponentsandLOCA Categories,availableonADAMSAccessionNumbersML080560008,ML080560010, ML080560011,ML080560013