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{{#Wiki_filter:LOCA Initiating Event Frequencies and Uncertainties (Draft)Risk Informed GSI-191 Resolution | {{#Wiki_filter:LOCA Initiating Event Frequencies and Uncertainties (Draft) | ||
Risk Informed GSI-191 Resolution Th d Thursday, July J l 7, 7 2011 1:00 pm - 2:00 p.m EDT Public Meeting with STP Nuclear Operating Company Karl N. Fleming KNF Consulting Services LLC Bengt O. Y. Lydell 7/5/11 Pre-Licensing Meeting 1 | |||
Risk Informed GSI-191 Discussion Topics | |||
*Resolution of NRC questions from June 2011 meeting | * LOCA frequencies scope and objectives | ||
* Technical approach | |||
* Step by step procedure with examples | |||
* Technical issues to be addressed | |||
* Resolution of NRC questions from June 2011 meeting 7/5/11 Pre-Licensing Meeting 2 | |||
Risk Informed GSI-191 LOCA Frequencies Objectives | |||
* Incorporate insights from previous work on LOCA frequencies | |||
* Characterize LOCA initiating events and there frequencies with respect to: | |||
- Specific components, materials, dimensions | |||
- Specific locations | |||
- Range of break sizes | |||
- Degradation mechanisms and mitigation effectiveness | |||
- Other break characteristics, characteristics ee.g. | |||
g speed | |||
* Quantify both aleatory and epistemic uncertainties; augment with sensitivity studies | |||
* Support interfaces with other parts of the GSI-191 evaluation | |||
- LOCA initiating event frequencies for PRA modeling | |||
- Break characterization for evaluation of debris formation | |||
* Participate in NRC workshops 3 7/5/11 Pre-Licensing Meeting | |||
LOCA | LOCA Frequency Technical Approach | ||
* Utilize passive component reliability methods and data from RI-ISI technology | |||
* Utilize PIPExp database to help resolve uncertainties in failure rates | |||
* Utilize information from NUREG-1829 and NUREG/CR-5750 in optimum manner | |||
* Consider probabilistic fracture mechanics evaluation on selected locations as may be required 4 7/5/11 Pre-Licensing Meeting | |||
LOCA IE Frequency Model 1 of 2 F ( LOCAx ) = mi ix (1) i jx = ix = ik P( Rx Fik ) I ik (2) k Where: | |||
F ( LOCAx ) = Frequency of LOCA of size x, per reactor calendar-year; subject to epistemic uncertainty calculated via Monte Carlo mi = Number of pipe welds of type i; each type determined by pipe size, weld type, applicable damage mechanisms, and inspection status (leak test and NDE); no uncertainty for STP ix = Frequency of rupture of pipe location j belonging to component type i with break size x, subject to epistemic uncertainty calculated via Monte Carlo and uncertainties on the RHS of Equation (2) ik = Failure rate per weld-year for pipe component type i due to failure mechanism k; subject to epistemic uncertainty determined by RI-ISI Bayes method and Eq. (3) | |||
P( Rx Fik ) = Conditional probability of rupture of size x given failure of pipe component type i due to damage mechanism k; subject to epistemic uncertainty determined via expert elicitation (NUREG-1829) | |||
I ik = Integrity management factor for weld type i and failure mechanism k; calculated via Markov Model; subject to epistemic uncertainty determined by Monte Carlo propagation of input parameters using Markov model equations and input parameter uncertainties. | |||
5 7/5/11 Pre-Licensing Meeting | |||
LOCA IE Frequency Model 2 of 2 For a Point Estimate of the Failure Rate for type i and failure mechanism k: | |||
nik nik ik = = (3) ik f ik N iTi nik = Number of failures in pipe component (i.e. weld) type i due to failure mechanism k, very little epistemic uncertainty ik = Component exposure population for welds of type i susceptible to failure mechanism k, subject to epistemic uncertainty determined by expert opinion f ik = Estimate of the fraction of the component exposure population for weld type i that is susceptible to failure mechanism k, subject to epistemic uncertainty; estimated from results of RI-ISI for population of plants and expert opinion. | |||
Ni = Estimate of the average number of pipe welds of type i per reactor in the applicable reactor years exposure for the data collection; subject to plant to plant variability and epistemic uncertainty; estimated from results of RI-ISI for sample population of plants and expert opinion Ti = Total number of reactor years exposure for the data collection for component type i; little or no uncertainty 6 7/5/11 Pre-Licensing Meeting | |||
Step by Step Procedure | |||
: 1. Determination of weld types (i) | |||
: 2. Perform data query for failure counts (n) | |||
: 3. Estimate component exposure (T) and uncertainty | |||
: 4. Develop component failure rate prior distributions for each DM | |||
: 5. Perform Bayes update for each exposure case (combination of weld count and DM susceptibility) | |||
: 6. Apply posterior weighting to combine results for different hypothesis yield conditional failure rate distributions; compute unconditional failure rates for locations with uncertain DM status | |||
: 7. Develop conditional probability of rupture size given failure probabilities for each weld type and associated epistemic uncertainties | |||
: 8. Combine the results of Step 6 and Step 7 by Monte Carlo in Eq. (1) for component LOCA frequencies and total LOCA frequencies for each component | |||
: 9. Apply Markov Model to specialize rupture frequencies for differences in integrity management | |||
: 10. For intermediate LOCA categories and break sizes, interpolate the results of Step 10 via log-log linear interpolation | |||
: 11. Calculate total LOCA frequencies from all components and reconcile differences with earlier LOCA frequency estimates 7/5/11 Pre-Licensing Meeting 7 | |||
Steps 1 and 2 Failure Data Query | |||
* Data query limited to Westinghouse and Framatome PWRs similar to STP | |||
* Failure defined as any event that involved repair or replacement of damaged component | |||
* Data query covers operating experience from 1970 through 2010 | |||
* Supports Steps 1 (define weld types) and 2 (failure counts) 7/5/11 Pre-Licensing Meeting 8 | |||
* | |||
* | |||
Preliminary Results of Data Query Pipe Failures by Mode (1), (2), (3) | |||
Nominal SYSTEM Pipe Size (NPS) Crack- Crack- Small Large Total Leak Full Part Leak Leak 1" 7 1 6 CVC 2" ø 4" 7 1 6 1" 2 2 Safety Injection 4" ø 10" 6 3 1 1 1 Pressurizer-Sample 2" 5 4 1 Pressurizer-PORV 4" ø 10" 2 2 1" 4 1 2 1 Pressurizer-SPRAY 4" ø 10" 3 2 1 Pressurizer-SRV 4" ø 10" 7 6 1 Example chosen Pressurizer-Surge 14" 3 3 to illustrate FR RCS 2" 76 4 10 53 4 5 RCS Cold Leg 32" 4 4 Approach RCS Hot Leg 32" 6 5 1 RHR 1" 6 6 RHR 4" ø 10" 1 1 RC Hot Leg - S/G- 19 19 32" Inlet S/G-System 2" 8 2 2 4 TOTALS 166 12 59 83 6 6 Notes (1) Query accounts for 3914 reactor years based on date of initial criticality from 1970-2010. | |||
(2) Failure is defined as any event that required repair or replacement of damaged component. | |||
(3) Small leaks have leak flows << 1gpm; Leaks < 1gpm; Large Leaks < 10gpm. | |||
7/5/11 Pre-Licensing Meeting 9 | |||
Step by Step Procedure | |||
: 1. Determination of weld types (i) | |||
: 2. Perform data query for failure counts (n) | |||
: 3. Estimate component exposure (T) and uncertainty | |||
: 4. Develop component failure rate prior distributions for each DM | |||
: 5. Perform Bayes update for each exposure case (combination of weld count and DM susceptibility) | |||
: 6. Apply posterior weighting to combine results for different hypothesis yield conditional failure rate distributions; compute unconditional failure rates for locations with uncertain DM status | |||
: 7. Develop conditional probability of rupture size given failure probabilities for each weld type and associated epistemic uncertainties | |||
: 8. Combine the results of Step 6 and Step 7 by Monte Carlo in Eq. (1) for component LOCA frequencies and total LOCA frequencies for each component | |||
: 9. Apply Markov Model to specialize rupture frequencies for differences in integrity management | |||
: 10. For intermediate LOCA categories and break sizes, interpolate the results of Step 10 via log-log linear interpolation | |||
: 11. Calculate total LOCA frequencies from all components and reconcile differences with earlier LOCA frequency estimates 7/5/11 Pre-Licensing Meeting 10 | |||
Step 3 Component Exposure | |||
* Need Reactor-years of service experience in failure data query | |||
* Need estimates of component populations per plant | |||
* Need fractions of the component population susceptible to each damage mechanism (DM) for conditional failure rates given knowledge of applicable damage mechanisms 7/5/11 Pre-Licensing Meeting 11 | |||
Reactor Years in Data Query Reactor-Calendar Years WE Type Rx Initial Grid Initial Criticality Connection 2-Loop 570.1 581.4 3-Loop 2052.6 2096.1 4-Loop 1193.9 1236.5 3816.6 3914 Total 7/5/11 Pre-Licensing Meeting 12 | |||
Data for Estimating Surge Line Weld Population Weld Population[Note (1)] | |||
PWR Branch Connection to Plant B-F Welds Inline B-J Welds Type Hot Leg Braidwood-1 4-Loop 1 8 2 Braidwood-2 4-Loop 1 7 2 Byron-1 4-Loop 1 6 2 Byron-2 4-Loop 1 6 2 Kewaunee 2-Loop 1 6 2 Koeberg-1 3-Loop 1 5 2 Koeberg-2 3-Loop 1 5 2 STP-1 4-Loop 1 8 2 STP-2 4-Loop 1 8 2 V.C. Summer 3-Loop 1 10 2 Note (1) Kewaunee surge line is NPS10, Remaining plants are NPS 14 to 16 7/5/11 Pre-Licensing Meeting 13 | |||
Damage Mechanism Characterization | |||
* EPRI developed screening criteria to evaluated susceptibility of piping to known damage mechanisms to support RI-ISI | |||
* Criteria applied in STP RI-ISI application to all welds on Class 1 and 2 pressure boundary | |||
* PIPExp data base also identifies generic susceptibilities to some damage and failure mechanisms | |||
- Bi-metallic welds with Ni-based allows susceptible to PWSCC | |||
- All welds especially field welds subject to design and construction defects | |||
* If we know that a specific weld location is susceptible to a given damage mechanism (s) we can specialize the failure rates to that knowledge, i.e. conditional failure rates | |||
* If we do not know the specific susceptibility to DMs we apply unconditional failure rates 7/5/11 Pre-Licensing Meeting 14 | |||
Example Surge Line Damage Mechanism Characterization Confidence Weld Susceptibility Fractions Location Level C-F D&C ECSCC Fretting IGSCC PWSCC TF TGSCC TAE V-F Low N/A 1 N/A N/A N/A 1 N/A N/A N/A N/A B-F 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 Low N/A 1 N/A N/A N/A N/A 0.01 N/A N/A N/A B-J 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 RC-HL Branch Low N/A 1 N/A N/A N/A N/A 1 N/A N/A N/A C | |||
Connection ti 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 ID Description C-F Corrosion-Fatigue D&C Design & Construction Flaws ECSCC External Chloride-induced SCC IGSCC Intergranular SCC LC-FAT Low-Cycle Fatigue PWSCC Primary Water SCC OVLD Overload TF Thermal Fatigue TGSCC Transgranular SCC TAE Thermal Aging Embrittlement V-F Vibration Fatigue 7/5/11 Pre-Licensing Meeting 15 | |||
Example DM evaluation for Surge Line Welds | |||
* All B-F welds at the pressurizer nozzle are susceptible to PWSCC - no uncertainty for this DM | |||
* All branch connection welds are susceptible to TF - no uncertainty for this DM | |||
* Some unknown fraction of B-J welds susceptible to TF - uncertainty in the fraction susceptible for this DM | |||
* For STP we have a deterministic evaluation of DM Susceptibility for each location 7/5/11 Pre-Licensing Meeting 16 | |||
Example Exposure Uncertainty Model for Surge Line Welds | |||
* BF Welds (at pressurizer nozzle) | |||
- No DM Uncertainty or Weld count Uncertainty | |||
- Only need one Bayes update for one case of exposure | |||
* BC Welds | |||
- No DM uncertainty | |||
- Some S plant l t tto plant l t variability i bilit iin numberb off bbranch h connections ti | |||
- Need three updates for weld count uncertainty one for each of high, medium, and low estimates for weld counts | |||
* BJ Welds | |||
- DM Uncertainty | |||
- Weld Count Uncertainty | |||
- Need Bayes update of priors for each combination of weld count and DM susceptibility Cases ( 3 X 3 = 9) 7/5/11 Pre-Licensing Meeting 17 | |||
Treatment of Exposure Uncertainty for B-J Welds and Thermal Fatigue Welds/Rx 6.9 Rx-yrs 3914 Base Exposure 27006.6 Fraction of B-J Welds Exposure Weld Count Exposure Susceptible to Thermal Case Exposure Uncertainty Multiplier Fatigue Probability 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) 7/5/11 Pre-Licensing Meeting 18 | |||
- | |||
Step by Step Procedure | |||
: 1. Determination of weld types (i) | |||
: 2. Perform data query for failure counts (n) | |||
: 3. Estimate component exposure (T) and uncertainty | |||
: 4. Develop component failure rate prior distributions for each DM | |||
: 5. Perform Bayes update for each exposure case (combination of weld count and DM susceptibility) | |||
: 6. Apply posterior weighting to combine results for different hypothesis yield conditional failure rate distributions; compute unconditional failure rates for locations with uncertain DM status | |||
: 7. Develop conditional probability of rupture size given failure probabilities for each weld type and associated epistemic uncertainties | |||
: 8. Combine the results of Step 6 and Step 7 by Monte Carlo in Eq. (1) for component LOCA frequencies and total LOCA frequencies for each component | |||
: 9. Apply Markov Model to specialize rupture frequencies for differences in integrity management | |||
: 10. For intermediate LOCA categories and break sizes, interpolate the results of Step 10 via log-log linear interpolation | |||
: 11. Calculate total LOCA frequencies from all components and reconcile differences with earlier LOCA frequency estimates 7/5/11 Pre-Licensing Meeting 19 | |||
Step 4 Prior Distributions | |||
* Initially developed in EPRI RI-ISI Program (EPRI TR-111880) | |||
* Based on Wash-1400 era state of knowledge on LOCA frequencies with estimates for SLOCA ranging from 10-2 to 10-6 per year and allocation down to welds based on weld count estimates in EPRI TR-111880 | |||
* Lognormal distributions with large range factors (100) | |||
* Means adjusted based on gross estimates from service data | |||
* Justification for STP priors will be provided if different from EPRI TR-111880 | |||
* Priors updated with results of data queries and exposure estimates to determine failure rates 7/5/11 Pre-Licensing Meeting 20 | |||
technical | Example Prior Distributions Prior Distribution (Failures per Weld-Year) | ||
*CRP method combined with failure rate | Damage Mechanism Range Dist. Type Mean Median Factor Stress Corrosion Cracking Lognormal 4.27E-05 8.48E-07 100 Design and Construction Lognormal 2.75E-06 5.46E-08 100 Thermal Fatigue Lognormal 1.34E-05 2.66E-07 100 7/5/11 Pre-Licensing Meeting 21 | ||
Step by Step Procedure | |||
: 1. Determination of weld types (i) | |||
: 2. Perform data query for failure counts (n) | |||
: 3. Estimate component exposure (T) and uncertainty | |||
: 4. Develop component failure rate prior distributions for each DM | |||
: 5. Perform Bayes update for each exposure case (combination of weld count and DM susceptibility) | |||
: 6. Apply posterior weighting to combine results for different hypothesis yield conditional f il failure rate t di distributions; t ib ti compute t unconditional diti l ffailure il rates t ffor llocations ti with ith uncertain t i DM status | |||
: 7. Develop conditional probability of rupture size given failure probabilities for each weld type and associated epistemic uncertainties | |||
: 8. Combine the results of Step 6 and Step 7 by Monte Carlo in Eq. (1) for component LOCA frequencies and total LOCA frequencies for each component | |||
: 9. Apply Markov Model to specialize rupture frequencies for differences in integrity management | |||
: 10. For intermediate LOCA categories and break sizes, interpolate the results of Step 10 via log-log linear interpolation | |||
: 11. Calculate total LOCA frequencies from all components and reconcile differences with earlier LOCA frequency estimates 7/5/11 Pre-Licensing Meeting 22 | |||
Step 5 Bayes Updates | |||
* Need library of failure rates for each weld type and damage mechanism | |||
* This library was first developed in EPRI TR 111880 for the EPRI RI-ISI program; will be updated for STP to reflect operating experience through 2010 | |||
* For each failure rate we perform 1 Bayes Bayes update for each exposure hypothesis and then combine the results of those into one probabilistically weighted distribution | |||
* For each weld type and damage mechanism need | |||
- Unconditional failure rates for cases where DM status at a location is unknown | |||
- Conditional failure rates for cases where DM status is known | |||
* Perform using RDAT-Plus' software 7/5/11 Pre-Licensing Meeting 23 | |||
Step 5 Example Bayes Updates for Surge Line Welds Weld Type DM Prior Distribution[Note (1)] Evidence[Note (2)] Bayes Posterior Distribution[Note (1)] | |||
Weld and DM[Note Susceptibility (3)] | |||
Count Case Type Median RF Failures Exposure Mean 5th 50th 95th RF Case Surge BF SC Base Base Lognormal 8.48E-07 100 3 3914 5.62E-04 1.23E-04 4.83E-04 1.27E-03 3.2 Surge BF DC Base Base Lognormal 5.46E-08 100 0 3914 1.41E-06 5.41E-10 5.33E-08 4.77E-06 93.9 Surge BC TF Base Base Lognormal 2.66E-07 100 0 7828 3.25E-06 2.53E-09 2.34E-07 1.47E-05 76.1 Surge BC DC Base Base Lognormal 5.46E-08 100 0 7828 1.17E-06 5.37E-10 5.24E-08 4.37E-06 90.1 Surge BJ TF Low Low Lognormal 2.66E-07 100 0 135 9.75E-06 2.66E-09 2.65E-07 2.58E-05 98.5 Surge g BJ TF Low Medium Lognormal g 2.66E-07 100 0 675 7.17E-06 2.64E-09 2.61E-07 2.36E-05 94.6 Surge BJ TF Low High Lognormal 2.66E-07 100 0 3376 4.48E-06 2.59E-09 2.48E-07 1.85E-05 84.5 Surge BJ TF Medium Low Lognormal 2.66E-07 100 0 270 8.70E-06 2.65E-09 2.64E-07 2.51E-05 97.4 Surge BJ TF Medium Medium Lognormal 2.66E-07 100 0 1350 5.98E-06 2.62E-09 2.57E-07 2.18E-05 91.2 Surge BJ TF Medium High Lognormal 2.66E-07 100 0 6752 3.46E-06 2.54E-09 2.37E-07 1.54E-05 77.7 Surge BJ TF High Low Lognormal 2.66E-07 100 0 540 7.55E-06 2.64E-09 2.62E-07 2.41E-05 95.4 Surge BJ TF High Medium Lognormal 2.66E-07 100 0 2701 4.83E-06 2.60E-09 2.51E-07 1.94E-05 86.4 Surge BJ TF High High Lognormal 2.66E-07 100 0 13503 2.58E-06 2.47E-09 2.22E-07 1.21E-05 69.8 Surge BJ DC Low Base Lognormal 5.46E-08 100 0 13503 9.83E-07 5.33E-10 5.14E-08 3.96E-06 86.2 Surge BJ DC Medium Base Lognormal 5.46E-08 100 0 27007 7.66E-07 5.25E-10 4.94E-08 3.34E-06 79.8 Surge BJ DC High Base Lognormal 5.46E-08 100 0 54013 5.77E-07 5.12E-10 4.65E-08 2.67E-06 72.2 Notes (1) Failure rates in units of failures per weld-year (2) Exposure in units of weld-years (3) SC = stress corrosion cracking; TF = thermal fatigue; DC = design and construction defects; BF = B-F weld; BC = Branch connection weld; BJ = B-J weld 7/5/11 Pre-Licensing Meeting 24 | |||
Step by Step Procedure | |||
: 1. Determination of weld types (i) | |||
: 2. Perform data query for failure counts (n) | |||
: 3. Estimate component exposure (T) and uncertainty | |||
: 4. Develop component failure rate prior distributions for each DM | |||
: 5. Perform Bayes update for each exposure case (combination of weld count and DM susceptibility) | |||
: 6. Apply posterior weighting to combine results for different hypothesis yield conditional failure rate distributions; compute unconditional failure rates for locations with uncertain DM status | |||
: 7. Develop conditional probability of rupture size given failure probabilities for each weld type and associated epistemic uncertainties | |||
: 8. Combine the results of Step 6 and Step 7 by Monte Carlo in Eq. (1) for component LOCA frequencies and total LOCA frequencies for each component | |||
: 9. Apply Markov Model to specialize rupture frequencies for differences in integrity management | |||
: 10. For intermediate LOCA categories and break sizes, interpolate the results of Step 10 via log-log linear interpolation | |||
: 11. Calculate total LOCA frequencies from all components and reconcile differences with earlier LOCA frequency estimates 7/5/11 Pre-Licensing Meeting 25 | |||
Step 6 Posterior Weighting | |||
* Purpose is to develop a single uncertainty distribution for the failure rate that probabilistically weights each exposure hypothesis | |||
* Use a discrete probability distribution across the cases as developed in the previous event tree | |||
* Method established and applied in EPRI RI-ISI program | |||
* Method referred to as Bayes posterior weighting 7/5/11 Pre-Licensing Meeting 26 | |||
Failure Rate Options for Thermal Fatigue in B-J Welds | |||
* Case 1 FR for B-J Weld susceptible to TF | |||
- Sum of applicable contributions: TF+D&C | |||
- TF failure rate conditional on TF susceptibility ( f in Eq. (3) < 1) | |||
* Case 2 FR for B-J weld whose susceptibility to TF is unknown | |||
- Sum of applicable contributions: TF+D&C | |||
- TF failure f il rate t isi unconditional diti l ( f iin E Eq. (3) | |||
(3)= 1) | |||
* Case 3 FR for B-J weld not susceptible to TF | |||
- Includes only contributions from D&C Case No. Evaluation Case Mean 5%tile 50%tile 95%tile 1 B-J Total Conditional on TF 6.75E-06 9.60E-09 3.23E-07 1.55E-05 2 B-J Total Unconditional 2.62E-06 8.21E-09 2.23E-07 7.69E-06 3 B-J Total Conditional on no TF 7.66E-07 5.25E-10 4.94E-08 3.34E-06 7/5/11 Pre-Licensing Meeting 27 | |||
Impact of RI-ISI Damage Mechanism Evaluation on RCS Weld Failure Rates (2005 RI-ISI for Koeberg) 7/5/11 Pre-Licensing Meeting 28 | |||
Step by Step Procedure | |||
: 1. Determination of weld types (i) | |||
: 2. Perform data query for failure counts (n) | |||
: 3. Estimate component exposure (T) and uncertainty | |||
: 4. Develop component failure rate prior distributions for each DM | |||
: 5. Perform Bayes update for each exposure case (combination of weld count and DM susceptibility) | |||
: 6. Apply posterior weighting to combine results for different hypothesis yield conditional failure rate distributions; compute unconditional failure rates for locations with uncertain DM status | |||
: 7. Develop conditional probability of rupture size given failure probabilities for each weld type and associated epistemic uncertainties | |||
: 8. Combine the results of Step 6 and Step 7 by Monte Carlo in Eq. (1) for component LOCA frequencies and total LOCA frequencies for each component | |||
: 9. Apply Markov Model to specialize rupture frequencies for differences in integrity management | |||
: 10. For intermediate LOCA categories and break sizes, interpolate the results of Step 10 via log-log linear interpolation | |||
: 11. Calculate total LOCA frequencies from all components and reconcile differences with earlier LOCA frequency estimates 7/5/11 Pre-Licensing Meeting 29 | |||
Step 7 Conditional Probability of Pipe Rupture | |||
* Service experience includes 178 pipe failures and millions of weld-years of exposure, which is sufficient to support failure rate estimates | |||
* Model assumption that pipe failures are precursors to LOCAs such that LOCA frequencies are the product of failure rates and conditional LOCA probabilities | |||
* NUREG-1829 viewed as most relevant and up to date source of information on LOCA frequencies and uncertainty | |||
* Our approach for this step is to convert information in terms of LOCA frequencies into conditional probabilities of pipe ruptures 7/5/11 Pre-Licensing Meeting 30 | |||
Step 7 Conditional Probability of Pipe Rupture | |||
* Step 7.1 Benchmark of Lydells Base Case LOCA frequencies for PWR hot leg, surge line, and HPI line | |||
* Step 7.2 Compare results of individual expert elicitation LOCA Frequencies from NUREG-1829 to base case | |||
* Step 7 7.3 3 Set Target LOCA frequencies that encompass elicitation results | |||
* Step 7.4 Derive conditional rupture probability distributions that when combines with Lydell failure rate estimates match the target LOCA frequencies | |||
* Step 7.5 Perform Bayes updates that incorporate evidence on pipe failures without LOCAs 7/5/11 Pre-Licensing Meeting 31 | |||
7.1 Benchmark of Lognormal Model to Lydell HPI Base Case -HPI 7/5/11 Pre-Licensing Meeting 32 | |||
7.1 Benchmark of Lognormal Model to Lydell HPI Base Case -Surge Line 7/5/11 Pre-Licensing Meeting 33 | |||
Individual Estimates by Component in Appendix L NUREG-1829 7/5/11 Pre-Licensing Meeting 34 | |||
Step 7.2 Review of NUREG-1829 Data | |||
* Used supporting information for NUREG-1829 recently released by NRC some of which is in Appendix L | |||
* 9 experts provided estimates for LOCA frequencies for specific components | |||
* Each expert estimate treated as lognormal distribution for each LOCA Category frequency | |||
* Lognormal distributions combined using posterior weighting procedure to produce a single composite experts distribution | |||
* Each of the nine experts given equal weight | |||
* Sanity check performed by comparing results to the component failure rate distribution in the Lydell Base case results 7/5/11 Pre-Licensing Meeting 35 | |||
Steps 7.2 and 7.3 Selection of HPI Target LOCA Frequencies 7/5/11 Pre-Licensing Meeting 36 | |||
Steps 7.2 and 7.3 Selection of Surge Line Target Frequencies 7/5/11 Pre-Licensing Meeting 37 | |||
Step 7.4 Benchmarking Target Frequencies - HPI 7/5/11 Pre-Licensing Meeting 38 | |||
Step 7.4 Benchmarking Target Frequencies - Surge Line 7/5/11 Pre-Licensing Meeting 39 | |||
Step 7.4 CRPs that Match HPI Targets 7/5/11 Pre-Licensing Meeting 40 | |||
Step 7.4 CRPs that Match Surge Line Targets 7/5/11 Pre-Licensing Meeting 41 | |||
Step 7.4 CRPs that Match Hot Leg Targets 7/5/11 Pre-Licensing Meeting 42 | |||
Step 7.4 Example Conditional Probability Distributions Distribution Input Parameters Truncated Distribution Parameters LOCA Break Component Median Range Category Size (in.) Type [Note (1) | |||
Median Mean 5%tile 95%tile Factor 1 .5 1.39E-04 2.09E+01 1.39E-04 7.69E-04 6.69E-06 2.89E-03 2 1.5 2.49E-05 2.94E+01 2.49E-05 2.02E-04 8.37E-07 7.38E-04 RCS-Hot Leg 3 3 8.65E-06 3.64E+01 8.62E-06 9.59E-05 2.36E-07 3.24E-04 4 6.76 2.43E-06 4.76E+01 2.43E-06 3.75E-05 5.20E-08 1.16E-04 5 14 8.10E-07 5.90E+01 7.96E-07 2.38E-05 1.34E-08 4.82E-05 6 31.5 2.20E-07 7.53E+01 2.19E-07 6.79E-06 2.96E-09 1.66E-05 Lognormal 1 .5 4.73E-02 1.40E+02 4.73E-03 1.19E-01 2.66E-04 6.11E-01 truncated at RCS-Surge 2 1.5 6.06E-03 1.92E+02 6.06E-03 5.83E-02 2.89E-05 3.49E-01 1.0 Line 3 3 2.06E-03 2.45E+02 2.06E-03 3.85E-02 7.96E-06 2.23E-01 4 6.76 6.43E-04 3.68E+02 6.43E-04 2.54E-02 1.69E-06 1.31E-01 5 14 2.24E-04 4.85E+02 2.24E-04 1.70E-02 4.51E-07 7.26E-02 1 .5 5.85E-03 2.20E+01 5.78E-03 2.15E-02 3.77E-04 8.88E-02 HPI Line 2 1.5 1.20E-03 8.61E+00 1.18E-03 5.87E-03 6.34E-05 2.30E-02 3 3 4.56E-04 8.61E+00 4.59E-04 2.61E-03 2.07E-05 1.01E-02 Note (1) These are medians to specify the input distribution to Crystal Ball' prior to truncation; the median of the truncated distribution is generally different following truncation. | |||
7/5/11 Pre-Licensing Meeting 43 | |||
Step 7.5 Bayes Update to Incorporate Service Data | |||
* Results of Steps 7.1 - 7.4 produce Bayes prior distributions for CRP for each LOCA category | |||
* Prior distributions are Lognormal truncated at CRP = 1.0 | |||
* We update these priors with the service data for surge line welds: 0 LOCAs in each Category out of 3 failures. | |||
* Even though this is weak evidence, it impacts the upper tails and changes the mean CRPs - | |||
could impact risk significance 7/5/11 Pre-Licensing Meeting 44 | |||
Step 7.5 Bayes Update of Surge CRP Priors: 0 LOCAs in 3 Failures Distribution Parameters(2) | |||
LOCA Break Distribution Type (1) Range Category Size (in.) Mean 5%tile 50%tile 95%tile Factor(3) 1 0.5 Prior Truncated Lognormal 1.05E-01 5.38E-04 2.59E-02 5.36E-01 53.6 Posterior Lognormal-Binomial 4.43E-02 4.11E-04 1.45E-02 1.95E-01 21.8 2 1.5 Prior Truncated Lognormal 3.46E-02 7.41E-05 3.97E-03 1.76E-01 48.8 Posterior Lognormal-Binomial Lognormal Binomial 1 75E 02 1.75E-02 6 75E 05 6.75E-05 3 17E 03 3.17E-03 8 45E 02 8.45E-02 35 4 35.4 3 3 Prior Truncated Lognormal 1.85E-02 1.99E-05 1.34E-03 8.24E-02 64.3 Posterior Lognormal-Binomial 1.00E-02 1.88E-05 1.17E-03 4.79E-02 50.5 4 6.76 Prior Truncated Lognormal 9.09E-03 4.34E-06 3.88E-04 3.32E-02 87.5 Posterior Lognormal-Binomial 5.27E-03 4.22E-06 3.60E-04 2.33E-02 74.3 5 14 Prior Truncated Lognormal 5.16E-03 1.12E-06 1.34E-04 1.55E-02 117 Posterior Lognormal-Binomial 3.10E-03 1.11E-06 1.28E-04 1.21E-02 105 Notes (1) Prior lognormal distributions truncated at 1.0. | |||
(2) Values for means and percentiles represent conditional probability of LOCA category given pipe failure. | |||
(3) Range Factor = SQRT(95%tile/5%tile) 7/5/11 Pre-Licensing Meeting 45 | |||
Step by Step Procedure | |||
: 1. Determination of weld types (i) | |||
: 2. Perform data query for failure counts (n) | |||
: 3. Estimate component exposure (T) and uncertainty | |||
: 4. Develop component failure rate prior distributions for each DM | |||
: 5. Perform Bayes update for each exposure case (combination of weld count and DM susceptibility) | |||
: 6. Apply posterior weighting to combine results for different hypothesis yield conditional failure rate distributions; compute unconditional failure rates for locations with uncertain DM status | |||
: 7. Develop conditional probability of rupture size given failure probabilities for each weld type and associated epistemic uncertainties | |||
: 8. Combine the results of Step 6 and Step 7 by Monte Carlo in Eq. (1) for component LOCA frequencies and total LOCA frequencies for each component | |||
: 9. Apply Markov Model to specialize rupture frequencies for differences in integrity management | |||
: 10. For intermediate LOCA categories and break sizes, interpolate the results of Step 10 via log-log linear interpolation | |||
: 11. Calculate total LOCA frequencies from all components and reconcile differences with earlier LOCA frequency estimates 7/5/11 Pre-Licensing Meeting 46 | |||
Step 8 Calculate Component LOCA Frequencies | |||
* Need to calculate LOCA frequencies for each component | |||
* LOCA frequency is the product of the failure rate and the conditional probability y of LOCA vs. | |||
Break Size | |||
* Calculated via Monte Carlo simulation by sampling from the applicable failure rate and CRP distributions | |||
* Will be performed on a STP specific basis for each component 7/5/11 Pre-Licensing Meeting 47 | |||
Step 8 Calculate Component LOCA Frequencies | |||
* Base Case Results | |||
- Assume all BJ welds are susceptible to thermal fatigue (TF) and D&C | |||
- All BC welds are susceptible to TF and D&C | |||
- All BF welds are susceptible to SC and D&C | |||
* Sensitivity Case | |||
- Assume no BJ welds are susceptible to TF | |||
- Assume BF welds mitigate SC via weld overlay | |||
- Other assumptions same as Base Case 7/5/11 Pre-Licensing Meeting 48 | |||
LOCA Frequencies for Each Weld Type Distribution Parameters (1) | |||
Weld Type Parameter RF Mean 5%tile 50%tile 95%tile Failure Rate 5.61E-04 1.37E-04 4.38E-04 1.40E-03 3.2 Category 1 2.13E-05 1.44E-07 3.81E-06 9.35E-05 25.5 Category 2 1.03E-05 2.44E-08 1.01E-06 4.26E-05 41.7 B-F Category 3 6.71E-06 6.94E-09 4.10E-07 2.38E-05 58.6 Category 4 3.67E-06 1.55E-09 1.36E-07 1.16E-05 86.6 Category 5 2.22E-06 4.27E-10 5.05E-08 5.95E-06 118.0 Failure Rate 4.16E-06 4.16E 06 9.75E-09 9.75E 09 2.91E-07 2.91E 07 1.17E-05 1.17E 05 34.7 Category 1 1.43E-07 2.65E-11 2.58E-09 2.87E-07 104.1 Branch Category 2 8.14E-08 5.02E-12 6.87E-10 1.12E-07 149.3 Connection Category 3 4.35E-08 1.51E-12 2.81E-10 5.73E-08 194.9 Category 4 2.87E-08 3.68E-13 9.32E-11 2.55E-08 263.1 Category 5 1.45E-08 1.06E-13 3.45E-11 1.23E-08 339.4 Failure Rate 2.03E-07 2.66E-11 2.86E-09 3.74E-07 118.6 Category 1 4.38E-08 1.12E-12 2.68E-10 6.33E-08 238.3 Category 2 2.13E-08 2.34E-13 7.40E-11 2.38E-08 319.0 B-J Category 3 1.49E-08 7.21E-14 2.98E-11 1.15E-08 398.5 Category 4 8.68E-09 1.85E-14 9.77E-12 4.92E-09 515.9 Category 5 2.07E-09 1.26E-13 2.23E-11 3.84E-09 175.0 Note (1) RF = SQRT(95%tile/5%tile) 7/5/11 Pre-Licensing Meeting 49 | |||
LOCA Frequencies for Surge Line Distribution Parameters (2) | |||
Weld Type Parameter RF Mean 5%tile 50%tile 95%tile Failure Rate 5.71E-04 1.37E-04 4.39E-04 1.42E-03 3.2 Category 1 2.19E-05 1.44E-07 3.81E-06 9.45E-05 25.6 Base Case Category 2 1.06E-05 2.45E-08 1.02E-06 4.29E-05 41.9 Total Surge (1) Category 3 6.90E-06 6.94E-09 4.11E-07 2.40E-05 58.8 Line Category 4 3.79E-06 1.55E-09 1.36E-07 1.17E-05 86.9 Category 5 2.26E-06 4.28E-10 5.07E-08 6.00E-06 118.4 Total Surge Failure Rate 1.50E-05 2.37E-08 9.77E-07 5.13E-05 46.5 Line Case with Category 1 4.39E-07 5.35E-11 5.45E-09 7.25E-07 116.4 B-F weld Category 2 3.04E-07 1.01E-11 1.46E-09 3.02E-07 172.9 overlay and no TF Category 3 1.90E-07 3.04E-12 6.01E-10 1.68E-07 235.3 Susceptibility Category 4 1.46E-07 7.41E-13 2.02E-10 8.45E-08 337.8 for B-J welds Category 5 8.73E-08 2.17E-13 8.12E-11 5.29E-08 493.6 Note (1) Total surge line results are based on 1 B-F weld, 2 BC welds, and 6.9 B-J welds. | |||
(2) RF = SQRT( 95%tile/5%tile) 7/5/11 Pre-Licensing Meeting 50 | |||
Comparison of Calculated Surge Line LOCA Frequencies 7/5/11 Pre-Licensing Meeting 51 | |||
Step by Step Procedure | |||
: 1. Determination of weld types (i) | |||
: 2. Perform data query for failure counts (n) | |||
: 3. Estimate component exposure (T) and uncertainty | |||
: 4. Develop component failure rate prior distributions for each DM | |||
: 5. Perform Bayes update for each exposure case (combination of weld count and DM susceptibility) | |||
: 6. Apply posterior weighting to combine results for different hypothesis yield conditional failure rate distributions; compute unconditional failure rates for locations with uncertain DM status | |||
: 7. Develop conditional probability of rupture size given failure probabilities for each weld type and associated epistemic uncertainties | |||
: 8. Combine the results of Step 6 and Step 7 by Monte Carlo in Eq. (1) for component LOCA frequencies and total LOCA frequencies for each component | |||
: 9. Apply Markov Model to specialize rupture frequencies for differences in integrity management | |||
: 10. For intermediate LOCA categories and break sizes, interpolate the results of Step 10 via log-log linear interpolation | |||
: 11. Calculate total LOCA frequencies from all components and reconcile differences with earlier LOCA frequency estimates 7/5/11 Pre-Licensing Meeting 52 | |||
Step 9 Markov Model | |||
===Background=== | |||
* Purpose of model is to evaluate the impact of changes to inspection on pipe failure rates | |||
* Markov Model originally developed for EPRI RI-ISI Program | |||
* Applied to 26 plant specific RI-ISI programs in U.S. and South Africa | |||
* Applied pp to PBMR to support pp new ASME Code development p for in-service inspections | |||
* Applied in NUREG-1829 LOCA frequency update | |||
* Currently being applied to address CANDU feeder pipe cracking issue | |||
* Recently applied to LWRs to guide efforts to reduce internal flood and HELB contributions to CDF | |||
* Enhanced version of model developed in DOE/INL RISMC to address aging issues; transition rates based on physics of failure 53 7/5/11 Pre-Licensing Meeting | |||
Markov Model Of Pipe Element S | |||
Pipe Element States | |||
S - success, no detectable damage F - detectable flaw L - detectable leak F R - rupture | |||
State Transition Rates | |||
- flaw occurrence rate F L - leak failure rate F - rupture failure rate given flaw L - rupture failure rate given leak L - repair rate via ISI exams | |||
- repair rate via leak detection R | |||
7/5/11 Pre-Licensing Meeting 54 | |||
Estimating Input Parameters | |||
* Degradation related parameters | |||
- Uses failure rates for flaws and leaks and rupture frequencies as developed in previous slides | |||
- Leaks estimated using leak data and conditional leak given failure model similar to that used for ruptures | |||
- Flaws estimated as a multiple of leaks based on insights from service data | |||
- Modeled solved separately for each rupture mode (LOCA category) | |||
* Test and inspection parameters estimated using simple and easy to quantify models | |||
- One model for leak tests and inspections | |||
- One model for NDE 55 7/5/11 Pre-Licensing Meeting | |||
Modeling Impact Of NDE Inspections | |||
* Capture by : the repair rate for flaws PF I PF D | |||
= | |||
(T I + TR ) | |||
where: | |||
- PFI = probability that segment element with flaw will be inspected | |||
- PFD= probability that flaw is detected given inspection | |||
- TI = mean time between inspections | |||
- TR = mean time to repair after detection is set to 0.0 for weld that is not in ISI program 56 7/5/11 Pre-Licensing Meeting | |||
Modeling Impact of Leak Tests and Inspections | |||
* Capture by : the repair rate for leaks PLD | |||
= | |||
( TLI + TR ) | |||
where: | |||
- PLD= probability that leak is detected given inspection | |||
- TI = mean time between inspections | |||
- TR = mean time to repair after detection is set to 0.0 if there is no leak inspections 57 7/5/11 Pre-Licensing Meeting | |||
Example Application of Markov Model to Evaluate Strategies for Fire Protection Piping 1.0E-04 Frequency of Rupture Size Greater than o or Equal to X (events per ROY-ft.) | |||
Current Study w/ WH 1.0E-05 Current Study no WH EPRI 1013141 FP NPS > 10" Current Study No WH + Yearly Leak Test Current Study No WH + Quaterly Leak Test 1.0E-06 1.0E-07 1.0E-08 1.0E-09 0.01 0.10 1.00 10.00 100.00 X, Equivalent Break Size (in.) | |||
58 7/5/11 Pre-Licensing Meeting | |||
BWR Recirculation Pipe LOCA Frequency Example from NUREG-1860 1.0E-04 No ISI/No Leak Inspection No ISI/ Leak Inspection 1/Refueling Outage No ISI/ Leak Inspection 1/Week ISI/Leak Inspection 1/Refueling Outage BWR Recirculation Piping LO OCA Frequency/year 1.0E-05 ISI/Leak Inspection 1/Week 1.0E-06 1.0E-07 1.0E-08 1.0E-09 5 15 25 35 45 55 Plant Age (Years) 59 7/5/11 Pre-Licensing Meeting | |||
Impact of RIM Strategies on SC Susceptible RCS Weld Failure Rate (2005 RI-ISI for Koeberg) 7/5/11 Pre-Licensing Meeting 60 | |||
Step by Step Procedure | |||
: 1. Determination of weld types (i) | |||
: 2. Perform data query for failure counts (n) | |||
: 3. Estimate component exposure (T) and uncertainty | |||
: 4. Develop component failure rate prior distributions for each DM | |||
: 5. Perform Bayes update for each exposure case (combination of weld count and DM susceptibility) | |||
: 6. Apply posterior weighting to combine results for different hypothesis yield conditional failure rate distributions; compute unconditional failure rates for locations with uncertain DM status | |||
: 7. Develop conditional probability of rupture size given failure probabilities for each weld type and associated epistemic uncertainties | |||
: 8. Combine the results of Step 6 and Step 7 by Monte Carlo in Eq. (1) for component LOCA frequencies and total LOCA frequencies for each component | |||
: 9. Apply Markov Model to specialize rupture frequencies for differences in integrity management | |||
: 10. For intermediate LOCA categories and break sizes, interpolate the results of Step 10 via log-log linear interpolation | |||
: 11. Calculate total LOCA frequencies from all components and reconcile differences with earlier LOCA frequency estimates 7/5/11 Pre-Licensing Meeting 61 | |||
Step 9 Application of Markov Model | |||
* Failure rates and rupture frequencies calculated in Step 8 are for an average integrity management program | |||
* For Class 1 welds in the service data an average integrity management has | |||
- 25% that are included in NDE program and subjected to leak testing once every refueling cycle | |||
- 75% that are not included in NDE program and subjected to leak testing once every refueling cycle | |||
* For STP welds the integrity management factors will be: | |||
- Greater than 1.0 for welds not in ISI program | |||
- Less than 1.0 for welds in ISI program | |||
* If some specific weld locations have an unusually high potential for debris induced core damage, inspection locations can be added or changed to offset risk impacts 7/5/11 Pre-Licensing Meeting 62 | |||
Steps 10 Interpolation for Intermediate LOCA Sizes | |||
* LOCA categories used in PRA and NUREG-1829 are defined as discrete ranges over continuum of possible break sizes | |||
* Results of expert elicitation for 6 LOCA categories are well behaved | |||
* For a given pipe size there is no reason to expect sharp discontinuties over the range of possible break sizes | |||
* STP model will assume linear interpolation between break sizes used to define 6 LOCA categories | |||
* STP model will extrapolate curves to account for double ended break of each pipe at the location of the weld 7/5/11 Pre-Licensing Meeting 63 | |||
Step 11 Aggregation of Results for PRA Model | |||
* LOCA frequency distributions to be developed for all unique weld-types typified by pipe size, weld type, DM status, and NDE program status and assigned to each location for Case Grande debris formation analysis | |||
* Results will be probabilistically summed up over each PRA LOCA category (small, medium, large LOCA) via Monte Carlo 7/5/11 Pre-Licensing Meeting 64 | |||
Step 12 | |||
* Results of Step 11 will be compared against other available LOCA frequency sources, e.g. NUREG-1150, NUREG/CR-5750 | |||
* Differences will be identified and reconciled; may lead to refinements in technical approach 7/5/11 Pre-Licensing Meeting 65 | |||
Technical Issues | |||
* Need to better understand aggregation methods used in NUREG-1829 and reason why uncertainties in aggregated results appear much smaller than those of the component level expert estimates | |||
* Need to resolve questions about whether all the experts i NUREG in NUREG-1829 1829 provided id d cumulative l ti vs. di discrete t input i t | |||
* Need to confirm that CRP method can be easily extended to other components | |||
* Need to incorporate insights about DMs since EPRI RI-ISI program developed 7/5/11 Pre-Licensing Meeting 66 | |||
Summary of LOCA Frequency Approach | |||
* Method of deriving CRP distributions from NUREG-1829 has been demonstrated for hot leg, surge line, and HP injection line; appears to be applicable to other components | |||
* Adjustments needed to prevent CRP from exceeding 1.0 | |||
* CRP method combined with failure rate uncertainty y method yields very large uncertainties in component level LOCA frequencies | |||
* Capability to specialize frequencies to address key variables impacting pipe reliability (e.g. pipe size, materials, damage mechanisms, inspection status) | |||
* Capability to augment RI-ISI program to optimize NDE element selection 7/5/11 Pre-Licensing Meeting 67 | |||
For more information, please contact: | |||
Karl Fleming fleming@ti-sd.com Bengt Lydell bly@scandpower.com Karl Fleming Consulting Service LLC 68 7/5/11 Pre-Licensing Meeting}} |
Revision as of 18:40, 12 November 2019
ML111890380 | |
Person / Time | |
---|---|
Site: | South Texas ![]() |
Issue date: | 07/07/2011 |
From: | Kreslyon Fleming, Lydell B KNF Consulting Services, Scandpower, Risk Management |
To: | Balwant Singal Plant Licensing Branch IV |
Singal, B K, NRR/DORL, 301-415-301 | |
Shared Package | |
ML111890371 | List: |
References | |
TAC ME5358, TAC ME5359, GSI-191 | |
Download: ML111890380 (68) | |
Text
LOCA Initiating Event Frequencies and Uncertainties (Draft)
Risk Informed GSI-191 Resolution Th d Thursday, July J l 7, 7 2011 1:00 pm - 2:00 p.m EDT Public Meeting with STP Nuclear Operating Company Karl N. Fleming KNF Consulting Services LLC Bengt O. Y. Lydell 7/5/11 Pre-Licensing Meeting 1
Risk Informed GSI-191 Discussion Topics
- LOCA frequencies scope and objectives
- Technical approach
- Step by step procedure with examples
- Technical issues to be addressed
- Resolution of NRC questions from June 2011 meeting 7/5/11 Pre-Licensing Meeting 2
Risk Informed GSI-191 LOCA Frequencies Objectives
- Incorporate insights from previous work on LOCA frequencies
- Characterize LOCA initiating events and there frequencies with respect to:
- Specific components, materials, dimensions
- Specific locations
- Range of break sizes
- Degradation mechanisms and mitigation effectiveness
- Other break characteristics, characteristics ee.g.
g speed
- Quantify both aleatory and epistemic uncertainties; augment with sensitivity studies
- Support interfaces with other parts of the GSI-191 evaluation
- LOCA initiating event frequencies for PRA modeling
- Break characterization for evaluation of debris formation
- Participate in NRC workshops 3 7/5/11 Pre-Licensing Meeting
LOCA Frequency Technical Approach
- Utilize passive component reliability methods and data from RI-ISI technology
- Utilize PIPExp database to help resolve uncertainties in failure rates
- Utilize information from NUREG-1829 and NUREG/CR-5750 in optimum manner
- Consider probabilistic fracture mechanics evaluation on selected locations as may be required 4 7/5/11 Pre-Licensing Meeting
LOCA IE Frequency Model 1 of 2 F ( LOCAx ) = mi ix (1) i jx = ix = ik P( Rx Fik ) I ik (2) k Where:
F ( LOCAx ) = Frequency of LOCA of size x, per reactor calendar-year; subject to epistemic uncertainty calculated via Monte Carlo mi = Number of pipe welds of type i; each type determined by pipe size, weld type, applicable damage mechanisms, and inspection status (leak test and NDE); no uncertainty for STP ix = Frequency of rupture of pipe location j belonging to component type i with break size x, subject to epistemic uncertainty calculated via Monte Carlo and uncertainties on the RHS of Equation (2) ik = Failure rate per weld-year for pipe component type i due to failure mechanism k; subject to epistemic uncertainty determined by RI-ISI Bayes method and Eq. (3)
P( Rx Fik ) = Conditional probability of rupture of size x given failure of pipe component type i due to damage mechanism k; subject to epistemic uncertainty determined via expert elicitation (NUREG-1829)
I ik = Integrity management factor for weld type i and failure mechanism k; calculated via Markov Model; subject to epistemic uncertainty determined by Monte Carlo propagation of input parameters using Markov model equations and input parameter uncertainties.
5 7/5/11 Pre-Licensing Meeting
LOCA IE Frequency Model 2 of 2 For a Point Estimate of the Failure Rate for type i and failure mechanism k:
nik nik ik = = (3) ik f ik N iTi nik = Number of failures in pipe component (i.e. weld) type i due to failure mechanism k, very little epistemic uncertainty ik = Component exposure population for welds of type i susceptible to failure mechanism k, subject to epistemic uncertainty determined by expert opinion f ik = Estimate of the fraction of the component exposure population for weld type i that is susceptible to failure mechanism k, subject to epistemic uncertainty; estimated from results of RI-ISI for population of plants and expert opinion.
Ni = Estimate of the average number of pipe welds of type i per reactor in the applicable reactor years exposure for the data collection; subject to plant to plant variability and epistemic uncertainty; estimated from results of RI-ISI for sample population of plants and expert opinion Ti = Total number of reactor years exposure for the data collection for component type i; little or no uncertainty 6 7/5/11 Pre-Licensing Meeting
Step by Step Procedure
- 1. Determination of weld types (i)
- 2. Perform data query for failure counts (n)
- 3. Estimate component exposure (T) and uncertainty
- 4. Develop component failure rate prior distributions for each DM
- 5. Perform Bayes update for each exposure case (combination of weld count and DM susceptibility)
- 6. Apply posterior weighting to combine results for different hypothesis yield conditional failure rate distributions; compute unconditional failure rates for locations with uncertain DM status
- 7. Develop conditional probability of rupture size given failure probabilities for each weld type and associated epistemic uncertainties
- 8. Combine the results of Step 6 and Step 7 by Monte Carlo in Eq. (1) for component LOCA frequencies and total LOCA frequencies for each component
- 9. Apply Markov Model to specialize rupture frequencies for differences in integrity management
- 10. For intermediate LOCA categories and break sizes, interpolate the results of Step 10 via log-log linear interpolation
- 11. Calculate total LOCA frequencies from all components and reconcile differences with earlier LOCA frequency estimates 7/5/11 Pre-Licensing Meeting 7
Steps 1 and 2 Failure Data Query
- Failure defined as any event that involved repair or replacement of damaged component
- Data query covers operating experience from 1970 through 2010
- Supports Steps 1 (define weld types) and 2 (failure counts) 7/5/11 Pre-Licensing Meeting 8
Preliminary Results of Data Query Pipe Failures by Mode (1), (2), (3)
Nominal SYSTEM Pipe Size (NPS) Crack- Crack- Small Large Total Leak Full Part Leak Leak 1" 7 1 6 CVC 2" ø 4" 7 1 6 1" 2 2 Safety Injection 4" ø 10" 6 3 1 1 1 Pressurizer-Sample 2" 5 4 1 Pressurizer-PORV 4" ø 10" 2 2 1" 4 1 2 1 Pressurizer-SPRAY 4" ø 10" 3 2 1 Pressurizer-SRV 4" ø 10" 7 6 1 Example chosen Pressurizer-Surge 14" 3 3 to illustrate FR RCS 2" 76 4 10 53 4 5 RCS Cold Leg 32" 4 4 Approach RCS Hot Leg 32" 6 5 1 RHR 1" 6 6 RHR 4" ø 10" 1 1 RC Hot Leg - S/G- 19 19 32" Inlet S/G-System 2" 8 2 2 4 TOTALS 166 12 59 83 6 6 Notes (1) Query accounts for 3914 reactor years based on date of initial criticality from 1970-2010.
(2) Failure is defined as any event that required repair or replacement of damaged component.
(3) Small leaks have leak flows << 1gpm; Leaks < 1gpm; Large Leaks < 10gpm.
7/5/11 Pre-Licensing Meeting 9
Step by Step Procedure
- 1. Determination of weld types (i)
- 2. Perform data query for failure counts (n)
- 3. Estimate component exposure (T) and uncertainty
- 4. Develop component failure rate prior distributions for each DM
- 5. Perform Bayes update for each exposure case (combination of weld count and DM susceptibility)
- 6. Apply posterior weighting to combine results for different hypothesis yield conditional failure rate distributions; compute unconditional failure rates for locations with uncertain DM status
- 7. Develop conditional probability of rupture size given failure probabilities for each weld type and associated epistemic uncertainties
- 8. Combine the results of Step 6 and Step 7 by Monte Carlo in Eq. (1) for component LOCA frequencies and total LOCA frequencies for each component
- 9. Apply Markov Model to specialize rupture frequencies for differences in integrity management
- 10. For intermediate LOCA categories and break sizes, interpolate the results of Step 10 via log-log linear interpolation
- 11. Calculate total LOCA frequencies from all components and reconcile differences with earlier LOCA frequency estimates 7/5/11 Pre-Licensing Meeting 10
Step 3 Component Exposure
- Need Reactor-years of service experience in failure data query
- Need estimates of component populations per plant
- Need fractions of the component population susceptible to each damage mechanism (DM) for conditional failure rates given knowledge of applicable damage mechanisms 7/5/11 Pre-Licensing Meeting 11
Reactor Years in Data Query Reactor-Calendar Years WE Type Rx Initial Grid Initial Criticality Connection 2-Loop 570.1 581.4 3-Loop 2052.6 2096.1 4-Loop 1193.9 1236.5 3816.6 3914 Total 7/5/11 Pre-Licensing Meeting 12
Data for Estimating Surge Line Weld Population Weld Population[Note (1)]
PWR Branch Connection to Plant B-F Welds Inline B-J Welds Type Hot Leg Braidwood-1 4-Loop 1 8 2 Braidwood-2 4-Loop 1 7 2 Byron-1 4-Loop 1 6 2 Byron-2 4-Loop 1 6 2 Kewaunee 2-Loop 1 6 2 Koeberg-1 3-Loop 1 5 2 Koeberg-2 3-Loop 1 5 2 STP-1 4-Loop 1 8 2 STP-2 4-Loop 1 8 2 V.C. Summer 3-Loop 1 10 2 Note (1) Kewaunee surge line is NPS10, Remaining plants are NPS 14 to 16 7/5/11 Pre-Licensing Meeting 13
Damage Mechanism Characterization
- EPRI developed screening criteria to evaluated susceptibility of piping to known damage mechanisms to support RI-ISI
- Criteria applied in STP RI-ISI application to all welds on Class 1 and 2 pressure boundary
- PIPExp data base also identifies generic susceptibilities to some damage and failure mechanisms
- Bi-metallic welds with Ni-based allows susceptible to PWSCC
- All welds especially field welds subject to design and construction defects
- If we know that a specific weld location is susceptible to a given damage mechanism (s) we can specialize the failure rates to that knowledge, i.e. conditional failure rates
- If we do not know the specific susceptibility to DMs we apply unconditional failure rates 7/5/11 Pre-Licensing Meeting 14
Example Surge Line Damage Mechanism Characterization Confidence Weld Susceptibility Fractions Location Level C-F D&C ECSCC Fretting IGSCC PWSCC TF TGSCC TAE V-F Low N/A 1 N/A N/A N/A 1 N/A N/A N/A N/A B-F 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 Low N/A 1 N/A N/A N/A N/A 0.01 N/A N/A N/A B-J 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 RC-HL Branch Low N/A 1 N/A N/A N/A N/A 1 N/A N/A N/A C
Connection ti 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 ID Description C-F Corrosion-Fatigue D&C Design & Construction Flaws ECSCC External Chloride-induced SCC IGSCC Intergranular SCC LC-FAT Low-Cycle Fatigue PWSCC Primary Water SCC OVLD Overload TF Thermal Fatigue TGSCC Transgranular SCC TAE Thermal Aging Embrittlement V-F Vibration Fatigue 7/5/11 Pre-Licensing Meeting 15
Example DM evaluation for Surge Line Welds
- All branch connection welds are susceptible to TF - no uncertainty for this DM
- Some unknown fraction of B-J welds susceptible to TF - uncertainty in the fraction susceptible for this DM
- For STP we have a deterministic evaluation of DM Susceptibility for each location 7/5/11 Pre-Licensing Meeting 16
Example Exposure Uncertainty Model for Surge Line Welds
- BF Welds (at pressurizer nozzle)
- No DM Uncertainty or Weld count Uncertainty
- Only need one Bayes update for one case of exposure
- BC Welds
- No DM uncertainty
- Some S plant l t tto plant l t variability i bilit iin numberb off bbranch h connections ti
- Need three updates for weld count uncertainty one for each of high, medium, and low estimates for weld counts
- BJ Welds
- DM Uncertainty
- Weld Count Uncertainty
- Need Bayes update of priors for each combination of weld count and DM susceptibility Cases ( 3 X 3 = 9) 7/5/11 Pre-Licensing Meeting 17
Treatment of Exposure Uncertainty for B-J Welds and Thermal Fatigue Welds/Rx 6.9 Rx-yrs 3914 Base Exposure 27006.6 Fraction of B-J Welds Exposure Weld Count Exposure Susceptible to Thermal Case Exposure Uncertainty Multiplier Fatigue Probability 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) 7/5/11 Pre-Licensing Meeting 18
Step by Step Procedure
- 1. Determination of weld types (i)
- 2. Perform data query for failure counts (n)
- 3. Estimate component exposure (T) and uncertainty
- 4. Develop component failure rate prior distributions for each DM
- 5. Perform Bayes update for each exposure case (combination of weld count and DM susceptibility)
- 6. Apply posterior weighting to combine results for different hypothesis yield conditional failure rate distributions; compute unconditional failure rates for locations with uncertain DM status
- 7. Develop conditional probability of rupture size given failure probabilities for each weld type and associated epistemic uncertainties
- 8. Combine the results of Step 6 and Step 7 by Monte Carlo in Eq. (1) for component LOCA frequencies and total LOCA frequencies for each component
- 9. Apply Markov Model to specialize rupture frequencies for differences in integrity management
- 10. For intermediate LOCA categories and break sizes, interpolate the results of Step 10 via log-log linear interpolation
- 11. Calculate total LOCA frequencies from all components and reconcile differences with earlier LOCA frequency estimates 7/5/11 Pre-Licensing Meeting 19
Step 4 Prior Distributions
- Based on Wash-1400 era state of knowledge on LOCA frequencies with estimates for SLOCA ranging from 10-2 to 10-6 per year and allocation down to welds based on weld count estimates in EPRI TR-111880
- Lognormal distributions with large range factors (100)
- Means adjusted based on gross estimates from service data
- Priors updated with results of data queries and exposure estimates to determine failure rates 7/5/11 Pre-Licensing Meeting 20
Example Prior Distributions Prior Distribution (Failures per Weld-Year)
Damage Mechanism Range Dist. Type Mean Median Factor Stress Corrosion Cracking Lognormal 4.27E-05 8.48E-07 100 Design and Construction Lognormal 2.75E-06 5.46E-08 100 Thermal Fatigue Lognormal 1.34E-05 2.66E-07 100 7/5/11 Pre-Licensing Meeting 21
Step by Step Procedure
- 1. Determination of weld types (i)
- 2. Perform data query for failure counts (n)
- 3. Estimate component exposure (T) and uncertainty
- 4. Develop component failure rate prior distributions for each DM
- 5. Perform Bayes update for each exposure case (combination of weld count and DM susceptibility)
- 6. Apply posterior weighting to combine results for different hypothesis yield conditional f il failure rate t di distributions; t ib ti compute t unconditional diti l ffailure il rates t ffor llocations ti with ith uncertain t i DM status
- 7. Develop conditional probability of rupture size given failure probabilities for each weld type and associated epistemic uncertainties
- 8. Combine the results of Step 6 and Step 7 by Monte Carlo in Eq. (1) for component LOCA frequencies and total LOCA frequencies for each component
- 9. Apply Markov Model to specialize rupture frequencies for differences in integrity management
- 10. For intermediate LOCA categories and break sizes, interpolate the results of Step 10 via log-log linear interpolation
- 11. Calculate total LOCA frequencies from all components and reconcile differences with earlier LOCA frequency estimates 7/5/11 Pre-Licensing Meeting 22
Step 5 Bayes Updates
- Need library of failure rates for each weld type and damage mechanism
- This library was first developed in EPRI TR 111880 for the EPRI RI-ISI program; will be updated for STP to reflect operating experience through 2010
- For each failure rate we perform 1 Bayes Bayes update for each exposure hypothesis and then combine the results of those into one probabilistically weighted distribution
- For each weld type and damage mechanism need
- Unconditional failure rates for cases where DM status at a location is unknown
- Conditional failure rates for cases where DM status is known
- Perform using RDAT-Plus' software 7/5/11 Pre-Licensing Meeting 23
Step 5 Example Bayes Updates for Surge Line Welds Weld Type DM Prior Distribution[Note (1)] Evidence[Note (2)] Bayes Posterior Distribution[Note (1)]
Weld and DM[Note Susceptibility (3)]
Count Case Type Median RF Failures Exposure Mean 5th 50th 95th RF Case Surge BF SC Base Base Lognormal 8.48E-07 100 3 3914 5.62E-04 1.23E-04 4.83E-04 1.27E-03 3.2 Surge BF DC Base Base Lognormal 5.46E-08 100 0 3914 1.41E-06 5.41E-10 5.33E-08 4.77E-06 93.9 Surge BC TF Base Base Lognormal 2.66E-07 100 0 7828 3.25E-06 2.53E-09 2.34E-07 1.47E-05 76.1 Surge BC DC Base Base Lognormal 5.46E-08 100 0 7828 1.17E-06 5.37E-10 5.24E-08 4.37E-06 90.1 Surge BJ TF Low Low Lognormal 2.66E-07 100 0 135 9.75E-06 2.66E-09 2.65E-07 2.58E-05 98.5 Surge g BJ TF Low Medium Lognormal g 2.66E-07 100 0 675 7.17E-06 2.64E-09 2.61E-07 2.36E-05 94.6 Surge BJ TF Low High Lognormal 2.66E-07 100 0 3376 4.48E-06 2.59E-09 2.48E-07 1.85E-05 84.5 Surge BJ TF Medium Low Lognormal 2.66E-07 100 0 270 8.70E-06 2.65E-09 2.64E-07 2.51E-05 97.4 Surge BJ TF Medium Medium Lognormal 2.66E-07 100 0 1350 5.98E-06 2.62E-09 2.57E-07 2.18E-05 91.2 Surge BJ TF Medium High Lognormal 2.66E-07 100 0 6752 3.46E-06 2.54E-09 2.37E-07 1.54E-05 77.7 Surge BJ TF High Low Lognormal 2.66E-07 100 0 540 7.55E-06 2.64E-09 2.62E-07 2.41E-05 95.4 Surge BJ TF High Medium Lognormal 2.66E-07 100 0 2701 4.83E-06 2.60E-09 2.51E-07 1.94E-05 86.4 Surge BJ TF High High Lognormal 2.66E-07 100 0 13503 2.58E-06 2.47E-09 2.22E-07 1.21E-05 69.8 Surge BJ DC Low Base Lognormal 5.46E-08 100 0 13503 9.83E-07 5.33E-10 5.14E-08 3.96E-06 86.2 Surge BJ DC Medium Base Lognormal 5.46E-08 100 0 27007 7.66E-07 5.25E-10 4.94E-08 3.34E-06 79.8 Surge BJ DC High Base Lognormal 5.46E-08 100 0 54013 5.77E-07 5.12E-10 4.65E-08 2.67E-06 72.2 Notes (1) Failure rates in units of failures per weld-year (2) Exposure in units of weld-years (3) SC = stress corrosion cracking; TF = thermal fatigue; DC = design and construction defects; BF = B-F weld; BC = Branch connection weld; BJ = B-J weld 7/5/11 Pre-Licensing Meeting 24
Step by Step Procedure
- 1. Determination of weld types (i)
- 2. Perform data query for failure counts (n)
- 3. Estimate component exposure (T) and uncertainty
- 4. Develop component failure rate prior distributions for each DM
- 5. Perform Bayes update for each exposure case (combination of weld count and DM susceptibility)
- 6. Apply posterior weighting to combine results for different hypothesis yield conditional failure rate distributions; compute unconditional failure rates for locations with uncertain DM status
- 7. Develop conditional probability of rupture size given failure probabilities for each weld type and associated epistemic uncertainties
- 8. Combine the results of Step 6 and Step 7 by Monte Carlo in Eq. (1) for component LOCA frequencies and total LOCA frequencies for each component
- 9. Apply Markov Model to specialize rupture frequencies for differences in integrity management
- 10. For intermediate LOCA categories and break sizes, interpolate the results of Step 10 via log-log linear interpolation
- 11. Calculate total LOCA frequencies from all components and reconcile differences with earlier LOCA frequency estimates 7/5/11 Pre-Licensing Meeting 25
Step 6 Posterior Weighting
- Purpose is to develop a single uncertainty distribution for the failure rate that probabilistically weights each exposure hypothesis
- Use a discrete probability distribution across the cases as developed in the previous event tree
- Method established and applied in EPRI RI-ISI program
- Method referred to as Bayes posterior weighting 7/5/11 Pre-Licensing Meeting 26
Failure Rate Options for Thermal Fatigue in B-J Welds
- Case 1 FR for B-J Weld susceptible to TF
- Sum of applicable contributions: TF+D&C
- TF failure rate conditional on TF susceptibility ( f in Eq. (3) < 1)
- Case 2 FR for B-J weld whose susceptibility to TF is unknown
- Sum of applicable contributions: TF+D&C
- TF failure f il rate t isi unconditional diti l ( f iin E Eq. (3)
(3)= 1)
- Case 3 FR for B-J weld not susceptible to TF
- Includes only contributions from D&C Case No. Evaluation Case Mean 5%tile 50%tile 95%tile 1 B-J Total Conditional on TF 6.75E-06 9.60E-09 3.23E-07 1.55E-05 2 B-J Total Unconditional 2.62E-06 8.21E-09 2.23E-07 7.69E-06 3 B-J Total Conditional on no TF 7.66E-07 5.25E-10 4.94E-08 3.34E-06 7/5/11 Pre-Licensing Meeting 27
Impact of RI-ISI Damage Mechanism Evaluation on RCS Weld Failure Rates (2005 RI-ISI for Koeberg) 7/5/11 Pre-Licensing Meeting 28
Step by Step Procedure
- 1. Determination of weld types (i)
- 2. Perform data query for failure counts (n)
- 3. Estimate component exposure (T) and uncertainty
- 4. Develop component failure rate prior distributions for each DM
- 5. Perform Bayes update for each exposure case (combination of weld count and DM susceptibility)
- 6. Apply posterior weighting to combine results for different hypothesis yield conditional failure rate distributions; compute unconditional failure rates for locations with uncertain DM status
- 7. Develop conditional probability of rupture size given failure probabilities for each weld type and associated epistemic uncertainties
- 8. Combine the results of Step 6 and Step 7 by Monte Carlo in Eq. (1) for component LOCA frequencies and total LOCA frequencies for each component
- 9. Apply Markov Model to specialize rupture frequencies for differences in integrity management
- 10. For intermediate LOCA categories and break sizes, interpolate the results of Step 10 via log-log linear interpolation
- 11. Calculate total LOCA frequencies from all components and reconcile differences with earlier LOCA frequency estimates 7/5/11 Pre-Licensing Meeting 29
Step 7 Conditional Probability of Pipe Rupture
- Service experience includes 178 pipe failures and millions of weld-years of exposure, which is sufficient to support failure rate estimates
- Model assumption that pipe failures are precursors to LOCAs such that LOCA frequencies are the product of failure rates and conditional LOCA probabilities
- NUREG-1829 viewed as most relevant and up to date source of information on LOCA frequencies and uncertainty
- Our approach for this step is to convert information in terms of LOCA frequencies into conditional probabilities of pipe ruptures 7/5/11 Pre-Licensing Meeting 30
Step 7 Conditional Probability of Pipe Rupture
- Step 7.2 Compare results of individual expert elicitation LOCA Frequencies from NUREG-1829 to base case
- Step 7 7.3 3 Set Target LOCA frequencies that encompass elicitation results
- Step 7.4 Derive conditional rupture probability distributions that when combines with Lydell failure rate estimates match the target LOCA frequencies
- Step 7.5 Perform Bayes updates that incorporate evidence on pipe failures without LOCAs 7/5/11 Pre-Licensing Meeting 31
7.1 Benchmark of Lognormal Model to Lydell HPI Base Case -HPI 7/5/11 Pre-Licensing Meeting 32
7.1 Benchmark of Lognormal Model to Lydell HPI Base Case -Surge Line 7/5/11 Pre-Licensing Meeting 33
Individual Estimates by Component in Appendix L NUREG-1829 7/5/11 Pre-Licensing Meeting 34
Step 7.2 Review of NUREG-1829 Data
- Used supporting information for NUREG-1829 recently released by NRC some of which is in Appendix L
- 9 experts provided estimates for LOCA frequencies for specific components
- Each expert estimate treated as lognormal distribution for each LOCA Category frequency
- Lognormal distributions combined using posterior weighting procedure to produce a single composite experts distribution
- Each of the nine experts given equal weight
- Sanity check performed by comparing results to the component failure rate distribution in the Lydell Base case results 7/5/11 Pre-Licensing Meeting 35
Steps 7.2 and 7.3 Selection of HPI Target LOCA Frequencies 7/5/11 Pre-Licensing Meeting 36
Steps 7.2 and 7.3 Selection of Surge Line Target Frequencies 7/5/11 Pre-Licensing Meeting 37
Step 7.4 Benchmarking Target Frequencies - HPI 7/5/11 Pre-Licensing Meeting 38
Step 7.4 Benchmarking Target Frequencies - Surge Line 7/5/11 Pre-Licensing Meeting 39
Step 7.4 CRPs that Match HPI Targets 7/5/11 Pre-Licensing Meeting 40
Step 7.4 CRPs that Match Surge Line Targets 7/5/11 Pre-Licensing Meeting 41
Step 7.4 CRPs that Match Hot Leg Targets 7/5/11 Pre-Licensing Meeting 42
Step 7.4 Example Conditional Probability Distributions Distribution Input Parameters Truncated Distribution Parameters LOCA Break Component Median Range Category Size (in.) Type [Note (1)
Median Mean 5%tile 95%tile Factor 1 .5 1.39E-04 2.09E+01 1.39E-04 7.69E-04 6.69E-06 2.89E-03 2 1.5 2.49E-05 2.94E+01 2.49E-05 2.02E-04 8.37E-07 7.38E-04 RCS-Hot Leg 3 3 8.65E-06 3.64E+01 8.62E-06 9.59E-05 2.36E-07 3.24E-04 4 6.76 2.43E-06 4.76E+01 2.43E-06 3.75E-05 5.20E-08 1.16E-04 5 14 8.10E-07 5.90E+01 7.96E-07 2.38E-05 1.34E-08 4.82E-05 6 31.5 2.20E-07 7.53E+01 2.19E-07 6.79E-06 2.96E-09 1.66E-05 Lognormal 1 .5 4.73E-02 1.40E+02 4.73E-03 1.19E-01 2.66E-04 6.11E-01 truncated at RCS-Surge 2 1.5 6.06E-03 1.92E+02 6.06E-03 5.83E-02 2.89E-05 3.49E-01 1.0 Line 3 3 2.06E-03 2.45E+02 2.06E-03 3.85E-02 7.96E-06 2.23E-01 4 6.76 6.43E-04 3.68E+02 6.43E-04 2.54E-02 1.69E-06 1.31E-01 5 14 2.24E-04 4.85E+02 2.24E-04 1.70E-02 4.51E-07 7.26E-02 1 .5 5.85E-03 2.20E+01 5.78E-03 2.15E-02 3.77E-04 8.88E-02 HPI Line 2 1.5 1.20E-03 8.61E+00 1.18E-03 5.87E-03 6.34E-05 2.30E-02 3 3 4.56E-04 8.61E+00 4.59E-04 2.61E-03 2.07E-05 1.01E-02 Note (1) These are medians to specify the input distribution to Crystal Ball' prior to truncation; the median of the truncated distribution is generally different following truncation.
7/5/11 Pre-Licensing Meeting 43
Step 7.5 Bayes Update to Incorporate Service Data
- Results of Steps 7.1 - 7.4 produce Bayes prior distributions for CRP for each LOCA category
- Prior distributions are Lognormal truncated at CRP = 1.0
- We update these priors with the service data for surge line welds: 0 LOCAs in each Category out of 3 failures.
- Even though this is weak evidence, it impacts the upper tails and changes the mean CRPs -
could impact risk significance 7/5/11 Pre-Licensing Meeting 44
Step 7.5 Bayes Update of Surge CRP Priors: 0 LOCAs in 3 Failures Distribution Parameters(2)
LOCA Break Distribution Type (1) Range Category Size (in.) Mean 5%tile 50%tile 95%tile Factor(3) 1 0.5 Prior Truncated Lognormal 1.05E-01 5.38E-04 2.59E-02 5.36E-01 53.6 Posterior Lognormal-Binomial 4.43E-02 4.11E-04 1.45E-02 1.95E-01 21.8 2 1.5 Prior Truncated Lognormal 3.46E-02 7.41E-05 3.97E-03 1.76E-01 48.8 Posterior Lognormal-Binomial Lognormal Binomial 1 75E 02 1.75E-02 6 75E 05 6.75E-05 3 17E 03 3.17E-03 8 45E 02 8.45E-02 35 4 35.4 3 3 Prior Truncated Lognormal 1.85E-02 1.99E-05 1.34E-03 8.24E-02 64.3 Posterior Lognormal-Binomial 1.00E-02 1.88E-05 1.17E-03 4.79E-02 50.5 4 6.76 Prior Truncated Lognormal 9.09E-03 4.34E-06 3.88E-04 3.32E-02 87.5 Posterior Lognormal-Binomial 5.27E-03 4.22E-06 3.60E-04 2.33E-02 74.3 5 14 Prior Truncated Lognormal 5.16E-03 1.12E-06 1.34E-04 1.55E-02 117 Posterior Lognormal-Binomial 3.10E-03 1.11E-06 1.28E-04 1.21E-02 105 Notes (1) Prior lognormal distributions truncated at 1.0.
(2) Values for means and percentiles represent conditional probability of LOCA category given pipe failure.
(3) Range Factor = SQRT(95%tile/5%tile) 7/5/11 Pre-Licensing Meeting 45
Step by Step Procedure
- 1. Determination of weld types (i)
- 2. Perform data query for failure counts (n)
- 3. Estimate component exposure (T) and uncertainty
- 4. Develop component failure rate prior distributions for each DM
- 5. Perform Bayes update for each exposure case (combination of weld count and DM susceptibility)
- 6. Apply posterior weighting to combine results for different hypothesis yield conditional failure rate distributions; compute unconditional failure rates for locations with uncertain DM status
- 7. Develop conditional probability of rupture size given failure probabilities for each weld type and associated epistemic uncertainties
- 8. Combine the results of Step 6 and Step 7 by Monte Carlo in Eq. (1) for component LOCA frequencies and total LOCA frequencies for each component
- 9. Apply Markov Model to specialize rupture frequencies for differences in integrity management
- 10. For intermediate LOCA categories and break sizes, interpolate the results of Step 10 via log-log linear interpolation
- 11. Calculate total LOCA frequencies from all components and reconcile differences with earlier LOCA frequency estimates 7/5/11 Pre-Licensing Meeting 46
Step 8 Calculate Component LOCA Frequencies
- Need to calculate LOCA frequencies for each component
Break Size
- Calculated via Monte Carlo simulation by sampling from the applicable failure rate and CRP distributions
- Will be performed on a STP specific basis for each component 7/5/11 Pre-Licensing Meeting 47
Step 8 Calculate Component LOCA Frequencies
- Base Case Results
- Assume all BJ welds are susceptible to thermal fatigue (TF) and D&C
- All BC welds are susceptible to TF and D&C
- All BF welds are susceptible to SC and D&C
- Sensitivity Case
- Assume no BJ welds are susceptible to TF
- Assume BF welds mitigate SC via weld overlay
- Other assumptions same as Base Case 7/5/11 Pre-Licensing Meeting 48
LOCA Frequencies for Each Weld Type Distribution Parameters (1)
Weld Type Parameter RF Mean 5%tile 50%tile 95%tile Failure Rate 5.61E-04 1.37E-04 4.38E-04 1.40E-03 3.2 Category 1 2.13E-05 1.44E-07 3.81E-06 9.35E-05 25.5 Category 2 1.03E-05 2.44E-08 1.01E-06 4.26E-05 41.7 B-F Category 3 6.71E-06 6.94E-09 4.10E-07 2.38E-05 58.6 Category 4 3.67E-06 1.55E-09 1.36E-07 1.16E-05 86.6 Category 5 2.22E-06 4.27E-10 5.05E-08 5.95E-06 118.0 Failure Rate 4.16E-06 4.16E 06 9.75E-09 9.75E 09 2.91E-07 2.91E 07 1.17E-05 1.17E 05 34.7 Category 1 1.43E-07 2.65E-11 2.58E-09 2.87E-07 104.1 Branch Category 2 8.14E-08 5.02E-12 6.87E-10 1.12E-07 149.3 Connection Category 3 4.35E-08 1.51E-12 2.81E-10 5.73E-08 194.9 Category 4 2.87E-08 3.68E-13 9.32E-11 2.55E-08 263.1 Category 5 1.45E-08 1.06E-13 3.45E-11 1.23E-08 339.4 Failure Rate 2.03E-07 2.66E-11 2.86E-09 3.74E-07 118.6 Category 1 4.38E-08 1.12E-12 2.68E-10 6.33E-08 238.3 Category 2 2.13E-08 2.34E-13 7.40E-11 2.38E-08 319.0 B-J Category 3 1.49E-08 7.21E-14 2.98E-11 1.15E-08 398.5 Category 4 8.68E-09 1.85E-14 9.77E-12 4.92E-09 515.9 Category 5 2.07E-09 1.26E-13 2.23E-11 3.84E-09 175.0 Note (1) RF = SQRT(95%tile/5%tile) 7/5/11 Pre-Licensing Meeting 49
LOCA Frequencies for Surge Line Distribution Parameters (2)
Weld Type Parameter RF Mean 5%tile 50%tile 95%tile Failure Rate 5.71E-04 1.37E-04 4.39E-04 1.42E-03 3.2 Category 1 2.19E-05 1.44E-07 3.81E-06 9.45E-05 25.6 Base Case Category 2 1.06E-05 2.45E-08 1.02E-06 4.29E-05 41.9 Total Surge (1) Category 3 6.90E-06 6.94E-09 4.11E-07 2.40E-05 58.8 Line Category 4 3.79E-06 1.55E-09 1.36E-07 1.17E-05 86.9 Category 5 2.26E-06 4.28E-10 5.07E-08 6.00E-06 118.4 Total Surge Failure Rate 1.50E-05 2.37E-08 9.77E-07 5.13E-05 46.5 Line Case with Category 1 4.39E-07 5.35E-11 5.45E-09 7.25E-07 116.4 B-F weld Category 2 3.04E-07 1.01E-11 1.46E-09 3.02E-07 172.9 overlay and no TF Category 3 1.90E-07 3.04E-12 6.01E-10 1.68E-07 235.3 Susceptibility Category 4 1.46E-07 7.41E-13 2.02E-10 8.45E-08 337.8 for B-J welds Category 5 8.73E-08 2.17E-13 8.12E-11 5.29E-08 493.6 Note (1) Total surge line results are based on 1 B-F weld, 2 BC welds, and 6.9 B-J welds.
(2) RF = SQRT( 95%tile/5%tile) 7/5/11 Pre-Licensing Meeting 50
Comparison of Calculated Surge Line LOCA Frequencies 7/5/11 Pre-Licensing Meeting 51
Step by Step Procedure
- 1. Determination of weld types (i)
- 2. Perform data query for failure counts (n)
- 3. Estimate component exposure (T) and uncertainty
- 4. Develop component failure rate prior distributions for each DM
- 5. Perform Bayes update for each exposure case (combination of weld count and DM susceptibility)
- 6. Apply posterior weighting to combine results for different hypothesis yield conditional failure rate distributions; compute unconditional failure rates for locations with uncertain DM status
- 7. Develop conditional probability of rupture size given failure probabilities for each weld type and associated epistemic uncertainties
- 8. Combine the results of Step 6 and Step 7 by Monte Carlo in Eq. (1) for component LOCA frequencies and total LOCA frequencies for each component
- 9. Apply Markov Model to specialize rupture frequencies for differences in integrity management
- 10. For intermediate LOCA categories and break sizes, interpolate the results of Step 10 via log-log linear interpolation
- 11. Calculate total LOCA frequencies from all components and reconcile differences with earlier LOCA frequency estimates 7/5/11 Pre-Licensing Meeting 52
Step 9 Markov Model
Background
- Purpose of model is to evaluate the impact of changes to inspection on pipe failure rates
- Markov Model originally developed for EPRI RI-ISI Program
- Applied to 26 plant specific RI-ISI programs in U.S. and South Africa
- Applied pp to PBMR to support pp new ASME Code development p for in-service inspections
- Applied in NUREG-1829 LOCA frequency update
- Currently being applied to address CANDU feeder pipe cracking issue
- Enhanced version of model developed in DOE/INL RISMC to address aging issues; transition rates based on physics of failure 53 7/5/11 Pre-Licensing Meeting
Markov Model Of Pipe Element S
Pipe Element States
S - success, no detectable damage F - detectable flaw L - detectable leak F R - rupture
State Transition Rates
- flaw occurrence rate F L - leak failure rate F - rupture failure rate given flaw L - rupture failure rate given leak L - repair rate via ISI exams
- repair rate via leak detection R
7/5/11 Pre-Licensing Meeting 54
Estimating Input Parameters
- Degradation related parameters
- Uses failure rates for flaws and leaks and rupture frequencies as developed in previous slides
- Leaks estimated using leak data and conditional leak given failure model similar to that used for ruptures
- Flaws estimated as a multiple of leaks based on insights from service data
- Modeled solved separately for each rupture mode (LOCA category)
- Test and inspection parameters estimated using simple and easy to quantify models
- One model for leak tests and inspections
- One model for NDE 55 7/5/11 Pre-Licensing Meeting
Modeling Impact Of NDE Inspections
- Capture by : the repair rate for flaws PF I PF D
=
(T I + TR )
where:
- PFI = probability that segment element with flaw will be inspected
- PFD= probability that flaw is detected given inspection
- TI = mean time between inspections
- TR = mean time to repair after detection is set to 0.0 for weld that is not in ISI program 56 7/5/11 Pre-Licensing Meeting
Modeling Impact of Leak Tests and Inspections
- Capture by : the repair rate for leaks PLD
=
( TLI + TR )
where:
- PLD= probability that leak is detected given inspection
- TI = mean time between inspections
- TR = mean time to repair after detection is set to 0.0 if there is no leak inspections 57 7/5/11 Pre-Licensing Meeting
Example Application of Markov Model to Evaluate Strategies for Fire Protection Piping 1.0E-04 Frequency of Rupture Size Greater than o or Equal to X (events per ROY-ft.)
Current Study w/ WH 1.0E-05 Current Study no WH EPRI 1013141 FP NPS > 10" Current Study No WH + Yearly Leak Test Current Study No WH + Quaterly Leak Test 1.0E-06 1.0E-07 1.0E-08 1.0E-09 0.01 0.10 1.00 10.00 100.00 X, Equivalent Break Size (in.)
58 7/5/11 Pre-Licensing Meeting
BWR Recirculation Pipe LOCA Frequency Example from NUREG-1860 1.0E-04 No ISI/No Leak Inspection No ISI/ Leak Inspection 1/Refueling Outage No ISI/ Leak Inspection 1/Week ISI/Leak Inspection 1/Refueling Outage BWR Recirculation Piping LO OCA Frequency/year 1.0E-05 ISI/Leak Inspection 1/Week 1.0E-06 1.0E-07 1.0E-08 1.0E-09 5 15 25 35 45 55 Plant Age (Years) 59 7/5/11 Pre-Licensing Meeting
Impact of RIM Strategies on SC Susceptible RCS Weld Failure Rate (2005 RI-ISI for Koeberg) 7/5/11 Pre-Licensing Meeting 60
Step by Step Procedure
- 1. Determination of weld types (i)
- 2. Perform data query for failure counts (n)
- 3. Estimate component exposure (T) and uncertainty
- 4. Develop component failure rate prior distributions for each DM
- 5. Perform Bayes update for each exposure case (combination of weld count and DM susceptibility)
- 6. Apply posterior weighting to combine results for different hypothesis yield conditional failure rate distributions; compute unconditional failure rates for locations with uncertain DM status
- 7. Develop conditional probability of rupture size given failure probabilities for each weld type and associated epistemic uncertainties
- 8. Combine the results of Step 6 and Step 7 by Monte Carlo in Eq. (1) for component LOCA frequencies and total LOCA frequencies for each component
- 9. Apply Markov Model to specialize rupture frequencies for differences in integrity management
- 10. For intermediate LOCA categories and break sizes, interpolate the results of Step 10 via log-log linear interpolation
- 11. Calculate total LOCA frequencies from all components and reconcile differences with earlier LOCA frequency estimates 7/5/11 Pre-Licensing Meeting 61
Step 9 Application of Markov Model
- Failure rates and rupture frequencies calculated in Step 8 are for an average integrity management program
- For Class 1 welds in the service data an average integrity management has
- 25% that are included in NDE program and subjected to leak testing once every refueling cycle
- 75% that are not included in NDE program and subjected to leak testing once every refueling cycle
- For STP welds the integrity management factors will be:
- Greater than 1.0 for welds not in ISI program
- Less than 1.0 for welds in ISI program
- If some specific weld locations have an unusually high potential for debris induced core damage, inspection locations can be added or changed to offset risk impacts 7/5/11 Pre-Licensing Meeting 62
Steps 10 Interpolation for Intermediate LOCA Sizes
- LOCA categories used in PRA and NUREG-1829 are defined as discrete ranges over continuum of possible break sizes
- Results of expert elicitation for 6 LOCA categories are well behaved
- For a given pipe size there is no reason to expect sharp discontinuties over the range of possible break sizes
- STP model will extrapolate curves to account for double ended break of each pipe at the location of the weld 7/5/11 Pre-Licensing Meeting 63
Step 11 Aggregation of Results for PRA Model
- LOCA frequency distributions to be developed for all unique weld-types typified by pipe size, weld type, DM status, and NDE program status and assigned to each location for Case Grande debris formation analysis
- Results will be probabilistically summed up over each PRA LOCA category (small, medium, large LOCA) via Monte Carlo 7/5/11 Pre-Licensing Meeting 64
Step 12
- Results of Step 11 will be compared against other available LOCA frequency sources, e.g. NUREG-1150, NUREG/CR-5750
- Differences will be identified and reconciled; may lead to refinements in technical approach 7/5/11 Pre-Licensing Meeting 65
Technical Issues
- Need to better understand aggregation methods used in NUREG-1829 and reason why uncertainties in aggregated results appear much smaller than those of the component level expert estimates
- Need to resolve questions about whether all the experts i NUREG in NUREG-1829 1829 provided id d cumulative l ti vs. di discrete t input i t
- Need to confirm that CRP method can be easily extended to other components
- Need to incorporate insights about DMs since EPRI RI-ISI program developed 7/5/11 Pre-Licensing Meeting 66
Summary of LOCA Frequency Approach
- Method of deriving CRP distributions from NUREG-1829 has been demonstrated for hot leg, surge line, and HP injection line; appears to be applicable to other components
- Adjustments needed to prevent CRP from exceeding 1.0
- CRP method combined with failure rate uncertainty y method yields very large uncertainties in component level LOCA frequencies
- Capability to specialize frequencies to address key variables impacting pipe reliability (e.g. pipe size, materials, damage mechanisms, inspection status)
- Capability to augment RI-ISI program to optimize NDE element selection 7/5/11 Pre-Licensing Meeting 67
For more information, please contact:
Karl Fleming fleming@ti-sd.com Bengt Lydell bly@scandpower.com Karl Fleming Consulting Service LLC 68 7/5/11 Pre-Licensing Meeting