ML111890380
| 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
J l 7 2011 7/5/11 Pre-Licensing Meeting 1
Thursday, July 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
Discussion Topics
- LOCA frequencies scope and objectives
- Technical approach
- Step by step procedure with examples Risk Informed GSI-191 7/5/11 Pre-Licensing Meeting 2
Step by step procedure with examples
- Technical issues to be addressed
- Resolution of NRC questions from June 2011 meeting
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 e g speed Risk Informed GSI-191 Other break characteristics, e.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
=
i ix i
x m
LOCA F
)
(
(1) ik ik x
k ik ix jx I
F R
P
)
(
=
=
(2)
Where:
=
)
(
x LOCA F
Frequency of LOCA of size x, per reactor calendar-year; subject to epistemic uncertainty calculated via Monte Carlo
=
i m
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 5
7/5/11 Pre-Licensing Meeting (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)
=
)
(
ik x F R
P 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)
=
ik I
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.
LOCA IE Frequency Model 2 of 2 For a Point Estimate of the Failure Rate for type i and failure mechanism k:
i i
ik ik ik ik ik T
N f
n n
=
=
(3)
=
ik n
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 6
7/5/11 Pre-Licensing Meeting expert opinion
=
ikf 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.
=
i N
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
=
iT Total number of reactor years exposure for the data collection for component type i; little or no uncertainty
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 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
- 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 Example chosen SYSTEM Nominal Pipe Size (NPS)
Pipe Failures by Mode (1), (2), (3)
Total Crack-Full Crack-Part Small Leak Leak Large Leak CVC 1"
7 1
6 2" ø 4" 7
1 6
Safety Injection 1"
2 2
4" ø 10" 6
3 1
1 1
Pressurizer-Sample 2"
5 4
1 Pressurizer-PORV 4" ø 10" 2
2 Pressurizer-SPRAY 1"
4 1
2 1
4" ø 10" 3
2 1
7/5/11 Pre-Licensing Meeting 9
Example chosen to illustrate FR Approach Pressurizer-SRV 4" ø 10" 7
6 1
Pressurizer-Surge 14" 3
3 RCS 2"
76 4
10 53 4
5 RCS Cold Leg 32" 4
4 RCS Hot Leg 32" 6
5 1
RHR 1"
6 6
RHR 4" ø 10" 1
1 RC Hot Leg - S/G-Inlet 32" 19 19 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.
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 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 WE Type Rx Reactor-Calendar Years Initial Grid Connection Initial Criticality 7/5/11 Pre-Licensing Meeting 12 Connection 2-Loop 570.1 581.4 3-Loop 2052.6 2096.1 4-Loop 1193.9 1236.5 Total 3816.6 3914
Data for Estimating Surge Line Weld Population Plant PWR Type Weld Population[Note (1)]
B-F Welds Inline B-J Welds Branch Connection to 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 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 Location Confidence Level Weld Susceptibility Fractions C-F D&C ECSCC Fretting IGSCC PWSCC TF TGSCC TAE V-F B-F 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 B-J 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 RC-HL Branch C
ti Low N/A 1
N/A N/A N/A N/A 1
N/A N/A N/A
/
/
/
/
/
/
/
/
Connection 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 7/5/11 Pre-Licensing Meeting 15 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
Example DM evaluation for Surge Line Welds
- 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 S
l t t l
t i bilit i b
f b h
ti
- Some plant to plant variability in number of branch connections
- 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 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)
Exposure 7/5/11 Pre-Licensing Meeting 18 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)
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 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)
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
Example Prior Distributions Damage Mechanism Prior Distribution (Failures per Weld-Year)
Dist. Type Mean Median Range 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 t
di t ib ti t
diti l f il t
f l
ti ith t i 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 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 update for
- For each failure rate we perform 1 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 and DM[Note (3)]
Weld Count Case DM Susceptibility Case Prior Distribution[Note (1)]
Evidence[Note (2)]
Bayes Posterior Distribution[Note (1)]
Type Median RF Failures Exposure Mean 5th 50th 95th RF 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 BJ TF Low Medium Lognormal 2.66E-07 100 0
675 7.17E-06 2.64E-09 2.61E-07 2.36E-05 94.6 g
g 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 f il t
i diti l ( f i E
(3) 1)
- TF failure rate is unconditional ( f in Eq. (3)= 1)
Case 3 FR for B-J weld not susceptible to TF
- Includes only contributions from D&C 7/5/11 Pre-Licensing Meeting 27 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
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 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 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 3 Set Target LOCA frequencies that encompass
- Step 7.3 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 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 Component LOCA Category Break Size (in.)
Distribution Input Parameters Truncated Distribution Parameters Type Median
[Note (1)
Range Factor Median Mean 5%tile 95%tile RCS-Hot Leg 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 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 Lognormal truncated at 1.0 6
31.5 2.20E-07 7.53E+01 2.19E-07 6.79E-06 2.96E-09 1.66E-05 RCS-Surge Line 1
.5 4.73E-02 1.40E+02 4.73E-03 1.19E-01 2.66E-04 6.11E-01 2
1.5 6.06E-03 1.92E+02 6.06E-03 5.83E-02 2.89E-05 3.49E-01 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 HPI Line 1
.5 5.85E-03 2.20E+01 5.78E-03 2.15E-02 3.77E-04 8.88E-02 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 LOCA Category Break Size (in.)
Distribution Type (1)
Distribution Parameters(2)
Mean 5%tile 50%tile 95%tile Range 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 1 75E 02 6 75E 05 3 17E 03 8 45E 02 35 4 7/5/11 Pre-Licensing Meeting 45 Posterior Lognormal Binomial 1.75E-02 6.75E-05 3.17E-03 8.45E-02 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)
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 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
y 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 Weld Type Parameter Distribution Parameters RF(1)
Mean 5%tile 50%tile 95%tile B-F 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 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 9.75E-09 2.91E-07 1.17E-05 34.7 7/5/11 Pre-Licensing Meeting 49 Branch Connection Failure Rate 4.16E 06 9.75E 09 2.91E 07 1.17E 05 34.7 Category 1 1.43E-07 2.65E-11 2.58E-09 2.87E-07 104.1 Category 2 8.14E-08 5.02E-12 6.87E-10 1.12E-07 149.3 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 B-J 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 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)
LOCA Frequencies for Surge Line Weld Type Parameter Distribution Parameters RF(2)
Mean 5%tile 50%tile 95%tile Base Case Total Surge Line(1)
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 Category 2 1.06E-05 2.45E-08 1.02E-06 4.29E-05 41.9 Category 3 6.90E-06 6.94E-09 4.11E-07 2.40E-05 58.8 Category 4 3.79E-06 1.55E-09 1.36E-07 1.17E-05 86.9 7/5/11 Pre-Licensing Meeting 50 Category 5 2.26E-06 4.28E-10 5.07E-08 6.00E-06 118.4 Total Surge Line Case with B-F weld overlay and no TF Susceptibility for B-J welds Failure Rate 1.50E-05 2.37E-08 9.77E-07 5.13E-05 46.5 Category 1 4.39E-07 5.35E-11 5.45E-09 7.25E-07 116.4 Category 2 3.04E-07 1.01E-11 1.46E-09 3.02E-07 172.9 Category 3 1.90E-07 3.04E-12 6.01E-10 1.68E-07 235.3 Category 4 1.46E-07 7.41E-13 2.02E-10 8.45E-08 337.8 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)
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 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 to PBMR to support new ASME Code development for pp pp p
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
F
S F
S F
Pipe Element States S - success, no detectable damage F - detectable flaw L - detectable leak R - rupture L
R
F L
L R
L R
F L
State Transition Rates
- flaw occurrence rate
- leak failure rate F - rupture failure rate given flaw L - rupture failure rate given leak
- repair rate via ISI exams
- repair rate via leak detection 54 7/5/11 Pre-Licensing Meeting
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
(
)
=
+
P P
T T
F I F D I
R 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
(
)
+
T T
I R
56 7/5/11 Pre-Licensing Meeting
Modeling Impact of Leak Tests and Inspections
- Capture by : the repair rate for leaks
=
+
P T
T LD LI R
(
)
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
+
T T
LI R
(
)
57 7/5/11 Pre-Licensing Meeting
Example Application of Markov Model to Evaluate Strategies for Fire Protection Piping 1.0E-06 1.0E-05 1.0E-04 or Equal to X (events per ROY-ft.)
Current Study w/ WH 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-09 1.0E-08 1.0E-07 0.01 0.10 1.00 10.00 100.00 X, Equivalent Break Size (in.)
Frequency of Rupture Size Greater than o 58 7/5/11 Pre-Licensing Meeting
BWR Recirculation Pipe LOCA Frequency Example from NUREG-1860 1.0E-06 1.0E-05 1.0E-04 OCA Frequency/year No ISI/No Leak Inspection No ISI/ Leak Inspection 1/Refueling Outage No ISI/ Leak Inspection 1/Week ISI/Leak Inspection 1/Refueling Outage ISI/Leak Inspection 1/Week 1.0E-09 1.0E-08 1.0E-07 5
15 25 35 45 55 Plant Age (Years)
BWR Recirculation Piping LO 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 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 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 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 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 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 1829 id d l ti di t
i t
in NUREG-1829 provided cumulative vs. discrete input
- 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 method y
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