1. An Approach to Evaluation of Uncertainties in Level 2 PSAs
T. Ishigami, J. Ishikawa, K. Shintani,
M. Mayumi and K. Muramatsu
Japan Atomic Energy Research Institute
OECD/NEA/CSNI/WGRISK Workshop, Cologne,
March , 2004

2. Introduction Background
PSA application study at JAERI on safety goals, emergency planning, basic technical study for legal system for compensation of nuclear damage, and so on
The first phase PSA at JAERI in 1990 did not address AM, source terms for energetic events, and uncertainty
Uncertainty is one of the most important issues in PSA application
Purpose of This Study
To develop an uncertainty analysis method for Level 2 PSA
JAERI

3. Study on Uncertainty Evaluation at JAERI
Type of Uncertainties
Parameter uncertainty
Model uncertainty
Completeness uncertainty
　Parameter and model uncertainties are addressed in this study
Study on Uncertainty Evaluation at JAERI
Development and improvement of computer codes
Assessment of uncertain parameters
Development of uncertainty analysis method for source terms
JAERI

4. Framework of uncertainty analysis for Level 2 PSA
Analysis step
Uncertain parameters
Core damage frequency analysis
・Component
failure rates etc.
Resources
・Existing PSA 　　　　results
・Analysis method 　　(DET, ROAAM)
・Experiment
　- Steam explosion　- Release of fission 　 products from 　　 fuel
SAPHIRE
Accident progression analysis
Uncertainty analysis
・CET branch 　　 　probabilities etc.
PREP/SPOP
CET
・Release rates of 　　　fission products 　　from fuel 　etc.
Source term　analysis
THALES2
Frequency of exceeding X
95%
50%
Computer codes
　　SAPHIRE: System analysis
　　CET: Containment ET analysis
　　THALES2: Sever accident analysis
　　PREP/SPOP:Uncertainty propagation analysis 5%
Source term, X
Conceptual figure of uncertainty analysis results
JAERI

5. Computer Codes SAPHIRE (USNRC) CET Analysis Code (JAERI)
- Analysis of core damage frequency with ET/FT model
- Capability of uncertainty analysis
CET Analysis Code (JAERI)
- Analysis of containment function failure probability
- Object-oriented programming
THALES2 (JAERI)
Integrated severe accident analysis code
Analysis of thermal hydraulics and fission product transport
PREP/SPOP (JRC Ispra)
- Analysis of parameter uncertainty propagation through a model
- Monte Carlo or Latin Hypercube sampling method
JAERI

6. Assessment of Uncertain Parameters - Core Damage Frequency and Accident Progression Analyses -
Approach
Component failure rates
Use of the failure rates evaluated by Central Research Institute of Electric Power Industry from operation data of 49 Japanese plants for 16 years ( )
CET branch probabilities for CV failure modes
Overpressure
Overtemperature
Steam explosion
Direct containment heating
Hydrogen burning
Survey of recent experimental and analytical research results
Use of analytical methods such as DET and ROAAM
- Probability of containment failure due to energetic events
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7. Example of Assessment of Uncertain Parameter - Probability of Containment Failure due to Ex-Vessel Steam Explosion at PWR -
Possible phenomena
Steam explosion at cavity
Load energy brought into containment
Cavity wall failure
Loss of containment integrity at penetration
Piping tenseness
Movement of reactor vessel
“Load energy > Critical load energy ” 　　“Loss of containment integrity”
Preceding analysis for Japanese APWR (Nuclear Safety Research Association)
Point estimate with DET method
Survey of research results
Structural analysis
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8. Present Analysis for 4-loop PWR
Approach
Use of the DET for APWR
Similar physical processes at both plants
Type of containment is PCCV at both plants
Reevaluation of physical quantities depending on plants
Flow rate of molten core at large scale RV failure
Critical load energy resulting in containment failure
→ These quantities were scaled according to reactor powers of 　　 the two plants (APWR: 4,451MWt, PWR: 3,411MWt)
New Feature
Evaluation of uncertainty in containment failure probability caused by uncertainties in
Branch probabilities of “reactor vessel failure mode (large/small)” and “Occurrence of triggering (Yes/No)”, and
Aleatory and epistemic uncertainties were addressed
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9. Decomposition Event TreeRV
Failure
Mode
Melt
Flow
Rate
Internal
Energy
Triggering
Mass in
Premixture
Conversion
Load
Probability
Small
Scale
Large
Low
High No
Yes
Medium E1 E2 E3 En
・・・・・・・・・・
Lower
Higher
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10. Aleatory and Epistemic Uncertainties
Aleatory uncertainty : Randomness or stochastic properties
Epistemic uncertainty : Lack of our knowledge,
Possible to reduce
Treatment in present analysis
Uncertainties in the branch probabilities : Epistemic
Uncertainty in the critical load energy (capacity) of the containment: Aleatory and epistemic
Epistemic
Critical load energy
PDF
Aleatory
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11. Cumulative probability of
Probability Distribution of Load Energy and Containment Failure Probability
Load energy (MJ)
0.0
0.2
0.4
0.6
0.8
1.0
200
400
600
800
Cumulative probability of
containment failure 5%
50%
95%
Load energy (MJ)
Aleatory
Epistemic
Scenarios with higher load energy caused from larger size of RV failure contribute to containment failure
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12. Uncertainty Analysis Result of Containment Failure Probability (conditional probability)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 1
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
Containment failure probability
Cumulative probability
Aleatory
Epistemic
(Dotted line)
Aleatory+Epistemic
(Solid line)
Uncertainty range : 0 – (95th)
Epistemic uncertainty is dominant
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13. Uncertainty Analysis Method for Source Terms
Subject
Approach
A large number of accident sequences
Uncertainty propagation
Parameter uncertainty
Model uncertainty
Classification of sequences
Direct use of THALES2, instead of parametric model (XSOR in NUREG-1150), with Monte Carlo simulation
Survey of recent experimental and analytical research results
Comparison of the model results with experimental data or different model results
Repeated calculation X1 X2
Code
(THALES2)
・・・ Y
Input Parameters
Output
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14. Classification of sequences for uncertainty analysis (BWR Mark-II)
Sequence group
PRV Pressure
Sequences subgroup
Loss of containment heat removal function with high pressure coolant injection available
High ～ Medium
Transient or SB-LOCA
Medium ～ Low
MB- ～ LB-LOCA
Low
Transient with reactor depressurized by failure of SRV reclose
Loss of containment heat removal function with low pressure coolant injection available
Transient or SB-　～　LB-LOCA
Loss of coolant injection
Station blackout
Anticipated transient without scram (ATWS)
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15. Uncertain Parameters in THALES2 and Parametric Model
Uncertain parameters is denoted by ＊
THALES2 ＊ ＊ ＊ ＊
-Failure pressure
Input
Heat transfer coefficient
Release rate coefficient
Deposition rate ・・
・・・
・・・
・・・
-Size of rupture
Thermal-Hydraulic behavior
Release from fuel
FP behavior in RV
・・・
Environmental release
Model
　　　　Data
Calculated
Release fraction from fuel
Pressure
Temperature
Release fraction from RV
Release fraction to the environment
Parametric
Model ＊ ＊
Release fraction from fuel
Release fraction from RV
Release fraction to the environment ×
・・・ ＝
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16. Comparison of the two Methods
Direct Use of Code Parametric Model
- Rather fundamental 　　(Some are related to 　　experimental data)
- Not fundamental (To 　　be obtained from a 　　　model)
Characteristics of uncertain parameters
- Less dependent on 　　time or sequence 　　
- Dependent on time 　　　and sequence 　
- Individual representative 　sequence in a set of 　　　sequences classified by
　state of safety systems
- Possible to compare the 　results with different 　　model results
- a set of sequences classified by physical state (Zr-oxidation level, RCS pressure)
- Difficult to assess the results
Accident sequences to be analyzed
Calculation time
- Long
- Short
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17. Approach to Assessment of Uncertain Parameters
Survey preceding PSAs (NUREG-1150) and comparative study of THALES2 and MELCOR to determine uncertain parameters
Select parameters in THALES2 relating to the above uncertain parameters
- Representative parameters are selected to reduce the number of uncertain parameters
e.g. One correction factor for deposition rate in RCS for all 　　　 the deposition mechanisms
Determine the uncertainties by surveying recent experimental and analytical research results as well as preceding PSA study
- Experiments on FCI (FARO, COTELS, …)
- Experiment on FP release from fuel (VEGA,…) etc.
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18. Associated parameters
An example of uncertain items and associated parameters in THALES2 (BWR Mark-II)
Uncertain items
Associated parameters
Release of FPs from Fuel (in-vessel)
Release rate of FPs
Coolability of molten core (in-vessel)
Heat transfer coefficient between molten core and coolant/or lower head wall
Fraction of fragmented molten core in FCI
Average particle size of molten core droplets
Deposition of FPs (in-vessel)
Deposition rate of FPs to the wall
Deposition rate of FPs to the floor
Deposition of FPs (ex-vessel)
Release of FPs from molten core (ex-vessel)
- Release rate of FPs
Coolability of molten core (ex-vessel)
- Heat transfer coefficient between molten core and coolant
Integrity of containment
Failure pressure by overpressure
Size of rapture
Pool scrubbing
Size of bubble
Rising velocity of bubble
LOCA
- Break size in LOCA
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19. Summary
Study on developing uncertainty analysis method for Level 2 PSA at JAERI includes
Development and improvement of computer codes
Assessment of uncertain parameters
Development of uncertainty analysis method for source terms
To quantify uncertain parameters
- Recent experimental and analytical research results are surveyed
- Analytical method such as DET is used to evaluate uncertainty in 　　　containment failure probability due to steam explosion, where 　　　　　　aleatory and epistemic uncertainties are considered
Uncertainty analysis method for source terms is
　　- Direct use of THALES2 with Monte Carlo simulation, where
- Uncertain parameters in THLES2 are assessed by surveying recent 　　research results
JAERI