Risk Analysis Framework for Severe Accident Mitigation Strategy in Nordic BWR: An Approach to Communication and Decision Making

Transcription

1 International Topical Meeting on Probabilistic Safety Assessment And Analysis, PSA 2017, September 24-28, Pittsburgh, PA. Risk Analysis Framework for Severe Accident Mitigation Strategy in Nordic BWR: An Approach to Communication and Decision Making Sergey Galushin, Dmitry Grishchenko, Pavel Kudinov Division of Nuclear Power Safety Royal Institute of Technology (KTH) Stockholm, Sweden

2 Motivation: Nordic BWR Severe Accident Severe accident mitigation strategy in Nordic BWRs: Lower drywell is flooded with water to prevent cable penetrations failure in the containment floor. Core melt is released from the vessel into (7-12 m) deep water pool. The melt is expected to fragment quench and form a coolable debris bed. Threats to containment integrity Steam explosion. Formation of non-coolable debris bed. depend on melt release and pool conditions. Melt release and pool conditions are affected by the accident progression uncertainty: Epistemic (phenomena) Aleatory (scenarios). Risk uncertainty in effectiveness of the strategy for preventing containment failure. 2

3 ROAAM+ framework ROAAM+ framework is currently under development in KTH, for quantification of the conditional threats to containment integrity The ROAAM+ framework for Nordic BWR decomposes severe accident progression into a set of connected causal relationships (CR) Each CR is represented by respective surrogate model (SM) Computational efficiency of the framework is necessary for extensive sensitivity and uncertainty analysis in forward (failure probability) and reverse (failure domain) analyses: 3

4 Goals and tasks The ultimate goal of ROAAM+ application for Nordic BWR is to provide a scrutable background in order to achieve convergence of experts opinions in decision making: Keep SAM strategy: Possibility of containment failure is low even with conservative treatment of uncertainty, thus current strategy is reliable» classical ROAAM, focus on failure domain : is it sufficiently small?. Modify SAM strategy: Necessity of containment failure in the course of accident is high» i.e. possibility that containment doesn t fail is low even with optimistic treatment of uncertainty, thus the current strategy is unreliable and changes should be considered. Focus on safety domain : is it sufficiently large? (Improve knowledge) Task: Develop an approach for communication of ROAAM+ results. Develop a decision support model. 4

5 Approach to risk assessment in ROAAM+ 5

6 6 Quantitative Definition of Risk The risk R i associated with specific scenario s i can be characterized by its frequency f i and consequences c i. Consequences result from an assessment which is subject to uncertainty due to incomplete knowledge. Such epistemic uncertainty (or degree of confidence) can be quantified as probability P i (likelihood) of c i R i = s i, f i, P i c i (1) Separation of epistemic and aleatory uncertainties is one of the cornerstones of ROAAM.

7 Failure probability For each plant damage state D i there is a set of respective scenarios s ii characterized by frequencies (f ii ). Scenarios (s i ) define combinations of initial and boundary conditions for causal relationships (CR) and structure of the framework. The CR provides assessment of the load (L i ) and the capacity (C i ). Epistemic uncertainty is introduced by multidimensional probability density function (ppp d i, i i ) of intangible (i i ) and deterministic (d i ) modeling parameters. These distributions determine the probability of failure (P FF = P L i C i ) in scenario (s i ). P FF = P L i C i = pdf Ci L i c, l dddd L i C i s i, f i CR [SM] pdf Load=L i Capacity=C i Modeling Parameters pdf d i, i i Failure Probability=P Fi System parameters 7

8 8 Second Order Probability - ROAAM+ In ROAAM+ framework for Nordic BWR we use the concept of second-order probability in quantification of conditional containment failure probability. The need for the second-order probabilities comes from the nature of epistemic uncertainties in prediction of failure probability (i.e. partial probabilistic knowledge). Modelling (i.e. epistemic uncertain) parameters in ROAAM+ framework are separated into two groups: Model deterministic parameters complete probabilistic knowledge (i.e. range and probability distribution). Model intangible parameters partial probabilistic knowledge (i.e. one can only speculate regarding the possible range and expected type(s) of distribution).

9 9 Treatment of Model Intangible Parameters For given p k different values of P f, including the bounding ones, can be obtained by sampling in the space of the distributions. Result of the sampling is presented as a complementary cumulative distribution function CCCC(P F ) 1 Scenario parameters s i Input p N 1,i CC N p N,i = L, C Output ppp 1 (L, C) P FF (ppp 1 (i NN )) Complimentary Cumulative Distribution Function CCDF of Pf for fixed value of p N 1,i Intangible parameters ppp 1 (i NN ) P F (p N 1,i ) P FF P F

10 10 Treatment of Model Intangible Parameters For given p k different values of P f, including the bounding ones, can be obtained by sampling in the space of the distributions. Result of the sampling is presented as a complementary cumulative distribution function CCCC(P F ) 1 Scenario parameters s i Input p N 1,i CC N p N,i = L, C Output ppp 1 (L, C) P FF (ppp 1 (i NN )) ppp 2 (L, C) P F2 (ppp 2 (i NN )) Complimentary Cumulative Distribution Function CCDF of Pf for fixed value of p N 1,i Intangible parameters ppp 1 (i NN ) ppp 2 (i NN ) P F (p N 1,i ) P FF P F2 P F

11 11 Treatment of Model Intangible Parameters For given p k different values of P f, including the bounding ones, can be obtained by sampling in the space of the distributions. Result of the sampling is presented as a complementary cumulative distribution function CCCC(P F ) Complimentary Cumulative Distribution Function CCDF of Pf for fixed value of p N 1,i 1 Scenario parameters s i Input p N 1,i Intangible parameters CC N ppp 1 (i NN ) ppp 2 (i NN ) ppp M (i NN ) p N,i = L, C Output ppp 1 (L, C) P FF (ppp 1 (i NN )) ppp 2 (L, C) P F2 (ppp 2 (i NN )) ppp M (L, C) P FM (ppp M (i NN )) P F (p N 1,i ) P FF P F2 P FM P F

12 12 Treatment of Model Intangible Parameters For given p k different values of P f, including the bounding ones, can be obtained by sampling in the space of the distributions. Result of the sampling is presented as a complementary cumulative distribution function CCCC(P F ) Complimentary Cumulative Distribution Function CCDF of Pf for fixed value of p N 1,i 1 Scenario parameters s i p N,i = L, C Output Input p N 1,i CC N ppp 1 (i NN ) ppp 2 (i NN ) ppp M (i NN ) ppp 1 (L, C) P FF (ppp 1 (i NN )) ppp 2 (L, C) P F2 (ppp 2 (i NN )) ppp M (L, C) P FM (ppp M (i NN )) P F (p N 1,i ) P FF P F2 P FM P F

13 How do we use CCDF of Pf? From the interval analysis (P-box shown in the Figure), we can only say that P f is between 0 and 1. Such information is not very helpful for making conclusions on the risk acceptance. For every vector of the input parameters p i we compute a CCDF of Pf. For green point in p i : 95% of the possible P f values are below the screening frequency. For blue point in p i : 50% of the possible P f values exceed screening frequency. For red point in p i : 95% of the possible P f values exceed screening frequency. The system is not safe with most (>95%) of the considered distributions of intangible parameters. Improvement of knowledge about actual distribution of intangible parameters is not likely to change the decision. For green and red points It is possible to identify specific probability distributions of model intangible parameters that result in P f above and below acceptability value, respectively. Once identified, those distributions can be a subject to further research and quantification. p N,i s i Interval analysis P-box [0..1] CC N L, C CCDF of Pf 0.5 ppf 1 (i Ni ) ppf M (i Ni ) Domain of probability distributions of model intangible parameters 0.05 P 1 s Acceptability criterion P f (L>C) 13

14 Communication of ROAAM+ results 14

15 1 Failure domains Failure domains are built in the space of scenario parameters. Failure domain is colour coded to reflect the fraction of cases in which P f exceed screening frequency P s = 10 3, i.e. CCCC P f > If the fraction of cases where failure probability exceeds screening frequency is <5%, we consider such scenario safe (green) >95%, we consider such scenario failed (red) [5%; 95%], assessment of effectiveness of the mitigation strategy is sensitive to the knowledge about the distributions (blue and purple). CCDF of P f % CCDF(P f ) % 0.25 CDF(P CDF(P CDF(P CDF(P f >1e-03) > 95% - red f > 1e-03) < 5% - green f > 1e-03) - [5-50%] - blue f > 1e-03) - [50-95%] - purple P (Impulse (95%) on the wall > Capacity(20kPa*s)) f % P s Jet radius [m ] Probability of failure - P f Water pool temperature [K ] 15

16 16 Example: Failure Domain maps for ex-vessel steam explosion in Nordic BWR Non-reinforced hatch door: 6 kpa.s fragility limit. Significant fraction of melt release scenarios result in the failure of the containment. Reinforced hatch door: 50 kpa.s fragility limit. Majority of melt release scenarios do not result in containment failure. Only in case of oxidic melt releases some uncertainty in the outcome remains for scenarios with deep (>6 m) water pools, large jet diameters (>25 cm).

17 Establishing connections with the decision models: Utility based approach Regulatory oriented approach 17

18 Problem Structure and Decision Model The ROAAM+ framework is being designed to enable a decision on either: (i) maintaining the current SAM strategy, (ii) modifying the current SAM strategy or (iii) improving knowledge. For the case of ex-vessel steam explosion, based on ROAAM+ results, a decision maker is supposed to choose between three options: (i) to reinforce the hatch; (ii) not to reinforce the hatch; (iii) to reduce epistemic uncertainty by getting more information on: most influential parameters of melt release, distribution of modelling deterministic and intangible parameters. 18

19 19 Payoff Matrix We propose a payoff matrix which consists of two decision options: to reinforce the door not to reinforce the door Outcome variables: failure\no failure, where P f0i probability of failure with nonreinforced door, P fmm probability of failure with reinforced door) both for scenario s i ; and consequences in terms of utilities for every decision option - P f0i U fi + 0 = P f0i U fi, P fmm U m + U fi + (1 P fmm )U m = P fmm U fi + U m, where U fi cost of large release for scenario s i, U m cost of design modification (hatch door reinforcement). Decision\Outcome Sever accident No sever accident Utility Non-reinforced door P f0i U fi 0 P f0i U fi Reinforced door P fmm (U m + U fi ) (1 P fmm )U m P fmm U fi + U m

20 Criterion for Decision Effectiveness The purpose of sensitivity analysis in decision making context is to find sensitivity of the results (decision preference) with respect to input parameters of decision model i.e. it can be viewed as search for turn-over points, i.e. point in terms of input parameters when decision preference changes. Considering equilibrium point between decision options, i.e. Utility Decision Option 1 equals to Utility Decision option 2, will yield P fmm U fi + U m = P f0i U fi ; Thus P f0i P fmm = U m U fi or alternatively in more general form: (P f0i P fmm )U fi C s U = M ei m where, M ei -measure of design modification effectiveness and C s safety coefficient multiplicator of design modification costs or, alternatively of the measure of design modification effectiveness; if M ei >1, then containment hatch door reinforcement is justified. The parameters affecting the decision will be the difference between P f0i and P fmm, or alternatively, by how much the probability of failure due to ex-vessel steam explosion will be reduced with hatch door reinforcement; and relationship between the cost of reinforcement and massive release cost. 20

21 Effect of Uncertainty in Probabilistic Knowledge and Costs Since in ROAAM+ framework for Nordic BWR we deal with second order probabilities, P f0i, P fmm together with U fi are not single values but distributions. The resultant difference (P f0i P fmm ) will be also a distribution with μ P f0i P fmm = μ P f0i μ P fmm and VVV P f0i P fmm = VVV P f0i + VVV P fmm ; the relation U m U fi will also be a scenario dependent (s i ) distribution. M ei - design modification effectiveness criterion for scenario s i robust decision regarding design modification can be made in case where all values in the distribution of M ei < 1(red curve) which means that reduction in probability of failure due to design medication does not justify the costs regardless of uncertainty M ei > 1 (green curve) which means that whatever uncertainty is the design modification is justified for a given value of U m. Now, the question is what should we consider as a decision criterion when dealing with intermediate case, where decision preference can change due to uncertainty? One of the possible options is to consider different percentiles of the distribution of (M ei ), e.g. 50,95,99% - as turningover points for the decision making, considering every possible severe accident scenario s i separately. Gain more knowledge to reduce uncertainty? 21

22 22 Example of decision model: utility based approach To illustrate an approach for decision making, let us consider the following values: n rrrrrrr = 10 number of reactors n yyyyy = 40 remaining years of operation n r/y = 400 reactor years; f si = 1.e-5 severe accident scenario frequency (PDS frequency); Cost of hatch door reinforcement U m = 10 5 n rrrrrrr = 10 6 (approximate estimate) Cost of large release (consequences) U f = n r\y f si = = 4ee Given values of U m and U f ; (P f0 P fm ) 4ee 1ee C s = M e.

23 Example of decision model: utility based approach Assume that the values of P f0, P fm have the following distribution as in the figure LHS, distributions are presented as CCDF(P f0 ) - red curve; CCDF(P fm ) blue curve, and the distribution of M e is presented in figure RHS with C s =1 (red) and C s =2 (blue). If C s = 1 values of M e exceed its threshold in ~15% of the cases therefore, within 15% confidence level the decision to reinforce the door can be justified. If we consider C s = 2 then only in ~5% of the cases the difference M e > 1 making decision in the favor of nonreinforced door CCDF(P CCDF(P f 0 ) f m ) C s = 2 C s = CCDF(P f ) CCDF(M e ) P f M e 23

24 Establishing connections with the decision models: Utility based approach Regulatory oriented approach 24

25 Example of decision model: regulatory oriented approach Decisions based on criteria for unacceptable release frequency UUU(yr 1 ) of a plant. In case of inconclusive UUU estimate, variance reduction, reduction of conservatism etc. may be justified. There is uncertainty in the assessment of the UUU that can be characterized as a CCCC UUU. 1 CCCC UUU CCCC UUF 1 CCCC UUF 0 Maintain safety Continue systematic safety improvement Urgent safety improvements necessary Unacceptable for safe operation UUU(yr 1 ) 25

26 SAM mitigation window ROAAM+ in combination with PSA-L1, L2 and L3 can combine information on frequencies of scenarios and probability of unacceptable release to assess the risk R i = s i, f i, P i c i Probabilistic treatment => CCC(yr 1 ) Prevention regime (PSA L1) Continue Systematic Safety Improvement Urgent Safety Improvement Necessary Mitigation Window Remote and speculative sequences Maintain Safety 1 CCCC UUU Maintain safety Unacceptable for Safe Operation CCCC UUF Continue systematic safety improvement CPUU Urgent safety improvements necessary CCCC UUF 0 Unacceptabl e for safe operation UUU(yr 1 ) <= Integrated treatment Frequency for scenarios Conditional probability of unacceptable release (CCCC) For the sake of conservatism at current stage CCCC can be considered equal to conditional containment failure probability CCFP. 28

27 SAM mitigation window and uncertainty in CCFP ROAAM+ can help to Assess the uncertainty Reduce the uncertainty By improving knowledge and or modifying the design. CCC(yr 1 ) Scenario s i box-and-whisker plot or CCCC

28 30 Summary and outlook We use: The concept of second-order probability in quantification of conditional containment failure probability. The need for the second-order probabilities comes from the nature of epistemic uncertainties: Model deterministic parameters complete probabilistic knowledge (i.e. range and probability distribution). Model intangible parameters partial probabilistic knowledge (i.e. one can only speculate regarding the possible range and type(s) of the distribution). Failure domain maps for communication of the results in terms of scenario parameters Two decision approaches (under development): Utility based demonstrated economic feasibility of a decision. Regulatory oriented marries the concept of unacceptable release frequency and distribution of conditions containment failure probability Further development and generalisation of both approaches is necessary: Design modification effectiveness (M e ) maps Multidimensional representation of the mitigation window Criteria for merging of the SAM window and CCDF of Pf.

29 Thank you for your attention! 31