A MULTI-STATE PHYSICS MODELING FOR ESTIMATING THE SIZE- AND LOCATION-DEPENDENT LOSS OF COOLANT ACCIDENT INITIATING EVENT PROBABILITY

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1 MULTI-STTE PHYSICS MODELING FOR ESTIMTING THE SIZE- ND LOCTION-DEPENDENT LOSS OF COOLNT CCIDENT INITITING EVENT PROBBILITY Francesco Di Maio 1, Davide Colli 1, Enrico Zio 1,2, Liu Tao 3, Jiejuan Tong 3 1 Energy Department, Politecnico di Milano, Via La Masa 34, Milano, Italy francesco.dimaio@polimi.it 2 Chair System Science and the Energy Challenge, Fondation Electricité de France (EDF), CentraleSupélec, Université Paris Saclay, Paris, France 3 3Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing, China

2 Problem Statement In PR, Loss of Coolant ccidents (LOCs) are categorized with respect to: - Size - Location Both can indeed influence the timing and duration of the mitigating action [1,2] For each category, different strategies of intervention are to be designed for preventing core damage.. GULER, T. LDEMIR and R. DENNING, Uncertainty Evaluation in Multi-State Based ging ssessment of Passive Components. Probabilistic Safety ssessment and Management PSM 12, Honolulu, Hawaii (2014). R. TREGONING, L. BRMSON and P. SCOTT, Estimating Loss-of-Coolant ccident (LOC) Frequencies Through the Elicitation Process, Main report (2008).

3 Problem Statement: LOCs in FTs/ETs PIPING FILURE PROBBILITY ESTIMTION Statistics based on field data by by by Stochastic Model (e.g., Markov Chain Model (MCM)) Probabilistic Fracture Mechanics (PFM) Pros: consolidated approaches that fit real failure data Cons: lack of data due to the high reliability of nuclear piping system

4 Problem Statement: LOCs in FTs/ETs PIPING FILURE PROBBILITY ESTIMTION Statistics based on field data Pros: consolidated approaches that fit real failure data Cons lack of data due to the high reliability of nuclear piping system Stochastic Model (e.g., Markov Chain Model (MCM)) Probabilistic Fracture Mechanics Model (PFM) Pros: explicit modelling of crack initiation and growth Cons: Demanding on data for parameters calibration No consideration of the the effects of inspections and detection strategies

5 Problem Statement: LOCs in FTs/ETs Statistics based on field data Pros: consolidated approaches that fit real failure data PIPING FILURE PROBBILITY ESTIMTION Cons: lack of data due to the high reliability of nuclear piping system Pros: explicit modelling of the interactions between damage mechanisms and inspection, detection and repair strategies Stochastic Model (e.g., Markov Chain Model (MCM)) Cons: Pros: explicit modelling of crack initiation and growth Probabilistic Fracture Mechanics Model Cons: Demanding on data for parameters calibration No consideration of the the effects of inspections and detection strategies constant transition rates: exponentially distributed holding times not acceptable for components with different geometry, material properties

6 Problem Statement: LOCs in FTs/ETs PIPING FILURE PROBBILITY ESTIMTION Statistics based on field data Stochastic Model (e.g., Markov Chain Model (MCM)) Probabilistic Fracture Mechanics Model Multi-state transition setting + scarse data available + Physics modelling Pros: Multi-State Physics Model (MSPM) Feasible also with scarce data Cons: estimation of transition rates effects of the repair strategy included can be challenging pplicable also to new piping systems because the degradation process is described by physical models

7 The pproach: Multi-State Physics Model (MSPM) The degradation process is described by transitions among discrete states : S F L R no detectable damage detectable flaw detectable leak rupture The transition rates, λ i,j τ i,j, δ, are assumed to be functions of: The influencing factors δ (i.e., material properties) S λ S,F τ S,F, δ F The holding times τ i,j P t, δ = p S t, δ, p F t, δ, p L t, δ, p R (t, δ) Monte Carlo (MC) simulation framework

8 The case study Component: mixing tee between the hot and cold legs in the Reactor Cooling System (RCS) of a Pressurized Water Reactor (PWR) Operating conditions: pressure 36 bar hot leg water temperature 180 C cold leg water temperature 20 C Piping material: austenitic stainless steel 304L δ

9 MC simulation: transition rate evaluation Transition rates evaluation procedure: 1) Build the physical models that describe the degradation process

10 1) Degradation mechanism description Degradation mechanism: thermal fatigue Temperature fluctuation at the inner surface r i of the pipe due to turbolent mixing or vortices cold Hypotheis: sinusoidal transient thermal loading hot

11 1) Degradation mechanism description Degradation mechanism: thermal fatigue Temperature fluctuation at the inner surface r i of the pipe due to turbolent mixing or vortices cold Hypotheis: sinusoidal transient thermal loading θ r i, t = θ 0 sin 2πφ hot

12 1) Degradation mechanism description Degradation mechanism: thermal fatigue Temperature fluctuation at the inner surface r i of the pipe due to turbolent mixing or vortices cold Hypotheis: sinusoidal transient thermal loading θ r i, t = θ 0 sin 2πφ hot mplitude Θ 0 uniform distribution: Lower value 0 C Upper value 60 C

13 1) Degradation mechanism description Degradation mechanism: thermal fatigue Temperature fluctuation at the inner surface r i of the pipe due to turbolent mixing or vortices cold Hypotheis: sinusoidal transient thermal loading θ r i, t = θ 0 sin 2πφ hot mplitude Θ 0 uniform distribution: Lower value 0 C Upper value 60 C Frequency φ uniform distribution: Lower value 11 4 Hz Upper value 11 2 Hz δ

14 1) Degradation mechanism description First degradation step: from No detectable damage S to detectable Flaw F Circumferential Crack Onset S

15 MC simulation: transition rate evaluation Transition rates evaluation procedure: 1) Build the physical models that describe the degradation process 2) Sample the values of the parameters δ of the physical models

16 2) Sample the influencing factor δ values First degradation step: from No detectable damege S to detectable Flaw F Circumferential Crack Onset S θ r i, t = θ 0 sin 2πφ Stress distribution radial σ r r axial σ z r hoop σ θ r

17 MC simulation: transition rate evaluation Transition rates evaluation procedure: 1) Build the physical models that describe the degradation process 2) Sample the values of the parameters δ of the physical models 3) Select a characteristic variable x that describes the degradation process

18 3) The characteristic variable x for degradation assessment First degradation step: from No detectable damege S to detectable Flaw F Circumferential Crack Onset S radial σ r r axial σ z r hoop σ θ r Total equivalent strain rate ttt ε ee θ r i, t = θ 0 sin 2πφ

19 MC simulation: transition rate evaluation Transition rates evaluation procedure: 1) Build the physical models that describe the degradation process 2) Sample the values of the parameters δ of the physical models 3) Select a characteristic variable x that describes the degradation process 4) Select a threshold value X cc that defines transition among states

20 4) Setting of the threshold value X cc First degradation step: from No detectable damege S to detectable Flaw F Circumferential Crack Onset Number of thermal cycles to have the crack onset 1 S ttt ε ee tot ε eq 0.5 N f N f θ r i, t = θ 0 sin 2πφ radial σ r r axial σ z r hoop σ θ r

21 4) Setting of the threshold value X cc First degradation step: from No detectable damege S to detectable Flaw F Circumferential crack Onset S N f State holding time τ S,F (yyyyy) = N f φ θ r i, t = θ 0 sin 2πφ radial σ r r axial σ z r ttt ε ee N f hoop σ θ r

22 MC simulation: transition rate evaluation Transition rates evaluation procedure: 1) Build the physical models that describe the degradation process 2) Sample the values of the parameters δ of the physical models 3) Select a characteristic variable x that describes the degradation process 4) Select a threshold value X cc that defines transition among states 5) Simulate the degradation process N c times for estimating the cumulative distribution function F τ i,j δ of τ i,j

23 5) Degradation process simulation for estimating F τ S,F δ First degradation step: from No detectable damege S to detectable Flaw F Circumferential crack Onset S Number of simulation N c = τ S,F F τ S,F δ τ S,F θ r i, t = θ 0 sin 2πφ radial σ r r axial σ z r hoop σ θ r ttt ε ee N f

24 5) Calculation of λ τ S,F δ First degradation step: from No detectable damege S to detectable Flaw F Circumferential crack Onset S F τ S,F δ λ S,F τ S,F, δ τ S,F θ r i, t = θ 0 sin 2πφ radial σ r r axial σ z r hoop σ θ r ttt ε ee N f τ S,F F τ S,F δ

25 pplication to a PWR piping system: developing the MSPM First degradation step: from No detectable damege S to detectable Flaw F Circumferential crack Onset λ S,F τ S,F, δ S τ S,F F θ r i, t = θ 0 sin 2πφ radial σ r r axial σ z r hoop σ θ r ttt ε ee N f τ S,F F τ S,F δ 28μm 28μm

26 Developed MSPM: rupture probability evaluation Rupture probability evaluation p R t, δ Rupture: crack size reaches the whole circumference Hypotheses: the considered piping system is not subjected to severe loading conditions repair transition rates are considered constant and the state transition time follows an exponential distribution as in [Fleming, 2004] λ S,F τ S,F, δ μ ω λ F,L τ F,L, δ λ F,R τ F,R, δ λ L,R τ L,R, δ S F L R F. Di Maio, D. Colli, E. Zio, L. Tao, J. Tong, Multi-State Physics Modeling pproach for the Reliability ssessment of Nuclear Power Plants Piping Systems, nnals of Nuclear Energy, 80, , K.N. Fleming, Markov Models for Evaluating Risk-Informed In-Service Inspection Strategies for Nuclear Power Plant Piping Systems, Reliability Engineering and System Safety, 83, pp , 2004.

27 Developed MSPM: LOC probability evaluation Size and location-dependent LOC probability evaluation LOC: Loss of Reactor Coolant ccidenti due to the breach in the Reactor Coolant pressure boundary Hypotheses: breaches of size 254 mm < x mm (LOC category 14) are accounted as leakages repair transition rates are considered constant and the state transition time will follow exponential distribution as in [Fleming, 2004] μ ω λ S,F τ S,F, δ λ F,LL τ F,LL, δ λ LL,L τ LL,L, δ λ L,R τ L,R, δ S F L1 L R μ 1 λ F,R τ F,R, δ K.N. Fleming, Markov Models for Evaluating Risk-Informed In-Service Inspection Strategies for Nuclear Power Plant Piping Systems, Reliability Engineering and System Safety, 83, pp , K.N. Fleming, B.O.Y. Lydell, D. Chrun, Development of LOC Initiating Event Frequencies for South Texas Progect GSI-191, Final report for 2011 work scope Revision 1, 2011.

28 Developed MSPM: LOC probability evaluation Size and location-dependent LOC probability evaluation LOC: Loss of Reactor Coolant ccidenti due to the breach in the Reactor Coolant pressure boundary Hypotheses: breaches of size 254 mm < x mm (LOC category 14) are accounted as leakages repair transition rates are considered constant and the state transition time will follow exponential distribution as in [Fleming, 2004] μ ω λ S,F τ S,F, δ λ F,LL τ F,LL, δ λ LL,L τ LL,L, δ λ L,R τ L,R, δ S F L1 L R μ 1 λ F,R τ F,R, δ K.N. Fleming, Markov Models for Evaluating Risk-Informed In-Service Inspection Strategies for Nuclear Power Plant Piping Systems, Reliability Engineering and System Safety, 83, pp , K.N. Fleming, B.O.Y. Lydell, D. Chrun, Development of LOC Initiating Event Frequencies for South Texas Progect GSI-191, Final report for 2011 work scope Revision 1, 2011.

29 Developed MSPM model : LOC probability evaluation Size and location-dependent LOC probability evaluation Break size : 254 mm < x mm GSI-191 p L 14, a, t MSPM p L t, δ p L t, δ p L 14, a, t t early stage, p L t, δ, obtained with the MSPM is smaller than p L 14, a, t obtained by GSI-191 t larger time, the probabilities p L t, δ, obtained with the MSPM, is larger than p L 14, a, t obtained by GSI-191 t Inappropriate maintenance Underestimated risk

30 Conclusions Safety assessment of NPPs Failure probability estimation integrating Physical modelling MSPM MSPM framework applied to the Size and location-dependent Loss of Coolant ccident (LOC) probability evaluation occurring in the mixing tee of the RCS of a PWR MC simulation framework for the transition rates estimation Comparison with benchmark results shows the benefits of introducing physics models not to underestimate the failure probability