# Nuclear Reaction Pressure Vessel Safety Assessment

Authors:

Name | Affiliation | Phone Number | Email Address |
---|---|---|---|

Matt Butchers | matt.butchers@ktn-uk.org |

Industrial Sectors:

Energy

1. DESCRIPTION OF USE CASE

This use case is taken from Ref [1]
**The nuclear reactor pressure vessel (NRPV)**

- A key component
- Height: 13 m, Internal diameter: 4 m, thickness: 0,2 m, weight: 270 t
- Contains the fuel bars
- Where the thermal exchange between fuel
- bars and primary fluid takes place
- It is the second “safety barrier”
- It cannot be replaced !
- Nuclear Unit Lifetime < Vessel Lifetime

- Extremely harsh operating conditions
- Pressure: 155 bar
- Temperature: 300 deg C
- Irradiation effects: the steel of the vessel becomes progressibly brittle, increasing the failure risk dueing an accidental situation

**The problem formulation is typical in most nuclear safety problems:**- Given some hard (and indeed very rare) accidental conditions, what is the “failure probability” of the component?
- It is the case of “structural reliability analysis” (SRA)
- The physical phenomenon is described by a computer code

__Safety Assessment Example [Muoz-Zuniga et al., 2009] Step A__Accidental conditions scenario: cooling water (about 20 °C) is injected in the vessel, to prevent over-warming- Thermal cold choc -> Risk of fast fracture around a manufacturing flaw

- thermo-hydraulic representation of the accidental event (cooling water injection, primary fluid temperature, pressure, heat transfer coefficient)
- thermo-mechanical model of the vessel cladding thickness, incorporating the vessel material properties depending on the temperature t
- a fracture mechanics model around a manufacturing flaw

- Stress Intensity \(K_{CP}(t)\) in the most stressed point
- Steel toughness, \(K_{IC}(t)\) in the most stressed point

*t*, the function \(G = K_{IC} - K_{CP}\) is negative2. KEY UQ&M CONSIDERATIONS

2.1 Process Inputs

A more complex example with 7 randomised inputs is given in [Munoz-Zuniga et al, 2010]

A huge number of physical variables. In this example, three are considered as random. Penalised values are given to the remaining variables

- Toughness low limit, playing in the steel toughness law $$K_{IC}$$ . Normal dispersion around a reference value $K_{IC}^{RCC}$
- Dimension of the flaw
*h* - Distance between the flaw and the interface steel-clad
*d*

Variable | Distribution | Distribution Parameters | Comments |

\(u_{K_{I}_{C}_1\) | Normal | \(K^{RCC-M}_{I_C}\) and variation coefficient : \(c_K_I_C = 15 %\) | Support truncated at [\(-4\sigma ; +4\sigma\)] |

h |
Weibull | Scale parameter \(\alpha\) = 3.09 mm and shape \(\Beta\) = 1.08 mm | Distribution estimated by fitting exercise over inspection data |

d |
Uniform | [0.1; 100] (mm) | The flaw is supposed to be in the inner half-thickness |

2.2 Propagation

A numerical challenge

- High CPU time consuming model
- Standard Monte Carlo Methods are inappropriate to give an accurate estimate of \(P_f\)
- An innovative Monte Carlo sampling strategy has been developed: ''ADS-2'' (Advanced Directional Stratification)

- Standard transformation
- Directional sampling
- Adaptive strategy to sample more ''useful'' direction

Method | p |
n |
\(f_1(n)\) | \{\hat{P}_f (X 10^{-6})\) | 95 % CI Length (X 10\(^{-6}\)) | Nb. of Calls to \(G_{Min}\) | |

1 | DS | 3 | 50 | / | 4.3 | 13 | 208 |

2 | 2-ADS | 3 | 50 | 10 | 6.3 | 7.0 | 820 |

3 | DS | 3 | 200 | / | 3.7 | 16 | 822 |

4 | 2-ADS | 3 | 200 | 40 | 8.0 | 5.0 | 3290 |

5 | DS | 3 | 1000 | / | 7.66 | 7.0 | 4028 |

2.3 Interpretation and Communication of Results

3. CURRENT STATE OF MATURITY

References:

http://math.nist.gov/IFIP-UQSC-2011/slides/Pasanini.pdf