Calculating failure probabilities for TRISO-coated fuel particles using an integral formulation

The fundamental design for a gas-cooled reactor relies on the safe behavior of the coated particle fuel. The coating layers surrounding the fuel kernels in these spherical particles, termed the TRISO coating, act as a pressure vessel that retains fission products. The quality of the fuel is reflected in the number of particle failures that occur during reactor operation, where failed particles become a source for fission products that can then diffuse through the fuel element. The failure probability for any batch of particles, which has traditionally been calculated using the Monte Carlo method, depends on statistical variations in design parameters and on variations in the strengths of coating layers among particles in the batch. An alternative approach to calculating failure probabilities is developed herein that uses direct numerical integration of a failure probability integral. Because this is a multiple integral where the statistically varying parameters become integration variables, a fast numerical integration approach is also developed. In sample cases analyzed involving multiple failure mechanisms, results from the integration methods agree closely with Monte Carlo results. Additionally, the fast integration approach, particularly, is shown to significantly improve efficiency of failure probability calculations. These integration methods have been implemented in the PARFUME fuel performance code along with the Monte Carlo method, where each serves to verify accuracy of the others.