Bayesian Uncertainty Analysis of BWR Core Parameters based on Flux Measurements

Paper in proceeding, 2011

During the last two decades, fuel loading strategies of many nuclear power plants have been based on best estimate (BE) calculations, allowing an optimization of the fuel depletion efficiency along the different cycles of the plant life. Core BE simulators aim to solve the twogroup diffusion equation in order to predict the spatial dependence of the scalar neutron flux. Their input parameters are the two-group macroscopic cross-sections and diffusion coefficients, respectively, as a function of the state variables such as moderator temperature, void fraction, history variables, burnup, etc. Ringhals 1 (R1) is an ASEA-Atom Boling Water Reactor (BWR) located at the Ringhals power plant complex in western Sweden. 36 Traversing Incore Prove (TIP) detectors are permanently positioned within the core, and during each cycle a few TIP measurements at different burnup conditions are performed in order to estimate the actual spatial neutron flux throughout the core and thus, the spatial distribution of the power and thermal margins. Therefore, the accuracy of core simulator calculations along the cycle can be assessed by computing the difference between predicted and measured quantities; such a procedure builds confidence in using the simulator for the long term fuel loading plans. In this paper, discrepancies between spatial measured and calculated fluxes in R1 are used to perform an inverse uncertainty analysis on the spatial dependence of the input parameters of the Westinghouse POLCA7 [1] core simulator (i.e. macroscopic cross-sections and diffusion coefficients per control volume or node, that are inputs to the discretized two-group diffusion equation). This analysis is carried out using Bayesian statistics, where, for a certain cycle, the frequency distributions of the simulator inputs at every assembly node are updated based on the error distribution of the spatial thermal flux.