Nuclear data uncertainties propagation methods in Boltzmann/Bateman coupled problems: Application to reactivity in MTR

Abstract

A novel method has been developed to calculate sensitivity coefficients in coupled Boltzmann/Bateman problem for nuclear data (ND) uncertainties propagation on the reactivity and is here extended to power factors. Different uncertainty propagation methodologies, such as One-Ata-Time and hybrid Monte-Carlo / deterministic methods have been tested and are discussed on an actual example of ND uncertainty problem on a MTR-type reactor benchmark. Those methods, unlike total Monte Carlo sampling for uncertainty propagation and quantification (UQ), allow obtaining sensitivity coefficients, as well as correlations values between nuclear data, during the depletion calculation for global neutronics parameters such as reaction rates. The methodologies are compared to a pure MC sampling method, usually considered as the "reference" method. The present paper extends the development to power factor by introducing a new methodology enabling to decorrelate direct and transmutation terms for local factors. The total uncertainty can be decomposed in two effects: a direct effect coming from the perturbation and an effect coming from transmutation. The most impacting ND are the scattering reactions, principally coming from 27 Al and H 2 O. The overall effect is a reduction of the propagated uncertainties throughout the cycle thanks to negatively correlated terms.

Extension of Bayesian inference for multi-experimental and coupled problem in neutronics − a revisit of the theoretical approach

“…S C and manufacturing parameters from M E can be obtained following the methods described in [13][14][15].…”

Manufacturing Data Uncertainties Propagation Method in Burn-Up Problems

“…The method used to evaluate the uncertainties comes from complete work performed in [8,9]. The complete evaluation of propagated uncertainties on neutronics parameters requires a precise knowledge of both nuclear data and manufacturing uncertainties.…”

“…The calculation is performed on a 2D quarter of core with ad hoc symmetries. The full Boltzmann/Bateman calculation scheme is described in [8]. Each plate is discretized in 8 sectors, to get a more precise estimation of the local power factor and the concentrations.…”

“…The bias observed on the reactivity is only the result of the convergence of MC estimator. The bias is weak compared to the total uncertainty of the reactivity (including nuclear data [8,9]). Increasing the number of samples is possible but not efficient because of the large CPU time needed for each calculation.…”

“…The total propagated uncertainty coming from both nuclear data (fission yield and cross sections) and manufacturing data is obtained by applying the process previously described in [8,9]. The covariance matrices used are the same as those used in [9] (read [14,15] for fission yields and [11,[16][17][18] for cross sections).…”