Stochastic Uncertainty Propagation in Monte Carlo Depletion Calculations

The Monte Carlo (MC) method is becoming popular for three-dimensional fuel depletion analyses to compute quantities of interest in used nuclear fuel including isotopic compositions. However, there are some questions concerning the effect of MC uncertainties on predicted results in MC depletion calculations. The MC method introduces stochastic uncertainty in the computed fluxes. These fluxes are used to collapse cross sections, estimate power distributions, and deplete the fuel within depletion calculations; therefore, the predicted number densities also contain random and propagated uncertainties due to the MC solution to the neutron transport equation. The linear uncertainty nuclide group approximation (LUNGA) method was developed to calculate the propagated stochastic uncertainty in the nuclear isotopics, using the time-varying flux subjected to the power normalization constraint. Verification of the LUNGA method demonstrated that the standard deviation in the number densities and infinite multiplication factor (k_inf) predicted by this method agree well with the uncertainty obtained from the statistical analysis of 100 different simulations performed with coupled MC depletion calculations. Future research includes (a) expanding the LUNGA methodology to include more nuclides, (b) fully automating the methodology, and (c) investigating the use of an axial segmented fuel rod.