Spatially Continuous Depletion Algorithm for Monte Carlo Simulations

Abstract

To correctly predict reactor behavior during cycle operations, the evolution of nuclide number densities throughout the core must be accurately modeled. The time-varying spatial distribution of nuclide number densities is typically resolved by discretizing the Monte Carlo geometry into smaller cells over which number densities are assumed to be spatially invariant. The nuclide number densities in these smaller cells are integrated through time using reaction rate tallies on the same discretized geometry. However, detailed distributions of nuclide number densities in a full three dimensional simulation can require a prohibitive amount of tallies, and the spatial discretization of the base geometry makes coupling to external multiphysics tools difficult. In this paper a method for solving for spatially continuous number density distributions during depletion calculations will be described. The spatially continuous number densities can be used in the transport method proposed by Brown and Martin which allows for transporting neutrons through a material with continuously varying properties such as temperature and nuclide number densities. Coupled with the ability of Functional Expansion Tallies (FETs) [2] to represent tallied quantities as continuous functions, it is possible to both solve for and make use of spatially continuous nuclide number densities. The need for this capability was alluded to by Brown et. al., but no solution has yet been proposed. With a continuous depletion method, recent work which utilized FETs and continuous material tracking to incorporate multiphysics feedback in Monte Carlo simulations can be extended to simulations that include depletion analysis.