A Transport-Free Method for Predicting the Post-Depletion Spatial Neutron Flux Distribution

Abstract

An adjoint-based method to predict the variation in spatial flux distribution during a depletion interval is presented in this paper. Burnup analyses require dividing a fuel cycle into multiple time intervals. At the start of each interval, the neutron transport equation is solved, and a subsequent depletion calculation is performed to obtain isotopic concentrations at the end of the interval. The most common approaches are to assume that either the flux or the power are constant through this depletion interval. In reality, changes in material compositions cause the flux and power distribution to change instantaneously, and thus, these assumptions are not valid in general except in the limit of infinitesimally small time steps. To overcome these assumptions, a method for predicting the spatial flux variation (SFV) due to changes in material compositions is derived, implemented, and verified. The formulation relies on the first-order perturbation formulation in conjunction with the forward and adjoint moments of the fission source, obtained from the fission matrix. Moreover, multiple adjoint modes are used to better predict the flux variation following materials transmutations. Such a prediction is capable of mimicking a transport calculation across a depletion interval based on the beginning-of-step transport solution and could be used to extend the simulated time between transport simulations in depletion and fuel cycle analysis. The SFV method is applied to a single three-dimensional fuel pin, depleted using a variety of depletion step sizes and verified against a reference simulation. The results show that the method produces accurate prediction of the end-of-step spatial flux distribution.

Keywords:

• Monte Carlo
• depletion
• perturbation theory

Acknowledgments

This work was partially funded through U.S. Nuclear Regulatory Commission project number NRC-HQ-84-14-G-0058. The authors would also like to thank Stefano Terlizzi for his help regarding the fission matrix.