Probabilistic approach of solving burnup problems

Abstract

This paper presents a new approach to solve nuclear burnup problems using a probabilistic method. Unlike the traditional methods that rely on complex matrix exponential calculations, the proposed method tracks the transformation of nuclei over a period of time, enabling the estimation of nuclide concentrations. The method is implemented in a C++ program CNUCTRAN and verified against the Chebyshev Rational Approximation Method (CRAM). Three sample calculations are presented, showing a detailed comparison of results obtained using CNUCTRAN and CRAM48. The relative error analysis emphasizes the accuracy of the probabilistic method, with the most significant error observed below 0.001%. The computational efficiency is discussed in terms of CPU time, indicating that CNUCTRAN requires more CPU time than CRAM but with improved accuracy as the time step decreases. The numerical results for various burnup problems demonstrate the accuracy and efficiency of the probabilistic method, making it a promising alternative for simulating realistic nuclear transmutations.