Monte Carlo solution convergence analysis via COMET in a stylized integral inherently safe LWR benchmark problem

Abstract

In this paper, the coarse mesh radiation transport (COMET) method is used to study the convergence of the Monte Carlo solution in a stylized benchmark problem based on the beginning of the equilibrium cycle of the Integral Inherently Safe Light Water Reactor concept (I2S-LWR) with silicide U3Si2 fuel. The benchmark problem is comprised of 121 fuel assemblies with radial, top and bottom reflectors. COMET consists of a stochastic local solver (response function generator) for generating a library of incident flux response expansion coefficients for the unique coarse meshes (e.g., all fuel assembly types and reflector/non-fuel blocks) and a deterministic iterative solver for whole-core calculations using this response library. The Monte Carlo method is regarded as the gold standard for benchmarking other numerical transport methods. However, for eigenvalue problems, Monte Carlo results require careful analysis to ensure the convergence of the fission source distribution. It is known that this issue can be of concern, particularly for large eigenvalue problems typical of realistic (i.e., operating) reactors. This became evident when the radially-integrated axial fission density distributions predicted by 50 independent MCNP runs in the I2S-LWR benchmark problem were compared to each other and were found to be significantly different, with the difference ranging from −9% to +9%. However, the average of the fission density distributions from these 50 runs agreed very well with that predicted by COMET, with a relative difference varying from −0.18% to 0.13%, being within one standard deviation of the average. This agreement confirms that the averaged Monte Carlo solution is converged.