Uncertainty analyses for localized tallies in Monte Carlo Eigenvalue calculations

It is well known that statistical estimates obtained from Monte Carlo criticality simulations can be adversely affected by cycle-to-cycle correlations in the fission source. In addition there are several other more fundamental issues that may lead to errors in Monte Carlo results. These factors can have a significant impact on the calculated eigenvalue, localized tally means and their associated standard deviations. In fact, modern Monte Carlo computational tools may generate standard deviation estimates that are a factor of five or more lower than the true standard deviation for a particular tally due to the inter-cycle correlations in the fission source. The magnitude of this under-prediction can climb as high as one hundred when combined with an ill-converged fission source or poor sampling techniques. Since Monte Carlo methods are widely used in reactor analysis (as a benchmarking tool) and criticality safety applications, an in-depth understanding of the effects of these issues must be developed in order to support the practical use of Monte Carlo software packages. A rigorous statistical analysis of localized tally results in eigenvalue calculations is presented using the SCALE/KENO-VI and MCNP Monte Carlo codes. The purpose of this analysis is to investigate the under-prediction in the uncertainty and its sensitivity to problem characteristics and calculational parameters, and to provide a comparative study between the two codes with respect to this under-prediction. It is shown herein that adequate source convergence along with proper specification of Monte Carlo parameters can reduce the magnitude of under-prediction in the uncertainty to reasonable levels; below a factor of 2 when inter-cycle correlations in the fission source are not a significant factor. In addition, through the use of a modified sampling procedure, the effects of inter-cycle correlations on both the mean value and standard deviation estimates can be isolated. (author)