Uncertainty Underprediction 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, which can lead to estimates of statistical uncertainties that are lower than the true uncertainty by a factor of 5 or more. However, several other more fundamental issues such as adequate source sampling over the fissionable regions and source convergence can have a significant impact on the uncertainties for the calculated eigenvalue and localized tally means, and these issues may be mistaken for effects resulting from cycle-to-cycle correlations. In worst-case scenarios, the uncertainty may be underpredicted by a factor of 40 or more. Since Monte Carlo methods are widely used in criticality safety applications and are increasingly being used for benchmarking reactor analyses, 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 eigenvalue and localized tally results in Monte Carlo criticality calculations is presented using the SCALE/KENO-VI (continuous-energy version) and MCNP codes. The purpose of this analysis is to investigate the underprediction of uncertainty and its sensitivity to problem characteristics and calculational parameters using two of the most widely used Monte Carlo criticality codes. For the problems considered here, which are fuel rod and fuel assembly problems with reflecting boundary conditions on all four horizontal sides, we show that adequate source convergence along with proper specification of Monte Carlo parameters can reduce the magnitude of uncertainty underprediction to reasonable levels, below a factor of 2 in most cases.