Propagation of Statistical and Nuclear Data Uncertainties in Monte-Carlo Burn-up Calculations

Two methodologies to propagate the uncertainties on the nuclide inventory in combined Monte Carlo-spectrum and burn-up calculations are presented, based on sensitivity/uncertainty and random sampling techniques (uncertainty Monte Carlo method). Both enable the assessment of the impact of uncertainties in the nuclear data as well as uncertainties due to the statistical nature of the Monte Carlo neutron transport calculation. The methodologies are implemented in our MCNP–ACAB system, which combines the neutron transport code MCNP-4C and the inventory code ACAB. A high burn-up benchmark problem is used to test the MCNP–ACAB performance in inventory predictions, with no uncertainties. A good agreement is found with the results of other participants. This benchmark problem is also used to assess the impact of nuclear data uncertainties and statistical flux errors in high burn-up applications. A detailed calculation is performed to evaluate the effect of cross-section uncertainties in the inventory prediction, taking into account the temporal evolution of the neutron flux level and spectrum. Very large uncertainties are found at the unusually high burn-up of this exercise (800 MWd/kgHM). To compare the impact of the statistical errors in the calculated flux with respect to the cross uncertainties, a simplified problem is considered, taking a constant neutron flux level and spectrum. It is shown that, provided that the flux statistical deviations in the Monte Carlo transport calculation do not exceed a given value, the effect of the flux errors in the calculated isotopic inventory are negligible (even at very high burn-up) compared to the effect of the large cross-section uncertainties available at present in the data files

Effect of Error Propagation of Nuclide Number Densities on Monte Carlo Burn-up Calculations. Annals of Nuclear Energy 33

Abstract As a result of improvements in computer technology, the continuous energy Monte Carlo burn-up calculation has received attention as a good candidate for an assembly calculation method. However, the results of Monte Carlo calculations contain the statistical errors. The results of Monte Carlo burn-up calculations, in particular, include propagated statistical errors through the variance of the nuclide number densities. Therefore, if statistical error alone is evaluated, the errors in Monte Carlo burn-up calculations may be underestimated. To make clear this effect of error propagation on Monte Carlo burn-up calculations, we here proposed an equation that can predict the variance of nuclide number densities after burn-up calculations, and we verified this equation using enormous numbers of the Monte Carlo burn-up calculations by changing only the initial random numbers. We also verified the effect of the number of burn-up calculation points on Monte Carlo burn-up calculations. From these verifications, we estimated the errors in Monte Carlo burn-up calculations including both statistical and propagated errors. Finally, we made clear the effects of error propagation on Monte Carlo burnup calculations by comparing statistical errors alone versus both statistical and propagated errors. The results revealed that the effects of error propagation on the Monte Carlo burn-up calculations of 8 · 8 BWR fuel assembly are low up to 60 GWd/t

A New Method for the Calculation of Diffusion Coefficients with Monte Carlo

This paper presents a new Monte Carlo-based method for the calculation of diffusion coefficients. One distinctive feature of this method is that it does not resort to the computation of transport cross sections directly, although their functional form is retained. Instead, a special type of tally derived from a deterministic estimate of Fick’s Law is used for tallying the total cross section, which is then combined with a set of other standard Monte Carlo tallies. Some properties of this method are presented by means of numerical examples for a multi-group 1-D implementation. Calculated diffusion coefficients are in general good agreement with values obtained by other methods