Estimation of Error Propagation in Monte-Carlo Burnup Calculations

Abstract

A formulation has been established to estimate the error propagation in Monte-Carlo burnup calculations. The uncertainties in cross sections and the statistical errors in Monte-Carlo calculations are considered as error sources, and the error propagation of number densities of individual nuclides over a burnup period is formulated. The present formulation is applied to the burnup calculation of a simplified fast reactor core. The components of the errors in number densities due to the statistical error are up to 0.92% even when the history number is small as 10⁴. On the other hand, the components due to the cross section error are about 2–5% for the number densities of ²³⁵U, ²³⁹Pu, ²⁴⁰Pu, ²⁴¹Pu and ²⁴²Pu, and about 7.3% for the fission-product. Thus the contribution is mainly due to the cross section errors. The error propagation of the number densities due to the statistical errors at individual burnup steps is investigated by dividing the burnup period into two steps. The error propagation is not serious for the problem treated here because the component due to the statistical error is much smaller than that due to the cross section error.

KEYWORDS:

• burnup
• Monte Carlo method
• calculation method
• error propagation
• covariance data
• LMFBR
• cross sections
• uncertainty
• errors
• reliability
• data covariances