基于抽样方法的燃耗计算核素积存量不确定度分析

基于抽样基本原理研究了应用于燃耗计算的不确定度分析方法，并开发了燃耗计算不确定度分析程序。基于评价核数据库ENDF/B-Ⅷ.0的裂变产额标准差和衰变常量标准差计算得到了衰变常量协方差矩阵和带相关性的裂变产额协方差矩阵，并结合SCALE6.2程序包的56群反应截面协方差数据库，对Takahama-3压水堆组件基准题中SF95-4样品进行不确定度分析。计算了反应截面、衰变常量和裂变产额不确定度引起的核素积存量的不确定度。计算结果表明，反应截面的不确定度是锕系核素积存量不确定度的主要来源，裂变产额和衰变常量的不确定度对部分裂变产物的积存量会引入较大的不确定度。但考虑裂变产额相关性后，裂变产额引起的不确定度显著降低。

Nuclide Inventory Uncertainty Analysis of Burnup Calculation Based on Statistical Sampling Method

Burnup calculation is an important component of reactor physics calculations, which provides the evolution of the isotopic inventory during the reactor operation. Reliable prediction of nuclide density with information of uncertainty is of importance for reactor operation and safety, waste transport and management. Nuclear data are the basic input parameters for the reactor physics calculation. With the improvement of calculation models and computer technology, the nuclear-data uncertainties become the main uncertainty sources for the burnup calculation. In order to perform the uncertainty propagations from nuclear cross sections to the responses of burnup calculations, two categories of methodologies have been widely applied: the deterministic method and the statistical sampling method. In this paper, a code was developed to calculate burnup calculation uncertainty caused by nuclear data based on statistical sampling method. There are three main steps to perform uncertainty propagation from the uncertainties of input parameters to the responses: firstly, determine the distribution ranges of input parameters; secondly, generate the samples of the input parameters; finally, statistically calculate for responses of corresponding input samples. Uncertainties coming from nuclear data including cross sections, decay constants and fission yields were propagated to the nuclide densities of SF95-4 sample in the Takahama-3 reactor with this newly developed code. 300 stand-alone burnup calculations were performed, each time with a different perturbed library. The 56-group cross-section covariance information from SCALE6.2 was propagated and the results show that this contribution most affect the uncertainties of actinides. Then the decay constant uncertainties from ENDF/B-Ⅷ.0 was propagated. The decay data uncertainties have inappreciable impacts on the uncertainty of nuclide densities. This effect is negligible for all actinides and most of the fission products with the exception of 151Eu, of which the 9.0% of uncertainty reflects the uncertainty of 8.9% on the decay constant of its direct parent 151Sm. Finally, the uncertainties of the fission yields were propagated and we can conclude that the uncertainties on the fission yields are the main source of uncertainty of fission products, ranging up to almost 25%. The fission yield data were taken from the original ENDF/B-Ⅷ.0 library and they were given without correlations. We generated fission yield correlations for ²³⁵U and ²³⁹Pu thermal systems using a simplified generalized least-squares method and propagated the new covariance matrices in the same model. The comparison between the inventory calculation results obtained by sampling the correlated and non-correlated ENDF/B-Ⅷ.0 fission yields shows that the introduction of correlations significantly reduce the effect of the fission yield uncertainties.