Uncertainty Quantification of Few-Group Diffusion Theory Constants Generated by the B₁ Theory-Augmented Monte Carlo Method

The B₁ theory-augmented Monte Carlo (MC) method has been recently presented as a new MC method to generate homogenized few-group diffusion theory constants (FGCs) of nuclear systems such as a fuel pin cell or a fuel assembly (FA). It is demonstrated that it can produce FGCs that are well qualified for highly accurate two-step core neutronics analyses. However, it is unavoidable for FGCs from it to carry uncertainties that are ascribed to statistical uncertainties, as well as nuclear cross-section and nuclide number density input data uncertainties, of MC calculations pivotal in the new MC method. In order to evaluate the impact of these uncertainties of FGCs on the core neutronics design applications, therefore, it becomes essential to present their uncertainties quantitatively in addition to FGCs themselves. The purpose of this paper is to develop a mathematical formulation for separately quantifying contributions of statistical and input data uncertainties to uncertainties of FGCs from the new MC method and to illustrate its applications for computing uncertainties of the burnup-dependent FGCs. To do so, the basic mathematical equations linking input uncertainties to output uncertainties are established in terms of an arbitrary single-step computational problem that requires either a MC or a deterministic method calculation. It is shown that repeated applications of the basic equations stepwise from steps 1 through 5 of the new MC method at the very beginning of the preset burnup intervals lead to a desired formulation that can not only quantify uncertainties of the burnup-dependent FGCs but also separately identify individual contributions of uncertain sources to them. The formulation is incorporated into the Seoul National University MC code McCARD. It is then used to compute the uncertainties of the burnup-dependent homogenized two-group constants of a low-enriched UO₂ fuel pin cell and a pressurized water reactor FA on the assumption that nuclear cross-section input data of ²³⁵U and ²³⁸U have uncertainties as reflected in covariance files of the JENDL 3.3 library. The effects of the cross-section input data uncertainties of the two U isotopes on the uncertainties of two-group constants and on those of neutron multiplication factors of the UO₂ pin cell and the FA are quantified. The utilities of uncertainty quantifications are then discussed from the standpoint of evaluation of feasibility of nuclear design results of new reactor systems and improvement of the nuclear data including covariance files of the evaluated nuclear data libraries.