Uncertainty Quantification Framework for High-Temperature Gas-Cooled Reactors Using VSOP and DAKOTA

Advanced nuclear reactors hold strong potential for clean and safe energy production. From the various designs, high-temperature gas-cooled reactors (HTGRs) are among the most promising ones. One fundamental aspect for their safety evaluation is the uncertainty quantification (UQ) of HTGR models. This study introduces a UQ framework developed around the VSOP code system. The framework uses the DAKOTA statistical toolkit to sample various case-dependent inputs, such as manufacturing parameters and boundary conditions. A Python driver script is developed to create an interface between DAKOTA and VSOP. Dedicated sampling modules are developed for perturbing the case-independent inputs that include: background microscopic cross sections, fission yields, decay constants, and resonance integral parameters. The capabilities of the UQ framework are demonstrated on an 80-MW(thermal) pebble-bed small modular reactor equilibrium core model. Four different UQ studies are performed to understand and quantify the impact of various sets of inputs. Initially, perturbations in the cross sections are analyzed, given their inherent complex nature. The results show that the predicted (Formula presented.) uncertainty is ~420 pcm, a value consistent with those reported in the literature for pebble-bed reactors. The most statistically significant cross sections are the ²³⁵U number of average neutrons per fission, the ²³⁵U and ²³⁹Pu fission, and the ²³⁵U and ²³⁹Pu capture in thermal energies. Small uncertainties are obtained for the maximum burnup and fuel temperature, with values less than 0.15%. The second study assessed the additional impact of the fission yields and decay constants. The results show an impact of 50 pcm on the (Formula presented.), with a negligible impact on the other outputs of interest. The third study involved the perturbation of all the inputs, which resulted in unrealistically large uncertainties to most outputs due to the fuel kernel radius. This is attributed to the VSOP limitations for such uncertainty studies, since individual fuel kernels cannot be explicitly modeled, requiring the same fuel kernel radius perturbation to be applied in every coated particle for all fuel pebbles of the core. A more realistic approach is discussed and investigated in the fourth study. The results show that the cross sections remain the most important contributors for the (Formula presented.), the thermal flux distribution, and the power density distribution. However, for the maximum burnup, the maximum fuel temperature, and the gas temperature distribution, the power and mass flow rate boundary conditions are the most statistically significant inputs. Future work will aim to further refine and expand the VSOP UQ framework, and to perform code-to-code uncertainty comparison studies for different HTGR cores, such as the PBMR-400.