Improved Collision Probability Analysis of the Double-Heterogeneity Problem Based on Matrix Chord Length Correction

Dispersion fuel exhibits excellent safety performance and effectively reduces the risk of radioactive leakage, making it widely applied in high-temperature gas-cooled reactors (HTGRs) and other advanced nuclear reactors. The presence of stochastic media in dispersion fuel leads to the challenging double-heterogeneity problem in neutron transport calculations. Hébert proposed a collision probability analysis model for treating stochastic media, which has been implemented in the DRAGON5 code. As one important basis of derivation, it is assumed in the Hébert model that the neutron transmission probability is identical to the neutron escaping probability in matrix material. In this paper, it is figured out that the assumption is not rigorous for realistic stochastic media. Then, an improved approach based on the Hébert model is proposed to take into account the realistic chord length distribution as well as to ensure the conservation and reciprocity of collision probabilities. The proposed methodology has been implemented in the HTGR lattice physics code XPZ. By numerical analysis against Monte Carlo reference solutions, it is demonstrated that the improved Hébert model with chord length correction gives good accuracy for addressing realistic double-heterogeneity problems.