A New Collision Probability Approach for Solution of the Transport Equation in the Random Medium of High-Plutonium-Content HTR Lattice Cells

The fuel in high-temperature reactors (HTRs) is made up of tiny fuel particles (called TRISO particles) dispersed randomly in a graphite matrix. For the commonly used fuels, namely, enriched uranium or low-enriched uranium/²³³U mixed with Th, this dispersion may be treated as a homogeneous mixture at almost all neutron energies except at the resonances of the major nuclide (²³⁸U or ²³²Th) where the macroscopic cross section is so large that the neutron mean free path is comparable to the fuel kernel radius. In the equivalence theory approach used in many codes based on the WIMS-D library, this heterogeneity is accounted for by the escape cross section from a fuel kernel together with a carefully evaluated Dancoff correction factor.

In HTRs designed to burn plutonium, the fuel kernel contains oxides of various isotopes of Pu, and there is no fertile nuclide. Hence, the macroscopic cross section of the fuel is rather high in the thermal region, i.e., below 4 eV in the WIMS-D library (which also includes the two major resonances of ²⁴⁰Pu and ²³⁹Pu). For such fuels, the treatment of neutron transport in the thermal energy range must also include the random heterogeneous distribution of fuel in the graphite matrix. Since the resonance treatment method in the WIMS-D library, described above, is neither available nor applicable for thermal energies, a different method is clearly necessary.

HTR lattice codes such as WIMS and DRAGON use approximate collision probabilities between the various microscopic regions, namely, the fuel kernel, the coating layers, and the graphite matrix in the solution of the multigroup transport equation to account for this heterogeneity. In an earlier paper, we developed a simple though heuristic approach for solving this problem. In the present paper, we develop a more systematic theoretical method for solving the transport equation in a random dispersion by an exact evaluation of the collision probabilities in various regions of the lattice cell. The method has been incorporated in the collision probability code BOXER3. Comparison with benchmarks of Pu-based HTR fuels shows very good agreement thus validating the new approach. The method is likely to have application beyond the problem discussed in the paper.