A resonance calculation using a deterministic statistical geometry (DSTG) method has been developed to efficiently treat the double heterogeneity of coated fuel particles loaded in a high-temperature gas-cooled reactor. Using the DSTG method, neutron flux spatial distribution can be calculated in a heterogeneous geometry containing the randomly dispersed fuel particles and surrounding graphite matrix, which is consistent with statistical geometry in a Monte Carlo method.

We applied the DSTG method to resonance calculations based on the equivalence theory and the ultra-fine-group energy treatment in the heterogeneous transport calculation code GALAXY-Z developed by Mitsubishi Heavy Industries, Ltd. In the GALAXY-Z code, DSTG can directly treat the heterogeneity of dispersed fuel particles in fuel compacts. The ultra-fine-group fixed-source DSTG calculation is applied to a high-energy range beyond 30 eV in which upscattering can be ignored. The fixed-source DSTG calculation is applied to a Dancoff-factor calculation for the equivalence theory in a low-energy range of less than 30 eV. In the low-energy range, the SHEM 361-group structure is applied, and the energy grids are detailed enough to allow a continuous treatment of the neutron spectrum. In other words, the upscattering effects and the resonance self-shielding effects are automatically considered in the multigroup transport calculation. The homogenized and collapsed multigroup cross sections of fuel particles are provided to lattice calculations of fuel elements.

The comparison of reaction rates (effective cross sections) between GALAXY-Z and the continuous-energy Monte Carlo code MVP is carried out for fuel particles within a fuel element of the high-temperature engineering test reactor. The numerical results indicate that the present method well reproduces the fuel particle’s effective cross sections, k-infinity, and fission rate distribution calculated by MVP.