The fuel in high-temperature reactors (HTRs) consists of a large number of tiny (a few hundred microns in size) TRISO-coated particles dispersed randomly in a graphite matrix. At the resonances of the major nuclide (238U or 232Th) of the fuel, the neutron mean free path in the fuel is often comparable to the kernel dimensions, and hence the dispersion of particles in the graphite matrix must be treated as a heterogeneous medium for obtaining self-shielded cross sections in the resonance (epithermal) groups. HTRs containing only plutonium as fuel (as may be the case in reactors designed for burning plutonium) have high concentrations of the isotopes 239Pu and 240Pu in the kernels. This fact together with their rather large resonance cross section in the thermal groups results in a very short neutron mean free path in the fuel that is comparable to the kernel dimensions. In such cases the fuel zone must be treated as a heterogeneous medium in the thermal energy region as well. However, the resonance treatment method in libraries such as the WIMS library does not cover the two large resonances of plutonium lying in the thermal region. Instead, a large number of groups are used to cover the details of cross-section variation in this region.

The heterogeneity of the fuel region together with the heterogeneous distribution of fuel region, graphite moderator, and coolant is referred to as the double heterogeneity of HTRs. The paper describes work we carried out for addressing these problems. A new method for generating a random distribution of TRISO particles in the fuel zone of a pebble or fuel compact and Monte Carlo calculation of the Dancoff factor in the heterogeneous random medium, required for calculating the self-shielded resonance group cross sections, is presented. Dancoff factors obtained by our method are compared with values available in published literature on the subject. The paper also discusses a new methodology developed to solve the double-heterogeneity problem at the stage of the multigroup transport theory solution, which is particularly important in the thermal region occurring in high-content Pu-fueled HTRs. These features have been incorporated in the WIMS library–based lattice code BOXER3. An option for handling the spherical geometry of the lattice cell of a pebble bed reactor has been added in the code. Results of analysis of a number of HTR lattice cell benchmark problems are presented.