A New Equivalence Theory Method for Treating Doubly Heterogeneous Fuel—I: Theory

A new methodology has been developed to treat resonance self-shielding in doubly heterogeneous very high temperature gas-cooled reactor systems in which the fuel compact region of a reactor lattice consists of small fuel grains dispersed in a graphite matrix. The new method first homogenizes the fuel grain and matrix materials using an analytically derived disadvantage factor from a two-region problem with equivalence theory and intermediate resonance method. The disadvantage factor accounts for spatial self-shielding effects inside each grain within the framework of an infinite array of grains. Then the homogenized fuel compact is self-shielded using a Bondarenko method to account for interactions between the fuel compact regions in the fuel lattice. In the final form of the equations for actual implementations, the double-heterogeneity effects are accounted for by simply using a modified definition of a background cross section, which includes geometry parameters and cross sections for both the grain and fuel compact regions. With the new method, the doubly heterogeneous resonance self-shielding effect can be treated easily even with legacy codes programmed only for a singly heterogeneous system by simple modifications in the background cross section for resonance integral interpolations. This paper presents a detailed derivation of the new method and a sensitivity study of double-heterogeneity parameters introduced during the derivation. The implementation of the method and verification results for various test cases are presented in the companion paper.