A Generalized Treatment of Heterogeneity Effects for the Shielding Factor Method

A practical method for self-shielding resonance cross sections for fast reactors with complex heterogeneity results in a multiregion equivalence relation that is identical in appearance to the conventional two-region equivalence relation. The effects of heterogeneity are accounted for in terms of material- and region-dependent escape cross sections. The escape cross sections are explicitly given in terms of the first-flight collision probabilities or transport coefficient. The formulation is well suited for use with the shielding factor method. A detailed validation of the heterogeneity calculations with the proposed formulation has been carried out for plate-type cells, and good agreement with Monte Carlo results has been obtained. Sensitivity studies were performed to compare the proposed multiregion heterogeneity treatment with conventional two-region treatments. The results suggest that it may be important to self-shield explicitly and heterogeneously all the fuel and structural materials in the analysis of fast critical assemblies.