Distributed Resonance Self-Shielding Using the Equivalence Principle

This paper presents an extension of the equivalence principle to allow distributed resonance self-shielding in a multiregion fuel configuration. Rational expansion of fuel-to-fuel collision probability is applied to establish equivalence between the actual fuel configuration and a homogeneous mixture of hydrogen and resonant absorber, which is a commonly used model to calculate library tables of resonance integrals. The main steps in the derivation are given along with the basic physics assumptions on which the presented approach relies. The method has been implemented in the WIMS-AECL lattice code and is routinely used for calculation of CANDU-type reactor lattices. Its capabilities are illustrated by comparison of WIMS-AECL and MCNP results of ²³⁸U resonance capture in a CANDU lattice cell. To determine the optimal rational expansion of the fuel-to-fuel collision probability, the calculations were carried out by varying the number of rational terms from one to six. The results show that four terms are sufficient. Further increase of the number of terms affects the computing time, while the effect on accuracy is negligible. To illustrate the convergence of the results, the fuel subdivision is gradually refined varying the number of fuel pin subdivisions from 1 to 32 equal-area annuli. The results show very good agreement with the reference MCNP calculation.