Depletion Perturbation Theory in decay heat calculation context

Abstract

This article describes an implementation of Depletion Perturbation Theory (DPT) using deterministic neutronics code APOLLO3® alongside depletion code MENDEL. We use DPT to calculate the sensitivity coefficients of decay heat (DH) to various nuclear data such as reaction cross-sections, fissions yields, and reaction energy. DPT allows for the coupling of the Bateman, Boltzmann, and normalization equations, and has the advantage of needing only one calculation per cooling time to compute the sensitivity coefficient to all input parameters, as opposed to usual finite differences schemes which need as many calculation as there are input parameters. The calculation of sensitivity coefficients is done using both the DPT methodology and a finite differences scheme as a mean of numerical verification. Both methods showed good agreement, although we found that DPT should be used with care when studying short cooling times. Sensitivity coefficients were then used to perform deterministic uncertainty propagation, the resulting uncertainty calculation were used to compare the effect of various coupling configurations.