Depletion Calculations Based on Perturbations. Application to the Study of a Rep-Like Assembly at Beginning of Cycle with TRIPOLI-4^®.

Commissariat à l’Energie Atomique et aux Energies Alternatives, Centre de Saclay, Service d’Etude des Réacteurs et de Mathématiques Appliquées (DEN/DANS/DM2S/SERMA/LTSD) F91191 Gif-sur-Yvette CEDEX, France

^* Corresponding Author, E-mail: eric.dumonteil@cea.fr

Abstract

For several years, Monte Carlo burnup/depletion codes have appeared, which couple Monte Carlo codes to simulate the neutron transport to deterministic methods, which handle the medium depletion due to the neutron flux. Solving Boltzmann and Bateman equations in such a way allows to track fine 3-dimensional effects and to get rid of multi-group hypotheses done by deterministic solvers. The counterpart is the prohibitive calculation time due to the Monte Carlo solver called at each time step.

In this paper we present a methodology to avoid the repetitive and time-expensive Monte Carlo simulations, and to replace them by perturbation calculations: indeed the different burnup steps may be seen as perturbations of the isotopic concentration of an initial Monte Carlo simulation. In a first time we will present this method, and provide details on the perturbative technique used, namely the correlated sampling. In a second time the implementation of this method in the TRIPOLI-4^® code will be discussed, as well as the precise calculation scheme a meme to bring important speed-up of the depletion calculation. Finally, this technique will be used to calculate the depletion of a REP-like assembly, studied at beginning of its cycle. After having validated the method with a reference calculation we will show that it can speed-up by nearly an order of magnitude standard Monte-Carlo depletion codes.