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Science and Technology of Nuclear Installations
Volume 2012 (2012), Article ID 149089, 6 pages
Research Article

A Fast Numerical Method for the Calculation of the Equilibrium Isotopic Composition of a Transmutation System in an Advanced Fuel Cycle

Centro de Investigaciones Energ├ęticas, Medioambientales y Tecnológicas (CIEMAT), Avenida. Complutense 40. Ed. 17, 28040 Madrid, Spain

Received 15 November 2011; Accepted 30 January 2012

Academic Editor: Alberto Talamo

Copyright © 2012 F. Álvarez-Velarde and E. M. González-Romero. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A fast numerical method for the calculation in a zero-dimensional approach of the equilibrium isotopic composition of an iteratively used transmutation system in an advanced fuel cycle, based on the Banach fixed point theorem, is described in this paper. The method divides the fuel cycle in successive stages: fuel fabrication, storage, irradiation inside the transmutation system, cooling, reprocessing, and incorporation of the external material into the new fresh fuel. The change of the fuel isotopic composition, represented by an isotope vector, is described in a matrix formulation. The resulting matrix equations are solved using direct methods with arbitrary precision arithmetic. The method has been successfully applied to a double-strata fuel cycle with light water reactors and accelerator-driven subcritical systems. After comparison to the results of the EVOLCODE 2.0 burn-up code, the observed differences are about a few percents in the mass estimations of the main actinides.