Abstract
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.
Highlights
The implementation of the advanced technologies of partitioning and transmutation (P&T) depends on the particular topics that energy policy makers of a country or region choose to optimize because of its singular constraints or motivations
We describe a fast numerical method for the calculation of the equilibrium isotopic composition in a zero-dimensional approach, taking advantage of the Banach fixed point theorem [5] for the demonstration of uniqueness and existence of a solution
The isotopic composition of the accelerator-driven subcritical system (ADS) fuel at BOL has been calculated for the following cycle Vn+1 by means of the advanced burn-up code EVOLCODE 2.0 for checking purposes
Summary
The implementation of the advanced technologies of partitioning and transmutation (P&T) depends on the particular topics that energy policy makers of a country or region choose to optimize because of its singular constraints or motivations. The full potential of any P&T policy can be exploited only if the advanced fuel cycle strategy is utilized for a minimum time period of about a hundred years [1, 2] During this period of time, the irradiated fuels of the advanced reactors are reprocessed to obtain the useful elements for their later recycling as part of the new fresh fuel, in an iterative procedure along successive cycles. The calculation of the equilibrium isotopic composition of a transmutation system in an advanced fuel cycle is a matter of special interest since this composition is often used as representative of the nuclear reactor through the whole fuel cycle [3, 4]. With the aim of validating the methodology, a simulation of the fuel cycle with the advanced burn-up code EVOLCODE 2.0 [6, 7] has been performed, checking that the isotopic composition has successfully reached the equilibrium and discussing the range of the possible deviations
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