Modelling of Intra-Granular Diffusion, Production and Removal in SOURCE 2.0

Abstract

In this paper, the Release by Diffusion module of SOURCE IST 2.0 is discussed. The paper presents the physical processes modelled in this code module and discusses some of the numerical methods applied to the solution of the resulting equations. Application of Fick's Law requires solution of the concentration profile within the grain for isotopes of interest. which in turn requires modelling of isotope production through fission. decay of parent isotopes and neutron capture processes, isotope removal through radioactive decay and neutron capture, and transport via diffusion. The central calculational driver for the Release by Diffusion module, which evaluates the concentration profile, is the GrainDist subroutine and its sub-programs: its overall structure and place in the Release by Diffusion module is briefly described. The differential equation for the combined diffusion/depletion/production equation is discretized using a Crank- Nicholson approach (i.e., second-order spatial discretization and first order temporal discretization). The central node is approached differently: the boundary condition that the spatial derivative of the concentration profile must he zero at the centre of the grain is used to derive the numerical expression solved for. Some discussion is provided on the handling of precursor isotopes and their effect on the evolution of the concentration profile o f isotopes of interest. Some testing of the module has been performed and an example is given in which the calculated release rate for 135I is compared to an analytical solution for a range of intra-granular spatial discretizations.