Moving Boundary Model for Leaching of Nuclear Waste Glass

Abstract

AbstractThe leaching experiments of Soxhlet type have been carried out[l, 2] and on the basis of the results we developed the mathematical leaching model which used one dimensional diffusion and could treat the growth of surface layers. The model adopted the following assumptions: 1) The velocity of the bulk glass-surfacé layers boundary depends on time alone. 2) Some of the diffusing substances are immobilized in the surface layers by an irreversible first-order reaction. 3) A fictitious film exists at the solution-surface layers interface. The fundamental equations were established based on these assumptions and the numerical solutions were obtained by the Crank-Nicholson implicit method. The values of the diffusion coefficient, the reaction rate and the film mass transfer coefficient were obtained by a trial-and-error method. The applicability of the model was confirmed by the fact that the leaching mechanisms deduced from the calculated results were consistent with those mechanisms deduced from the experimental results. The present study showed the proposed model was valid for calculation of the leach rates of waste glasses when surface layers grew during leaching, and the study also indicated which parameters should be measured experimentally to predict the leach rates.