Diffusion-based leaching models for glassy waste forms

Most scenarios for the disposal of high-level nuclear wastes assume burial under conditions in which only a limited quantity of groundwater will contact the waste form. In order to model these conditions, it is necessary to describe the release of species from a waste form matrix in contact with a limited volume of leachant in which the concentration of released species is not zero and is itself a function of release rate. Eight leaching models are presented that include the cases of a dissolving and a nondissolving matrix, finite, infinite, and replenished leachant volumes, and a matrix covered by a surface layer with different properties. The equations that describe these models assume a linear concentration profile of the diffusing species within the waste form and apply Fick's first law to obtain the leach rate. In three cases a direct comparison is possible between the solutions of these equations and solutions obtained by use of the diffusion equation derived from Fick's second law. Good agreement is found. The equations given are convenient for use with programmable calculators