Dissolution/precipitation of a two-member chain at a dissolving waste matrix

When the matrix of a nuclear waste in porous rock dissolves in ground water, other species in the waste are also released. Some species, such as the actinides and rare-earths, are of such low solubility that they may precipitate as soon as they are dissolved, depending on the rate of matrix dissolution, their concentration in the waste solid, their solubilities, and the ground water transport rate. We have previously studied the solubility-limited dissolution of single species as controlled by the rate of advective mass transfer from the waste surface. When the waste constituents include low-solubility members of a decay chain, the radioactive decay daughter can form a precipitate at the waste surface or in the rock away from the waste surface. Here we present a simplified analysis of the precipitate formation and dissolution of species in a two- member decay chain. For this purpose it is assumed that flowing ground water becomes saturated with the chemical species of the nuclides as it flows past the waste, resulting in a constant rate of solubility-limited dissolution of the waste matrix. Assuming congruent release of other waste constituents from the solid, the time-dependent amounts of precipitates of the first and second member of the decay chain at the waste surface can be calculated. Numerical illustrations for the 234U→230Th chain from spent fuel are given in this paper