Modelling glass dissolution in clay with analytic and stochastic methods

We present a stochastic method to model the dissolution of nuclear glass. Using this method, we solve the diffusion equation in a stochastic way. We do this by giving a large number of particles Brownian displacements. Simultaneously, these particles can participate in other processes, like a chemical reaction or convection. We apply this method to solve the Pescatore model for the dissolution of nuclear glass in clay. This model combines diffusion of silica in the pore water of the clay with the glass dissolution rate law proposed by Grambow. We use the model for fitting the dissolution data of four glasses in clay slurries (with a high and with a low clay content) and in pure clay. We present the values of the fitting parameters. The solution of the model, obtained by the simulation method, agrees with the analytical solution. We also extend the Pescatore model with a moving boundary, taking into account the receding of the glass surface by corrosion.