Brownian Simulation of Matrix Diffusion

Abstract

The commonly used approach in dealing with matrix diffusion is to assign an effective diffusion constant for the radionuclide in the rock matrix. The idea behind this approach is that, on a scale much larger than the pore size, the irregularities tend to cancel out. Although it might look plausible at first sight, this approach has been questioned both for theoretical and experimental reasons.

Here, Brownian simulation has been used to investigate the transport of dissolved material in a rock matrix modeled as a system of pores with a wide variability in size and shape. The Boltzmann distribution is used locally, although the system globally is far from equilibrium.

The simulation consists of two main parts. First, the model rock is formed by precipitation of irregular mineral grains from a liquid phase. As the grains grow, they tend to form a mostly solid piece of rock.

In the second part of the simulation, a dissolved species is introduced at one side of the rock and allowed to diffuse through its pore system. It is found that no apparent diffusion constant, D, can explain the properties of the system. Rather, D is found to be a function of both distance and time.