Simulation of porosity reduction in random structures

Abstract

We describe an algorithm for computing the motion of a solid-liquid interface in 2D, which is applicable to geological pressure solution or to pressure sintering. The backward motion (toward the solid) of the interface is due to dissolution of the solid, and the forward motion (away from the solid) is due to the inverse process of reprecipitation. The interface velocity is assumed proportional to the difference between the solubility of the solid and the concentration of the solution. The former is dependent upon stress (the phenomenon of “pressure solution”), so our algorithm must also keep track of the stress. We use a Lagrangian grid, with constant-stress periodic boundary conditions. The method has been applied to porosity reduction in sandstone. It is applicable to other interface-following problems, such as freezing, if the motion is slow enough that heat transport is not rate-limiting.