A diffuse interface model for solid-liquid-air dissolution problems based on a porous medium theory

Abstract

The underground rock may be dissolved by the flows of groundwater where the dissolution mainly happens at the liquid-solid interface. In many practical cases, the underground cavities are not occupied only by the water, but also the gas phase, e.g., air, CO2. In this case, there are solid-liquid-gas three phases. Normally, the air does not participate the dissolution. However, it may influence the dissolution as the position of the solid-liquid interface may gradually change with the dissolution process. Simulating the dissolution problems with multi-moving interfaces is a difficult but rather interesting task. In this paper, we propose a diffuse interface model (DIM) to simulate the three-phase dissolution problem, based on a porous medium theory and a volume averaging theory. The interfaces are regarded as continuous layers where the phase indicator (for the solid-liquid interface) and the phase saturation (for the liquid-gas interface) vary rapidly but smoothly.