Crystal Precipitation and Dissolution in a Porous Medium: Effective Equations and Numerical Experiments

We investigate a two-dimensional micro-scale model for crystal dissolution and precipitation in a porous medium. The model contains a free boundary and allows for changes in the pore volume. Using a level-set formulation of the free boundary, we apply a formal homogenization procedure to obtain upscaled equations. For general micro-scale geometries, the homogenized model that we obtain falls in the class of distributed microstructure models. For circular initial inclusions the distributed microstructure model reduces to system of partial differential equations coupled with an ordinary differential equation. In order to investigate how well the upscaled equations describe the behavior of the micro-scale model, we perform numerical computations for a test problem. The numerical simulations show that for the test problem the solution of the homogenized equations agrees very well with the averaged solution of the micro-scale model.