Crystal precipitation and dissolution in a thin strip

We present a two-dimensional micro-scale model for crystal dissolution and precipitation in a porous medium. The local geometry of the pore is represented as a thin strip and the model allows for changes in the pore volume. A formal limiting argument, for the limit of the width of the strip going to zero, leads to a system of one-dimensional effective upscaled equations. We show that the effective equations allow for travelling-wave solutions and prove the existence and uniqueness of these. Numerical solutions of the effective equations are compared with numerical solutions of the original equations on the thin strip and with analytical results. We also show that a model from the literature that does not allow changes in the pore volume can be obtained from the present model as a formal limit.