Homogenization of a pore scale model for precipitation and dissolution in porous media

Abstract

In this paper we employ homogenization techniques to provide a rigorous derivation of the Darcy scale model for precipitation and dissolution in porous media proposed in [19]. The starting point is the pore scale model in [12], which is a coupled system of evolution equations, involving a parabolic equation and an ordinary differential equation. The former models ion transport and is defined in a periodically perforated medium. It is further coupled through the boundary conditions to the latter, defined on the boundaries of the perforations and modelling the dissolution and precipitation of the precipitate. The main challenge is in dealing with the dissolution and precipitation rates, which involve a monotone but multi-valued mapping. Due to this, the micro-scale solution lacks regularity. With $\ep$ being the scale parameter (the ratio between the micro scale and the macro scale length), we adopt the 2-scale framework to achieve the convergence of the homogenization procedure as $\ep$ approaches zero.