A Numerical Scheme for the Pore-Scale Simulation of Crystal Dissolution and Precipitation in Porous Media

Abstract

Abstract.In this paper we analyze a numerical scheme for a dissolution and precipitation in porous media. We focus here on the chemistry, which is modeled by a parabolic problem that is coupled through the boundary conditions to an ordinary differential inclusion defined on the boundary. We use a regularization approach for constructing a semi-implicit scheme that is stable and convergent. For dealing with the emerging time discrete nonlinear problems, we propose a simple fixed point iterative procedure. The paper is concluded by numerical results.

Analysis and Upscaling of a Reactive Transport Model in Fractured Porous Media with Nonlinear Transmission Condition

“…Proof Here we use again mathematical induction and follow ideas in [8]. The statement holds trivially for k = 0.…”

Rigorous upscaling of rough boundaries for reactive flows

“…The existence and uniqueness results derived for the pore scale model in [13,17,44] remain valid in the present context. In [13,17] the following is proved Theorem 2.4 Under assumptions (A.1) and (A.2), there exists a weak solution in the sense of Definition 2.2.…”

“…In [13,17] the following is proved Theorem 2.4 Under assumptions (A.1) and (A.2), there exists a weak solution in the sense of Definition 2.2. In addition, the solution satisfies…”

“…For the numerical results we refer to [13], where the convergence of an Euler implicit discretization for the pore scale model (similar to the present one) is proved.…”

“…The model (2) is a simplified setting for the model considered in [13,[15][16][17] and we refer to the cited literatures for more details.…”