Numerical modelling of microscopic dynamics of in-situ leaching

Dissolution of the solid ground by an acid is one of subprocesses of in-situ leaching. The objective of this paper is the numerical simulation of these processes at the porous level. The case of two spatial variables is considered. We admit the fluid dynamics to be described by stationary Stokes equations, while acid concentration is described by the convection-diffusion equation. The problem is completed with boundary and initial conditions.
For the numerical simulation of the problem, the method of finite differences on staggered grids is used. At each time step, the fluid velocity components are computed iteratively by the successive over-relaxation method. The fluid pressure, the concentration of acid and the position of the free boundary are determined using an explicit scheme. To define the boundary condition for the acid concentration at the free boundary, a system of nonlinear equations is solved by the iterative Newton method.
Results of the numerical experiments are presented and discussed. In particular, the results obtained can help in analyzing the motion of the free solid/liquid interface and the mechanisms of physical and chemical processes there.