Exact and numerical solutions to the moving boundary problem resulting from reversible heterogeneous reactions and aqueous diffusion in a porous medium

Abstract

Numerical finite difference calculations for diffusional mass transport incorporating reactions between minerals and a fluid phase, based on a continuum representation of porous media, are compared with the exact solution. The finite difference algorithm is based on the weak formulation of the moving boundary problem in which a fixed grid of node points is used. Mineral reactions are considered to be in local equilibrium with a fluid phase and may take place either at sharp reaction fronts or distributed homogeneously throughout a control volume. The theory is applied to one‐ and two‐component systems. Analytical solutions to the finite difference equations for the first and second node points provide for a detailed comparison with the exact solution. It was found that on a time scale that is small compared with the time required for the solid to completely dissolve at a single node point, the finite difference approximation yields a spurious behavior for the concentration and solid phase volume fraction. However, the finite difference algorithm reproduces the average behavior of the motion of the reaction front and concentration of the reacting species provided the advance of the front is sufficiently slow resulting in a quasi‐steady state solution. A numerical example is presented for the dissolution of quartz at 550°C and 1000 bars to illustrate the general theory.