Analysis and Modeling of Dissolution of Porous Media as Moving Boundary Problems.

Abstract

When a porous medium is dissolved by the reacting acid, its pore geometry is changed. The acid that is transported by convection and diffusion etches the surface of the pore by chemical reaction. The acid enlarges the pore radius as it penetrates into the medium producing channels referred to as wormholes. Previous models have not explicitly accounted for the rate of pore growth as a result of the radial movement of the boundary by chemical reaction, and separate solutions were obtained for the two limiting cases of diffusion or chemical reaction control. We demonstrate in this paper that this problem can be described by a unified model for both kinetic and diffusion limited regimes and in a manner analogous to a plug-flow reactor with axial and radial dispersions with the rate of chemical reaction introduced as a moving boundary condition at the pore surface. Numerical solutions were obtained taking into account the different values of the Damkohler number, Biot number, Acid number, and initial pore structure appropriate for each regime, rate of pore growth, and penetration distance.