Effects of Medium Permeability Anisotropy on Chemical-Dissolution Front Instability in Fluid-Saturated Porous Media

摘要

This paper deals with the theoretical aspects of chemical-dissolution front instability problems in two-dimensional fluid-saturated porous media including medium anisotropic effects. Since a general anisotropic medium can be described as an orthotropic medium in the corresponding principal directions, a two-dimensional orthotropic porous medium is considered to derive the analytical solution for the critical condition, which is used to judge whether or not the chemical dissolution front can become unstable during its propagation. In the case of the mineral dissolution ratio (that is defined as the ratio of the dissolved-mineral equilibrium concentration in the pore-fluid to the molar concentration of the dissolvable mineral in the solid matrix of the fluid-saturated porous medium) approaching zero, the corresponding critical condition has been mathematically derived when medium permeability anisotropic effects are considered. As a complementary tool, the computational simulation method is used to simulate the morphological evolution of chemical dissolution fronts in two-dimensional fluid-saturated porous media including medium anisotropic effects. The related theoretical and numerical results demonstrated that: (1) a decrease in the medium anisotropic permeability factor (or ratio), which is defined as the ratio of the principal permeability in the transversal direction to that in the longitudinal direction parallel to the pore-fluid inflow direction, can stabilize the chemical dissolution front so that it becomes more difficult for a planar chemical-dissolution front to evolve into different morphologies in the chemical dissolution system; (2) the medium anisotropic permeability ratio can have significant effects on the morphological evolution of the chemical dissolution front. When the Zhao number of the chemical dissolution system is greater than its critical value, the greater the medium anisotropic permeability ratio, the faster the irregular chemical-dissolution front grows.