An accurate porosity-velocity-concentration approach for solving reactive mass transport problems involving chemical dissolution in fluid-saturated porous media with arbitrarily initial porosity distributions

This article presents an accurate porosity-velocity-concentration approach, in which porosity, pore-fluid velocity and the concentration of dissolvable substances in the pore fluid are selected as four primary unknown variables for solving reactive mass transport problems involving chemical dissolution in fluid-saturated porous media with arbitrarily initial porosity distributions. The first advantage of using the proposed approach is that since pore-fluid velocity, instead of pore-fluid pressure, is selected as the primary unknown variable to describe the pore-fluid flow process, the pore-fluid velocity obtained from the proposed approach is more accurate than that obtained from the numerical simulation, in which pore-fluid pressure is selected as the primary unknown variable to describe the pore-fluid flow. The second advantage of using the proposed approach is that because the property matrices of a four-node rectangular element are precisely calculated in a purely mathematical way, the overall accuracy of numerical solutions can be ensured. After the proposed approach is verified by a benchmark problem, it has been applied for solving reactive mass transport problems involving chemical dissolution in fluid-saturated porous media with three different kinds of initial porosity distributions. It has been demonstrated that: (1) the proposed approach can produce highly-accurate numerical solutions for solving reactive mass transport problems involving chemical dissolution in fluid-saturated porous media with arbitrarily initial porosity distributions; (2) the initial porosity distribution in a porous medium can have remarkable effects on the reactive mass transport process in the porous medium; (3) the porosity and dimensionless concentration fronts propagate from the entrance to the exit of the problem domain, which is identical to the pore-fluid flow direction.