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. (5th October 2021) - Zhao, Chongbin; Hobbs, Bruce; Ord, Alison
Abstract: 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.