Morphological evolution of three‐dimensional chemical dissolution front in fluid‐saturated porous media: a numerical simulation approach

This paper is concerned with the morphological evolution of three‐dimensional chemical dissolution fronts that occur in fluid‐saturated porous media. A fully coupled system between porosity, pore‐fluid flow and reactive chemical species transport is considered to describe this phenomenon. Using the newly presented concept of the generalized dimensionless pore fluid pressure‐gradient, which can be used to represent the interaction between solute advection, solute diffusion, chemical kinetics and the shape factor of the soluble mineral, a theoretical criterion has been established to assess the likelihood of instability at a chemical dissolution front in the reactive transport system. To simulate the chemical dissolution front evolution in a three‐dimensional fluid‐saturated porous medium, a numerical procedure combining both the finite difference method and the finite element method has been proposed. As the problem belongs to a complex system science problem, a small randomly generated perturbation of porosity is added to the initial porosity of a three‐dimensional homogeneous domain to trigger instability of a planar chemical dissolution front during its propagation within the fluid‐saturated porous medium. To test the correctness and accuracy of the proposed numerical procedure, a three‐dimensional benchmark problem has been constructed and the related analytical solution has been derived. This enables using the proposed numerical procedure for simulating the morphological evolution of a three‐dimensional chemical dissolution front from a stable, planar state into an unstable, fingering state. The related numerical results demonstrate that the proposed numerical procedure is useful for, and capable of, simulating the morphological instability of a three‐dimensional chemical dissolution front within a fluid‐saturated porous medium.