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

Abstract

Abstract 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.