A novel algorithm for implementing perturbations in computational simulations of chemical dissolution-front instability problems within fluid-saturated porous media

This paper deals with how to implement perturbations in the computational simulations of chemical dissolution-front instability (CDFI) problems in fluid-saturated porous media. On the basis of theoretical analysis, it is found that the application of a perturbation to the chemical dissolution front is equivalent to the application of an alternative perturbation to the dimensionless pore-fluid normal velocity (relative to the planar chemical dissolution front) in the chemical dissolution zone, where the chemical dissolution front is located. This avoids the difficulty to find the spatial coordinates of the chemical dissolution front locations in the computational simulations of CDFI problems. Based on this new finding, a novel algorithm for implementing perturbations in the computational simulations of CDFI problems is proposed. The key point of the proposed algorithm is that the perturbed pore-fluid normal velocity (relative to the planar chemical dissolution front) is used to directly replace the original pore-fluid normal velocity (relative to the planar chemical dissolution front) in the related mathematical governing equations (MGEs), so that the proposed algorithm works for the porosity-velocity-concentration scheme when it is used to solve CDFI problems in fluid-saturated porous media. In addition, the related theoretical analysis in this study has answered the previous unanswered question why the application of a perturbation to porosity works in the porosity-pressure-concentration scheme but does not work in the porosity-velocity-concentration scheme for solving the same CDFI problems in fluid-saturated porous media. Through solving two illustrative examples with two different distributions of initial porosity, in which one is homogeneous and another is heterogeneous in the chemical dissolution system, the validity and usefulness of the proposed algorithm for implementing perturbations in the computational simulations of CDFI problems have been demonstrated.