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

Abstract

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.

Semi‐analytical solution for a simplified 1D chemo‐hydro‐mechanical model in fluid‐saturated viscoelastic clay

“…Third, chemical reactions, which should be considered in realistic CHM models, [44][45][46][47][48][48][49][50] are neglected in this study. Fourth, since the simplified CHM model of this study is one-dimensional, both chemical dissolution-front instability and physical dissolution-front instability [33][34][35][36][37][38] are neglected in this study. These limitations should be removed in future studies.…”

“…Extensive theoretical studies [33][34][35][36] and computational simulations 37,38 have demonstrated that chemical reactions are strongly coupled with the pore-fluid flow process, porosity evolution process, solute transport process, and medium deformation process in fluid-saturated soils and rocks. This means that chemical reactions should be considered in realistic CHM models.…”

Analytical solution for one‐dimensional steady‐state VOCs diffusion in simplified capillary cover systems

“…The diffusion of VOCs through the unsaturated cover soil i can be given by 18 $$$$\begin{equation}\frac{{\rm{d}}}{{{\rm{d}}z}}\left[ {{D_{r,i}}\left( {{\theta _i}} \right)\frac{{{\rm{d}}{C_{r,i}}\left( z \right)}}{{{\rm{d}}z}}} \right] = 0\end{equation}$$$$where, $${C_{r,i}}( z )$$ is the vapour‐phase VOC concentration in soil i ; and $${D_{r,i}}( \theta )$$ is the VOC effective diffusion coefficient in the soil i . It was indicated in Equation (10), the mass advection and source/sink terms, which are caused by chemical reactions 18–50,62–64 and physical reactions, 51,57 are neglected in the mass transport process 62–64 . This is another major limitation of this study.…”

“…where, 𝐶 𝑟,𝑖 (𝑧) is the vapour-phase VOC concentration in soil i; and 𝐷 𝑟,𝑖 (𝜃) is the VOC effective diffusion coefficient in the soil i. It was indicated in Equation ( 10), the mass advection and source/sink terms, which are caused by chemical reactions [62][63][64] and physical reactions, 51,57 are neglected in the mass transport process. [62][63][64] This is another major limitation of this study.…”

“…It was indicated in Equation ( 10), the mass advection and source/sink terms, which are caused by chemical reactions [62][63][64] and physical reactions, 51,57 are neglected in the mass transport process. [62][63][64] This is another major limitation of this study.…”