Theoretical and numerical analyses of chemical‐dissolution front instability in fluid‐saturated porous rocks

Abstract

SUMMARYThe chemical-dissolution front propagation problem exists ubiquitously in many scientific and engineering fields. To solve this problem, it is necessary to deal with a coupled system between porosity, porefluid pressure and reactive chemical-species transport in fluid-saturated porous media. Because there was confusion between the average linear velocity and the Darcy velocity in the previous study, the governing equations and related solutions of the problem are re-derived to correct this confusion in this paper. Owing to the morphological instability of a chemical-dissolution front, a numerical procedure, which is a combination of the finite element and finite difference methods, is also proposed to solve this problem. In order to verify the proposed numerical procedure, a set of analytical solutions has been derived for a benchmark problem under a special condition where the ratio of the equilibrium concentration to the solid molar density of the concerned chemical species is very small. Not only can the derived analytical solutions be used to verify any numerical method before it is used to solve this kind of chemical-dissolution front propagation problem but they can also be used to understand the fundamental mechanisms behind the morphological instability of a chemical-dissolution front during its propagation within fluid-saturated porous media. The related numerical examples have demonstrated the usefulness and applicability of the proposed numerical procedure for dealing with the chemical-dissolution front instability problem within a fluid-saturated porous medium.

Theoretical analyses of nonaqueous phase liquid dissolution‐induced instability in two‐dimensional fluid‐saturated porous media

“…Compared with the previous case when dispersion is considered as the scalar of a constant [29,36,37], two new terms, namely…”

HYTEC results of the MoMas reactive transport benchmark

“…Several possiblities are open to test the precision and accuracy of the codes. Analytical solutions are the ideal tool, when available [5,15,21,13]; however, they are not easy to devise and are limited to simplified systems: specific hydrodynamic, simplistic chemistry, weak feedbacks. It is also possible to use laboratory or field experiments [6,12].…”

Parallel simulation of wormhole propagation with the Darcy–Brinkman–Forchheimer framework

“…3) and a number of semi-empirical equations that bridge the scale differences, as described earlier (Eqs. [4][5][6] [30]. They can be listed as follows:…”

“…Engineers and hydrologists appeal to this technique when the efficiency of oil production wells deteriorates due to the deposition of mud and fines at the perforated well pore pipe. In geo-environmental engineering [13][14][15][16][17] and petroleum engineering [1][2][3], Zhao and his co-workers have conducted extensive and systematic theoretical studies in recent years [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. In particular, many important factors such as the mineral reactive surface area [6], mineral dissolution ratio [8], solute dispersion [9], medium anisotropy [12], temperature effect [18,19], and medium and fluid compressibility [10] have been successfully considered in both theoretical analyses and computational simulations.…”

“…In this framework, field variables represent continuous functions of space and time, and the governing conservation equations are described in the form of differential equations [34][35][36]. Zhao et al [3][4][5] used a combination of the finite element method and the finite difference method to simulate wormhole generation and propagation in carbonate rocks. However, compared with Zhao's methods, our proposed finite difference method is more easily parallelized.…”