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Theoretical and numerical analyses of chemical-dissolution front instability in fluid-saturated porous rocks. (English) Zbl 1273.74332

Summary: The 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, pore-fluid 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.

MSC:

74L10 Soil and rock mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74F25 Chemical and reactive effects in solid mechanics
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