A numerical method for cavity dissolution in salt formation
Résumé
Solution mining is a well known method for extracting salt by dissolving this mineral with water. In this analysis about cavity dissolution modeling, we consider the case of a binary system, i.e., a chemical solute constitutes the solid that is dissolved by a "solvent" (mainly water). Rock salt dissolution is controlled by thermodynamic equilibrium at the interface, i.e., equality of the chemical potentials. In this paper, a local non-equilibrium Diffuse Interface Model (DIM) and an explicit treatment of the brine-salt interface (using an ALE (Arbitrary Lagrangian-Eulerian) technique) are introduced in order to describe dissolution problems in such binary cases. The control equations are obtained by upscaling micro-scale balance equations for a solid-liquid dissolution problem using a volume averaging theory. This results in a diffuse DIM model for dissolution. After the mathematical formulation, dissolution test cases are presented. We show the main features of the method. An optimum expression for the solid liquid exchange coefficient is obtained by comparison with reference solutions obtained by ALE simulations. Illustrations of the interaction between natural convection and forced convection in dissolution problems are presented. The ability of the method to track accurately the time and space evolution of the rock salt-fluid interface is shown through several examples.