Extraction of salt by leaching process is used intensively nowadays. This process extracts salt by dissolving the mineral with water. In this analysis about cavity dissolution modeling, we consider the case of a binary system, i.e., a chemical solute corresponding to 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 solve such dissolution problems. The control equations are obtained by upscaling micro-scale equations for a solid-liquid dissolution problem using a volume averaging theory. Based on this mathematical formulation, dissolution test cases are presented. We introduce and discuss the main features of the method. Illustrations of the interaction between natural convection and forced convection in dissolution problems are presented and the time and space evolution of the rock salt-fluid interface is shown through several examples.