Abstract

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.

1. INTRODUCTION

Dissolution of porous media or solids is widely concerned in many industrial fields, e.g., acid injection into petroleum reservoirs, dissolution of rocks caused by underground water, etc. In the latter, rock dissolution creates underground cavities of different shapes and sizes, which induces a potential risk of collapse as shown in Fig.1. In most applications, modeling such liquid/solid dissolution problems is of paramount importance.

Among all methods used for modeling dissolution process, we present two ways for simulating this problem. The first one is a direct treatment of the evolution of the fluid-solid interface, for instance using an ALE (Arbitrary Lagrangian-Eulerian) method [4]. The second uses a Diffuse Interface Model (DIM) to smooth the interface with continuous quantities [1, 3, 6 ], like the liquid phase volume fraction, species mass fractions, etc.

However, there are several difficulties associated with ALE method for the dissolution problem: in particular, the need for fine meshes near the dissolving interface can lead to severely deformed grid elements inducing numerical problems (instabilities, need for remeshing, etc.).

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