On the classical solution of the macroscopic model of in-situ leaching of rare metals

A. M. Meirmanov

Izvestiya. Mathematics , Tome 86 (2022) no. 4, pp. 727-769

Résumé

We consider initial-boundary value problems describing the in-situ leaching of rare metals (uranium, nickel and so on) with an acid solution. Assuming that the solid skeleton of the ground is an absolutely rigid body, we describe the physical process in the pore space at the microscopic level (with characteristic size about 5–20 microns) by the Stokes equations for an incompressible fluid coupled with diffusion–convection equations for the concentrations of the acid and the chemical reaction products in the pore space. Since the solid skeleton changes its geometry during dissolution, the boundary ‘pore space–solid skeleton’ is unknown (free). Using the homogenization method for media with a special periodic structure, we rigorously derive a macroscopic mathematical model (with characteristic size of several meters or tens of meters) of incompressible fluid corresponding to the original microscopic model of the physical process and prove the global-in-time existence and uniqueness theorems for classical solutions of the resulting macroscopic mathematical model.

Détail

Keywords: free boundary problems, two-scale convergence, homogenization of periodic structures, fixed point theorem.