Homogenization of a nonlinear stochastic model with nonlinear random forces for chemical reactive flows in porous media

Abstract

In this study, we establish new homogenization results for chemical reactive fluxes in porous media using a nonlinear stochastic model with nonlinear random forces. This model is mathematically represented by a linear stochastic response equation, a nonlinear boundary condition, a nonlinear stochastic diffusion equation, and external nonlinear random forces that affect the solute concentration and diffusion in the fluid phase. A homogenized model made up of a nonlinear stochastic diffusion equation with extra terms reflecting the impact of the adsorption and chemical reactions occurring on the boundaries of the perforations and a stochastic differential equation with extra nonlinear term representing the limit for the surface problem is derived using the periodic unfolding operator method and probabilistic compactness results. To guarantee that the entire sequence converges, we also show the uniqueness result for the limit problem. Finally, we go over some applications for the interaction of chemical fluxes.