Homogenization of a Nonlinear Stochastic Convection-Diffusion Model for Reactive Flows with Noise Boundary

In this paper, we address the transport of a solute through a porous media that involves both convection and diffusion, along with a linear chemical reaction (desorption/adsorption) occurring on the pore surfaces, all of which are influenced by external nonlinear random forces. The mathematical representation of this model is a system of a non-linear stochastic convection-diffusion equation in the saturated fluid phase and a linear stochastic convection-diffusion equation on the surface of porosity coupled with a linear reaction term. We use the method of two-scale convergence with drift and probabilistic compactness results to obtain a homogenized model consisting of a nonlinear stochastic diffusion equation where the concentration of the fluid on the pore surface contributes to the diffusion coefficient of the homogenized model.