Existence and uniqueness results of unsteady reactive flows in porous media

Abstract: Miscible reactive flows in porous media play crucial roles in many engineering and industrial applications. In this work, we establish several results regarding the existence and uniqueness of solutions for a system of time-dependent, nonlinear partial differential equations that describe the flow and transport of miscible reactive fluids with variable viscosity in heterogeneous porous media with variable permeability. Fluid flow is modelled via the unsteady Darcy-Brinkman equation with Korteweg stresses coupled with an advection-diffusion-reacton equation for the transport of a solute responsible for the viscosity variation and the Korteweg stresses. Our analysis is based on the semi-discrete Galerkin method, which allows us to pass the limit and establish that the approximate solution converges to the solution of the proposed problem. We also discuss particular cases that are widely used in the studies of miscible fingering instabilities in the porous media with application in oil recovery and/or geological carbon sequestration.