Understanding Reactive Flows in Porous Medium: A Numerical Approach

Reactive flows are the flows involving fluids undergoing a chemical reaction when in contact. We explore the reactive flows in porous medium in connection with the enhanced oil recovery, CO₂ sequestration, fluid mixing, to name a few. We consider miscible fluids undergoing radial displacement and a second order chemical reaction to generate a product. We model the flow using Darcy’s law coupled to a system of convection-diffusion-reaction equations. A hybrid numerical scheme based on compact finite difference and pseudo-spectral method is used to understand various scalings of the amount of product generated and the spreading of the product with time. The product having different viscosity than the reactants results a hydrodynamic instability called viscous fingering (VF). The deformation of the fluid-fluid interface into finger-like patterns when a less viscous fluid displaces a more viscous fluid is termed as VF. A novel linear stability analysis is performed to understand the onset of the instability wherein similarity and differences with rectilinear displacement are discussed.