Numerical Simulations of Radial Viscous Fingering Induced by an Instantaneous Chemical Reaction

Convective flows in a porous medium are ubiquitous in various physical phenomena such as enhanced oil recovery, chromatography separation, and contamination in aquifers. When a high viscous fluid is displaced by a less viscous fluid, the interface deforms into finger-like patterns. This phenomenon is known as viscous fingering (VF). We consider radial displacement of miscible and reactive fluids undergoing an instantaneous chemical reaction which induces viscosity variation and hence VF. The flow dynamics are controlled by the forces due to convection, diffusion, and reaction where diffusion stabilizes the flow. We model this flow as a system of coupled non-linear partial differential equations consisting of Darcy’s law and convection-reaction-diffusion equations for mass conservation. For a slow to moderately fast chemical reaction, the existence of some critical viscosity ratio for instability is reported as a consequence of the radial displacement. We gain insight into an infinitely fast chemical reaction by computing the onset of instability for various Péclet number (Pe) and viscosity ratios. It is found that the onset time can be made independent of Pe by a suitable rescaling.