A linear stability analysis of instabilities with reactive flows in porous medium

Abstract

Convection, diffusion, and reaction dynamics of radial displacement of reactive fluids undergoing second-order chemical reaction in a porous medium are modeled and understood numerically. In the case of iso-viscous reactants and products, reaction dynamics are examined to understand the effect of reaction rate after solving a system of convection–diffusion–reaction equations using a method of lines. Various temporal scalings for reaction characteristics like the total amount of product and width of reaction front are obtained in terms of the Damköhler number (Da) for the first time in this work. The generation of the product having different viscosity than the reactants results in a hydrodynamic instability called viscous fingering. The numerical technique based on hybrids of compact finite difference and pseudo-spectral methods is utilized, for the first time, for the linear stability analysis (LSA) of miscible viscous fingering induced by chemical reaction. The onset time of instability (ton) is found to depend on the reaction rate, and we obtain a stable zone sandwiched between two unstable zones in the Mc,ton plane for a fixed Péclet number and Damköhler number, where Mc is the log-mobility ratio. The results agree with existing numerical studies validating the novel LSA technique utilized.