Control of radial miscible viscous fingering

Abstract

We investigate the stability of radial viscous fingering (VF) in miscible fluids. We show that the instability is determined by an interplay between advection and diffusion during the initial stages of flow. Using linear stability analysis and nonlinear simulations, we demonstrate that this competition is a function of the radius r0 of the circular region initially occupied by the less-viscous fluid in the porous medium. For each r0, we further determine the stability in terms of Peclet number (Pe) and log-mobility ratio (M). The Pe-M parameter space is divided into stable and unstable zones: the boundary between the two zones is well approximated by Mc Dff.r0 /Pe 0:55 c. In the unstable zone, the instability is reduced with an increase in r0. Thus, a natural control measure for miscible radial VF in terms of r0 is established. Finally, the results are validated by performing experiments that provide good qualitative agreement with our numerical study. Implications for observations in oil recovery and other fingering instabilities are discussed.