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 Péclet 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 =α(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.
