Miscible viscous fingering under injection and withdrawal

Abstract

We examine rectilinear two-dimensional miscible viscous fingering in response to both injection and withdrawal of low-viscosity fluid using numerical simulations. We consider sinusoidal injection-withdrawal cycles. In the injection period, the input flow rate increases initially before decreasing; we perform a linear stability analysis and examine the development of nonlinear fingering regimes. The instability can progress through the regimes of independent finger growth, coalescence and interaction, the emergence of a single finger, and finally shutdown. Whether or not substantial fingering occurred during the injection controls the dynamics in the withdrawal period. The amount by which fin..