Effect of No-Flow Boundaries on Viscous Fingering in Porous Media of Large Aspect Ratio

Summary We report on a boundary effect associated with the preferential propagation of viscous fingers along no-flow boundaries in miscible displacements in two-dimensional (2D) rectilinear geometries near conditions of transverse equilibrium (TE) (large values of the generalized aspect ratio RL). It is shown that this effect intensifies with an increase in the mobility ratio, and diminishes with increased permeability disorder, and as the system departs from conditions of TE. The effect disappears altogether if periodic boundary conditions are used. We show that this effect results from the violation of the no-slip condition at no-flow boundaries, associated with Darcy's law. It must be considered in simulations of viscous fingering in relatively homogeneous media, near conditions of TE, particularly when gravity segregation occurs.