Fractal viscous fingering in inhomogeneous porous models

Abstract

Immiscible fluid-fluid displacement was studied experimentally and numerically in porous models consisting of uniform pores on a square lattice where all nearest neighbors were connected by bonds randomly given one of two permeabilities. Patterns formed by a high-viscosity fluid (glycerol) being displaced by a low-viscosity fluid (air) injected at the center of the model network were studied and compared with the results of diffusion-limited-aggregation (DLA) simulations using a network with identical geometry. For a bond permeability ratio κ≃0.004 close to the bond percolation threshold ${\mathit{f}}_{\mathit{c}}$=0.5 of high-permeability bonds, simulated and experimental patterns exhibit a high degree of overlap. The displacement patterns generated in experiments and in simulations can be characterized by the same effective fractal dimension ${\mathit{D}}_{\mathit{c}}$≃1.5. We find that the model geometry strongly influences the structure of the displacement pattern formed, and that Meakin et al.’s [Physica A 115, 1 (1989)] modified-DLA algorithm provides a good model for the displacement.