Crossover from capillary fingering to viscous fingering for immiscible unstable flow: Experiment and modeling

Invasion percolation with trapping (IPT) and diffusion-limited aggregation (DLA) are simple fractal models, which are known to describe two-phase flow in porous media at well defined, but unphysical limits of the fluid properties and flow conditions. A decade ago, Fernandez, Rangel, and Rivero predicted a crossover from IPT (capillary fingering) to DLA (viscous fingering) for the injection of a zero-viscosity fluid as the injection velocity was increased from zero. [ J. F. Fernandez, R. Rangel, and J. Rivero, Phys. Rev. Lett. 67, 2958 (1991) ]. We have performed experiments in which air is injected into a glass micromodel to displace water. These experiments clearly demonstrate this crossover as the injection velocity of the air is increased. Furthermore, simulations, using our standard pore-level model, also support the predicted IPT-to-DLA crossover, as well as the predicted power-law behavior of the characteristic crossover length.