Slow Two-phase Flow in Single Fractures: Fragmentation, Migration, and Fractal Patterns Simulated Using Invasion Percolation Models

The slow displacement of a wetting fluid by an invading non-wetting fluid in single fractures was studied using experiments and simulations. In the experiments, the fracture aperture was modeled by the gap between a rough plate and a smooth transparent plate. The displacement was simulated using invasion percolation models and two types of self-affine fracture aperture models; model A with an infinite in-plane correlation length, and model B with a finite in-plane correlation length. Simulations were also performed on self-affine models that precisely represented the aperture fields of the experiments. At length scales below the in-plane correlation length, the simulated displacement patterns show scaling properties that may be tuned by changing the characteristics of the underlying geometry. In the experiment-matched simulations, we observed closely corresponding displacement patterns.