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 i n single fractures was studied using experiments and simulations. In the ex periments, the fracture aperture was modeled by the gap between a rough pla te and a smooth transparent plate. The displacement was simulated using inv asion percolation models and two types of self-affine fracture aperture mod els, model A with an infinite in-plane correlation length, and model B with a finite in-plane correlation length. Simulations were also performed on s elf-affine models that precisely represented the aperture fields of the exp eriments. At length scales below the in-plane correlation length, the simul ated displacement patterns show scaling properties that may be tuned by cha nging the characteristics of the underlying geometry. In the experiment-mat ched simulations, we observed closely corresponding displacement patterns.