Fracture-scale model of immiscible fluid flow

We present a method for modeling immiscible fluid flow in narrow fractures. The method combines a parallel-plate flow model with a recoloration approach adapted from multiple-component lattice-Boltzmann methods. The resulting numerical method is straightforward to implement and accurately reproduces the relevant fluid behavior. To demonstrate the method, single-droplet simulations are compared to analytical solutions that isolate the contributions from the in-plane and normal curvature. Simulations reproducing capillary forces inside a widening aperture are also presented. Excellent agreement is found in all cases considered. Finally, the method's ability to model fracture flow is demonstrated by deriving relative permeability curves for flow through a heterogeneous aperture created between two fractal surfaces.