Factors controlling satiated relative permeability in a partially-saturated horizontal fracture

Recent work demonstrates that phase displacements within horizontal fractures large with respect to the spatial correlation length of the aperture field lead to a satiated condition that constrains the relative permeability to be less than one. We use effective media theory to develop a conceptual model for satiated relative permeability, then compare predictions to existing experimental measurements, and numerical solutions of the Reynolds equation on the measured aperture field within the flowing phase. The close agreement among all results and data show that for the experiments considered here, in-plane tortuosity induced by the entrapped phase is the dominant factor controlling satiated relative permeability. We also find that for this data set, each factor in the conceptual model displays an approximate power law dependence on the satiated saturation of the fracture.