Many studies focus on the flow of multiple phases in smooth fractures yet most real fractures are rough thus flow regime maps and results for multiphase flow in smooth fractures are not completely applicable to flow in rough fractures. The effect of wall roughness is difficult to understand in multiphase flow in fractures since it leads to heterogeneities of the fracture aperture and potentially alters the roles of capillary and viscous forces in the flow. Here, the effects of wall roughness, fracture orientation, and fluids flow direction within a fracture, modeled as narrow gap in a Hele-Shaw cell, on co-current flow of oil and water were examined. The results are presented in the form of oil and water relative permeability curves. The results demonstrate that roughness impacts phase distribution, flow regimes, and phase relative permeability (a measure of phase interference); roughness increases oil–water phase interference and hysteresis of the flow resistance when scanning up and down in water saturation. Fractal analysis of images of the phase arrangement in the fracture reveals that the fractal dimension (reflects geometry and complexity), lacunarity (gappiness and complexity), and tortuosity relate the complexity of flow and the change in relative permeability behavior. The experimentally derived relative permeability data were fitted to the saturation exponent model and to an equivalent homogenous single-phase model.
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