Modeling the relative permeability of gas and water flow in rock fractures with surface morphology parameters

Rock fracture morphology influences two-phase fluid flow in rock fractures. However, the role of the surface morphology of rock fractures in two-phase flow remains to be fully quantified. In this study, an analytical model for gas and water relative permeability in rough rock fractures was developed, incorporating surface roughness factor, hydraulic tortuosity, and surface tortuosity to quantify fracture morphology. The performance of the proposed model was evaluated through a comparison with empirical permeability models and experimental data. The proposed model accurately characterized two-phase fluid flow in rough fractures and examined the impact of surface morphology and flow dynamics on the relative permeability of two-phase fluids in rock fractures, demonstrating that increased surface roughness shifts the equal-permeability point toward higher water saturation and lower relative permeability. To investigate the influence of the flow dynamics on relative permeability, the proposed model was extended to express the Reynolds number of two-phase fluids as a function of water saturation and relative permeability, enabling a detailed exploration of the evolution law of relative permeability with Reynolds number.