Effects of wettability on relative permeability of rough-walled fracture at pore-scale: A lattice Boltzmann analysis

Two-phase flow in fractured geo-material plays a significant role in various subsurface processes. In this study, the realistic issues regarding two-phase flow in rough-walled fractures (RWFs) with different surface wettability are initially investigated with an improved approach based on the free energy multiphase lattice Boltzmann model and a novel rough-walled discrete fracture network model. After validation with analytical solutions, the proposed model is applied to investigate the co-current flow of two immiscible fluids in RWFs at different surface wettability conditions, and the impact of contact angle and fracture aperture on fluid flow distribution, velocity field, and relative permeability curves are further clarified. For fluid initially distributed near the surface, its relative permeability increases monotonically with its saturation. For fluid flowing as the bulk phase, when its saturation is low, its relative permeability decreases with the decrease of its saturation. However, when its saturation is high (about 0.6-0.9), its relative permeability in RWFs exposes instabilities and could be lower than that in smoothed wall fractures, meaning additional flow resistance exists in RWFs. According to our simulation results and theoretical analysis, this phenomenon is mainly caused by the wettability-related microscale fluid distribution. In RWFs with small aperture, the fluid-solid surface interaction dominates, the distribution and flow pattern of fluid flowing near the surface alters the "apparent roughness" of the fracture and further impact the relative permeability curves.