A new insight into the breakup distance and capillary pressure of liquid bridges formed in rough fractures

The formation of a liquid bridge between two adjacent surfaces has a crucial role in many industrial and scientific applications, such as waste disposal management, granular materials, and flow through fractured porous media. Despite numerous studies, the understanding of how the stability and capillary pressure of liquid bridges formed in rough fractures may controlled by the geometrical properties of fracture surface roughness has received limited attention. In this study, a natural fracture profile of a subsurface carbonate rock is analyzed and the geometrical properties of cone-plate roughness models are extracted. Combined with the numerical solution of the Young-Laplace capillarity equation, the liquid bridge capillary pressure and breakup distance in the rough fracture systems are characterized, and more realistic data of fracture capillary pressure and breakup distance of liquid bridges are provided. The results show that increasing the roughness height causes the breakup distance of liquid bridge increases, while the capillary pressure decreases. When, the liquid volume in the fracture is less than 5% and the fracture width is sufficiently thin (<0.2 $mm$), the liquid bridge capillary pressure is as high as 14 $KPa$, which is a significant value. In the context of natural fractured reservoirs, where fractures possess different widths and roughness characteristics, a new generalized capillary pressure model is developed, which enables the estimation of capillary pressure for liquid bridges formed in rough-walled fractures. The capillary pressure data of rough fractures presented in this work, may fill a gap in the literature and providing required information for simulating oil recovery in fractured reservoirs.