The effect of topology on two-fluid flow in porous media

The topological arrangement of fluids has important consequences for two-fluid flow in porous media. Fluid topology influences both the thermodynamic equilibrium conditions and the pathways available for flow. Average topological measures provide a way to characterize the complex fluid arrangements at the pore-scale and relate the geometric properties of a system to transport processes. We combine fast micro-computed tomography with large-scale simulations to examine these relationships. Flow at fixed saturation is considered for a wide range of capillary numbers and contact angles. The mean curvature, interfacial area, and Euler number are determined to characterize the geometric changes that take place as flow occurs. Simulations of fluid displacement during imbibition are also performed. We show that topology is an important source of hysteresis in macroscale capillary pressure and relative permeability relationships. Challenges associated with the use of topological relationships in macroscale models are also discussed, in particular noting that the average capillary pressure does not in general balance the average phase pressure difference in a macroscale system with disconnected phases. Possible solutions to this dilemma are explored.