Flow-Area Relations in Immiscible Two-Phase Flow in Porous Media

We present a theoretical framework for immiscible incompressible two-phase flow in homogeneous porous media that connects the distribution of local fluid velocities to the average seepage velocities. By dividing the pore area along a cut transversal to the average flow direction up into differential areas associated with the local flow velocities, we construct a distribution function that allows us to not only re-establish existing relationships of between the seepage velocities of the immiscible fluids, but also to find new relations between their higher moments. We support and demonstrate the formalism through numerical simulations using a dynamic pore-network model for immiscible two-phase flow with two- and three-dimensional pore networks. Our numerical results are in agreement with the theoretical considerations.