  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
cross-section transversal to the average flow direction up into differential
areas associated with the local flow velocities, we construct a distribution
function that allows us not only to re-establish existing relationships 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.
