  Based on thermodynamic considerations we derive a set of equations relating
the seepage velocities of the fluid components in immiscible and incompressible
two-phase flow in porous media. They necessitate the introduction of a new
velocity function, the co-moving velocity. This velocity function is a
characteristic of the porous medium. Together with a constitutive relation
between the velocities and the driving forces, such as the pressure gradient,
these equations form a closed set. We solve four versions of the capillary tube
model analytically using this theory. We test the theory numerically on a
network model.
