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Based on thermodynamic considerations we derive a set of equations relatingthe seepage velocities of the fluid components in immiscible and incompressibletwo-phase flow in porous media. They necessitate the introduction of a newvelocity function, the co-moving velocity. This velocity function is acharacteristic of the porous medium. Together with a constitutive relationbetween the velocities and the driving forces, such as the pressure gradient,these equations form a closed set. We solve four versions of the capillary tubemodel analytically using this theory. We test the theory numerically on anetwork model.

Relations between Seepage Velocities in Immiscible, Incompressible Two-Phase Flow in Porous Media