  Based on non-equilibrium thermodynamics we derive a set of general equations
relating the partial volumetric flow rates to each other and to the total
volumetric flow rate in immiscible two-phase flow in porous media. These
equations together with the conservation of saturation reduces the immiscible
two-phase flow problem to a single-phase flow problem of a complex fluid. We
discuss the new equation in terms of the relative permeability equations. We
test the equations on model systems, both analytically and numerically.
