A new set of equations describing immiscible two-phase flow in isotropic   porous media
  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. 
Alex Hansen, Santanu Sinha, Dick Bedeaux, Signe Kjelstrup, Isha   Savani, Morten Vassvik
physics.flu-dyn