  We derive the entropy production for transport of multi-phase fluids in a
non-deformable, porous medium exposed to differences in pressure, temperature,
and chemical potentials. Thermodynamic extensive variables on the macro-scale
are obtained by integrating over a representative elementary volume (REV).
Using Euler homogeneity of the first order, we obtain the Gibbs equation for
the REV. From this we define the intensive variables, the temperature, pressure
and chemical potentials and, using the balance equations, derive the entropy
production for the REV. The entropy production defines sets of independent
conjugate thermodynamic fluxes and forces in the standard way. The transport of
two-phase flow of immiscible components is used to illustrate the equations.
