  We introduce a new global pressure formulation for immiscible three-phase
compressible flows in porous media which is fully equivalent to the original
equations, unlike the one introduced in \cite{CJ86}. In this formulation, the
total volumetric flow of the three fluids and the global pressure follow a
classical Darcy law, which simplifies the resolution of the pressure equation.
However, this global pressure formulation exists only for Total Differential
(TD) three-phase data, which depend only on two functions of saturations and
global pressure: the global capillary pressure and the global mobility. Hence
we introduce a class of interpolation which constructs such TD-three-phase data
from any set of three two-phase data (for each pair of fluids) which satisfy a
TD-compatibility condition.
