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The aim of the paper is an analytical and numerical approach to the pseudo-compositionah black-oil model for simulating a 3-13 isothermal constrained polyphasic flow in porous media, taking into account realistic boundary coneitions. The handling of tite component conservation laws leads to a strongly coupled system including parabolic quasilinear degenerated equations and fxrst-order hyperbolic inequahities: tite introduction of unilateral problems arises from tite nature of the thermodynamical equilibrium functions and of tite governing equations describing tite model: it depends locally whether tite gas-pitase exists (satured oil) or the gas- pitase does not exist (sub-saturated oil), witich leads to a free bound~ry value problem, according to Gibb's laws.

Analyse Mathématique de Modéles Variationnels en Simulation Pétroliére. Le Cas du Modéle Black-Oil Pseudo-Compositionnel Standard Isotherme