Analyse mathématique de modèles variationnels en simulation pétrolière
The aim of the paper is an analytical and numerical approach to the pseudo-compositional black-oil model for simulating a 3-D isothermal constrained polyphasic flow in porous media, taking into account realistic boundary conditions. The handling of the component conservation laws leads to a strongly coupled system including parabolic quasilinear degenerated equations and first-order hyperbolic inequalities: the introduction of unilateral problems arises from the nature of the thermodynamical equilibrium functions and of the governing equations describing the model: it depends locally whether the gas-phase exists (satured oil) or the gas-phase does not exist (sub-satured oil), which leads to a free boundary value problem, according to Gibb’s laws.
1980 Mathematics Subject Classification (1985 revision): 35G30.