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Analyse mathématique de modèles variationnels en simulation pétrolière. Le cas du modèle black-oil pseudo-compositionnel standard isotherme. (Mathematical analysis of variational models of petrol reservoir simulation. The standard isothermal pseudo-compositional black-oil model). (French) Zbl 0688.76067

Summary: 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 thermodynmical equilibrium functions and of the governing equations describing the model: it depends locally whether the gas-phase exists (saturated oil) or the gas-phase does not exist (sub-saturated oil), which leads to a free boundary value problem, according to Gibb’s laws.

MSC:

76S05 Flows in porous media; filtration; seepage
76T99 Multiphase and multicomponent flows
35G30 Boundary value problems for nonlinear higher-order PDEs
86A20 Potentials, prospecting
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