Gagneux, Gérard; Lefevere, Anne-Marie; Madaune-Tort, Monique 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 Rev. Mat. Univ. Complutense Madr. 2, No. 1, 119-148 (1989). 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. Cited in 1 ReviewCited in 2 Documents 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 Keywords:pseudo-compositional black-oil model; isothermal constrained polyphasic flow; porous media; realistic boundary conditions; component conservation laws; parabolic quasilinear degenerated equations; first-order hyperbolic inequalities; thermodynmical equilibrium functions; gas-phase exists; sub-saturated oil; free boundary value problem; Gibb’s laws PDFBibTeX XMLCite \textit{G. Gagneux} et al., Rev. Mat. Univ. Complutense Madr. 2, No. 1, 119--148 (1989; Zbl 0688.76067) Full Text: EuDML