Gagneux, Gérard; Lefevere, Anne-Marie; Madaune-Tort, Monique Une approche analytique d’un modèle black oil des écoulements triphasiques compressibles en ingénierie pétrolière. (An analytical approach to a black-oil model for three-phase compressible flows in petroleum engineering). (French) Zbl 0629.76109 J. Méc. Théor. Appl. 6, 547-569 (1987). The aim of the paper is a study of three-phase compressible isothermal flows in porous media. The variational formulation of the problem is derived. It consists of a strongly coupled system of two equations and an inequality, which are parabolic quasilinear degenerated and contain a nonlinear convection term. To this complex problem a time-discretized regularized problem is associated. The latter is shown to possess a unique solution. Reviewer: M.Fila Cited in 6 Documents MSC: 76T99 Multiphase and multicomponent flows 35R35 Free boundary problems for PDEs 76S05 Flows in porous media; filtration; seepage 35K85 Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators Keywords:secondary recovery processes; free boundary problem; three-phase compressible isothermal flows; porous media; variational formulation; nonlinear convection term; discretized regularized problem; unique solution PDFBibTeX XMLCite \textit{G. Gagneux} et al., J. Méc. Théor. Appl. 6, 547--569 (1987; Zbl 0629.76109)