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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

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

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
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