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.
@article{urn:eudml:doc:43313,
title = {Analyse math\'ematique de mod\`eles variationells en simulation p\'etroli\`ere. Le cas du mod\`ele black-oil pseudo-compositionnel standard isoterme.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {2},
year = {1989},
pages = {119-148},
zbl = {0688.76067},
mrnumber = {MR1012108},
language = {fr},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:43313}
}
Gagneux, Gérard; Lefevere, Ann-Marie; Madaune-Tort, Monique. Analyse mathématique de modèles variationells en simulation pétrolière. Le cas du modèle black-oil pseudo-compositionnel standard isoterme.. Revista Matemática de la Universidad Complutense de Madrid, Tome 2 (1989) pp. 119-148. http://gdmltest.u-ga.fr/item/urn:eudml:doc:43313/