Mathematical analysis of variational models of petrol reservoir simulation. The standard isothermal pseudo-compositional black-oil model

Gérard Gagneux; Ann-Marie Lefevere; Monique Madaune-Tort

Revista Matemática de la Universidad Complutense de Madrid (1989)

  • Volume: 2, Issue: 1, page 119-148
  • ISSN: 1139-1138

Abstract

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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.

How to cite

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Gagneux, Gérard, Lefevere, Ann-Marie, and 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 2.1 (1989): 119-148. <http://eudml.org/doc/43313>.

@article{Gagneux1989,
author = {Gagneux, Gérard, Lefevere, Ann-Marie, Madaune-Tort, Monique},
journal = {Revista Matemática de la Universidad Complutense de Madrid},
keywords = {Simulación numérica; Industria petrolquímica; Sistemas dinámicos; Modelo dinámico; 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},
language = {fre},
number = {1},
pages = {119-148},
title = {Analyse mathématique de modèles variationells en simulation pétrolière. Le cas du modèle black-oil pseudo-compositionnel standard isoterme.},
url = {http://eudml.org/doc/43313},
volume = {2},
year = {1989},
}

TY - JOUR
AU - Gagneux, Gérard
AU - Lefevere, Ann-Marie
AU - Madaune-Tort, Monique
TI - Analyse mathématique de modèles variationells en simulation pétrolière. Le cas du modèle black-oil pseudo-compositionnel standard isoterme.
JO - Revista Matemática de la Universidad Complutense de Madrid
PY - 1989
VL - 2
IS - 1
SP - 119
EP - 148
LA - fre
KW - Simulación numérica; Industria petrolquímica; Sistemas dinámicos; Modelo dinámico; 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
UR - http://eudml.org/doc/43313
ER -

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