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Numerical simulators for oil reservoirs have been developed over the last twenty years and are now widely used by oil companies. The research, however, has taken place largely within the industry itself, and has remained somewhat inaccessible to the scientific community. This book hopes to remedy the situation by means of its synthesized presentation of the models used in reservoir simulation, in a form understandable to both mathematicians and engineers.The book aims to initiate a rigorous mathematical study of the immiscible flow models, partly by using the novel `global pressure' approach in treating incompressible two-phase problems. A finite element approximation technique based on the global pressure variational model is presented, and new approaches to the modelling of various kinds of multiphase flow through porous media are introduced.Much of the material is highly original, and has not been presented elsewhere. The mathematical and numerical models should be of great interest to applied mathematicians, and to engineers seeking an alternative approach to reservoir modelling.
ANALYSE D'ECOULEMENTS COMPRESSIBLES REGIS PAR UNE LOI QUADRATIQUE DE PERTE DE CHARGE. LA MODELISATION CONDUIT A UNE EQUATION PARABOLIQUE NON LINEAIRE DEGENEREE. APPROXIMATION NUMERIQUE D'UN PROBLEME A FRONTIERE LIBRE D'EVOLUTION, MODELISANT LE DEPLACEMENT DE L'INTERFACE DE DEUX FLUIDES NON MISCIBLES INCOMPRESSIBLES. HOMOGENEISATION D'EQUATIONS HYPERBOLIQUES DU PREMIER ORDRE INTERVENANT DANS DEUX MODELES D'ECOULEMENTS MISCIBLES INCOMPRESSIBLES