Volume 37, Number 6, November-December 2003
|Page(s)||937 - 972|
|Published online||15 November 2003|
Mathematical study of a petroleum-engineering scheme
Université de Marne-la-Vallée, 5 Bld Descartes, Bat. Lavoisier, 77454 Marne-la-Vallée, France.
2 Université de Aix-Marseille 1, 39 rue Joliot Curie, 13453 Marseille, France. email@example.com.
3 Institut Français du Pétrole, 1 et 4 avenue Bois Préau, 92000 Rueil-Malmaison, France. firstname.lastname@example.org.
Models of two phase flows in porous media, used in petroleum engineering, lead to a system of two coupled equations with elliptic and parabolic degenerate terms, and two unknowns, the saturation and the pressure. For the purpose of their approximation, a coupled scheme, consisting in a finite volume method together with a phase-by-phase upstream weighting scheme, is used in the industrial setting. This paper presents a mathematical analysis of this coupled scheme, first showing that it satisfies some a priori estimates: the saturation is shown to remain in a fixed interval, and a discrete L2(0,T;H1(Ω)) estimate is proved for both the pressure and a function of the saturation. Thanks to these properties, a subsequence of the sequence of approximate solutions is shown to converge to a weak solution of the continuous equations as the size of the discretization tends to zero.
Mathematics Subject Classification: 35K65 / 76S05 / 65M12
Key words: Multiphase flow / Darcy's law / porous media / finite volume scheme.
© EDP Sciences, SMAI, 2003
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.