DOI: 10.1051/m2an:2003062 MATHEMATICAL STUDY OF A PETROLEUM-ENGINEERING SCHEME

Abstract. 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 nite 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, rst showing that it satises some a priori estimates: the saturation is shown to remain in a xed 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