Mathematical study of a petroleum-engineering scheme
Mathematical study of a petroleum-engineering scheme
复制标题
石油工程方案的数学研究
DOI：
10.1051/m2an:2003062
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
A. Michel
中科院分区：
文献类型：
--
作者：
R. Eymard;R. Herbin;A. Michel
石油工程中使用的多孔介质中的两相流模型产生了两个耦合方程组，其中包含椭圆和抛物线简并项以及两个未知数（饱和度和压力）。为了进行近似，在工业环境中使用了耦合方案，该方案由有限体积法和逐相上游加权方案组成。本文对这种耦合方案进行了数学分析，首先表明它满足一些先验估计：饱和度保持在固定区间内，并且证明了压力和饱和度函数的离散 L2 (0,T;H1 (Ω)) 估计。由于这些特性，当离散化的大小趋于零时，近似解序列的子序列会收敛到连续方程的弱解。
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.