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A phase-by-phase upstream scheme that converges to the vanishing capillarity solution for countercurrent two-phase flow in two-rocks media
Abstract
International audienceWe discuss the convergence of the upstream phase-by-phase scheme (or upstream mobility scheme) towards the vanishing capillarity solution for immiscible incompressible two-phase flows in porous media made of several rock types. Troubles in the convergence where recently pointed out in [S. Mishra & J. Jaffré, Comput. Geosci., 2010] and [S. Tveit & I. Aavatsmark, Comput. Geosci, 2012]. In this paper, we clarify the notion of vanishing capillarity solution, stressing the fact that the physically relevant notion of solution differs from the one inferred from the results of [E. F. Kaasschieter, Comput. Geosci., 1999]. In particular, we point out that the vanishing capillarity solution de- pends on the formally neglected capillary pressure curves, as it was recently proven in by the authors [B. Andreianov & C. Canc'es, Comput. Geosci., 2013]. Then, we propose a numerical procedure based on the hybridization of the interfaces that converges towards the vanishing capillarity solution. Numerical illustrations are provided- info:eu-repo/semantics/article
- Journal articles
- [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
- [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph]
- [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Mechanics of the fluids [physics.class-ph]
- [SDE.IE]Environmental Sciences/Environmental Engineering
- [MATH]Mathematics [math]