A phase-by-phase upstream scheme that converges to the vanishing capillarity solution for countercurrent two-phase flow in two-rocks media

Abstract : We 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.
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00833522
Contributeur : Clément Cancès <>
Soumis le : mercredi 12 juin 2013 - 23:53:28
Dernière modification le : vendredi 4 janvier 2019 - 17:32:30
Document(s) archivé(s) le : vendredi 13 septembre 2013 - 10:10:07

Fichier

AC-upstream.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00833522, version 1

Citation

Boris Andreianov, Clément Cancès. A phase-by-phase upstream scheme that converges to the vanishing capillarity solution for countercurrent two-phase flow in two-rocks media. Computational Geosciences, Springer Verlag, 2014, 18 (2), pp.211-226. 〈hal-00833522〉

Partager

Métriques

Consultations de la notice

450

Téléchargements de fichiers

285