Homogenization of two-phase flows in porous media with hysteresis in the capillary relation

European Journal of Applied Mathematics

Volumn 14, Issue 1, 2003, Pages 61-84

  Beliaev, A ^a,b  

^a WATER PROBLEMS INSTITUTE   (Russian Federation)

^b VU UNIVERSITY AMSTERDAM   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037309096     PISSN: 09567925     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0956792502004965     Document Type: Article

References (17)

1. ALLAIRE, G. (1992) Homogenization and two-scale convergence. SIAM J. Math. Anal. 23(6), 1482-1518.
2. ALT, H. W. & DI BENEDETTO, E. (1985) Nonsteady flow of water and oil through inhomogeneous porous media. Annali Scuola Norm. Sup. Pisa Cl. Sci. (4) 12, 335-392.
3. ANTONTSEV, S. N., KAZHIKHOV, A. V. & MONAKHOV, V. N. (1990) Boundary Value Problems in Mechanics of Non-homogeneous Fluids. North-Holland.
4. CUESTA, C., VAN DUIJN, C. J. & HULSHOF, J. (2000) Infiltration in porous media with dynamic capillary pressure: travelling waves. Euro. J. Appl. Math. 11, 381-397.
5. BELIAEV, A. YU. & HASSANIZADEH, S. M. (2001) A theoretical model of hysteresis and dynamic effects in the capillary relation for two-phase flow in porous media. Transport in Porous Media, 43(3), 487-510.
6. BELIAEV, A. & SCHOTTING, R. J. (2001) Analysis of a new model for unsaturated flow in porous media including hysteresis and dynamic effects. Computational Geosciences. Accepted.
7. BOURGEAT, A., KOZLOV, S. & MIKELIĆ, A. (1995) Effective equations of two-phase in random media. Calculus of Variations and Partial Differential Equations, 3, 385-406.
8. BOURGEAT, A., LUCKHAUS, S. & MIKELIĆ, A. (1996) A rigorous result for a double porosity model of immiscible two-phase flows. SIAM J. Math. Anal. 27, 1520-1543.
9. BOURGEAT, A., MIKELIĆ, A. & WRIGHT, S. (1994).Stochastic two-scale convergence in the mean and applications. J. reine angew. Math. 456, 19-51.
10. BOURGEAT, A. & PANFILOV, M. (1998) Effective two-phase flow through highly heterogeneous porous media: capillary nonequilibrium effects. Computational Geosciences, 2, 191-215.
11. COLLINS, R. E. (1961) Flow of Fluids through Porous Materials. Reinhold.
12. JIKOV, V. V., KOZLOV, S. M. & OLEINIK, O. A. (1994) Homogenization of Differential Equations and Integral Functionals. Springer-Verlag.
13. KRÖNER, D. & LUCKHAUS, S. (1984) Flow of oil and water in a porous medium. J. Diff. Equations, 55, 276-288.
14. LADYZHENSKAYA, O. A. & URAL'TSEVA, N. N. (1968) Linear and Quazilinear Elliptic Equations. Academic Press.
15. MIKELIĆ, A. (1989) A convergence theorem for homogenization of two-phase miscible flow through fractured reservoirs with uniform fracture distributions. Applicable Analysis, 33, 203-214.
16. NGUETSENG, G. (1989) A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 20, 608-623.
17. VISINTIN, A. (1994) Differential Models of Hysteresis. Springer-Verlag.