no. 2
A degenerate parabolic system for three-phase flows in porous media
Shelukhin, Vladimir1
1 Lavrentyev Institute of Hydrodynamics Av. Lavrentyev 15 Novosibirsk Russia
Annales mathématiques Blaise Pascal, Tome 14 (2007) no. 2, pp. 243-254

A classical model for three-phase capillary immiscible flows in a porous medium is considered. Capillarity pressure functions are found, with a corresponding diffusion-capillarity tensor being triangular. The model is reduced to a degenerate quasilinear parabolic system. A global existence theorem is proved under some hypotheses on the model data.

DOI : 10.5802/ambp.234

Shelukhin, Vladimir 1

1 Lavrentyev Institute of Hydrodynamics Av. Lavrentyev 15 Novosibirsk Russia 
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Shelukhin, Vladimir. A degenerate parabolic system for three-phase flows in porous media. Annales mathématiques Blaise Pascal, Tome 14 (2007) no. 2, pp. 243-254. doi: 10.5802/ambp.234

[1] Allen, M. B.; Behie, J. B. Multiphase flows in porous media: Mechanics, mathematics and numerics, Springer-Verlag, New York, 1988 (Lecture Notes in Engineering no. 34) | Zbl | MR

[2] Amann, H. Dynamic theory of quasi-linear parabolic systems III. Global existence, Math. Z., Volume 202 (1989), pp. 219-250 | DOI | Zbl | MR

[3] Chen, Z.; Ewing, R. E. Comparison of various formulations of three-phase flow in porous media, Journal of Computational Physics, Volume 132 (1997), pp. 362-373 | DOI | Zbl | MR

[4] Frid, H.; Shelukhin, V. A quasilinear parabolic system for three-phase capillary flow in porous media, SIAM J. Math. Anal., Volume 35 no. 4 (2003), pp. 1029-1041 | DOI | Zbl | MR

[5] Frid, H.; Shelukhin, V. Initial boundary value problems for a quasilinear parabolic system in three-phase capillary flow in porous media, SIAM J. Math. Anal., Volume 36 no. 5 (2005), pp. 1407-1425 | DOI | Zbl | MR

[6] Hassanizadeh, S. M.; Gray, W. G. Theormodynamic basis of capillary pressure in porous media, Water Resources Research, Volume 29 (1993), pp. 3389-3405 (no. 10) | DOI

[7] Ladyženskaja, O. A.; Solonnikov, V. A.; Ural’ceva, N. N. Linear and quasi-linear equations of parabolic type, AMS, Rhode Island: Providence, 1968 | Zbl

[8] Ovsiannikov, L. V. Group Analysis of Differential Equations, Academic Press, New York, London, 1982 | Zbl | MR

[9] Peaceman, D. W. Fundamentals of Numerical Reservoir Simulation, Elsevier Scientific Publishing Company, Amsterdam Oxford New York, 1977

[10] Stone, H. L. Probability model for estimating three-phase relative permeability, J. of Petroleum Technology, Volume 22 (1970), pp. 214-218

[11] Varchenko, A. N.; Zazovskii, A. F.; Gamkrelidze, R. V. Three-phase filtration of immiscible fluids, Itogi Nauki i Tekhniki, Seriya Kompleksnie i spetsial’nie Razdely Mekhaniki no. 4 (in Russian), VINITI, 1991, pp. 98-154

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