Annales Mathématiques
Blaise Pascal
no. 2
A degenerate parabolic system for three-phase flows in porous media
Vladimir Shelukhin1
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

Vladimir Shelukhin 1

1 Lavrentyev Institute of Hydrodynamics Av. Lavrentyev 15 Novosibirsk Russia 
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Vladimir Shelukhin. 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. https://ambp.centre-mersenne.org/articles/10.5802/ambp.234/

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

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

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

[4] H. Frid; V. Shelukhin 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 | MR | Zbl

[5] H. Frid; V. Shelukhin 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 | MR | Zbl

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

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

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

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

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

[11] A. N. Varchenko; A. F. Zazovskii; R. V. Gamkrelidze 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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