The hyperbolisity of equations of isotermal multiphase compositional filtration
Matematičeskoe modelirovanie, Tome 23 (2011) no. 1, pp. 65-80.

Voir la notice de l'article provenant de la source Math-Net.Ru

Hyperbolic properties of equations of isothermal multiphase compositional filtration were investigated. It was shown that quasilinear form of these equations may be presented in symmetric form. Propagation velocities of weak discontinuities of concentrations and saturations are solutions of eigenvalue problem, which is decomposed on thermodynamical and hydrodynamical subproblems. Conditions which guarantee full set of eigenvalues for this problem were formulated. The filtration of quasiideal mixtures was considered.
Mots-clés : multiphase compositional filtration
Keywords: quasiideal mixtures, weak discontinuities, hyperbolisity.
@article{MM_2011_23_1_a5,
     author = {A. V. Koldoba and E. V. Koldoba},
     title = {The hyperbolisity of equations of isotermal multiphase compositional filtration},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {65--80},
     publisher = {mathdoc},
     volume = {23},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2011_23_1_a5/}
}
TY  - JOUR
AU  - A. V. Koldoba
AU  - E. V. Koldoba
TI  - The hyperbolisity of equations of isotermal multiphase compositional filtration
JO  - Matematičeskoe modelirovanie
PY  - 2011
SP  - 65
EP  - 80
VL  - 23
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2011_23_1_a5/
LA  - ru
ID  - MM_2011_23_1_a5
ER  - 
%0 Journal Article
%A A. V. Koldoba
%A E. V. Koldoba
%T The hyperbolisity of equations of isotermal multiphase compositional filtration
%J Matematičeskoe modelirovanie
%D 2011
%P 65-80
%V 23
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2011_23_1_a5/
%G ru
%F MM_2011_23_1_a5
A. V. Koldoba; E. V. Koldoba. The hyperbolisity of equations of isotermal multiphase compositional filtration. Matematičeskoe modelirovanie, Tome 23 (2011) no. 1, pp. 65-80. http://geodesic.mathdoc.fr/item/MM_2011_23_1_a5/

[1] Aziz Kh., Settari E., Matematicheskoe modelirovanie plastovykh sistem, Nedra, M., 1982, 408 pp.

[2] Nikolaevskii V. N., Bondarev E. A., Mirkin M. I., Stepanova G. S., Terzi V. P., Dvizhenie uglevodorodnykh smesei v poristoi srede, Nedra, M., 1968

[3] Rozenberg M. D., Kundin S. A., Mnogofaznaya mnogokomponentnaya filtratsiya pri dobyche nefti i gaza, Nedra, M., 1978

[4] Bedrikovetsky P. G., Mathematical Theory of Oil and Gas Recovery (with applications to ex-USSR oil and gas condensate fields), Kluwer Academic Publishers, London–Boston–Dordrecht, 1993

[5] Harten A., “On the symmetric form of Systems of Concervation Laws with Entropy”, J. Comp. Phys., 49 (1983), 151–164 | DOI | MR | Zbl

[6] Koldoba A. V., Koldoba E. V., Razryvnye resheniya mnogokomponentnoi filtratsii, preprint No 85, IPM RAN, M., 1999, 20 pp.

[7] Koldoba A. V., Koldoba E. V., “The Discontinuous Solutions of the Transport Equations for Compositional Flow in Porous Media”, Transport in Porous Media, 52:2, August (2003), 267–277 | DOI | MR

[8] Barenblatt G. I., Entov V. M., Ryzhik V. M., Dvizhenie zhidkostei i gazov v prirodnykh plastakh, Nedra, M., 1984

[9] Entov V. M., Zazovskii A. F., Gidrodinamika protsessov povysheniya nefteotdachi, Nedra, M., 1988, 231 pp.

[10] Radvogin Yu. B., Kharakteristicheskie svoistva uravnenii dvukhkomponentnoi filtratsii, preprint No 37, IPM RAN, M., 2001

[11] Prigozhin I., Defei R., Khimicheskaya termodinamika, Nauka, Novosibirsk, 1966, 509 pp.

[12] Schaefer D. G., Shearer M., “The classification of $2\times 2$ system of non-strictly hyperbolic conservation laws with application to oil recovery”, Communications on Pure and Applied Mathimatics, 40 (1987), 141–178 | DOI | MR

[13] Orr F. M. (jr.), Theory of Gas Injection Processes, Stanford University, California, 2005, 283 pp.

[14] Bedrikovetskii P. G., Chumak M. L., “Tochnye resheniya zadach dvukhfaznoi mnogokomponentnoi filtratsii”, DAN SSSR, 322:4 (1992), 668–673 | MR

[15] Voskov D. V., Entov V. M., “K zadache o vytesnenii nefti smesyami gazov”, Izv. RAN. Ser. MZhG, 2001, no. 2, 112–121 | Zbl

[16] Rozhdestvenskii B. L., Yanenko N. N., Sistemy kvazilineinykh uravnenii i ikh prilozhenie k gazovoi dinamike, Nauka, M., 1978 | MR

[17] Koldoba A. V., Koldoba E. V., Giperbolichnost uravnenii izotermicheskoi mnogokomponentnoi filtratsii, preprint No 77, IPM RAN, M., 2008, 28 pp.