Geodesic
The generalized Backley–Leverett problem
Matematičeskoe modelirovanie, Tome 22 (2010) no. 8, pp. 3-23 Cet article a éte moissonné depuis la source Math-Net.Ru

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The specified problems of mathematical modeling arise under exploitation of the oil fields of bazhen formation. They concern the interaction between hot operation agent and hydrocarbon stratums. These processes are described with dynamics of porous saturated medium with many phases and many components fluid been exposed to thermo-gas action under chemical and physical-chemical transformations. We consider these processes with help of simplified analytical model. The hot water agent pumps into bazhen stratum. The physical problem statement general-izes the Backley–Leverett problem. As a example we make use of analytical expression for the Backley–Leverett function. This analytical model has given understanding quality features of this process and possibility to make some important conclusions. The results can be used for investigation of sweeping out processes in porous media with two phases and many component fluid.
Mots-clés : bazhen formation
Keywords: Backley–Leverett problem, analytical model, quality analysis. 
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A. V. Karakin. The generalized Backley–Leverett problem. Matematičeskoe modelirovanie, Tome 22 (2010) no. 8, pp. 3-23. http://geodesic.mathdoc.fr/item/MM_2010_22_8_a0/

[1] A. N. Tikhonov, A. A. Samarskii, “O razryvnykh resheniyakh kvazilineinykh uravnenii pervogo poryadka”, DAN SSSR, 99:1 (1954), 27–30 | Zbl

[2] I. M. Gelfand, “Nekotorye zadachi teorii kvazilineinykh uravnenii”, UMN, 14:2(86) (1959), 87–158 | MR | Zbl

[3] O. A. Oleinik, “Razryvnye resheniya nelineinykh differentsialnykh uravnenii”, UMN, 12:3(75) (1957), 3–73 | MR | Zbl

[4] O. A. Oleinik, “O edinstvennosti i ustoichivosti obobschennogo resheniya zadachi Koshi dlya kvazilineinogo uravneniya”, UMN, 14:2(86) (1959), 3–73 | MR | Zbl

[5] B. L. Rozhdestvenskii, N. N. Yanenko, Sistemy kvazilineinykh uravnenii, Nauka, M., 1978, 687 pp. | MR

[6] R. I. Nigmatulin, Dinamika mnogofaznykh sred, v. II, Nauka, M., 1987, 359 pp.

[7] G. I. Barenblatt, V. M. Entov, V. M. Ryzhik, Dvizhenie zhidkostei i gazov v prirodnykh plastakh, Nedra, M., 1984, 211 pp.

[8] Ya. B. Zeldovich, Yu. P. Raizer, Fizika udarnykh voln i vysokotemperaturnykh gidrodinamicheskikh yavlenii, Nauka, M., 1966, 688 pp.

[9] M. F. Yambaev, Osnovnye rezultaty chislennogo issledovaniya termogazovogo metoda uvelicheniya nefteotdachi, Kand. diss., RGU im. Gubkina, M., 2005

[10] A. A. Bokserman, “Dinamika zon progreva plasta pri zakachke v nego para”, Nauchn. tekhn. sb. po dobyche nefti, 2, Nedra, M., 1971, 159–169

[11] Yu. P. Zheltov, Mekhanika neftegazonosnogo plasta, Nedra, M., 1975, 216 pp.

[12] J. W. Marx, R. N. Langenheim, “Reservoir heating by hot fluid injection”, Trans. AJME, 216 (1959), 312–315