Abstract
The work consists of two parts. The first part (Qualitative Studies) considered the three-dimensional (3D) mathematical model of the two-phase (2F, oil–water) filtration in porous medium of the bottom zone of a horizontal well. The model was intended for controlling oil extraction from the reservoirs of the oil fields. Some results presented in the paper were concerned with the qualitative theory of partial differential equations underlying the models under consideration. The second part (Numerical Methods) presented numerical methods of solution and identification of the parameters of the model equation system.
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REFERENCES
Aziz, G. and Settari, A., Petroleum Reservoir Simulation, London: Applied Science, 1979. Translated under the title Matematicheskoe modelirovanie plastovykh sistem, Moscow: Nedra, 1982.
Ladyzhenskaya, O.A., Solonnikov, V.A., and Ural'tseva, N.N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa (Linear and Quasilinear Parabolic Equations), Moscow: Nauka, 1967.
Ladyzhenskaya, O.A. and Ural'tseva, N.N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa (Linear and Quasilinear Elliptic Equations), Moscow: Nauka, 1973.
Andriasov, R.S., Mishchenko, I.T., Petrov, A.I., et al., Spravochnoe rukovodstvo po proektirovaniyu razrabotki i ekspluatatsii neftyanykh mestorozhdenii. Dobycha nefti (Handbook of Designing Development and Operation of Oil Fields. Oil Extraction), Gimatudinov, Sh.K., Ed., Moscow: Nedra, 1983.
Bernshtein, S.N., Limiting the Modules of a Sequence of Derivative Solutions of Parabolic Equations, Dokl. Akad. Nauk SSSR, 1938, no. 18, pp. 385-388.
Friedman, A., Partial Differential Equations of Parabolic Type, Englewood Cliffs: Prentice Hall, 1964. Translated under the title Uravneniya s chastnymi proizvodnymi parabolicheskogo tipa, Moscow: Mir, 1968.
Schwartz, N. and Dunford, J., Linear Operators. Part I: General Theory, New York: Interscience, 1958. Translated under the title Lineinye operatory. Obshchaya teoriya, Moscow: Inostrannaya Literatura, 1962.
Kruzhkov, S.N. and Sukoryanskii, S.M., Boundary Problems for Systems of Equation of the Two-phase Filtration Type, Mat. Sb., New Series, vol. 104, issue 1, Moscow: Nauka, 1977.
Kolmogorov, A.N. and Fomin, S.V., Elementy teorii funktsii i funktsional'nogo analiza (Elements of the Theory of Functions and Functional Analysis), Moscow: Nauka, 1968.
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Akhmetzyanov, A.V., Kulibanov, V.N. The 2F3D-Model of Filtration in the Bottom Zones of Horizontal Oil Wells. I. Qualitative Studies. Automation and Remote Control 62, 1407–1416 (2001). https://doi.org/10.1023/A:1011687407731
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DOI: https://doi.org/10.1023/A:1011687407731