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Optimum shape of a cavity for the collection of a soil-saturating viscous fluid

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Abstract

The process of inflow of an oil-bearing fluid from an infinite region of porous soil into a cavity (reservoir) and its subsequent pumping into a well located at the center of the reservoir is investigated. The cavity is chosen from the class of flattened ellipsoids of revolution. Thus, a combined problem of the optimization of the shape of a cavity of given volume for which the maximum seepage flow is achieved and the approximate determination of the additional constraints on the cavity dimensions necessary to ensure the outflow of the oil-bearing fluid is considered.

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References

  1. H. Abe, T. Mura, and L.M. Keer, “Growth Rate of a Penny-Shaped Crack in Hydraulic Fracturing of Rocks,” J. Geophys. Res. 81, No. 29, 5335–5340 (1976).

    Article  ADS  Google Scholar 

  2. A.F. Zazovskii, “Propagation of a Circular Hydraulic Fracture through an Impermeable Rock,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 2, 103–109 (1979).

  3. Yu.A. Peslyak, “Calculation of a Circular Hydraulic Fracture,” in Dynamics of Multiphase Media (Institute of Theoret. and Applied Mechanics of the Siberian Branch of the Academy of Sciences of the USSR, Novosibirsk, 1985) [in Russian], 188–193.

    Google Scholar 

  4. A.F. Zazovskii, M.G. Odishariya, and Yu.A. Peslyak, “Self-Similar Solutions of the Problem of Propagation of a Hydraulic Fracture through an Impermeable Rock,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 5, 92–100 (1986).

  5. M.J. Economides and K.G. Nolte, Reservoir Stimulation (Wiley, N. Y., 2000).

  6. G.I. Barenblatt, V.M. Entov, and V.M. Ryzhyk, Flow of Fluids and Gases through Natural Reservoirs (Nedra, Moscow, 1984) [in Russian].

    Google Scholar 

  7. V.M. Entov, A.V. Kosterin, and É.V. Skvortsov, “Estimation of the Rate of Flow in Porous Media,” Fluid Dynamics 21, No. 2, 235–241 (1986).

    Article  Google Scholar 

  8. M. Kaviany, Principles of Heat Transfer in Porous Media (Springer, N. Y. etc., 1999).

    Google Scholar 

  9. G.N. Duboshin, Celestial Mechanics (Nauka, Moscow, 1975) [in Russian].

    Google Scholar 

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Authors
  1. A. N. Golubyatnikov
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  2. N. N. Smirnov
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  3. V. P. Tagirova
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Additional information

Original Russian Text © A.N. Golubyatnikov, N. N. Smirnov, V.P. Tagirova, 2008, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2008, Vol. 43, No. 5, pp. 113–119.

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Golubyatnikov, A.N., Smirnov, N.N. & Tagirova, V.P. Optimum shape of a cavity for the collection of a soil-saturating viscous fluid. Fluid Dyn 43, 772–778 (2008). https://doi.org/10.1134/S0015462808050116

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  • DOI: https://doi.org/10.1134/S0015462808050116

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