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Pressure distribution in the neighborhood of a growing fracture with a constant wedge force

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Abstract

Exact solutions of the problem of the pressure field in the neighborhood of a hydraulic fracture developing in accordance with a square root law in a permeable porous medium with a constant wedge force acting on the fracture edges are constructed. A particular case admitting a self-similar formulation and an exact solution and, as a result, the fairly complete investigation, is considered. The solution constructed holds for an arbitrary self-similar pressure distribution over the fracture edges. The problem considered reduces to the solution of a mixed boundary-value problem for the Helmholtz equation. The solution found can be useful both in itself and for testing more universal numerical algorithms.

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References

  1. K. G. Nolte and M. B. Smith, “Interpretation of fracturing processes,” J. Petrol. Technol., 33, No. 9, 1764–1775 (1981).

    Google Scholar 

  2. M. J. Economides and K. G. Nolte (Eds.), Reservoir Stimulation, Houston, Texas (1989).

  3. V. N. Shchelkachev, “Governing equations of motion of an elastic fluid in an elastic porous medium, ” Dokl. Akad. Nauk SSSR, 52, No. 2, 103–106 (1946).

    MathSciNet  Google Scholar 

  4. E. Detournay and D. I. Garagash, “The near-tip region of a fluid-driven fracture propagating in a permeable elastic solid,” J. Fluid. Mech., 494, 1–32 (2003).

    Article  MATH  ADS  Google Scholar 

  5. G. I. Barenblatt, “Mathematical theory of equilibrium cracks formed in brittle fracture,” Zh. Prikl. Mekh. Tekh. Fiz., No. 4, 3–56 (1961).

  6. Yu. N. Gordeev and V. M. Entov, “Pressure distribution in the neighborhood of a growing fracture, ” Prikl. Mat. Mekh., 61, No. 6, 1060–1064 (1997).

    MATH  Google Scholar 

  7. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series. Special Functions [in Russian], Nauka, Moscow (1983).

    MATH  Google Scholar 

  8. L. I. Sedov, Two-Dimensional Problems in Hydrodynamics and Aerodynamics, Wiley (1965).

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Authors
  1. Yu. N. Gordeev
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  2. A. E. Sandakov
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Additional information

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Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, 2006, pp. 121–126.

Original Russian Text Copyright © 2006 by Gordeev and Sandakov.

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Gordeev, Y.N., Sandakov, A.E. Pressure distribution in the neighborhood of a growing fracture with a constant wedge force. Fluid Dyn 41, 593–598 (2006). https://doi.org/10.1007/s10697-006-0077-0

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  • DOI: https://doi.org/10.1007/s10697-006-0077-0

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