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Crack growth in hydraulic rock fracturing


Various mining processes involve the injection of liquid under pressure into existing or newlyproduced points; examples are hydraulic fracturing in oil, fracturing in coal seams, and oil displacement at elevated pressures [1, 2]. Studies have been made [3, 4] of vertical and horizontal crack growth in response to a noninfiltrating liquid. In those cases, the actual pressure distribution in a joint was replaced by the statically equivalent uniform pressure on part of the joint surface. Here we propose a treatment that handles such topics reasonably effectively and does not involve the assumption of uniform pressure distribution. A system of equations has been derived for a vertical symmetrical crack to define the Cauchy problem for the crack volume. The quasistatic equilibrium condition for the crack and the solution are very much simplified if a system of mobile elliptical coordinates related to the crack is used. An analogous approach has been used in examining the growth of a circular horizontal crack.

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Literature cited

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    G. C. Howard and C. R. Fast, Hydraulic Fracturing, AIME, New York-Dallas (1970), p. 210.

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    B. F. Gubanov, Yu. P. Zhelmov, and G. Yu. Shovkrinskii, “Physical principles of accelerated petroleum exploitation and oil recovery increase at elevated injection pressures,” in: All-Union Scientific-Research Institute Year Book [in Russian], Nedra, Moscow (1971), pp. 236–245.

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    S. A. Kristianovich and Yu. P. Zhelmov, Production of Vertical Cracks with a Very Viscous Liquid [in Russian], Izd. Akad. Nauk SSSR, Moscow (1955), p. 33.

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    Yu. V. Zhelmov and Yu. P. Zhelmov, “Propagation of a horizontal crack in a rock in response to a noninfiltrating liquid for a constant rock pressure,” Izv. Akad. Nauk. Otd. Tekh. Nauk, SSSR, Mekh. Mashinostr., No. 5, 166–169 (1959).

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Translated from Zhurnal Prikladnoi Mekhanika i Tekhnicheskoi Fiziki, No. 3, pp. 156–163, May–June, 1975.

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Peslyak, Y.A. Crack growth in hydraulic rock fracturing. J Appl Mech Tech Phys 16, 443–448 (1975).

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  • Cauchy Problem
  • Pressure Distribution
  • Industrial Mathematic
  • Coal Seam
  • Hydraulic Fracture