Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Tatosov A. V., Shlyapkin A. S. The Motion of Propping Agent in an Opening Crack in Hydraulic Fracturing Plast. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2018, vol. 18, iss. 2, pp. 217-226. DOI: 10.18500/1816-9791-2018-18-2-217-226, EDN: URLITG

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The Motion of Propping Agent in an Opening Crack in Hydraulic Fracturing Plast

Tatosov Alexey V., Tyumen State University
Shlyapkin Alexey S., Tyumen State University

In the present study the process of hydraulic fracture formation when pumping a viscous fluid with an admixture of particles into a well is considered. A model of a crack propagation taking account of the loss of liquid on seepage into a porous medium and the sedimentation of suspended particles under the action of gravity is developed. Detailed analysis of the sedimentation growth caused by leakage of hydraulic fracturing fluid into a porous medium is carried out. It is shown that the presence of particles has a significant effect on the process of crack opening. The crack growth in the presence of particles is limited, its final state depends on the composition of the mixture, injection method, inlet pressure, the volume content of the particles, the volume of the rim (pure fracturing fluid without admixture). All these factors are taken into consideration in the proposed model based on special dimensionless forms of the equations of motion. The results make it possible to estimate the crack residual and choose the technological parameters to provide the desired state of the ruptured formation.

  1. Perkins T. K., Kern L. R. Widths of Hydraulic Fractures. Journal of Petroleum Technology, 1961, vol. 13, iss. 09, paper SPE 89, pp. 937–949. DOI: https://doi.org/10.2118/89-PA
  2. Nordgren R. P. Propagation of a Vertical Hydraulic Fracture. Society of Petroleum Engineers, 1972, vol. 12, iss. 04, paper 7834, pp. 306–314. DOI: https://doi.org/10.2118/3009PA
  3. Zheltov Yu. P., Khristianovich S. A. O gidravlicheskom razryve neftenosnogo plasta [Onhydraulic fracturing of oil reservoirs]. Izv. AN SSSR, Otd-nie tekhn. nauk [Proc. USSRAcad. Sci. Sect. Tech. Sci.], 1955, no. 5, pp. 3–41 (in Russian).
  4. Esipov D. V., Kuranakov D. S., Lapin V. N., Chernyi S. G. Mathematical models of hydraulic fracturing. Computational technologies, 2014, vol. 19, no. 2, pp. 33–61 (inRussian).
  5. Mobbs A. T., Hammond P. S. Computer Simulations of Propp ant Transport in a Hydraulic Fracture. SPE Production & Facilities, 2001, vol. 16, no. 2, pp. 112–121. DOI: https://doi.org/10.2118/69212-PA
  6. Dontsov E. V., Peirce A. P. Slurry flow, gravitational settling and a proppant transportmodel for hydraulic fractures. Journal of Fluid Mechanics, 2014, vol. 760, pp. 567–590. DOI: https://doi.org/10.1017/jfm.2014.606
  7. Novatsky B. Teorija uprugosti [Theory of Elasticity]. Moscow, Mir, 1975. 256 p. (in Russian).
  8. Ivashnev O. E., Smirnov N. N. Formirovanie treshhiny gidrorazryva v poristoj srede [Formation of a hydraulic fracture in a porous medium]. Vestnik Moskovskogo Universiteta.  Ser. 1, Matematika. Mekhanika, 2003, no. 6, pp. 28–36 (in Russian).
  9. Smirnov N. N., Tagirova V. P. Analiz stepennyh avtomodel’nyh reshenij zadachi o formirovanii treshhiny gidrorazryva [Analysis of power-law self-similar solutions of the problem of fracture formation]. Vestnik Moskovskogo Universiteta. Ser. 1, Matematika.Mekhanika, 2007, no. 1, pp. 48–54 (in Russian).
  10. Tatosov A. V. Model of crack filling in hydraulic fracturing . Computational technologies,2005, vol. 10, no. 6, pp. 91–101 (in Russian).
  11. Samarskii A. A., Galaktionov V. A., Kurdyumov S. P., Mikhailov A. P. Rezhimy s obostreniem v zadachah dlja kvazilinejnyh parabolicheskih uravnenij [Regimes with peaking in problems for quasilinear parabolic equations]. Moscow, Nauka, 1987. 480 p. (in Russian).
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