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ELASTIC FILTRATION OF FLUID TO A WELLBORE THROUGH A FRACTURE PERPENDICULAR TO IT AND FORMED DURING HYDRAULIC FRACTURING

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Abstract

The problem of fluid withdrawal/injection from a reservoir into a wellbore in the presence of a hydraulic fracture that is perpendicular to the wellbore at a constant pressure difference between the wellhead and the reservoir is under consideration. Analytical solutions that describe the evolution of pressure in the fracture and fluid flow into the wellbore are obtained. Approximate solutions are constructed using the method of successive change of steady states. Exact and approximate solutions of problems for determining the pressure fields in the fracture and the volumetric flow rate of fluid from the wellbore into the fracture are compared, and it is shown that they practically match (the relative difference does not exceed 1–2%). In this case, calculation time for approximate solutions is significantly reduced. This contributes to the development of effective computational algorithms for transient modes of the wellbore operation in reservoirs with complicated reservoir characteristics. The influence of the characteristics of a reservoir and a fracture on the evolution of pressure in the fracture and fluid flow into the wellbore is analyzed.

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REFERENCES

  1. R. E. Oligney, P. Valko, and M. J. Economide, Unified Fracture Design: Bridging the Gap Between Theory and Practice (Orsa Press, 2001).

    Google Scholar 

  2. R. D. Kanevskaya, Mathematical Modeling of the Development of Oil and Gas Fields Using Hydraulic Fracturing (Nedra, Moscow, 1999) [in Russian].

    Google Scholar 

  3. H. Cinco-Ley, V. F. Samaniego, and A. N. Dominguez, “Transient Pressure Behavior for a Well with a Finite-Conductivity Vertical Fracture," Soc. Petroleum. Engrs. J. 18 (4), 253–264 (1978).

    Article  Google Scholar 

  4. S. S. Apte and W. J. Lee, “Elliptical Flow Regimes in Horizontal Wells with Multiple Hydraulic Fractures," in Proc. of the SPE Hydraulic Fracturing Technology Conf. and Exhibit., Woodlands (USA), 24–26 Jan. 2017 (OnePetro, S. l., 2017).

  5. I. L. Khabibullin and A. A. Khisamov, “Modeling of Unsteady Filtration Around the Well with Vertical Hydraulic Fracture," Vestnik Bashkirskogo Universiteta 22 (2), 309–314 (2017).

    Google Scholar 

  6. I. L. Khabibullin and A. A. Khisamov, “Unsteady Flow through a Porous Stratum with Hydraulic Fracture," Izvestiya Rossiiskoi Akademii Nauk. Mekhanika Zhidkosti I Gaza, No. 5, 6C14 (2019) [Fluid Dynamics, V. 54, No 5, 594-602 (2019)].

  7. V. Sh. Shagapov and Z. M. Nagaeva, “On the Theory of Seepage Waves of Pressure in a Fracture in a Porous Permeable Medium," Prikl. Mekh. Tekh. Fiz. 58 (5), 121–130 (2017) [J. Appl. Mech. Tech. Phys. 58 (5), 862–870 (2017)].

    Article  MathSciNet  ADS  Google Scholar 

  8. Z. M. Nagaeva and V. Sh. Shagapov, “Elastic Seepage in a Fracture Located in an Oil or Gas Reservoir," Prikladnaya Matematika I Mekhanika 81 (3), 319–329 (2017) [J. Appl. Math. Mech. 81, (3), 214–222 (2017)].

    Article  MathSciNet  ADS  Google Scholar 

  9. V. Sh. Shagapov and Z. M. Nagaeva, “Approximate Solution of the Problem on Elastic-Liquid Filtration in a Fracture Formed in an Oil Stratum," Inzhenerno-Fizicheskii Zh. 93 (1), 206–215 (2020) [J. Eng. Phys. Thermophy. 93 (1), 201–209 (2020)].

    Article  ADS  Google Scholar 

  10. V. Sh. Shagapov, E. P. Anosova, and Z. M. Nagaeva, “On the Dynamics of Harmonic Filtration Waves in a Hydraulic Fracture Perpendicular to the Wellbore," Akusticheskii Zh. 66 (6), 669–674 (2020) [Acoust. Phys. 66, 666–670 (2020)].

    Article  ADS  Google Scholar 

  11. R. I. Nigmatulin, Dynamics of Multiphase MediaVol. 1 (CRC Press, 1990).

    Google Scholar 

  12. A. N. Tikhonov and A. N. Samarskii, Equations of Mathematical Physics (Nauka, Moscow, 1972) [in Russian].

    Google Scholar 

  13. V. A. Ditkin and A. P. Prudnikov, Operational Calculus (Vysshaya Shkola, Moscow, 1975) [in Russian].

    MATH  Google Scholar 

  14. V. F. Zaitsev and A. D. Polyanin, Handbook of Ordinary Differential Equations (Fizmatlit, Moscow, 2001) [in Russian].

    MATH  Google Scholar 

  15. I. A. Charnyi, Underground Fluid Dynamics (Gostoptekhizdat, Moscow, 1963) [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. Mavlyutov Institute of Mechanics of the Ufa Investigation Center, Russian Academy of Sciences, 450054, Ufa, Russia

    V. Sh. Shagapov & Z. M. Nagaeva

  2. Ufa State Petroleum Technological University, 450062, Ufa, Russia

    Z. M. Nagaeva & E. P. Anosova

Authors
  1. V. Sh. Shagapov
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  2. Z. M. Nagaeva
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  3. E. P. Anosova
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Corresponding author

Correspondence to Z. M. Nagaeva.

Additional information

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2021, Vol. 63, No. 4, pp. 105-115. https://doi.org/10.15372/PMTF20220411.

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Shagapov, V.S., Nagaeva, Z.M. & Anosova, E.P. ELASTIC FILTRATION OF FLUID TO A WELLBORE THROUGH A FRACTURE PERPENDICULAR TO IT AND FORMED DURING HYDRAULIC FRACTURING. J Appl Mech Tech Phy 63, 643–651 (2022). https://doi.org/10.1134/S0021894422040113

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  • DOI: https://doi.org/10.1134/S0021894422040113

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