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On Theory of Bottomhole Zone Echoscopy in Low-Permeability Formation Subject to Hydraulic Fracturing

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Abstract

A mathematical model is built describing the evolution of a pulse signal in a well at a longitudinal or a transverse fracture in the bottomhole section. It is assumed that the signal is sent from the wellhead with a wavelength exceeding the well diameter and the length of the open section of the well. The behavior of the echo of the pulse signal returning to the wellhead makes it possible to assess the quality of hydraulic fracturing. The results of numerical calculations for a bell-shaped pulse are presented. It is shown that in diagnosing fractures, water is preferable to oil as a fluid in which the signal propagates.

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REFERENCES

  1. M. I. Kremenetskii and A. I. Ipatov, Hydrodynamic and Field-Technological Studies of Wells (MAKS Press, Moscow, 2008) [in Russian].

    Google Scholar 

  2. M. J. Economides, E. O. Ronald, and P. Valko, Unified Fracture Design Bridging the Gap between Theory and Practice (Orsa Press, Alvin, TX, 2002).

    Google Scholar 

  3. V. A. Baikov, G. T. Bulgakova, A. M. Il’yasov, and D. V. Kashapov, Fluid Dyn. 53 (5), 642–653 (2018). http://ras.jes.su/mzg/s207987840000962-7-2-en.

    Article  ADS  MathSciNet  Google Scholar 

  4. R. A. Bashmakov, D. A. Nasyrova, and V. Sh. Shagapov, “Natural vibrations of a fluid in a well connected with formation in the presence of a hydraulic fracture,” Fluid Dyn. 56 (8), 1049–1061 (2021). https://doi.org/10.1134/S0015462821080024

    Article  ADS  MathSciNet  Google Scholar 

  5. G. R. Holzhausen and R. P. Gooch, “Impedance of hydraulic fractures: its measurement and use for estimating fracture closure pressure and dimensions,” in Proc. SPE/DOE Low Permeability Gas Reservoirs Symp. (Denver, CO, May 1985), Pap. No. SPE-SPE-13892-MS.

  6. X. Wang, K. Hovem, D. Moos, and Y. Quan, “Water hammer effects on water injection well performance and longevity,” in Proc. SPE Int. Symp. & Exhibition on Formation Damage Control (Lafayette, LA, 2008), Paper No. SPE-112282-MS. https://doi.org/10.2118/112282-MS.

  7. V. S. Shagapov, E. V. Galiakbarova, and Z. R. Khakimova, “On the theory of local sounding of hydraulic fractures using pulsed pressure waves,” J. Appl. Mech. Tech. Phys. 62 (4), 563–572 (2021). https://doi.org/10.1134/S0021894421040052

    Article  ADS  MathSciNet  Google Scholar 

  8. E. V. Galiakbarova, “How the conductivity of a hydraulic fracturing crack influences onto the diagnostic possibility with an acoustic “TV”,” Vestn. Bashk. Univ. 26 (4), 866–870 (2021). https://doi.org/10.33184/bulletin-bsu-2021.4.2

    Article  Google Scholar 

  9. V. S. Shagapov, Z. M. Nagaeva, and E. P. Anosova, “Elastic filtration of fluid to a wellbore through a fracture perpendicular to it and formed during hydraulic fracturing,” J Appl. Mech. Tech. Phys. 63 (4), 643–651 (2022). https://doi.org/10.1134/S0021894422040113

    Article  ADS  MathSciNet  Google Scholar 

  10. Z. M. Nagaeva and V. Sh. Shagapov, “Elastic seepage in a fracture located in an oil or gas reservoir,” J. Appl. Math. Mech. 81 (3), 214–222 (2017).

    Article  MathSciNet  Google Scholar 

  11. R. G. Lyons, Understanding Digital Signal Processing (Prentice Hall PTR, Upper Saddle River, NJ, 2001).

    Google Scholar 

  12. L. D. Landau and E. M. Lifshits, Theoretical Physics, Vol. 6: Hydrodynamics (Nauka, Moscow, 1986) [in Russian].

  13. E. C. Ifeachor and B. W. Jervis, Digital Signal Processing (Addison-Wesley Publ. Co., 1993).

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Funding

This study was financially supported by the Russian Science Foundation, project no. 21-11-00207, https://rscf.ru/project/21-11-00207/

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Authors and Affiliations

  1. Mavlutov Institute of Mechanics, Ufa Federal Research Center, Russian Academy of Sciences, Ufa, Russia

    R. A. Bashmakov, E. V. Galiakbarova, Z. R. Khakimova & V. Sh. Shagapov

  2. Ufa University of Science and Technology, Ufa, Russia

    R. A. Bashmakov

  3. Ufa State Petroleum Technological University, Ufa, Russia

    E. V. Galiakbarova & Z. R. Khakimova

Authors
  1. R. A. Bashmakov
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  2. E. V. Galiakbarova
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  3. Z. R. Khakimova
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  4. V. Sh. Shagapov
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Corresponding authors

Correspondence to R. A. Bashmakov, E. V. Galiakbarova, Z. R. Khakimova or V. Sh. Shagapov.

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The authors declare that they have no conflicts of interest.

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Translated by S. Kuznetsov

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Bashmakov, R.A., Galiakbarova, E.V., Khakimova, Z.R. et al. On Theory of Bottomhole Zone Echoscopy in Low-Permeability Formation Subject to Hydraulic Fracturing. Mech. Solids 58, 2703–2713 (2023). https://doi.org/10.3103/S0025654423070038

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  • DOI: https://doi.org/10.3103/S0025654423070038

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