Skip to main content
SpringerLink
Log in

Analytical solution of hydraulic fracture problem for a non-Newtonian fluid

  • Geomechanics
  • Published:
Journal of Mining Science Aims and scope

Abstract

The paper presents the analytical solution to a hydraulic fracture driven by a non-Newtonian fluid and propagating under plane strain conditions in cross sections parallel to the fracture front. Conclusions are drawn on the influence of fluid properties on the fracture propagation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Zheltov, Yu.P. and Khristianovich S.A., Hydraulic Fracturing in an Oil Reservoir, Izv. AN SSSR, OTN, 1955, no. 5.

    Google Scholar 

  2. Khristianovich, S.A. and Zheltov, V.P., Formation of Vertical Fractures by Means of Highly Viscous Liquid, Proc. 4th World Petroleum Congress, Rome, 1955.

    Google Scholar 

  3. Geertsma, J. and F. de Klerk, A Rapid Method of Predicting Width and Extent of Hydraulically Induced Fractures, J. Pet. Tech., 1969, December.

    Google Scholar 

  4. Alekseenko, O.P. and Vaisman, A.M., Certain Aspects of a Two-Dimensional Problem of the Hydraulic Fracturing of an Elastic Medium, Journal of Mining Science, 1999, vol. 35, no. 3, pp. 269–275.

    Article  Google Scholar 

  5. Perkins, T.K. and Kern, L.F., Widths of Hydraulic Fractures, J. Pet. Tech., 1961, Sept.

    Google Scholar 

  6. Nordgren, R.P., Propagation of a Vertical Hydraulic Fracture, Soc. Pet. Eng. J., 1972, August.

    Google Scholar 

  7. Adachi, J., E. Siebrits, E., et al., Computer Simulation of Hydraulic Fractures, Int. J. Rock Mech. Mining Sci., 2007, vol. 44.

  8. Kovalyshen, Y. and Detournay, E., A Re-Examination of the Classical PKN model of Hydraulic Fracture, Transport in Porous Media, 2009, vol. 81.

  9. Hu, J. and Garagash, D.I., Plane Strain Propagation of a Fluid-Driven Crack in a Permeable Rock with Fracture Toughness, ASCE J. Eng. Mech., 2010, vol. 136.

  10. Garagash, D.I., Detournay, E., and Adachi, J.I., Multiscale Tip Asymptotics in Hydraulic Fracture with Leak-off, J. Fluid Mech., 2011, vol. 669.

  11. Mikhailov, D.N., Economides, M.J., and Nikolaevsky V.N., Fluid Leak-Off Determines Hydraulic Fracture Dimensions: Approximate Solution for Non-Newtonian Fracturing Fluid, Int. J. Engineering Sci., 2011, vol. 49.

  12. Spence, D.A. and Sharp, P.W., Self-Similar Solutions for Elastohydrodynamic Cavity Flow, Proc. Roy Soc., London, Ser. A, 1985, vol. 400.

  13. Adachi, J. and Detournay, E., Self-Similar Solution of Plane-Strain Fracture Driven by a Power-Law Fluid, Int. J. Numer. Anal. Meth. Geomech., 2002, vol. 26.

  14. Garagash, D.I., Transient Solution for a Plane-Strain Fracture Driven by a Shear-Thinning, Power-Law Fluid, Int. J. Numer. Anal. Meth. Geomech., 2006, vol. 30.

  15. Adachi, J.I. and Detournay, E., Plane Strain Propagation of a Hydraulic Fracture in a Permeable Rock, Eng. Fracture Mech., 2008, vol. 75.

  16. Linkov, A.M., Velocity Equation and its Application to Solve Ill-Posed Hydrofracturing Problems, Dokl. Akad. Nauk, 2011, vol. 439, no. 4.

    Google Scholar 

  17. Linkov, A.M., Use of Speed Equation for Numerical Simulation of Hydraulic Fractures // available at: http://arxiv.org/abs/1108.6146, Date: Wed, 31 Aug 2011 07:47:52 GMT (726kb), Cite as: arXiv: 1108.6146v1 [physics.flu-dyn].

  18. Linkov, A.M., On Efficient Simulation of Hydraulic Fracturing in Terms of Particle Velocity, Int. J. Engineering Sci., 2012, vol. 52.

  19. Mishuris, G., Wrobel, M., and Linkov, A.M., On Modeling Hydraulic Fracture in Proper Variables: Stiffness, Accuracy, Sensitivity, Int. J. Engineering Sci., 2012, vol. 61.

  20. Linkov, A.M., Numerical Modeling of Hydraulic Fractures: State of Art and New Results, Proc. XL Summer School-Conference “Advanced Problems in Mechanics, APM 2012”, Institute for Problems of Mechanical Engineering, RAS, CD-ROM, 2012.

    Google Scholar 

  21. Kresse, O., Cohen, C., Weng, X., et al., Numerical Modeling of Hydraulic Fracturing in Naturally Fractured Formations, Proc. 5th US Rock Mechanics Symposium, American Rock Mechanics Association, 2011.

    Google Scholar 

  22. Cipola, C., Weng, X., Mack M., et al., Integrating Microseismic Mapping and Complex Fracture Modeling to Characterize Fracture Complexity, Soc. Pet. Eng., Paper SPE 140185, 2011.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, Bol’shoi pr. V. O. 61, Saint Petersburg, 199178, Russia

    A. M. Linkov

Authors
  1. A. M. Linkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. M. Linkov.

Additional information

Original Russian Text © A.M. Linkov, 2013, published in Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, 2013, No. 1, pp. 11–21.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Linkov, A.M. Analytical solution of hydraulic fracture problem for a non-Newtonian fluid. J Min Sci 49, 8–18 (2013). https://doi.org/10.1134/S1062739149010024

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1062739149010024

Key words

Search

Navigation