Peculiarities of the hydraulic fracture propagation caused by pumping of proppant-fluid slurry


A new numerical model for hydraulic fracturing has been developed. This model takes into account several simultaneous processes: pumping of proppant-laden slurry and its flow through the fracture, fracture growth with variable height and length, proppant settling, forming of proppant packing, and fluid filtration through this packing. Simulation experiments demonstrated that proppant particle diameter has significant influence on forming the proppant packing, fluid filtration through the packing, and, finally, on the fracture length and ultimate distribution of fracture width.

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  1. 1.

    S.A. Boronin and A.A. Osiptsov, Two-continua model of suspension flow in a hydraulic fracture, Doklady Phys-ics, 2010, Vol. 55, No. 4, P. 199–202.

    ADS  Article  Google Scholar 

  2. 2.

    S.A. Boronin and A.A. Osiptsov, Effects of particle migration on suspension flow in a hydraulic fracture, Fluid Mechanics, 2014, Vol. 49, No.2, P. 208–221.

    MathSciNet  MATH  Google Scholar 

  3. 3.

    E.V. Dontsov and A.P. Peirce, Slurry flow, gravitational settling and a proppant transport model for hydraulic fractures, J. Fluid Mech., 2014, Vol. 760, P. 567–590.

    ADS  MathSciNet  Article  Google Scholar 

  4. 4.

    B. Lecampion and D.I. Garagash, Confined flow of suspensions modelled by a frictional rheology, J. Fluid Mech., 2014, Vol. 759, P. 197–235.

    ADS  MathSciNet  Article  Google Scholar 

  5. 5.

    A.A. Osiptsov, Fluid mechanics of hydraulic fracturing: a review, J. Petroleum Science and Engng, 2017, Vol. 156, P. 513–535.

    Article  Google Scholar 

  6. 6.

    T.K. Perkins and L.R. Kern, Widths of hydraulic fractures, J. Petroleum Technology, 1961, Vol. 13, No. 9, P. 937–949.

    Article  Google Scholar 

  7. 7.

    R.P. Nordgren, Propagation of a vertical hydraulic fracture, SPE J., 1972, Vol. 12, No. 4, P. 306–314.

    Google Scholar 

  8. 8.

    P.S. Hammond, Settling and slumping in a newtonian slurry, and implications for proppant placement during hydraulic fracturing of gas wells, Chemical Engng Sci., 1995, Vol. 50, No. 20, P. 3247–3260.

    Article  Google Scholar 

  9. 9.

    A.T. Mobbs and P.S. Hammond, Computer simulations of proppant transport in a hydraulic fracture, SPE Production & Facilities, 2001, Vol. 16, No. 2, P. 112–121.

    Article  Google Scholar 

  10. 10.

    R.D. Barree and M.W. Conway, Proppant holdup, bridging, and screenout behavior in naturally fractured reser-voirs, SPE Production and Operations Symposium. Soc. Petroleum Engineers, 2001, No. SPE-67298-MS, P. 1–7.

    Google Scholar 

  11. 11.

    J. Adachi, E. Siebrits, A. Peirce, and J. Desroches, Computer simulation of hydraulic fractures, Int. J. Rock Mech. and Mining Sci., 2007, Vol. 44, No. 5, P. 739–757.

    Article  Google Scholar 

  12. 12.

    A. Lakhtychkin, D. Eskin, and O. Vinogradov, Modelling of transport of two proppant laden immiscible power-law fluids through an expanding fracture, Canadian J. Chemical Engng, 2012, Vol. 90, No. 3, P. 528–543.

    Article  Google Scholar 

  13. 13.

    P.B. Gadde and M.M. Sharma, The impact of proppant retardation on propped fracture lengths, in: 2005 SPE Annual Technical Conference and Exhibition, USA, Dallas, Texas, 2005, P. 9–12.

    Google Scholar 

  14. 14.

    S. Shiozawa and M. McClure, Simulation of proppant transport with gravitational settling and fracture closure in a three-dimensional hydraulic fracturing simulator, J. Petroleum Sci. and Engng, 2016, Vol. 138, P. 298–314.

    Article  Google Scholar 

  15. 15.

    E.V. Dontsov and A.P. Peirce, Proppant transport in hydraulic fracturing: Crack tip screen-out in KGD and P3D models, Int. J. Solids and Structures, 2015, Vol. 63, P. 206–218.

    Article  Google Scholar 

  16. 16.

    F. Boyer, E. Guazzelli, and O. Pouliquen, Unifying suspension and granular rheology, Phys. Rev. Letters, 2011, Vol. 107, No. 18, P. 188301–1–188301–5.

    ADS  Article  Google Scholar 

  17. 17.

    G.R. Coulter and R.D. Wells, The advantages of high proppant concentration in fracture stimulation, J. Petroleum Technology, 1972, Vol. 24, No. 06, P. 643–650.

    Article  Google Scholar 

  18. 18.

    Yu. Shokin, S. Cherny, D. Esipov, V. Lapin, A. Lyutov, and D. Kuranakov, Three-dimensional model of fracture propagation from the cavity caused by quasistatic load or viscous fluid pumping, Commun. in Computer and Information Sci., 2015, Vol. 549, P. 143–157.

    Article  Google Scholar 

  19. 19.

    S. Cherny, V. Lapin, D. Esipov, D. Kuranakov, A. Avdyushenko, A. Lyutov, and P. Karnakov, Simulating fully 3D non-planar evolution of hydraulic fractures, Int. J. Fracture, 2016, Vol. 201, No. 2, P. 181–211.

    Article  Google Scholar 

  20. 20.

    S.G. Cherny, V.N. Lapin, D.V. Esipov, and D.S. Kuranakov, Methods for Simulation of Fracture Initiation and Growth, SB RAS Publ., Novosibirsk, 2016.

    Google Scholar 

  21. 21.

    E. Detournay, Mechanics of hydraulic fractures, Annual Review of Fluid Mechanics, 2016, Vol. 48, No. 1, P. 311–339.

    ADS  MathSciNet  MATH  Article  Google Scholar 

  22. 22.

    R.D. Carter, Derivation of the general equation for estimating the extent of the fractured area. Appendix I of drilling and production practice, G.C. Howard and C.R. Fast (Eds.), N.Y.: American Petroleum Institute, 1957, P. 261–270.

  23. 23.

    I.N. Sneddon, The distribution of stress in the neighborhood of a crack in an elastic solid, in: Proc. Roy. Soc. A: Math., Phys., and Engng Sci., 1946, Vol. 187, No. 1009, P. 229–260.

    ADS  Article  Google Scholar 

  24. 24.

    B.R. Meyer, L.W. Bazan, and D. Walls, Modeling of proppant permeability and inertial factor for fluid flow through packed columns, in: ISRM Int. Conf. for Effective and Sustainable Hydraulic Fracturing, Int. Society for Rock Mechanics, 2013, P. 549–569.

    Google Scholar 

  25. 25.

    S.H. Maron and P.E. Pierce, Application of Ree-Eyring generalized flow theory to suspensions of spherical particles, J. Colloid Sci., 1956, Vol. 11, No. 1, P. 80–95.

    Article  Google Scholar 

  26. 26.

    S. Mueller, E.W. Llewellin, and H.M. Mader, The rheology of suspensions of solid particles, The Roy. Soc., 2009, Vol. 466, P. 1201–1228.

    Article  Google Scholar 

  27. 27.

    P.V. Karnakov, V.N. Lapin, and S.G. Cherny, Model of formation fracturing including the mechanism of proppant bridging, Vestnik NGU, series: Information Technology, 2014, Vol. 12, No. 1, P. 19–33.

    Google Scholar 

  28. 28.

    J.P. Van Doormaal and G.D. Raithby, Enhancements of the simple method for predicting incompressible fluid flows, Numerical Heat Transfer. 1984. Vol. 7, No. 2. P. 147–163.

    ADS  MATH  Google Scholar 

  29. 29.

    F.H. Harlow and M.W. Evans, A machine calculation method for hydrodynamic problems, Los Alamos Scientific Laboratory report LAMS-1956.

  30. 30.

    M.J. Economides and K.G. Nolte, Reservoir Stimulation. Third edition. John Wiley & Sons, 2000.

    Google Scholar 

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Corresponding author

Correspondence to S. G. Cherny.

Additional information

Research was supported by the Russian Science Foundation grant (Project No. 17-71-20139).

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Karnakov, P.V., Kuranakov, D.S., Lapin, V.N. et al. Peculiarities of the hydraulic fracture propagation caused by pumping of proppant-fluid slurry. Thermophys. Aeromech. 25, 587–603 (2018).

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Key words

  • growth of hydraulic fracture
  • proppant slurry flow
  • fluid filtration through a proppant pack
  • well production