Scaling of Physical Processes in Fluid-Driven Fracture: Perspective from the Tip

  • Dmitry I. Garagash
Part of the Iutam Bookseries book series (IUTAMBOOK, volume 10)


A particular class of fractures driven in a solid by pressurized viscous fluids is considered. These fractures could be either tens or hundreds meters long man-made hydraulic fractures in oil and gas reservoirs, or natural fractures, such as kilometers-long volcanic dikes driven by magma coming from upper mantle beneath the Earth’s crust. Different physical mechanisms governing propagation of a fluid-driven fracture include (i) dissipation in the viscous fluid flow along the fracture, (ii) dissipation in the solid due to fracturing, (iii) lagging of the fluid front behind the fracture front, (iv) fluid leak-off (into the permeable solid), and others. Dissipation in the viscous fluid flow is often considered to be the dominant mechanism on fracture length and time scales of practical interest. Universal scaling of the non-dominant mechanisms (dissipation in the solid, fluid lag, etc.) in the global solution of fluid-driven fracture is derived in this paper based on the analysis of the boundary layer structure near the fracture leading edge. This scaling may be particularly important in guiding numerical solution of fractures when non-trivial fracture geometry or/and spatially varying properties of the solid prevent analytical investigation of the global solution.


Hydraulic fracture scaling asymptotic solutions 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. R. Lister. Buoyancy-driven fluid fracture: The effects of material toughness and of low-viscosity precursors. J. Fluid Mech., 210:263–280, 1990.zbMATHCrossRefGoogle Scholar
  2. 2.
    J. Desroches, E. Detournay, B. Lenoach, P. Papanastasiou, J. R. A. Pearson, M. Thiercelin, and A. H-D. Cheng. The crack tip region in hydraulic fracturing. Proc. R. Soc. Lond., A(447): 39–48, 1994.zbMATHCrossRefGoogle Scholar
  3. 3.
    D. I. Garagash and E. Detournay. The tip region of a fluid-driven fracture in an elastic medium. ASME J. Appl. Mech., 67(1):183–192, 2000.zbMATHGoogle Scholar
  4. 4.
    D. I. Garagash and E. Detournay. Plane-strain propagation of a fluid-driven fracture: Small toughness solution. ASME J. Appl. Mech., 72(6):916–928, 2005.zbMATHCrossRefGoogle Scholar
  5. 5.
    D. I. Garagash, E. Detournay, and J. I. Adachi. Tip solution of a fluid-driven fracture in permeable rock. J. Mech. Phys. Solids, 2008. submitted.Google Scholar
  6. 6.
    S. L. Mitchell, E. Kuske, and A. P. Peirce. An asymptotic framework for the analysis of hydraulic fractures: The impermeable case. ASME J. Appl. Mech., 74:365–372, 2007.zbMATHGoogle Scholar
  7. 7.
    D. A. Spence and P. W. Sharp. Self-similar solution for elastohydrodynamic cavity flow. Proc. R. Soc. Lond. A(400):289–313, 1985.MathSciNetGoogle Scholar
  8. 8.
    E. Detournay. Propagation regimes of fluid-driven fractures in impermeable rocks. Int. J. Geomech., 4(1):1–11, 2004.CrossRefGoogle Scholar
  9. 9.
    D. I. Garagash. Propagation of a plane-strain hydraulic fracture with a fluid lag: Early-time solution. Int. J. Solids Struct. 43:5811–5835, 2006.zbMATHCrossRefGoogle Scholar
  10. 10.
    A.A. Savitski and E. Detournay. Propagation of a fluid-driven penny-shaped fracture in an impermeable rock: Asymptotic solutions. Int. J. Solids Struct. 39(26):6311–6337, 2002.zbMATHCrossRefGoogle Scholar
  11. 11.
    E. Detournay and D. I. Garagash. General scaling laws for fluid-driven fractures. Proc. R. Soc. Lond. A, 2008. submittedGoogle Scholar
  12. 12.
    J. R. Rice. Mathematical analysis in the mechanics of fracture. In H. Liebowitz, editor, Fracture, an Advanced Treatise, volume II, chapter 3, pages 191–311. Academic Press, New York NY, 1968.Google Scholar
  13. 13.
    M. F. Kanninen and C. H. Popelar. Advanced Fracture Mechanics, volume 15 of The Oxford Engineering Science Series. Oxford University Press, Oxford UK, 1985.zbMATHGoogle Scholar
  14. 14.
    D. I. Garagash. Relevance of fluid lag, toughness, and leak-off for hydraulic fracture propagation. unpublished, 2004.Google Scholar
  15. 15.
    S.A. Khristianovic and Y.P. Zheltov. Formation of vertical fractures by means of highly viscous fluids. In Proceedings of the 4th World Petroleum Congress, Rome, volume II, pages 579–586, 1955.Google Scholar
  16. 16.
    J. Geertsma and F. de Klerk. A rapid method of predicting width and extent of hydraulic induced fractures. J. Pet. Tech., 246:1571–1581, 1969. (SPE 2458).Google Scholar
  17. 17.
    J. I. Adachi and E. Detournay. Self-similar solution of a plane-strain fracture driven by a power-law fluid. Int. J. Numer. Anal. Meth. Geomech., 26:579–604, 2002.zbMATHCrossRefGoogle Scholar
  18. 18.
    R.H. Nilson. Gas driven fracture propagation. ASME J. Appl. Mech., 48:757–762, 1981.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Dmitry I. Garagash
    • 1
  1. 1.Department of Civil and Resource EngineeringDalhousie UniversityHalifax NSCanada B3J 1Z1

Personalised recommendations