Advertisement

Transport in Porous Media

, Volume 67, Issue 3, pp 487–499 | Cite as

On the problem of fluid leakoff during hydraulic fracturing

  • Michael J. Economides
  • Dmitry N. Mikhailov
  • Victor N. NikolaevskiyEmail author
Original Paper

Abstract

While a hydraulic fracture is propagating, fluid flow and associated pressure drops must be accounted for both along the fracture path and perpendicularly, into the formation that is fractured, because of fluid leakoff. The accounting for the leakoff shows that it is the main factor that determines the crack length. The solved problem is useful for the technology of hydraulic fracturing and a good example of mass transport in a porous medium. To find an effective approach for the solution, the thin crack is represented here as the boundary condition for pore pressure spreading in the formation. Earlier such model was used for heat conduction into a rock massif from a seam under injection of hot water. Of course, the equations have other physical sense and mathematically they are somewhat different. The new plane solution is developed for a linearized form that permits the application of the integral transform. The linearization itself is analogous to the linearization of the natural gas equation using the real gas pseudo-pressure function and where the flux rates are held constant and approximations are introduced only into the time derivatives. The resulting analytical solution includes some integrals that can be calculated numerically. This provides rigorous tracking of the created fracture volume, leakoff volume and increasing fracture width. The solutions are an advance over existing discreet formulations and allow ready calculations of the resulting fracture dimensions during the injection of the fracturing fluid.

Keywords

Hydraulic fracture Pressure diffusion Mass transport Porous media Leakage Integral transform Non-steady fluid flows Special boundary condition Heat conductivity 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Economides M.J., Oligney R., Valko P. (2002) Unified Fracture Design. Orsa Press, Alvinm, TexasGoogle Scholar
  2. Griffith A.A. (1920) The phenomenon of rupture and flow in solids. Phil. Trans. Roy, Soc. A221, 163–198Google Scholar
  3. Sneddon, I.N.: Integral transform methods. In Mechanics of fracture, Part 1, Methods of analysis and solution of crack problems. (ed.) Sih G.C. Nordhoff Int. Leyden (1973)Google Scholar
  4. Christianovich, S.A., Zheltov, Yu. P, Barenblatt, G.I., Maximovich, G.K.: Theoretical principles of hydraulic fracturing of oil strata. The 5th World oil Congress, Section II, p. 23 (1959)Google Scholar
  5. Zheltov Yu P.(1975) Mechanics of Oil/Gas Seam. Moscow, NedraGoogle Scholar
  6. Perkins, T.K., Kern, L.R.: Width of the hydraulic fractures. J. Petrol. Technology. 937–949, Espt, (1961)Google Scholar
  7. Nordgren R.P. (1972) Propagation of a vertical hydraulic fracture. J. Petrol. Technology. 253, 306–314 (SPE 3009)Google Scholar
  8. Garagash D., Detournay E.(2000) The tip region of a fluid-driven fracture in an elastic medium. J. Appl. Mech. 67 March, 183–192CrossRefGoogle Scholar
  9. Detournay E., Garagash D.I. (2003) The near – tip region of a fluid-driven fracture propagating in a permeable elastic solid. J. Fluid Mech. 494, 1–32CrossRefGoogle Scholar
  10. Rubinshtein L.I. (1972) Temperature Fields in Oil Formations. Nedra, MoscowGoogle Scholar
  11. Nikolaevskiy V.N. (1996) Geomechanics and Fluidodynamics (with Applications to Reservoir Engineering). Kluwer, DordrechtGoogle Scholar
  12. Polubarinova–Kochina P.Ya. (1977) Theory of Ground Water Flows.2nd ed. Nauka, MoscowGoogle Scholar
  13. Ditkin V.A., Kuznetzov P.I. (1951) Handbook on Operation Calculus. Gostekhizdat, MoscowGoogle Scholar
  14. Sneddon, I.: Fourier Transforms. New York (1961)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  • Michael J. Economides
    • 1
  • Dmitry N. Mikhailov
    • 2
  • Victor N. Nikolaevskiy
    • 2
    Email author
  1. 1.University of HoustonHoustonUSA
  2. 2.Institute of Earth PhysicsRussian Academy of SciencesMoscowRussian Federation

Personalised recommendations