Propagation Regimes of Fluid-Driven Fractures in Impermeable Rocks
Publication: International Journal of Geomechanics
Volume 4, Issue 1
Abstract
This paper reviews recent results of a research program aimed at developing a theoretical framework to understand and predict the different modes of propagation of a fluid-driven fracture. The research effort involves constructing detailed solutions of the crack tip region, developing global models of hydraulic fractures for plane strain and radial geometry, and identifying the parameters controlling the fracture growth. The paper focuses on the propagation of hydraulic fractures in impermeable rocks. The controlling parameters are identified from scaling laws that recognize the existence of two dissipative processes: fracturing of the rock (toughness) and dissipation in the fracturing fluid (viscosity). It is shown that the two limit solutions (corresponding to zero toughness and zero viscosity) are characterized by a power law dependence on time and that the transition between these two asymptotic solutions depends on a single number, which can be chosen to be either a dimensionless toughness or a dimensionless viscosity. The viscosity- and toughness-dominated regime of crack propagation are then identified by comparing the general solutions with the asymptotic solutions. This analysis yields the ranges of the dimensionless parameter for which the solution can be approximated for all practical purposes either by the zero toughness or by the zero viscosity solution.
Get full access to this article
View all available purchase options and get full access to this article.
References
Abé, H., Mura, T., and Keer, L. M.(1976). “Growth rate of a penny-shaped crack in hydraulic fracturing of rocks.” J. Geophys. Res., 81, 5335–5340.
Adachi, J. I. (2001). “Fluid-driven fracture in permeable rock.” PhD. thesis, Univ. of Minnesota, Minneapolis.
Adachi, J. I., and Detournay, E.(2002). “Self-similar solution of a plane-strain fracture driven by a power-law fluid.” Int. J. Numer. Analyt. Meth. Geomech., 26(6), 579–604.
Advani, S. H., Lee, T. S., and Lee, J. K.(1990). “Three-dimensional modeling of hydraulic fractures in layered media: Finite element formulations.” ASME J. Energy Resour. Technol., 112, 1–18.
Advani, S. H., Torok, J. S., Lee, J. K., and Choudhry, S.(1987). “Explicit time-dependent solutions and numerical evaluations for penny-shaped hydraulic fracture models.” J. Geo- Phys. Res., 92(B8), 8049–8055.
Barenblatt, G. (1962). “The mathematical theory of equilibrium cracks in brittle fracture.” Adv. Appl. Mech., VII, 55–129.
Batchelor, G. K. (1967). An introduction to fluid dynamics, Cambridge University Press, Cambridge, U.K.
Carbonell, R. (1996). “Self-similar solution of a fluid-driven fracture.” PhD thesis, Univ. of Minnesota, Minneapolis.
Carbonell, R., Desroches, J., and Detournay, E.(1999). “A comparison between a semianalytical and a numerical solution of a two-dimensional hydraulic fracture.” Int. J. Solids Struct., 36(31-32), 4869–4888.
Clifton, R. J., and Abou-Sayed A. S. (1981). “A variational approach to the prediction of the three-dimensional geometry of hydraulic fractures.” Proc., SPE/DOE Low Permeability Reservoir Symp., Denver, SPE 9879.
Desroches, J., and Thiercelin, M.(1993). “Modeling propagation and closure of microhydraulic fractures.” Int. J. Rock Mech. Min. Sci., 30, 1231–1234.
Desroches, J., Detournay, E., Lenoach, B., Papanastasiou, P., Pearson, J. R. A., Thiercelin, M., and Cheng, A. H.-D.(1994). “The crack tip region in hydraulic fracturing.” Proc. R. Soc. London, Ser. A, 447, 39–48.
Detournay, E. (1999). Fluid and solid singularities at the tip of a fluid-driven fracture. In Proc., IUTAM Symp. on Nonlinear Singularities in deformation and flow, Haifa, D. Durban and J. Pearson, eds., Kluwer Academic, Dordrecht, The Netherlands, 27–42.
Garagash, D. (1998). “Near-tip processes of fluid-driven fractures.” PhD thesis, Univ. of Minnesota, Minneapolis.
Garagash, D. (2000). “Hydraulic fracture propagation in elastic rock with large toughness.” Proc. 4th North American Rock Mechanics Symp., J. Girard, M. Liebman, C. Breeds, and T. Doe, eds., Balkema, Rotterdam, The Netherlands, 221–228.
Garagash, D. I., and Detournay, E.(2000). “The tip region of a fluid-driven fracture in an elastic medium.” ASME J. Appl. Mech., 67, 183–192.
Garagash, D. and Detournay, E. (2002). “Viscosity-dominated regime of a fluid-driven fracture in an elastic medium,” Solid mechanics and its applications, B. L. Karihaloo, ed., Kluwer Academic, Dordrecht, The Netherlands, 97.
Geertsma, J., and de Klerk, F.(1969). “A rapid method of predicting width and extent of hydraulic induced fractures.” J. Pet. Technol., 246, 1571–1581.
Khristianovic, S., and Zheltov, Y. (1955). “Formation of vertical fractures by means of highly viscous fluids.” Proc., 4th World Petroleum Congress, Rome, II, 579–586.
Lister, J. R.(1990). “Buoyancy-driven fluid fracture: The effects of material toughness and of low-viscosity precursors.” J. Fluid Mech., 210, 263–280.
Nordgren, R.(1972). “Propagation of vertical hydraulic fractures.” J. Pet. Technol., 253, 306–314.
Peirce, A. P., and Siebrits, E.(2001). “The scaled flexibility matrix method for the efficient solution of boundary value problems in 2D and 3D layered elastic media.” Comput. Methods Appl. Mech. Eng., 190, 5935–5956.
Perkins, T. K., and Kern, L. R.(1961). “Widths of hydraulic fractures.” J. Pet. Technol., 222, 937–949.
Rice, J. R. (1968). “Mathematical analysis in the mechanics of fracture.” Fracture, an advanced treatise, H. Liebowitz, ed., Academic, New York, II, 3, 191–311.
Savitski, A. A. (2000). “Propagation of a penny-shaped hydraulic fracture in an impermeable rock.” PhD thesis, Univ. of Minnesota, Minneapolis.
Savitski, A. A., and Detournay, E.(2002). “Propagation of a fluid-driven penny-shaped fracture in an impermeable rock: Asymptotic solutions.” Int. J. Solids Struct. 39, 6311–6337.
Shah, K. R., Carter, B. J., and Ingraffea, A. R.(1997). “Hydraulic fracturing simulation in parallel computing environments.” Int. J. Rock Mech. Min. Sci., 34(3/4), 474.
Siebrits, E., and Peirce, A. P.(2002). “An efficient multilayer planar 3D fracture growth algorithm using a fixed mesh approach.” Int. J. Numer. Methods Eng., 53, 691–717.
Sneddon, I., and Lowengrub, M. (1969). Crack problems in the classical theory of elasticity, Wiley, New York.
Sousa, J. L. S., Carter, B. J., and Ingraffea, A. R.(1993). “Numerical simulation of 3D hydraulic fracture using Newtonian and power-law fluids.” Int. J. Rock Mech. Min. Sci., 30(7), 1265–1271.
Spence, D. A., and Sharp, P. W.(1985). “Self-similar solution for elastohydrodynamic cavity flow.” Proc. R. Soc. London, Ser. A, 400, 289–313.
Spence, D., and Turcotte, D.(1985). “Magma-driven propagation crack.” J. Geophys. Res., 90, 575–580.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 4 • Issue 1 • March 2004
Pages: 35 - 45
Copyright
Copyright © 2004 American Society of Civil Engineers.
History
Received: Oct 19, 2001
Accepted: Jul 15, 2002
Published online: Feb 19, 2004
Published in print: Mar 2004
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.