0
TECHNICAL PAPERS

The Tip Region of a Fluid-Driven Fracture in an Elastic Medium

[+] Author and Article Information
D. Garagash, E. Detournay

Department of Civil Engineering, University of Minnesota, 500 Pillsbury Drive SE, Minneapolis, MN 55455

J. Appl. Mech 67(1), 183-192 (Jun 22, 1999) (10 pages) doi:10.1115/1.321162 History: Received August 14, 1998; Revised June 22, 1999
Copyright © 2000 by ASME
Your Session has timed out. Please sign back in to continue.

References

Khristianovic, S. A., and Zheltov, Y. P., “Formation of Vertical Fractures by Means of Highly Viscous Fluids,” Proc. 4th World Petroleum Congress, Vol. II, pp. 579–586.
Barenblatt,  G. I., 1962, “The Mathematical Theory of Equilibrium Cracks in Brittle Fracture,” Adv. Appl. Mech., VII, pp. 55–129.
Perkins,  T. K., and Kern,  L. R., 1961, “Widths of Hydraulic Fractures,” SPEJ, 222, pp. 937–949.
Nordgren,  R. P., 1972, “Propagation of Vertical Hydraulic Fracture,” SPEJ, 253, pp. 306–314.
Abe,  H., Mura,  T., and Keer,  L. M., 1976, “Growth Rate of a Penny-Shaped Crack in Hydraulic Fracturing of Rocks,” J. Geophys. Res., 81, pp. 5335–5340.
Geertsma,  J., and Haafkens,  R., 1979, “A Comparison of the Theories for Predicting Width and Extent of Vertical Hydraulically Induced Fractures.” ASME J. Energy Resour. Technol., 101, pp. 8–19.
Spence,  D. A., and Sharp,  P., 1985, “Self-Similar Solution for Elastohydrodynamic Cavity Flow,” Proc. R. Soc. London, Ser. A, 400, pp. 289–313.
Spence,  D. A., and Turcotte,  D. L., 1985, “Magma-Driven Propagation Crack,” J. Geophys. Res., 90, pp. 575–580.
Lister,  J. R., 1990, “Buoyancy-Driven Fluid Fracture: The Effects of Material Toughness and of Low-Viscosity Precursors,” J. Fluid Mech., 210, pp. 263–280.
Carbonell, R. S., and Detournay, E., 2000, “Self-Similar Solution of a Fluid Driven Fracture in a Zero Toughness Elastic Solid,” Proc. R. Soc. London, Ser. A, to be submitted.
Savitski, A., and Detournay, E., 1999, “Similarity Solution of a Penny-Shaped Fluid-Driven Fracture in a Zero-Toughness Linear Elastic Solid,” C. R. Acad. Sci. Paris, submitted for publication.
Bui,  H. D., and Parnes,  R., 1992, “A Reexamination of the Pressure at the Tip of a Fluid-Filled Crack,” Int. J. Eng. Sci., 20, No. 11, pp. 1215–1220.
Medlin, W. L., and Masse, L., 1984, “Laboratory Experiments in Fracture Propagation,” SPEJ, pp. 256–268.
Rubin,  A. M., 1993, “Tensile Fracture of Rock at High Confining Pressure: Implications for Dike Propagation,” J. Geophys. Res., 98, No. B9, pp. 15919–15935.
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, pp. 39–48.
Lenoach,  B., 1995, “The Crack Tip Solution for Hydraulic Fracturing in a Permeable Solid,” J. Mech. Phys. Solids, 43, No. 7, pp. 1025–1043.
Advani,  S. H., Lee,  T. S., Dean,  R. H., Pak,  C. K., and Avasthi,  J. M., 1997, “Consequences of Fluid Lag in Three-Dimensional Hydraulic Fractures,” Int. J. Numer. Anal. Meth. Geomech., 21, pp. 229–240.
Papanastasiou,  P., 1997, “The Influence of Plasticity in Hydraulic Fracturing,” Int. J. Fract., 84, pp. 61–97.
Garagash,  D., and Detournay,  E., 1998, “Similarity Solution of a Semi-Infinite Fluid-Driven Fracture in a Linear Elastic Solid,” C. R. Acad. Sci., Ser. II b, 326, pp. 285–292.
Detournay, E., and Garagash, D., 1999, “The Tip Region of a Fluid-Driven Fracture in a Permeable Elastic Solid,” J. Fluid Mech., submitted for publication.
Carbonell,  R., Desroches,  J., and Detournay,  E., 2000, “A Comparison Between a Semi-analytical and a Numerical Solution of a Two-Dimensional Hydraulic Fracture,” Int. J. Solids Struct., 36, No. 31–32, pp. 4869–4888.
Detournay, E., 1999, “Fluid and Solid Singularities at the Tip of a Fluid-Driven Fracture,” Non-Linear Singularities in Deformation and Flow, D. Durban and J. R. A. Pearson, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 27–42.
Garagash, D., and Detournay, E., 2000, “Plane Strain Propagation of a Hydraulic Fracture: Influence of Material Toughness, Fluid Viscosity, and Injection Rate,” Proc. R. Soc. London, Ser. A, to be submitted.
Huang,  N., Szewczyk,  A., and Li,  Y., 1990, “Self-Similar Solution in Problems of Hydraulic Fracturing,” ASME J. Appl. Mech., 57, pp. 877–881.
Batchelor, G. K., 1967, An Introduction to Fluid Mechanics, Cambridge University Press, Cambridge, UK.
Rice, J. R., 1968, “Mathematical Analysis in the Mechanics of Fracture,” Fracture: An Advanced Treatise, Vol II, Academic Press, San Diego, CA, pp. 191–311.
van Dam, D. B., de Pater, C. J., and Romijn, R., 1998, “Analysis of Hydraulic Fracture Closure in Laboratory Experiments, SPE/ISRM 47380. Proc. Of EuRock’98, Rock Mechanics in Petroleum Engineering, SPE, Trondheim, Norway, pp. 365–374.
van Dam, D. B., 1999, “The Influence of Inelastic Rock Behaviour on Hydraulic Fracture Geometry,” Ph.D. thesis, Delft Institute of Technology, Delft University Press, Delft, The Netherlands.
Srivastava, H. M., and Buschman, R. G., 1992, Theory and Applications of Convolution Integral Equations: Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands.

Figures

Grahic Jump Location
Dimensionless net-loading Π along the crack for κ=0, 2.08, 3.33, 4.11. The dashed line corresponds to Π(ξ).
Grahic Jump Location
Dimensionless fluid pressure Π along the crack for κ=0, 2.08, 3.33, 4.11 in semi-log scale. Corresponding values of fluid lag Λ are given by the intersection of a curve with the ξ-axis. The dashed line corresponds to Π(ξ).
Grahic Jump Location
The dimensionless crack opening Ω along the crack in log-log scale for dimensionless toughness varying from κ=0 (Λ≃0.3574) to κ=4.1 (Λ=10−6), (see Table 1). The dashed line corresponds to the asymptotic solution at infinity, Ω(ξ).
Grahic Jump Location
The opening Ω along the crack in near tip region for κ varying from κ=0 (Λ≃0.3574) to κ=4.1 (Λ=10−6), (see Table 1). The dashed line corresponds to Ω(ξ).
Grahic Jump Location
Scaled opening Ω̃ along the crack in log-log scales. Dashed lines correspond to the solution asymptotes and black dots to ξ̃o and ξ̃.
Grahic Jump Location
Scaled pressure Π̃ along the crack in semi-logarithmic scales. Dashed lines correspond to the solution asymptotes and black dots to ξ̃o and ξ̃.
Grahic Jump Location
Semi-infinite fluid driven crack with the lag zone adjacent to the tip
Grahic Jump Location
Bounds ξo and ξ of the regions where solution is dominated by corresponding asymptotes, and lag Λ versus dimensionless toughness κ in log-log scale. (Dashed lines show the large κ asymptotes of ξo(κ),ξ(κ).)
Grahic Jump Location
Dimensionless lag length Λ versus dimensionless toughness κ (solid line), together with the large κ asymptote (dashed line)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In