Plane-strain propagation of a fluid-driven fracture: Small toughness solution

Journal of Applied Mechanics, Transactions ASME

Volumn 72, Issue 6, 2005, Pages 916-928

  Garagash, Dmitry I ^a   Detournay, Emmanuel ^b  

^a Clarkson University   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

IMPERMEABLE ELASTIC SOLIDS; VICINITY; ZERO-TOUGHNESS SOLUTION;

BOUNDARY LAYERS; ELASTICITY; HYDRAULIC FRACTURING; HYDROCARBONS; ROCKS; STRAIN; VISCOSITY OF LIQUIDS; WAVE PROPAGATION;

FRACTURE TOUGHNESS;

EID: 27744492501     PISSN: 00218936     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2047596     Document Type: Article

References (29)

1. Economides, M. J., and Nolte, K. G., eds., 2000, Reservoir Stimulation, 3rd ed., Wiley, Chichester, UK.
2. Spence, D., and Turcotte, D., 1985, "Magma-Driven Propagation Crack," J. Geophys. Res., 90, pp. 575-580.
3. Jeffrey, R. G., and Mills, K. W., 2000, "Hydraulic Fracturing Applied to Inducing Longwall Coal Mine Goaf Falls," Pacific Rocks 2000: Proceedings of the 4th American Rock Mechanics Symposium, J. Girard, M. Liebman, C. Breeds, and T. Doe, eds., Balkema, Rotterdam, pp. 423-430.
4. Murdoch, L. C., 2002, "Mechanical Analysis of Idealized Shallow Hydraulic Fracture," J. Geotech. Geoenviron. Eng., 128(6), pp. 488-495.
5. Khristianovic, S., and Zheltov, Y., 1955, "Formation of Vertical Fractures by Means of Highly Viscous Fluids," Proc. 4th World Petroleum Congress, Rome, II, pp. 579-586.
6. Spence, D. A., and Sharp, P. W., 1985, "Self-Similar Solution for Elastohydro-dynamic Cavity Flow," Proc. R. Soc. London, Ser. A, 400, pp. 289-313.
7. 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.
8. 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.
9. Garagash, D. I., and Detournay, E., 2000, "The Tip Region of a Fluid-Driven Fracture in an Elastic Medium," ASME J. Appl. Mech., 67, pp. 183-192.
10. Detournay, E., and Garagash, D., 2003, "The Tip Region of a Fluid-Driven Fracture in a Permeable Elastic Solid," J. Fluid Mech., 494, pp. 1-32.
11. Batchelor, G. K., 1967, An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge UK.
12. Geertsma, J., and de Klerk, F., 1969, "A Rapid Method of Predicting Width and Extent of Hydraulic Induced Fractures," JPT, 246, pp. 1571-1581.
13. Nilson, R., 1981, "Gas Driven Fracture Propagation," ASME J. Appl. Mech., 48, pp. 757-762.
14. Nilson, R., 1988, "Similarity Solutions for Wedge-Shaped Hydraulic Fracture Driven into a Permeable Medium by a Constant Inlet Pressure," Int. J. Numer. Analyt. Meth. Geomech., 12, pp. 477-495.
15. Huang, N., Szewczyk, A., and Li, Y., 1990, "Self-Similar Solution in Problems of Hydraulic Fracturing," ASME J. Appl. Mech., 57, pp. 877-881.
16. 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, pp. 579-604.
17. Garagash, D. I., 2005, "Transient Solution for a Plane-Strain Fracture Driven by a Power-Law Fluid," Int. J. Numer. Analyt. Meth. Geomech., (to be published).
18. Detournay, E., 1999, "Fluid and Solid Singularities at the Tip of a Fluid-Driven Fracture," Proc. IUTAM Symp. on Non-Linear Singularities in Deformation and Flow, D. Durban and J. Pearson, eds., Haifa, Kluwer, Dordrecht, pp. 27-42.
19. Detournay, E., 2004, "Propagation Regimes of Fluid-Driven Fractures in Impermeable Rocks," Int. J. Geomech., 4(1), pp. 1-11.
20. Adachi, J. I., 2001, "Fluid-Driven Fracture in Permeable Rock," PhD thesis, University of Minnesota.
21. Garagash, D. I., 2000, "Hydraulic Fracture Propagation in Elastic Rock With Large Toughness," Pacific Rocks 2000 - Proc. 4th North American Rock Mechanics Symp., J. Girard, M. Liebman, C. Breeds, and T. Doe, eds., Balkema, Rotterdam, pp. 221-228.
22. Garagash, D. I., 2004, "Plane Strain Propagation of a Hydraulic Fracture During Injection and Shut-In: Asymptotics of Large Toughness," Eng. Fract. Mech., (to be published).
23. Carbonell, R., Desroches, J., and Detournay, E., 1999, "A Comparison Between a Semi-Analytical and a Numerical Solution of a Two-Dimensional Hydraulic Fracture," Int. J. Solids Struct., 36(31-32), pp. 4869-4888.
24. Rice, J. R., 1968, "Mathematical Analysis in the Mechanics of Fracture," Fracture, an Advanced Treatise, H. Liebowitz, ed., Academic, New York, Chap. 3, pp. 191-311.
25. Garagash, D. I., 2005, "Propagation of a Plane-Strain Fluid-Driven Fracture With a Fluid Lag: Early-Time Solution," Int. J. Solids Struct., (to be published).
26. Abramowitz, M., and Stegun, I. A., eds., 1965, Handbook of Mathematical Functions, Dover, New York.
27. Kevorkian, J., and Cole, J., 1996, Multiple Scale and Singular Perturbation Methods, Springer, New York, NY.
28. Garagash, D. I., 2004, "Relevance of Fluid Lag, Toughness, and Leak-Off for Hydraulic Fracture Propagation," unpublished.
29. Savitski, A., and Detournay, E., 2002, "Propagation of a Fluid-Driven Penny-Shaped Fracture in an Impermeable Rock: Asymptotic Solutions," Int. J. Solids Struct., 39(26), pp. 6311-6337.