Propagation of a penny-shape hydraulic fracture in an impermeable rock

Vail Rocks 1999 - 37th U.S. Symposium on Rock Mechanics (USRMS)

Volumn , Issue , 1999, Pages 851-858

  Savitski, Alexei ^a   Detournay, Emmanuel ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EXPANSION; FRACTURE MECHANICS; HYDRAULIC FRACTURING; NEWTONIAN LIQUIDS; POLYNOMIALS; ROCK MECHANICS;

FRACTURE OPENING; INCOMPRESSIBLE NEWTONIAN FLUID; JACOBI POLYNOMIALS; LINEAR ELASTIC FRACTURE MECHANICS; SELF-SIMILAR SOLUTION; SEMI-ANALYTICAL; SERIES EXPANSION; SIMILARITY SOLUTION;

ROCKS;

EID: 85018321773     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (29)

1. H. Abe, L.M. Keer, and T. Mura. Theoretical study of hydraulically fractured penny-shaped cracks in hot, dry rocks. Int. J. Numer. Anal. Methods Geomech., 3:79-96, 1979.
2. H. Abe, T. Mura, and L.M. Keer. Growth rate of a penny-shaped crack in hydraulic fracturing of rocks. J. Geophys. Res., 81:5335-5340, 1976.
3. M. Abramowitz and I.A. Stegun, editors. Handbook of Mathematical Functions. Dover, 1965.
4. S.H. Advani, T.S. Lee, and J.K. Lee. Three dimensional modeling of hydraulic fractures in layered media: Finite element formulations. ASME J. Energy Res. Tech., 112:1-18, 1990.
5. S.H. Advani, J.S. Torok, J.K. Lee, and S. Choudhry. Explicit time-dependent solutions and numerical evaluations for penny-shaped hydraulic fracture models. J. Geophys. Res., 92(B8):8049-3055, 1987.
6. G.I. Barenblatt. The formation of equilibrium cracks during brittle fracture: General ideas and hypotheses: Axially-symmetric cracks. Prikl. Mat. Mech., 23:434-444, 1959.
7. G.I. Barenblatt. The mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics, VII:55-129, 1962.
8. D.T. Barr. Leading-Edge Analysis for Correct Simulaiton of Interface Separation and Hydraulic Fracturing. PhD thesis, MIT, June 1991.
9. G. K. Batchelor. An Introduction to Fluid Mechanics. Cambridge University Press, 1967.
10. R. Carbonell, J. Desroches, and E. Detournay. A comparison between a semi-analytical and a numerical solution of a two-dimensional hydraulic fracture. Int. J. Solids Structures, 1999. in print.
11. R. S. Carbonell and E. Detournay. Self-similar solution of a fluid driven fracture in a zero toughness elastic solid. Proc. Roy. Soc. London, Ser. A, 1999. submitted.
12. R.J. Clifton and A.S. Abou-Sayed. A variational approach to the prediction of the three-dimensional geometry of hydraulic fractures. In SPE/DOE Low Permeability Reservoir Symposium, Denver, 1981.
13. C.J. de Pater, J. Desroches, J. Groenenboom, and L. Weijers. Physical and numerical modeling of hydraulic fracture closure. SPE Production and Facilities, pages 122-127, May 1996.
14. 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. Roy. Soc. London, Ser. A, A447:39-48, 1994.
15. E. Detournay. Fluid and solid singularities at the tip of a fluid-driven fracture. In D. Durban and J.R.A. Pearson, editors, Non-Linear Singularities in Deformation and Flow, pages 27-42, Dordrecht, 1999. Kluwer Academic Publishers.
16. D. Garagash and E. Detournay. Plane strain propagation of a hydraulic fracture: Influence of material toughness, fluid viscosity, and injection rate. Proc. Roy. Soc. London, Ser. A, 1999. to be submitted.
17. D. Garagash and E. Detournay. Similarity solution of a semi-infinite fluid-driven fracture in a linear elastic solid. G R. Acad. Sc. Paris, t. 326(Serie II b):285-292, 1998.
18. J. Geertsma and R. Haafkens. A comparison of the theories for predicting width and extent of vertical hydraulically induced fractures. ASME J. Energy Res. Tech., 101:8-19, 1979.
19. M.K. Kassir and G.C. Sih. Three-dimensional crack problems. In Mechanics of Fracture, Volume 2. Noordhoof International Publishing, Leyden, 1975.
20. S.A. Khristianovic and Y.P. Zheltov. Formation of vertical fractures by means of highly viscous fluids. Proc. 4th World Petroleum Congress, Vol. II, Rome, pages 579-586, 1955.
21. R. P. Nordgren. Propagation of vertical hydraulic fracture. Soc. Pet. Eng. J., 253:306-314, 1972.
22. T. K. Perkins and L. R. Kern. Widths of hydraulic fractures. J. Pet. Tech., 222:937-949, 1961.
23. W.J. Proffer R.H. Nilson and R.E. Duff. Modeling of gas-driven fractures induced by propellant combustion within a borehole. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 22(1):3-19, 1985.
24. J. R. Rice. Mathematical analysis in the mechanics of fracture. In Fracture, an Advanced Treatise, Volume II, chapter 3, pages 191-311. Academic Press, 1968.
25. K.R. Shah, B.J. Carter, and A.R. Ingraffea. Hydraulic fracturing simulation in parallel computing environments. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 34(3/4):474, 1997.
26. I.N. Sneddon. Fourier Transforms. McGraw-Hill Book Company, Inc., 1951.
27. J.L.S. Sousa, B.J. Carter, and A.R. Ingraffea. Numerical simulation of 3D hydraulic fracture using newtonian and power-law fluids. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 30(7):1265-1271, 1993.
28. D. A. Spence and P. Sharp. Self-Similar solution for elastohydrodynamic cavity flow. Proc. Roy. Soc. London, Ser. A, A400:289-313, 1985.
29. Y. Yuan. Simulation of Penny-Shaped Hydraulic Fracturing in Porous Media. PhD thesis, The University of Oklahoma, 1997.