메뉴 건너뛰기




Volumn 196, Issue 49-52, 2007, Pages 4863-4880

An implicit algorithm for the propagation of a hydraulic fracture with a fluid lag

Author keywords

Fluid driven crack; Hydraulic fracture; Moving boundary; Tip cavity

Indexed keywords

ALGORITHMS; CRACK PROPAGATION; CRACK TIPS; HYDRAULICS; NUMERICAL METHODS; VELOCITY DISTRIBUTION;

EID: 34548761354     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.06.011     Document Type: Article
Times cited : (183)

References (72)
  • 1
  • 2
    • 0026307756 scopus 로고
    • Fluid-mechanical models of crack propagation and their application to magma transport in dykes
    • Lister J.R., and Kerr R.C. Fluid-mechanical models of crack propagation and their application to magma transport in dykes. J. Geophys. Res. (1991) 10049-10077
    • (1991) J. Geophys. Res. , pp. 10049-10077
    • Lister, J.R.1    Kerr, R.C.2
  • 3
    • 0028812985 scopus 로고
    • Propagation of magma-filled cracks
    • Rubin A.M. Propagation of magma-filled cracks. Ann. Rev. Earth Planetary Sci. 23 (1995) 287-336
    • (1995) Ann. Rev. Earth Planetary Sci. , vol.23 , pp. 287-336
    • Rubin, A.M.1
  • 4
    • 0018441467 scopus 로고
    • On the mechanical interaction between a fluid-filled fracture and the earth's surface
    • Pollard D.D., and Hozlhausen G. On the mechanical interaction between a fluid-filled fracture and the earth's surface. Tectonophysics 53 (1979) 27-57
    • (1979) Tectonophysics , vol.53 , pp. 27-57
    • Pollard, D.D.1    Hozlhausen, G.2
  • 5
    • 0034896485 scopus 로고
    • On origin of near-axis volcanism and faulting at fast spreading mid-ocean ridges
    • Fialko Y. On origin of near-axis volcanism and faulting at fast spreading mid-ocean ridges. Earth Planet. Sci. Lett. 190 (1979) 31-39
    • (1979) Earth Planet. Sci. Lett. , vol.190 , pp. 31-39
    • Fialko, Y.1
  • 6
    • 0033687359 scopus 로고    scopus 로고
    • Water pressure in propagating concrete cracks
    • Slowik V., and Saouma V.E. Water pressure in propagating concrete cracks. ASCE J. Struct. Engrg. 126 2 (2000) 235-242
    • (2000) ASCE J. Struct. Engrg. , vol.126 , Issue.2 , pp. 235-242
    • Slowik, V.1    Saouma, V.E.2
  • 7
    • 0038363828 scopus 로고    scopus 로고
    • Direct assessment of structural resistance against pressurized fracture
    • Bolzon G., and Cochetti G. Direct assessment of structural resistance against pressurized fracture. Int. J. Numer. Anal. Methods Geomech. 27 (2003) 353-378
    • (2003) Int. J. Numer. Anal. Methods Geomech. , vol.27 , pp. 353-378
    • Bolzon, G.1    Cochetti, G.2
  • 8
    • 0017534473 scopus 로고
    • The failure of the Teton dam
    • Penman A.D.M. The failure of the Teton dam. Ground Engrg. 10 6 (1977) 18-27
    • (1977) Ground Engrg. , vol.10 , Issue.6 , pp. 18-27
    • Penman, A.D.M.1
  • 9
    • 0029239839 scopus 로고    scopus 로고
    • Remediation of low permeability subsurface formations by fracturing enhancements of soil vapor extraction
    • Frank U., and Barkley N. Remediation of low permeability subsurface formations by fracturing enhancements of soil vapor extraction. J. Hazard. Mater. 40 (2005) 191-201
    • (2005) J. Hazard. Mater. , vol.40 , pp. 191-201
    • Frank, U.1    Barkley, N.2
  • 10
    • 0036606814 scopus 로고    scopus 로고
    • Mechanical analysis of idealized shallow hydraulic fracture
    • Murdoch L.C. Mechanical analysis of idealized shallow hydraulic fracture. J. Geotech. Geoenviron. 128 6 (2002) 488-495
    • (2002) J. Geotech. Geoenviron. , vol.128 , Issue.6 , pp. 488-495
    • Murdoch, L.C.1
  • 11
    • 0036606813 scopus 로고    scopus 로고
    • Forms of hydraulic fractures in shallow fine-grained formations
    • Murdoch L.C., and Slack W.W. Forms of hydraulic fractures in shallow fine-grained formations. J. Geotech. Geoenviron. 128 6 (2002) 479-487
    • (2002) J. Geotech. Geoenviron. , vol.128 , Issue.6 , pp. 479-487
    • Murdoch, L.C.1    Slack, W.W.2
  • 12
    • 0024944119 scopus 로고    scopus 로고
    • A.S. Abou-Sayed, D.E. Andrews, I.M. Buhidma, Evaluation of oily waste injection below the permafrost in Prudhoe Bay field, in: Proceedings of the California Regional Meetings, Bakersfield, CA, Society of Petroleum Engineers, Richardson, TX, 1989, pp. 129-142.
  • 13
    • 79952827863 scopus 로고    scopus 로고
    • A.S. Abou-Sayed, Safe injection pressures for disposing of liquid wastes: a case study for deep well injection (SPE/ISRM-28236), in: Proceedings of the Second SPE/ISRM Rock Mechanics in Petroleum Engineering, Balkema, 1994, pp. 769-776.
  • 14
    • 84877581865 scopus 로고    scopus 로고
    • C. Young. Controlled-foam injection for hard rock excavation, in: Rock Mechanics for Industry, Proceedings of 37th US Rock Mechanics Symposium, Vail, CO, vol. 1, Balkema, Rotterdam, 1999, pp. 115-122.
  • 15
    • 85016786904 scopus 로고    scopus 로고
    • R.G. Jeffrey, K.W. Mills. Hydraulic fracturing applied to inducing longwall coal mine goaf falls, in: Pacific Rocks 2000, Balkema, Rotterdam, 2000, pp. 423-430.
  • 16
    • 85042537893 scopus 로고    scopus 로고
    • A. van As, R.G. Jeffrey, Caving induced by hydraulic fracturing at Northparkes mines, in: Pacific Rocks 2000, Balkema, Rotterdam, 2000, pp. 353-360.
  • 17
    • 0024905592 scopus 로고    scopus 로고
    • J.L. Gidley, S.A. Holditch, D.E. Nierode, R.W. Veatch (Eds.), Recent Advances in Hydraulic Fracturing, SPE Monograph Series, vol. 12, Society of Petroleum Engineers, Richardson, TX, 1989.
  • 19
    • 0003983848 scopus 로고    scopus 로고
    • Economides M.J., and Nolte K.G. (Eds), John Wiley & Sons, Chichester, UK
    • In: Economides M.J., and Nolte K.G. (Eds). Reservoir Stimulation. third ed. (2000), John Wiley & Sons, Chichester, UK
    • (2000) Reservoir Stimulation. third ed.
  • 20
    • 0018298542 scopus 로고    scopus 로고
    • R.J. Clifton, A.S. Abou-Sayed, On the computation of the three-dimensional geometry of hydraulic fractures, in: Proc. SPE Symp. on Low Permeability Gas Reservoirs, Denver, Society of Petroleum Engineers (SPE 7943), Richardson, TX, 1979, pp. 307-313.
  • 21
    • 0024946392 scopus 로고    scopus 로고
    • R.J. Clifton, Three-dimensional fracture-propagation models, in: J.L. Gidley, S.A. Holditch, D.E. Nierode, R.W. Veatch (Eds.), Recent Advances in Hydraulic Fracturing - SPE Monographs, vol. 12, Society of Petroleum Engineers, 1989, pp. 95-108.
  • 22
    • 0034155604 scopus 로고    scopus 로고
    • The tip region of a fluid-driven fracture in an elastic medium
    • Garagash D.I., and Detournay E. The tip region of a fluid-driven fracture in an elastic medium. ASME J. Appl. Mech. 67 (2000) 183-192
    • (2000) ASME J. Appl. Mech. , vol.67 , pp. 183-192
    • Garagash, D.I.1    Detournay, E.2
  • 23
    • 34548718788 scopus 로고    scopus 로고
    • E. Detournay, J.I. Adachi, D.I. Garagash. Asymptotic and intermediate asymptotic behavior near the tip of a fluid-driven fracture propagating in a permeable elastic medium, in: A.V. Dyskin, X. Hu, E. Sahouryeh (Eds.), Structural Integrity and Fracture, Lisse, Swets & Zeitlinger, The Netherlands, 2002, pp. 9-18.
  • 24
    • 27744492501 scopus 로고    scopus 로고
    • Plane-strain propagation of a fluid-driven fracture: small toughness solution
    • Garagash D.I., and Detournay E. Plane-strain propagation of a fluid-driven fracture: small toughness solution. ASME J. Appl. Mech 72 (2005) 916-928
    • (2005) ASME J. Appl. Mech , vol.72 , pp. 916-928
    • Garagash, D.I.1    Detournay, E.2
  • 25
    • 34248223775 scopus 로고    scopus 로고
    • An asymptotic framework for the analysis of hydraulic fractures: the impermeable case
    • Mitchell S.L., Kuske R., and Peirce A.P. An asymptotic framework for the analysis of hydraulic fractures: the impermeable case. ASME J. Appl. Mech. 74 2 (2007) 365-372
    • (2007) ASME J. Appl. Mech. , vol.74 , Issue.2 , pp. 365-372
    • Mitchell, S.L.1    Kuske, R.2    Peirce, A.P.3
  • 26
    • 34548807073 scopus 로고    scopus 로고
    • J.I. Adachi, E. Detournay, Plane-strain propagation of a fluid-driven fracture in a permeable medium, Engrg. Fract. Mech., submitted for publication.
  • 27
    • 34548744085 scopus 로고    scopus 로고
    • M.V. Madyarova, E. Detournay, Fluid-driven penny-shaped fracture in permeable rock, Int. J. Numer. Anal. Methods Geomech., submitted for publication.
  • 28
    • 33645300365 scopus 로고    scopus 로고
    • Localized Jacobian ILU preconditioners for hydraulic fractures
    • Peirce A.P. Localized Jacobian ILU preconditioners for hydraulic fractures. Int. J. Numer. Methods Engrg. 65 12 (2006) 1935-1946
    • (2006) Int. J. Numer. Methods Engrg. , vol.65 , Issue.12 , pp. 1935-1946
    • Peirce, A.P.1
  • 29
    • 34548729766 scopus 로고    scopus 로고
    • J.J. Wang, R.J. Clifton, Numerical modeling of hydraulic fracturing in layered formations with multiple elastic moduli, in: Rock Mechanics Contributions and Challenges, Balkema, Rotterdam, 1990, pp. 303-310.
  • 30
    • 0003223712 scopus 로고    scopus 로고
    • Simulating fully 3D hydraulic fracturing
    • Zaman M., Gioda G., and Booker J. (Eds), John Wiley & Sons, New York
    • Carter B.J., Desroches J., Ingraffea A.R., and Wawrzynek P.A. Simulating fully 3D hydraulic fracturing. In: Zaman M., Gioda G., and Booker J. (Eds). Modeling in Geomechanics (2000), John Wiley & Sons, New York
    • (2000) Modeling in Geomechanics
    • Carter, B.J.1    Desroches, J.2    Ingraffea, A.R.3    Wawrzynek, P.A.4
  • 31
    • 0035979621 scopus 로고    scopus 로고
    • The scaled flexibility matrix method for the efficient solution of boundary value problems in 2D and 3D layered elastic media
    • Peirce A.P., and Siebrits E. The scaled flexibility matrix method for the efficient solution of boundary value problems in 2D and 3D layered elastic media. Comput. Methods Appl. Mech. Engrg. 190 (2001) 5935-5956
    • (2001) Comput. Methods Appl. Mech. Engrg. , vol.190 , pp. 5935-5956
    • Peirce, A.P.1    Siebrits, E.2
  • 32
    • 0037196218 scopus 로고    scopus 로고
    • An efficient multi-layer planar 3D fracture growth algorithm using a fixed mesh approach
    • Siebrits E., and Peirce A.P. An efficient multi-layer planar 3D fracture growth algorithm using a fixed mesh approach. Int. J. Numer. Methods Engrg. 53 (2002) 691-717
    • (2002) Int. J. Numer. Methods Engrg. , vol.53 , pp. 691-717
    • Siebrits, E.1    Peirce, A.P.2
  • 33
    • 0024900778 scopus 로고    scopus 로고
    • G.S. Penny, M.W. Conway, Fluid leakoff, in: J.L. Gidley, S.A. Holditch, D.E. Nierode, R.W. Veatch (Eds.), Recent Advances in Hydraulic Fracturing - SPE Monographs, vol. 12, Society of Petroleum Engineers, Richardson TX, 1989, pp. 147-176 (Chapter 8).
  • 34
    • 0037030044 scopus 로고    scopus 로고
    • Self-similar solution of a plane-strain fracture driven by a power-law fluid
    • Adachi J.I., and Detournay E. Self-similar solution of a plane-strain fracture driven by a power-law fluid. Int. J. Numer. Anal. Methods Geomech. 26 (2002) 579-604
    • (2002) Int. J. Numer. Anal. Methods Geomech. , vol.26 , pp. 579-604
    • Adachi, J.I.1    Detournay, E.2
  • 35
    • 33750991892 scopus 로고    scopus 로고
    • Transient solution for a plane-strain fracture driven by a power-law fluid
    • Garagash D.I. Transient solution for a plane-strain fracture driven by a power-law fluid. Int. J. Numer. Anal. Methods Geomech. 30 14 (2006) 1439-1475
    • (2006) Int. J. Numer. Anal. Methods Geomech. , vol.30 , Issue.14 , pp. 1439-1475
    • Garagash, D.I.1
  • 36
    • 0030663023 scopus 로고    scopus 로고
    • The influence of plasticity in hydraulic fracturing
    • Papanastasiou P. The influence of plasticity in hydraulic fracturing. Int. J. Fract. 84 (1997) 61-97
    • (1997) Int. J. Fract. , vol.84 , pp. 61-97
    • Papanastasiou, P.1
  • 37
    • 0033405802 scopus 로고    scopus 로고
    • The effective fracture toughness in hydraulic fracturing
    • Papanastasiou P. The effective fracture toughness in hydraulic fracturing. Int. J. Fract. 96 (1999) 127-147
    • (1999) Int. J. Fract. , vol.96 , pp. 127-147
    • Papanastasiou, P.1
  • 38
    • 85056805921 scopus 로고    scopus 로고
    • S.A. Khristianovic, Y.P. Zheltov, Formation of vertical fractures by means of highly viscous fluids, in: Proc. 4th World Petroleum Congress, Rome, vol. II, 1955, pp. 579-586.
  • 39
    • 0000310783 scopus 로고
    • On the formation of horizontal cracks in hydraulic fracture of an oil-bearing stratum
    • Barenblatt G.I. On the formation of horizontal cracks in hydraulic fracture of an oil-bearing stratum. Prikl. Mater. Mech. 20 (1956) 475-486
    • (1956) Prikl. Mater. Mech. , vol.20 , pp. 475-486
    • Barenblatt, G.I.1
  • 40
    • 0014618169 scopus 로고
    • A rapid method of predicting width and extent of hydraulic induced fractures
    • SPE 2458
    • Geertsma J., and de Klerk F. A rapid method of predicting width and extent of hydraulic induced fractures. J. Petrol. Tech. 246 (1969) 1571-1581 SPE 2458
    • (1969) J. Petrol. Tech. , vol.246 , pp. 1571-1581
    • Geertsma, J.1    de Klerk, F.2
  • 41
    • 0024933795 scopus 로고    scopus 로고
    • R.G. Jeffrey, The combined effect of fluid lag and fracture toughness on hydraulic fracture propagation, in: Joint Rocky Mountain Regional/Low Permeability Reservoirs Symposium and Exhibition, Denver, CO, March 6-8, 1989, Society of Petroleum Engineers, pp. 269-276.
  • 42
    • 0021437382 scopus 로고
    • Laboratory experiments in fracture propagation
    • Medlin W.L., and Masse L. Laboratory experiments in fracture propagation. Soc. Pet. Engrg. J. (1984) 256-268
    • (1984) Soc. Pet. Engrg. J. , pp. 256-268
    • Medlin, W.L.1    Masse, L.2
  • 43
    • 0025839525 scopus 로고    scopus 로고
    • E. Johnson, M.P. Cleary, Implications of recent laboratory experimental results for hydraulic fractures (SPE 21846), in: Proc. of the Rocky Mountain Regional Meeting and Low-Permeability Reservoirs Symposium, Denver, CO, no. 21846, Society of Petroleum Engineers, Richardson, TX, 1991, pp. 413-428.
  • 44
    • 0031655157 scopus 로고    scopus 로고
    • D.B. van Dam, C.J. de Pater, R. Romijn, Analysis of hydraulic fracture closure in laboratory experiments, in: Proc. EuRock'98 - Rock Mechanics in Petroleum Engineering, Trondheim, Society of Petroleum Engineers (SPE 47380), Richardson TX, 1998, pp. 365-374.
  • 45
    • 22344444861 scopus 로고    scopus 로고
    • Asymptotic solution for a penny-shaped near-surface hydraulic fracture
    • Bunger A.P., and Detournay E. Asymptotic solution for a penny-shaped near-surface hydraulic fracture. Engrg. Fract. Mech. 72 16 (2005) 2468-2486
    • (2005) Engrg. Fract. Mech. , vol.72 , Issue.16 , pp. 2468-2486
    • Bunger, A.P.1    Detournay, E.2
  • 46
    • 0021789239 scopus 로고
    • Measurement of width and pressure in a propagating hydraulic fracture
    • (SPE 11648)
    • Warpinski N.R. Measurement of width and pressure in a propagating hydraulic fracture. SPEJ 25 1 (1985) 46-54 (SPE 11648)
    • (1985) SPEJ , vol.25 , Issue.1 , pp. 46-54
    • Warpinski, N.R.1
  • 47
    • 33746009551 scopus 로고    scopus 로고
    • Propagation of plane-strain hydraulic fracture with a fluid lag: early-time solution
    • Garagash D.I. Propagation of plane-strain hydraulic fracture with a fluid lag: early-time solution. Int. J. Solids Struct. 43 (2006) 5811-5835
    • (2006) Int. J. Solids Struct. , vol.43 , pp. 5811-5835
    • Garagash, D.I.1
  • 48
    • 0022421455 scopus 로고
    • Self-similar solution for elastohydrodynamic cavity flow
    • Spence D.A., and Sharp P.W. Self-similar solution for elastohydrodynamic cavity flow. Proc. Roy. Soc. London Ser. A 400 (1985) 289-313
    • (1985) Proc. Roy. Soc. London Ser. A , vol.400 , pp. 289-313
    • Spence, D.A.1    Sharp, P.W.2
  • 49
    • 0025240136 scopus 로고
    • Buoyancy-driven fluid fracture: the effects of material toughness and of low-viscosity precursors
    • Lister J.R. Buoyancy-driven fluid fracture: the effects of material toughness and of low-viscosity precursors. J. Fluid Mech. 210 (1990) 263-280
    • (1990) J. Fluid Mech. , vol.210 , pp. 263-280
    • Lister, J.R.1
  • 51
    • 34548775776 scopus 로고    scopus 로고
    • E. Detournay, Fluid and solid singularities at the tip of a fluid-driven fracture, in: D. Durban, J.R.A. Pearson (Eds.), Proc. IUTAM Symp. on Non-Linear Singularities in Deformation and Flow, Haifa, Kluwer Academic Publ., Dordrecht, 1999, pp. 27-42.
  • 52
    • 34548772430 scopus 로고    scopus 로고
    • J.I. Adachi, E. Detournay, Plane-strain propagation of a fluid-driven fracture: finite toughness self-similar solution, Int. J. Solids Struct., to be submitted for publication.
  • 54
    • 0142009995 scopus 로고    scopus 로고
    • Cohesive fracture mechanics for a multi-phase porous medium
    • Simoni L., and Secchi S. Cohesive fracture mechanics for a multi-phase porous medium. Engrg. Comput. 20 (2003) 675-698
    • (2003) Engrg. Comput. , vol.20 , pp. 675-698
    • Simoni, L.1    Secchi, S.2
  • 55
    • 27744521353 scopus 로고    scopus 로고
    • On adaptive refinement techniques in multi-field problems including cohesive fracture
    • Schrefler B.A., Secchi S., and Simoni L. On adaptive refinement techniques in multi-field problems including cohesive fracture. Comput. Methods Appl. Mech. Engrg. 195 (2006) 444-461
    • (2006) Comput. Methods Appl. Mech. Engrg. , vol.195 , pp. 444-461
    • Schrefler, B.A.1    Secchi, S.2    Simoni, L.3
  • 57
    • 0002294867 scopus 로고
    • Application of finite-part integrals to the singular equations of crack
    • Ioakimidis N.I. Application of finite-part integrals to the singular equations of crack. Acta Mech. 45 (1982) 31-47
    • (1982) Acta Mech. , vol.45 , pp. 31-47
    • Ioakimidis, N.I.1
  • 60
    • 0003077565 scopus 로고
    • Mathematical analysis in the mechanics of fracture
    • Fracture. Liebowitz H. (Ed), Academic Press, New York, NY (Chapter 3)
    • Rice J.R. Mathematical analysis in the mechanics of fracture. In: Liebowitz H. (Ed). Fracture. An Advanced Treatise vol. II (1968), Academic Press, New York, NY 191-311 (Chapter 3)
    • (1968) An Advanced Treatise , vol.II , pp. 191-311
    • Rice, J.R.1
  • 61
    • 0014852532 scopus 로고
    • A novel principle for the computation of stress intensity factors
    • Bueckner H.F. A novel principle for the computation of stress intensity factors. Z. Angew. Math. Mech. 50 9 (1970) 529-546
    • (1970) Z. Angew. Math. Mech. , vol.50 , Issue.9 , pp. 529-546
    • Bueckner, H.F.1
  • 62
    • 49649142983 scopus 로고
    • Some remarks on elastic crack-tip stress fields
    • Rice J.R. Some remarks on elastic crack-tip stress fields. Int. J. Solids Struct. 8 6 (1972) 751-758
    • (1972) Int. J. Solids Struct. , vol.8 , Issue.6 , pp. 751-758
    • Rice, J.R.1
  • 63
    • 34249757147 scopus 로고
    • On the fundamental energy argument of elastic fracture mechanics
    • Keating R.F., and Sinclair G.B. On the fundamental energy argument of elastic fracture mechanics. Int. J. Fract. 74 (1995) 43-61
    • (1995) Int. J. Fract. , vol.74 , pp. 43-61
    • Keating, R.F.1    Sinclair, G.B.2
  • 64
    • 3242799593 scopus 로고    scopus 로고
    • Propagation regimes of fluid-driven fractures in impermeable rocks
    • Detournay E. Propagation regimes of fluid-driven fractures in impermeable rocks. Int. J. Geomech. 4 1 (2004) 1-11
    • (2004) Int. J. Geomech. , vol.4 , Issue.1 , pp. 1-11
    • Detournay, E.1
  • 65
    • 34548804993 scopus 로고    scopus 로고
    • E. Detournay, D.I. Garagash, Scaling laws for a radial hydraulic fracture propagating in a permeable rock, Proc. Roy. Soc. London, Ser. A, to be submitted for publication.
  • 66
    • 29844440993 scopus 로고    scopus 로고
    • Plane-strain propagation of a fluid-driven fracture during injection and shut-in: asymptotics of large toughness
    • Garagash D.I. Plane-strain propagation of a fluid-driven fracture during injection and shut-in: asymptotics of large toughness. Engrg. Fract. Mech. 73 4 (2006) 456-481
    • (2006) Engrg. Fract. Mech. , vol.73 , Issue.4 , pp. 456-481
    • Garagash, D.I.1
  • 67
    • 34548790756 scopus 로고    scopus 로고
    • S.L. Crouch, A.M. Starfield, Boundary Element Methods in Solid Mechanics, George Allen and Unwin, London, 1983.
  • 68
    • 22744436295 scopus 로고    scopus 로고
    • A dual mesh multigrid preconditioner for the efficient solution of hydraulically driven fracture problems
    • Peirce A.P., and Siebrits E.. A dual mesh multigrid preconditioner for the efficient solution of hydraulically driven fracture problems. Int. J. Numer. Methods Engrg. 63 (2005) 1797-1823
    • (2005) Int. J. Numer. Methods Engrg. , vol.63 , pp. 1797-1823
    • Peirce, A.P.1    Siebrits, E..2
  • 69
    • 34548745836 scopus 로고    scopus 로고
    • A.P. Bunger, Near-surface hydraulic fracture, PhD thesis, University of Minnesota, 2005.
  • 70
    • 0036900316 scopus 로고    scopus 로고
    • Propagation of a fluid-driven penny-shaped fracture in an impermeable rock: asymptotic solutions
    • Savitski A.A., and Detournay E. Propagation of a fluid-driven penny-shaped fracture in an impermeable rock: asymptotic solutions. Int. J. Solids Struct. 39 26 (2002) 6311-6337
    • (2002) Int. J. Solids Struct. , vol.39 , Issue.26 , pp. 6311-6337
    • Savitski, A.A.1    Detournay, E.2
  • 72
    • 34548791819 scopus 로고    scopus 로고
    • B. Lecampion, E. Detournay, Plane strain fluid-driven fracture with lag in an impermeable medium, Technical report, Report to Schlumberger, University of Minnesota, 2003.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.