1932
0
  1. Home
  2. A-Z Publications
  3. Annual Review of Fluid Mechanics
  4. Volume 48, 2016
  5. Article

Annual Review of Fluid Mechanics

Volume 48, 2016

Mechanics of Hydraulic Fractures

Abstract

Hydraulic fractures represent a particular class of tensile fractures that propagate in solid media under pre-existing compressive stresses as a result of internal pressurization by an injected viscous fluid. The main application of engineered hydraulic fractures is the stimulation of oil and gas wells to increase production. Several physical processes affect the propagation of these fractures, including the flow of viscous fluid, creation of solid surfaces, and leak-off of fracturing fluid. The interplay and the competition between these processes lead to multiple length scales and timescales in the system, which reveal the shifting influence of the far-field stress, viscous dissipation, fracture energy, and leak-off as the fracture propagates.

Keyword(s): multiscale, penny-shaped fracture, similarity solutions, tip asymptotics
Loading

Article metrics loading...

/content/journals/10.1146/annurev-fluid-010814-014736
2016-01-03
2024-05-09
Loading full text...

Full text loading...

/deliver/fulltext/fluid/48/1/annurev-fluid-010814-014736.html?itemId=/content/journals/10.1146/annurev-fluid-010814-014736&mimeType=html&fmt=ahah

Literature Cited

  1. Abé H, Keer LM, Mura T. 1979. Theoretical study of hydraulically fractured penny-shaped cracks in hot, dry rocks. Int. J. Numer. Anal. Methods Geomech. 3:79–96 [Google Scholar]
  2. Abé H, Mura T, Keer LM. 1976. Growth rate of a penny-shaped crack in hydraulic fracturing of rocks. J. Geophys. Res. Solid Earth 81:5335–40 [Google Scholar]
  3. Abramowitz M, Stegun IA. 1972. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables New York: Dover
  4. Adachi JI. 2001. Fluid-driven fracture in permeable rock PhD Thesis, Univ. Minnesota, Minneapolis
  5. Adachi JI, Detournay E. 2002. Self-similar solution of a plane-strain fracture driven by a power-law fluid. Int. J. Numer. Anal. Methods Geomech. 26:579–604 [Google Scholar]
  6. Adachi JI, Detournay E. 2008. Plane strain propagation of a hydraulic fracture in a permeable rock. Eng. Fract. Mech. 75:4666–94 [Google Scholar]
  7. Adachi JI, Detournay E, Peirce AP. 2010. Analysis of the classical pseudo-3D model for hydraulic fracture with equilibrium height growth across stress barriers. Int. J. Rock Mech. Min. Sci. 47:625–39 [Google Scholar]
  8. Adachi JI, Siebrits E, Peirce AP, Desroches J. 2007. Computer simulation of hydraulic fractures. Int. J. Rock Mech. Min. Sci. 44:739–57 [Google Scholar]
  9. Advani SH, Lee TS, Lee JK. 1990. Three-dimensional modeling of hydraulic fractures in layered media: finite element formulations. ASME J. Energy Res. Technol. 112:1–9 [Google Scholar]
  10. Advani SH, Torok JS, Lee JK, Choudhry S. 1987. Explicit time-dependent solutions and numerical evaluations for penny-shaped hydraulic fracture models. J. Geophys. Res. Solid Earth 92:8049–55 [Google Scholar]
  11. Barenblatt GI. 1956. On the formation of horizontal cracks in hydraulic fracture of an oil-bearing stratum. Prikl. Mat. Mech. 20:475–86 [Google Scholar]
  12. Batchelor GK. 1967. An Introduction to Fluid Dynamics Cambridge, UK: Cambridge Univ. Press
  13. Bunger AP. 2006. A photometry method for measuring the opening of fluid-filled fractures. Meas. Sci. Technol. 17:3237–44 [Google Scholar]
  14. Bunger AP. 2013. Analysis of the power input needed to propagate multiple hydraulic fractures. Int. J. Solids Struct. 50:1538–49 [Google Scholar]
  15. Bunger AP, Cruden AR. 2011. Modeling the growth of laccoliths and large mafic sills: the role of magma body forces. J. Geophys. Res. Solid Earth 116:B02203 [Google Scholar]
  16. Bunger AP, Detournay E. 2005. Asymptotic solution for a penny-shaped near-surface hydraulic fracture. Eng. Fract. Mech. 72:2468–86 [Google Scholar]
  17. Bunger AP, Detournay E. 2007. Early time solution for a penny-shaped hydraulic fracture. J. Eng. Mech. 133:534–40 [Google Scholar]
  18. Bunger AP, Detournay E. 2008. Experimental validation of the tip asymptotics for a fluid-driven crack. J. Mech. Phys. Solids 56:3101–15 [Google Scholar]
  19. Bunger AP, Detournay E, Garagash DI. 2005a. Toughness-dominated hydraulic fracture with leak-off. Int. J. Fract. 134:175–90 [Google Scholar]
  20. Bunger AP, Detournay E, Garagash DI, Peirce AP. 2007. Numerical simulation of hydraulic fracturing in the viscosity-dominated regime. Proc. 2007 SPE Hydraul. Fract. Technol. Conf. SPE 110115. Richardson, TX: Soc. Petrol. Eng.
  21. Bunger AP, Detournay E, Jeffrey RG. 2005b. Crack tip behavior in near-surface fluid-driven fracture experiments. C. R. Méc. 333:299–304 [Google Scholar]
  22. Bunger AP, Gordeliy E, Detournay E. 2013a. Comparison between laboratory experiments and coupled simulations of saucer-shaped hydraulic fractures in homogeneous brittle-elastic solids. J. Mech. Phys. Solids 61:1636–54 [Google Scholar]
  23. Bunger AP, Jeffrey RG, Detournay E. 2005c. Experimental investigation of crack opening asymptotics for fluid-driven fracture. Int. J. Strength Fract. Complex. 3:139–47 [Google Scholar]
  24. Bunger AP, McLennan J, Jeffrey RG. 2013b. Effective and Sustainable Hydraulic Fracturing Rijeka, Croat: InTech
  25. Bunger AP, Zhang X, Jeffrey RG. 2012. Parameters effecting the interaction among closely-spaced hydraulic fractures. Soc. Petrol. Eng. J. 17:292–306 [Google Scholar]
  26. Cameron J, Prud'homme R. 1989. Rheology of fracturing fluids. Recent Advances in Hydraulic Fracturing J Gidley, S Holditch, D Nierode, R Veatch Jr. 177–209 Richardson, TX: Soc. Petrol. Eng. [Google Scholar]
  27. Carbonell RS, Desroches J, Detournay E. 1999. A comparison between a semi-analytical and a numerical solution of a two-dimensional hydraulic fracture. Int. J. Solids Struct. 36:4869–88 [Google Scholar]
  28. Carrier B, Granet S. 2012. Numerical modeling of hydraulic fracture problem in permeable medium using cohesive zone model. Eng. Fract. Mech. 79:312–28 [Google Scholar]
  29. Carter E. 1957. Optimum fluid characteristics for fracture extension. Drilling and Production Practices G Howard, C Fast 261–70 Tulsa, OK: Am. Petrol. Inst. [Google Scholar]
  30. Clifton RJ. 1989. Three-dimensional fracture-propagation models. Recent Advances in Hydraulic Fracturing JL Gidley, SA Holditch, DE Nierode, RW Veatch Jr. 95–108 Richardson, TX: Soc. Petrol. Eng. [Google Scholar]
  31. Clifton RJ, Abou-Sayed AS. 1979. On the computation of the three-dimensional geometry of hydraulic fractures. Proc. 1979 SPE Symp. Low Permeability Gas Reserv. SPE 7943 Richardson TX: Soc. Petrol. Eng. [Google Scholar]
  32. Constien VG, Hawkins GW, Prud'homme RK, Navarrete R. 2000. Performance of fracturing materials. See Economides & Nolte 2000, ch. 8
  33. Crouch SL, Starfield AM. 1983. Boundary Element Methods in Solid Mechanics London: Allen & Unwin
  34. Dahi Taleghani A. 2011. Modeling simultaneous growth of multi-branch hydraulic fractures. Proc. 45th US Rock Mech. Symp. ARMA 11-436 Alexandria, VA: Am. Rock Mech. Assoc. [Google Scholar]
  35. Damjanac B, Detournay C, Cundall PA, Varun. 2013. Three-dimensional numerical model of hydraulic fracturing in fractured rock mass. See Bunger et al. 2013b, ch. 41. doi: 10.5772/56313
  36. Desroches J, Detournay E, Lenoach B, Papanastasiou P, Pearson JRA. et al. 1994. The crack tip region in hydraulic fracturing. Proc. R. Soc. Lond. A 447:39–48 [Google Scholar]
  37. Detournay E, Garagash DI. 2003. The near-tip region of a fluid-driven fracture propagating in a permeable elastic solid. J. Fluid Mech. 494:1–32 [Google Scholar]
  38. Detournay E, Peirce AP. 2014. On the moving boundary conditions for a hydraulic fracture. Int. J. Eng. Sci. 84:147–55 [Google Scholar]
  39. Detournay E, Peirce AP, Bunger AP. 2007. Viscosity-dominated hydraulic fractures. Rock Mechanics: Meeting Society's Challenges and Demands E Eberhardt, D Stead, T Morrison 1649–56 London: Taylor & Francis [Google Scholar]
  40. Dontsov EV, Peirce AP. 2014. Slurry flow, gravitational settling and a proppant transport model for hydraulic fractures. J. Fluid Mech. 760:567–90 [Google Scholar]
  41. Economides MJ, Nolte KG. 2000. Reservoir Stimulation New York: Wiley, 3rd ed..
  42. Emerman SH, Turcotte DL, Spence DA. 1986. Transport of magma and hydrothermal solutions by laminar and turbulent fluid fracture. Phys. Earth Planet. Interior 36:276–84 [Google Scholar]
  43. Garagash DI. 2000. Hydraulic fracture propagation in elastic rock with large toughness. Rock Around the Rim: Proc. 4th N. Am. Rock Mech. Symp. J Girard, M Liebman, C Breeds, T Doe 221–28 Rotterdam: Balkema [Google Scholar]
  44. Garagash DI. 2006a. Plane-strain propagation of a fluid-driven fracture during injection and shut-in: asymptotics of large toughness. Eng. Fract. Mech. 73:456–81 [Google Scholar]
  45. Garagash DI. 2006b. Propagation of plane-strain hydraulic fracture with a fluid lag: early-time solution. Int. J. Solids Struct. 43:5811–35 [Google Scholar]
  46. Garagash DI. 2006c. Transient solution for a plane-strain fracture driven by a power-law fluid. Int. J. Numer. Anal. Methods Geomech. 30:1439–75 [Google Scholar]
  47. Garagash DI, Detournay E. 2000. The tip region of a fluid-driven fracture in an elastic medium. J. Appl. Mech. 67:183–92 [Google Scholar]
  48. Garagash DI, Detournay E. 2005. Plane-strain propagation of a fluid-driven fracture: small toughness solution. J. Appl. Mech. 72:916–28 [Google Scholar]
  49. Garagash DI, Detournay E, Adachi JI. 2011. Multiscale tip asymptotics in hydraulic fracture with leak-off. J. Fluid Mech. 669:260–97 [Google Scholar]
  50. Geertsma J, de Klerk F. 1969. A rapid method of predicting width and extent of hydraulic induced fractures. J. Petrol. Technol. 21:1571–81 [Google Scholar]
  51. Gordeliy E, Detournay E. 2011a. Displacement discontinuity method for modeling axisymmetric cracks in an elastic half-space. Int. J. Solids Struct. 48:2614–29 [Google Scholar]
  52. Gordeliy E, Detournay E. 2011b. A fixed grid algorithm for simulating the propagation of a shallow hydraulic fracture with a fluid lag. Int. J. Numer. Anal. Methods Geomech. 35:602–29 [Google Scholar]
  53. Gordeliy E, Peirce A. 2013. Coupling schemes for modeling hydraulic fracture propagation using the XFEM. Comput. Methods Appl. Mech. Eng. 253:305–22 [Google Scholar]
  54. Gordeliy E, Peirce A. 2015. Enrichment strategies and convergence properties of the XFEM for hydraulic fracture problems. Comput. Methods Appl. Mech. Eng. 283:474–502 [Google Scholar]
  55. Hills DA, Kelly PA, Dai DN, Korsunsky AM. 1996. Solution of Crack Problems: The Distributed Dislocation Technique Dordrecht: Kluwer Acad.
  56. Hu J, Garagash DI. 2010. Plane-strain propagation of a fluid-driven crack in a permeable rock with fracture toughness. J. Eng. Mech. 136:1152–66 [Google Scholar]
  57. Irwin GR. 1957. Analysis of stresses and strains near the end of a crack traversing a plate. J. Appl. Mech. 29:361–64 [Google Scholar]
  58. Jeffrey RG, Bunger AP. 2007. A detailed comparison of experimental and numerical data on hydraulic fracture height growth through stress contrasts. Proc. 2007 SPE Hydraul. Fract. Technol. Conf. SPE 106030 Richardson, TX: Soc. Petrol. Eng. [Google Scholar]
  59. Jeffrey RG, Bunger AP, Lecampion B, Zhang X, Chen ZR, van As A, Allison DP. et al. 2009a. Measuring hydraulic fracture growth in naturally fractured rock. Proc. SPE Annu. Tech. Conf. Exhib. SPE124919 Richardson, TX: Soc. Petrol. Eng. [Google Scholar]
  60. Jeffrey RG, Chen Z, Mills K, Pegg S. 2013. Monitoring and measuring hydraulic fracturing growth during preconditioning of a roof rock over a coal longwall panel. See Bunger et al. 2013b, ch. 45. doi: 10.5772/56325
  61. Jeffrey RG, Zhang X, Thiercelin M. 2009b. Hydraulic fracture offsetting in naturally fractured reservoirs: quantifying a long-recognized process. Proc. 2009 SPE Hydraul. Fract. Technol. Conf. SPE 119351 Richardson, TX: Soc. Petrol. Eng. [Google Scholar]
  62. Kanninen MF, Popelar CH. 1985. Advanced Fracture Mechanics New York: Oxford Univ. Press
  63. Khristianovic SA, Zheltov YP. 1955. Formation of vertical fractures by means of highly viscous fluids. Proc. 4th World Petrol. Congr., Rome II579–86 London: World Petroleum Council [Google Scholar]
  64. Kovalyshen Y, Detournay E. 2013. Fluid-driven fracture in a poroelastic rock. See Bunger et al. 2013b, ch. 29. doi: 10.5772/56460
  65. Kresse O, Weng X, Wu R, Gu H. 2012. Numerical modeling of hydraulic fractures interaction in complex naturally fractured formations. Proc. 46th US Rock Mech./Geomech. Symp. ARMA-292 Washington, DC: Am. Rock Mech. Assoc. [Google Scholar]
  66. Lecampion B, Desroches J. 2015. Simultaneous initiation and growth of multiple radial hydraulic fractures from a horizontal wellbore. J. Mech. Phys. Solids 82:235–58 [Google Scholar]
  67. Lecampion B, Garagash DI. 2014. Confined flow of suspensions modelled by a frictional rheology. J. Fluid Mech. 759:197–235 [Google Scholar]
  68. Lecampion B, Peirce A, Detournay E, Zhang X, Chen Z. et al. 2013. The impact of the near-tip logic on the accuracy and convergence rate of hydraulic fracture simulators compared to reference solutions. See Bunger et al. 2013b, ch. 43. doi: 10.5772/56212
  69. Lenoach B. 1995. The crack tip solution for hydraulic fracturing in a permeable solid. J. Mech. Phys. Solids 43:1025–43 [Google Scholar]
  70. Lhomme T, Detournay E, Jeffrey RG. 2005. Effects of fluid compressibility and borehole radius on the propagation of a fluid-driven fracture. Int. J. Strength Fract. Complex. 3:149–62 [Google Scholar]
  71. Lister JR. 1990. Buoyancy-driven fluid fracture: the effects of material toughness and of low-viscosity precursors. J. Fluid Mech. 210:263–80 [Google Scholar]
  72. Lister JR, Kerr RC. 1991. Fluid-mechanical models of crack propagation and their application to magma transport in dykes. J. Geophys. Res. Solid Earth 96:10049–77 [Google Scholar]
  73. Madyarova M. 2004. Propagation of a penny-shaped hydraulic fracture in elastic rock MSc Thesis, Univ. Minnesota, Minneapolis
  74. Medlin WL, Masse L. 1984. Laboratory experiments in fracture propagation. Soc. Petrol. Eng. J. 24:256–68 [Google Scholar]
  75. Mendelsohn D. 1984. A review of hydraulic fracture modeling—part I: general concepts, 2D models, motivation for 3D modeling. ASME J. Energy Res. Technol. 106:369–76 [Google Scholar]
  76. Mikelić M, Wheeler MF, Wick T. 2015. A phase-field method for propagating fluid-filled fractures coupled to a surrounding porous medium. SIAM Multiscale Model. Simul. 13:367–98 [Google Scholar]
  77. Murdoch LC. 2002. Mechanical analysis of idealized shallow hydraulic fracture. J. Geotech. Geoenviron. 128:488–95 [Google Scholar]
  78. Nilson RH. 1986. An integral method for predicting hydraulic fracture propagation driven by gases or liquids. Int. J. Numer. Anal. Methods Geomech. 10:191–211 [Google Scholar]
  79. Nilson RH, Griffiths SK. 1983. Numerical analysis of hydraulically-driven fractures. Comput. Methods Appl. Mech. Eng. 36:359–70 [Google Scholar]
  80. Olson JE, Dahi Taleghani A. 2009. Modeling simultaneous growth of multiple hydraulic fractures and their interaction with natural fractures. Proc. 2009 SPE Hydraul. Fract. Technol. Conf. SPE 119739 Richardson, TX: Soc. Petrol. Eng. [Google Scholar]
  81. Osher S, Sethian JA. 1988. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79:12–49 [Google Scholar]
  82. Peirce AP. 2010. A Hermite cubic collocation scheme for plane strain hydraulic fractures. Comput. Methods Appl. Mech. Eng. 199:1949–62 [Google Scholar]
  83. Peirce AP. 2015. Modeling multi-scale processes in hydraulic fracture propagation using the implicit level set algorithm. Comput. Methods Appl. Mech. Eng. 283:881–908 [Google Scholar]
  84. Peirce AP, Detournay E. 2008. An implicit level set method for modeling hydraulically driven fractures. Comput. Methods Appl. Mech. Eng. 197:2858–85 [Google Scholar]
  85. Pollard DD, Hozlhausen G. 1979. On the mechanical interaction between a fluid-filled fracture and the Earth's surface. Tectonophysics 53:27–57 [Google Scholar]
  86. Rice JR. 1968. Mathematical analysis in the mechanics of fracture. Fracture: An Advanced Treatise H Liebowitz 191–311 New York: Academic [Google Scholar]
  87. Rice JR. 1972. Some remarks on elastic crack-tip stress fields. Int. J. Solids Struct. 8:751–58 [Google Scholar]
  88. Roper SM, Lister JR. 2005. Buoyancy-driven crack propagation from an over-pressured source. J. Fluid Mech. 536:79–98 [Google Scholar]
  89. Roper SM, Lister JR. 2007. Buoyancy-driven crack propagation: the limit of large fracture toughness. J. Fluid Mech. 580:359–80 [Google Scholar]
  90. Rubin AM. 1995. Propagation of magma-filled cracks. Annu. Rev. Earth Planet. Sci. 23:287–336 [Google Scholar]
  91. Sarris E, Papanastasiou P. 2012. Modeling of hydraulic fracturing in a poroelastic cohesive formation. Int. J. Geomech. 12:160–67 [Google Scholar]
  92. Savitski A, Detournay E. 2002. Propagation of a fluid-driven penny-shaped fracture in an impermeable rock: asymptotic solutions. Int. J. Solids Struct. 39:6311–37 [Google Scholar]
  93. Sethian JA. 1999. Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science Cambridge, UK: Cambridge Univ. Press
  94. Settari A. 1985. A new general model of fluid loss in hydraulic fracturing. Soc. Petrol. Eng. J. 25:491–501 [Google Scholar]
  95. Settari A, Cleary MP. 1986. Development and testing of a pseudo-three-dimensional model of hydraulic fracture geometry. SPE Product. Eng. 1:449–66 [Google Scholar]
  96. Shah KR, Carter BJ, Ingraffea AR. 1997. Hydraulic fracturing simulation in parallel computing environments. Int. J. Rock Mech. Min. Sci. 34:474 [Google Scholar]
  97. Sneddon IN. 1946. The distribution of stress in the neighbourhood of a crack in an elastic solid. Proc. R. Soc. Lond. A 187:229–60 [Google Scholar]
  98. Sousa JLS, Carter BJ, Ingraffea AR. 1993. Numerical simulation of 3D hydraulic fracture using Newtonian and power-law fluids. Int. J. Rock Mech. Min. Sci. 30:1265–71 [Google Scholar]
  99. Spence DA, Sharp PW. 1985. Self-similar solution for elastohydrodynamic cavity flow. Proc. R. Soc. Lond. A 400:289–313 [Google Scholar]
  100. Spence DA, Sharp PW, Turcotte DL. 1987. Buoyancy-driven crack propagation: a mechanism for magma migration. J. Fluid Mech. 174:135–53 [Google Scholar]
  101. Tsai VC, Rice JR. 2010. A model for turbulent hydraulic fracture and application to crack propagation at glacier beds. J. Geophys. Res. 115:F03007 [Google Scholar]
  102. van As A, Jeffrey RG. 2002. Hydraulic fracture growth in naturally fractured rock: mine through mapping and analysis. Mining and Tunn. Innov. Oppor.: Proc. 5th N. Am. Rock Mech. Symp. 17th Tunn. Assoc. Can. Conf.: NARMS-TAC 2002 R Hammah, W Bawden, J Curran, M Telesnicki 1461–69 Toronto: Univ. Toronto Press [Google Scholar]
  103. van Dam DB, de Pater CJ, Romijn R. 1999. Reopening of hydraulic fractures in laboratory experiments. Proc. 9th Int. Congr. Rock Mech. 2791–94 Rotterdam: Balkema [Google Scholar]
  104. Vandamme L, Curran JH. 1989. A three-dimensional hydraulic fracturing simulator. Int. J. Numer. Methods Eng. 28:909–27 [Google Scholar]
  105. Voller VR. 2009. Basic Control Volume Finite Element Methods for Fluids and Solids Singapore: World Sci.
  106. Warpinski NR, Teufel LW. 1987. Influence of geologic discontinuities on hydraulic fracture propagation. J. Petrol. Technol. 39:209–20 [Google Scholar]
  107. Weng X. 2015. Modeling of complex hydraulic fractures in naturally fractured formation. J. Unconv. Oil Gas Resour. 9:114–35 [Google Scholar]
  108. Williams ML. 1952. Stress singularities resulting from various boundary conditions in angular corners of plates in extension. J. Appl. Mech. 19:526–28 [Google Scholar]
  109. Zhang X, Detournay E, Jeffrey RG. 2002. Propagation of a penny-shaped hydraulic fracture parallel to the free-surface of an elastic half-space. Int. J. Fract. 115:125–58 [Google Scholar]
  110. Zhang X, Jeffrey RG. 2008. Reinitiation or termination of fluid-driven fractures at frictional bedding interfaces. J. Geophys. Res. 113:B08416 [Google Scholar]
  111. Zhang X, Jeffrey RG, Thiercelin M. 2007. Deflection and propagation of fluid-driven fractures at frictional bedding interfaces: a numerical investigation. J. Struct. Geol. 29:396–410 [Google Scholar]
/content/journals/10.1146/annurev-fluid-010814-014736
Loading
Mechanics of Hydraulic Fractures
Annual Review of Fluid Mechanics 48, 311 (2016); https://doi.org/10.1146/annurev-fluid-010814-014736
/content/journals/10.1146/annurev-fluid-010814-014736
/content/journals/10.1146/annurev-fluid-010814-014736
Loading

Data & Media loading...

  • Article Type: Review Article

Most Cited Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error