An approximate solution for toughness-dominated near-surface hydraulic fractures
Source abstract
Abstract
Asymptotic solutions for fracture opening, volume and specific surface energy for small and large fracture radii are presented from the literature. By comparison to numerical simulation of static circular fractures subject to constant and uniform internal pressures, it is found that a good approximation for fracture opening, for intermediate fracture radii, is obtained from a power mean (with exponent 1/2) of the small and large fracture radii limiting cases. The power mean equation for fracture opening is used to derive corresponding equations for fracture volume, specific surface energy and mode I and II stress intensities. These are then combined to form an approximate solution to describe the propagation of circular toughness-dominated near-surface hydraulic fractures, suitable for small, large and intermediate fracture radii. The approximate solution is shown to closely approximate results from equivalent numerical simulation.
Source: expertdata · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Hydraulic Fracturing and Reservoir Analysis · Drilling and Well Engineering · Rock Mechanics and Modeling
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (25)
Show source-provided references
1. Broek D (1997) Elementary engineering fracture mechanics. Kluwer, Dordrecht
2. Bunger AP (2005) Near-surface hydraulic fracture. PhD thesis, University of Minnesota
3. Bunger AP, Detournay E (2005) Asymptotic solution for a penny-shaped near-surface hydraulic fracture. Eng Fract Mech 72: 2468–2486. doi: 10.1016/j.engfracmech.2005.03.00510.1016/j.engfracmech.2005.03.005 ↗
4. Bunger AP, Jeffery RG, Detournay E (2004) Toughness-dominated near-surface hydraulic fracture experiments. In: Yale DP, ASA Willson SM (eds) Proceedings of 6th North American rock mechanics symposium, Houston. ARMA, Paper No. 468
5. Detournay E (2004) Propagation regimes of fluid-driven fractures in impermeable rocks. Int J Geomech 4: 35–45. doi: 10.1061/(ASCE)1532-3641(2004)4:1(35)10.1061/(ASCE)1532-3641(2004)4:1(35) ↗
6. Dyskin A, Germanovich L, Ustinov K (2000) Asymptotic analysis of crack interaction with free boundary. Int J Solids Struct 37: 857–88610.1016/S0020-7683(99)00063-3 ↗
7. Galland O, Cobbold PR, de Bremond d’Ars J, Hallot E (2007) Rise and emplacement of magma during horizontal shortening of the brittle crust: insights from experimental modeling. J Geophys Res 112: B06402. doi: 10.1029/2006JB00460410.1029/2006JB004604 ↗
8. Hibbitt, Karlsson, Sorensen, Inc (2004) ABAQUS/standard users manual, v. 6.5. Pawtucket, Rhode Island
9. Hutchinson JW, Suo Z (1992) Mixed mode cracking in layered materials. Adv Appl Mech 29: 63–19110.1016/S0065-2156(08)70164-9 ↗
10. Labuz JF, Riedel JJ, Dai ST (2006) Shear fracture in sandstone under plane-strain compression. Eng Frac Mech 73: 820–828. doi: 10.1016/j.engfracmech.2004.11.00710.1016/j.engfracmech.2004.11.007 ↗
11. Mathias SA, Van Reeuwijk M (2009) Hydraulic fracture propagation with 3-D leak-off. Transp Porous Media 80: 499–518. doi: 10.1007/s11242-009-9375-410.1007/s11242-009-9375-4 ↗
12. Mathias SA, Tsang C, Van Reeuwijk M (2010) Investigation of hydromechanical processes during cyclic extraction recovery testing of a deformable rock fracture. Int J Rock Mech Min Sci 47: 517–522. doi: 10.1016/j.ijrmms.2009.12.00810.1016/j.ijrmms.2009.12.008 ↗
13. Murdoch L (2002) Mechanical analysis of idealized shallow hydraulic fracture. J Geotech Geoenviron Eng 128: 488. doi: 10.1061/(ASCE)1090-0241(2002)128:6(488)10.1061/(ASCE)1090-0241(2002)128:6(488) ↗
14. Murdoch L, Slack W (2002) Forms of hydraulic fractures in shallow fine-grained formations. J Geotech Geoenviron Eng 128: 479. doi: 10.1061/(ASCE)1090-0241(2002)128:6(479)10.1061/(ASCE)1090-0241(2002)128:6(479) ↗
15. Murdoch LC, Germanovich LN (2006) Analysis of a deformable fracture in permeable material. Int J Numer Anal Meth Geomech 30: 529–561. doi: 10.1002/nag.49210.1002/nag.492 ↗
16. Paynter RJH, Hills DA, Sackfield A (2006) The penny crack beneath the surface of a half-space: with application to the blister test. Int J Fract 142: 173–182. doi: 10.1007/s10704-006-9042-510.1007/s10704-006-9042-5 ↗
17. Perkins TK, Kern LR (1961) Widths of hydraulic fractures. J Pet Technol 222: 937–94910.2118/89-PA ↗
18. Polteau P, Mazzini A, Galland O, Planke S, Malthe-Sorenssen A (2008) Saucer-shaped intrusions: occurrences, emplacement and implications. Earth Plan Sci Lett 266: 195–204. doi: 10.1016/j.epsl.2007.11.01510.1016/j.epsl.2007.11.015 ↗
19. Rice JR (1968) A path independent integral and the approximate analysis of strain concentrations by notches and cracks. J Appl Mech 35: 379–38610.1115/1.3601206 ↗
20. Savitski A, Detournay E (2002) Propagation of a penny-shaped fluid-driven fracture in an impermeable rock: asymptotic solutions. Int J Solids Struct 39(26): 6311–633710.1016/S0020-7683(02)00492-4 ↗
21. Sneddon I (1946) The distribution of stress in the neighbourhood of a crack in an elastic solid. Philos T Roy Soc A 187(1009): 229–260. doi: 10.1098/rspa.1946.0077
22. Williams J (1984) Fracture mechanics of polymers. Halsted Press, New York
23. Zhang X, Detournay E, Jeffrey RG (2002) Propagation of a penny-shaped hydraulic fracture parallel to the free-surface on an elastic half-space. Int J Fract 115: 125–158. doi: 10.1023/A:101634590631510.1023/A:1016345906315 ↗
24. Zhang X, Detournay E, Jeffrey RG (2005) Propagation of a hydraulic fracture parallel to a free surface. Int J Numer Anal Meth Geomech 29: 1317–1340. doi: 10.1002/nag.46110.1002/nag.461 ↗
25. Zlatin AN, Khrapkov AA (1986) A semi-infinite crack parallel to the boundary of the elastic half-plane. Sov Phys-Doklady 31(12): 1009–1010