journal article·2022-09

On the loss of symmetry in toughness dominated hydraulic fractures

Erwan Tanné, Blaise Bourdin, Keita Yoshioka

International Journal of Fracture· Volume 237· Issue 1-2
Publisher page

Abstract

International audience ; Fracking, or hydraulic fracturing, is a ubiquitous technique for generating fracture networks in rocks for enhanced geothermal systems or hydrocarbon extraction from shales. For decades, models, numerical simulation tools, and practical guidelines have been based on the assumption that this process generates networks of self-similar parallel cracks. Yet, some field and laboratory observations show asymmetric crack growth, and material heterogeneity is routinely attributed for it. Here, we show that simultaneous growth of multiple parallel cracks is impossible and that a single crack typically propagates asymmetrically in toughness dominated hydraulic fracturing, in which viscous dissipation of the fluid is negligible. In other words, loss of symmetry is a fundamental feature of hydraulic fracturing in a toughness dominated regime and not necessary the result of material heterogeneities. Our findings challenge the assumptions of symmetrical growth of hydraulic fractures commonly made in practice, and point to yet another instability other than material heterogeneity.
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Research context

OpenAlex topics: Hydraulic Fracturing and Reservoir Analysis · Rock Mechanics and Modeling · Seismic Imaging and Inversion Techniques

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References (42)

Show source-provided references
1. Bažant ZP, Salviato M, Chau VT, Viswanathan H, Zubelewicz A (2014) Why fracking works. J Appl Mech 81(10):101010–1. https://doi.org/10.1115/1.402819210.1115/1.4028192 ↗
2. Bourdin B (2019) mef90/vDef: variational models of defect mechanics. https://github.com/bourdin/mef90
3. Bourdin B, Francfort G, Marigo JJ (2000) Numerical experiments in revisited brittle fracture. J Mech Phys Solids 48(4):797–826. https://doi.org/10.1016/S0022-5096(99)00028-910.1016/S0022-5096(99)00028-9 ↗
4. Bourdin B, Francfort G, Marigo JJ (2008) The variational approach to fracture. J Elasticity 91(1–3):1–148. https://doi.org/10.1007/s10659-007-9107-310.1007/s10659-007-9107-3 ↗
5. Bourdin B, Chukwudozie C, Yoshioka K (2012) A variational approach to the numerical simulation of hydraulic fracturing. In: Proceedings of the 2012 SPE annual technical conference and exhibition, vol. SPE 159154. https://doi.org/10.2118/159154-MS10.2118/159154-MS ↗
6. Bunger A (2013) Analysis of the power input needed to propagate multiple hydraulic fractures. Int J Solids Struct 50(10):1538–1549. https://doi.org/10.1016/j.ijsolstr.2013.01.00410.1016/j.ijsolstr.2013.01.004 ↗
7. Bunger AP, Jeffrey RG, Detournay E (2008) Evolution and morphology of saucer-shaped sills in analogue experiments. In: Structure and emplacement of high-level magmatic systems, pp. 109–120. Geological Society, London. https://doi.org/10.1144/SP302.810.1144/SP302.8 ↗
8. Bunger AP, Gordeliy E, Detournay E (2013) Comparison between laboratory experiments and coupled simulations of saucer-shaped hydraulic fractures in homogeneous brittle-elastic solids. J Mech Phys Solids 61(7):1636–1654. https://doi.org/10.1016/j.jmps.2013.01.00510.1016/j.jmps.2013.01.005 ↗
9. Bunger A, Jeffrey RG, Zhang X (2014) Constraints on simultaneous growth of hydraulic fractures from multiple perforation clusters in horizontal wells. SPE J 19(04):608–620. https://doi.org/10.2118/163860-PA10.2118/163860-PA ↗
10. Castonguay ST, Mear ME, Dean RH, Schmidt JH, et al (2013) Predictions of the growth of multiple interacting hydraulic fractures in three dimensions. In: SPE annual technical conference and exhibition. Soc Pet Eng. https://doi.org/10.2118/166259-MS10.2118/166259-MS ↗
11. Chen X, Zhao J, Li Y, Yan W, Zhang X (2019) Numerical simulation of simultaneous hydraulic fracture growth within a rock layer: implications for stimulation of low-permeability reservoirs. J Geophys Res-Sol Ea 124(12):13227–13249. https://doi.org/10.1029/2019JB01794210.1029/2019JB017942 ↗
12. Chukwudozie C, Bourdin B, Yoshioka K (2019) A variational phase-field model for hydraulic fracturing in porous media. Comput Methods Appl Mech Eng 347:957–982. https://doi.org/10.1016/j.cma.2018.12.03710.1016/j.cma.2018.12.037 ↗
13. Cramer D, Friehauf K, Roberts G, Whittaker J, et al (2019) Integrating DAS, treatment pressure analysis and video-based perforation imaging to evaluate limited entry treatment effectiveness. In: SPE Hydraulic Fracturing Technology Conference and Exhibition. Society of Petroleum Engineers. https://doi.org/10.2118/194334-MS10.2118/194334-MS ↗
14. Dahi-Taleghani A, Olson JE (2011) Numerical modeling of multistranded-hydraulic-fracture propagation: accounting for the interaction between induced and natural fractures. SPE J 16(3):575–581. https://doi.org/10.2118/124884-PA10.2118/124884-PA ↗
15. Dean RH, Schmidt JH (2009) Hydraulic-fracture predictions with a fully coupled geomechanical reservoir simulator. SPE J 14(December):707–714. https://doi.org/10.2118/116470-PA10.2118/116470-PA ↗
16. Detournay E (2016) Mechanics of hydraulic fractures. Ann Rev Fluid Mech 48(1):311–339. https://doi.org/10.1146/annurev-fluid-010814-01473610.1146/annurev-fluid-010814-014736 ↗
17. 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. https://doi.org/10.1017/S002211200300527510.1017/S0022112003005275 ↗
18. Dontsov E, Suarez-Rivera R (2020) Propagation of multiple hydraulic fractures in different regimes. Int J Rock Mech Min 128:104270. https://doi.org/10.1016/j.ijrmms.2020.10427010.1016/j.ijrmms.2020.104270 ↗
19. Fischer T, Hainzl S, Eisner L, Shapiro SA, Le Calvez J (2008) Microseismic signatures of hydraulic fracture growth in sediment formations: observations and modeling. J Geophys Res-Sol Ea 113(2):1–12. https://doi.org/10.1029/2007JB00507010.1029/2007JB005070 ↗
20. Francfort G, Marigo JJ (1998) Revisiting brittle fracture as an energy minimization problem. J Mech Phys Solids 46(8):1319–1342. https://doi.org/10.1016/S0022-5096(98)00034-910.1016/S0022-5096(98)00034-9 ↗
21. Gao H, Rice JR (1987) Somewhat circular tensile cracks. Int J Fract 33(3):155–174. https://doi.org/10.1007/BF0001316810.1007/BF00013168 ↗
22. Gordeliy E, Abbas S, Peirce A (2019) Modeling nonplanar hydraulic fracture propagation using the XFEM: an implicit level-set algorithm and fracture tip asymptotics. Int J Solids Struct 159:135–155. https://doi.org/10.1016/j.ijsolstr.2018.09.02510.1016/j.ijsolstr.2018.09.025 ↗
23. Griffith AA (1921) The phenomena of rupture and flow in solids. Philos Trans R Soc S-A 221:163–198. https://doi.org/10.1098/rsta.1921.000610.1098/rsta.1921.0006 ↗
24. Kresse O, Weng X (2018) Numerical modeling of 3d hydraulic fractures interaction in complex naturally fractured formations. Rock Mech Rock Eng 51(12):3863–3881. https://doi.org/10.1007/s00603-018-1539-510.1007/s00603-018-1539-5 ↗
25. Kresse O, Weng X, Gu H, Wu R (2013) Numerical modeling of hydraulic fractures interaction in complex naturally fractured formations. Rock Mech Rock Eng 46(3):555–568. https://doi.org/10.1007/s00603-012-0359-210.1007/s00603-012-0359-2 ↗
26. Lecampion B, Desroches J (2015) Simultaneous initiation and growth of multiple radial hydraulic fractures from a horizontal wellbore. J Mech Phys Solids 82:235–258. https://doi.org/10.1016/j.jmps.2015.05.01010.1016/j.jmps.2015.05.010 ↗
27. Marigo JJ, Maurini C, Pham K (2016) An overview of the modelling of fracture by gradient damage models. Meccanica 51(12):3107–3128. https://doi.org/10.1007/s11012-016-0538-410.1007/s11012-016-0538-4 ↗
28. McClure MW, Mohsen B, Sogo S, Jian H (2016) Fully coupled hydromechanical simulation of hydraulic fracturing in 3D discrete-fracture networks. SPE J 21(4):1302–1320. https://doi.org/10.2118/173354-PA10.2118/173354-PA ↗
29. Meyer C (2000) Matrix analysis and applied linear algebra. SIAM, Philadelphia10.1137/1.9780898719512 ↗
30. Murakami Y et al (1987) Handbook of stress intensity factors. Pergamon Press, Oxford
31. Pham K, Amor H, Marigo JJ, Maurini C (2011) Gradient damage models and their use to approximate brittle fracture. Int J Damage Mech 20(4):618–652. https://doi.org/10.1177/105678951038685210.1177/1056789510386852 ↗
32. Shauer N, Duarte CA (2019) Improved algorithms for generalized finite element simulations of three-dimensional hydraulic fracture propagation. Int J Numer Anal Met 43(18):2707–2742. https://doi.org/10.1002/nag.297710.1002/nag.2977 ↗
33. Sneddon I, Elliott H (1946) The opening of a Griffith crack under internal pressure. Q Appl Math 4:262. https://doi.org/10.1090/QAM/1716110.1090/QAM/17161 ↗
34. Sneddon I, Lowengrub M (1969) Crack problems in the classical theory of elasticity. Wiley, New York
35. Tanné E, Li T, Bourdin B, Marigo JJ, Maurini C (2018) Crack nucleation in variational phase-field models of brittle fracture. J Mech Phys Solids 110:80–99. https://doi.org/10.1016/j.jmps.2017.09.00610.1016/j.jmps.2017.09.006 ↗
36. Wang HY (2016) Poro-elasto-plastic modeling of complex hydraulic fracture propagation: simultaneous multi-fracturing and producing well interference. Acta Mech 227(2):507–525. https://doi.org/10.1007/s00707-015-1455-710.1007/s00707-015-1455-7 ↗
37. Warpinski N, Teufel L (1987) Influence of geologic discontinuities on hydraulic fracture propagation. J Petrol Technol 39(02):209–220. https://doi.org/10.2118/13224-PA10.2118/13224-PA ↗
38. Weinhaus F, Barker W (1978) On the equilibrium states of interconnected bubbles or balloons. Am J Phys 46(10):978–982. https://doi.org/10.1119/1.1148710.1119/1.11487 ↗
39. Wu K, Olson J, Balhoff MT, Yu W (2016) Numerical analysis for promoting uniform development of simultaneous multiple-fracture propagation in horizontal wells. SPE Prod Oper 32(1):41–50. https://doi.org/10.2118/174869-PA10.2118/174869-PA ↗
40. Yamamoto K, Shimamoto T, Sukemura S (2004) Multiple fracture propagation model for a three-dimensional hydraulic fracturing simulator. Int J Geomech 4(1):46–57. https://doi.org/10.1061/(ASCE)1532-3641(2004)4:1(46)10.1061/(ASCE)1532-3641(2004)4:1(46) ↗
41. Zeng Q, Liu Z, Wang T, Gao Y, Zhuang Z (2017) Stability analysis of the propagation of periodic parallel hydraulic fractures. Int J Fract 208(1–2):191–201. https://doi.org/10.1007/s10704-017-0233-z10.1007/s10704-017-0233-z ↗
42. Zhang X, Jeffrey RG, Thiercelin M (2009) Mechanics of fluid-driven fracture growth in naturally fractured reservoirs with simple network geometries. J Geophys Res-Sol Ea 114:B12. https://doi.org/10.1029/2019JB01794210.1029/2019JB017942 ↗