Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-17T13:18:13.461Z Has data issue: false hasContentIssue false
  • English
  • Français

Tip region of a hydraulic fracture driven by a laminar-to-turbulent fluid flow

Published online by Cambridge University Press:  24 May 2016

E. V. Dontsov
E. V. Dontsov*
Affiliation:
Department of Civil and Environmental Engineering, University of Houston, Houston, TX 77204, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The focus of this study is to analyse the tip region of a hydraulic fracture, for which a fluid flow inside the crack transitions from the laminar to the turbulent regime away from the tip. To tackle the problem, a phenomenological formula for flow in pipes has been adapted to describe flow in a fracture through the concept of a hydraulic diameter. The selected model is able to capture laminar, turbulent and transition regimes of the flow. The near-tip region of a hydraulic fracture is analysed by focusing on steady propagation of a semi-infinite hydraulic fracture with leak-off, for which the aforementioned phenomenological formula for the fluid flow is utilized. First, the distance from the tip within which a laminar solution applies is estimated. Then, expressions for asymptotic solutions that are associated with fully developed turbulent flow inside the semi-infinite hydraulic fracture are derived. Finally, the laminar zone size and the asymptotic solutions are compared with the numerical solution, where the latter captures all regimes of the fluid flow.

JFM classification

Boundary Layers: Boundary Layers Geophysical and Geological Flows: Geophysical and Geological Flows Turbulent Flows: Turbulent Flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 797 , 25 June 2016 , R2
Check for updates
Copyright
© 2016 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ames, B. C. & Bunger, A. P.2015 Role of turbulent flow in generating short hydraulic fractures with high net pressure in slickwater treatments. In Proceedings SPE Hydraulic Fracturing Technology Conference, Texas, USA, SPE 173373.Google Scholar
Anthonyrajah, M., Mason, D. P. & Fareo, A. G. 2013 Propagation of a pre-existing turbulent fluid fracture. Intl J. Non-Linear Mech. 54, 105–114.CrossRefGoogle Scholar
Benedict, R. P.(Ed.) 1980 Fundamentals of Pipe Flow. Wiley.Google Scholar
Churchill, S. W. 1977 Friction factor equation spans all fluid flow regimes. Chem. Engng 7, 91–92.Google Scholar
Desroches, J., Detournay, E., Lenoach, B., Papanastasiou, P., Pearson, J. R. A., Thiercelin, M. & Cheng, A. H.-D. 1994 The crack tip region in hydraulic fracturing. Proc. R. Soc. Lond. A 447, 39–48.Google Scholar
Dontsov, E. & Peirce, A. 2015 A non-singular integral equation formulation to analyze multiscale behaviour in semi-infinite hydraulic fractures. J. Fluid. Mech. 781, R1.CrossRefGoogle Scholar
Economides, M. J. & Nolte, K. G.(Eds) 2000 Reservoir Stimulation, 3rd edn. Wiley.Google Scholar
Emerman, S. H., Turcotte, D. L. & Spence, D. A. 1986 Transport of magma and hydrothermal solutions by laminar and turbulent fluid fracture. Phys. Earth Planet. Inter. 41, 249–259.CrossRefGoogle Scholar
Garagash, D. I., Detournay, E. & Adachi, J. I. 2011 Multiscale tip asymptotics in hydraulic fracture with leak-off. J. Fluid Mech. 669, 260–297.CrossRefGoogle Scholar
Kresse, O. & Weng, X. 2013 Hydraulic fracturing in formations with permeable natural fractures. In Effective and Sustainable Hydraulic Fracturing (ed. Bunger, A. P., McLennan, J. & Jeffrey, R.), chap. 14, pp. 287–310. Intech.Google Scholar
Lister, J. R. 1990 Buoyancy-driven fluid fracture: the effects of material toughness and of low-viscosity precursors. J. Fluid Mech. 210, 263–280.CrossRefGoogle Scholar
Manning, R. 1891 On the flow of water in open channels and pipes. Trans. Inst. Civil Engrs 20, 161–207.Google Scholar
Moody, L. F. 1944 Friction factors for pipe flow. Trans. ASME 66, 671–684.Google Scholar
Nilson, R. H. 1981 Gas-driven fracture propagation. Trans. ASME J. Appl. Mech. 48, 757–762.CrossRefGoogle Scholar
Peirce, A. & Detournay, E. 2008 An implicit level set method for modeling hydraulically driven fractures. Comput. Meth. Appl. Mech. Engng 197, 2858–2885.CrossRefGoogle Scholar
Spence, D. & Turcotte, D. 1985 Magma-driven propagation of cracks. J. Geophys. Res. 90, 575–580.CrossRefGoogle Scholar
Strickler, A.1981 Contributions to the question of a velocity formula and roughness data for streams, channels and closed pipelines. Rep. T-10. Translated from German by T. Roesgen et al., Laboratory of Hydraulics and Water Resources, California Institute of Technology, Pasadena.Google Scholar
Tsai, V. C. & Rice, J. R. 2010 A model for turbulent hydraulic fracture and application to crack propagation at glacier beds. J. Geophys. Res. 115, F03007.Google Scholar