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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]
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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
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Copyright
© 2016 Cambridge University Press 

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