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Multiscale tip asymptotics in hydraulic fracture with leak-off

Published online by Cambridge University Press:  16 February 2011

DMITRY I. GARAGASH ,
EMMANUEL DETOURNAY  and
JOSE I. ADACHI
DMITRY I. GARAGASH*
Affiliation:
Dalhousie University, Department of Civil and Resource Engineering, 1360 Barrington Street, Halifax, Nova Scotia B3J 1Z1, Canada
EMMANUEL DETOURNAY
Affiliation:
University of Minnesota, Department of Civil Engineering, 500 Pillsbury Drive, Minneapolis, MN 55455, USA, and CSIRO Earth Science and Resource Engineering, Technology Park, Kensington, WA 6151, Australia
JOSE I. ADACHI
Affiliation:
Schlumberger DCS, 1325 South Dairy Ashford Road, Houston, TX 77077, USA
*
†Email address for correspondence: garagash@dal.ca
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Abstract

This paper is concerned with an analysis of the near-tip region of a fluid-driven fracture propagating in a permeable saturated rock. The analysis is carried out by considering the stationary problem of a semi-infinite fracture moving at constant speed V. Two basic dissipative processes are taken into account: fracturing of the rock and viscous flow in the fracture, and two fluid balance mechanisms are considered – leak-off and storage of the fracturing fluid in the fracture. It is shown that the solution is characterized by a multiscale singular behaviour at the tip, and that the nature of the dominant singularity depends both on the relative importance of the dissipative processes and on the scale of reference. This solution provides a framework to understand the interaction of representative physical processes near the fracture tip, as well as to track the changing nature of the dominant tip process(es) with the tip velocity and its impact on the global fracture response. Furthermore, it gives a universal scaling of the near-tip processes on the scale of the entire fracture and sets the foundation for developing efficient numerical algorithms relying on accurate modelling of the tip region.

JFM classification

Boundary Layers: Boundary layer structure Geophysical and Geological Flows: Magma and lava flow Low-Reynolds-number flows: Porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 669 , 25 February 2011 , pp. 260 - 297
Copyright
Copyright © Cambridge University Press 2011

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