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A semi-infinite hydraulic fracture with leak-off driven by a power-law fluid

Published online by Cambridge University Press:  20 December 2017

E. V. Dontsov Open the ORCID record for E. V. Dontsov [Opens in a new window]  and
O. Kresse
E. V. Dontsov*
Affiliation:
Department of Civil and Environmental Engineering, University of Houston, Houston, TX 77204, USA
O. Kresse
Affiliation:
Schlumberger, 110 Schlumberger Drive, MD-2, Sugar Land, TX 77478, USA
*
†Email address for correspondence: edontsov@central.uh.edu
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Abstract

This study investigates the problem of a semi-infinite hydraulic fracture that propagates steadily in a permeable formation. The fracturing fluid rheology is assumed to follow a power-law behaviour, while the leak-off is modelled by Carter’s model. A non-singular formulation is employed to effectively analyse the problem and to construct a numerical solution. The problem under consideration features three limiting analytic solutions that are associated with dominance of either toughness, leak-off or viscosity. Transitions between all the limiting cases are analysed and the boundaries of applicability of all these limiting solutions are quantified. These bounds allow us to determine the regions in the parametric space, in which these limiting solutions can be used. The problem of a semi-infinite fracture, which is considered in this study, provides the solution for the tip region of a hydraulic fracture and can be used in hydraulic fracturing simulators to facilitate solving the moving fracture boundary problem. To cater for such applications, for which rapid evaluation of the solution is necessary, the last part of this paper constructs an approximate closed form solution for the problem and evaluates its accuracy against the numerical solution inside the parametric space.

JFM classification

Boundary Layers: Boundary Layers Geophysical and Geological Flows: Geophysical and Geological Flows Non-Newtonian Flows: Non-Newtonian Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 837 , 25 February 2018 , pp. 210 - 229
Copyright
© 2017 Cambridge University Press 

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