This paper presents a novel asymptotic framework to obtain detailed solutions describing the propagation of hydraulic fractures in an elastic material. The problem consists of a system of nonlinear integro-differential equations and a free boundary problem. This combination of local and nonlocal effects leads to transitions on a small scale near the crack tip, which control the behavior across the whole fracture profile. These transitions depend upon the dominant physical process(es) and are identified by simultaneously scaling the associated parameters with the distance from the tip. A smooth analytic solution incorporating several physical processes in the crucial tip region can be constructed using this new framework. In order to clarify the exposition of the new methodology, this paper is confined to considering the impermeable case in which only the two physical processes of viscous dissipation and structure energy release compete.
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March 2007
Technical Papers
An Asymptotic Framework for the Analysis of Hydraulic Fractures: The Impermeable Case
S. L. Mitchell,
S. L. Mitchell
Department of Mathematics,
e-mail: sarah@iam.ubc.ca
University of British Columbia
, Vancouver, BC, V6T 1Z2, Canada
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R. Kuske,
R. Kuske
Department of Mathematics,
University of British Columbia
, Vancouver, BC, V6T 1Z2, Canada
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A. P. Peirce
A. P. Peirce
Department of Mathematics,
University of British Columbia
, Vancouver, BC, V6T 1Z2, Canada
Search for other works by this author on:
S. L. Mitchell
Department of Mathematics,
University of British Columbia
, Vancouver, BC, V6T 1Z2, Canadae-mail: sarah@iam.ubc.ca
R. Kuske
Department of Mathematics,
University of British Columbia
, Vancouver, BC, V6T 1Z2, Canada
A. P. Peirce
Department of Mathematics,
University of British Columbia
, Vancouver, BC, V6T 1Z2, CanadaJ. Appl. Mech. Mar 2007, 74(2): 365-372 (8 pages)
Published Online: March 13, 2006
Article history
Received:
October 31, 2005
Revised:
March 13, 2006
Citation
Mitchell, S. L., Kuske, R., and Peirce, A. P. (March 13, 2006). "An Asymptotic Framework for the Analysis of Hydraulic Fractures: The Impermeable Case." ASME. J. Appl. Mech. March 2007; 74(2): 365–372. https://doi.org/10.1115/1.2200653
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