We present analytical tip region solutions for fracture width and pressure when a power law fluid drives a plane strain fracture in an impermeable linear elastic solid. Our main result is an intermediate asymptotic solution in which the tip region stress is dominated by a singularity which is particular to the hydraulic fracturing problem. Moreover this singularity is weaker than the inverse square root singularity of linear elastic fracture mechanics. We also show how the solution for a semi-infinite crack may be exploited to obtain a useful approximation for the finite case.

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This Issue

08 October 1994

Volume 447Issue 1929

Article Information

DOI:https://doi.org/10.1098/rspa.1994.0127
Published by:Royal Society
Print ISSN:0962-8444
Online ISSN:2053-9177

History:

Manuscript received10/05/1993
Manuscript accepted10/08/1994
Published online01/01/1997
Published in print08/10/1994

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The crack tip region in hydraulic fracturing

Abstract

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This Issue