Multiscale tip asymptotics for a deflating hydraulic fracture with leak-off

Anthony Peirce, Emmanuel Detournay

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


This paper deals with the construction of the tip asymptotes for a hydraulic fracture deflating in a permeable elastic medium. Specifically, the paper describes the changing nature of the asymptotic fields during the arrest and recession phases following propagation of the fracture after fluid injection has ended. It shows that as the fracture deflates in the arrest phase, the region of dominance of the linear elastic fracture mechanics tip asymptote of the fracture aperture with distance from the front shrinks to the benefit of an intermediate asymptote. Hence only the velocity-independent asymptote is left at the arrest-recession transition. Furthermore, with increasing receding velocity of the front, a linear asymptote develops progressively at the fracture tip, with again becoming an intermediate asymptote. These universal multiscale asymptotes for the arrest and recession phases are key to determining, in combination with a computational algorithm that can simulate the evolution of a finite fracture, the decaying stress intensity factor during arrest, the time at which the fracture transitions from arrest to recession, and the negative front velocity during recession.

Original languageEnglish (US)
Article numberA17
JournalJournal of Fluid Mechanics
StatePublished - Sep 25 2022

Bibliographical note

Funding Information:
A.P. was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) (grant no. RGPIN-2015-06039) and the British Columbia Oil and Gas Commission. E.D. gratefully acknowledges support provided by the T.W. Bennett Chair in Mining Engineering and Rock Mechanics.

Publisher Copyright:
© The Author(s), 2022. Published by Cambridge University Press.


  • Boundary layer structure
  • Lubrication theory


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