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Viscous backflow from a model fracture network: influence of a permeable boundary

Published online by Cambridge University Press:  01 February 2021

Asaf Dana
Affiliation:
The Nancy and Stephen Grand Technion Energy Program; and Department of Civil and Environmental Engineering, Technion - Israel Institute of Technology, Haifa 3200003, Israel Department of Mechanical Engineering, Technion - Israel Institute of Technology, Haifa 3200003, Israel
Gunnar G. Peng
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
Howard A. Stone
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Herbert E. Huppert
Affiliation:
Institute of Theoretical Geophysics, King's College, Cambridge CB2 1ST, UK
Guy Z. Ramon*
Affiliation:
The Nancy and Stephen Grand Technion Energy Program; and Department of Civil and Environmental Engineering, Technion - Israel Institute of Technology, Haifa 3200003, Israel
*Corresponding
Email address for correspondence: ramong@technion.ac.il

Abstract

The leakage from a fracture network to a surrounding medium during drainage, or backflow, driven by elastic relaxation, is considered. A network model is extended to include the effects of permeable boundaries, with the permeation through the wall assumed to be proportional to the local pressure. The regimes in which leakage is dominant relative to the parallel flow along the channel are evaluated at different times. Results show that, when the aperture of the channel is large enough, the parallel flow is greater than the permeation through the wall, and the channel thickness decreases in time, $t$, with a $t^{-1/3}$ behaviour, as reported previously. However, when the aperture is small, the channel thickness decreases exponentially in time. An asymptotic investigation of the solution for a single fracture is performed and extended to network systems. The study provides insight into the influence leakage may have on squeezing-induced flows, which is relevant to natural and engineering systems.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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