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The effects of fluid transport on the creation of a dense cluster of activated fractures in a porous medium

Published online by Cambridge University Press:  21 May 2018

Mohammed G. Alhashim  and
Donald L. Koch Open the ORCID record for Donald L. Koch [Opens in a new window]
Mohammed G. Alhashim
Affiliation:
Robert Frederick Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA
Donald L. Koch*
Affiliation:
Robert Frederick Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA
*
†Email address for correspondence: dlk15@cornell.edu
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Abstract

The formation of a cluster of activated fractures when fluid is injected in a low permeability rock is analysed. A fractured rock is modelled as a dual porosity medium that consists of a growing cluster of activated fractures and the rock’s intrinsic porosity. An integro-differential equation for fluid pressure in the developing cluster of fractures is introduced to account for the pressure-driven flow through the cluster, the loss of fluid into the porous matrix and the evolution of the cluster’s permeability and porosity as the fractures are activated. Conditions under which the dependence of the permeability and porosity on the fluid pressure can be derived from percolation theory are discussed. It is shown that the integro-differential equation admits a similarity solution for the fluid pressure and that the cluster radius grows as a power law of time in two regimes: (i) a short-time regime, when many fractures are activated but pressure-driven flow in the network still dominates over fluid loss; and (ii) a long-time regime, when fluid loss dominates. The power law exponents in the two regimes are functions of the Euclidean dimension of the cluster, percolation universal exponents and the injection protocol. The model predicts that the effects of the fluid properties on the morphology of the formed network are different in the two similarity regimes. For example, increasing the injection rate with time, in the flow dominant regime, produces a smaller cluster of activated fractures than that formed by injecting the fluid at a constant rate. In the fluid loss dominated regime, however, ramping up the injection rate produces a larger cluster.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Gravity currents Low-Reynolds-number flows: Low-Reynolds-number flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 847 , 25 July 2018 , pp. 286 - 328
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Copyright
© 2018 Cambridge University Press 

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