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Viscous flow through high-permeability channels in a layered porous medium

Published online by Cambridge University Press:  11 June 2025

Anoop Rathore ,
Zhong Zheng Open the ORCID record for Zhong Zheng [Opens in a new window]  and
Chunendra K. Sahu Open the ORCID record for Chunendra K. Sahu [Opens in a new window]
Anoop Rathore
Affiliation:
Department of Civil Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016, India
Zhong Zheng*
Affiliation:
State Key Laboratory of Ocean Engineering, School of Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China MOE Key Laboratory of Hydrodynamics, School of Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China
Chunendra K. Sahu*
Affiliation:
Department of Civil Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016, India
*
Corresponding authors: Zhong Zheng, zzheng@alumni.princeton.edu, zhongzheng@sjtu.edu.cn; Chunendra K. Sahu, cksahu@iitk.ac.in
Corresponding authors: Zhong Zheng, zzheng@alumni.princeton.edu, zhongzheng@sjtu.edu.cn; Chunendra K. Sahu, cksahu@iitk.ac.in
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Abstract

Viscous flow through high-permeability channels occurs in many environmental and industrial applications, including carbon sequestration, groundwater flow and enhanced oil recovery. In this work, we study the displacement of a less-viscous fluid by a more-viscous fluid in a layered porous medium in a rectilinear configuration, where two low-permeability layers sandwich a higher-permeability layer. We derive a theoretical model that is validated using corroborative laboratory experiments, when the influence of the density difference is negligible. We find that the location of the propagating front increases with time according to a power-law form $x_f \propto t^{1/2}$, while the fluid–fluid interface exhibits a self-similar shape, when the motion of the displaced fluid is negligible in an unconfined porous medium. In the experimental set-up, distinct permeability layers were constructed using various sizes of spherical glass beads. The working fluids comprised fresh water as the less-viscous ambient fluid, and a glycerine–water mixture as the more-viscous injecting fluid. Our experimental measurement show a better match with the theory for the experiments performed at low Reynolds numbers and with permeable boundaries in the far field.

JFM classification

Low-Reynolds-number flows: Lubrication theory Low-Reynolds-number flows: Hele-Shaw flows Low-Reynolds-number flows: Porous media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1013 , 25 June 2025 , A1
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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