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Coupled electrohydrodynamic transport in rough fractures: a generalized lubrication theory

Published online by Cambridge University Press:  17 May 2022

Mainendra Kumar Dewangan ,
Uddipta Ghosh Open the ORCID record for Uddipta Ghosh [Opens in a new window] ,
Tanguy Le Borgne  and
Yves Méheust Open the ORCID record for Yves Méheust [Opens in a new window]
Mainendra Kumar Dewangan
Affiliation:
Discipline of Mechanical Engineering, Indian Institute of Technology Gandhinagar, Palaj 382355, Gujrat, India
Uddipta Ghosh*
Affiliation:
Discipline of Mechanical Engineering, Indian Institute of Technology Gandhinagar, Palaj 382355, Gujrat, India Univ. Rennes, CNRS, Géosciences Rennes (UMR6118), 35042 Rennes, France
Tanguy Le Borgne
Affiliation:
Univ. Rennes, CNRS, Géosciences Rennes (UMR6118), 35042 Rennes, France
Yves Méheust*
Affiliation:
Univ. Rennes, CNRS, Géosciences Rennes (UMR6118), 35042 Rennes, France
*
†Email addresses for correspondence: uddipta.ghosh@iitgn.ac.in, yves.meheust@univ-rennes1.fr
†Email addresses for correspondence: uddipta.ghosh@iitgn.ac.in, yves.meheust@univ-rennes1.fr
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Abstract

Fractures provide pathways for fluids and solutes through crystalline rocks and low permeability materials, thus playing a key role in many subsurface processes and applications. In small aperture fractures, solute transport is strongly impacted by the coupling of electrical double layers at mineral–fluid interfaces to bulk ion transport. Yet, most models of flow and transport in fractures ignore these effects. Solving such coupled electrohydrodynamics in realistic three-dimensional (3-D) fracture geometries poses computational challenges which have so far limited our understanding of those electro-osmotic effects’ impact. Starting from the Poisson–Nernst–Planck–Navier–Stokes (PNPNS) equations and using a combination of rescaling, asymptotic analysis and the Leibniz rule, we derive a set of nonlinearly coupled conservation equations for the local fluxes of fluid mass, solute mass and electrical charges. Their solution yields the fluid pressure, solute concentration and electrical potential fields. The model is validated by comparing its predictions to the solutions of the PNPNS equations in 3-D rough fractures. Application of the model to realistic rough fracture geometries evidences several phenomena hitherto not reported in the literature, including: (i) a dependence of the permeability and electrical conductivity on the fracture walls’ charge density, (ii) local (sometimes global) flow reversal, and (iii) spatial heterogeneities in the concentration field without any imposed concentration gradient. This new theoretical framework will allow systematically addressing large statistics of fracture geometry realizations of given stochastic parameters, to infer the impact of the geometry and various hydrodynamic and electrical parameters on the coupled transport of fluid and ions in rough fractures.

JFM classification

MHD and Electrohydrodynamics: Electrokinetic flows Low-Reynolds-number flows: Lubrication theory Low-Reynolds-number flows: Stokesian dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 942 , 10 July 2022 , A11
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© The Author(s), 2022. Published by Cambridge University Press

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References

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