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Boundary-induced shear and tracer transport in heterogeneous porous rock

Published online by Cambridge University Press:  17 December 2020

Neeraja Bhamidipati Open the ORCID record for Neeraja Bhamidipati [Opens in a new window]  and
Andrew W. Woods Open the ORCID record for Andrew W. Woods [Opens in a new window]
Neeraja Bhamidipati*
Affiliation:
BP Institute, University of Cambridge, Madingley Road, CambridgeCB3 0EZ, UK
Andrew W. Woods
Affiliation:
BP Institute, University of Cambridge, Madingley Road, CambridgeCB3 0EZ, UK
*
†Email address for correspondence: neeraja@bpi.cam.ac.uk
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Abstract

We study the longitudinal dispersion of a passive tracer by a two-dimensional pressure-driven flow through a layer of heterogeneous porous rock which is bounded above and below by impermeable seal rock. We assume there are localised regions of different permeability at random vertical positions within an otherwise uniform layer. This leads to a Fickian-type dispersion (Eames & Bush, Proc. R. Soc. Lond. A, vol. 455, issue 1990, 1999, pp. 3665–3686) and a shear near the boundaries (Rabinovich et al., Phys. Rev. E, vol. 86, issue 4, 2012, 046601). We illustrate this effect in a long two-dimensional layer, consisting of $(a)$ long and thin lenses and $(b)$ elliptical lenses, using expressions for depth-dependent mean speed and dispersivity to derive a depth-averaged transport equation for the flow. We derive asymptotic solutions for the layer-averaged dispersal of tracer, showing that at long times the spreading of the tracer is controlled by the shear. We discuss the importance of our results for the interpretation of tracer dispersal tests in layered permeable rocks.

JFM classification

Low-Reynolds-number flows: Porous media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 908 , 10 February 2021 , A45
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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