Shear dispersion in a porous medium. Part 1. Fixed-extent immiscible intrusion.

Hinton, Edward M and Woods, Andrew W. (2020) Shear dispersion in a porous medium. Part 1. Fixed-extent immiscible intrusion. Journal of Fluid Mechanics. ISSN 0022-1120, ESSN: 1469-7645 (Submitted)

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Abstract

The dispersion of tracer through a liquid injected into a confined aquifer with vertically varying permeability is studied theoretically. The injected fluid is buoyant and of high viscosity relative to the original fluid in the aquifer, which causes the nose region of the flow, where the thickness of the injected fluid is less than the thickness of the aquifer, to advance with constant velocity and fixed shape. Behind the nose, tracer is sheared at early times owing to the vertically varying permeability. At later times, cross-aquifer diffusion homogenises the tracer distribution, which becomes independent of depth but spreads longitudinally in this shear dispersion regime, which leads to much faster spreading than by diffusion alone. As tracer diffuses symmetrically in the longitudinal direction, it eventually reaches the nose. Subsequently, the nose acts as a no-flux boundary and the concentration profile transitions to a half-Gaussian, with the maximum concentration at the front. The centre of mass of the tracer spreads backwards relative to the fixed nose at a rate proportional to [D(T −T 0 )] 1/2 where D is the dispersion coefficient and T 0 is a time offset owing to the adjustment to shear dispersion and the interaction with the nose. The initial release of tracer may not be vertically uniform owing to the heterogeneity and we show that this can lead to the centre of mass of tracer initially advancing faster than the mean flow. We consider the implications of our results on tracer migration in sedimentary layers.

Item Type: Article
Uncontrolled Keywords: 2020AREP; IA76
Subjects: 02 - Geodynamics, Geophysics and Tectonics
Divisions: 02 - Geodynamics, Geophysics and Tectonics
08 - Green Open Access
Journal or Publication Title: Journal of Fluid Mechanics
Depositing User: Sarah Humbert
Date Deposited: 22 May 2020 16:44
Last Modified: 22 May 2020 16:44
URI: http://eprints.esc.cam.ac.uk/id/eprint/4747

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