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Fluid transport in geological reservoirs with background flow

Published online by Cambridge University Press:  24 August 2017

Samuel S. Pegler Open the ORCID record for Samuel S. Pegler [Opens in a new window] ,
Alexandra S. D. Maskell ,
Katherine A. Daniels  and
Mike J. Bickle
Samuel S. Pegler*
Affiliation:
School of Mathematics, University of Leeds, Leeds LS2 9JT, UK Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK
Alexandra S. D. Maskell
Affiliation:
Department of Earth Sciences, University of Cambridge, Cambridge CB2 3EQ, UK
Katherine A. Daniels
Affiliation:
Department of Earth Sciences, University of Cambridge, Cambridge CB2 3EQ, UK British Geological Survey, Keyworth, NG12 599, UK
Mike J. Bickle
Affiliation:
Department of Earth Sciences, University of Cambridge, Cambridge CB2 3EQ, UK
*
†Email address for correspondence: S.Pegler@leeds.ac.uk
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Abstract

This paper presents fundamental analysis of the injection and release of fluid into porous media or geological reservoirs saturated by a different fluid undergoing a background flow, and tests the predictions using analogue laboratory experiments. The study reveals new results important for an understanding of the transport of hazardous contaminants through aquifers and the long-term fate of carbon dioxide ($\text{CO}_{2}$) in geological $\text{CO}_{2}$ sequestration. Using numerical and asymptotic analysis, we describe a variety of flow regimes that arise, and demonstrate an almost instantaneous control of injected fluid by the far field conditions in geological reservoirs. For a continuous input, the flow develops a horizontal interface between the injected and ambient fluids. The background flow thereby effectively caps the height of the injected fluid into a shallower region of vertical confinement. For a released parcel of fluid, gravitational spreading is found to become negligible after a short time. A dominant control of the interface by the background pressure gradient arises, and stems from the different velocities at which it drives the injected and ambient fluids individually. Similarity solutions describing these dynamics show that the parcel approaches a slender triangular profile that grows horizontally as $t^{1/2}$, where $t$ is time, a rate faster than relaxation under gravity. Shock layers develop at the front or back of the parcel, depending on whether it is more or less viscous than the ambient fluid. New analytical results describing the long-term effects of residual trapping due to capillary retention are developed, which yield explicit predictions for the time and length scales on which a parcel of $\text{CO}_{2}$ becomes retained. We end by applying our results to geological contexts, concluding that even slight background motion can have considerable implications for long-term transport through the subsurface.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Gravity currents Low-Reynolds-number flows: Porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 827 , 25 September 2017 , pp. 536 - 571
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Copyright
© 2017 Cambridge University Press 

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Pegler et al. supplementary movie

Movie of run 4, showing the injection of dyed brine into a porous bead pack containing an ambient background flow of saturating water. The theoretical prediction is shown as a red dashed curve.

Download Pegler et al. supplementary movie(Video)
Video 11.8 MB