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$\text{CO}_{2}$ dissolution in a background hydrological flow

Published online by Cambridge University Press:  26 January 2016

H. Juliette T. Unwin ,
Garth N. Wells  and
Andrew W. Woods
H. Juliette T. Unwin
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
Garth N. Wells
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
Andrew W. Woods*
Affiliation:
BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK
*
†Email address for correspondence: [email protected]
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Abstract

During $\text{CO}_{2}$ sequestration into a deep saline aquifer of finite vertical extent, $\text{CO}_{2}$ will tend to accumulate in structural highs such as offered by an anticline. Over times of tens to thousands of years, some of the $\text{CO}_{2}$ will dissolve into the underlying groundwater to produce a region of relatively dense, saturated water directly below the plume of $\text{CO}_{2}$. Continued dissolution then requires the supply of unsaturated aquifer water. In an aquifer of finite vertical extent, this may be provided by a background hydrological flow, or a laterally-spreading buoyancy-driven flow caused by the greater density of the $\text{CO}_{2}$ saturated water relative to the original aquifer water.

We investigate long time steady-state dissolution in the presence of a background hydrological flow. In steady state, the distribution of $\text{CO}_{2}$ in the groundwater upstream of the aquifer involves a balance between three competing effects: (i) the buoyancy-driven flow of $\text{CO}_{2}$ saturated water; (ii) the diffusion of $\text{CO}_{2}$ from saturated to under-saturated water; and (iii) the advection associated with the oncoming background flow. This leads to three limiting regimes. In the limit of very slow diffusion, a nearly static intrusion of dense fluid may extend a finite distance upstream, balanced by the pressure gradient associated with the oncoming background flow. In the limit of fast diffusion relative to the flow, a gradient zone may become established in which the along-aquifer diffusive flux balances the advection associated with the background flow. However, if the buoyancy-driven flow speed exceeds the background hydrological flow speed, then a third, intermediate regime may become established. In this regime, a convective recirculation develops upstream of the anticline involving the vertical diffusion of $\text{CO}_{2}$ from an upstream propagating flow of dense $\text{CO}_{2}$ saturated water into the downstream propagating flow of $\text{CO}_{2}$ unsaturated water. For each limiting case, we find analytical solutions for the distribution of $\text{CO}_{2}$ upstream of the anticline, and test our analysis with full numerical simulations. A key result is that, although there may be very different controls on the distribution and extent of $\text{CO}_{2}$ bearing water upstream of the anticline, in each case the dissolution rate is given by the product of the background volume flux and the difference in concentration between the $\text{CO}_{2}$ saturated water and the original aquifer water upstream.

JFM classification

Geophysical and Geological Flows: Gravity currents Low-Reynolds-number flows: Porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 789 , 25 February 2016 , pp. 768 - 784
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Copyright
© 2016 Cambridge University Press 

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