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Convective carbon dioxide dissolution in a closed porous medium at low pressure

Published online by Cambridge University Press:  31 August 2018

Baole Wen Open the ORCID record for Baole Wen [Opens in a new window] ,
Daria Akhbari ,
Li Zhang Open the ORCID record for Li Zhang [Opens in a new window]  and
Marc A. Hesse
Baole Wen
Affiliation:
Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX 78712, USA
Daria Akhbari
Affiliation:
Department of Geological Sciences, University of Texas at Austin, Austin, TX 78712, USA
Li Zhang
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China
Marc A. Hesse*
Affiliation:
Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX 78712, USA Department of Geological Sciences, University of Texas at Austin, Austin, TX 78712, USA
*
†Email address for correspondence: [email protected]
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Abstract

Motivated by the persistence of natural carbon dioxide ($\text{CO}_{2}$) fields, we investigate the convective dissolution of $\text{CO}_{2}$ at low pressure (below 1 MPa) in a closed system, where the pressure in the gas declines as convection proceeds. This introduces a negative feedback that reduces the convective dissolution rate even before the brine becomes saturated. We analyse the case of an ideal gas with a solubility given by Henry’s law, in the limits of very low and very high Rayleigh numbers. The equilibrium state in this system is determined by the dimensionless dissolution capacity, $\unicode[STIX]{x1D6F1}$, which gives the fraction of the gas that can be dissolved into the underlying brine. Analytic approximations of the pure diffusion problem with $\unicode[STIX]{x1D6F1}>0$ show that the diffusive base state is no longer self-similar and that diffusive mass transfer declines rapidly with time. Direct numerical simulations at high Rayleigh numbers show that no constant flux regime exists for $\unicode[STIX]{x1D6F1}>0$; nevertheless, the quantity $F/C_{s}^{2}$ remains constant, where $F$ is the dissolution flux and $C_{s}$ is the dissolved concentration at the top of the domain. Simple mathematical models are developed to predict the evolution of $C_{s}$ and $F$ for high-Rayleigh-number convection in a closed system. The negative feedback that limits convection in closed systems may explain the persistence of natural $\text{CO}_{2}$ accumulations over millennial time scales.

JFM classification

Convection: Convection Convection: Convection in porous media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 854 , 10 November 2018 , pp. 56 - 87
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Copyright
© 2018 Cambridge University Press 

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