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

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.

Authors:
ORCiD logo; ; ORCiD logo;
Publication Date:
Research Org.:
Energy Frontier Research Centers (EFRC) (United States). Center for Frontiers of Subsurface Energy Security (CFSES); Univ. of Texas, Austin, TX (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1538917
DOE Contract Number:  
SC0001114
Resource Type:
Journal Article
Journal Name:
Journal of Fluid Mechanics
Additional Journal Information:
Journal Volume: 854; Journal ID: ISSN 0022-1120
Publisher:
Cambridge University Press
Country of Publication:
United States
Language:
English
Subject:
Mechanics; Physics

Citation Formats

Wen, Baole, Akhbari, Daria, Zhang, Li, and Hesse, Marc A. Convective carbon dioxide dissolution in a closed porous medium at low pressure. United States: N. p., 2018. Web. doi:10.1017/jfm.2018.622.
Wen, Baole, Akhbari, Daria, Zhang, Li, & Hesse, Marc A. Convective carbon dioxide dissolution in a closed porous medium at low pressure. United States. doi:10.1017/jfm.2018.622.
Wen, Baole, Akhbari, Daria, Zhang, Li, and Hesse, Marc A. Fri . "Convective carbon dioxide dissolution in a closed porous medium at low pressure". United States. doi:10.1017/jfm.2018.622.
@article{osti_1538917,
title = {Convective carbon dioxide dissolution in a closed porous medium at low pressure},
author = {Wen, Baole and Akhbari, Daria and Zhang, Li and Hesse, Marc A.},
abstractNote = {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.},
doi = {10.1017/jfm.2018.622},
journal = {Journal of Fluid Mechanics},
issn = {0022-1120},
number = ,
volume = 854,
place = {United States},
year = {2018},
month = {8}
}

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