Convective carbon dioxide dissolution in a closed porous medium at low pressure
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.
- Research Organization:
- Energy Frontier Research Centers (EFRC) (United States). Center for Frontiers of Subsurface Energy Security (CFSES); Univ. of Texas, Austin, TX (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- DOE Contract Number:
- SC0001114
- OSTI ID:
- 1538917
- Journal Information:
- Journal of Fluid Mechanics, Vol. 854; ISSN 0022-1120
- Publisher:
- Cambridge University Press
- Country of Publication:
- United States
- Language:
- English
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