Dissolution-driven porous-medium convection in the presence of chemical reaction

Motivated by processes occurring during ${\mathrm{CO}}_2$ sequestration in an underground saline aquifer, we examine two-dimensional convection in a finite-depth porous medium induced by a solute introduced at the upper boundary. Once dissolved, the solute concentration is assumed to decay via a fir...

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Bibliographic Details
Published in:Journal of fluid mechanics 2014-05, Vol.747, p.316-349
Main Authors: Ward, T. J., Cliffe, K. A., Jensen, O. E., Power, H.
Format: Article
Language:English
Subjects:
Boundary layer
Chemical reactions
Convection
Dissolution
Earth sciences
Earth, ocean, space
Exact sciences and technology
Fluid mechanics
Hydrogeology
Hydrology. Hydrogeology
Numerical analysis
Porous materials
Porous media
Stability analysis
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Summary:Motivated by processes occurring during ${\mathrm{CO}}_2$ sequestration in an underground saline aquifer, we examine two-dimensional convection in a finite-depth porous medium induced by a solute introduced at the upper boundary. Once dissolved, the solute concentration is assumed to decay via a first-order chemical reaction, restricting the depth over which solute can penetrate the domain. Using spectral and asymptotic methods, we explore the resulting convective mixing using linear stability analysis, computation of nonlinear steady solution branches and time-dependent simulations, as a function of Rayleigh number, Damköhler number and domain size. Long-wave eigenmodes show how deep recirculation can be driven by a shallow solute field while explicit approximations are derived for the growth of short-wave eigenmodes. Steady solution branches undergo numerous secondary bifurcations, forming an intricate network of mixed states. Although many of these states are unstable, some play an important role in organising the phase space of time-dependent states, providing approximate bounds for time-averaged mixing rates.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2014.149