Skip to main content Accessibility help
×
×
Home

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

  • T. J. Ward (a1), K. A. Cliffe (a1), O. E. Jensen (a2) and H. Power (a3)
Abstract

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.

Copyright
Corresponding author
Email address for correspondence: oliver.jensen@manchester.ac.uk
References
Hide All
Andres, J. T. H. & Cardoso, S. S. S. 2011 Onset of convection in a porous medium in the presence of chemical reaction. Phys. Rev. E 83, 046312.
Armbruster, D. & Dangelmayr, G. 1986 Corank-two bifurcations for the Brusselator with no-flux boundary conditions. Dyn. Stab. Syst. 1 (3), 187200.
Armbruster, D. & Dangelmayr, G. 1987 Coupled stationary bifurcations in non-flux boundary value problems. Math. Proc. Camb. Phil. Soc. 101, 167192.
Backhaus, S., Turitsyn, K. & Ecke, R. E. 2011 Convective instability and mass transport of diffusion layers in a Hele–Shaw geometry. Phys. Rev. Lett. 106, 104501.
Bestehorn, M. & Firoozabadi, A. 2012 Effect of fluctuations on the onset of density-driven convection in porous media. Phys. Fluids 24, 114102.
Boyd, J. P. 2001 Chebyshev and Fourier Spectral Methods. Dover.
Cliffe, K. A., Spence, A. & Tavener, S. J. 2000 The numerical analysis of bifurcation problems with application to fluid mechanics. Acta Numerica 9, 39131.
De Wit, A. 2001 Fingering of chemical fronts in porous media. Phys. Rev. Lett. 87, 054502.
De Wit, A. 2004 Miscible density fingering of chemical fronts in porous media: nonlinear simulations. Phys. Fluids 16, 163175.
Ennis-King, J. & Paterson, L. 2005 Role of convective mixing in the long-term storage of carbon dioxide in deep saline formations. Soc. Petrol. Engrs J. 10, 349356.
Ennis-King, J. & Paterson, L. 2007 Coupling of geochemical reactions and convective mixing in the long-term geological storage of carbon dioxide. Intl J. Green Gas Control 1, 8693.
Ennis-King, J., Preston, I. & Paterson, L. 2005 Onset of convection in anisotropic porous media subject to a rapid change in boundary conditions. Phys. Fluids 17, 084107.
Ghesmat, K., Hassanzadeh, H. & Abedi, J. 2009 The impact of geochemistry on convective mixing in a gravitationally unstable diffusive boundary layer in porous media: ${\mathrm{CO}}_2$ storage in saline aquifers. J. Fluid Mech. 673, 480512.
Hartline, B. K. & Lister, C. R. B. 1977 Thermal convection in a Hele–Shaw cell. J. Fluid Mech. 79, 379389.
Hassanzadeh, H., Pooladi-Darvish, M. & Keith, D. W. 2007 Scaling behavior of convective mixing, with application to geological storage of ${\mathrm{CO}}_2$ . AIChE J. 53 (5), 11211131.
Hesse, M. A., Orr, F. M. & Tchelepi, H. A. 2008 Gravity currents with residual trapping. J. Fluid Mech. 611, 3560.
Hewitt, D. R., Neufeld, J. A. & Lister, J. R. 2012 Ultimate regime of high Rayleigh number convection in a porous medium. Phys. Rev. Lett. 108 (22), 224503.
Hewitt, D. R., Neufeld, J. A. & Lister, J. R. 2013 Convective shutdown in a porous medium at high Rayleigh number. J. Fluid Mech. 719, 551586.
Hidalgo, J. J., Fe, J., Cueto-Felgueroso, L. & Juanes, R. 2012 Scaling of convective mixing in porous media. Phys. Rev. Lett. 109, 264503.
IPCC, 2005 International Panel on Climate Change Special Report on Carbon Dioxide Capture and Storage (ed. Metz, B., Davidson, O., de Coninck, H., Loos, M. & Meyer, L.), Cambridge University Press.
Kim, M. C. & Choi, C. K. 2012 Linear stability analysis on the onset of buoyancy-driven convection in liquid-saturated porous medium. Phys. Fluids 24, 044102.
Kneafsey, T. J. & Pruess, K. 2010 Laboratory flow experiments for visualizing carbon dioxide-induced, density-driven brine convection. Transp. Porous Med. 82, 123139.
Lal, R. 2008 Carbon sequestration. Phil. Trans. R. Soc. Lond. B 363, 815830.
Lemieux, J.-M. 2011 Review: the potential impact of underground geological storage of carbon dioxide in deep saline aquifers on shallow groundwater resources. Hydrol. J. 19, 757778.
Luquot, L. & Gouze, P. 2009 Experimental determination of porosity and permeability changes induced by injection of ${\mathrm{CO}}_2$ into carbonate rocks. Chem. Geol. 265 (1), 148159.
Mitchell, M. J., Jensen, O. E., Cliffe, K. A. & Maroto-Valer, M. M. 2010 A model of carbon dioxide dissolution and mineral carbonation kinetics. Proc. R. Soc. Lond. A 466, 12651290.
Neufeld, J. A., Hesse, M. A., Riaz, A., Hallworth, M. A., Tchelepi, H. A. & Huppert, H. E. 2010 Convective dissolution of carbon dioxide in saline aquifers. Geophys. Res. Lett. 37, L22404.
Otero, J., Dontcheva, L. A., Johnston, H., Worthing, R. A., Kurganov, A., Petrova, G. & Doering, C. R. 2004 High-Rayleigh-number convection in a fluid-saturated porous layer. J. Fluid Mech. 500, 263281.
Pau, G. S. H., Bell, J. B., Pruess, K., Almgren, A. S., Lijewski, M. J. & Zhang, K. 2010 High-resolution simulation and characterization of density-driven flow in ${\mathrm{CO}}_2$ storage in saline aquifers. Adv. Water Resour. 33, 443455.
Ranganathan, P., Farajzadeh, R., Bruining, H. & Zitha, P. L. J. 2012 Numerical simulation of natural convection in heterogeneous porous media for ${\mathrm{CO}}_2$ geological storage. Transp. Porous Med. 95, 2554.
Riaz, A., Hesse, M., Tchelepi, H. A. & Orr, F. M. 2005 Onset of convection in a gravitationally unstable diffusive boundary layer in porous media. J. Fluid Mech. 548, 87111.
Riley, D. S. & Winters, K. H. 1990 A numerical bifurcation study of natural convection in a tilted two-dimensional porous cavity. J. Fluid Mech. 215, 309329.
Riley, D. S. & Winters, K. H. 1991 Time-periodic convection in porous media: the evolution of Hopf bifurcations with aspect ratio. J. Fluid Mech. 223, 457474.
Ritchie, L. T. & Pritchard, D. 2011 Natural convection and the evolution of a reactive porous medium. J. Fluid Mech. 673, 286317.
Slim, A. C., Bandi, M. M., Miller, J. C. & Mahadevan, L. 2013 Dissolution-driven convection in a Hele–Shaw cell. Phys. Fluids 25, 024101.
Slim, A. C. & Ramakrishnan, T. S. 2010 Onset and cessation of time-dependent, dissolution-driven convection in porous media. Phys. Fluids 22, 124103.
Trefethen, L. N. 2000 Spectral Methods in MATLAB. Society for Industrial and Applied Mathematics.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed