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Dissolution-driven convection in a heterogeneous porous medium

Published online by Cambridge University Press:  15 October 2018

Ashwanth K. R. Salibindla ,
Rabin Subedi ,
Victor C. Shen ,
Ashik U. M. Masuk  and
Rui Ni Open the ORCID record for Rui Ni [Opens in a new window]
Ashwanth K. R. Salibindla
Affiliation:
Department of Mechanical and Nuclear Engineering, Pennsylvania State University, University Park, PA 16802, USA
Rabin Subedi
Affiliation:
Department of Mechanical and Nuclear Engineering, Pennsylvania State University, University Park, PA 16802, USA
Victor C. Shen
Affiliation:
Department of Mechanical and Nuclear Engineering, Pennsylvania State University, University Park, PA 16802, USA
Ashik U. M. Masuk
Affiliation:
Department of Mechanical and Nuclear Engineering, Pennsylvania State University, University Park, PA 16802, USA
Rui Ni*
Affiliation:
Department of Mechanical and Nuclear Engineering, Pennsylvania State University, University Park, PA 16802, USA Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
*
†Email address for correspondence: [email protected]
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Abstract

Motivated by subsurface carbon sequestration, an experimental investigation of dissolution-driven Rayleigh–Darcy convection using two miscible fluids in a Hele-Shaw cell is conducted. A thin horizontal layer of circular impermeable discs is inserted to create an environment with heterogeneous and anisotropic permeability. The Sherwood number that measures the convective mass transfer rate between two fluids at the interface is linked to different parameters of the disc layer, including the disc size, spacing, layer permeability and its relative height with respect to the fluid interface. It is surprising that the convective mass transfer rate in our configuration is dominated by the disc spacing, but almost independent of either the disc size or the mean permeability of the layer. To explain this dependence, the convective mass transfer rate is decomposed into the number, velocity and density contrast of fingers travelling through the disc layer. Both the number and density contrast of fingers show dependences on the disc layer permeability, even though the product of them, the mass transfer rate, does not. In addition, the density contrast also shows a non-monotonic dependence on the disc spacing. The transition point is at a spacing that is close to the finger width. Based on this observation, a simple model based on mixing and scale competition is proposed, and it shows an excellent agreement with the experimental results.

JFM classification

Convection: Convection Convection: Convection in porous media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 857 , 25 December 2018 , pp. 61 - 79
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Copyright
© 2018 Cambridge University Press 

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References

Agartan, E., Trevisan, L., Cihan, A., Birkholzer, J., Zhou, Q. & Illangasekare, T. H. 2015 Experimental study on effects of geologic heterogeneity in enhancing dissolution trapping of supercritical CO2 . Water Resour. Res. 51 (3), 1635–1648.Google Scholar
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 (10), 104501.Google Scholar
Cavanagh, A. J. & Haszeldine, R. S. 2014 The Sleipner storage site: capillary flow modeling of a layered CO2 plume requires fractured shale barriers within the Utsira Formation. Intl J. Greenh. Gas Control 21, 101–112.Google Scholar
Cheng, P., Bestehorn, M. & Firoozabadi, A. 2012 Effect of permeability anisotropy on buoyancy-driven flow for CO2 sequestration in saline aquifers. Water Resour. Res. 48 (9), W09539.Google Scholar
Ecke, R. E. & Backhaus, S. 2016 Plume dynamics in Hele-Shaw porous media convection. Phil. Trans. R. Soc. Lond. A 374 (2078), 20150420.Google Scholar
Elenius, M. T. & Johannsen, K. 2012 On the time scales of nonlinear instability in miscible displacement porous media flow. Comput. Geosci. 16 (4), 901–911.Google Scholar
Emami-Meybodi, H., Hassanzadeh, H., Green, C. P. & Ennis-King, J. 2015 Convective dissolution of CO2 in saline aquifers: progress in modeling and experiments. Intl J. Greenh. Gas Control 40, 238–266.Google Scholar
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 (8), 084107.Google Scholar
Farajzadeh, R., Meulenbroek, B., Daniel, D., Riaz, A. & Bruining, J. 2013 An empirical theory for gravitationally unstable flow in porous media. Comput. Geosci. 17 (3), 515–527.Google Scholar
Farajzadeh, R., Ranganathan, P., Zitha, P. L. J. & Bruining, J. 2011 The effect of heterogeneity on the character of density-driven natural convection of CO2 overlying a brine layer. Adv. Water Resour. 34 (3), 327–339.Google Scholar
Foster, T. D. 1965 Stability of a homogeneous fluid cooled uniformly from above. Phys. Fluids 8 (7), 1249–1257.Google Scholar
Green, C. P. & Ennis-King, J. 2014 Steady dissolution rate due to convective mixing in anisotropic porous media. Adv. Water Resour. 73, 65–73.Google Scholar
Hassanzadeh, H., Pooladi-Darvish, M. & Keith, D. W. 2007 Scaling behavior of convective mixing, with application to geological storage of CO2 . AIChE J. 53 (5), 1121–1131.Google Scholar
Hewitt, D. R.2014 High Rayleigh number convection in a porous medium. PhD thesis, University of Cambridge.Google Scholar
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.Google Scholar
Hewitt, D. R., Neufeld, J. A. & Lister, J. R. 2014 High Rayleigh number convection in a porous medium containing a thin low-permeability layer. J. Fluid Mech. 756, 844–869.Google Scholar
Hidalgo, J. J. & Carrera, J. 2009 Effect of dispersion on the onset of convection during CO2 sequestration. J. Fluid Mech. 640, 441–452.Google Scholar
Hidalgo, J. J., Fe, J., Cueto-Felgueroso, L. & Juanes, R. 2012 Scaling of convective mixing in porous media. Phys. Rev. Lett. 109 (26), 264503.Google Scholar
Horton, C. W. & Rogers, F. T. Jr. 1945 Convection currents in a porous medium. J. Appl. Phys. 16 (6), 367–370.Google Scholar
Hubel, A., Bidault, N. & Hammer, B. 2002 Transport characteristics of glycerol and propylene glycol in an engineered dermal replacement. In ASME 2002 International Mechanical Engineering Congress and Exposition, pp. 121–122. American Society of Mechanical Engineers.Google Scholar
Huppert, H. E. & Neufeld, J. A. 2014 The fluid mechanics of carbon dioxide sequestration. Annu. Rev. Fluid Mech. 46, 255–272.Google Scholar
Lapwood, E. R. 1948 Convection of a fluid in a porous medium. In Mathematical Proceedings of the Cambridge Philosophical Society, vol. 44, pp. 508–521. Cambridge University Press.Google Scholar
MacBeth, G. & Thompson, A. R. 1951 Densities and refractive indexes for propylene glycol–water solutions. Analyt. Chem. 23 (4), 618–619.Google Scholar
McKibbin, R. & O’Sullivan, M. J. 1980 Onset of convection in a layered porous medium heated from below. J. Fluid Mech. 96 (2), 375–393.Google Scholar
McKibbin, R. & O’Sullivan, M. J. 1981 Heat transfer in a layered porous medium heated from below. J. Fluid Mech. 111, 141–173.Google Scholar
Meybodi, H. E. & Hassanzadeh, H. 2013 Mixing induced by buoyancy-driven flows in porous media. AIChE J. 59 (4), 1378–1389.Google Scholar
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 (22), L22404.Google Scholar
Nield, D. A. 1983 The boundary correction for the Rayleigh–Darcy problem: limitations of the Brinkman equation. J. Fluid Mech. 128, 37–46.Google Scholar
Nield, D. A. & Bejan, A. 2006 Convection in Porous Media, vol. 3. Springer.Google Scholar
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, 263–281.Google Scholar
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 CO2 storage in saline aquifers. Adv. Water Resour. 33 (4), 443–455.Google Scholar
Rahbari-Sisakht, M., Taghizadeh, M. & Eliassi, A. 2003 Densities and viscosities of binary mixtures of poly(ethylene glycol) and poly(propylene glycol) in water and ethanol in the 293.15–338.15 K temperature range. J. Chem. Engng Data 48 (5), 1221–1224.Google Scholar
Rapaka, S., Pawar, R. J., Stauffer, P. H., Zhang, D. & Chen, S. 2009 Onset of convection over a transient base-state in anisotropic and layered porous media. J. Fluid Mech. 641, 227–244.Google Scholar
Rees, D. A. S. & Bassom, A. P. 2000 The onset of Darcy–Bénard convection in an inclined layer heated from below. Acta Mechanica 144 (1–2), 103–118.Google Scholar
Rees, D. A. S. & Genç, G. 2011 The onset of convection in porous layers with multiple horizontal partitions. Intl J. Heat Mass Transfer 54 (13–14), 3081–3089.Google Scholar
Rees, D. A. S. & Riley, D. S. 1990 The three-dimensional stability of finite-amplitude convection in a layered porous medium heated from below. J. Fluid Mech. 211, 437–461.Google Scholar
Settles, G. S. 2012 Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media. Springer.Google Scholar
Slim, A. C. 2014 Solutal-convection regimes in a two-dimensional porous medium. J. Fluid Mech. 741, 461–491.Google Scholar
Slim, A. C. & Ramakrishnan, T. S. 2010 Onset and cessation of time-dependent, dissolution-driven convection in porous media. Phys. Fluids 22 (12), 124103.Google Scholar
Szulczewski, M. L., Hesse, M. A. & Juanes, R. 2013 Carbon dioxide dissolution in structural and stratigraphic traps. J. Fluid Mech. 736, 287–315.Google Scholar
Xu, X., Chen, S. & Zhang, D. 2006 Convective stability analysis of the long-term storage of carbon dioxide in deep saline aquifers. Adv. Water Resour. 29 (3), 397–407.Google Scholar