Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-02T22:05:16.410Z Has data issue: false hasContentIssue false
  • English
  • Français

Thermosolutal convection in an evolving soluble porous medium

Published online by Cambridge University Press:  26 October 2017

Lindsey T. Corson Open the ORCID record for Lindsey T. Corson [Opens in a new window]  and
David Pritchard Open the ORCID record for David Pritchard [Opens in a new window]
Lindsey T. Corson*
Affiliation:
Department of Civil and Environmental Engineering, University of Strathclyde, 75 Montrose Street, Glasgow G1 1XJ, Scotland, UK Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, Scotland, UK
David Pritchard
Affiliation:
Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, Scotland, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We describe a mathematical model of double-diffusive (thermosolutal) convection in a saturated porous layer, when the solubility of the solute depends on the temperature, and the porosity and permeability of the porous medium evolve through dissolution and precipitation. We present the results of linear and weakly nonlinear stability analyses and explore the longer-term development of the system numerically. When the solutal concentration gradient is destabilising, the dynamics are somewhat similar to those previously found for single-species convection (Ritchie & Pritchard, J. Fluid Mech., vol. 673, 2011, pp. 286–317), including the occurrence of subcritical instabilities driven by a reaction–diffusion mechanism. However, when the solutal concentration gradient is stabilising and the thermal gradient is destabilising, novel dynamics emerge. These include a vertical segregation of circulation cells and porosity perturbations near the onset of convection, and over longer time scales the formation of a low-permeability region in the middle of the layer, pierced by occasional high-permeability channels. Under these conditions, convection may die away to nearly zero for extended periods before resuming vigorously in localised regions at later times.

JFM classification

Convection: Convection in porous media Convection: Double diffusive convection Geophysical and Geological Flows: Geophysical and Geological Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 832 , 10 December 2017 , pp. 666 - 696
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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.Google Scholar
Barba Rossa, G., Cliffe, K. A. & Power, H. 2017 Effects of hydrodynamic dispersion on the stability of buoyancy-driven porous media convection in the presence of first order chemical reaction. J. Engng Maths 103, 55–76.CrossRefGoogle Scholar
Bolton, E. W., Lasaga, A. C. & Rye, D. M. 1996 A model for the kinetic control of quartz dissolution and precipitation in porous media flow with spatially variable permeability: formulation and examples of thermal convection. J. Geophys. Res. 101 (B10), 22157–22187.Google Scholar
Bolton, E. W., Lasaga, A. C. & Rye, D. M. 1997 Dissolution and precipitation via forced-flux injection in a porous medium with spatially variable permeability: kinetic control in two dimensions. J. Geophys. Res. 102 (B6), 12159–12171.Google Scholar
Bolton, E. W., Lasaga, A. C. & Rye, D. M. 1999 Long-term flow/chemistry feedback in a porous medium with heterogenous permeability: kinetic control of dissolution and precipitation. Am. J. Sci. 299, 1–68.CrossRefGoogle Scholar
Celia, M. A., Bachu, S., Nordbotten, J. M. & Bandilla, K. W. 2015 Status of CO2 storage in deep saline aquifers with emphasis on modeling approaches and practical simulations. Water Resour. Res. 51, 6846–6892.Google Scholar
Chadam, J., Ortoleva, P., Qin, Y. & Stamicar, R. 2001 The effect of hydrodynamic dispersion on reactive flows in porous media. Eur. J. Appl. Maths 12, 557–569.CrossRefGoogle Scholar
Cherezov, I. & Cardoso, S. S. S. 2016 Acceleration of convective dissolution by chemical reaction in a Hele-Shaw cell. Phys. Chem. Chem. Phys. 18, 23727–23736.CrossRefGoogle Scholar
Ching, J.-H., Chen, P. & Tsai, P. A. 2017 Convective mixing in homogeneous porous media flow. Phys. Rev. Fluids 2, 014102.CrossRefGoogle Scholar
Corson, L. T.2012 Geochemical effects on natural convection in porous media. PhD thesis, University of Strathclyde, available online http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.576412.Google Scholar
Gatica, J. E., Viljoen, H. J. & Hlavacek, V. 1989 Interaction between chemical reaction and natural convection in porous media. Chem. Engng Sci. 44 (9), 1853–1870.CrossRefGoogle Scholar
Ghoshal, P., Kim, M. C. & Cardoso, S. S. S. 2017 Reactive–convective dissolution in a porous medium: the storage of carbon dioxide in saline aquifers. Phys. Chem. Chem. Phys. 19, 644–655.Google Scholar
Hidalgo, J. J., Dentz, M., Cabeza, Y. & Carrera, J. 2015 Dissolution patterns and mixing dynamics in unstable reactive flow. Geophys. Res. Lett. 42 (15), 6357–6364.CrossRefGoogle Scholar
Horton, C. W. & Rogers, F. T. 1945 Convection currents in a porous medium. J. Appl. Phys. 16, 367–370.CrossRefGoogle Scholar
Huppert, H. E. & Neufeld, J. A. 2014 The fluid mechanics of carbon dioxide sequestration. Annu. Rev. Fluid Mech. 46, 255–272.CrossRefGoogle Scholar
Lapwood, E. R. 1948 Convection of a fluid in a porous medium. Proc. Camb. Phil. Soc. 44, 508–521.Google Scholar
Malashetty, M. S. & Biradar, B. S. 2011 The onset of double diffusive reaction–convection in an anisotropic porous layer. Phys. Fluids 23, 064102.Google Scholar
Mou, J., Zhu, D. & Hill, A. D. 2010 Acid-etched channels in heterogeneous carbonates – a newly discovered mechanism for creating acid-fracture conductivity. SPE J. 15 (2), 404–416.CrossRefGoogle Scholar
Nield, D. A. & Bejan, A. 2006 Convection in Porous Media, 3rd edn. Springer.Google Scholar
Panga, M. K. R., Ziauddin, M. & Balakotaiah, V. 2005 Two-scale continuum model for simulation of wormholes in carbonate acidization. AIChE J. 51 (12), 3231–3248.CrossRefGoogle Scholar
Petrus, K. & Szymczak, P. 2016 Influence of layering on the formation and growth of solution pipes. Front. Phys. 3, 92.CrossRefGoogle Scholar
Phillips, O. M. 2009 Geological Fluid Dynamics: Sub-Surface Flow and Reactions. Cambridge University Press.CrossRefGoogle Scholar
Pritchard, D. & Richardson, C. N. 2007 The effect of temperature-dependent solubility on the onset of thermosolutal convection in a horizontal porous layer. J. Fluid Mech. 571, 59–95.Google Scholar
Riaz, A., Hesse, M., Tchelepi, H. A. & Orr, F. M. 2006 Onset of convection in a gravitationally unstable diffusive boundary layer in porous media. J. Fluid Mech. 548, 87–111.Google Scholar
Ritchie, L. T. & Pritchard, D. 2011 Natural convection and the evolution of a reactive porous medium. J. Fluid Mech. 673, 286–317.Google Scholar
Steinberg, V. & Brand, H. 1983 Convective instabilities of binary mixtures with fast chemical reaction in a porous medium. J. Chem. Phys. 78 (5), 2655–2660.CrossRefGoogle Scholar
Steinberg, V. & Brand, H. 1984 Amplitude equations for the onset of convection in a reactive mixture in a porous medium. J. Chem. Phys. 80 (1), 431–435.Google Scholar
Szymczak, P. & Ladd, A. J. C. 2014 Reactive-infiltration instabilities in rocks. Part 2. Dissolution of a porous matrix. J. Fluid Mech. 738, 591–630.CrossRefGoogle Scholar
Viljoen, H. J., Gatica, J. E. & Hlavacek, V. 1990 Bifurcation analysis of chemically driven convection. Chem. Engng Sci. 45 (2), 503–517.Google Scholar
Vreme, A., Nadal, F., Pouligny, B., Jeandet, P., Liger-Belair, G. & Meunier, P. 2016 Gravitational instability due to the dissolution of carbon dioxide in a Hele-Shaw cell. Phys. Rev. Fluids 1, 064301.CrossRefGoogle Scholar
Ward, T., Cliffe, K. A., Jensen, O. E. & Power, H. 2014a Dissolution-driven porous-medium convection in the presence of chemical reaction. J. Fluid Mech. 747, 316–349.Google Scholar
Ward, T., Jensen, O. E., Power, H. & Riley, D. S. 2014b High-Rayleigh-number convection of a reactive solute in a porous medium. J. Fluid Mech. 760, 95–126.Google Scholar
Ward, T., Jensen, O. E., Power, H. & Riley, D. S. 2015 Substrate degradation in high-Rayleigh-number reactive convection. Phys. Fluids 27, 116601.Google Scholar
Weis, P. 2015 The dynamic interplay between saline fluid flow and rock permeability in magmatic–hydrothermal systems. Geofluids 15, 350–371.CrossRefGoogle Scholar
Worster, M. G. 1997 Convection in mushy layers. Annu. Rev. Fluid Mech. 29, 91–122.CrossRefGoogle Scholar
Zhang, Y., Yang, S., Zhang, S. & Mou, J. 2014 Wormhole propagation behavior and its effect on acid leakoff under in situ conditions in acid fracturing. Trans. Porous Med. 101, 99–114.CrossRefGoogle Scholar
Zhao, C., Hobbs, B. E., Ord, A., Hornby, P. & Peng, S. 2008 Morphological evolution of three-dimensional chemical dissolution front in fluid-saturated porous media: a numerical simulation approach. Geofluids 8, 113–127.Google Scholar