Heat and Mass Transfer

, Volume 49, Issue 11, pp 1603–1612 | Cite as

Onset of instability in CO2 sequestration into saline aquifer: scaling relationship and the effect of perturbed boundary

  • Reza AzinEmail author
  • Seyed Mostafa Jafari Raad
  • Shahriar Osfouri
  • Rooholla Fatehi


Storage and disposal of greenhouse gases in saline aquifers is an important solution for reduction of these gases from atmosphere. Understanding the concepts and mechanisms involved in the storage process, especially natural convection and their impact on long-term fate of injected CO2 are essential. Natural convection is an effective mechanism which increases solubility of carbon dioxide in the storage process. In this work, injection of carbon dioxide into aquifer is numerically simulated. First, numerical criteria are developed to provide numerical accuracy and stability by mesh resolution. Then, changes in input wave number in surface perturbation and order of element used in finite element method were analyzed. It was found that depending on Rayleigh number, there is a wave number at which instability occurs earlier and grows faster. Also, onset of CO2 convective mixing in saline aquifers was obtained and correlated for a number of field cases. Results show that onset of convection can be approximated by a scaling relationship for dimensionless time as a function of inverse square of Rayleigh number, Ra2, for Rayleigh range used in this work. This scaling relationship provides a predictive tool for onset of convection and also long-term fate of disposed CO2 in large scale geological sequestration.


Convection Natural Convection Rayleigh Number Linear Stability Analysis Sherwood Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols


CO2 concentration (mol/m3)


Constant interface concentration (mol/m3)

c1, c2

Correlation constants


Courant number (−)


Fraction of ultimate CO2 dissolution (−)


Interface concentration due to imposed perturbation (mol/m3)


Molecular diffusion coefficient (m2/s)


Numerical error in pure diffusion region (−)


First-order, second-order, and third-order elements


Height of the porous medium (m)


Permeability of the porous medium (m−2)


Wave number


Length of the porous medium (m)


Summation index


Number of elements


Pressure (pa)


Peclet number (−)


Rayleigh number (−)


Random function


Sherwood number (−)


Time (s)


Time of the onset of convection (s)


Dimensionless time (−)


Dimensionless time of the onset of convection (−)


Darcy velocity in x-coordinate (m/s)


Vector of Darcy velocity (m/s)


Grid Darcy’s velocity (m/s)


Darcy velocity in z-coordinate (m/s)


Dimensionless distance in x-coordinate


Dimensionless distance in z-coordinate

∆l(l = x, z)

Grid sizes (L)


Simulation time-step (s)

Greek symbols


Mixture CO2-brine density (kg/m3)


Brine density (kg/m3)

Porosity of the porous medium (−)


Density difference between CO2 saturated brine and fresh brine (kg/m3)


Volumetric expansion factor (m3/mol)


Brine viscosity (kg/m s)



Numerical solution


Analytical solution in pure diffusion region


Quantity in x-direction


Quantity in z-direction


  1. 1.
    Marchetti C (1977) On geoengineering and the CO2 problem. Clim Change 1:59–68CrossRefGoogle Scholar
  2. 2.
    Ghesmat K, Hassanzadeh H, Abadi J (2010) The effect of anisotropic dispersion on the convective mixing in long-term CO2 storage in saline aquifers. AIChE 57(3):561–570CrossRefGoogle Scholar
  3. 3.
    Keith DW (2002) Towards a Strategy for Implementing CO2 Capture and Storage in Canada. Catalogue No: En40-657/2002E. ISBN: 0- 662-31755-6Google Scholar
  4. 4.
    Flett M, Gurton R, Taggart I (2004) The function of gas-water relative permeability hysteresis in the sequestration of carbon dioxide in saline formations. In: SPE Asia Pacific oil and gas conference and exhibition. Perth, AustraliaGoogle Scholar
  5. 5.
    Bachu S, Adams JJ (2003) Estimating CO2 sequestration capacity in solution in deep saline aquifers. Energy Convers Manag 44(20):3151–3175CrossRefGoogle Scholar
  6. 6.
    Gunter W, Perkins EH, Wiwchar B (1997) Aquifer disposal of CO2-rich greenhouse gases: Extension of the time scale of experiment for CO2 sequestering reactions by geochemical modeling. Mineralo Petrol 59:121–140 CrossRefGoogle Scholar
  7. 7.
    Hassanzadeh H, Pooladi-Darvish M, Keith D (2007) Scaling behavior of convective mixing, with application to geological storage of CO2. AIChE 53:1121–1131CrossRefGoogle Scholar
  8. 8.
    Farajzadeh R, Salimi H, Zitha PLJ, Bruining H (2007) Numerical simulation of density-driven natural convection in porous media with application for CO2 injection projects. Int J Heat Mass Transf 50:5054–5064CrossRefGoogle Scholar
  9. 9.
    Yang C, Gu Y (2006) Accelerated mass transfer of CO2 in reservoir brine due to density-driven natural convection at high pressures and elevated temperatures. Ind Eng Chem 45:2430–2436CrossRefGoogle Scholar
  10. 10.
    Lindeberg EGB, Wessel-Berg D (1996) Vertical convection in an aquifer column under a gas cap of CO2. Energy Convers Manag 38:229–234CrossRefGoogle Scholar
  11. 11.
    Hassanzadeh H, Pooladi-Darvish M, Keith D (2005) Modeling of convective mixing in CO2 storage. J Can Pet Technol 44:43–51CrossRefGoogle Scholar
  12. 12.
    Ennis-King J, Paterson L (2005) Role of convective mixing in the long-term storage of carbon dioxide in deep saline formations. SPE J 10(3):349–356CrossRefGoogle Scholar
  13. 13.
    Ennis-King J, Preston L, Paterson L (2005) Onset of convection in anisotropic porous media subject to a rapid change in boundary conditions. J Phys Fluids 17:84107–84115CrossRefGoogle Scholar
  14. 14.
    Riaz A, Hesse M, Tchelepi A, Orr FM (2006) Onset of convection in a gravitationally unstable diffusive boundary layer in porous medium. J Fluid Mech 548:87–111MathSciNetCrossRefGoogle Scholar
  15. 15.
    Hassanzadeh H, Pooladi-Darvish M, Keith D (2006) Stability of a fluid in a horizontal saturated porous layer: effect of non-linear concentration profile, initial and initial conditions. Transp Porous Media 65:193–211MathSciNetCrossRefGoogle Scholar
  16. 16.
    Hassanzadeh H, Pooladi-Darvish M, Keith D (2008) The effect of natural flow of aquifers and associated dispersion on the onset of buoyancy-driven convection in a saturated porous medium. AIChE 55:475–485CrossRefGoogle Scholar
  17. 17.
    Javaheri M, Abedi J, Hassanzadeh H (2009) Onset of convection in CO2 sequestration in deep inclined saline aquifers. J Can Pet Technol 48(8):22–27CrossRefGoogle Scholar
  18. 18.
    Ennis-King J, Paterson L (2002) Rate of dissolution due to convective mixing in the underground storage of carbon dioxide. Paper presented at the 6th International conference on greenhouse gas control Technologies Kyoto, JapanGoogle Scholar
  19. 19.
    Ghesmat K, Hassanzadeh H, Abedi J (2011) The impact of geochemistry on convective mixing in a gravitationally unstable diffusive boundary layer in porous media: CO2 storage in saline aquifers. J Fluid Mech 673:480–512CrossRefGoogle Scholar
  20. 20.
    Aziz K, Settari A (1979) Petroleum reservoir simulation. Elsevier Applied Science Publishers, LondonGoogle Scholar
  21. 21.
    Horton CW, Rogers FT (1945) Convection currents in porous media. J Appl Phys 20:367–369CrossRefGoogle Scholar
  22. 22.
    Lapwood E (1948) Convection of a fluid in a porous medium. Proc Camb Philos Soc 44:508–521MathSciNetCrossRefGoogle Scholar
  23. 23.
    Burnett R, Frind E (1987) Simulation of contaminant transport in three dimensions 1: the alternate direction Galerkin technique. Water Resour Res 23:689–694Google Scholar
  24. 24.
    Burnett R, Frind E (1987) Simulation of contaminant transport in three dimensions 2 dimensionality effects. Water Resour Res 23:695–705CrossRefGoogle Scholar
  25. 25.
    Carslaw H, Jaeger J (1959) Conduction of heat in solids. University Press, OxfordzbMATHGoogle Scholar
  26. 26.
    Elder JW (1968) The unstable thermal interface. J Fluid Mech 32:69–96CrossRefGoogle Scholar
  27. 27.
    Wooding RA (1969) Growth of fingers at an unstable diffusing interface in a porous medium or Hele-Shaw cell. J Fluid Mech 39:477–495CrossRefGoogle Scholar
  28. 28.
    Bird R, Stewart W, Lightfoot E (1960) Transport phenomena. Wiley, New YorkGoogle Scholar
  29. 29.
    Horton C, Rogers FJ (1945) Convection currents in porous media. Appl Phys 20:367–369CrossRefGoogle Scholar
  30. 30.
    Xu X, Chen S, Zhang Z (2006) Convective stability analysis of the longterm storage of carbon dioxide in deep saline aquifers. Adv Water Resour 29:397–497CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Reza Azin
    • 1
    Email author
  • Seyed Mostafa Jafari Raad
    • 1
  • Shahriar Osfouri
    • 2
  • Rooholla Fatehi
    • 3
  1. 1.Department of Petroleum Engineering, Faculty of Oil, Gas, and Petrochemical EngineeringPersian Gulf UniversityBushehrIran
  2. 2.Department of Chemical Engineering, Faculty of Oil, Gas, and Petrochemical EngineeringPersian Gulf UniversityBushehrIran
  3. 3.Department of Mechanical Engineering, Faculty of EngineeringPersian Gulf UniversityBushehrIran

Personalised recommendations