Skip to main content
SpringerLink
Log in

Visualization and Numerical Investigation of Natural Convection Flow of CO2 in Aqueous and Oleic Systems

  • Chapter
  • First Online:
Mechanisms for CO2 Sequestration in Geological Formations and Enhanced Gas Recovery

Part of the book series: Springer Theses ((Springer Theses))

Abstract

Optimal storage of carbon dioxide (CO2) in aquifers requires dissolution in the aqueous phase. Nevertheless, transfer of CO2 from the gas phase to the aqueous phase would be slow if it were only driven by diffusion. Dissolution of CO2 in water forms a mixture that is denser than the original water or brine. This causes a local density increase, which induces natural convection currents accelerating the rate of CO2 dissolution. The same mechanism also applies to carbon dioxide enhanced oil recovery. This study compares numerical models with a set of high pressure visual experiments, based on the Schlieren technique, in which we observe the effect of gravity-induced fingers when sub- and super-critical CO2 at in situ pressures and temperatures is brought above the liquid, i.e., water, brine or oil. A short but comprehensive description of the Schlieren set-up and the transparent pressure cell is presented. The Schlieren set-up is capable of visualizing instabilities in natural convection flows; a drawback is that it can only be practically applied in bulk flow, i.e., in the absence of a porous medium. All the same many features that occur in a porous medium also occur in bulk, e.g., unstable gravity fingering. The experiments show that natural convection currents are weakest in highly concentrated brine and strongest in oil, due to the higher and lower density contrasts respectively. Therefore, the set-up can screen aqueous salt solutions or oil for the relative importance of natural convection flows. The Schlieren pattern consists of a dark region near the equator and a lighter region below it. The dark region indicates a region where the refractive index increases downward, either due to the presence of a gas liquid interface, or due to the thin diffusion layer, which also appears in numerical simulations. The experiments demonstrate the initiation and development of the gravity induced fingers. The experimental results are compared to numerical results. It is shown that natural convection effects are stronger in cases of high density differences. However, due to numerical limitations, the simulations are characterized by much larger fingers.

Published in: Petroleum Science and Engineering volume 122, October 2014, pages 230–239 and COMSOL 2012.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Abbreviations

C :

concentration (mol/m3)

C g :

concentration (mol/m3)

D :

molecular diffusion coefficient, (m2/ s)

D g :

molecular diffusion coefficient in gas phase, (m2/ s)

K :

permeability, mD

β :

volumetric expansion coefficient (m3/mol)

V :

velocity (m/s)

P :

pressure (bar)

t :

time

ν :

kinematic viscosity (m2/s)

\( \rho \) :

density (kg/m3)

A :

the area exposed to CO2 (m2)

μ :

viscosity of the solvent (kg.m.s)

g :

acceleration due to gravity (kg/m)

Ra :

Rayleigh number

K H :

Henry’s constant

n :

refractive index

n w :

refractive index of pure water

\( n_{CO_{2}} \) :

refractive index of pure CO2

\( \rho_{w}^{(0)} \) :

density of pure water at the reference temperature(kg/m3)

α :

polarizability

L :

Avogadro’s number

\( m_{w,CO_{2}} \) :

molality of carbon dioxide in the water phase(mol/kg)

\( \gamma_{w,CO_{2}} \) :

activity coefficient

\( f_{g,CO_{2}(g)} \) :

fugacity of carbon dioxide in the gas phase(bar)

0 :

reference value of the quantity

g :

gas

i :

initial value

w :

water

References

  1. Eftekhari, A. A., Van Der Kooi, H., & Bruining, H. (2012). Exergy analysis of underground coal gasification with simultaneous storage of carbon dioxide. Energy, 45(1), 729–745.

    Article  Google Scholar 

  2. Van der Meer, L. (1992). Investigations regarding the storage of carbon dioxide in aquifers in the Netherlands. Energy Conversion and Management, 33(5), 611–618.

    Article  Google Scholar 

  3. Gmelin, L. (1973). Gmelin Handbuch der anorganischen Chemie, 8. Auflage. Kohlenstoff, Teil C3, Verbindungen. ISBN 3-527-81419-1.

    Google Scholar 

  4. Bachu, S., Gunter, W., & Perkins, E. (1994). Aquifer disposal of CO2: Hydrodynamic and mineral trapping. Energy Conversion and Management, 35(4), 269–279.

    Article  Google Scholar 

  5. Class, H., et al. (2009). A benchmark study on problems related to CO2 storage in geologic formations. Computational Geosciences, 13(4), 409–434.

    Article  MATH  Google Scholar 

  6. Elder, J. (1968). The unstable thermal interface. Journal of Fluid Mechanics, 32(1), 69–96.

    Article  Google Scholar 

  7. Ennis-King, J., Preston, I., & Paterson, L. (2005). Onset of convection in anisotropic porous media subject to a rapid change in boundary conditions. Physics of Fluids 17(8), 084107–084107-15.

    Google Scholar 

  8. Foster, T. D. (1965). Onset of convection in a layer of fluid cooled from above. Physics of Fluids, 8, 1770.

    Article  Google Scholar 

  9. Gasda, S. E. (2010). Numerical models for evaluating CO2 storage in deep saline aquifers: Leaky wells and large-scale geological features. Ph.D. Thesis. http://arks.princeton.edu/ark:/88435/dsp01j098zb09n.

  10. Nordbotten, J. M., & Celia, M. A. (2011). Geological Storage of CO 2 : Modeling Approaches for Large-Scale Simulation2011: Wiley. com.

    Google Scholar 

  11. Nordbotten, J. M., Celia, M. A., & Bachu, S. (2005). Injection and storage of CO2 in deep saline aquifers: Analytical solution for CO2 plume evolution during injection. Transport in Porous Media, 58(3), 339–360.

    Article  Google Scholar 

  12. Ranganathan, P., et al. (2012). Numerical simulation of natural convection in heterogeneous porous media for CO2 geological storage. Transport in Porous Media, 95(1), 25–54.

    Article  Google Scholar 

  13. Riaz, A., et al. (2006). Onset of convection in a gravitationally unstable diffusive boundary layer in porous media. Journal of Fluid Mechanics, 548, 87–111.

    Article  MathSciNet  Google Scholar 

  14. Walker, K. L., & Homsy, G.M. (1978). Convection in a porous cavity. Journal of Fluid Mechanics, 87(Part 3), 449–474.

    Google Scholar 

  15. Van Duijn, C., Pieters, G., & Raats, P. (2004). Steady flows in unsaturated soils are stable. Transport in Porous Media, 57(2), 215–244.

    Article  MathSciNet  Google Scholar 

  16. Meulenbroek, B., Farajzadeh, R., & Bruining, H. (2013). The effect of interface movement and viscosity variation on the stability of a diffusive interface between aqueous and gaseous CO2. Physics of Fluids (1994-present) 25(7), 074103.

    Google Scholar 

  17. Myint, P. C., & Firoozabadi, A. (2013). Onset of convection with fluid compressibility and interface movement. Physics of Fluids, 25, 094105.

    Article  Google Scholar 

  18. Lapwood, E. (1948). Convection of a fluid in a porous medium. Proceedings of the Cambridge.

    Google Scholar 

  19. Weir, G., White, S., & Kissling, W. (1995). Reservoir storage and containment of greenhouse gases. Energy Conversion and Management, 36(6), 531–534.

    Article  Google Scholar 

  20. Farajzadeh, R., et al. (2007). Mass transfer of CO2 into water and surfactant solutions. Petroleum Science and Technology, 25(12), 1493–1511.

    Article  Google Scholar 

  21. Farajzadeh, R., et al. (2007). Numerical simulation of density-driven natural convection in porous media with application for CO2 injection projects. International Journal of Heat and Mass Transfer, 50(25), 5054–5064.

    Article  MATH  Google Scholar 

  22. Farajzadeh, R., Zitha, P. L., & Bruining, J. (2009). Enhanced mass transfer of CO2 into water: Experiment and modeling. Industrial and Engineering Chemistry Research, 48(13), 6423–6431.

    Article  Google Scholar 

  23. 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. Industrial and Engineering Chemistry Research, 45(8), 2430–2436.

    Article  Google Scholar 

  24. Nazari Moghaddam, R., & Rostami, B. (2012). Reply to the “Comments on the paper ‘Quantification of density-driven natural convection for dissolution mechanism in CO2 sequestration’ by R. Nazari Moghaddam et al. (2011)”. Transport in Porous Media, 93(1), 175–178.

    Google Scholar 

  25. Okhotsimskii, A., & Hozawa, M. (1998). Schlieren visualization of natural convection in binary gas–liquid systems. Chemical Engineering Science, 53(14), 2547–2573.

    Article  Google Scholar 

  26. Kneafsey, T. J., & Pruess, K. (2010). Laboratory flow experiments for visualizing carbon dioxide-induced, density-driven brine convection. Transport in Porous Media, 82(1), 123–139.

    Article  Google Scholar 

  27. Settles, G. S. (2001). Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media. 2001. Berlin: Springer.

    Google Scholar 

  28. Parkhurst, D. L., & Appelo, C. (2013). Description of input and examples for PHREEQC version 3- A computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations. US Geological Survey Techniques and Methods, Book 6, Modeling Techniques, 2013.

    Google Scholar 

  29. Randall, M., & Failey, C. F. (1927). The Activity Coefficient of Gases in Aqueous Salt Solutions. Chemical Reviews, 4(3), 271–284.

    Article  Google Scholar 

  30. Feynman, R., Leighten, R., & Sands, M. (1965). The Feynman Lectures on Physics. Reading: Addison-Wesley Pub. Comp.

    Google Scholar 

  31. Song, Y., et al. (2003). Measurement on CO2 Solution Density by Optical Technology. Journal of Visualization, 6(1), 41–51.

    Article  Google Scholar 

  32. Subedi, D., et al. (2006). Study of temperature and concentration dependence of refractive index of liquids using a novel technique. Kathmandu University Journal of Science, Engineering and Technology, 2(1), 1–7.

    Google Scholar 

  33. Mosteiro, L., et al. (2001). Density, speed of sound, refractive index and dielectric permittivity of (diethyl carbonate+ n-decane) at several temperatures. The Journal of Chemical Thermodynamics, 33(7), 787–801.

    Article  Google Scholar 

  34. Bao, B., et al. (2012). Detecting Supercritical CO2 in Brine at Sequestration Pressure with an Optical Fiber Sensor. Environmental Science and Technology, 47(1), 306–313.

    Article  Google Scholar 

  35. Gatej, A., Wasselowski, J., & Loosen, P. (2012). Using adaptive weighted least squares approximation for coupling thermal and optical simulation. Applied Optics, 51(28), 6718–6725.

    Article  Google Scholar 

  36. Rimmer, M.P. (1983). Ray tracing in inhomogeneous media. in 1983 International Technical Conference/Europe. International Society for Optics and Photonics.

    Google Scholar 

  37. Sharma, A., Kumar, D. V., & Ghatak, A. K. (1982). Tracing rays through graded-index media: A new method. Applied Optics, 21(6), 984–987.

    Article  Google Scholar 

  38. van der Net, A., et al. (2007). Simulating and interpretating images of foams with computational ray-tracing techniques. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 309(1), 159–176.

    Google Scholar 

  39. Wu, Z. S., et al. (1997). Improved algorithm for electromagnetic scattering of plane waves and shaped beams by multilayered spheres. Applied Optics, 36(21), 5188–5198.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. TU Delft, Delft, The Netherlands

    Roozbeh Khosrokhavar

Authors
  1. Roozbeh Khosrokhavar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roozbeh Khosrokhavar .

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Khosrokhavar, R. (2016). Visualization and Numerical Investigation of Natural Convection Flow of CO2 in Aqueous and Oleic Systems. In: Mechanisms for CO2 Sequestration in Geological Formations and Enhanced Gas Recovery. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-23087-0_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-23087-0_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23086-3

  • Online ISBN: 978-3-319-23087-0

  • eBook Packages: EnergyEnergy (R0)

Publish with us

Policies and ethics

Search

Navigation