Computational Geosciences

, Volume 20, Issue 3, pp 623–635 | Cite as

A generalized cubic equation of state with application to pure CO2 injection in aquifers

  • Ivar Aavatsmark
  • Bawfeh Kingsley Kometa
  • Sarah E. Gasda
  • Tor Harald Sandve
  • Halvor Møll Nilsen


A generalized cubic equation of state is given. The Peng-Robinson and the Soave-Redlich-Kwong equations are special cases of this equation. The generalized equation of state is precisely as simple and computationally efficient as these classical equations. Through comparison with the Span-Wagner equation for CO 2, we obtain an improved density accuracy in predefined temperature-pressure domains. The generalized equation is then verified through two relevant examples of CO 2 injection and migration. Comparisons are made with other standard cubic EOS in order to show the range of solutions obtained with less accurate EOS.


Equation of state Carbon dioxide CCS 


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  1. 1.
    Aavatsmark, I.: Mathematische Einführung in die Thermodynamik der Gemische. Akademie Verlag, Berlin (1995)Google Scholar
  2. 2.
    Abbott, M.M.: Cubic equations of state. AIChE J. 19(3), 596–601 (1973)CrossRefGoogle Scholar
  3. 3.
    Adachi, Y., Lu, B.C.-Y., Sugie, H.: A four parameter equation of state. Fluid Phase Equilibr. 11, 29–48 (1983)CrossRefGoogle Scholar
  4. 4.
    Altunin, V.V.: Teplofizičeskie svojstva dvuokisi ugleroda. Moskva, Izdatel’stvo standartov (1975)Google Scholar
  5. 5.
    Bachu, S.: Screening and ranking of sedimentary basins for sequestration of CO2 in geological media in response to climate change. Environ. Geol. 44, 277–289 (2003)CrossRefGoogle Scholar
  6. 6.
    Bell, I.H., Wronski, J., Quoilin, S., Lemort, V.: Pure and pseudo-pure fluid thermophysical property evaluation and the open-source thermophysical property library. CoolProp. Ind. Eng. Chem. Res. 53(6), 2498–2508 (2014)CrossRefGoogle Scholar
  7. 7.
    Bielinski, A.: Numerical simulation of CO2 sequestration in geological formations. PhD diss, University of Stuttgart, Germany (2006).
  8. 8.
    Class, H., Ebigbo, A., Helmig, R., Dahle, H.K., Nordbotten, J.M., Celia, M.A., Audigane, P., Darcis, M., Ennis-King, J., Fan, Y., Flemisch, B., Gasda, S.E., Jin, M., Krug, S., Labregere, D., Naderi Beni, A., Pawar, R.J., Sbai, A., Thomas, S.G., Trenty, L., Wei, L.: A benchmark study on problems related to CO2 storage in geologic formations. Comput. Geosci. 13(4), 409–434 (2009)CrossRefGoogle Scholar
  9. 9.
    Edmister, W.C., Lee, B.I.: Applied Hydrocarbon Thermodynamics. I. Gulf Publishing Company, Houston (1984)Google Scholar
  10. 10.
    Eiken, O., Ringrose, P., Hermanrud, C., Nazarian, B., Torp, T.A., Hier, L.: Lessons learned from 14 years of CCS operations: Sleipner. In Salah and Snøhvit. Energy Procedia, 4 (2011)Google Scholar
  11. 11.
    Fenghour, A., Wakeham, W.A., Vesovic, V.: The viscosity of carbon dioxide. J. Phys. Chem. Ref. Data 27(1), 31–44 (1998)CrossRefGoogle Scholar
  12. 12.
    Flemisch, B., Darcis, M., Erbertseder, K., Faigle, B., Lauser, A., Mosthaf, K., Müthing, S., Nuske, P., Tatomir, A., Wolff, M., Helmig, R.: DuMu x: DUNE for multi-{phase, component, scale, physics,...} flow and transport in porous media. Adv. Water Resour. 34 (9), 1102–1112 (2011)CrossRefGoogle Scholar
  13. 13.
    Fletcher, R.: A modified Marquardt subroutine for non-linear least squares. Technical Report AERE - R 6799, Atomic Energy Research Establishment, Harwell (1971)Google Scholar
  14. 14.
    Gasda, S.E., Nilsen, H.M., Dahle, H.K.: Upscaled models for CO2 migration in geological formations with structural heterogeneity. In: Proceedings of 13th European Conference on the Mathematics of Oil Recovery. Biarritz (2012)Google Scholar
  15. 15.
    Lie, K.A., Krogstad, S., Ligaarden, I.S., Natvig, J.R., Nilsen, H.M., Skaflestad, B.: Open-source MATLAB implementation of consistent discretisations on complex grids. Comput. Geosci. 16(2), 297–322 (2012)CrossRefGoogle Scholar
  16. 16.
    Nordbotten, J.M., Flemisch, B., Gasda, S.E., Nilsen, H.M., Fan, Y., Pickup, G.E., Wiese, B., Celia, M.A., Dahle, H.K., Eigestad, G.T., Pruess, K.: Uncertainties in practical simulation of CO2 storage. Int. J. Greenhouse Gas Control 9, 234–242 (2012)CrossRefGoogle Scholar
  17. 17.
    Pedersen, K.S., Milter, J., Sørensen, H.: Cubic equations of state applied to HT/HP and highly aromatic fluids. SPE J. 9, 186–192 (2004)CrossRefGoogle Scholar
  18. 18.
    Péneloux, A., Rauzy, E., Frèze, R.: A consistent correction for Redlich-Kwong-Soave volumes. Fluid Phase Equilibr. 8(1), 7–23 (1982)CrossRefGoogle Scholar
  19. 19.
    Peng, D.Y., Robinson, D.B.: A new two-constant equation of state. Ind. Eng. Chem. Fundam. 15(1), 59–64 (1976)CrossRefGoogle Scholar
  20. 20.
    Pruess, K., Oldenburg, C., Moridis, G.: TOUGH2 User’s guide, Version 2. Technical Report LBNL-43134, Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA (2012)Google Scholar
  21. 21.
    Redlich, O., Kwong, J.N.S.: On the thermodynamics of solutions. V: an equation of state. Fugacities of gaseous solutions. Chem. Rev. 44(1), 233–244 (1949)CrossRefGoogle Scholar
  22. 22.
    Robinson, D.B., Peng, D.Y.: The characterization of heptanes and heavier fractions for the GPA Peng-Robinson programs. Report RR-28, Gas Processors Association, Tulsa (1978)Google Scholar
  23. 23.
    Soave, G.: Equilibrium constants from a modified Redlich-Kwong equation of state. Chem. Eng. Sci. 27(6), 1197–1203 (1972)CrossRefGoogle Scholar
  24. 24.
    Span, R., Wagner, W.: A new equation of state for carbon dioxide covering the fluid region from the triple-point temperature to 1100 K at pressures up to 800 MPa. J. Phys. Chem. Ref. Data 25(6), 1509–1596 (1996)CrossRefGoogle Scholar
  25. 25.
    Spycher, N., Pruess, K.: A phase-partitioning model for CO2-brine mixtures at elevated temperatures and pressures: application to CO2-enhanced geothermal systems. Transp. Porous Med. 82(1), 173–196 (2010)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Ivar Aavatsmark
    • 1
  • Bawfeh Kingsley Kometa
    • 2
  • Sarah E. Gasda
    • 1
  • Tor Harald Sandve
    • 3
  • Halvor Møll Nilsen
    • 4
  1. 1.Uni Research CIPRBergenNorway
  2. 2.Department of MathematicsUniversity of BergenBergenNorway
  3. 3.IRISBergenNorway
  4. 4.SINTEF ICTOsloNorway

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