Computational Geosciences

, 13:469 | Cite as

Vertical equilibrium with sub-scale analytical methods for geological CO2 sequestration

Original paper


Large-scale implementation of geological CO2 sequestration requires quantification of risk and leakage potential. One potentially important leakage pathway for the injected CO2 involves existing oil and gas wells. Wells are particularly important in North America, where more than a century of drilling has created millions of oil and gas wells. Models of CO2 injection and leakage will involve large uncertainties in parameters associated with wells, and therefore a probabilistic framework is required. These models must be able to capture both the large-scale CO2 plume associated with the injection and the small-scale leakage problem associated with localized flow along wells. Within a typical simulation domain, many hundreds of wells may exist. One effective modeling strategy combines both numerical and analytical models with a specific set of simplifying assumptions to produce an efficient numerical–analytical hybrid model. The model solves a set of governing equations derived by vertical averaging with assumptions of a macroscopic sharp interface and vertical equilibrium. These equations are solved numerically on a relatively coarse grid, with an analytical model embedded to solve for wellbore flow occurring at the sub-gridblock scale. This vertical equilibrium with sub-scale analytical method (VESA) combines the flexibility of a numerical method, allowing for heterogeneous and geologically complex systems, with the efficiency and accuracy of an analytical method, thereby eliminating expensive grid refinement for sub-scale features. Through a series of benchmark problems, we show that VESA compares well with traditional numerical simulations and to a semi-analytical model which applies to appropriately simple systems. We believe that the VESA model provides the necessary accuracy and efficiency for applications of risk analysis in many CO2 sequestration problems.


Geological CO2 sequestration Wellbore leakage Vertical equilibrium method Sharp interface models Numerical simulation Sub-scale analytical methods 


  1. 1.
    Intergovernmental Panel on Climate Change (IPCC): Climate change 2007: the physical science basis. Fourth assessment report, IPCC Secretariat, Geneva, Switzerland (2007)Google Scholar
  2. 2.
    Socolow, R.H.: Can we bury global warming? Sci. Am. 293(1), 49–55 (2005)CrossRefGoogle Scholar
  3. 3.
    Pacala, S., Socolow, R.: Stabilization wedges: solving the climate problem for the next 50 years with current technology. Sci. 305, 968–972 (2004). doi:10.1126/science.1100103 CrossRefGoogle Scholar
  4. 4.
    Bachu, S.: CO2 storage in geological media: role, means, status and barriers to deployment. Prog. Energy Combust. Sci. 3(2), 254–273 (2008). doi:10.1016/j.pecs.2007.10.001 CrossRefGoogle Scholar
  5. 5.
    Bachu, S.: Sequestration of CO2 in geological media in response to climate change: road map for site selection using the transform of the geological space into the CO2 phase space. Energy Convers. Manag. 43(1), 87–102 (2003). doi:10.1016/S0196-8904(01)00009-7 CrossRefGoogle Scholar
  6. 6.
    Nordbotten, J.M., Celia, M.A., Bachu, S.: Analytical solutions for leakage rates through abandoned wells. Water Resour. Res. 40(4), W04204 (2004). doi:10.1029/2003WR002997 CrossRefGoogle Scholar
  7. 7.
    Celia, M.A., Bachu, S., Nordbotten, J.M., Kavetski, D., Gasda, S.E.: A risk assessment tool to quantify CO2 leakage through wells in mature sedimentary basins. 8th International Greenhouse Gas Control Technologies (2006)Google Scholar
  8. 8.
    Bachu, S., Celia, M.A.: Assessing the potential for CO2 leakage, particularly through wells, from geological storage sites. In: McPherson, B.J.O.L., Sundquis, E. (eds.) The Science of CO2 Storage, AGU monograph, in press. American Geophysical Union, Washington, DC (2009)Google Scholar
  9. 9.
    Koide, H.G., Tazaki, Y., Noguchi, Y., Nakayama, S., Iijima, M., Ito, K., Shindo, Y.: Subterranean containment and long-term storage of carbon dioxide in unused aquifers and in depleted natural gas reservoirs. Energy Convers. Manag. 33(5–8), 619–626 (1992). doi:10.1016/0196-8904(92)90064-4 CrossRefGoogle Scholar
  10. 10.
    Holloway, S.: Storage of fossil fuels-derived carbon dioxide beneath the surface of the earth. Annu. Rev. Energy Environ. 26, 145–166 (2001). doi:10.1146/ CrossRefGoogle Scholar
  11. 11.
    Bruant, R.G., Guswa, A.J., Celia, M.A., Peters, C.A.: Safe storage of CO2 in deep saline aquifers. Environ. Sci. Technol. 36(17), 240A–245A (2002). doi:10.1021/es0223325 CrossRefGoogle Scholar
  12. 12.
    Intergovernmental Panel on Climate Change (IPCC): Special report on carbon dioxide capture and storage. Cambridge University Press, Cambridge (2005)Google Scholar
  13. 13.
    Energy Information Administration (EIA): Annual Energy Review 2005, DOE/EIA-0384 (2005)Google Scholar
  14. 14.
    Gasda, S.E., Bachu, S., Celia, M.A.: Spatial characterization of the location of potentially leaky wells penetrating a deep saline aquifer in a mature sedimentary basin. Environ. Geol. 46, 707–720 (2004). doi:10.1007/s00254-004-1073-5 CrossRefGoogle Scholar
  15. 15.
    Gasda, S.E., Nordbotten, J.M., Celia, M.A.: Determining effective wellbore permeability from a field pressure test: a numerical analysis of detection limits. Environ. Geol. 54(6), 1207–1215 (2007). doi:10.1007/s00254-007-0903-7 CrossRefGoogle Scholar
  16. 16.
    White, M.D., Oostrom, M.: STOMP, Subsurface Transport Over Multiple Phases. Pacific Northwest National Laboratory, Report PNNL-11218, Richland, WA (1997)Google Scholar
  17. 17.
    Pruess, K., Oldenburg, C., Moridis, G.: TOUGH2 User’s Guide, Version 2.0, Lawrence Berkeley National Laboratory Report LBNL-43134. Berkeley, CA (1999)Google Scholar
  18. 18.
    Pruess, K., García, J., Kovscek, T., Oldenburg, C., Rutqvist, J., Steefel, C., Xu, T.: Code intercomparison builds confidence in numerical simulation models for geologic disposal of CO2. Energy 29(9–10), 1431–1444 (2004). doi:10.1016/ CrossRefGoogle Scholar
  19. 19.
    Schlumberger: Eclipse Technical Description 2007.1 (2007)Google Scholar
  20. 20.
    Nordbotten, J.M., Celia, M.A., Bachu, S.: Injection and storage of CO2 in deep saline aquifers: analytical solution for CO2 plume evolution during injection. Transp. Porous Media 58(3), 339–360 (2005). doi:10.1007/s11242-004-0670-9 CrossRefGoogle Scholar
  21. 21.
    Nordbotten, J.M., Celia, M.A., Bachu, S.: Semianalytical solution for CO2 leakage through an abandoned well. Environ. Sci. Technol. 39(2), 602–611 (2005). doi:10.1021/es035338i CrossRefGoogle Scholar
  22. 22.
    Nordbotten, J.M., Kavetski, D., Celia, M.A., Bachu, S.: A semi-analytical model estimating leakage associated with CO2 storage in large-scale multi-layered geological systems with multiple leaky wells. Environ. Sci. Technol. 43(3), 743–749 (2009)CrossRefGoogle Scholar
  23. 23.
    Hesse, M.A., Orr, F.M., Jr., Tchelepi, H.A.: Gravity currents with residual trapping. J. Fluid Mech. 611, 35–60 (2008). doi:10.1017/S002211200800219X MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Nordbotten, J.M., Celia, M.A.: An improved analytical solution for interface upconing around a well. Water Resour. Res. 46(8), W08433 (2006). doi:10.1029/2005WR004738 CrossRefGoogle Scholar
  25. 25.
    Nordbotten, J.M., Celia, M.A.: Similarity solutions for fluids injected into confined aquifers. J. Fluid Mech. 561, 307–327 (2006). doi:10.1017/S0022112006000802 MATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Bear, J.: Dynamics of Fluids in Porous Media. Elsevier, New York (1972)Google Scholar
  27. 27.
    Bear, J.: Hydraulics of Groundwater. McGraw-Hill, New York (1979)Google Scholar
  28. 28.
    Lake, L.: Enhanced Oil Recovery. Prentice Hall, Upper Saddle River (1989)Google Scholar
  29. 29.
    Coats, K.H., Dempsey, J.R., Henderson, J.H.: The use of vertical equilibrium in two-dimensional simulation of three-dimensional reservoir performance. Soc. Pet. Eng. J. 11(1), 63–71 (1971). doi:10.2118/2797-PA Google Scholar
  30. 30.
    Dietz, D.N.: A theoretical approach to the problem of encroaching and by-passing edge water. In: Proceedings Akademie van Wetenschappen, pp. 83–94 (1953)Google Scholar
  31. 31.
    Juanes, R., Spiteri, E.J., Orr, F.M., Jr., Blunt, M.J.: Impact of relative permeability hysteresis on geological CO2 storage. Water Resour. Res. 42, W12418 (2006). doi:10.1029/2005WR004806 CrossRefGoogle Scholar
  32. 32.
    Bachu, S., Bennion, B.: Effects of in-situ conditions on relative permeability characteristics of CO2–brine systems. Environ. Geol. 54, 1707–1722 (2008). doi:10.1007/s00254-007-0946-9 CrossRefGoogle Scholar
  33. 33.
    Peaceman, D.W.: Interpretation of wellblock pressures in numerical reservoir simulation. Soc. Pet. Eng. J. 6, 183–194 (1978)Google Scholar
  34. 34.
    Muskat, M.: Physical Principles of Oil Production. McGraw-Hill, New York (1949)Google Scholar
  35. 35.
    Class, H., Ebigbo, A., Helmig, R., Dahle, H., Nordbotten, J.M., Celia, M.A., Audigane, P., Darcis, M., Ennis-King, J., Fan, Y., Flemisch, B., Gasda, S., Krug, S., Labregere, D., Min, J., Sbai, A., Thomas, S., Trenty, L.: A benchmark study on problems related to CO2 storage in geologic formations. Comput. Geosci. (2009; this issue)Google Scholar
  36. 36.
    Eigestad, G.T., Dahle, H.K., Hellevang, B., Johansen, W.T., Riis, F., Øian, E.: Geological Modeling and Simulation of CO2 injection in the Johansen Formation. Comput. Geosci. (2009; this issue)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Environmental Sciences and EngineeringUniversity of North Carolina at Chapel HillChapel HillUSA
  2. 2.Department of MathematicsUniversity of BergenBergenNorway
  3. 3.Civil and Environmental EngineeringPrinceton UniversityPrincetonUSA

Personalised recommendations