Transport in Porous Media

, Volume 89, Issue 3, pp 383–397 | Cite as

Pressure Buildup During CO2 Injection into a Closed Brine Aquifer

  • Simon A. MathiasEmail author
  • Gerardo J. González Martínez de Miguel
  • Kate E. Thatcher
  • Robert W. Zimmerman


CO2 injected into porous formations is accommodated by reduction in the volume of the formation fluid and enlargement of the pore space, through compression of the formation fluids and rock material, respectively. A critical issue is how the resulting pressure buildup will affect the mechanical integrity of the host formation and caprock. Building on an existing approximate solution for formations of infinite radial extent, this article presents an explicit approximate solution for estimating pressure buildup due to injection of CO2 into closed brine aquifers of finite radial extent. The analysis is also applicable for injection into a formation containing multiple wells, in which each well acts as if it were in a quasi-circular closed region. The approximate solution is validated by comparison with vertically averaged results obtained using TOUGH2 with ECO2N (where many of the simplifying assumptions are relaxed), and is shown to be very accurate over wide ranges of the relevant parameter space. The resulting equations for the pressure distribution are explicit, and can be easily implemented within spreadsheet software for estimating CO2 injection capacity.


CO2 injection Forchheimer’s equation Closed formation Pressure buildup 

List of symbols


Formation plan area [L2]


Forchheimer parameter [L−1]


Relative Forchheimer parameter [-]


Compressibility of CO2 [M−1 LT2]


Compressibility of geological formation [M−1 LT2]


Compressibility of brine [M−1 LT2]


CO2 brine interface elevation [L]

hD = h/H

Dimensionless interface elevation [-]


Formation thickness [L]


Permeability [L2]


Relative permeability [-]


Mass injection rate [MT−1]


Fluid pressure [ML−1 T−2]

pD = 2π Hρokrkp/M0μo

Dimensionless pressure [-]


CO2 flux [LT−1]

qoD = 2π Hrwρoqo/M0

Dimensionless CO2 flux [-]


Brine flux [LT−1]

qwD = 2π Hrwρoqw/M0

Dimensionless brine flux [-]


Radial distance [L]


Radial extent of reservoir [L]

rcD = rc/rw

Dimensionless radial extent of reservoir [-]

rD = r/rw

Dimensionless radius [-]


Well radius [L]


Residual brine saturation [-]


Time [T]

\({t_{c{D}}= \alpha r_{c{D}}^2 / 2.246\gamma}\)

Dimensionless time at which the pressure disturbance meets the reservoir boundary [-]

\({t_{D}=M_0t/2\pi(1-S_{r})\phi Hr_{w}^2\rho_{o}}\)

Dimensionless time [-]

α = M0μo(cr + cw)/2π(1 − Sr) okrk

Dimensionless compressibility [-]

β = M0krkbrb/2π Hrwμo

Dimensionless Forchheimer parameter [-]

γ = μo/krμw

Viscosity ratio [-]


Normalized fluid compressibility difference [-]


Viscosity of CO2 [ML−1 T−1]


Viscosity of brine [ML−1 T−1]


Density of CO2 [ML−3]


Density of brine [ML−3]

σ = brρo/ρw

Density ratio [-]


Porosity [-]


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  1. Bear J.: Hydraulics of Groundwater. McGraw-Hill, New York (1979)Google Scholar
  2. Bennion, D.B., Bachu, S.: Drainage and imbibition relative permeability relationships for supercritical CO2/brine and H2S/brine systems in intergranular sandstone, carbonate, shale, and annhydrite rocks. SPE Reserv. Eval. Eng. June, 487–496 (2008)Google Scholar
  3. Birkholzer J.T., Zhou Q., Tsang C.F.: Large-scale impact of CO2 storage in deep saline aquifers: A sensitivity study on pressure response in stratified systems. Int. J. Greenhouse Gas Control 3, 181–194 (2009). doi: 10.1016/j.ijggc.2008.08.002 CrossRefGoogle Scholar
  4. Buckley S.E., Leverett M.C.: Mechanism of fluid displacement in sands. Trans. Am. Inst. Min. Metall. Pet. Eng. 146, 107–116 (1942)Google Scholar
  5. Burton, M., Kumar, N., Bryant, S.L.: Time-dependent injectvity during co2 storage in aquifers. In: SPE/DOE Improved Oil Recovery Symposium held in Tulsa, Oklahoma, USA, 19–23 April (2008). SPE 113937Google Scholar
  6. Chadwick, A., Hodrien, C., Hovorka, S., Mackay, E., Mathias, S., Lovell, B., Kalaydjian, F., Sweeney, G., Benson, S., Dooley, J., Davidson, C.: The realities of storing carbon dioxide—a response to CO2 storage capacity issues raised by Ehlig-Economides & Economides. Technical report, Published by the European Technology Platform for Zero Emission Fossil Fuel Power Plants (ZEP) (2010). doi: 10.1038/npre.2010.4500.1
  7. Dake L.P.: Fundamentals of Reservoir Engineering. 17th Impression. Elsevier, Amsterdam (1978)Google Scholar
  8. Dentz M., Tartakovsky D.M.: Abrupt-interface solution for carbon dioxide injection into porous media. Transp. Porous Media 79, 15–27 (2009). doi: 10.1007/s11242-008-9268-y CrossRefGoogle Scholar
  9. Ehlig-Economides C.A., Economides M.J.: Sequestering carbon dioxide in a closed underground volume. J. Pet. Sci. Eng. 70, 123–130 (2010). doi: 10.1016/j.petrol.2009.11.002 CrossRefGoogle Scholar
  10. Forchheimer P.: Wasserbewegung durch Boden. Z. Ver. Dtsch. Ing 45, 1782–1788 (1901)Google Scholar
  11. Gasda S., Nordbotten J.M., Celia M.A.: Vertical equilibrium with sub-scale analytical methods for geological CO2 sequestration. Comput. Geosci. 13(4), 469–481 (2009). doi: 10.1007/s10596-009-9138-x CrossRefGoogle Scholar
  12. Lu C., Lee S.Y., Han W.S., McPherson B.J., Lichtner P.C.: Comments on “abrupt-interface solution for carbon dioxide injection into porous media” by M. Dentz and D. Tartakovsky. Transp. Porous Media 79, 29–37 (2009). doi: 10.1007/s11242-009-9362-9 CrossRefGoogle Scholar
  13. Mathias S.A., Todman L.C.: Step-drawdown tests and the Forchheimer equation. Water Resour. Res. 46, W07514 (2010). doi: 10.1029/2009WR008635 CrossRefGoogle Scholar
  14. Mathias S.A., Butler A.P., Zhan H.: Approximate solutions for Forchheimer flow to a well. J. Hydraul. Eng. 134(9), 1318–1325 (2008). doi: 10.1061/(ASCE)0733-9429(2008)134:9(1318) CrossRefGoogle Scholar
  15. Mathias S.A., Hardisty P.E., Trudell M.R., Zimmerman R.W.: Screening and selection of sites for CO2 sequestration based on pressure buildup. Int. J. Greenhouse Gas Control 3, 577–585 (2009a). doi: 10.1016/j.ijggc.2009.05.002 CrossRefGoogle Scholar
  16. Mathias, S.A., Hardisty, P.E., Trudell, M.R., Zimmerman, R.W.: Erratum to screening and selection of sites for CO2 sequestration based on pressure buildup [Int. J. Greenhouse Gas Control 3(5) (2009) 577–585]. Int. J. Greenhouse Gas Control 4, 108–109 (2009b). doi: 10.1016/j.ijggc.2009.11.004
  17. Mathias S.A., Hardisty P.E., Trudell M.R., Zimmerman R.W.: Approximate solutions for pressure buildup during CO2 injection in brine aquifers. Transp. Porous Media 79, 265–284 (2009c). doi: 10.1007/s11242-008-9316-7 CrossRefGoogle Scholar
  18. Nordbotten J.M., Celia M.A., Bachu S.: Injection and storage of CO2 in deep saline aquifers: analytic solution for CO2 plume evolution during injection. Transp. Porous Media 58, 339–360 (2005). doi: 10.1007/s11242-004-0670-9 CrossRefGoogle Scholar
  19. Pruess, K., Oldenburg, C.M., Moridis, G.: TOUGH2 user’s guide, version 2.0. Report LBNL-43134, Lawrence Berkeley National Laboratory, Berkeley, CA, USA (1999)Google Scholar
  20. Pruess, K.: ECO2N: A TOUGH2 fluid property module for mixtures of water, NaCl, and CO2. Report LBNL-57952, Lawrence Berkeley National Laboratory, Berkeley, CA, USA (2005)Google Scholar
  21. Rutqvist J., Birkholzer J.T., Tsang C.F.: Coupled reservoir—geomechanical analysis of the potential for tensile and shear failure associated with CO2 injection in multilayered reservoir—caprock systems. Int. J. Rock Mech. Min. Sci. 45, 132–143 (2008). doi: 10.1016/j.ijrmms.2007.04.006 CrossRefGoogle Scholar
  22. Saripalli P., McGrail P.: Semi-analytical approaches to modeling deep well injection of CO2 for geological sequestration. Energy Convers. Manag. 43(2), 185–198 (2002)CrossRefGoogle Scholar
  23. van Genuchten M.Th.: A closed form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44, 892–898 (1980)CrossRefGoogle Scholar
  24. Vilarrasa V., Bolster D., Dentz M., Olivella S., Carrera J.: Effects of CO2 compressibility on CO2 storage in deep saline aquifers. Transp. Porous Media 85, 619–639 (2010). doi: 10.1007/s11242-010-9582-z CrossRefGoogle Scholar
  25. Welge H.J.: A simplified method for computing oil recovery by gas or water drive. Trans. Am. Inst. Min. Metall. Pet. Eng. 195, 91–98 (1952)Google Scholar
  26. Yamamoto, H., Doughty, C.: Investigation of gridding effects for numerical simulations of CO2 geologic sequestration. Int. J. Greenhouse Gas Control (2011). doi: 10.1016/j.ijggc.2011.02.007
  27. Zhou Q., Birkholzer J., Tsang C., Rutqvist J.: A method for quick assessment of CO2 storage capacity in closed and semi-closed saline formations. Int. J. Greenhouse Gas Control 2(4), 626–639 (2008)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Simon A. Mathias
    • 1
    Email author
  • Gerardo J. González Martínez de Miguel
    • 1
    • 2
  • Kate E. Thatcher
    • 1
  • Robert W. Zimmerman
    • 3
  1. 1.Department of Earth SciencesDurham UniversityDurhamUK
  2. 2.ERC Equipoise LimitedLondonUK
  3. 3.Department of Earth Science and EngineeringImperial College LondonLondonUK

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