Skip to main content
SpringerLink
Log in

Effects of CO2 Compressibility on CO2 Storage in Deep Saline Aquifers

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

The injection of supercritical CO2 in deep saline aquifers leads to the formation of a CO2 plume that tends to float above the formation brine. As pressure builds up, CO2 properties, i.e. density and viscosity, can vary significantly. Current analytical solutions do not account for CO2 compressibility. In this article, we investigate numerically and analytically the effect of this variability on the position of the interface between the CO2-rich phase and the formation brine. We introduce a correction to account for CO2 compressibility (density variations) and viscosity variations in current analytical solutions. We find that the error in the interface position caused by neglecting CO2 compressibility is relatively small when viscous forces dominate. However, it can become significant when gravity forces dominate, which is likely to occur at late times of injection.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

c r :

Rock compressibility

c α :

Compressibility of fluid α (α = c, w)

d :

Aquifer thickness

E rel :

Relative error of the interface position

g :

Gravity

h w :

Hydraulic head of water

k :

Intrinsic permeability

\({k_{{\rm r}_\alpha}}\) :

α-Phase relative permeability (α = c, w)

N :

Gravity number

\({P_{{\rm t}_0}}\) :

Fluid pressure at the top of the aquifer prior to injection

P DT :

Fluid pressure for Dentz and Tartakovsky (2009a) approach

\({\overline{P}_{\rm DT}}\) :

Vertically averaged fluid pressure for Dentz and Tartakovsky (2009a) approach

\({\overline{P}_{\rm N}}\) :

Vertically averaged fluid pressure for Nordbotten et al. (2005) approach

\({\overline{P}_{0}}\) :

Vertically averaged fluid pressure prior to injection

P α :

Fluid pressure of α-phase (α = c, w)

Q m :

CO2 mass flow rate

Q 0 :

CO2 volumetric flow rate

q α :

Volumetric flux of α-phase (α = c, w)

R :

Radius of influence

R c :

CO2 plume radius at the top of the aquifer for compressible CO2

R i :

CO2 plume radius at the top of the aquifer for incompressible CO2

r :

Radial distance

r 0 :

CO2 plume radius at the top of the aquifer

r b :

CO2 plume radius at the base of the aquifer

r c :

Characteristic length

r w :

Injection well radius

S s :

Specific storage coefficient

\({S_{{\rm r _w}}}\) :

Residual saturation of the formation brine

S α :

Saturation of α-phase (α = c, w)

t :

Time

z :

Vertical coordinate

z 0 :

Depth of the top of the aquifer

z b :

Depth of the base of the aquifer

V :

CO2 plume volume

α :

Phase index, c CO2 and w brine

β :

CO2 compressibility

\({\epsilon_{\rm v}}\) :

Volumetric strain

γ cw :

A dimensionless parameter that measures the relative importance of viscous and gravity forces

λ α :

Mobility of α-phase (α = c, w)

μ α :

Viscosity of α-phase (α = c, w)

ρ 0 :

CO2 density at the reference pressure \({P_{\rm t_0}}\)

ρ 1 :

Constant for the CO2 density

\({\overline{\rho}_{\rm c}}\) :

Mean CO2 density

\({\overline{\rho}_{{\rm c}_{\rm DT}}}\) :

Mean CO2 density for Dentz and Tartakovsky (2009a) approach

\({\overline{\rho}_{{\rm c}_{\rm N}}}\) :

Mean CO2 density for Nordbotten et al. (2005) approach

ρ α :

Density of α-phase (α = c, w)

σ′:

Effective stress

\({\phi}\) :

Porosity

ζ :

Interface position from the bottom of the aquifer

References

  • Altunin V.V., Sakhabetdinov M.A.: Viscosity of liquid and gaseous carbon dioxide at temperatures 220-1300 K and pressure up to 1200 bar. Teploenergetika, 8, 85–89 (1972)

    Google Scholar 

  • Angus, A., Armstrong, B., Reuck, K.M. (eds): International thermodynamics tables of the fluid state. Carbon dioxide. International Union of Pure and Applied Chemistry. Pergamon Press, Oxford (1976)

    Google Scholar 

  • Aziz, K., Settari, A. (eds): Petroleum Reservoir Simulation. 2nd edn. Blitzprint Ltd., Calgary (2002)

    Google Scholar 

  • 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)

    Article  Google Scholar 

  • Bachu S., Adams J.J.: Sequestration of CO2 in geological media in response to climate change: capacity of deep saline aquifers to sequester CO2 in solution. Energy Convers. Manag. 44, 3151–3175 (2003)

    Article  Google Scholar 

  • Bear, J. (eds): Dynamics of Fluids in Porous Media. Elsevier, New York (1972)

    Google Scholar 

  • Bolster, D., Barahona, M., Dentz, M., Fernandez Garcia, D., Sanchez-Vila, X., Trichero, P., Volhondo, C., Tartakovsky, D.M. : Probabilistic risk assessment applied to contamination scenarios in porous media. Water Resour. Res. 45, w06413. (2009a) doi:10.1029/2008wR007551

  • Bolster D., Dentz M., Carrera J.: Effective two phase flow in heterogeneous media under temporal pressure fluctuations. Water Resour. Res. 45, W05408 (2009b). doi:10.1029/2008WR007460

    Article  Google Scholar 

  • Cantucci B., Montegrossi G., Vaselli O., Tassi F., Quattrocchi F., Perkins E.H.: Geochemical modeling of CO2 storage in deep reservoirs: the Weyburn Project (Canada) case study. Chem. Geol. 265, 181–197 (2009)

    Article  Google Scholar 

  • Celia M.A., Nordbotten J.M.: Practical modeling approaches for geological storage of carbon dioxide. Ground Water 47(5), 627–638 (2009)

    Article  Google Scholar 

  • Chen, Z., Huan, G., Ma, Y. (eds): Computational methods for multiphase flows in porous media. SIAM, Philadelphia (2006)

    Google Scholar 

  • Cooper H.H., Jacob C.E.: A generalized graphical method for evaluating formation constants and summarizing well field history. Am. Geophys. Union Trans. 27, 526–534 (1946)

    Google Scholar 

  • Dake, L.P. (eds): Fundamentals of Reservoir Engineering. Elsevier, Oxford (1978)

    Google Scholar 

  • Dentz M., Tartakovsky D.M.: Abrupt-interface solution for carbon dioxide injection into porous media. Trans. Porous Media 79, 15–27 (2009a)

    Article  Google Scholar 

  • Dentz M., Tartakovsky D.M.: Response to “Comments on abrupt-interface solution for carbon dioxide injection into porous media by Dentz and Tartakovsky (2008)” by Lu et al. Trans. Porous Media 79, 39–41 (2009b)

    Article  Google Scholar 

  • Ennis-King J., Paterson L.: The role of convective mixing in the long-term storage of carbon dioxide in deep saline formations. J. Soc. Pet. Eng. 10(3), 349–356 (2005)

    Google Scholar 

  • Garcia, J.E.: Fluid Dynamics of Carbon Dioxide Disposal into Saline Aquifers. PhD thesis, University of California, Berkeley (2003)

  • Garcia, J.E., Pruess, K.: Flow Instabilities during injection of CO2 into saline aquifers. Proceedings Tough Symposium 2003, LBNL, Berkeley (2003)

  • GHS: Spreadsheet with CO2 compressibility correction. http://www.h2ogeo.upc.es/publicaciones/2009/Transport%20in%20porous%20media/Effects%20of%20CO2%20Compressibility%20on%20CO2%20Storage%20in%20Deep%20Saline%20Aquifers.xls (2009)

  • Hesse M.A., Tchelepi H.A., Cantwell B.J., Orr F.M. Jr: Gravity currents in horizontal porous layers: Transition from early to late self-similarity. J. Fluid Mech. 577, 363–383 (2007)

    Article  Google Scholar 

  • Hesse M.A., Tchelepi H.A., Orr F.M. Jr: Gravity currents with residual trapping. J. Fluid Mech. 611, 35–60 (2008)

    Article  Google Scholar 

  • Hidalgo J.J., Carrera J.: Effect of dispersion on the onset of convection during CO2 sequestration. J. Fluid Mech. 640, 443–454 (2009)

    Article  Google Scholar 

  • Hitchon B., Gunter W.D., Gentzis T., Bailey R.T.: Sedimentary basins and greenhouse gases: a serendipitous association. Energy Convers. Manag. 40, 825–843 (1999)

    Article  Google Scholar 

  • Huppert H.E., Woods A.W.: Gravity-driven flows in porous media. J. Fluid Mech. 292, 55–69 (1995)

    Article  Google Scholar 

  • Juanes, R., MacMinn, C.W., Szulczewski, M.L.: The footprint of the CO2 plume during carbon dioxide storage in saline aquifers: storage efficiency for capillary trapping at the basin scale. Trans. Porous Media. doi:10.1007/s11242-009-9420-3 (2009)

  • Katz, D.L., Lee, R.L. (eds): Natural Gas Engineering. McGraw-Hill, New York (1990)

    Google Scholar 

  • Kopp A., Class H., Helmig R.: Investigation on CO2 storage capacity in saline aquifers Part 1. Dimensional analysis of flow processes and reservoir characteristics. J. Greenh. Gas Control 3, 263–276 (2009)

    Article  Google Scholar 

  • Korbol R., Kaddour A.: Sleipner vest CO2 disposal—injection of removed CO2 into the Utsira formation. Energy Convers. Manag. 36(6–9), 509–512 (1995)

    Article  Google Scholar 

  • Lake, L.W. (eds): Enhanced Oil Recovery. Prentice-Hall, Englewood Cliffs, New Jercey (1989)

    Google Scholar 

  • Law D.H.S., Bachu S.: Hydrogeological and numerical analysis of CO2 disposal in deep aquifers in the Alberta sedimentary basin. Energy Convers. Manag. 37(6-8), 1167–1174 (1996)

    Article  Google Scholar 

  • 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. Trans. Porous Media 79, 29–37 (2009)

    Article  Google Scholar 

  • Lyle S., Huppert H.E., Hallworth M., Bickle M., Chadwick A.: Axisymmetric gravity currents in a porous medium. J Fluid Mech. 543, 293–302 (2005)

    Article  Google Scholar 

  • Mathias, S.A., Hardisty, P.E., Trudell, M.R., Zimmerman, R.W.: Approximate solutions for pressure buildup during CO2 injection in brine aquifers. Trans. Porous Media. doi:10.1007/s11242-008-9316-7 (2008)

  • McPherson B.J.O.L., Han W.S., Cole B.S.: Two equations of state assembled for basic analysis of multiphase CO2 flow and in deep sedimentary basin conditions. Comput. Geosci. 34, 427–444 (2008)

    Article  Google Scholar 

  • Neuweiller I., Attinger S., Kinzelbach W., King P.: Large scale mixing for immiscible displacement in heterogenous porous media. Trans. Porous Media 51, 287–314 (2003)

    Article  Google Scholar 

  • Neuzil C.E.: Groundwater flow in low-permeability environments. Water Resour. Res. 22(8), 1163–1195 (1986)

    Article  Google Scholar 

  • Nooner S.L., Eiken O., Hermanrud C., Sasagawa G.S., Stenvold T., Zumberge M.A.: Constraints on the in situ density of CO2 within the Utsira formation from time-lapse seafloor gravity measurements. J. Greenh. Gas Control 1, 198–214 (2007)

    Article  Google Scholar 

  • 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. Trans. Porous Media 58, 339–360 (2005)

    Article  Google Scholar 

  • 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). doi:10.1021/es801135v

    Article  Google Scholar 

  • Olivella S., Carrera J., Gens A., Alonso E.E.: Non-isothermal multiphase flow of brine and gas through saline media. Trans. Porous Media 15, 271–293 (1994)

    Article  Google Scholar 

  • Olivella S., Gens A., Carrera J., Alonso E.E.: Numerical formulation for a simulator (CODE_BRIGHT) for the coupled analysis of saline media. Eng. Comput. 13, 87–112 (1996)

    Article  Google Scholar 

  • Pruess K., Garcia J.: Multiphase flow dynamics during CO2 disposal into saline aquifers. Environ. Geol. 42, 282–295 (2002)

    Article  Google Scholar 

  • Pruess K., Garcia J., Kovscek T., Oldenburg C., Rutqvist J., Steelfel C., Xu T.: Code intercomparison builds confidence in numerical simulation models for geologic disposal of CO2. Energy 29, 1431–1444 (2004)

    Article  Google Scholar 

  • Riaz A., Hesse M., Tchelepi H., Orr F.M. Jr: Onset of convection in a gravitationally unstable diffusive boundary layer in porous media. J. Fluid Mech. 548, 87–111 (2006)

    Article  Google Scholar 

  • Rutqvist J., Birkholzer J., Cappa F., Tsang C.-F.: Estimating maximum sustainable geological sequestration of CO2 using coupled fluid flow and geomechanical fault-slip analysis. Energy Convers. Manag. 48, 1798–1807 (2007)

    Article  Google Scholar 

  • Saripalli P., McGrail P.: Semi-analytical approaches to modeling deep well injection of CO2 for geological sequestration. Energy Convers. Manag. 43, 185–198 (2002)

    Article  Google Scholar 

  • Sovova H., Prochazka J.: Calculations of compressed carbon dioxide viscosities. Ind. Eng. Chem. Res. 32(12), 3162–3169 (1993)

    Article  Google Scholar 

  • Span R., Wagner W.: A new equation of state for carbon dioxide covering the fluid region from the triple-point to 1100 K at pressures up to 88 MPa. J. Phys. Chem. Ref. Data 25(6), 1509–1596 (1996)

    Article  Google Scholar 

  • Stauffer P.H., Viswanathan H.S., Pawar R.J., Guthrie G.D.: A system model for geologic sequestration of carbon dioxide. Environ. Sci. Technol. 43(3), 565–570 (2009)

    Article  Google Scholar 

  • Tartakovsky D.M.: (2007) Probabilistic risk analysis in subsurface hydrology. Geophys. Res. Lett. 34, L05 404

    Google Scholar 

  • Tchelepi, H.A., Orr, F.M. Jr.: Interaction of viscous fingering, permeability inhomogeneity and gravity segregation in three dimensions. SPE Symposium on Reservoir Simulation, New Orleans, pp. 266–271, (1994)

  • Thiem, G. (eds): Hydrologische Methode. Leipzig, Gebhardt (1906)

    Google Scholar 

  • Tsang C.-F., Birkholzer J., Rutqvist J.: A comparative review of hydrologic issues involved in geologic storage of CO2 and injection disposal of liquid waste. Environ. Geol. 54, 1723–1737 (2008)

    Article  Google Scholar 

  • van Genuchten M.T.: A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil. Sci. Soc. Am. J. 44, 892–898 (1980)

    Article  Google Scholar 

  • Vilarrasa, V., Bolster, D., Olivella, S., Carrera, J.: Coupled hydromechanical modelling of CO2 sequestration in deep saline aquifers. Int. J. Greenh. Gas Control (submitted) (2010)

  • Zhou Q., Birkholzer J., Tsang C.-F., Rutqvist J.: A method for quick assessment of CO2 storage capacity in closed and semi-closed saline formations. J. Greenh. Gas Control 2, 626–639 (2008)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Environmental Assessment and Water Research, GHS, IDAEA, CSIC, Barcelona, Spain

    Victor Vilarrasa, Marco Dentz & Jesus Carrera

  2. Department of Geotechnical Engineering and Geosciences, Technical University of Catalonia (UPC), Barcelona, Spain

    Victor Vilarrasa, Diogo Bolster & Sebastia Olivella

Authors
  1. Victor Vilarrasa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Diogo Bolster
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marco Dentz
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Sebastia Olivella
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jesus Carrera
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Victor Vilarrasa.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vilarrasa, V., Bolster, D., Dentz, M. et al. Effects of CO2 Compressibility on CO2 Storage in Deep Saline Aquifers. Transp Porous Med 85, 619–639 (2010). https://doi.org/10.1007/s11242-010-9582-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11242-010-9582-z

Keywords

Search

Navigation