Vertically integrated dual-continuum models for CO2 injection in fractured geological formations

  • Yiheng Tao
  • Bo Guo
  • Karl W. Bandilla
  • Michael A. Celia
Original Paper


Various modeling approaches, including fully three-dimensional (3D) models and vertical-equilibrium (VE) models, have been used to study the large-scale storage of carbon dioxide (CO2) in deep saline aquifers. 3D models solve the governing flow equations in three spatial dimensions to simulate migration of CO2 and brine in the geological formation. VE models assume rapid and complete buoyant segregation of the two fluid phases, resulting in vertical pressure equilibrium and allowing closed-form integration of the governing equations in the vertical dimension. This reduction in dimensionality makes VE models computationally much more efficient, but the associated assumptions restrict the applicability of VE models to geological formations with moderate to high permeability. In the present work, we extend the VE models to simulate CO2 storage in fractured deep saline aquifers in the context of dual-continuum modeling, where fractures and rock matrix are treated as porous media continua with different permeability and porosity. The high permeability of fractures makes the VE model appropriate for the fracture domain, thereby leading to a VE dual-continuum model for the dual continua. The transfer of fluid mass between fractures and rock matrix is represented by a mass transfer function connecting the two continua, with a modified transfer function for the VE model based on vertical integration. Comparison of the new model with a 3D dual-continuum model shows that the new model provides comparable numerical results while being much more computationally efficient.


Geologic CO2 storage Fractured rock Dual-continuum models Vertically integrated models Multi-scale modeling 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



This work was supported in part by the Carbon Mitigation Initiative at Princeton University and by the U.S. Department of Energy (DOE) National Energy Technology Laboratory (NETL) under Grant Number DE-FE0023323. This project is managed and administered by Princeton University and funded by DOE/NETL and cost-sharing partners. Neither the U.S. Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the U.S. Government or any agency thereof. The views and opinions of the authors expressed herein do not necessarily state or reflect those of the U.S. Government or any agency thereof.


  1. 1.
    Celia, M.A.: Geological storage of captured carbon dioxide as a large-scale carbon mitigation option. Water. Resour. Res. 53(5), 3527–3533 (2017)CrossRefGoogle Scholar
  2. 2.
    International Energy Agency (IEA): Energy technology perspectives 2017. (2017). Accessed 30 January 2018
  3. 3.
    United Nations Framework Convention on Climate Change (UNFCCC): The Paris Agreement. (2017). Accessed 30 January 2018
  4. 4.
    Intergovernmental Panel on Climate Change (IPCC): Special report on carbon dioxide capture and storage, paper presented at Working Group III of the Intergovernmental Panel on Climate Change, 442 pp. Cambridge Univ. Press, Cambridge (2005)Google Scholar
  5. 5.
    Iding, M., Ringrose, P.: Evaluating the impact of fractures on the performance of the In Salah CO2 storage site. Int. J. Greenh. Gas Control 4(2), 242–248 (2010)CrossRefGoogle Scholar
  6. 6.
    Verdon, J.P., Kendall, J., Stork, A.L., Chadwick, R.A., White, D.J., Bissell, R.C.: Comparison of geomechanical deformation induced by megatonne-scale CO2 storage at Sleipner, Weyburn, and In Salah. Proc. Natl. Acad. Sci. U. S. A. 110(30), E2762–E2771 (2013)CrossRefGoogle Scholar
  7. 7.
    Li, C., Zhang, K., Wang, Y., Guo, C., Maggia, F.: Experimental and numerical analysis of reservoir performance for geological CO2 storage in the Ordos Basin in China. Int. J. Greenh. Gas Control 45, 216–232 (2016)CrossRefGoogle Scholar
  8. 8.
    Li, X., Li, Q., Bai, B., Wei, N., Yuan, W.: The geomechanics of Shenhua carbon dioxide capture and storage (CCS) demonstration project in Ordos Basin. China. J. Rock Mech. Geotech. Eng. 8(6), 948–966 (2016)CrossRefGoogle Scholar
  9. 9.
    Kazemi, H., Merrill, L.S., Porterfield, K.L., Zeman, P.R.: Numerical simulation of water–oil flow in naturally fractured reservoirs. Soc. Pet. Eng. J. 16(6), 317–326 (1976)CrossRefGoogle Scholar
  10. 10.
    Azom, P.N., Javadpour, F.: Dual-continuum modeling of shale and tight gas reservoirs (SPE159584). SPE Annual Technical Conference and Exhibition, San Antonio (2012)Google Scholar
  11. 11.
    Festoy, S., Van Golf-Racht, T.D.: Gas gravity drainage in fractured reservoirs through new dual-continuum approach. SPE Reservoir Eng. 4(3), 271–278 (1989)CrossRefGoogle Scholar
  12. 12.
    Pruess, K., Narasimhan, T.N.: A practical method for modeling fluid and heat flow in fractured porous media. Soc. Pet. Eng. J. 25(1), 14–26 (1985)CrossRefGoogle Scholar
  13. 13.
    Gilman, J.R.: An efficient finite-difference method for simulating phase segregation in the matrix blocks in double-porosity reservoirs. SPE Reservoir Eng. 1(4), 403–413 (1986)CrossRefGoogle Scholar
  14. 14.
    Gong, B., Karimi-Fard, M., Durlofsky, L.J.: Upscaling discrete fracture characterizations to dual-porosity, dual-permeability models for efficient simulation of flow with strong gravitational effects. SPE J. 13(1), 58–67 (2008)CrossRefGoogle Scholar
  15. 15.
    van Heel, A.P., Boerrigter, P.M., van Dorp, J.J.: Thermal and hydraulic matrix-fracture interaction in dual-permeability simulation. SPE Reservoir Eva. Eng. 11(4), 735–749 (2008)CrossRefGoogle Scholar
  16. 16.
    Fuentes-Cruz, G., Valko, P.P.: Revisiting the dual-porosity/dual-permeability modeling of unconventional reservoirs: the induced-interporosity flow field. SPE J. 20(1), 125–141 (2015)CrossRefGoogle Scholar
  17. 17.
    Gerke, H.H., van Genuchten, M.T.: A dual-porosity model for simulating the preferential movement of water and solutes in structured porous media. Water. Resour. Res. 29(2), 305–319 (1993)CrossRefGoogle Scholar
  18. 18.
    Bibby, R.: Mass transport of solutes in dual-porosity media. Water. Resour. Res. 17(4), 1075–1081 (1981)CrossRefGoogle Scholar
  19. 19.
    Coppola, A., Gerke, H.H., Comegna, A., Basile, A., Comegna, V.: Dual-permeability model for flow in shrinking soil with dominant horizontal deformation. Water. Resour. Res. 48(8), W08527 (2012)CrossRefGoogle Scholar
  20. 20.
    Duguid, J.O., Lee, P.C.Y.: Flow in fractured porous media. Water. Resour. Res. 13(3), 558–566 (1977)CrossRefGoogle Scholar
  21. 21.
    Jarvis, N.J., Jansson, P.-E., Dik, P.E., Messing, I.: Modeling water and solute transport in marcoporous soil. I. Model description and sensitivity analysis. J. Soil Sci. 42(1), 59–70 (1991)CrossRefGoogle Scholar
  22. 22.
    Vogel, T., Gerke, H.H., Zhang, R., van Genhchten, M.T.: Modeling flow and transport in a two-dimensional dual-permeability system with spatially variable hydraulic properties. J. Hydrol. 238(1–2), 78–89 (2000)CrossRefGoogle Scholar
  23. 23.
    Bandilla, K.W., Celia, M.A., Birkholzer, J.T., Cihan, A., Leister, E.C.: Multiphase modeling of geologic carbon sequestration in saline aquifers. Groundwater. 53(3), 362–377 (2015)CrossRefGoogle Scholar
  24. 24.
    Celia, M.A., Bachu, S., Nordbotten, J.M., Bandilla, K.W.: Status of CO2 storage in deep saline aquifers with emphasis on modeling approaches and practical simulations. Water. Resour. Res. 51(9), 6846–6892 (2015)CrossRefGoogle Scholar
  25. 25.
    Nordbotten, J.M., Celia, M.A.: Similarity solutions for fluid injection into confined aquifers. J. Fluid Mech. 561, 307–327 (2006)CrossRefGoogle Scholar
  26. 26.
    Hesse, M.A., Tchelepi, H.A., Cantwell, B.J., Orr, F.M.: Gravity currents in horizontal porous layers: transition from early to late self-similarity. J. Fluid Mech. 577, 363–383 (2007)CrossRefGoogle Scholar
  27. 27.
    Hesse, M.A., Orr, F.M., Tchelepi, H.A.: Gravity currents with residual trapping. J. Fluid Mech. 611, 35–60 (2008)CrossRefGoogle Scholar
  28. 28.
    Juanes, R., MacMinn, C., Szulczewski, M.: The footprint of the CO2 plume during carbon dioxide storage in saline aquifers: storage efficiency for capillary trapping at the basin scale. Transp. Porous Media 82(1), 19–30 (2010)CrossRefGoogle Scholar
  29. 29.
    Macminn, C.W., Szulczewshi, M.L., Juanes, R.: CO2 migration in saline aquifers. Part 1. Capillary trapping under slope and groundwater flow. J. Fluid Mech. 662, 329–351 (2010)CrossRefGoogle Scholar
  30. 30.
    Golding, M.J., Neufield, J.A., Hesse, M.A., Huppert, H.E.: Two-phase gravity currents in porous media. J. Fluid Mech. 678, 248–270 (2011)CrossRefGoogle Scholar
  31. 31.
    Macminn, C.W., Juanes, R.: Buoyant currents arrested by convective mixing. Geophys. Res. Lett. 40(10), 2017–2022 (2013)CrossRefGoogle Scholar
  32. 32.
    Zheng, Z., Guo, B., Christov, I.C., Celia, M.A., Stone, H.A.: Flow regimes for fluid injection into a confined porous medium. J. Fluid Mech. 767, 881–909 (2015)CrossRefGoogle Scholar
  33. 33.
    Guo, B., Zheng, Z., Celia, M.A., Stone, H.A.: Axisymmetric flows from fluid injection into a confined porous medium. Phys. Fluids 28, 022107 (2016)CrossRefGoogle Scholar
  34. 34.
    Nordbotten, J.M., Kavetski, D., Celia, M.A., Bachu, S.: Model for CO2 leakage including multiple geological layers and multiple leaky wells. Environ. Sci. Technol. 43(3), 743–749 (2009)CrossRefGoogle Scholar
  35. 35.
    Celia, M.A., Nordbotten, J.M., Court, B., Dobossy, M., Bachu, S.: Field-scale application of a semi-analytical model for estimation of CO2 and brine leakage along old wells. Int. J. Greenh. Gas Control 5(2), 257–269 (2011)CrossRefGoogle Scholar
  36. 36.
    Gasda, S.E., Nordbotten, J.M., Celia, M.A.: Vertical equilibrium with sub-scale analytical methods for geological CO2 sequestration. Comput. Geosci. 13, 469–481 (2009)CrossRefGoogle Scholar
  37. 37.
    Geiger, S., Emmanuel, S.: Non-fourier thermal transport in fractured geological media. Water. Resour. Res. 46(7), W07504 (2010)CrossRefGoogle Scholar
  38. 38.
    Gasda, S.E., Nordbotten, J.M., Celia, J.M.: Vertically-averaged approaches for CO2 migration with solubility trapping. Water. Resour. Res. 47(5), W05528 (2011)CrossRefGoogle Scholar
  39. 39.
    Bandilla, K.W., Celia, M.A., Elliot, T.R., Person, M., Ellet, K.M., Rupp, J.A., Gable, C., Zhang, Y.: Modeling carbon sequestration in the Illinois Basin using a vertically-integrated approach. Comput. Vis. Sci. 15(1), 39–51 (2012)CrossRefGoogle Scholar
  40. 40.
    Lake, L.W.: Enhanced oil recovery. Prentice-Hall, Upper Saddle River (1989)Google Scholar
  41. 41.
    Yortsos, Y.C.: A theoretical analysis of vertical flow equilibrium. Transp. Porous Media 18(2), 107–129 (1995)CrossRefGoogle Scholar
  42. 42.
    de Loubens, R., Ramakrishnan, T.S.: Analysis and computation of gravity-induced migration in porous media. J. Fluid Mech. 675, 60–86 (2011)CrossRefGoogle Scholar
  43. 43.
    Nordbotten, J.M., Dahle, H.K.: Impact of the capillary fringe in vertically integrated models for CO2 storage. Water. Resour. Res. 47(2), W02537 (2011)CrossRefGoogle Scholar
  44. 44.
    Nordbotten, J.M., Celia, M.A.: Geological Storage of CO2: Modeling Approaches for Large-Scale Simulation. Wiley, Hoboken (2012)Google Scholar
  45. 45.
    Hao, Y., Fu, P., Carrigan, C.R.: Application of a dual-continuum model for simulation of fluid flow and heat transfer in fractured geothermal reservoirs (SGP-TR-198). Proceedings, Thirty-Eighth Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California USA (2013)Google Scholar
  46. 46.
    Warren, J.E., Root, P.J.: The behavior of naturally fractured reservoirs. Soc. Pet. Eng. J. 3(3), 245–255 (1963)CrossRefGoogle Scholar
  47. 47.
    Gilman, J.R., Kazemi, H.: Improved calculations for viscous and gravity displacement in matrix blocks in dual-porosity simulators. J. Pet. Technol. 40(1), 60–70 (1988)CrossRefGoogle Scholar
  48. 48.
    Barenblatt, G.I., Zheltov, I.P., Kochina, I.N.: Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks. PMM (Sov. Appl. Math. Mech.) 24(5), 852–864 (1960)Google Scholar
  49. 49.
    Ramirez, B., Kazemi, H., Al-Kobaisi, M., Ozkan, E., Atan, S.: A critical review for proper use of water/oil/gas transfer functions in dual-porosity naturally fractured reservoirs: part I. SPE Reservoir Eva. Eng. 12(2), 200–210 (2009)CrossRefGoogle Scholar
  50. 50.
    Al-Kobaisi, M., Kazemi, H., Ramirez, B., Ozkan, E., Atan, S.: A critical review for proper use of water/oil/gas transfer functions in dual-porosity naturally fractured reservoirs: part II. SPE Reservoir Eva. Eng. 12(2), 211–217 (2009)CrossRefGoogle Scholar
  51. 51.
    March, R., Doster, F., Geiger, S.: Assessment of CO2 storage potential in naturally fractured reservoirs with dual-porosity models. Water Resour. Res. 54(3), 1650–1668 (2018)CrossRefGoogle Scholar
  52. 52.
    Brooks, R.H., Corey, A.T.: Hydraulic properties of porous media Hydrology paper, vol. 3. Colorado State University, Fort Collins (1964)Google Scholar
  53. 53.
    Court, B., Bandilla, K.W., Celia, M.A., Janzen, A., Dobossy, M., Nordbotten, J.M.: Applicability of vertical-equilibrium and sharp-interface assumptions in CO2 sequestration modeling. Int. J. Greenh. Gas Control 10, 134–147 (2012)CrossRefGoogle Scholar
  54. 54.
    Lang, P.S., Paluszny, A., Zimmerman, R.W.: Permeability tensor of three-dimensional fractured porous rock and a comparison to trace map predictions. J. Geophys. Res. Solid Earth 119(8), 6288–6307 (2014)CrossRefGoogle Scholar
  55. 55.
    Faybishenko, B., Benson, S. M., Gale, J. E.: Dynamics of Fluids and Transport in Complex Fractured-Porous Systems. AGU & Wiley, Hoboken (2015)CrossRefGoogle Scholar
  56. 56.
    March, R., Elder, H., Doster, F., Geiger, S.: Accurate dual-porosity modeling of CO2 storage in fractured reservoirs (SPE-182646-MS). SPE Reservoir Simulation Conference, Montgomery, Texas, USA (2017)Google Scholar
  57. 57.
    Balogun, A., Kazemi, H., Ozkan, E., Al-Kobaisi, M., Ramirez, B.: Verification and proper use of water-oil transfer function for dual-porosity and dual-permeability reservoirs. SPE Reservoir Eva. Eng. 12(2), 189–199 (2009)CrossRefGoogle Scholar
  58. 58.
    Fung, L.S.: Simulation of block-to-block processes in naturally fractured reservoirs. SPE Reservoir Eng 6(4), 477–484 (1991)CrossRefGoogle Scholar
  59. 59.
    Becker, B., Guo, B., Bandilla, K.W., Celia, M.A., Flemisch, B., Helmig, R.: A pseudo-vertical equilibrium model for slow gravity drainage dynamics. Water. Resour. Res. 53(12), 10491–10507 (2017)CrossRefGoogle Scholar
  60. 60.
    Guo, B., Bandilla, K.W., Doster, F., Keilegavlen, E., Celia, M.A.: A vertically integrated model with vertical dynamics for CO2 storage. Water. Resour. Res. 50(8), 6269–6284 (2014)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringPrinceton UniversityPrincetonUSA
  2. 2.Department of Hydrology and Atmospheric SciencesThe University of ArizonaTucsonUSA

Personalised recommendations