Relative permeabilities of supercritical CO2 and brine in carbon sequestration by a two-phase lattice Boltzmann method


In this paper, the migration of supercritical carbon dioxide (\(\hbox {CO}_{2}\)) in realistic sandstone rocks under conditions of saline aquifers, with applications to the carbon geological storage, has been investigated by a two-phase lattice Boltzmann method (LBM). Firstly the digital images of sandstone rocks were reproduced utilizing the X-ray computed microtomography (micro-CT), and high resolutions (up to 2.5 μm) were applied to the pore-scale LBM simulations. For the sake of numerical stability, the digital images were “cleaned” by closing the dead holes and removing the suspended particles in sandstone rocks. In addition, the effect of chemical reactions occurred in the carbonation process on the permeability was taken into account. For the wetting brine and non-wetting supercritical \(\hbox {CO}_{2}\) flows, they were treated as the immiscible fluids and were driven by pressure gradients in sandstone rocks. Relative permeabilities of brine and supercritical \(\hbox {CO}_{2}\) in sandstone rocks were estimated. Particularly the dynamic saturation was applied to improve the reliability of the calculations of the relative permeabilities. Moreover, the effects of the viscosity ratio of the two immiscible fluids and the resolution of digital images on the relative permeability were systematically investigated.

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  1. 1.

    Taylor KC, Nasr-El-Din HA (1998) Water-soluble hydrophobically associating polymers for improved oil recovery: a literature review. J Petrol Sci Eng 19:265

    Article  Google Scholar 

  2. 2.

    Thomas S (2008) Enhanced oil recovery—an overview. Oil Gas Sci Technol Rev IFP 63:9

    Article  Google Scholar 

  3. 3.

    Emberley S, Hutcheon I, Shevalier M, Durocher K, Mayer B, Gunter W, Perkins E (2005) Monitoring of fluid–rock interaction and CO2 storage through produced fluid sampling at the Weyburn CO2-injection enhanced oil recovery site, Saskatchewan, Canada. Appl Geochem 20:1131

    Article  Google Scholar 

  4. 4.

    Marley MC, Hazebrouck DJ, Walsh MT (1992) The application of in situ air sparging as an innovative soils and ground water remediation technology. Ground Water Monit Remediat 12:137

    Article  Google Scholar 

  5. 5.

    Bedient P, Rifai H, Newell C (1994) Ground water contamination: transport and remediation. Prentice Hall, New York

    Google Scholar 

  6. 6.

    Jiang F, Tsuji T, Hu C (2014) Elucidating the role of interfacial tension for hydrological properties of two-phase flow in natural sandstone by an improved lattice Boltzmann method. Transp Porous Media 104:205

    Article  Google Scholar 

  7. 7.

    Liu H, Valocchi AJ, Werth C, Kang Q, Oostrom M (2014) Pore-scale simulation of liquid CO2 displacement of water using a two-phase lattice Boltzmann model. Adv Water Resour 73:144

    Article  Google Scholar 

  8. 8.

    Huppert HE, Neufeld JA (2014) The fluid mechanics of carbon dioxide sequestration. Annu Rev Fluid Mech 46:255

    MathSciNet  Article  MATH  Google Scholar 

  9. 9.

    Nordbotten JM, Celia MA, Bachu S (2005) Injection and storage of CO2 in deep saline aquifers: analytical solution for CO2 plume evolution during injection. Transp Porous Media 58:339

    Article  Google Scholar 

  10. 10.

    Borglin SE, Moridis GJ, Oldenburg CM (2000) Experimental studies of the flow of ferrofluid in porous media. Transp Porous Media 41:61

    Article  Google Scholar 

  11. 11.

    Tallakstad KT, Knudsen HA, Ramstad T, Lovoll G, Maloy KJ, Toussaint R, Flekkoy EG (2009) Steady-state two-phase flow in porous media: statistics and transport properties. Phys Rev Lett 102:074502

    Article  Google Scholar 

  12. 12.

    Wang X, Nguyen TV, Hussey DS, Jacobson D (2010) Experimental study of relative permeability of porous media used in PEM fuel cells. ECS Trans 33:1151

  13. 13.

    Bakke S, Oren PE (1997) 3D pore-scale modelling of sandstones and flow simulations in the pore networks. SPE J 2:136

    Article  Google Scholar 

  14. 14.

    Meakin P, Tartakovsky AM (2009) Modeling and simulation of pore-scale multiphase fluid flow and reactive transport in fractured and porous media. Rev Geophys 47:RG3002

    Article  Google Scholar 

  15. 15.

    Brackbill JU, Kothe DB, Zemach C (1992) A continuum method for modeling surface-tension. J Comput Phys 100:335

    MathSciNet  Article  MATH  Google Scholar 

  16. 16.

    Sethian JA (1999) Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision and material science. Cambridge University Press, Cambridge

    Google Scholar 

  17. 17.

    Unverdi SO, Tryggvason G (1992) A front-tracking method for viscous, incompressible, multi-phase flows. J Comput Phys 100:25

  18. 18.

    Hao L, Cheng P (2010) Pore-scale simulations on relative permeabilities of porous media by lattice Boltzmann method. Int J Heat Mass Transf 53:1908

    Article  MATH  Google Scholar 

  19. 19.

    Landry CJ, Karpyn ZT, Ayala O (2014) Pore-scale lattice Boltzmann modeling and 4D X-ray computed microtomography imaging of fracture-matrix fluid transfer. Transp Porous Media 103:449

    Article  Google Scholar 

  20. 20.

    Gunstensen AK, Rothman DH, Zaleski S, Zanetti G (1991) Lattice Boltzmann model of immiscible fluids. Phys Rev A 43:4320

    Article  Google Scholar 

  21. 21.

    Rothman DH, Zaleski S (1994) Lattice-gas models of phase-separation—interfaces, phase-transitions, and multiphase flow. Rev Mod Phys 66:1417

    Article  Google Scholar 

  22. 22.

    Rothman DH (2004) Lattice-gas cellular automata: simple models of complex hydrodynamics. Cambridge University Press, Cambridge

    Google Scholar 

  23. 23.

    Redeker M, Rohde C, Sorin Pop I (2016) Upscaling of a tri-phase phase-field model for precipitation in porous media. IMA J Appl Math 81:898

    MathSciNet  Article  Google Scholar 

  24. 24.

    Quintard M, Whitaker S (1994) Transport in ordered and disordered porous media II: generalized volume averaging. Transp Porous Media 14:179

    Article  Google Scholar 

  25. 25.

    Gray WG, Miller CT (2011) TCAT analysis of capillary pressure in non-equilibrium, two-fluid-phase, porous medium systems. Adv Water Resour 34:770

    Article  Google Scholar 

  26. 26.

    Chen SY, Diemer K, Doolen D, Eggert K, Fu C, Gutman S, Travis BJ (1991) Lattice gas automata for flow through porous-media. Physica D 47:72

    Article  Google Scholar 

  27. 27.

    Shan XW, Chen HD (1993) Lattice Boltzmann model for simulating flows with multiple phases and components. Phys Rev E 47:1815

    Article  Google Scholar 

  28. 28.

    Guo ZL, Zheng CG, Shi BC (2002) An extrapolation method for boundary conditions in lattice Boltzmann method. Phys Fluids 14:2007

    Article  MATH  Google Scholar 

  29. 29.

    He X, Chen S, Zhang R (1999) A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh–Taylor instability. J Comput Phys 152:642

    MathSciNet  Article  MATH  Google Scholar 

  30. 30.

    Luo LS (2000) Theory of the lattice Boltzmann method: lattice Boltzmann models for nonideal gases. Phys Rev E 62:4982

    MathSciNet  Article  Google Scholar 

  31. 31.

    Inamuro T, T Ogata, Tajima S, Konishi N (2004) A lattice Boltzmann method for incompressible two-phase flows with large density differences. J Comput Phys 198:628

  32. 32.

    Aidun CK, Clausen JR (2010) Lattice-Boltzmann method for complex flows. Annu Rev Fluid Mech 42:439

    MathSciNet  Article  MATH  Google Scholar 

  33. 33.

    Kuznik F, Luo LS, Krafczyk M (2013) Mesoscopic methods in engineering and science. Comput Math Appl 65:813

    MathSciNet  Article  MATH  Google Scholar 

  34. 34.

    Chen SY, Doolen D (1998) Lattice Boltzmann method for fluid flows. Annu Rev Fluid Mech 30:72

    MathSciNet  Article  Google Scholar 

  35. 35.

    Succi S (2001) Lattice Boltzmann equation for fluid dynamics and beyond. Oxford University Press, Oxford

    Google Scholar 

  36. 36.

    Falcucci G, Ubertini S, Biscarini C, Francesco SD, Chiappini D, Palpacelli S, Maio AD, Succi S (2011) Lattice Boltzmann methods for multiphase flow simulations across scales. Commun Comput Phys 9:269

  37. 37.

    Swift MR, Osborn WR, Yeomans JM (1995) Lattice Boltzmann simulation of nonideal fluids. Phys Rev Lett 75:830

    Article  Google Scholar 

  38. 38.

    Swift MR, Orlandini E, Osborn WR, Yeomans JM (1996) Lattice Boltzmann simulations of liquid-gas and binary fluid systems. Phys Rev E 54:5041

    Article  Google Scholar 

  39. 39.

    Ramstad T, Oren PE, Bakke S (2010) Simulation of two-phase flow in reservoir rocks using a lattice Boltzmann method. SPE J 15:923

    Article  Google Scholar 

  40. 40.

    Ramstad T, Idowu N, Nardi C, Oren PE (2012) Relative permeability calculations from two-phase flow simulations directly on digital images of porous rocks. Transp Porous Media 94:487

    MathSciNet  Article  Google Scholar 

  41. 41.

    Huang H, Lu Xy (2009) Relative permeabilities and coupling effects in steady-state gas-liquid flow in porous media: a lattice Boltzmann study. Phys Fluids 61:341

    MATH  Google Scholar 

  42. 42.

    Zheng HW, Shu C, Chew YT (2005) Lattice Boltzmann interface capturing method for incompressible flows. Phys Rev E 72:056705

    Article  Google Scholar 

  43. 43.

    Zu YQ, He S (2012) Lattice Boltzmann modelling of migration for CO2 in porous media under conditions of saline aquifers. In: International symposium on heat transfer, ISHT-8, Beijing

  44. 44.

    Zu YQ, He S (2013) Phase-field-based lattice Boltzmann model for incompressible binary fluid systems with density and viscosity contrasts. Phys Rev E 87:043301

    Article  Google Scholar 

  45. 45.

    Qian YH, D'Humières D, Lallemand P (1992) Lattice BGK models for Navier–Stokes equation. Europhys Lett 17:479

    Article  MATH  Google Scholar 

  46. 46.

    Cahn JW, Hilliard JE (1958) Free energy of a nonuniform system. I. Interfacial free energy. J Chem Phys 28:258

    Article  Google Scholar 

  47. 47.

    Cahn JW, Hilliard JE (1959) Free energy of a nonuniform system. III. Nucleation in a two-component incompressible fluid. J Chem Phys 31:688

    Article  Google Scholar 

  48. 48.

    Li Q, Luo KH, Gao YJ, He YL (2012) Additional interfacial force in lattice Boltzmann models for incompressible multiphase flows. Phys Rev E 85:026704

    Article  Google Scholar 

  49. 49.

    Lee T, Fischer PF (2006) Eliminating parasitic currents in the lattice Boltzmann equation method for nonideal gases. Phys Rev E 74:046709

    Article  Google Scholar 

  50. 50.

    Spanne P, Thovert JF, Jacquin CJ, Lindquist WB, Jones KW, Adler PM (1994) Synchrotron computed microtomography of porous-media—topology and transports. Phys Rev Lett 73:2001

    Article  Google Scholar 

  51. 51.

    Lamy-Chappuis B, Angus D, Fisher Q, Grattoni C, Yardley BWD (2014) Rapid porosity and permeability changes of calcareous sandstone due to CO2 enriched brine injection. Geophys Res Lett 41:399

    Article  Google Scholar 

  52. 52.

    Chiquet P, Daridon JL, Broseta D, Thibeau S (2007) CO2/water interfacial tensions under pressure and temperature conditions of CO2 geological storage. Energy Convers Manag 48:736

    Article  Google Scholar 

  53. 53.

    Dullien FAL (1979) Porous media fluid transport and pore structure. Academic Press, New York

    Google Scholar 

  54. 54.

    Cancelliere A, Chang C, Foti E, Rothman DH, Succi S (1990) The permeability of a random medium—comparison of simulation with theory. Phys Fluids A 2:2085

    Article  Google Scholar 

  55. 55.

    Pan C, Luo LS, Miller CT (2006) An evaluation of lattice Boltzmann schemes for porous medium flow simulation. Comput Fluids 35:898

    Article  MATH  Google Scholar 

  56. 56.

    Juanes R, Spiteri EJ, Orr FM, Blunt MJ (2006) Impact of relative permeability hysteresis on geological CO2 storage. Water Resour Res 42:W12418

    Article  Google Scholar 

  57. 57.

    Chalbaud C, Robin M, Lombard JM, Martin F, Egermann P, Bertin H (2009) Interfacial tension measurements and wettability evaluation for geological CO2 storage. Adv Water Resour 32:98

    Article  Google Scholar 

  58. 58.

    Nielsen LC, Bourg IC, Sposito G (2012) Predicting CO2-water interfacial tension under pressure and temperature conditions of geologic CO2 storage. Geochim Cosmochim Acta 81:28

    Article  Google Scholar 

  59. 59.

    Zu Y (2015) Modelling of migration of CO2 in porous media under conditions of saline aquifers using lattice Boltzmann method. Proc Eng 126:471

    Article  Google Scholar 

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The authors were grateful to the financial support from the Engineering and Physical Science Research Council of the UK (Grant No. EP/I010971/1). J.F.X thanks the National Natural Science Foundation of China (Grant No. 51506110) and China Postdoctoral Science Foundation (Grant No. 2015M581090) for the support. Y.Q.Z thanks the support of Shanghai Pujiang Programme (Grant No. 14PJ1401600) and Fudan University Initiative Scientific Research Programme (Grant No. EZH2126504). J.F.X also thanks Professor Moran Wang from Tsinghua University for the very useful discussions about the carbon geological storage, and we gratefully acknowledge the anonymous reviewers for their valuable comments.

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Xie, J., He, S., Zu, Y.Q. et al. Relative permeabilities of supercritical CO2 and brine in carbon sequestration by a two-phase lattice Boltzmann method. Heat Mass Transfer 53, 2637–2649 (2017).

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  • Relative Permeability
  • Lattice Boltzmann Method
  • Saline Aquifer
  • Immiscible Fluid
  • Relative Permeability Curve