Simulation of Two-Phase Fluid Flow in the Digital Model of a Pore Space of Sandstone at Different Surface Tensions

A study is made of the influence of surface tension on two-phase drainage flows in a porous medium. Computational filtration experiments are conducted in a three-dimensional digital microtomographic model of sandstone. To simulate two-phase flows, use is made of lattice Boltzmann equations; interfacial phenomena and wetting effects are described using the color-gradient-based method. Calculations are carried out at the same rate of injection of a nonwetting fluid and at a ratio of the viscosities of nonwetting and wetting phases of 1:10. Results are obtained according to which growth in the interfacial tension contributes to the rise in the efficiency of displacement of the wetting fluid, which is recorded at the moment the injected phase breaks through, and to the decrease in the efficiency after its breakthrough. It is established that distinctive features of flows with capillary fingering that arise at high surface tensions are the stepwise character of travel of the leading front and the growth of displacement channels in directions different from the hydrodynamic pressure difference. It is shown that interfacial tension is a parameter whose variation enables us to change the type of two-phase flow. Increase in the interfacial tension contributes to the transition of the flow with viscous fingering to a flow with capillary fingering. The efficiency of displacement of the wetting fluid in the transition crossover zone is the lowest.

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References

  1. 1.

    R. Lenormand, E. Touboul, and C. Zarcone, Numerical models and experiments on immiscible displacements in porous media, J. Fluid Mech., 189, 165−187 (1988).

    Article  Google Scholar 

  2. 2.

    H. Liu, Y. Zhang, and A. J. Valocchi, Lattice Boltzmann simulation of immiscible fluid displacement in porous media: Homogeneous versus heterogeneous pore network, Phys. Fluids, 27, Issue 5, Article 052103 (2015).

  3. 3.

    E. W. Al-Shalabi and B. Ghosh, Effect of pore-scale heterogeneity and capillary-viscous fingering on commingled waterflood oil recovery in stratified porous media, J. Petroleum Eng., 2016, Article 1708929 (2016).

    Article  Google Scholar 

  4. 4.

    Y.-F. Chen, D.-S.Wu, Sh. Fang, and R. Hu, Experimental study on two-phase fl ow in rough fracture: Phase diagram and localized fl ow channel, Int. J. Heat Mass Transf., 122, 1298–1307 (2018).

    Article  Google Scholar 

  5. 5.

    F. Kazemifar, G. Blois, D. C. Kyritsis, and K. Christensen, Quantifying the flow dynamics of supercritical CO2–water displacement in a 2D porous micromodel using fluorescent microscopy and microscopic PIV, Adv. Water Res., 95, 352–368 (2016).

    Article  Google Scholar 

  6. 6.

    T. Tsuji, F. Jiang, and K. T. Christensen, Characterization of immiscible fluid displacement processes with various capillary numbers and viscosity ratios in 3D natural sandstone, Adv. Water Res., 95, 3−15 (2016).

    Article  Google Scholar 

  7. 7.

    S. Leclaire, A. Parmigiani, O. Malaspinas, B. Chopard, and J. Latt, Generalized three-dimensional lattice Boltzmann color-gradient method for immiscible two-phase pore-scale imbibition and drainage in porous media, Phys. Rev. E., 95, Article 033306 (2017).

    Article  Google Scholar 

  8. 8.

    T. R. Zakirov, A. A. Galeev, and M. G. Khramchenkov, Pore-scale investigation of two-phase flows in three-dimensional digital models of natural sandstones, Fluid Dyn., 53, No. 5, 76−91 (2018).

    Article  Google Scholar 

  9. 9.

    S. Berg, H. Ott, S. Klapp, A. Schwing, R. Neiteler, N. Brussee, A. Makurat, L. Leu, F. Enzmann, J.-O. Schwarz, M. Kersten, S. Irvine, and M. Stampanoni, Real-time 3D imaging of Haines jumps in porous media fl ow, Proc. Nat. Acad. Sci. USA, 10, 3755−3759 (2013).

    Article  Google Scholar 

  10. 10.

    M. Mehravaran and S. K. Hannani, Simulation of incompressible two-phase flows with large density differences employing lattice Boltzmann and level set methods, Comput. Methods Appl. Mech. Eng., 198, 223–233 (2008).

    Article  Google Scholar 

  11. 11.

    A. Q. Raeini, M. Blunt, and B. Bijeljic, Modeling two-phase flow in porous media at the pore scale using the volumeof- fluid method, J. Comput. Phys., 231, 5653–5668 (2012).

    MathSciNet  Article  Google Scholar 

  12. 12.

    X. Shan and H. Chen, Lattice Boltzmann model for simulating flows with multiple phases and components, Phys. Rev., 47, Issue 3, 1815–1819 (1993).

    Google Scholar 

  13. 13.

    I. Zacharoudiou and E. S. Boek, Capillary fi lling and Haines jump dynamics using free energy Lattice Boltzmann simulations, Adv. Water Res., 92, 43–56 (2016).

    Article  Google Scholar 

  14. 14.

    H. Huang, J.-J. Huang, and X.-Y. Lu, Study of immiscible displacements in porous media using a color-gradient-based multiphase lattice Boltzmann method, Comput. Fluids, 93, 164–172 (2014).

    MathSciNet  Article  Google Scholar 

  15. 15.

    H. Huang, L. Wang, and X. Lu, Evaluation of three lattice Boltzmann models for multiphase flows in porous media, Comput. Math. Appl., 61, 3606–3617 (2011).

    MathSciNet  Article  Google Scholar 

  16. 16.

    S. Chen and G. Doolen, Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech., 30, 329−364 (1998).

    MathSciNet  Article  Google Scholar 

  17. 17.

    T. R. Zakirov, A. A. Galeev, E. O. Statsenko, and L. I. Khaidarova, Calculation of fi ltration characteristics of porous media by their digitized images with the use of lattice Boltzmann equations, J. Eng. Phys. Thermophys., 91, No. 4, 1069−1078 (2018).

    Article  Google Scholar 

  18. 18.

    T. Reis and T. N. Phillips, Lattice Boltzmann model for simulating immiscible two-phase flows, J. Phys. A: Math. Theor., 40, 4033–4053 (2007).

    MathSciNet  Article  Google Scholar 

  19. 19.

    M. Latva-Kokko and D. H. Rothman, Static contact angle in lattice Boltzmann models of immiscible fluids, Phys. Rev. E, 72, Article 046701 (2005).

    Article  Google Scholar 

  20. 20.

    J. Huang, F. Xiao, and X. Yin, Lattice Boltzmann simulation of pressure-driven two-phase flows in capillary tube and porous medium, Comput. Fluids, 100, 164–172 (2014).

    Article  Google Scholar 

  21. 21.

    F. Moebius and D. Or, Interfacial jumps and pressure bursts during fluid displacement in interacting irregular capillaries, J. Colloid Interface Sci., 377, 406–415 (2012).

    Article  Google Scholar 

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Correspondence to T. R. Zakirov or M. G. Khramchenkov.

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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 93, No. 3, pp. 755–765, May–June, 2020.

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Zakirov, T.R., Khramchenkov, M.G. Simulation of Two-Phase Fluid Flow in the Digital Model of a Pore Space of Sandstone at Different Surface Tensions. J Eng Phys Thermophy (2020). https://doi.org/10.1007/s10891-020-02173-w

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Keywords

  • two-phase flows
  • surface tension
  • digital core
  • simulation
  • lattice Boltzmann equations (method)
  • capillary fingers