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Convection-Diffusion with the Colour Gradient Lattice Boltzmann Method for Three-Component, Two-Phase Flow

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Abstract

The Rothman-Keller colour gradient Lattice Boltzmann Method (LBM) provides a means to simulate two phase flow of immiscible fluids by modelling number densities of two fluids, plus a “recoloring” step that ensures separation of the two fluids. Here, we model an additional number density representing the concentration of an additive to fluid 1 which affects the viscosity of this fluid. The Peclet number – rate of advection to diffusion – is used to set the diffusion coefficient of the concentration. We present tests to demonstrate the method including flow and merging of two adjacent droplets with different additive concentrations, and two-phase flow tests in a 2D porous matrix involving injection of fluid with an additive that increases the viscosity and thus decreases viscous fingering (e.g. a polymer additive). We demonstrate that use of polymers from the start of waterflooding leads to a high saturation of 90% much sooner than when polymers are applied after breakthrough. This work demonstrates that the RK color gradient multiphase LBM can be used to study viscous fingering behavior in porous media in which the injected low viscosity fluid can have its viscosity varied with time by use of an additive. This is both of scientific interest and has economic implications to Enhanced Oil Recovery, in which water–potentially with a polymer additive to increase viscosity– is injected from an injection well into a rock layer saturated with a high viscosity fluid (oil) to help push out the oil into a production well.

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References

  • Abidin, A.Z., Puspasar, T., Nugroho, W.A.: Polymers for enhanced oil recovery technology. Procedia Chem. 4, 11–16 (2012). https://doi.org/10.1016/j.proche.2012.06.002

    Article  Google Scholar 

  • Armstrong, R.T., Berg, S., Dinariev, O., Evseev, N., Klemin, D., Koroteev, D., Safonov, S.: Modeling of Pore-Scale Two-Phase phenomena using density functional hydrodynamics. Transp. Porous Media 112, 577–607 (2016)

    Article  Google Scholar 

  • Blunt, M.J., Bijeljic, B., Dong, H., Gharbi, O., Iglauer, S., Mostaghimi, P., Paluszny, A., Pentland, C.: Pore-scale imaging and modelling. Adv. Water Resour. 51, 197–216 (2013)

    Article  Google Scholar 

  • Chen, J.D., Wilkinson, D.: Pore-scale viscous fingering in porous media. Phys. Rev. Lett. 55(18), 1892–1896 (1985)

    Article  Google Scholar 

  • Cueto-Felgueroso, L., Juanes, R.: A phase-field model of two-phase Hele-Shaw flow. J. Fluid Mech. 758, 522–552 (2014)

    Article  Google Scholar 

  • Cueto-Felgueroso, L., Fu, X., Juanes, R.: Pore-scale modeling of phase change in porous media. Phys. Rev. Fluids 3(8), 084302 (2018)

    Article  Google Scholar 

  • Deng, X., Kamal, M.S., Patil, S., Hussain, S.M.S., Zhou, X.: A review on wettability alteration in catbonate rocks: wettability modifiers. Energy Fuels 34, 31–54 (2020)

    Article  Google Scholar 

  • Demianov, A., Dinariev, O., Evseev, N.: Density functional modelling in multiphase compositional hydrodynamics. Can. J. Chem. Eng. 89, 207–226 (2011)

    Article  Google Scholar 

  • Grosfils, P., Boon, J.P., Chin, J., Boek, E.S.: Structural and dynamical characterization of Hele-Shaw viscous fingering, Philosophical Transactions of the Royal Society of London. Series A: Math, Phys. Eng. Sci. 362(1821), 1723–1734 (2004)

    Google Scholar 

  • Grunau, D., Chen, S., Eggert, K.: A lattice Boltzmann model for multiphase fluid flows. Phys. Fluids A: Fluid Dyan. 5(10), 2557–2562 (1993)

    Article  Google Scholar 

  • Gunstensen, A.K., Rothman, D.H., Zeleski, S., Zanetti, G.: Lattice Boltzmann model of immiscible fluids. Phys. Rev. A 43(8), 4320–4327 (1991)

    Article  Google Scholar 

  • He, X., Chen, S., Zhang, R.: A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh-Taylor instability. J. Comput. Phys. 152(2), 642–663 (1999)

    Article  Google Scholar 

  • Homsy, G.M.: Viscous fingering in porous media. Ann. Rev. Fluid Mech. 19, 271–311 (1997)

    Article  Google Scholar 

  • Huang, H., Sukop, M., Lu, X.: Multiphase lattice Boltzmann methods: Theory and application, p. 312. John Wiley & Sons, UK (2015)

    Book  Google Scholar 

  • Inamuro, T., Ogata, T., Tajima, S., Konishi, N.: A lattice Boltzmann method for incompressible two-phase flows with large density differences. J. Comput. Phys. 198(2), 628–644 (2004)

    Article  Google Scholar 

  • Jadhunandan, P.P., Morrow, N.R.: Effect of wettability on waterflood recovery for crude-oil/brine/rock systems, SPE Reserv. Eng. 10, 40–46 (1995)

    Google Scholar 

  • Kennedy, H.T., Burja, E.O., Boykin, R.S.: An investigation of the effects of wettability on the recovery of oil by water flooding. J. Phys. Chem. 59, 867–879 (1955)

    Article  Google Scholar 

  • Krüger, T., Kusumaatmaja, H., Kuzmin, O.: The Lattice Boltzmann Method: Principles and Practice (Chapter 8), Springer, https://doi.org/10.1007/978-3-319-44649-3_8

  • Latva-Kokko, M., Rothman, D.: Static contact angle in lattice Boltzmann models of immiscible fluids. Phys. Rev. E 74(4), 046701 (2005)

    Article  Google Scholar 

  • Leclaire, S., Reggio, M., Trépanier, J.-Y.: Isotropic color gradient for simulating very high-density ratios with a two-phase flow lattice Boltzmann model. Comput. Fluids 48(1), 98–112 (2011)

    Article  Google Scholar 

  • Lenormand, R., Touboul, E., Zarcone, C.: Numerical models and experiments on immiscible displacements in porous media. J. Fluid Mech. 1989, 165–187 (1988)

    Article  Google Scholar 

  • Måløy, K.J., Feder, J., Jøssang, T.: Viscous fingering fractals in porous media. Phys. Rev. Lett. 55(24), 2688–2691 (1985)

    Article  Google Scholar 

  • Mora, P., Morra, G., Yuen, D.: Optimal surface tension isotropy in the Rothman-Keller colour gradient Lattice Boltzmann Method for multi-phase flow. Phys. Rev. E 103(3), 033302 (2021). https://doi.org/10.1103/PhysRevE.103.033302

    Article  Google Scholar 

  • Mora, P., Morra, G., Yuen, D., Juanes, R.: Optimal wetting angles in Lattice Boltzmann simulations of viscous fingering. Transp. Porous Media 136, 831–842 (2021). https://doi.org/10.1007/s11242-020-01541-7

    Article  Google Scholar 

  • Mora, P., Morra, G., Yuen, D., Juanes, R.: Influence of wetting on viscous fingering via 2D Lattice Boltzmann simulations. Transp. Porous Media 138, 511–538 (2021). https://doi.org/10.1007/s11242-021-01629-8

    Article  Google Scholar 

  • Morrow, N., Buckley, J.: Improved oil recovery by low salinity waterflooding. J. Pet. Technol. 63, 106–112 (2011)

    Article  Google Scholar 

  • Reis, T., Phillips, T.N.: Lattice Boltzmann model for simulating immiscible two-phase flows. J. Phys. A Math. Theor. 40(14), 4033–4053 (2007)

    Article  Google Scholar 

  • Rothman, D., Keller, J.: Immiscible cellular automaton fluids. J. Stat. Phys. 52(3/4), 1119–1127 (1988)

    Article  Google Scholar 

  • Seethepalli, A., Adibhatla, B., Mohanty, K.K.: Physicochemical interactions during surfactant flooding of fractured carbonate reservoirs. SPE J. 9(4), 411–418 (2004). https://doi.org/10.2118/89423-PA

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Swift, M.R., Orlandini, E., Osborn, W.R., Yeomans, J.M.: Lattice Boltzmann simulations of liquid-gas and binary fluid systems. Phys. Rev. E 54(5), 5041 (1996)

    Article  Google Scholar 

  • Trojer, M., Szulczewski, M.L., Juanes, R.: Stabilizing fluid-fluid displacements in porous media through wettability alteration. Phys. Rev. Appl. 3(5), 054008 (2015)

    Article  Google Scholar 

  • Wang, H., Yuan, X., Liang, H., Chai, Z., Shi, B.: A brief review of the phase-field-based lattice Boltzmann method for multiphase flows. Capillarity 2(3), 33–52 (2019)

    Article  Google Scholar 

  • Yakimchuk, I., Evseev, N., Korobkov, D., Ridzel, O., Pletneva, V.: Study of polymer flooding at pore scale by digital core analysis for East-Messoyakhskoe Oil Field, in SPE Russian Petroleum Technology Conference, Virtual, October 2020, Paper Number: SPE-202013-MS, https://doi.org/10.2118/202013-MS (2020)

  • Yang, J., Boek, E.S.: A comparison study of multi-component Lattice Boltzmann models for flow in porous media applications. Computers & Mathematics with Applications 65(6), 882–890 (2013)

    Article  Google Scholar 

  • Zhang, Z., Li, Z., Wu, W.: Advection-diffusion Lattice Boltzmann Method with and without dynamical filter. Front. Phys. 10, 875628 (2022)

    Article  Google Scholar 

  • Zhao, B., MacMinn, C.W., Juanes, R.: Wettability control on multiphase flow in patterned microfluidics. Proc. Natl. Acad. Sci. U.S.A. 113(37), 10251–10256 (2016)

    Article  Google Scholar 

  • Zou, Q., He, X.: On pressure and velocity flow boundary conditions and bounce back for the lattice Boltzmann BGK model. Phys. Fluids 9, 1591–1598 (1997)

    Article  Google Scholar 

  • Zacharoudiou, I., Boek, E.S., Crawshaw, J.: Pore-scale modeling of drainage displacement patterns in association with geological sequestration of CO2. Water Resour. Res. 56(11), e2019WR026332 (2020). https://doi.org/10.1029/2019WR026332

    Article  Google Scholar 

  • Zhao, B., MacMinn, C.W., Primkulov, B.K., Chen, Y., Valocchi, A.J., Zhao, J., Juanes, R.: Comprehensive comparison of pore-scale models for multiphase flow in porous media. Proc. Nat. Acad. Sci. 116(28), 13799–13806 (2019)

    Article  Google Scholar 

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Acknowledgements

This research was supported by the College of Petroleum Engineering and Geosciences at King Fahd University of Petroleum and Minerals, Saudi Arabia. D.A. Yuen would like to thank National Science Foundations geochemistry and CISE program for support. In addition, this research was in part funded by the US Department of Energy Grant DE-SC0019759 (D.A.Y) by the National Science Foundation (NSF) Grant EAR-1918126 (D.A.Y).

Funding

This research was supported by the College of Petroleum Engineering and Geosciences at King Fahd University of Petroleum and Minerals, Saudi Arabia. In addition, this research was funded by the US Department of Energy Grant DE-SC0019759 (D A. Y) by the National Science Foundation (NSF) Grant EAR-1918126 (D.A.Y).

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Authors and Affiliations

  1. Geosciences Department, College of Petroleum Engineering and Geosciences, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Peter Mora

  2. Department of Physics, University of Louisiana at Lafayette, 104 E University Ave, Lafayette, LA, 70504, USA

    Gabriele Morra

  3. Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, 10027, USA

    Dave A. Yuen

  4. Department of Information Science and Engineering and College of Marine Geosciences, Ocean University of China, 238 Songling Road, Qingdao, 266100, China

    Dave A. Yuen

  5. Petroleum Engineering Department, College of Petroleum Engineering and Geosciences, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Shirish Patil

  6. Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Ruben Juanes

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Correspondence to Peter Mora.

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Mora, P., Morra, G., Yuen, D.A. et al. Convection-Diffusion with the Colour Gradient Lattice Boltzmann Method for Three-Component, Two-Phase Flow. Transp Porous Med 147, 259–280 (2023). https://doi.org/10.1007/s11242-023-01906-8

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