Study of Fingering Dynamics of Two Immiscible Fluids in a Homogeneous Porous Medium with Considering Wettability Effects Using a Pore-Scale Multicomponent Lattice Boltzmann Model
Keywords:Porous media, immiscible fluids, fingering regimes, lattice Boltzmann method
In the present study, a pore-scale multicomponent lattice Boltzmann method (LBM) is employed for the investigation of the immiscible-phase fluid displacement in a homogeneous porous medium. The viscous fingering and the stable displacement regimes of the invading fluid in the medium are quantified which is beneficial for predicting flow patterns in pore-scale structures, where an experimental study is extremely difficult. Herein, the Shan-Chen (S-C) model is incorporated with an appropriate collision model for computing the interparticle interaction between the immiscible fluids and the interfacial dynamics. Firstly, the computational technique is validated by a comparison of the present results obtained for different benchmark flow problems with those reported in the literature. Then, the penetration of an invading fluid into the porous medium is studied at different flow conditions. The effect of the capillary number (Ca), dynamic viscosity ratio (M), and the surface wettability defined by the contact angle (θ) are investigated on the flow regimes and characteristics. The obtained results show that for M<1, the viscous fingering regime appears by driving the invading fluid through the pore structures due to the viscous force and capillary force. However, by increasing the dynamic viscosity ratio and the capillary number, the invading fluid penetrates even in smaller pores and the stable displacement regime occurs. By the increment of the capillary number, the pressure difference between the two sides of the porous medium increases, so that the pressure drop Δp along with the domain at θ=40∘ is more than that of computed for θ=80∘. The present study shows that the value of wetting fluid saturation Sw at θ=40∘ is larger than its value computed with θ=80∘ that is due to the more tendency of the hydrophilic medium to absorb the wetting fluid at θ=40∘. Also, it is found that the magnitude of Sw computed for both the contact angles is decreased by the increment of the viscosity ratio from Log(M)=−1 to 1. The present study demonstrates that the S-C LBM is an efficient and accurate computational method to quantitatively estimate the flow characteristics and interfacial dynamics through the porous medium.
Keehm, Y. Computational rock physics: Transport properties in porous media and applications. 2003.
Yang, J., Multi-scale simulation of multiphase multi-component flow in porous media using the Lattice Boltzmann Method, in Chemical Engineering. 2013, Imperia College London: Imperial College London.
Ezzatabadipour, M. and H. Zahedi, Simulation of a fluid flow and investigation of a permeability-porosity relationship in porous media with random circular obstacles using the curved boundary lattice Boltzmann method. The European Physical Journal Plus, 2018. 133(11).
Ezzatneshan, E. and R. Goharimehr, Study of spontaneous mobility and imbibition of a liquid droplet in contact with fibrous porous media considering wettability effects. Physics of Fluids, 2020. 32(11): p. 113303.
Aidun, C.K. and J.R. Clausen, Lattice-Boltzmann Method for Complex Flows. Annual Review of Fluid Mechanics, 2010. 42(1): pp. 439–472.
Ridha Djebali, M.E.G., Habib Sammouda, Investigation of a side wall heated cavity by using lattice Boltzmann method. European Journal of Computational Mechanics, 2009. 18(2).
Ezzatneshan, E., Implementation of a curved wall- and an absorbing open-boundary condition for the D3Q19 lattice Boltzmann method for simulation of incompressible fluid flows. Scientia Iranica, 2018. 26(4): pp. 2329–2341.
Gunstensen, A.K., et al., Lattice Boltzmann model of immiscible fluids. Physical Review A, 1991. 43(8): pp. 4320–4327.
Shan, X. and H. Chen, Lattice Boltzmann model for simulating flows with multiple phases and components. Physical Review E, 1993. 47(3): pp. 1815–1819.
Shan, X. and H. Chen, Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation. Physical Review E, 1994. 49(4): pp. 2941–2948.
Swift, M.R., W.R. Osborn, and J.M. Yeomans, Lattice Boltzmann simulation of nonideal fluids. Physical Review Letters, 1995. 75(5): pp. 830–833.
He, X., S. Chen, and R. Zhang, A Lattice Boltzmann Scheme for Incompressible Multiphase Flow and Its Application in Simulation of Rayleigh-Taylor Instability. Journal of Computational Physics, 1999. 152(2): pp. 642–663.
Ezzatneshan, E., Study of surface wettability effect on cavitation inception by implementation of the lattice Boltzmann method. Physics of Fluids, 2017. 29(11).
Chen, S. and G.D. Doolen, Lattice Boltzmann Method for Fluid Flows. Annual Review of Fluid Mechanics, 2002. 30(1): pp. 329–364.
McCracken, M.E. and J. Abraham, Multiple-relaxation-time lattice-Boltzmann model for multiphase flow. Phys Rev E Stat Nonlin Soft Matter Phys, 2005. 71(3 Pt 2B): p. 036701.
Ezzatneshan, E., Comparative study of the lattice Boltzmann collision models for simulation of incompressible fluid flows. Mathematics and Computers in Simulation, 2019. 156: pp. 158–177.
Kuzmin, A., A.A. Mohamad, and S. Succi, Multi-Relaxation Time Lattice Boltzmann Model for Multiphase Flows. International Journal of Modern Physics C, 2008. 19(06): pp. 875–902.
Yu, Z. and L.S. Fan, Multirelaxation-time interaction-potential-based lattice Boltzmann model for two-phase flow. Phys Rev E Stat Nonlin Soft Matter Phys, 2010. 82(4 Pt 2): p. 046708.
Zhang, D., K. Papadikis, and S. Gu, Advances in Water Resources A lattice Boltzmann study on the impact of the geometrical properties of porous media on the steady state relative permeabilities on two-phase immiscible flows. Advances in Water Resources, 2016. 95: pp. 61–79.
Bakhshian, S., S.A. Hosseini, and N. Shokri, Pore-scale characteristics of multiphase flow in heterogeneous porous media using the lattice Boltzmann method. Sci Rep, 2019. 9(1): p. 3377.
Kupershtokh, A.L., D.A. Medvedev, and D.I. Karpov, On equations of state in a lattice Boltzmann method. Computers & Mathematics with Applications, 2009. 58(5): pp. 965–974.
Ezzatneshan, E. and R. Goharimehr, A Pseudopotential Lattice Boltzmann Method for Simulation of Two-Phase Flow Transport in Porous Medium at High-Density and High–Viscosity Ratios. Geofluids, 2021. 2021: pp. 1–18.
Pan, C., L.-S. Luo, and C.T. Miller, An evaluation of lattice Boltzmann schemes for porous medium flow simulation. Computers & Fluids, 2006. 35(8-9): pp. 898–909.
Huang, H., J.J. Huang, and X.Y. Lu, Study of immiscible displacements in porous media using a color-gradient-based multiphase lattice Boltzmann method. Computers and Fluids, 2014. 93: pp. 164–172.
Gao, C., R.-N. Xu, and P.-X. Jiang, Pore-scale numerical investigations of fluid flow in porous media using lattice Boltzmann method. International Journal of Numerical Methods for Heat & Fluid Flow, 2015. 25(8): pp. 1957–1977.
Xu, M. and H. Liu, Prediction of immiscible two-phase flow properties in a two-dimensional Berea sandstone using the pore-scale lattice Boltzmann simulation. Eur Phys J E Soft Matter, 2018. 41(10): p. 124.
Ju, Y., et al., Effects of pore characteristics on water-oil two-phase displacement in non-homogeneous pore structures: A pore-scale lattice Boltzmann model considering various fluid density ratios. International Journal of Engineering Science, 2020. 154: p. 103343.
Kupershtokh, A.L., D.A. Medvedev, and D.I. Karpov, On equations of state in a lattice Boltzmann method. Computers and Mathematics with Applications, 2009. 58: pp. 965–974.
Luo, L.-S., Theory of the lattice Boltzmann method: Lattice Boltzmann models for nonideal gases. Physical Review E, 2000. 62(4): pp. 4982–4996.
Huang, H., et al., Proposed approximation for contact angles in Shan-and-Chen-type multicomponent multiphase lattice Boltzmann models. Physical Review E, 2007. 76(6): p. 066701.
Martys, N.S. and H. Chen, Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann method. Physical Review E, 1996. 53(1): pp. 743–750.
Kang, Q., D. Zhang, and S. Chen, Displacement of a two-dimensional immiscible droplet in a channel. Physics of Fluids, 2002. 14(9): pp. 3203–3214.
Pan, C., M. Hilpert, and C.T. Miller, Lattice-Boltzmann simulation of two-phase flow in porous media. Water Resources Research, 2004. 40(1): pp. 1–14.
Baakeem, S.S., S.A. Bawazeer, and A.A. Mohamad, A Novel Approach of Unit Conversion in the Lattice Boltzmann Method. Applied Sciences, 2021. 11(14): p. 6386.
Huang, H., et al., Proposed approximation for contact angles in Shan-and-Chen-type multicomponent multiphase lattice Boltzmann models. Phys Rev E Stat Nonlin Soft Matter Phys, 2007. 76(6 Pt 2): p. 066701.
Schaap, M.G., et al., Comparison of pressure-saturation characteristics derived from computed tomography and lattice Boltzmann simulations. Water Resources Research, 2007. 43(12).
Weil, K.G., J. S. Rowlinson and B. Widom: Molecular Theory of Capillarity, Clarendon Press, Oxford 1982. 327 Seiten, Preis: pounds 30,-. Berichte der Bunsengesellschaft f u r physikalische Chemie, 1984. 88(6): pp. 586–586.
Liu, H., et al., Multiphase lattice Boltzmann simulations for porous media applications. Computational Geosciences, 2015. 20(4): pp. 777–805.
Zhang, B., et al., Beyond Cassie equation: local structure of heterogeneous surfaces determines the contact angles of microdroplets. Sci Rep, 2014. 4(1): p. 5822.
Washburn, E.W., The Dynamics of Capillary Flow. Physical Review, 1921. 17(3): pp. 273–283.
Chibbaro, S., Capillary filling with pseudo-potential binary Lattice-Boltzmann model. Eur Phys J E Soft Matter, 2008. 27(1): pp. 99–106.
Lenormand, R., E. Touboul, and C. Zarcone, Numerical models and experiments on immiscible displacements in porous media. Journal of Fluid Mechanics, 2006. 189(1988): pp. 165–187.
Zhang, C., et al., Influence of Viscous and Capillary Forces on Immiscible Fluid Displacement: Pore-Scale Experimental Study in a Water-Wet Micromodel Demonstrating Viscous and Capillary Fingering. Energy & Fuels, 2011. 25(8): pp. 3493–3505.
Liu, H., Y. Zhang, and A.J. Valocchi, Lattice Boltzmann simulation of immiscible fluid displacement in porous media: Homogeneous versus heterogeneous pore network. Physics of Fluids, 2015. 27(5): p. 052103.