Simulation of fluid penetration with high density ratio in layered porous media with lattice Boltzmann model by using equations of state

Document Type : Research Article

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Abstract

In this study, drop penetration with high density ratio in layered porous medium is simulated with pseudo- potential lattice boltzmann model. Due to inherent weakness of this model in simulation of flows with high density ratio, equations of state as Redlich-Kwong and Peng-Robinson are used. The influence of temperature in surface tension is studied. Some validation is done as comparison of continues curves with theoretical maxwell ones and another two simple tests that their results are according to previous ones. After validation of code with previous works, drop penetration is investigated in layered porous medium which is made of four sections with the same porosity to produce more homogenous porosity. The effect of different factors like porosity, hydrophobicity/ hyrophilicity property of surfaces on the penetration rate and pattern is studied. The results illustrate that by decreasing the porosity, penetration rate would decrease too and in general hydrophilic surface in low porosity increase the penetration rate; Also, the difference of penetration pattern in two situations is illustrated, in hydrophilic situation penetration pattern is cloy and piston – type and in hydrophobic one penetration is like a finger or finger-type. Then, for more investigation of penetration in porous medium and showing the ability of written code, it is improved to simulate two component- two phase flows. After validation, the penetration pattern in different capillary numbers and viscosity ratios, viscous fingering and capillary fingering regimes are observed. At the end, change of penetration pattern by consideration the surface hydrophilic is studied.

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References

[1] A.K. Gunstensen; D.H. Rothman; S. Zaleski and G.Zanetti, “Lattice Boltzmann model of immiscible
fluids”, J. Physical Review A, Vol. 43, pp. 4320-4327,1991.
[2] X. Shan and H. Chen, “Simulation of nonideal gases and liquid-gas phase transitions by the lattice
Boltzmann equation”, J. Physical Review E, Vol. 49,pp. 2941-2948, 1994.
[3] O.W. Swift MR, Yeomans JM, “Lattice Boltzmann simulation of nonideal fluids”, J. Phys Rev Lett, Vol.
75, pp. 830–833, 1995.
[4] X. He;S. Chen and R. Zhang, “A Lattice Boltzmann Scheme for Incompressible Multiphase Flow and
Its Application in Simulation of Rayleigh–Taylor Instability”, J. Journal of Computational Physics, Vol.
152, pp. 642-663, 1999.
[5] P. Yuan and L. Schaefer, “Equations of state in a lattice Boltzmann model”, J. Physics of Fluids (1994-present), Vol. 18, 2006.
[6] A.L. Kupershtokh; D.A. Medvedev and D.I. Karpov, “On equations of state in a lattice Boltzmann method”,
J. Computers & Mathematics with Applications, Vol.58, pp.965-974, 2009.
[7] T. Inamuro;T. Ogata;S. Tajima and N. Konishi, “A lattice Boltzmann method for incompressible twophase
flows with large density differences”, J. Journal of Computational Physics, Vol. 198, pp. 628-644,2004.
[8] R. Zhang and H. Chen, “Lattice Boltzmann method for simulations of liquid-vapor thermal flows”, J. Physical
Review E, Vol. 67, pp. 066711, 2003.
[9] A. Hu;L. Li;S. Chen;Q. Liao and J. Zeng, “On equations of state in pseudo-potential multiphase lattice oltzmann model with large density ratio”, J.International Journal of Heat and Mass Transfer, Vol.67, pp. 159-163, 2013.
[10] C. Zhang;M. Oostrom;T.W. Wietsma;J.W. Grate and M.G. Warner, “Influence of Viscous and Capillary
Forces on Immiscible Fluid Displacement: Pore-Scale Experimental Study in a Water-Wet Micromodel
Demonstrating Viscous and Capillary Fingering ”, J.Energy & Fuels, Vol. 25, pp. 3493-3505, 2011.
[11] B. Dong; Y.Y. Yan; W. Li and Y. Song, “Lattice Boltzmann simulation of viscous fingering phenomenon of immiscible fluids displacement in a channel”, J. Computers & Fluids, Vol. 39, pp. 768-779, 2010.
[12] M. Taghilou and M.H. Rahimian, “simulation of 2D droplet penetration in porous media using lattice boltzmann method ”, J. Modares Mechanical Engineering, Vol. 13, pp.43-56, 2014.
[13] M.C. Sukop, Thorne, Daniel T., “ Lattice Boltzmann Modeling ”. 1 ed., Florida USA: Springer-Verlag Berlin Heidelberg, 2006.
[14] M.R. kamali, “A Lattice Boltzmann Approach to Multi-Phase Surface Reactions with Heat Effects”, in Chemical Engineering. Delft‌ University of Technology, 2013.
[15] S. Gong and P. Cheng, “Numerical investigation of droplet motion and coalescence by an improved lattice
Boltzmann model for phase transitions and multiphase flows”, J. Computers & Fluids, Vol. 53, pp. 93-104,2012.
[16] A.T. Prashant K. Jain, Rizwan-uddin, “A lattice Boltzmann framework to simulate boiling‌water reactorcore hydrodynamics”, J. Computers and Mathematics with Applications, Vol. 58, pp. 975-986,2009.
[17] T. Reis, “The Lattice Boltzmann Method for Complex Flows”. University of Cardiff: United Kingdom, 2007.
[18] C.S. H.W. Zheng, Y.T. Chew, “A lattice Boltzmann model for multiphase flows with large density ratio”,J. Journal of Computational Physics, Vol. 218, pp.353–371, 2006.
[19] M. Taghilou and M.H. Rahimian, “Investigation of two-phase flow in porous media using lattice Boltzmann method”, J. Computers & Mathematics with Applications, Vol. 67, pp. 424-436, 2014.
[20] S. Chen and G.D. Doolen, “LATTICE BOLTZMANN METHOD FOR FLUID FLOWS”, J. Annual Review
of Fluid Mechanics, Vol. 30, pp. 329-364, 1998.
[21] X. Shan and H. Chen, “Lattice Boltzmann model for simulating flows with multiple phases and
components”, J. Physical Review E, Vol. 47, pp. 1815-1819, 1993.
[22] N.G.D. M. van Sint Annaland, J.A.M. Kuipers, “Numerical simulation of gas bubbles behavior using a three-dimensionalvolume of fluid method”,J. Chemical Engineering Science, Vol. 60, pp. 2999-3011, 2005.
[23] 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”, J. Computers & Fluids, Vol. 93, pp. 164- 172, 2014.
[24] A.M. Worthington, “On the forms assumed by drops of liquids falling vertically on a horizontal plate”, J.
Proc. R. Soc. Lond. Ser. A, Vol. 25, pp. 261–271, 1876.
Amirkabir Journal of Mechanical Engineering
Volume 48, Issue 1
June 2016
Pages 55-66

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