×

Pore-scale numerical investigations of fluid flow in porous media using lattice Boltzmann method. (English) Zbl 1356.76274

Summary: Purpose{ } - Lattice Boltzmann method (LBM) is employed to explore friction factor of single-phase fluid flow through porous media and the effects of local porous structure including geometry of grains in porous media and specific surface of porous media on two-phase flow dynamic behavior, phase distribution and relative permeability. The paper aims to discuss this issue. { }Design/methodology/approach{ } - The 3D single-phase LBM model and the 2D multi-component multi-phase Shan-Chen LBM model (S-C model) are developed for fluid flow through porous media. For the solid site, the bounce back scheme is used with non-slip boundary condition. { }Findings{ } - The predicted friction factor for single-phase fluid flow agrees well with experimental data and the well-known correlation. Compared with porous media with square grains, the two-phase fluids in porous media with circle grains are more connected and continuous, and consequently the relative permeability is higher. As for the factor of specific porous media surface, the relative permeability of wetting fluids varies a little in two systems with different specific surface areas. In addition, the relative permeability of non-wetting fluid decreases with the increasing of specific surface of porous media due to the large flow resistance. { }Originality/value{ } - Fluid-fluid interaction and fluid-solid interaction in the SC LBM model are presented, and schemes to obtain immiscible two-phase flow and different contact angles are discussed. Two-off mechanisms acting on the wetting fluids is proposed to illustrate the relative permeability of wetting fluids varies a little in two systems with different specific surface.

MSC:

76M28 Particle methods and lattice-gas methods
76S05 Flows in porous media; filtration; seepage
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Aerov, M.E. and Tojec, O.M. (1968), Hydraulic and Thermal Basis on the Performance of Apparatus with Stationary and Boiling Granular Layer , Himia Press, Leningrad.
[2] Bhatnagar, P.L. , Gross, E.P. and Krook, M. (1954), ”A model for collision processes in gases. I. small amplitude processes in charged and neutral one-component systems”, Physical Review , Vol. 94 No. 3, pp. 511. , · Zbl 0055.23609 · doi:10.1108/HFF-07-2014-0202
[3] Blunt, M. , King, M.J. and Scher, H. (1992), ”Simulation and theory of two-phase flow in porous media”, Physical Review A , Vol. 46 No. 12, pp. 7680-7699. , · Zbl 1356.76274 · doi:10.1108/HFF-07-2014-0202
[4] Boek, E.S. and Venturoli, M. (2010), ”Lattice-Boltzmann studies of fluid flow in porous media with realistic rock geometries”, Applied Mathematics and Computation , Vol. 59 No. 7, pp. 2305-2314. · Zbl 1193.76104
[5] Buckles, J.J. , Hazlett, R.D. , Chen, S. , Eggert, K.G. , Grunau, D.W. and Soll, W.E. (1994), ”Toward improved prediction of reservoir flow performance: simulating oil and water flows at the pore scale”, Los Alamos Science , No. 22, pp. 112-121.
[6] Chen, L. , Kang, Q. , Mu, Y. , He, Y.-L. and Tao, W.-Q. (2014), ”A critical review of the pseudopotential multiphase lattice Boltzmann model: methods and applications”, International Journal of Heat and Mass Transfer , Vol. 76, pp. 210-236. , · Zbl 1356.76274 · doi:10.1108/HFF-07-2014-0202
[7] Chen, L. , Kang, Q. , Robinson, B.A. , He, Y.-L. and Tao, W.-Q. (2013), ”Pore-scale modeling of multiphase reactive transport with phase transitions and dissolution-precipitation processes in closed systems”, Physical Review E , Vol. 87 No. 4, p. 43306. , · Zbl 1356.76274 · doi:10.1108/HFF-07-2014-0202
[8] Dou, Z. and Zhou, Z.F. (2013), ”Numerical study of non-uniqueness of the factors influencing relative permeability in heterogeneous porous media by lattice Boltzmann method”, International Journal of Numerical Methods for Heat & Fluid Flow , Vol. 42, pp. 23-32. , · Zbl 1356.76274 · doi:10.1108/HFF-07-2014-0202
[9] Ghassemi, A. and Pak, A. (2011), ”Numerical study of factors influencing relative permeabilities of two immiscible fluids flowing through porous media using lattice Boltzmann method”, Journal of Petroleum Science and Engineering , Vol. 77 No. 1, pp. 135-145. , · Zbl 1356.76274 · doi:10.1108/HFF-07-2014-0202
[10] Gunstensen, A.K. , Rothman, D.H. , Zaleski, S. and Zanetti, G. (1991), ”Lattice Boltzmann model of immiscible fluids”, Physical Review A , Vol. 43 No. 8, pp. 4320-4327. , · Zbl 1356.76274 · doi:10.1108/HFF-07-2014-0202
[11] Guo, Z.L. , Zheng, C.G. and Shi, B.C. (2002), ”An extrapolation method for boundary conditions in lattice Boltzamnn method”, Physics of Fluids , Vol. 14 No. 6, pp. 2007. , · Zbl 1356.76274 · doi:10.1108/HFF-07-2014-0202
[12] Hao, L. and Cheng, P. (2010), ”Pore-scale simulations on relative permeabilities of porous media by lattice Boltzmann method”, International Journal of Heat and Mass Transfer , Vol. 53 Nos 9/10, pp. 1908-1913. · Zbl 1305.76105 · doi:10.1108/HFF-07-2014-0202
[13] Honarpour, M. , Koederitz, L. and Harvey, A. (1986), Relative Permeability of Petroleum Reservoirs , CRC Press, Boca Raton, FL.
[14] Hou, S.L. , Shan, X.W. , Zou, Q.S. , Doolen, G.D. and Soll, W.E. (1997), ”Evaluation of two lattice Boltzmann models for multiphase flows”, Journal of Computational Physics , Vol. 138 No. 2, pp. 695-713. , · Zbl 0913.76094 · doi:10.1108/HFF-07-2014-0202
[15] Huang, H. , Li, Z. , Liu, S. and Lu, X. (2009), ”Shan-and-Chen-type multiphase lattice Boltzmann study of viscous coupling effects for two-phase flow in porous media”, The International Journal for Numerical Methods in Fluids , Vol. 63 No. 3, pp. 341-354. · Zbl 1173.76041
[16] Huang, H. , Thorne, D.T. , Schaap, M.G. and Sukop, M.C. (2007), ”Proposed approximation for contact angles in Shan-and-Chen-type multicomponent multiphase lattice Boltzmann models”, Physical Review E , Vol. 76 No. 6, 066701. · Zbl 1356.76274 · doi:10.1108/HFF-07-2014-0202
[17] Inamuro, T. , Yoshino, M. and Ogino, F. (1995), ”A non-slip boundary condition for lattice Boltzmann simulations”, Physics of Fluids , Vol. 7 No. 12, pp. 2928-2930. , · Zbl 1027.76631 · doi:10.1108/HFF-07-2014-0202
[18] Jia, X. , Mclaughlin, J.B. and Kontomaris, K. (2008), ”Lattice Boltzmann simulations of flows with fluid-fluid interfaces”, Asia-Pacific Journal of Chemical Engineering , Vol. 3 No. 2, pp. 124-143. , · Zbl 1356.76274 · doi:10.1108/HFF-07-2014-0202
[19] Jiang, P.X. and Lu, X.C. (2006), ”Numerical simulation of fluid flow and convection heat transfer in sintered porous plate channels”, International Journal of Heat and Mass Transfer , Vol. 49 Nos 9/10, pp. 1685-1695. · Zbl 1189.76538 · doi:10.1108/HFF-07-2014-0202
[20] Jiang, P.X. , Xu, R.N. and Gong, W. (2006), ”Particle-to-fluid heat transfer coefficients in miniporous media”, Chemical Engineering Science , Vol. 61 No. 2, pp. 7213-7222.
[21] Kang, Q. , Zhang, D. and Chen, S. (2002), ”Displacement of a two-dimensional immiscible droplet in a channel”, Physics of Fluids , Vol. 14 No. 9, pp. 3203-3214. , · Zbl 1185.76192 · doi:10.1108/HFF-07-2014-0202
[22] Kang, Q. , Zhang, D. and Chen, S. (2004), ”Immiscible displacement in a channel: simulations of fingering in two dimensions”, Advances in Water Resources , Vol. 27 No. 1, pp. 13-22. , · Zbl 1356.76274 · doi:10.1108/HFF-07-2014-0202
[23] Lewis, R.W. and Ghafouri, H.R. (1997), ”A novel finite element double porosity model for multiphase flow through deformable fractured porous media”, International Journal for Numerical and Analytical Methods in Geomechanics , Vol. 21 No. 11, pp. 789-816. , · Zbl 1356.76274 · doi:10.1108/HFF-07-2014-0202
[24] Lewis, R.W. , Pao, W. and Yang, X.S. (2003), ”Finite element analysis and approximate estimation of the cross coupling effect in fractured reservoirs”, Geophysical Research Letters , Vol. 30 No. 14, pp. 1737-1741. · Zbl 1356.76274 · doi:10.1108/HFF-07-2014-0202
[25] Lewis, R.W. , Pao, W. and Yang, X.S. (2004), ”Instability and reaction-diffusion transport of bacteria”, Communications in Numerical Methods in Engineering , Vol. 20 No. 10, pp. 777-787. , · Zbl 1077.92049 · doi:10.1108/HFF-07-2014-0202
[26] Li, H.N. , Pan, C.X. and Miller, C.T. (2005), ”Pore-scale investigation of viscous coupling effects for two-phase flow in porous media”, Physical Review E , Vol. 72 No. 2, 026705. · Zbl 1356.76274 · doi:10.1108/HFF-07-2014-0202
[27] Long, J.C.S. , Remer, J.S. , Wilson, C.R. and Witherspoon, P.A. (1982), ”Porous media equivalent for networks of discontinuous fractures”, Water Resources Research , Vol. 18 No. 3, pp. 645-658. , · Zbl 1356.76274 · doi:10.1108/HFF-07-2014-0202
[28] Lowry, M.I. and Miller, C.T. (1995), ”Pore-scale modeling of nonwetting-phase residual in porous media”, Water Resources Research , Vol. 31 No. 3, pp. 455-473. , · Zbl 1356.76274 · doi:10.1108/HFF-07-2014-0202
[29] Martys, N. and Chen, H. (1996), ”Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann method”, Physical Review E , Vol. 53 No. 1, pp. 743-750. , · Zbl 1356.76274 · doi:10.1108/HFF-07-2014-0202
[30] Nourgaliev, R.R. , Theofanous, T.G. and Joseph, D.D. (2003), ”The lattice Boltzmann equation method: theoretical interpretation, numerics and implications”, International Journal of Multiphase Flow , Vol. 29 No. 1, pp. 117-169. , · Zbl 1136.76594 · doi:10.1108/HFF-07-2014-0202
[31] Pan, C. , Hilpert, M. and Miller, C.T. (2004), ”Lattice-Boltzmann simulation of two-phase flow in porous media”, Water Resources Research , Vol. 40 No. 1, p. W01501.
[32] Pan, C. , Luo, L.-S. and Miller, C.T. (2006), ”An evaluation of lattice Boltzmann schemes for porous medium flow simulation”, Computers & Fluids , Vol. 35 Nos 8-9, pp. 898-909. , · Zbl 1177.76323 · doi:10.1108/HFF-07-2014-0202
[33] Pao, W. and Lewis, R.W. (2002), ”Three-dimensional finite element simulation of three-phase flow in a deforming fissured reservoir”, Computer Methods in Applied Mechanics and Engineering , Vol. 191 Nos 23-24, pp. 2631-2659. , · Zbl 1138.76387 · doi:10.1108/HFF-07-2014-0202
[34] Ramstad, T. , Idowu, N. , Nardi, C. and Øren, P.E. (2012), ”Relative permeability calculations from two-phase flow simulations directly on digital images of porous rocks”, Transport in Porous Media , Vol. 94 No. 2, pp. 487-504. , · Zbl 1356.76274 · doi:10.1108/HFF-07-2014-0202
[35] Shan, X. and Chen, H. (1993), ”Lattice Boltzmann model for simulating flows with multiple phases and components”, Physical Review E , Vol. 47 No. 3, pp. 1815-1819. , · Zbl 1356.76274 · doi:10.1108/HFF-07-2014-0202
[36] Shan, X. and Doolen, G.D. (1995), ”Multicomponent lattice-Boltzmann model with interparticle interaction”, The Journal of Statistical Physics , Vol. 81 Nos 1-2, pp. 379-393. , · Zbl 1106.82358 · doi:10.1108/HFF-07-2014-0202
[37] Swift, M.R. , Orlandini, E. , Osborn, W. and Yeomans, J.M. (1996), ”Lattice Boltzmann simulations of liquid-gas and binary fluid systems”, Physical Review E , Vol. 54 No. 5, pp. 5041-5052. , · Zbl 1356.76274 · doi:10.1108/HFF-07-2014-0202
[38] Swift, M.R. , Osborn, W. and Yeomans, J.M. (1995), ”Lattice Boltzmann simulation of nonideal fluids”, Physical Review Letters , Vol. 75 No. 5, pp. 830-833. , · Zbl 1356.76274 · doi:10.1108/HFF-07-2014-0202
[39] Xu, R.-N. and Jiang, P.-X. (2008), ”Numerical simulation of fluid flow in microporous media”, International Journal of Heat and Fluid Flow , Vol. 29 No. 5, pp. 4418-4424. · Zbl 1221.80004
[40] Xu, R.-N. , Luo, S. and Jiang, P.-X. (2011), ”Pore scale numerical simulation of supercritical CO_{2} injecting into porous media containing water”, Energy Procedia , Vol. 4, pp. 4418-4424. · Zbl 1356.76274 · doi:10.1108/HFF-07-2014-0202
[41] Yiotis, A.G. , Psihogios, J. , Kainourgiakis, M.E. , Papaioannou, A. and Stubos, A.K. (2007), ”A lattice Boltzmann study of viscous coupling effects in immiscible two-phase flow in porous media”, Colloids and Surfaces A , Vol. 300 Nos 1-2, pp. 35-49. , · Zbl 1356.76274 · doi:10.1108/HFF-07-2014-0202
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.