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LBM Mesoscale Modeling of Porous Media
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Abstract
Permeability is one of the most important bulk properties for the characterization of fluid flow in porous media. However, despite all the considerable body of research work over the past years using experimental, analytical, and numerical approaches, its determination is still a challenge. The methodologies, which have been used to measure, calculate and predict the permeability of different types of porous media, in general, tend to suffer from various levels of limitations in their applicability and, moreover, no general correlation for the permeability is available. Among the different predictive methods for the permeability, numerical pore level fluid flow analyses have been receiving increasing attention in recent years, due to its robustness and flexibility. In this approach, the viscous fluid flow is directly simulated in the pores of the porous medium with no further modeling required. A simple representation of the pore structure can be in the form of the ordered and random packings of spheres, cylinders or square obstacles. In the present paper, the main objective is to introduce the lattice Boltzmann method (LBM) as a powerful tool for the mesoscopic pore level fluid flow simulation in porous media; two and three dimensional case studies are presented to demonstrate the capabilities of the mesoscale modeling for porous media fluid flow problems using the LBM. To demonstrate an approximation to a reconstructed medium, the fluid flow simulation in a 2D random arrangement of square obstacles with different aspect ratios is presented. Results of the three dimensional simulations of the fluid flow in ordered and random packings of spheres are also reported; effect of the spheres’ radius and their arrangement on the permeability is also investigated. The results are in very good agreement with the available correlations.
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References
M. Kaviany, Principles of Heat Transfer in Porous Media (1st edition, Springer – Verlag, 1991).
K. Vafai, C.L. Tien, Boundary and inertia effects on flow and heat transfer in porous media, International Journal of Heat and Mass Transfer, Vol. 24, pp. 195-203, 1981.
M.M. Tomadakis, T.J. Robertson, Viscous permeability of random fiber structures: Comparison of electrical and diffusional estimates with experimental and analytical results, Journal of Composite Materials, Vol. 9, pp. 163-188, 2005.
H. Loosveldt, Z. Lafhaj, F. Skoczylas, Experimental study of gas and liquid permeability of a mortar, Cement and Concrete Research, Vol. 32, n. 9, pp. 1357-1363, 2002.
D. Seguin, A. Montillet, J. Comiti, Experimental characterization of flow regimes in various porous media - I: Limit of laminar flow regime, Chemical Engineering Science, Vol. 53, n.21, pp. 3751-3761, 1998.
O. Rahli, L. Tadrist, M. Miscevic, Experimental analysis of fibrous porous media permeability, AICHE Journal, Vol. 42, n. 12, pp. 3547-3549, 1996.
M. Rashidi, L. Peurrung, A.F.B. Tompson, T.J. Kulp, Experimental analysis of pore-scale flow and transport in porous media, Advances in Water Resources, Vol. 19, n. 3, pp. 163-180, 1996.
J. Comiti, M. Renaud, A new model for determining mean structure parameters of fixed-beds from pressure-drop measurements - application to beds packed with parallelepipedal particles, Chemical Engineering Science, Vol. 44, n. 7, pp. 1539-1545, 1989.
J.G. Williams, C.E.M. Morris, B.C. Ennis, Liquid Flow through Aligned Fiber Beds, Polymer Engineering and Science, Vol. 14, n. 6, pp. 413-419, 1974.
G.W. Jackson, D.F. James, The Permeability of Fibrous Porous-Media, Canadian Journal of Chemical Engineering, Vol. 64, n. 3, pp. 364-374, 1986.
L. Skartsis, B. Khomami, J.L. Kardos, Resin Flow through Fiber Beds during Composite Manufacturing Processes. Part II: Numerical and Experimental Studies of Newtonian Flow through Ideal and Actual Fiber Beds, Polymer Engineering and Science, Vol. 32, n. 4, pp. 231-239, 1992.
R.E. Larson, J.J.L. Higdon, Microscopic Flow near the Surface of Two-Dimensional Porous-Media. Part 1. Axial Flow, Journal of Fluid Mechanics, Vol. 166, pp. 449-472, 1986.
R.E. Larson, J.J.L. Higdon, Microscopic Flow near the Surface of Two-Dimensional Porous-Media. Part 2. Transverse Flow, Journal of Fluid Mechanics, Vol. 178, pp. 119-136, 1987.
J.B. Keller, Viscous flow through a grating or lattice of cylinders, Journal of Fluid Mechanics, Vol. 18, pp. 94-96, 1964.
A.S. Sangani, A. Acrivos, Slow flow past periodic arrays of cylinders with application to heat transfer, International Journal of Multiphase Flow, Vol. 8, n. 3, pp. 193-206, 1982.
J.E. Drummond, M.I. Tahir, Laminar viscous flow through regular arrays of parallel solid cylinders, International Journal of Multiphase Flow, Vol. 10, n. 5, pp. 515-540, 1984.
J.J.L. Higdon, G.D. Ford, Permeability of three-dimensional models of fibrous porous media, Journal of Fluid Mechanics, Vol. 308, pp. 341-361, 1996.
H. Hasimoto, On the periodic fundamental solutions of the stokes equations and their application to viscous flow past a cubic array of spheres, Journal of Fluid Mechanics, Vol. 5, pp. 317-328, 1959.
A.S. Sangani, A. Acrivos, Slow flow through a periodic array of spheres, International Journal of Multiphase Flow, Vol. 8, n. 4, pp. 343-360, 1982.
A.W.J. Heijs, C.P. Lowe, Numerical evaluation of the permeability and the Kozeny constant for two types of porous media, Physical Review E, Vol. 51, pp. 4346-4353, 1995.
R.D. Hazlett, Simulation of Capillary-Dominated Displacements in Microtomographic Images of Reservoir Rocks, Transport in Porous Media, Vol. 20, pp. 21-35, 1995.
M. Sahraoui, M. Kaviany, Slip and no slip velocity boundary conditions at interface of porous, plain media, International Journal of Heat and Mass Transfer, Vol. 35, n. 4, pp. 927-943, 1992.
A. Nakayama, F. Kuwahara, T. Umemoto, T. Hayashi, Heat and Fluid Flow Within an anisotropic porous medium, Journal of Heat Transfer, Vol. 124, pp. 746-753, 2002.
S. Succi, The Lattice Boltzmann Equation - For Fluid Dynamics and Beyond (1st edition, Oxford University Press, 2001).
S. Chen, G.D. Doolen, Lattice Boltzmann method for fluid flows, Annual Review of Fluid Mechanics, Vol. 30, pp. 329-364, 1998.
F. Jiang, M.S.A. Oliveira, A.C.M. Sousa, Mesoscale SPH modeling of fluid flow in isotropic porous media, Computer Physics Communications, Vol. 176, n. 7, pp. 471-480, 2007.
F. Jiang, A.C.M. Sousa, Smoothed Particle Hydrodynamics Modeling of Transverse Flow in Randomly Aligned Fibrous Porous Media, Transport in Porous Media, DOI: 10.1007/s11242-008-9206-z, available online since February 2008.
G.R. McNamara, G. Zanetti, Use of the Boltzmann Equation to Simulate Lattice-Gas Automata, Physical Review Letters, Vol. 61, n. 20, pp. 2332-2335, 1988.
Y.H. Qian, D. d’Humieres, P. Lallemand, Lattice BGK model for Navier- Stokes equation, Europhysics Letters, Vol. 17, n. 6BIS, pp. 479-484, 1992.
S. Succi, E. Foti, F. Higuera, Three-dimensional flows in Complex Geometries with the Lattice Boltzmann Method, Europhysics Letters, Vol. 10, n. 5, pp. 433-438, 1989.
A. Cancelliere, C. Chang, E. Foti, D.H. Rothman, S. Succi, The permeability of a random medium: Comparison of simulation with theory, Physics of Fluids A, Vol. 2, n. 12, pp. 2085-2088, 1990.
A. Koponen, M. Kataja, J. Timonen, Permeability and effective porosity of porous media, Physical Review E, Vol. 56, n. 3, pp. 3319-3325, 1997.
A. Nabovati, A.C.M. Sousa, Fluid Flow Simulation at the Open-Porous interface Using Lattice Boltzmann Method, International Journal for Numerical Methods in Fluids, Vol. 56, n. 8, pp. 1449 – 1456, 2008.
A. Nabovati, A.C.M. Sousa, Fluid Flow Simulation in Random Porous Media at Pore Level using the Lattice Boltzmann Method, Journal of Engineering Science and Technology, Vol. 2, n. 3, pp. 226- 237, 2007.
A. Nabovati, A.C.M. Sousa, E. Llewellin, Three-Dimensional Fluid Flow Simulation in Fibrous Porous Media, Fifth Intl. Conf. for Mesoscopic Methods in Engineering and Science, Amsterdam, Netherlands, June 2008.
W.J. Bosl, J. Dvorkin, A. Nur, A study of porosity and permeability using a lattice Boltzmann simulation, Geophysical Research Letters, Vol. 25 , n. 9 , pp. 1475-1478, 1998.
C. Pan, M. Hilpert, C.T. Miller, Pore-scale modeling of saturated permeabilities in random sphere packings, Physical Review E, Vol. 64, n. 6, Article Number 066702, 2001.
M.A. Van der Hoef, R. Beetstra, J.A.M. Kuipers, Lattice-Boltzmann simulations of low-Reynolds-number flow past mono- and bidisperse arrays of spheres: results for the permeability and drag force, Journal of Fluid Mechanics, Vol. 528, pp. 233-254, 2005.
S. Geller, M. Krafczyk, J. Tolke, S. Turek, J. Hron, Benchmark computations based on lattice-Boltzmann, finite element and finite volume methods for laminar flows, Computers and Fluids, Vol. 35, pp. 888–897, 2006.
C. Pan, Use of pore-scale modeling to understand transport phenomena in porous media, Ph.D. dissertation, Dept. Environmental Science and Engineering, University of North Carolina, Chapel Hill, NC, 2003.
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