Abstract
In the present study, the Lattice Boltzmann Method (LBM) is applied to simulate the flow of non-Newtonian shear-thinning fluids in three-dimensional digitally reconstructed porous domains. The non-Newtonian behavior is embedded in the LBM through a dynamical change of the local relaxation time. The relaxation time is related to the local shear rate in such a way that the power law rheology is recovered. The proposed LBM is applied to the study of power-law fluids in ordered sphere packings and stochastically reconstructed porous domains. A linear relation is found between the logarithm of the average velocity and the logarithm of the body force with a curve slope approximately equal to the inverse power-law index. The validity of the LBM for the flow of shear thinning fluids in porous media is also tested by comparing the average velocity with the well known semi-empirical Christopher–Middleman correlation. Good agreement is observed between the numerical results and the Christopher–Middleman correlation, indicating that the LBM combined with digital reconstruction constitutes a powerful tool for the study of non-Newtonian flow in porous media.
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Adler, P.M.: Porous Media: Geometry and Transports. Butterworth, London (1992)
Aharonov E. and Rothman D.H. (1993). Non-Newotonian flow (through Porous media): a lattice Boltzmann method. Geophys. Res. Lett. 20: 679–682
Aidun C.K., Lu Y. and Ding A.-J. (1998). Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation. J. Fluid Mech. 373: 287–311
Bekri S., Xu K., Yousefian F., Adler P.M., Thovert J.-F., Muller J., Iden K., Psyllos A., Stubos A.K. and Ioannidis M.A. (2000). Pore geometry and transport properties in North Sea chalk. J. Petroleum Sci. Eng. 25: 107–134
Berryman J.G. (1985). Measurement of spatial correlation functions using image processing techniques. J. Appl. Phys. 57: 2374–2384
Boek E.S., Chin J. and Coveney P.V. (2003). Lattice Boltzmann Simulation of the flow of Non-Newtonian fluids in Porous Media. Int. J. Mod. Phys. B 17: 99–102
Christopher, R.H., Middleman S. Power law flow through packed tube. Ind. Eng. Chem. Fund. 4, 422- (1965)
Crossley P.A., Schwartz L.M. and Banavar J.R. (1991). Image-based models of porous media-Application to Vycor glass and carbonate rocks. Appl. Phys. Lett. 59: 3553–3555
Gabbanelli S., Drazer G. and Koplik J. (2005). Lattice Boltzmann method for non-Newtonian (power-law) fluids. Phys. Rev. E 72: 046312
Guo Z., Zheng C. and Shi B. (2002). Discrete lattice effects on the forcing term in the lattice Boltzmann method. Phys. Rev. E 65: 046308
Idris Z., Orgéas L., Geindreau C., Bloch J.-F. and Auriault J.-L. (2004). Microstructural effects on the flow law of power-law fluids through fibrous media. Model. Simul. Mater. Sci. Eng. 12: 995–1015
Kainourgiakis M.E., Kikkinides E.S., Steriotis T.A., Stubos A.K., Tzevelekos K.P. and Kanellopoulos N.K. (2000). Structural and transport properties of alumina porous membranes from process-based and statistical reconstruction techniques. J. Colloid Interface Sci. 23: 158–167
Maier R.S., Kroll D.M., Kutsovsky Y.E., Davis H.T. and Bernard R.S. (1998). Simulation of flow through bead packs using the lattice Boltzmann method. Phys. Fluids 10: 60–74
Roberts A.P. (1997). Statistical reconstruction of three-dimensional porous media from two-dimensional images. Phys. Rev. E 56: 3203–3212
Shah C.B. and Yortsos Y.C. (1995). Aspects of flow of power law fluids in porous media. AIChE J. 41: 1099–1111
Succi, S.: The Lattice Boltzmann Equation For Fluid Dynamics and Beyond. Oxford University Press, Oxford (2001)
Sukop, M.C., Thorne, Jr. D.T.: Lattice Boltzmann Modeling. An Introduction for Geoscientists and Engineers. Springer (2006)
Sullivan S.P., Gladden L.F. and Johns M.L. (2006). Simulation of power-law fluid flow through porous media using lattice Boltzmann techniques. J. Non-Newtonian Fluid Mech. 133: 91–98
Talukdar M.S., Torsaeter O. and Ioannidis M.A. (2002). Stochastic reconstruction of particulate media from two-dimensional images. J. Colloid Interface Sci. 248: 419–428
Yeong C.L.Y. and Torquato S. (1998). Reconstructing random media. II. Three-dimensional media from two-dimensiomal cuts. Phys. Rev. E 58: 224–233
Zou Q. and He X. (1999). Derivation of the macroscopic continuum equations for multiphase flow. Phys. Rev. E 59: 1253–1255
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Psihogios, J., Kainourgiakis, M.E., Yiotis, A.G. et al. A Lattice Boltzmann study of non-newtonian flow in digitally reconstructed porous domains. Transp Porous Med 70, 279–292 (2007). https://doi.org/10.1007/s11242-007-9099-2
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DOI: https://doi.org/10.1007/s11242-007-9099-2