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Pore-scale simulation of dispersion
1.H. L. Brenner and D. A. Edwards, Macrotransport Processes (Butterworth-Heineman, Boston, 1993).
2.J. D. Seymour and P. T. Callaghan, “Generalized approach to NMR analysis of flow and dispersion in porous media,” AIChE J. 43, 2096 (1997).
3.J. Salles, J.-F. Thovert, R. Delannay, L. Prevors, J.-L. Auriault, and P. M. Adler, “Taylor dispersion in porous media. Determination of the dispersion tensor,” Phys. Fluids A 5, 2348 (1993).
4.D. Coelho, J.-F. Thovert, and P. M. Adler, “Geometrical and transport properties of random packings of spheres and aspherical particles,” Phys. Rev. E 55, 1959 (1997).
5.J. J. Tessier, K. J. Packer, J.-F. Thovert, and P. M. Adler, “NMR measurements and numerical simulation of fluid transport in porous solids,” AIChE J. 43, 1653 (1997).
6.S. Stapf, K. J. Packer, R. G. Graham, J.-F. Thovert, and P. M. Adler, “Spatial correlations and dispersion for fluid transport through packed glass beads studied by pulsed field-gradient NMR,” Phys. Rev. E 58, 6206 (1998).
7.D. L. Koch and J. F. Brady, “Dispersion in fixed beds,” J. Fluid Mech. 154, 399 (1985).
8.N.-W. Han, J. Bhakta, and R. G. Carbonell, “Longitudinal and lateral dispersion in packed beds: effect of column length and particle size distribution,” AIChE J. 31, 277 (1985).
9.C. P. Lowe and D. Frenkel, “Do hydrodynamic dispersion coefficients exist?” Phys. Rev. Lett. 77, 4552 (1996).
10.D. L. Koch, R. J. Hill, and A. S. Sangani, “Brinkman screening and the covariance of the fluid velocity in fixed beds,” Phys. Fluids 10, 3035 (1998).
11.D. L. Koch and J. F. Brady, “Nonlocal dispersion in porous media: nonmechanical effects,” Chem. Eng. 42, 1377 (1987).
12.R. Maier, D. M. Kroll, H. T. Davis, and R. Bernard, “Simulation of flow in bidisperse bead packings,” J. Colloid Interface Sci. 217, 341 (1999).
13.J. D. Sterling and S. Chen, “Stability analysis of lattice Boltzmann methods,” J. Comput. Phys. 123, 196 (1996).
14.G. McNamara and G. Zanetti, “Use of the Boltzmann equation to simulate lattice-gas automata,” Phys. Rev. Lett. 61, 2332 (1988).
15.D. Grunau, “Lattice Methods for Modeling Hydrodynamics,” Ph.D. Thesis, Department of Mathematics, Colorado State University, 1993.
16.M. Reider and J. Sterling, “Accuracy of discrete-velocity BGK models for the simulation of the incompressible Navier-Stokes equations,” Comput. Fluids 118, 459 (1995).
17.R. Maier, R. Bernard, and D. Grunau, “Boundary conditions for the lattice Boltzmann method,” Phys. Fluids 8, 1788 (1996).
18.R. Maier and R. Bernard, “Accuracy of the lattice Boltzmann method,” Int. J. Mod. Phys. C 8, 747 (1997).
19.R. Maier, D. M. Kroll, H. T. Davis, and R. Bernard, “Simulation of flow in bead packs using the lattice-Boltzmann method,” Phys. Fluids 10, 60 (1998).
20.P. M. Adler, M. Zuzovsky, and H. L. Brenner, Int. J. Multiphase Flow 11, 387 (1985).
21.A. Zick and G. Homsey, J. Fluid Mech. 115, 13 (1982).
22.R. Larson and J. Higdon, “A periodic grain consolidation model of porous media,” Phys. Fluids A 1, 38 (1989).
23.A. Chapman and J. Higdon, “Oscillatory Stokes flow in periodic porous media,” Phys. Fluids A 4, 2099 (1992).
24.C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method (Cambridge University Press, New York, 1987).
25.P. Roache, Computational fluid dynamics (Hermosa, Albuquerque, NM, 1976).
26.D. A. Edwards, M. Shapiro, H. Brenner, and M. Shapira, “Dispersion of inert solutes in spatially periodic two-dimensional model porous media,” Transp. Porous Media 6, 337 (1991).
27.E. Flekkoy, “Lattice Bhatnagar-Gross-Krook models for miscible fluids,” Phys. Rev. E 47, 4247 (1993).
28.S. Ponce Dawson, S. Chen, and G. D. Doolen, “Lattice Boltzmann computations for reaction diffusion equations,” J. Chem. Phys. 98, 1514 (1993).
29.H. W. Stockman, R. J. Glass, C. Cooper, and H. Rajaram, “Accuracy and computational efficiency in 3D dispersion via lattice-Boltzmann: models for dispersion in rough fractures and double-diffusive fingering,” Int. J. Mod. Phys. C 9, 1545–1558 (1998).
30.D. Frenkel and M. H. Ernst, “Simulation of diffusion in a two-dimensional lattice-gas cellular automaton: a test of mode-coupling theory,” Phys. Rev. Lett. 63, 2165 (1989).
31.A. F. Tompson, E. G. Vomvoris, and L. W. Gelhar, “Numerical simulation of solute transport in randomly heterogeneous porous media: motivation, model development and application,” Report Number 316, Ralph M. Parsons Laboratory, Massachusetts Institute of Technology, Cambridge, MA, February, 1988.
32.P. E. Kloeden and E. Platen, “Numerical Solution of Stochastic Differential Equations,” Applications of Mathematics Series, Vol. 23 (Springer-Verlag, Heidelberg, 1992).
33.D. J. Thomson and M. R. Montgomery, “Reflection boundary conditions for random walk models of dispersion in non-Gaussian turbulence,” Atmos. Environ. 28, 1981 (1994).
34.Measurement variance due to packing was reported by Gunn and Pryce (Ref. 39) and a perturbation analysis of their results suggests that the standard deviation of due to packing is on the order of 5% of the mean value. They obtained estimates of dispersion by injecting gas into the pack at a prescribed sinusoidal frequency, and measuring the amplitude attenuation downstream at two points. The resulting ratio of amplitude attenuation at the two measurement stations has a closed-form expression in terms of the dispersion rate, frequency, and velocity. Estimates of for a given frequency were made by fitting the expression to several observed values of Their error variance is reported in terms of
35.R. Maier, D. M. Kroll, H. T. Davis, and R. Bernard, “Pore-scale flow and dispersion,” Int. J. Mod. Phys. C 9, 1523 (1998).
36.D. L. Koch, R. G. Cox, H. Brenner, and J. F. Brady, “The effect of order on dispersion in porous media,” J. Fluid Mech. 200, 173 (1989).
37.H. L. Brenner, “Dispersion resulting from flow through spatially periodic porous media,” Philos. Trans. R. Soc. London, Ser. A 297, 81 (1980).
38.D. Grubert, “Using the FHP-BGK model to get effective dispersion constants for spatially periodic model geometries,” Int. J. Mod. Phys. C 8, 817 (1997).
39.D. J. Gunn and C. Pryce, “Dispersion in packed beds,” Trans. Inst. Chem. Eng. 47, T341 (1969).
40.J. Bear, Dynamics of Fluids in Porous Media (Elsevier, New York, 1972).
41.P. N. Sen, “Diffusion in a periodic porous medium with surface relaxation,” Physica A 211, 387 (1994).
42.H. O. Pfannkuch, “Contribution a l’étude des déplacements de fluiedes miscibles dans un milieu poreux,” Revue De L’Insitut Francais Du Pétrole XVIII, 215 (1963).
43.L. Lebon, J. Leblond, and J. P. Hulin, “Experimental measurement of dispersion processes at short times using a pulsed field gradient NMR technique,” Phys. Fluids 9, 481 (1997).
44.The method used by Seymour and Callaghan (Ref. 2) to estimate is based on a plot of the echo-attenuation function E versus the square of the gradient or wave vector q, where and is the average propagator. is obtained from the slope of the plot near the low- limit. An advantage of the method is that the data are in the original measurement units, whereas deconvolution of may introduce errors. Additional errors may be introduced by other methods which estimate by fitting a Gaussian to or computing time derivatives of second moments widely separated in time.
45.W. P. Halperin, F. D’Orazio, S. Bhattacharja, and J. C. Tarczon, “Magnetic resonance relaxation analysis of porous media,” in Molecular Dynamics in Restricted Geometries, edited by J. Klafter and J. M. Drake (Wiley, New York, 1989), pp. 273–309.
46.P. P. Mitra and P. N. Sen, “Effects of microgeometry and surface relaxation on NMR pulsed-field-gradient experiments: simple pore geometries,” Phys. Rev. B 45, 143 (1992).
47.J. R. Banavar and L. M. Schwartz, “Probing porous media with nuclear magnetic resonance,” in Molecular Dynamics in Restricted Geometries, edited by J. Klafter and J. M. Drake (Wiley, New York, 1989), pp. 273–309.
48.D. J. Bergman, K.-J. Dunn, L. M. Schwartz, and P. P. Mitra, “Self-diffusion in a periodic porous medium: a comparison of different approaches,” Phys. Rev. E 51, 3393 (1995).
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