Computation of permeability and dispersivities of solute or heat in periodic porous media

International Journal of Heat and Mass Transfer

Volumn 39, Issue 4, 1996, Pages 661-676

  Lee, Cheo K ^a   Sun, Chin Cheng ^a   Mei, Chiang C ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; CALCULATIONS; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; MECHANICAL PERMEABILITY; NUMERICAL METHODS; POROSITY; POROUS MATERIALS; PROBLEM SOLVING; VARIATIONAL TECHNIQUES;

FOURIER SERIES EXPANSION; GALERKIN METHOD; PECLET NUMBER; PERMEABILITY TENSOR;

DISPERSIONS;

EID: 0030108859     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/0017-9310(95)00174-3     Document Type: Article

References (52)

1. H. Hasimoto, On the periodic fundamental solution of the Stokes equations and their application to viscous flow past a cubic array of spheres, J. Fluid Mech. 5, 317-328 (1959).
2. A. S. Sangani and A. Acrivos. Slow flow through a periodic array of spheres, Int. J. Multiphase Flow 8(4), 343-360 (1982).
3. A. A. Zick and G. M. Homsy, Stokes flow through periodic arrays of spheres, J. Fluid Mech. 115, 13-26 (1982).
4. L. J. Snyder and W. E. Stewart, Velocity and pressure profiles for Newtonian creeping flow in regular packed beds of spheres, A.I.Ch.E. J. 12(1), 167-173 (1966).
5. J. P. Sorensen and W. E. Stewart, Computation of forced convection in slow flow through ducts and packed beds - II. Velocity profile in a simple cubic array of spheres, Chem. Engng Sci. 29, 819-825 (1974).
6. P. M. Adler, Porous Media: Geometry and Transports. Butterworth-Heinemann, London (1992).
7. H. Brenner, Dispersion resulting from flow through spatially periodic porous media, Phil. Trans. R. Soc. Lond. 297A, 81-133 (1980).
8. D. J. de Jong, Longitudinal and transverse diffusion in granular deposiles, Trans. Am. Geophys. Un. 39, 67-74 (1958).
9. P. G. Saffman, A theory of dispersion in a porous medium, J. Fluid Mech. 6, 321-349 (1959).
10. P. G. Saffman, Dispersion due to molecular diffusion and macroscopic mixing in flow through a network of capillaries, J. Fluid Mech. 1, 194-208 (1960).
11. R. E. Haring and R. A. Greenkorn, A statistical model of a porous media with nonunifonn pores, A.I.Ch.E. J. 16, 477-483 (1970).
12. D. L. Koch and J. F. Brady, Dispersion in fixed beds, J. Fluid Mech. 154, 399-427 (1985).
13. J. J. Fried and M. A. Combarnous. Dispersion in porous media, Adv. Hydrosci. 7, 169-282 (1971).
14. 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, 173-188 (1989).
15. M. Kaviany, Principle of Heat Transfer in Porous Media. Springer, Berlin. (1991).
16. R. G. Carbonell and S. Whitaker, Dispersion in pulsed systems II. Theoretical developments for passive dispersion in porous media, Chem. Engng Sci. 38, 1795-1802 (1983).
17. J. Rubinstein and R. Mauri, Dispersion and convection in periodic porous media, SIAM. J. Appl. Math. 46, 1018-1023 (1986).
18. R. Mauri, Dispersion, convection and reaction in porous media, Phys. Fluids 3, 743-756 (1991).
19. C. C. Mei, Heat dispersion in porous media by homogenization method. Multiphase Transport in Porous Media, ASME Winter Meeting, FED-Vol 122/HTD-Vol. 186, pp. 11-16 (1991).
20. C. C. Mei, Method of homogenization applied to dispersion in porous media, Transport in Porous Media 9, 262-274 (1992).
21. H. Brenner and D. A. Edwards, Macrotransport Processes. Bulterworth-Heinemann, London (1993).
22. H. Lee, Analysis of pseudo-continuum mass transfer in media with spatially periodic boundaries, Chem. Engng Sci. 34, 503-514 (1979).
23. A. Eidsath, R. G. Carbonell, S. Whitaker and L. R. Herrmann, Dispersion in pulsed systems - III. Comparison between theory and experiments for packed beds, Chem. Engng Sci. 38, 1803-1816 (1983).
24. R. A. Edwards, M. Shapiro, H. Brenner and M. Shapiro, Dispersion of inert solute in spatially periodic two-dimensional model porous media, Transport in Porous Media 6, 337-358 (1991).
25. 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 5, 2348-2376 (1993).
26. M. Sahraoui and M. Kaviany, Slip and no-slip temperature boundary conditions at the interface of porous, plain media : convection, Int. J. Heat Mass Transfer 37, 1029-1044 (1994).
27. G. Burns, Solid State Physics. Academic Press, New York (1985).
28. A. Bensoussan, J. L. Lions and G. Papanieolaou, Asymptotic Analysis for Periodic Structures. North-Holland, Amsterdam. (1978).
29. E. Sanchez-Palencia, Nonhomogeneous Media and Vibration Theory, Lecture Notes in Physics, Vol. 127. Springer, Berlin (1980).
30. J. B. Keller, Darcy's law for flow in porous media by the two space method. Nonlinear Partial Differential Equations in Engineering and Applied Sciences (Edited by R. L. Sternberg, A. J. Kalinowski and J. S. Papadakis), pp. 429-443. Dekker, New York (1980).
31. C. C. Mei and J. L. Auriault, The effects of weak inertia on flow through a porous medium, J. Fluid Mech. 222, 647-663 (1991).
32. H. Brenner and P. M. Adler, Dispersion resulting from flow through spatially periodic porous media - II. Surface and intraparticle transport, Phil. Trans. R. Soc. Lond. 307, 149-200 (1982).
33. M. Sahraoui and M. Kaviany, Slip and no-slip temperature boundary conditions at interface of porous, plain media: convection - I. Formulation. Proceedings of the 1992 National Heat Transfer Conference, San Diego, California, HTD-Vol. 193, pp. 25-33 (1993).
34. B. M. Irons, A frontal solution program, Int. J. Numer. Meth. Engng 2, 5-32 (1970).
35. P. C. Carman, Fluid flow through granular beds, Trans Instn Chem. Engrs 15, 150-166 (1937).
36. J. Bear, Dynamics of Fluids in Porous Media. Elsevier, Amsterdam (1972).
37. D. J. Gunn and C. Pryce, Dispersion in packed beds, Trans. Instn Chem. Engrs 47, T341-T350 (1969).
38. A. S. Sangani and A. Acrivos. The effective conductivity of a periodic array of spheres, Proc. R. Soc. Lond. A 386, 262-275 (1983).
39. E. A. Ebach and R. R. White, Mixing of fluids flowing through beds of packed solids, A.I.Ch.E. J. 4(2), 161-169 (1958).
40. M. F. Edwards and J. F. Richardson, Gas dispersion in packed beds, Chem. Engng Sci. 23, 109-123 (1968).
41. E. V. Evans and C. N. Kenney, Gaseous dispersion in packed beds at low Reynolds numbers, Trans. Instn Chem. Engrs 44, T189-T197 (1966).
42. D. R. F. Harleman and R. R. Rumer, Longitudinal and lateral dispersion in an isotropic porous medium, J. Fluid Mech. 16(3), 385-394 (1963).
43. J. W. Hiby, Longitudinal and transverse mixing during single-phase flow through granular beds. Proceedings of the Symposium on the Interaction Between Fluids and Particles, London, 20-22 June, pp. 312-325 (1962).
44. H. O. Pfannkuch, Contribution a L'Etude des Deplacements de Fluides Miscibles dans un Milieu Poreux, Revue de L'Institut Francais du Petrole. XVIII(2), 215-270 (1963).
45. M. N. E. Rifai, W. J. Kaufman and D. K. Todd, Dispersion phenomena in laminar flow through porous media, Sanitary Engineering Research Laboratory and Division of Civil Engineering, University of California, Berkeley, Report No. 2, I. E. R. Series 93 (1956).
46. R. Mauri, Lagrangian self-diffusion of Brownian particles in periodic flow fields, Phys. Fluids 7, 275-284 (1995).
47. R. J. Blackwell, Laboratory studies of microscopic dispersion phenomena, Soc. Petroleum Engrs J. 2, 1-8 (1962).
48. F. E. Grane and G. H. F. Gardner, Measurements of transverse dispersion in granular media, J. Chem. Engng Data 6(2), 283-287 (1961).
49. E. J. List and N. H. Brooks, Lateral dispersion in saturated porous media, J. Geophys. Res. 72(10), 2531-2541 (1967).
50. E. S. Simpson, Transverse dispersion in liquid flow through porous media, U.S. Geol. Surr. Prof. Paper 411-C (1962).
51. J. Levee and R. G. Carbonell, Longitudinal and lateral thermal dispersion in packed beds - 11. Comparison between theory and experiment, A.I.Ch.E. J. 31, 591-602 (1985).
52. D. W. Green, R. H. Perry and R. E. Babcock, Longitudinal dispersion of thermal energy through porous media with a flowing fluid, A.I.Ch.E. J. 10(5), 645-651 (1960).