An extended macroscopic model for solute dispersion in confined porous media

Chemical Engineering Journal

Volumn 137, Issue 3, 2008, Pages 614-635

  Hamdan, E ^a   Milthorpe, J F ^a   Lai, J C S ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Dispersion; Non Fickian; Packed bed; Transients

Indexed keywords

ASYMPTOTIC ANALYSIS; CONCENTRATION (PROCESS); MATHEMATICAL MODELS; PACKED BEDS; SOLUTE TRANSPORT;

CONVENTIONAL PLUG FLOW; CYLINDER RADIUS; FICKIAN TRANSIENTS; GAUSSIAN CONCENTRATION;

POROUS MATERIALS;

ASYMPTOTIC ANALYSIS; CONCENTRATION (PROCESS); MATHEMATICAL MODELS; PACKED BEDS; POROUS MATERIALS; SOLUTE TRANSPORT;

EID: 39749119944     PISSN: 13858947     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cej.2007.05.031     Document Type: Article

References (79)

1. Carvalho J.R.F., and Delgado J.M.P.Q. Overall map and correlation of dispersion data for flow through granular packed beds. Chem. Eng. Sci. 60 (2005) 365-375
2. Delgado J.M.P.Q. A critical review of dispersion in packed beds. Heat Mass Trans. 42 (2006) 279-310
3. Chandrasekhara B.C., Rudraiah N., and Nagaraj S.T. Velocity and dispersion in porous-media. Int. J. Eng. Sci. 18 (1980) 921-929
4. Han N., Bhakta J., and Carbonell R.G. Longitudinal and lateral dispersion in packed beds, effect of column length and particle size distribution. AIChE J. 31 (1985) 277-387
5. Taylor G.I. Dispersion of solute matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A 219 (1953) 186-203
6. Aris R. On the dispersion of a solute in a fluid flowing through a tube. Proc. R. Soc. Lond. A 235 (1956) 67-77
7. Scheidegger A.E. An evaluation of the accuracy of the diffusivity equation for describing miscible displacement in porous media. Proceedings of Theory of Fluid Flow in Porous Media Conference. University of Oklahoma (1959) 101-116
8. Silliman S.E., and Simpson E.S. Laboratory evidence of the scale effect in dispersion of solutes in porous-media. Water Resour. Res. 23 (1987) 1667-1673
9. Oswald S., Kinzelbach W.A.G., and BRIX G. Observation of flow and transport process in artificial porous media via magnetic resonance imaging in three dimensions. Geoderma 80 (1997) 417-429
10. Gelhar L.W., Gutjahr A.L., and Naff R.L. Stochastic analysis of macrodispersion in a stratified aquifer. Water Resour. Res. 15 (1979) 1387-1397
11. Neuman S.P., Winter C.L., and Newman C.M. Stochastic theory of field-scale Fickian dispersion in anistropic porous media. Water Resour. Res. 23 (1987) 453-466
12. Schumer R., Benson D.A., Meerschaert M.M., and Baeumer B. Fractal mobile/immobile solute transport. Water Resour. Res. 39 (2003) 1296 10.1029/2003WR002141
13. Pang L., and Hunt B. Solution and verification of a scale-dependent dispersion model. J. Contam. Hydrol. 53 (2001) 21-39
14. Piekens J.F., and Grisak G.E. Modelling of scale-dependent dispersion in hydro geologic systems. Water Resour. Res. 17 (1981) 1701-1711
15. Levy M., and Berkowitz B. Measurement and analysis of non-Fickian dispersion in heterogeneous porous media. J. Contam. Hydrol. 64 (2003) 203-226
16. Cortis A., Gallo C., Scher H., and Berkowitz B. Numerical simulation of non-Fickian transport geological formations with multiple-scale heterogeneities. Water Resour. Res. 40 (2004) (Art. No. W04209 April 21, 2004)
17. Fetter C.W. Contaminant Hydrology (1993), Macmillan, New York pp. 71-109
18. Benenati R.F., and Brosilow C.B. Void fraction distribution in beds of spheres. AIChE J. 8 (1962) 359-362
19. Maier R.S., Kroll D.M., Bernard R.S., Howington S.E., Peters J.F., and Davis H.T. Hydrodynamic dispersion in confined packed beds. Phys. Fluids 15 (2003) 3795-3815
20. Koch D.L., and Brady J.F. Anomalous diffusion in heterogeneous porous-media. Phys. Fluids 31 (1988) 965-973
21. Seymour J.D., Gage J.P., Codd S.L., and Gerlach R. Anomalous fluid transport in porous induced by biofilm growth. Phys. Rev. Lett. 93 (2004) 1-4
22. Verganelakis D.A., Crawshaw J., Jhons M.L., Mantle M.D., Scheven U., Sederman A.J., and Gladden L.F. Displacement propagators of brine flowing within different types of Sedimentary rock. Magn. Reson. Imaging 23 (2005) 349-351
23. Seymour J.D., and Callaghan P.T. Generalized approach to NMR analysis of flow and dispersion in porous media. AIChE J. 43 (1997) 2096-2111
24. Stapf S., Packer K.J., Graham R.G., Thovert J.-F., and Alder P.M. Spatial correlations and dispersion for fluid transport through packed glass beads studied by pulsed field-gradient NMR. Phys. Rev. E 58 (1998) 6206-6221
25. Tessier J.J., Packer K.J., Thovert J.-F., and Adler P.M. NMR measurements and numerical simulation of fluid transport in porous solids. AIChE J. 43 (1997) 1653-1661
26. Cenedese A., and Viotti P. Lagrangian analysis of non-reactive pollutant dispersion in porous media by means of the particle image velocimetry technique. Water Resour. Res. 32 (1996) 2329-2343
27. Viotti P. Scaling properties of tracer trajectories in a saturated porous medium. Trans. Porous Media 27 (1997) 1-16
28. Salles J., Thovert J.-F., Delannay R., Prevors L., Auriault J.-L., and Alder P.M. Taylor dispersion in porous media-determination of the dispersion tensor. Phys. Fluids A Fluid Dynam. 10 (1993) 2348-2376
29. Lowe C.P., and Frenkel D. Do hydrodynamic dispersion coefficients exist?. Phys. Rev. Lett. 77 (1996) 4552-4555
30. Maier R.S., Kroll D.M., Bernard R.S., Howington S.E., Peters J.F., and Davis H.T. Enhanced dispersion in cylindrical packed beds. Philos. Trans. R. Soc. Lond. A 360 (2002) 497-506
31. Bischoff K.B., and Levenspile O. Fluid dispersion-generalization and comparison of mathematical models: II. Chem. Eng. Sci. 17 (1962) 257-264
32. Koch D.L., and Brady J.F. Nonlocal dispersion in porous media-non mechanical effects. Chem. Eng. Sci. 42 (1987) 1377-1392
33. Maier R.S., Kroll D.M., Bernard R.S., Howington S.E., Peters J.F., and Davis H.T. Pore scale simulation of dispersion. Phys. Fluids 12 (2000) 2065-2079
34. Carbonell R.G. Flow nonuniformities in packed beds-effect on dispersion. Chem. Eng. Sci. 35 (1980) 1347-1456
35. Ozisik M.N. Heat Conduction (1980), John Wiley and Sons, New York p. 522
36. Chen B.H., McMillan A.F., and Wang S.T. An analytical solution for dispersion in packed-beds with low bed-to-particle diameter ratios. Chem. Eng. Sci. 38 (1983) 257-263
37. Young W.R., and Jones S. Shear dispersion. Phys. Fluids A 3 (1991) 1087-1101
38. Haber S., and Mauri R. Lagrangian approach to time-dependent laminar dispersion in rectangular conduits, Part 1. Two-dimensional flows. J. Fluid Mech. 190 (1988) 201-215
39. Dentz M., and Carrera J. Mixing and spreading in stratified flow. Phys. Fluids 19 (2007) 017107
40. Berentsen C.W.J., Verlaan M.L., and Van Kruijdijk C.P.J.W. Upscaling and reversibility of Taylor dispersion in heterogeneous porous media. Phys. Rev. E 71 (2005) 046308
41. Taylor G.I. Conditions under which dispersion of a solute in a stream of solvent can be used to measure molecular diffusion. Proc. R. Soc. Lond. A 225 (1954) 473-477
42. Danckwerts P.V. Continuous flow systems. Chem. Eng. Sci. 2 (1953) 1-13
43. Kramers H., and Alberda G. Frequency response analysis of continuous flow systems. Chem. Eng. Sci. 2 (1953) 173-181
44. G.L. Jacques, T. Vermeulen, Longitudinal dispersion in solvent- extraction columns: Peclet numbers for random and ordered packings. Univ. California Rad Lab. Rep. No. 8029, US Atomic Energy Commission, 1958, Washington, DC
45. Carberry J.J., and Bretton R.H. Axial dispersion of mass in flow through fixed beds. AIChE J. 4 (1958) 367-375
46. Ebach E.A., and White R.R. Mixing of fluids flowing through beds of packed solids. AIChE J. 4 (1958) 161-169
47. Strang D.A., and Geankopolis C.J. Longitudinal diffusivity of liquids in packed beds. Ind. Eng. Chem. 50 (1958) 1305
48. Cairns E.J., and Prausnitz J.M. Longitudinal mixing in packed beds. Chem. Eng. Sci. 12 (1960) 20-34
49. Liles A.W., and Geankopolis C.J. Axial diffusion of liquids in packed beds and End effects. AIChE J. 6 (1960) 591
50. Harrison D., Lane M., and Walne D.J. Axial dispersion of liquid on a column of spheres. Trans. IChemE 40 (1962) 214-220
51. Hiby J.W. Longitudinal dispersion in single-phase liquid flow through ordered and random packings, interact between Fluid & Particles. Lond. Inst. Chem. Eng. (1962) 312-325
52. A. Hennico, G. Jacques, T. Vermeulen, Longitudinal dispersion in single-phase liquid flow through ordered and random packings, Lawrence Rad Lab. Rept. UCRL, 1963, 10696.
53. Pfannkuch H.-O. Contribution a l'e'tude des de'placements de fluids miscibles dans un milieu poreux. Revue de l'institut du petro 18 (1963) 215-270
54. Miller S.S., and King C.J. Axial dispersion in liquid flow through backed beds. AICHE J. 12 (1966) 767-773
55. W.D. Smith, R.H. Bretton, Paper presented at AIChE Houston Meeting, Texas, 1967.
56. Chung S.F., and Wen C.Y. Longitudinal dispersion of liquid flowing through fixed and fluidized beds. AIChE J. 14 (1968) 857-866
57. Miyauchi T., and Kikuchi T. Axial dispersion in packed beds. Chem. Eng. Sci. 30 (1975) 343-348
58. Carvalho J.R.F., and Delgado J.M.P.Q. The effect of fluid properties on dispersion in flow through packed beds. AIChE J. 49 (2003) 1980-1985
59. McHenry J.R., and Wilhelm R.H. Axial mixing of binary gas mixtures flowing in a random bed of spheres. AIChE J. 3 (1957) 83-91
60. Blackwell R.J., Rayne J.R., and Terry W.M. Factors influencing the efficiency of miscible displacement. AIME Petroleum Trans. 216 (1959) 1-8
61. DeMaria F., and White R.R. Transient response study of a gas flowing through irrigated packing. AIChE J. 6 (1960) 473-481
62. Sinclair R.J., and Potter O.E. The dispersion of gas in flow through a bed of packed solids. Trans. IChemE 43 (1965) T3-T9
63. Evans E.V., and Kenney C.N. Gaseous dispersion in packed beds at low Reynolds numbers. Trans. Inst. Chem. Eng. 44 (1966) T189-T197
64. Edward M.F., and Richardson J.F. Gas dispersion in packed beds. Chem. Eng. Sci. 23 (1968) 109-123
65. Balla L.Z., and Weber T.W. Axial dispersion of gases in packed beds. AIChE J. 15 (1969) 146-149
66. Urban J.C., and Gomezplata A. Axial dispersion coefficients in packed beds at low Reynolds numbers. Can. J. Chem. Eng. 47 (1969) 353-363
67. Scott D.S., Lee W., and Papa J. The measurement of transport coefficients in gas-solid heterogeneous reactions. Chem. Eng. Sci. 29 (1974) 2155-2167
68. Hsiang T.C.S., and Haynes H.W. Axial dispersion in small diameter beds of large spherical-particles. Chem. Eng. Sci. 32 (1977) 678-681
69. Benneker A.H., Kronberg A.W., Post J.W., Van Der Han A.G.J., and Westerterp K.R. Axial dispersion in gases flowing through a packed bed at elevated pressures. Chem. Eng. Sci. 15 (1996) 2099-2108
70. Yu D., Jackson K., and Harmon T.C. Dispersion and diffusion in porous media under supercritical conditions. Chem. Eng. Sci. 54 (1999) 357-367
71. 2, gaseous and aqueous systems, Ph.D. Thesis, University of California, 1998.
72. Tan C.S., and Liou D.C. Axial dispersion of supercritical carbon dioxide in packed beds. Ind. Eng. Chem. Res. 28 (1989) 1246-1250
73. Daszkowski T., and Eigenberger G. A re-evaluation of fluid-flow, heat-transfer and chemical-reaction in catalyst filled tubes. Chem. Eng. Sci. 47 (1992) 2245-2250
74. Papageorgiou J.N., and Froment G.F. Simulation models accounting for radial voidage profiles in fixed bed reactors. Chem. Eng. Sci. 50 (1995) 3043-3056
75. Neuman D.A., and Kuzentsov A.V. Effects of heterogenity in forced convection in a porous medium: parallel plate channel or circular duct. Int. J. Heat Mass Trans. 43 (2000) 4119-4134
76. Carman P.C. Fluid flow through a granular bed. Trans. Inst. Chem. Eng. 15 (1937) 150-167
77. Chatwin P.C. Approach to normality of concentration distribution of a solute in a solvent flowing along a straight pipe. J. Fluid Mech. 43 (1970) 321
78. Harleman D.R.F., and Rumer R.R. Longitudinal and lateral dispersion in an isotropic porous medium. J. Fluid Mech. 16 (1963) 385-394
79. Kendall M. Kendall's Advanced Theory of Statistics. fifth ed. (1987), Charles Griffin Company Limited pp. 222-226