Comparison of theory and experiments for dispersion in homogeneous porous media

Advances in Water Resources

Volumn 33, Issue 9, 2010, Pages 1043-1052

  Porter, Mark L ^a   Valdés Parada, Francisco J ^b   Wood, Brian D ^a  

^a Oregon State University   (United States)

^b DEPARTAMENTO DE QUÍMICA   (Mexico)

Author keywords

Inverse modeling; Porous media; T sensor; Transverse dispersion; Upscaling; Volume averaging

Indexed keywords

INVERSE MODELING; POROUS MEDIA; T-SENSORS; TRANSVERSE DISPERSION; UPSCALING; VOLUME-AVERAGING;

BOLTZMANN EQUATION; INVERSE PROBLEMS; POROUS MATERIALS; SENSORS;

DISPERSIONS;

DISPERSION; EXPERIMENTAL STUDY; INVERSE ANALYSIS; POROUS MEDIUM; THEORETICAL STUDY;

BACTERIA (MICROORGANISMS);

EID: 77957017903     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2010.06.007     Document Type: Article

References (48)

1. Theodoropoulou M.A., Karoutos V., Kaspiris C., Tsakiroglou C.D. A new visualization technique for the study of solute dispersion in model porous media. J Hydrol 2003, 274:176-197. 10.1016/S0022-1694(02)00421-3.
2. Acharya R.C., Valocchi A.J., Werth C.J., Willingham T.W. Pore-scale simulation of dispersion and reaction along a transverse mixing zone in two-dimensional porous media. Water Resour Res 2007, 43:W10435. 10.1029/2007WR005969.
3. Long T., Ford R. Enhanced transverse migration of bacteria by chemotaxis in a porous T-sensor. Environ Sci Technol 2009, 43(5):1546-1552. 10.1021/es802558j.
4. Scheidegger A.E. The random-walk model with autocorrelation of flow through porous media. Can J Phys 1958, 36:649-659.
5. De Josselin De Jong G. Longitudinal and transverse diffusion in granular deposits. Trans Am Geophys Union 1958, 39(1):67-74.
6. Scheidegger A.E. General theory of dispersion in porous media. J Geophys Res 1961, 66:3273-3278.
7. Pfannkuch H.O. Contribution à l'étude des déplacements de fluides miscibles dans un milieu poreux. Rev Inst Français Pétrole 1963, XVIII(2):215-270.
8. Gunn D.J., Pryce C. Dispersion in packed beds. Trans Instn Chem Eng 1969, 47:T341-T350.
9. Brenner H. Dispersion resulting from flow through spatially periodic porous media. Philos Trans R Soc A 1980, 297(1430):81-133.
10. Brenner H., Adler P.M. Dispersion resulting from flow through spatially periodic porous media II. Surface and intraparticle transport. Philos Trans R Soc A 1982, 307(1498):149-200.
11. Carbonell R.G., Whitaker S. Dispersion in pulsed systems-II. Theoretical developments for passive dispersion in porous media. Chem Eng Sci 1983, 38(11):1795-1802.
12. Eidsath A., Carbonell R.G., Whitaker S., Herrmann L.R. Dispersion in pulsed systems-III. Comparison between theory and experiments for packed beds. Chem Eng Sci 1983, 38(11):1803-1816.
13. Han N.-W., Bhakta J., Carbonell R.G. Longitudinal and lateral dispersion in packed beds: effect of column length and particle size distribution. AIChE J 1985, 31(2):277-288.
14. Koch D.L., Cox R.G., Brenner H., Brady J.F. The effect of order on dispersion in porous media. J Fluid Mech 1989, 200:173-188.
15. Edwards D.A., Shapiro M., Brenner H., Shapira M. Dispersion of inert solutes in spatially periodic, two-dimensional model porous media. Trans Porous Media 1991, 6:337-358.
16. Kitanidis P.K. Analysis of macrodispersion through volume averaging: moment equations. Stoch Hydrol Hydraul 1992, 6:5-25.
17. Quintard M., Whitaker S. Convection, dispersion and interfacial transport of contaminants: homogeneous porous medium. Adv Water Res 1994, 17:221-239.
18. Didierjean S., Souto H.P.A., Delannay R., Moyne C. Dispersion in periodic porous media. Experience versus theory for two-dimensional systems. Chem Eng Sci 1997, 12:1861-1874.
19. Souto H.P.A., Moyne C. Dispersion in two-dimensional periodic porous media. Part II. Dispersion tensor. Phys Fluids 1997, 9(8):2253-2263.
20. Bijeljic B., Muggeridge A.H., Blunt M.J. Pore-scale modeling of longitudinal dispersion. Water Resour Res 2004, 40:W11501. 10.1029/2004WR003567.
21. Buyuktas D., Wallender W.W. Dispersion in spatially periodic porous media. Heat Mass Trans 2004, 40:261-270. 10.1007/s00231-003-0441-0.
22. Tsakiroglou C.D., Theodoropoulou M.A., Karoutos V., Papanicolaou D. Determination of the effective transport coefficients of pore networks from transient immiscible and miscible displacement experiments. Water Resour Res 2005, 41:W02014. 10.1029/2003WR002987.
23. Bijeljic B., Blunt M.J. Pore-scale modeling of transverse dispersion in porous media. Water Resour Res 2007, 43:W12S11. 10.1029/2006WR005700.
24. Aggelopoulos C.A. The longitudinal dispersion coefficient of soils as related to the variability of local permeability. Water Air Soil Pollut 2007, 185:223-237. 10.1007/s11270-9445-6.
25. Wood B.D. Inertial effects in dispersion in porous media. Water Resour Res 2007, 43:W12S16. 10.1029/2006WR005790.
26. Bolster D., Dentz M., Borgne T.L. Solute dispersion in channels with periodically varying apertures. Phys Fluids 2009, 21:056601. 10.1063/1.3131982.
27. Wood B.D. The role of scaling laws in upscaling. Adv Water Res 2009, 32(5):723-736. 10.1016/j.advwatres.2008.08.015.
28. Gray W.G. A derivation of the equations for multi-phase transport. Chem Eng Sci 1975, 30:229-233.
29. Wang J., Kitanidis P.K. Analysis of macrodispersion through volume averaging: comparison with stochastic theory. Stoch Env Res Risk A 1999, 13:66-84.
30. Whitaker S. The method of volume averaging 1999, Kluwer Academic Publishers.
31. Tartakovsky A.M., Redden G., Lichtner P.C., Sciebe T.D., Meakin P. Mixing-induced precipitation: experimental study and multiscale numerical analysis. Water Resour Res 2008, 44:W06S04. 10.1029/2006WR005725.
32. Zhu Y., Fox P.J. Simulation of pore-scale dispersion in periodic porous media using smoothed particle hydrodynamics. J Comput Phys 2002, 182:622-645. 10.1006/jcph.2002.7189.
33. Olsson A., Grathwohl P. Transverse dispersion of non-reactive tracers in porous media: a new nonlinear relationship to predict dispersion coefficients. J Contam Hydrol 2007, 92:149-161. 10.1016/j.jconhyd.2006.09.008.
34. Harleman D.R.F., Rumer R.R. Longitudinal and lateral dispersion in an isotropic porous medium. J Fluid Mech 1963, 16:385-394.
35. Salles J., Thovert J.F., Delannay R., Prevors L., Auriault J.L., Adler P. Taylor dispersion in porous media. Determination of the dispersion tensor. Phys Fluids A 1993, 5(10):2348-2376.
36. Saylor J.R., Sreenivasan K.R. Differential diffusion in low Reynolds number water jets. Phys Fluids 1998, 10(5):1135-1146.
37. Lewus P. Quantification of macroscopic and individual-cell bacterial-transport coefficients for mesophilic and thermophilic microorganisms, Ph.D. thesis, University of Virginia, 2000.
38. Park M., Kleinfelter N., Cushman J.H. Scaling laws and Fokker-Planck equations for 3-dimensional porous media with fractal mesoscale. Multiscale Model Simul 2005, 4(4):1233-1244.
39. Bear J. Dynamics of fluids in porous media 1988, Dover Publications, Inc.
40. Koch D.L., Brady J.F. A non-local description of advection-diffusion with application to dispersion in porous media. J Fluid Mech 1987, 180:387.
41. Cushman J.H., Ginn T.R. Nonlocal dispersion in media with continuously evolving scales of heterogeneity. Transp Porous Media 1993, 13:123-138.
42. Cushman J.H., Hu X., Ginn T.R. Nonequilibrium statistical mechanics of preasymptotic dispersion. J Stat Phys 1994, 75:859-878. 10.1007/BF02186747.
43. Moroni J., Cushman J.H., Cenedese A. A 3D-PTV two-projection study of pre-asymptotic dispersion in porous media which are heterogeneous on the bench scale. Int J Eng Sci 2003, 41:337-370.
44. Neumana S.P., Tartakovskyb D.M. Perspective on theories of non-Fickian transport in heterogeneous media. Adv Water Res 2009, 32(5):670-680. 10.1016/j.advwatres.2008.08.005.
45. Bear J. On the tensor form of dispersion. J Geophys Res 1961, 66(4):1185-1197.
46. Koch D.L., Brady J.F. The symmetry properties of the effective diffusivity tensor in anisotropic porous media. Phys Fluids 1987, 30:642-650.
47. Crank J. The mathematics of diffusion 1975, Oxford Science Publications. second ed.
48. Draper N.R., Smith H. Applied regression analysis 1968, John Wiley & Sons, Inc.