The Role of Tortuosity in Upscaling

Transport in Porous Media

Volumn 88, Issue 1, 2011, Pages 1-30

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

^a DEPARTAMENTO DE QUÍMICA   (Mexico)

^b Oregon State University   (United States)

Author keywords

Diffusion; Dispersion; Reaction; Tortuosity; Volume averaging

Indexed keywords

INTEGRAL PART; MASS DIFFUSION; MASS TRANSPORT; MICRO-SCALES; MULTI-SCALE SYSTEM; PASSIVE DIFFUSIONS; PATH LENGTH; POROUS MEDIA; REACTION; SHORTEST PATH; TORTUOSITY; TRANSPORT PHENOMENA; TRANSPORT PROCESS; UPSCALING; VOLUME AVERAGING;

DISPERSIONS; GRAPH THEORY; POROUS MATERIALS;

DIFFUSION;

CONVECTION; COUPLING; DIFFUSION; DISPERSION; FLOW MODELING; MASS TRANSPORT; NUMERICAL MODEL; POROUS MEDIUM; SOLUTE TRANSPORT; TORTUOSITY; UPSCALING; VOLUME TRANSPORT;

EID: 79955054604     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11242-010-9613-9     Document Type: Article

References (73)

1. Acharya R. C., Albert J Valocchi C. J. W., Willingham T. W.: Pore-scale simulation of dispersion and reaction along a transverse mixing zone in two-dimensional porous media. Water Resour. Res. 43, W10435 (2007).
2. Adler P. M.: Porous Media: Geometry and Transports. Butterworth-Heinemann, Boston (1992).
3. Archie G. E.: The electrical resistivity log as an aid in determining some reservoir characteristics. Trans. Am. Inst. Mech. Eng. 146, 54-67 (1942).
4. Aris R.: On the dispersion of a solute in a fluid flowing through a tube. Proc. R. Soc. Lond. A 235, 67-77 (1956).
5. Baveye P., Sposito G.: The operational significance of the continuum hypothesis in the theory of water movement through soils and aquifers. Water Resour. Res. 20, 521-530 (1984).
6. Bear J.: Hydrodynamic dispersion. In: De Wiest, R. (eds) Flow Through Porous Media, pp. 109-199. Wiley, New York (1969).
7. Bear J.: Dynamics of Fluids in Porous Media. Elsevier, New York (1972).
8. Bear, J., Bachmat, Y.: Hydrodynamic dispersion in non-uniform flow through porous media, taking into account density and viscosity differences (in Hebrew with English summary). P. N. 4/66. Hydraulic Laboratory, Technion, Haifa, Israel (1966).
9. Bear, J., Bachmat, Y.: A generalized theory on hydrodynamic dispersion in porous media. In: IAsH Symposium on Artifcial Recharge Management Aquifers, Haifa, Israel, IASH, PN vol. 72, pp. 7-16 (1967).
10. Bijeljic B., Blunt M. J.: Pore-scale modeling of transverse disperison in porous media. Water Resour. Res. 43, W12S11 (2007). doi: 10. 1029/2006WR005700.
11. Bijeljic B., Muggeridge A. H., Blunt M. J.: Pore-scale modeling of longitudinal disperison. Water Resour. Res. 40, W11501 (2004). doi: 10. 1029/2004WR003567.
12. Boudreau B. P.: The diffusive tortuosity of fine-grained unlithified sediments. Geochim. Cosmochim. Acta. 60, 3139-3142 (1996).
13. Buyuktas D., Wallender W.: Dispersion in spatially periodic porous media. Heat Mass Transf. 40, 261-270 (2004).
14. Carman P. C.: Fluid flow through granular beds. Trans. Inst. Chem. Eng. 50, 150-166 (1937).
15. Chang H. C.: Multiscale analysis of effective transport in periodic heterogeneous media. Chem. Eng. Commun. 15, 83-91 (1982).
16. Chang H. C.: Effective diffusion and conduction in two-phase media. AIChE J. 29, 846-853 (1983).
17. Clennell M. B.: Tortuosity: A Guide Through the Maze (Special Publication), vol no. 122, pp. 299-344. Geological Society, London (1997).
18. Cushman J. H.: On unifying the concepts of scale, instrumentation, and stochastics in the development of multiphase transport theory. Water Resour. Res. 20, 1668-1676 (1984).
19. De Josselin De Jong G.: Longitudinal and transverse diffusion in granular deposits. Trans. Am. Geophys. Union 39, 67-74 (1958).
20. 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. 12, 1861-1874 (1997).
21. Dullien F.: Porous Media Fluid Transport and Pore Structure, 2nd ed. Academic Press, New York (1992).
22. Edwards D., Shapiro M., Brenner H., Shapira M.: Dispersion of inert solutes in spatially periodic, two-dimensional model porous media. Trans. Porous Med. 6, 337-358 (1991).
23. Edwards D., Shapiro M., Brenner H.: Dispersion and reaction in two-dimemsional model porous media. Phys. Fluids 5, 837-848 (1993).
24. Eidsath A., Carbonell R., Whitaker S., Herrmann L.: Dispersion in pulsed systems. III. Comparison between theory and experiments for packed beds. Chem. Eng. Sci. 38, 1803-1816 (1983).
25. Golin Y. L., Karyarin V. E., Pospelov B. S., Sevedkin V. I.: Pore tortuosity estimates in porous media. Sov. Electrochem. 28, 87-91 (1992).
26. Gray W. G.: A derivation of the equations for multi-phase transport. Chem. Eng. Sci. 30, 229-233 (1975).
27. Greenkorn R. A.: Flow Phenomena in Porous Media. Marcel Dekker, New York (1983).
28. Gunn D., Pryce C.: Dispersion in packed beds. Trans. Inst. Chem. Eng. 47, T341-T350 (1969).
29. Han N. W., Bhakta J., Carbonell R.: Longitudinal and lateral dispersion in packed beds: Effect of column length and particle size distribution. AIChE J. 31(2), 277-288 (1985).
30. Harleman D., Rumer R.: Longitudinal and lateral dispersion in an isotropic porous medium. J. Fluid Mech. 16, 385-394 (1963).
31. Howes F. A., Whitaker S.: The spatial averaging theorem revisited. Chem. Eng. Sci. 40, 1387-1392 (1985).
32. Koch D. L., Cox R. G., Brenner H., Brady J. H.: The effect of order on dispersion in porous media. J. Fluid Mech. 200, 173-188 (1989).
33. Kozeny J.: Uber kapillare leitung des wassers im boden. Sitzungberichte der Akadämie der Wissenschaftung in Wein Abteilung IIa 136, 271-301 (1927).
34. Lehner F. K.: On the validity of Fick's law for transient diffusion through a porous medium. Chem. Eng. Sci. 34, 821-825 (1979).
35. 2 colloidal aggregates. J. Colloid Interface Sci. 164, 1-8 (1994).
36. Lux, J.: A non-periodic closure scheme for the determination of effective diffusivity in real porous media. Trans Porous Med. (2009). doi: 10. 1007/s11242-009-9423-0.
37. Maxwell J. C.: Treatise on electricity and magnetism, vol. I, 1st edn. Clarendon press, Oxford (1873).
38. Mitra P. P., Latour L. L., Kleinberg R. L., Sotak C. H.: Pulsed-field-gradient nmr measurements of restricted diffusion and the return-to-the-origin probability. J. Magn. Reson. A 114, 47-58 (1995).
39. Moyne C.: Two-equation model for a diffusive process in porous media using the volume averaging method with an unsteady-state closure. Adv. Water Resour. 20, 63-76 (1997).
40. Ochoa-Tapia J. A., Stroeve P., Whitaker S.: Diffusion and reaction in cellular media. Chem. Eng. Sci. 14(12), 2999-3013 (1986).
41. Ochoa-Tapia J. A., Stroeve P., Whitaker S.: Diffusive transport in two-phase media: spatially periodic models and Maxwell's theory for isotropic and anisotropic systems. Chem. Eng. Sci. 49, 709-726 (1994).
42. Ohkubo T.: Tortuosity based on anisotropic diffusion process in structured plate-like obstacles by Monte Carlo simulation. Transp. Porous Med. 72, 339-350 (2008).
43. Olsson A., Grathwohl P.: Transverse dispersion of non-reactive tracers in porous media: A new nonlinear relationship to predict dispersion coefficients. J. Contam. Hydrol. 92, 149-161 (2007).
44. Penman H. L.: Gas and vapor movement in soil. J. Agric. Sci. 30, 438-462 (1940).
45. Petersen E. E.: Diffusion in a pore of varying cross section. AIChE J. 4, 343-345 (1958).
46. Pfannkuch H. O.: Contribution à l'étude des déplacements de fluides miscibles dans un milieu poreux. Revue de l'Institute Français du Pétrole XVIII(2), 215-270 (1963).
47. Prachayawarakorn S., Mann R.: Effects of pore assembly architecture on catalyst particle tortuosity and reaction effectiveness. Catal. Today 128, 88-99 (2007).
48. Quintard M.: Diffusion in isotropic and anisotropic porous systems: Three-dimensional calculations. Transp. Porous Med. 3, 187-199 (1993).
49. Quintard M., Whitaker S.: Convection, dispersion and interfacial transport of contaminants: homogeneous porous medium. Adv. Water Resour. 17, 221-239 (1994a).
50. Quintard M., Whitaker S.: Transport in ordered and disordered porous media I: the cellular average and the use of weighting functions. Transp. Porous Med. 14, 163-177 (1994b).
51. Quintard M., Whitaker S.: Transport in ordered and disordered porous media II: Generalized volume averaging. Transp. Porous Med. 14, 179-206 (1994c).
52. Rayleigh L.: On the influence of obstacles arranged in rectangular order upon the properties of the medium. Philos. Mag. 34, 481-502 (1892).
53. Ryan, D.: Effective diffusivities in reactive porous media: a comparison between theory and experiments. Master's thesis, University of California at Davis (1983).
54. Ryan D., Carbonell R. G., Whitaker S.: A theory of diffusion and reaction in porous media. AIChE Symp. Ser. 71, 46-62 (1981).
55. Sahimi M.: Flow and Transport in Porous Media and Fractured Rock: From Classical Methods to Modern Approaches. VCH, Weinheim (1995).
56. 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 5(10), 2348-2376 (1993).
57. Satterfield C. N.: Mass Transfer in Heterogeneous Catalysts. MIT Press, Cambridge (1970).
58. Sharratt P. N., Mann R.: Some observations on the variation of tortuosity with thiele modulus and pore size distribution. Chem. Eng. Sci. 42, 1565-1575 (1987).
59. Souto H. P. A., Moyne C.: Disperison in two-dimensional periodic porous media. Part II. Disperison tensor. Phys. Fluids 9(8), 2253-2263 (1997).
60. Taylor G.: The dispersion of matter in turbulent flow through a pipe. Proc. R. Soc. Lond. A 223, 446-468 (1954).
61. Trihn S., Arce P., Locke B. R.: Effective diffusivities of point-like molecules in isotropic porous media by Monte Carlo simulation. Transp. Porous Med. 38, 241-259 (2000).
62. Trihn S., Arce P., Locke B. R.: Effective diffusivity tensors of point-like molecules in anisotropic porous media by Monte Carlo simulation. Transp. Porous Med. 47, 279-293 (2002).
63. Valdés-Parada F. J., Ochoa-Tapia J. A., Alvarez-Ramirez J.: Diffusive mass transport in fluid-porous medium inter-region: closure problem solution for the one-domain approach. Chem. Eng. Sci. 62, 6054-6068 (2007).
64. Vervoort R. W., Cattle S. R.: Linking hydraulic conductivity and tortuosity parameters to pore space geometry and pore-size distribution. J. Hydrol. 272, 36-49 (2003).
65. Whitaker S.: Diffusion and dispersion in porous media. AIChE J. 13, 420-427 (1967).
66. Whitaker S.: Mass transport and reaction in catalyst pellets. Transp. Porous Med. 2, 269-299 (1987).
67. Whitaker S.: The Method of Volume Averaging. Kluwer Academic Publishers, Dordrecht (1999).
68. Wood, B. D.: Inertial effects in dispersion in porous media. Water Resour. Res. 43 (2007). doi: 10. 1029/2006WR005790.
69. Wood B. D.: The role of scaling laws in upscaling. Adv. Water Resour. 32, 723-736 (2009).
70. Wood B. D.: Taylor-Aris dispersion: an explicit example for understanding multiscale analysis via volume averaging. Chem. Eng. Educ. 43, 29-38 (2009).
71. Wu Y. S., van Vliet L. J., Frijlink H. W., van der Voort Maarschalk K.: The determination of relative path lengths as a measure for tortuosity in compacts using image analysis. Eur. J. Pharma. Sci. 28, 433-440 (2006).
72. Wyllie M. R. J., Rose W. D.: Some theoretical considerations related to quantitative evaluation of the physical characteristics of reservoir rock from electric log data. Trans. Am. Inst. Mech. Eng. 189, 105-118 (1950).
73. Zhu Y., Fox P. J.: Simulation of pore-scale dispersion in periodic porous media using smoothed particle hydrodynamics. J. Comput. Phys. 182, 622-645 (2002).