Dispersion in porous media, continuous-time random walks, and percolation

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 85, Issue 1, 2012, Pages

  Sahimi, Muhammad ^a  

^a University of Southern California ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUOUS-TIME RANDOM WALK; CONTINUUM SYSTEMS; EFFECTIVE CONDUCTIVITY; EXPERIMENTAL DATA; FIELD SCALE; FLOWTHROUGH; HETEROGENEOUS POROUS MEDIA; LONG RANGE CORRELATIONS; MEAN-SQUARE DISPLACEMENT; NON-GAUSSIAN; NONUNIVERSALITY; PERCOLATION MODELS; PERCOLATION THRESHOLDS; POWER-LAW BEHAVIOR; POWER-LAW GROWTH; SCALING ANALYSIS; WAITING TIME DISTRIBUTIONS;

CONTINUOUS TIME SYSTEMS; DISPERSIONS; PERCOLATION (SOLID STATE); RANDOM PROCESSES; SOLVENTS;

POROUS MATERIALS;

EID: 84856656473     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.85.016316     Document Type: Article

References (90)

1. M. Sahimi, Flow and Transport in Porous Media and Fractured Rock, 2nd ed. (Wiley-VCH, Weinheim, Germany, 2011).
2. G. de Josselin de Jong, Trans. Am. Geophys. Union 39, 67 (1958);
3. P. G. Saffman, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112059000672 6, 321 (1959);
4. see also, P. M. Adler, Porous Media: Geometry and Transport (Butterworth, Boston, 1992).
5. M. Sahimi, H. T. Davis, and L. E. Scriven, Chem. Eng. Commun. CEGCAK 0098-6445 10.1080/00986448308940483 23, 329 (1983);
6. M. Sahimi, B. D. Hughes, L. E. Scriven, and H. T. Davis, Chem. Eng. Sci. CESCAC 0009-2509 10.1016/0009-2509(86)87128-7 41, 2103 (1986); (Pubitemid 16633985)
7. M. Sahimi, A. A. Heiba, H. T. Davis, and L. E. Scriven, Chem. Eng. Sci. CESCAC 0009-2509 10.1016/0009-2509(86)87129-9 41, 2123 (1986); (Pubitemid 16633984)
8. M. Sahimi and A. O. Imdakm, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/21/19/019 21, 3833 (1988).
9. L. de Arcangelis, J. Koplik, S. Redner, and D. Wilkinson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.57.996 57, 996 (1986);
10. J. Koplik, S. Redner, and D. Wilkinson, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.37.2619 37, 2619 (1988);
11. V. Alvarado, H. T. Davis, and L. E. Scriven, Chem. Eng. Sci. CESCAC 0009-2509 10.1016/S0009-2509(97)00100-0 52, 2865 (1997). (Pubitemid 27372370)
12. B. Bijeljic, A. H. Muggeride, and M. J. Blunt, Water Resour. Res. WRERAQ 0043-1397 10.1029/2004WR003567 40, W11501 (2004); (Pubitemid 40008850)
13. B. Bijeljic and M. J. Blunt, Water Resour. Res. WRERAQ 0043-1397 10.1029/2005WR004578 42, W01202 (2006); (Pubitemid 43352610)
14. B. Bijeljic and M. J. Blunt, Water Resour. Res. WRERAQ 0043-1397 10.1029/2006WR005700 43, W12S11 (2007); (Pubitemid 351162006)
15. B. Bijeljic, P. Mostaghimi, and M. J. Blunt, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.107.204502 107, 204502 (2011).
16. C. Bruderer and Y. Bernabé, Water Resour. Res. WRERAQ 0043-1397 10.1029/2000WR900362 37, 897 (2001); (Pubitemid 32516045)
17. R. C. Acharya, S. E. A. T. M. Van der Zee, and A. Leijnse, Adv. Water Resour. AWREDI 0309-1708 10.1016/j.advwatres.2005.11.015 30, 261 (2007). (Pubitemid 44817501)
18. Y. Lee, J. S. Andrade, S. V. Buldyrev, N. V. Dokholyan, S. Havlin, P. R. King, G. Paul, and H. E. Stanley, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.60.3425 60, 3425 (1999);
19. J. S. Andrade, U. M. S. Costa, M. P. Almeida, H. A. Makse, and H. E. Stanley, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.5249 82, 5249 (1999);
20. H. A. Makse, J. S. Andrade, and H. E. Stanley, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.61.583 61, 583 (2000).
21. S. Whitaker, AIChE J. AICEAC 0001-1541 10.1002/aic.690130308 13, 420 (1967).
22. D. L. Koch and J. F. Brady, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112085001598 154, 399 (1985);
23. D. L. Koch and J. F. Brady, Chem. Eng. Sci. CESCAC 0009-2509 10.1016/0009-2509(87)85010-8 42, 1377 (1987); (Pubitemid 17617158)
24. D. L. Koch and J. F. Brady, Phys. Fluids PHFLE6 1070-6631 10.1063/1.866716 31, 965 (1988).
25. L. W. Gelhar and C. L. Axness, Water Resour. Res. WRERAQ 0043-1397 10.1029/WR019i001p00161 19, 161 (1983).
26. L. Smith and F. W. Schwartz, Water Resour. Res. WRERAQ 0043-1397 10.1029/WR016i002p00303 16, 303 (1980);
27. L. Smith and F. W. Schwartz, Water Resour. Res. WRERAQ 0043-1397 10.1029/WR017i002p00351 17, 351 (1981).
28. A. G. Hunt and R. Ewing, Percolation Theory for Flow in Porous Media, 2nd ed. (Springer, Heidelberg, 2009);
29. A. G. Hunt and T. E. Skinner, Philos. Mag. WRERAQ 1478-6435 10.1080/14786430802395137 88, 2921 (2008);
30. A. G. Hunt and T. E. Skinner, Complexity COMPFS 1076-2787 10.1002/cplx.20322 16, 43 (2010);
31. A. G. Hunt, T. E. Skinner, R. P. Ewing, and B. Ghanbarian-Alavijeh, Eur. Phys. J. B 1434-6028 10.1140/epjb/e2011-10805-y 80, 411 (2011).
32. B. Berkowitz, S. Emmanual, and H. Scher, Water Resour. Res. WRERAQ 0043-1397 10.1029/2007WR005906 44, W03402 (2008). (Pubitemid 351628535)
33. E. W. Montroll and G. H. Weiss, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1704269 6, 167 (1965).
34. E. W. Montroll and H. Scher, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01016843 9, 101 (1973);
35. H. Scher and E. W. Montroll, Phys. Rev. B 1098-0121 10.1103/PhysRevB.12. 2455 12, 2455 (1975).
36. J. S. Aronofsky and J. P. Heller, Trans. AIME 210, 345 (1957).
37. B. Berkowitz, A. Cortis, M. Dentz, and H. Scher, Rev. Geophys. REGEEP 8755-1209 10.1029/2005RG000178 44, RG2003 (2006). (Pubitemid 46044201)
38. R. Zwanzig, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1731409 33, 1338 (1960);
39. J. Klafter and R. Silbey, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.44.55 44, 55 (1980).
40. M. Sahimi, B. D. Hughes, L. E. Scriven, and H. T. Davis, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.444631 78, 6849 (1983).
41. V. Kenkre, E. W. Montroll, and M. F. Shlesinger, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01016796 9, 45 (1973).
42. A. Cortis and B. Berkowitz, Ground Water GRWAAP 0017-467X 10.1111/j.1745-6584.2005.00045.x 43, 947 (2005). (Pubitemid 41681850)
43. H. Scher and M. Lax, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.7. 4502 7, 4502 (1973).
44. A. Cortis, Y. Chen, H. Scher, and B. Berkowitz, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.70.041108 70, 041108 (2004). (Pubitemid 40010427)
45. B. Berkowitz, J. Klafter, R. Metzler, and H. Scher, Water Resour. Res. WRERAQ 0043-1397 10.1029/2001WR001030 38, 1191 (2002);
46. M. Dentz, A. Cortis, H. Scher, and B. Berkowitz, Adv. Water Resour. AWREDI 0309-1708 10.1016/j.advwatres.2003.11.002 27, 155 (2004). (Pubitemid 38242169)
47. A. Cortis, C. Gallo, H. Scher, and B. Berkowitz, Water Resour. Res. WRERAQ 0043-1397 10.1029/2003WR002750 40, W04209 (2004).
48. H. Scher and M. Lax, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.7. 4491 7, 4491 (1973).
49. D. Stauffer and A. Aharony, Introduction to Percolation Theory, 2nd ed. (Taylor & Francis, London, 1994);
50. M. Sahimi, Applications of Percolation Theory (Taylor & Francis, London, 1994).
51. M. A. Knackstedt, A. P. Sheppard, and M. Sahimi, Adv. Water Resour. AWREDI 0309-1708 10.1016/S0309-1708(00)00057-9 24, 257 (2001).
52. V. Ambegaokar, B. I. Halperin, and J. S. Langer, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.4.2612 4, 2612 (1971);
53. M. Pollak, J. Non-Cryst. Solids JNCSBJ 0022-3093 10.1016/0022-3093(72) 90304-3 11, 1 (1972);
54. L. Friedman and M. Pollak, Philos. Mag. B JNCSBJ 1364-2812 10.1080/01418638108222584 44, 487 (1981);
55. J. Cottaar, L. J. A. Koster, R. Coehoorn, and P. A. Bobbert, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.107.136601 107, 136601 (2011).
56. M. Sahimi, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/20/18/013 20, L1293 (1987).
57. B. I. Halperin, S. Feng, and P. N. Sen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.54.2391 54, 2391 (1985);
58. S. Feng, B. I. Halperin, and P. N. Sen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.35.197 35, 197 (1987).
59. M. Sahimi and S. Mukhopadhyay, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.54.3870 54, 3870 (1996);
60. M. A. Knackstedt, M. Sahimi, and A. P. Sheppard, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.61.4920 61, 4920 (2000).
61. K. H. Coats and B. D. Smith, Soc. Pet. Eng. J. 4, 73 (1964).
62. Y. Gefen, A. Aharony, and S. Alexander, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.50.77 50, 77 (1983).
63. P. G. de Gennes, J. Fluid Mech. JFLSA7 0022-1120 10.1017/ S0022112083002116 136, 189 (1983).
64. R. Aris, Chem. Eng. Sci. CESCAC 0009-2509 10.1016/0009-2509(59)80086-5 11, 194 (1959);
65. see also, G. A. Turner, Chem. Eng. Sci. CESCAC 0009-2509 10.1016/0009-2509(59)80020-8 10, 14 (1959).
66. A. E. Scheidegger, in Proceedings of the Conference on Theory of Fluid Flow in Porous Media (University of Oklahoma, Norman, OK, 1959), p. 101.
67. S. E. Silliman and E. S. Simpson, Water Resour. Res. WRERAQ 0043-1397 10.1029/WR023i008p01667 23, 1667 (1987).
68. A. Cortis and B. Berkowitz, Soil Sci. Soc. Am. J. WRERAQ 0361-5995 10.2136/sssaj2004.1539 68, 1539 (2004);
69. A. Cortis and B. Berkowitz, Soil Sci. Soc. Am. J. 69, 295(E) (2004). The quoted estimates of the various quantities are from the erratum.
70. J. W. Biggar and D. R. Nielsen, Soil Sci. Soc. Am. J. WRERAQ 0361-5995 10.2136/sssaj1962.03615995002600020010x 26, 125 (1962).
71. P. M. Kogut and J. P. Straley, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/12/11/023 12, 2151 (1979);
72. A. Ben-Mizrahi and D. J. Bergman, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/14/6/015 14, 909 (1981);
73. J. P. Straley, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/15/11/013 15, 2333 (1982);
74. see also Ref. [19].
75. E. A. Sudicky and J. A. Cherry, Water Pollut. Res. Can. 14, 1 (1979);
76. E. A. Sudicky and E. O. Frind, Water Resour. Res. WRERAQ 0043-1397 10.1029/WR018i006p01634 18, 1634 (1982);
77. E. A. Sudicky, J. A. Cherry, and E. O. Frind, Water Resour. Res. WRERAQ 0043-1397 10.1029/WR021i007p01035 21, 1035 (1985);
78. J. F. Pickens and G. E. Grisak, Water Resour. Res. WRERAQ 0043-1397 10.1029/WR017i004p01191 17, 1191 (1981);
79. O. Güven, F. J. Molz, and J. G. Melville, Water Resour. Res. WRERAQ 0043-1397 10.1029/WR020i010p01337 20, 1337 (1984);
80. O. Güven, R. W. Falta, F. J. Molz, and J. G. Melville, Water Resour. Res. WRERAQ 0043-1397 10.1029/WR021i005p00676 21, 676 (1985);
81. F. J. Molz, O. Güven, and J. G. Melville, Ground Water GRWAAP 0017-467X 10.1111/j.1745-6584.1983.tb01942.x 21, 715 (1983).
82. A. Arya, T. A. Hewett, R. G. Larson, and L. W. Lake, SPE Reservoir Eng. 3, 139 (1988).
83. S. P. Neuman, Water Resour. Res. 0043-1397 10.1029/WR026i008p01749 26, 1749 (1990).
84. T. A. Hewett, SPE Paper 15386 (1986);
85. J. R. Philip, Transp. Porous Media TPMEEI 0169-3913 10.1007/BF00208041 1, 319 (1986);
86. R. Ababou and L. W. Gelhar, in Dynamics of Fluids in Hierarchical Porous Media, edited by, J. H. Cushman, (Academic, San Diego, 1990), p. 394.
87. B. Berkowitz and H. Scher, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.57.5858 57, 5858 (1998).
88. M. Sahimi and S. E. Tajer, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.71.046301 71, 046301 (2005); (Pubitemid 40619659)
89. H. Dashtian, G. R. Jafari, M. Sahimi, and M. Masihi, Physica A PHYADX 0378-4371 10.1016/j.physa.2011.01.010 390, 2096 (2011);
90. H. Dashtian, G. R. Jafari, Z. Koohi Lai, M. Masihi, and M. Sahimi, Transp. Porous Media TPMEEI 0169-3913 10.1007/s11242-011-9794-x 90, 445 (2011).