Anomalous dispersion in chemically heterogeneous media induced by long-range disorder correlation

Journal of Fluid Mechanics

Volumn 695, Issue , 2012, Pages 366-389

  Bolster, D ^a   Dentz, M ^b  

^a University of Notre Dame   (United States)

^b INSTITUTE OF ENVIRONMENTAL ASSESSMENT AND WATER RESEARCH   (Spain)

Author keywords

geophysical and geological flows; mixing and dispersion; porous media

Indexed keywords

CONTINUOUS TIME SYSTEMS; DISPERSION (WAVES); POROUS MATERIALS; RANDOM PROCESSES; STOCHASTIC SYSTEMS;

ANOMALOUS DISPERSION; CHEMICAL ADSORPTION; CONTINUOUS-TIME RANDOM WALK MODELS; GEOPHYSICAL AND GEOLOGICAL FLOWS; HETEROGENEOUS MEDIA; MIXING AND DISPERSIONS; POWER-LAW CORRELATIONS; RANDOM WALK PARTICLE TRACKING;

DISPERSIONS;

ADSORPTION; CORRELATION; HETEROGENEITY; HETEROGENEOUS MEDIUM; NUMERICAL MODEL; POROUS MEDIUM; STOCHASTICITY; TRANSPORT PROCESS;

EID: 84858633108     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/jfm.2012.25     Document Type: Article

References (64)

1. ABRAMOWITZ, M. & STEGUN, I. A. 1965 Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables. Dover.
2. ADAMS, E. E. & GELHAR, L. W. 1992 Field study of dispersion in a heterogeneous aquifer, 2, spatial moments analysis. Water Resour. Res. 28 (12), 3293-3307. (Pubitemid 23379496)
3. ANDRICEVIC, R. & CVETKOVIC, V. 1998 Relative dispersion for solute flux in aquifers. J. Fluid Mech. 361, 145-174. (Pubitemid 128488597)
4. ARIS, R. 1956 On the dispersion of a solute in a Fluid flowing through a tube. Proc. R. Soc. Lond. A 235, 67.
5. ATTINGER, S., DENTZ, M. & KINZELBACH, W. 2004 Exact transverse macro dispersion coefficients for transport in heterogeneous porous media. Stoch. Environ. Res. Risk Assess. 18, 9-15. (Pubitemid 38459579)
6. ATTINGER, S., DENTZ, M., KINZELBACH, H. & KINZELBACH, W. 1999 Temporal behaviour of a solute cloud in a chemically heterogeneous porous medium. J. Fluid Mech. 386, 77-104.
7. DE BARROS, F. J. & RUBIN, Y. 2011 Modelling of block-scale macrodispersion as a random function. J. Fluid Mech. 676, 514-545.
8. BATCHELOR, G. K. 1949 Diffusion in a field of homogeneous turbulence I, Eulerian analysis. Austral. J. Sci. Res. 2, 437-450.
9. BELLIN, A., RINALDO, A., BOSMA, W. J. P., VAN DER ZEE, S. E. A. T. M. & RUBIN, Y. 1993 Linear equilibrium adsorbing solute transport in physically and chemically heterogeneous porous formations: 1. Analytical solutions. Water Resour. Res. 29, 4019-4030.
10. BELLIN, A., SALANDIN, P. & RINALDO, A. 1992 Simulation of dispersion in heterogeneous porous formations: statistics, first-order theories, convergence of computations. Water Resour. Res. 28, 2211-2227. (Pubitemid 23386283)
11. BENSON, D. A., WHEATCRAFT, S. W. & MEERSCHAERT, M. M. 2000 Application of a fractional advection-dispersion equation. Water Resour. Res. 36, 1403-1412. (Pubitemid 30334241)
12. BERKOWITZ, B., CORTIS, A., DENTZ, M. & SCHER, H. 2006 Modeling non-Fickian transport in geological formations as a continuous time random walk. Rev. GeoPhys. 44, RG2003.
13. BERKOWITZ, B., KOSAKOWSKI, G., MARGOLIN, G. & SCHER, H. 2005 Application of continuous time random walk theory to tracer test measurements in fractured and heterogeneous porous media. Ground Water 39, 593-604. (Pubitemid 32632497)
14. BOLSTER, D., DENTZ, M. & LEBORGNE, T. 2009 Solute dispersion in channels with periodically varying apertuRes. Phys. Fluids 21, 056601.
15. BOUCHAUD, J.-P. & GEORGES, A. 1990 Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications. Phys. Rep. 195, 127-293.
16. BRENNER, H. 1980 Dispersion resulting from flow through spatially periodic porous media. Phil. Trans. R. Soc. Lond. Ser. A 297, 81-133.
17. CHRYSIKOPOULOS, C. V., KITANIDIS, P. K. & ROBERTS, P. V. 1990 Analysis of one-dimensional solute transport through porous media with spatially variable retardation factor. Water Resour. Res. 26, 437-446.
18. CVETKOVIC, V., DAGAN, G. & CHENG, H. 1998 Contaminant transport in aquifers with spatially variable hydraulic and sorption properties. Proc. R. Soc. Lond. A 454, 2173-2207. (Pubitemid 128733231)
19. DAGAN, G. 1984 Solute transport in hetereogeneous porous formations. J. Fluid Mech. 145, 151-177. (Pubitemid 15458995)
20. DAGAN, G. 1990 Transport in heterogeneous porous formations: spatial moments, ergodicity, and effective dispersion. Water Resour. Res. 26, 1281-1290.
21. DAGAN, G. 1991 Dispersion of a passive solute in non-ergodic transport by steady velocity fields in heterogeneous formations. J. Fluid Mech. 233, 197-210.
22. DAGAN, G. 1994 The significance of heterogeneity of evolving scales and of anomalous diffusion to transport in porous formations. Water Resour. Res. 30, 3327-3336. (Pubitemid 294009)
23. DAGAN, G. & NEUMAN, S. P. (Eds) 1997 Subsurface Flow and Transport. Cambridge University Press.
24. DENTZ, M. & BERKOWITZ, B. 2003 Transport behavior of a passive solute in continuous time random walks and multirate mass transfer. Water Resour. Res. 39, 1111.
25. DENTZ, M. & BOLSTER, D. 2010 Distribution- versus correlation-induced anomalous transport in quenched random velocity fields. Phys. Rev. Lett. 105, 244301.
26. DENTZ, M., BOLSTER, D. & LEBORGNE, T. 2009 Concentration statistics for transport in random media. Phys. Rev. E 80, 010101.
27. DENTZ, M. & CASTRO, A. 2009 Effective transport dynamics in porous media with heterogeneous retardation properties. GeoPhys. Res. Lett. 35, L03403.
28. DENTZ, M., KINZELBACH, H., ATTINGER, S. & KINZELBACH, W. 2000 Temporal behaviour of a solute cloud in a heterogeneous porous medium, 1, point-like injection. Water Resour. Res. 36 (12), 3591-3604. (Pubitemid 32039910)
29. DENTZ, M., KINZELBACK, H., ATTINGER, S. & KINZELBACH, W. 2003 Numerical studies of the transport behaviour of a passive solute in a two-dimensional incompressible random flow field. Phys. Rev. E 67, 046306.
30. DI FEDERICO, V. & ZHANG, Y. K. 1999 Solute transport in heterogeneous porous media with long-range correlations. Water Resour. Res. 35, 3185-3191.
31. EDWARDS, D. & BRENNER, H. 1993 Macrotransport Processes. Butterworth Heinemann.
32. FIORI, A. 2001 On the influence of local dispersion in solute transport through formations with evolving scales of heterogeneity. Water Resour. Res. 37, 235-242. (Pubitemid 32111431)
33. GELHAR, L. W. 1992 Stochastic Subsurface Hydrology. Prentice-Hall.
34. GELHAR, L., WELTY, C. & REHFELDT, K. A. 1992 A critical review of data on field scale dispersion in aquifers. Water Resour. Res. 28, 1955-1974. (Pubitemid 23373205)
35. GILL, W. N. & SANKARASUBRAMANIAN, R. 1970 Exact analysis of unsteady convective diffusion. Proc. R. Soc. Lond. A 316, 341.
36. GLIMM, J. & SHARP, D. H. 1991 A random field model for anomalous diffusion in heterogeneous porous media. J. Stat. Phys. 62, 415-424.
37. GRATHWOHL, P. 1998 Diffusion in Natural Porous Media: Contaminant Transport, Sorption/Desorption and Dissolution Kinetics. Springer.
38. HERRICK, M. G., BENSON, D. A., MEERSCHAERT, M. M. & MCCALL, K. R. 2002 Hydraulic conductivity, velocity, and the order of the fractional dispersion derivative in a highly heterogeneous system. Water Resour. Res. 38 (11), 1227.
39. JARMAN, K. D. & TARTAKOVSKY, A. M. 2008 Divergence of solutions to solute transport moment equations. GeoPhys. Res. Lett. 35, L15401.
40. JONES, S. W. & YOUNG, W. R. 1994 Shear dispersion and anomalous diffusion by chaotic advection. J. Fluid Mech. 280, 149-172. (Pubitemid 290910)
41. KENKRE, V. M., MONTROLL, E. W. & SCHLESINGER, F. M. 1973 Generalized master equations for continuous time random walks. J. Stat. Phys. 9, 45.
42. KINZELBACH, W. 1987 Methods for the simulation of pollutant transport in ground water: a model comparison. In Proceedings of the NWWA Conference on Solving Ground Water Problems with Models, pp. 656-675. National Water Well Association.
43. KITANIDIS, P. K. 1988 Prediction by the method of moments of transport in heterogeneous formations. J. Hydrol. 102, 453-473. (Pubitemid 19299580)
44. KOCH, D. L. & BRADY, J. F. 1985 Dispersion in fixed beds. J. Fluid Mech. 154, 399-427.
45. KOCH, D. L. & BRADY, J. F. 1987 A non-local description of advection-diffusion with application to dispersion in porous media. J. Fluid Mech. 180, 387-403.
46. LATINI, M. & BERNOFF, A. J. 2001 Transient anomalous diffusion in Poiseuille flow. J. Fluid Mech. 441, 399-411. (Pubitemid 32779151)
47. LAWRENCE, A. E. & RUBIN, Y. 2007 Block-effective macrodispersion for numerical simulations of sorbing solute transport in heterogeneous porous formations. Adv. Water Resour. 30, 1272-1285. (Pubitemid 46323438)
48. LEBORGNE, T., DENTZ, M. & CARRERA, J. 2008 Lagrangian statistical model for transport in highly heterogeneous velocity fields. Phys. Rev. Lett. 101, 090601.
49. LENZ, R. D. & KUMAR, S. 2007 Competitive displacement of thin liquid films on chemically patterned substrates. J. Fluid Mech. 571, 33-57. (Pubitemid 46056002)
50. LEVY, M. & BERKOWITZ, B. 2003 Measurement and analysis of non-Fickian dispersion in heterogeneous porous media. J. ContAm. Hydrol. 64, 203-226. (Pubitemid 36694143)
51. LUNATI, I., ATTINGER, S. & KINZELBACH, W. 2002 Macrodispersivity for transport in arbitrary nonuniform flow fields: asymptotic and preasymptotic results. Water Resour. Res. 38 (10), 1187.
52. MATHERON, G. & DE MARSILY, G. 1980 Is transport in porous media always diffusive? A counter example. Water Resour. Res. 16, 901.
53. MIRALLES-WILHELM, F. & GELHAR, L. W. 1996 Stochastic analysis of sorption macrokinetics in heterogeneous aquifers. Water Resour. Res. 32, 1541-1549.
54. MORONI, M. & CUSHMAN, J. H. 2001 Statistical mechanics with three-dimensional particle tracking velocimetry experiments in the study of anomalous dispersion. I. Theory. Phys. Fluids 13, 75.
55. NEUMAN, S. P. 1990 Universal scaling of hydraulic conductivities and dispersivities in geologic media. Water Resour. Res. 26, 1749-1758.
56. NEUMAN, S. P. & TARTAKOVSKY, D. M. 2009 Perspective on theories of anomalous transport in heterogeneous media. Adv. Water Res. 32, 670-680.
57. RAJARAM, H. & GELHAR, L. W. 1995 Plume-scale dependent dispersion in aquifers with a wide range of scales of heterogeneity. Water Resour. Res. 31 (10), 2469-2482. (Pubitemid 26460607)
58. RISKEN, H. 1992 The FokkerJ.Planck Equation. Springer.
59. RUBIN, Y., SUN, A., MAXWELL, R. & BELLIN, A. 1999 The concept of block-effective macrodispersivity and a unified approach for grid-scale- and plume-scale-dependent transport. J. Fluid Mech. 395, 161-180. (Pubitemid 129657776)
60. SANCHEZ-VILA, X. & BOLSTER, D. 2009 An analytical approach to transient homovalent cation exchange problems. J. Hydrol. 378, 281-289.
61. SILLIMAN, S. E. & SIMPSON, E. S. 1987 Laboratory evidence of the scale effect in dispersion of solutes in porous media. Water Resour. Res. 23 (8), 1667-1673. (Pubitemid 17634263)
62. TARTAKOVSKY, D. M. & WINTER, C. L. 2008 Uncertain future of hydrogeology. ASCE J. Hydrol. Engrg 13 (1), 37-39.
63. TREFRY, M. G., RUAN, F. P. & MCLAUGHLIN, D. 2003 Numerical simulations of preasymptotic transport in heterogeneous porous media: departures from the Gaussian limit. Water Resour. Res. 39, 1063.
64. WHITE, B. L. & NEPF, H. M. 2003 Scalar transport in random cylinder arrays at moderate Reynolds number. J. Fluid Mech. 487, 43-79. (Pubitemid 36996801)