Effective pore-scale dispersion upscaling with a correlated continuous time random walk approach

Water Resources Research

Volumn 47, Issue 12, 2011, Pages

  Le Borgne, T ^a   Bolster, D ^b   Dentz, M ^c   De Anna, P ^a   Tartakovsky, A ^d  

^a UNIVERSITÉ DE RENNES 1   (France)

^b University of Notre Dame   (United States)

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

^d PACIFIC NORTHWEST NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUOUS TIME RANDOM WALK APPROACHES; CONTINUOUS-TIME RANDOM WALK; CORRELATION EFFECT; LAGRANGIAN VELOCITY; NON-TRIVIAL DEPENDENCE; PORE BOUNDARIES; PORE SCALE; PORE SPACE; PORE THROAT; PORE-SCALE SIMULATION; SPATIAL VELOCITY; TEMPORAL EVOLUTION; TIME INCREMENTS; TRANSPORT MODELS; UPSCALING; VELOCITY FIELD; WAVY CHANNELS;

COMPUTER SIMULATION; CONTINUOUS TIME SYSTEMS; DISPERSIONS; LAGRANGE MULTIPLIERS; MARKOV PROCESSES;

VELOCITY;

DISPERSION; FLOW VELOCITY; LAGRANGIAN ANALYSIS; MARKOV CHAIN; MIXING; PARAMETERIZATION; PORE SPACE; RANDOM WALK METHOD; TRANSPORT PROCESS; UPSCALING; VELOCITY PROFILE;

EID: 84855467218     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2011WR010457     Document Type: Article

References (67)

1. Aris, R. (1956), On the dispersion of solute in a fluid flowing through a tube, Proc. R. Soc. London, Ser. A, 235, 67-77.
2. Attinger, S., I. Neuweiler, and W. Kinzelbach (2001), Macrodispersion in a radially diverging flow field with finite Peclet numbers: 2. Homogenization theory approach, Water Resour. Res., 37, 495-505. (Pubitemid 32526054)
3. Auriault, J., and P. Adler (1995), Taylor dispersion in porous media: Analysis by multiple scale expansions, Adv. Water Resour., 18, 217-226. (Pubitemid 26443145)
4. Bear, J. (1972), Dynamics of Fluids in Porous Media, Elsevier, New York.
5. Benson, D., S. Wheatcraft, and M. Meerschaert (2000), The fractional-order governing equation of Levymotion, Water Resour. Res., 36, 1413-1423.
6. Benson, D., R. Schumer, M. M. Meerschaert, and S. Wheatcraft (2001), Fractional dispersion, Levy motion, and the MADE tracer tests, Transp. Porous Media, 42, 211-240.
7. Berkowitz, B., and H. Scher (1995), On characterization of anomalous dispersion in porous and fractured media, Water Resour. Res., 31, 1461-1466. (Pubitemid 26440573)
8. Berkowitz, B., and H. Scher (2010), Anomalous transport in correlated velocity fields, Phys. Rev. E, 81, 011128, doi:10.1103/PhysRevE.81.011128.
9. Berkowitz, B., A. Cortis, M. Dentz, and H. Scher (2006), Modeling non-Fickian transport in geological formations as a continuous time random walk, Rev. Geophys., 44, RG2003, doi:10.1029/2005RG000178. (Pubitemid 46044201)
10. Bijeljic, B., and M. J. Blunt (2006), Pore-scale modeling and continuous time random walk analysis of dispersion in porous media, Water Resour. Res., 42, W01202, doi:10.1029/2005WR004578. (Pubitemid 43352610)
11. Bolster, D., T. Le Borgne, and M. Dentz (2009), Solute dispersion in channels with periodically varying apertures, Phys. Fluids, 21, 056601.
12. Bouchaud, J. P., and A. Georges (1990), Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications, Phys. Rep., 195(4-5), 127-293.
13. Brenner, H. (1980), Dispersion resulting from flow through spatially periodic porous media, Philos. Trans. R. Soc. London, Ser. A, 297, 81-133.
14. Brenner, H., and P. Adler (1982), Dispersion resulting from flow through spatially periodic porous media II. Surface and intraparticle transport, Philos. Trans. R. Soc. London, Ser. A, 307, 149-200.
15. Carrera, J., X. Sanchez-Vila, I. Benet, A. Medina, G. Galarza, and J. Guimera (1998), On matrix diffusion: Formulations, solution methods and qualitative effects, Hydrogeol. J., 6, 178-190. (Pubitemid 128546161)
16. Chastanet, J., and B. D.Wood (2008), The mass transfer process in a two-region medium, Water Resour. Res., 44,W05413, doi:10.1029/2006WR005553. (Pubitemid 351897326)
17. Cherblanc, F., A. Ahmadi, and M. Quintard (2007), Two-domain description of solute transport in heterogeneous porous media: Comparison between theoretical predictions and numerical experiments, Adv. Water Resour., 20, 1127-1143. (Pubitemid 46349933)
18. Cushman, J., and T. Ginn (1993), Nonlocal dispersion in media with continuously evolving scales of heterogeneity, Transp. Porous Media, 13, 123-138.
19. Cushman, J., and T. Ginn (1994), Nonequilibrium statistical mechanics of preasymptotic dispersion, J. Stat. Phys., 75, 859-878.
20. Cushman, J. H., and T. R. Ginn (2000), Fractional advection-dispersion equation: A classical mass balance with convolution-Fickian flux, Water Resour. Res., 36, 3763-3766. (Pubitemid 32039925)
21. Deng, F.-W., and J. Cushman (1995), Comparison of moments for classical-, quasi-, and convolution-Fickian dispersion of a conservative tracer, Water Resour. Res., 31, 1147-1149. (Pubitemid 26436362)
22. Deng, F.-W., J. H. Cushman, and J. W. Delleur (1993), A fast Fourier transform stochastic analysis of the contaminant transport process, Water Resour. Res., 29, 3241-3247.
23. Dentz, M., and D. Bolster (2011), Distribution- versus correlation-induced anomalous transport in quenched random velocity fields, Phys. Rev. Lett., 105, 244301.
24. Dentz, M., and A. Castro (2009), Effective transport dynamics in porous media with heterogeneous retardation properties, Geophys. Res. Lett., 36, L03403, doi:10.1029/2008GL036846.
25. Dentz, M., H. Kinzelbach, S. Attinger, and W. Kinzelbach (2000), Temporal behavior of a solute cloud in a heterogeneous porous medium: 1. Point-like injection, Water Resour. Res., 36, 3591-3604. (Pubitemid 32039910)
26. Dentz, M., D. Bolster, and T. Le Borgne (2009), Concentration statistics for transport in porous media, Phys. Rev. E, 80, 010101.
27. Dentz, M., T. Le Borgne, A. Englert, and B. Bijeljic (2011), Mixing, spreading and reaction in heterogeneous media: A brief review, J. Contam. Hydrol., 120-121, 1-17.
28. Drazer, G., and J. Koplick (2002), Transport in rough self-affine fractures, Phys. Rev. E, 66, 026303.
29. Drazer, G., H. Auradou, J. Koplik, and J. Hulin (2004), Self-affine front in self-affine fractures: Large and small-scale structure, Phys. Rev. Lett.,92, 014501.
30. Dykaar, B., and P. Kitanidis (1996), Macrotransport of a biologically reacting solute through porous media, Water Resour. Res., 32, 307-329.
31. Edwards, D., and H. Brenner (1993), Macrotransport Processes, Butterworth-Heinemann, Boston, Mass.
32. Edwards, D., M. Shapiro, H. Brenner, and M. Shapira (1991), Dispersion of inert solutes in spatially periodic, two-dimensional model porous media, Transp. Porous Media, 6, 337-358. (Pubitemid 21730270)
33. Frankel, I., and H. Brenner (1989), On the foundations of generalized Taylor dispersion theory, J. Fluid. Mech., 204, 97-119.
34. Gelhar, L. (1993), Stochastic Subsurface Hydrology, Prentice Hall, Englewood Cliffs, N. J.
35. Gelhar, L., C. Welty, and K. Rehfeldt (1992), A critical review of data on field-scale dispersion in aquifers, Water Resour. Res., 28, 1955-1974. (Pubitemid 23373205)
36. Gill, W., and R. Sankarasubramanian (1970), Exact analysis of unsteady convective diffusion, Proc. R. Soc. London, Ser. A, 316, 341-350.
37. Haggerty, R., and S. Gorelick (1995), Multiple-rate mass transfer for modeling diffusion and surface reactions in media with pore-scale heterogeneity, Water Resour. Res., 31, 2383-2400. (Pubitemid 26475182)
38. Kitanidis, P., and B. Dykaar (1997), Stokes flow in a slowly varying twodimensional periodic pore, Transp. Porous Media, 26, 89-98.
39. Latini, M., and A. Bernoff (2001), Transient anomalous diffusion in Poiseille flow, J. Fluid. Mech., 441, 399-411. (Pubitemid 32779151)
40. Le Borgne, T., and P. Gouze (2008), Non-Fickian dispersion in porous media: 2. Model validation from measurements at different scales, Water Resour. Res., 44, W06427, doi:10.1029/2007WR006279.
41. Le Borgne, T., J. de Dreuzy, P. Davy, and O. Bour (2007), Characterization of the velocity field organization in heterogeneous media by conditional correlation, Water Resour. Res., 43,W02419, doi:10.1029/ 2006WR004875. (Pubitemid 46502886)
42. Le Borgne, T., M. Dentz, and J. Carrera (2008a), Lagrangian statistical model for transport in highly heterogeneous velocity fields, Phys. Rev. Lett., 101, 090601, doi:10.1103/PhysRevLett.101.090601.
43. Le Borgne, T., M. Dentz, and J. Carrera (2008b), Spatial Markov processes for modeling Lagrangian particle dynamics in heterogeneous porous media, Phys. Rev. E, 78, 026308, doi:10.1103/PhysRevE.78.026308.
44. Le Borgne, T., M. Dentz, P. Davy, D. Bolster, J. Carrera, J.-R. de Dreuzy, and O. Bour (2011), Persistence of incomplete mixing: A key to anomalous transport, Phys. Rev. E, 84, 015301.
45. Levy, M., and B. Berkowitz (2003), Measurement and analysis of non-Fickian dispersion in heterogeneous porous media, J. Contam. Hydrol., 23, 2145-2154.
46. Lunati, I., S. Attinger, and W. Kinzelbach (2002), Macrodispersivity for transport in arbitrary nonuniform flow fields: Asymptotic and preasymptotic results, Water Resour. Res., 38(10), 1187, doi:10.1029/2001 WR001203.
47. Matheron, G., and G. de Marsily (1980), Is transport in porous media always diffusive? A counterexample, Water Resour. Res., 16, 901-917.
48. Meyer, D. W., and H. Tchelepi (2010), Particle-based transport model with Markovian velocity processes for tracer dispersion in highly heterogeneous porous media, Water Resour. Res., 46, W11552, doi:10.1029/2009WR008925.
49. Morales-Casique, E., S. Neuman, and A. Guadagnini (2006), Nonlocal and localized analyses of nonreactive solute transport in bounded randomly heterogeneous porous media: Theoretical framework, Adv. Water Resour., 29, 1238-1255. (Pubitemid 44109098)
50. Moroni, M., N. Kelinfelter, and J. Cushman (2007), Analysis of dispersion in porous media via matched-index particle tracking velocimetry experiments, Adv. Water Resour., 30, 1-15. (Pubitemid 44734670)
51. Neuman, S. (1993), Eulerian-Lagrangian theory of transport in space-time nonstationary velocity fields: Exact nonlocal formalism by conditional moments and weak approximation, Water Resour. Res., 29, 633-645. (Pubitemid 23382797)
52. Neuman, S., and D. Tartakovsky (2009), Perspective on theories of anomalous transport in heterogeneous media, Adv. Water Resour., 32, 670-680.
53. Nicolaides, C., L. Cueto-Felgueroso, and R. Juanes (2010), Anomalous physical transport in complex networks, Phys. Rev. E, 82, 055101.
54. Plumb, O., and S. Whitaker (1988), Dispersion in heterogeneous porous media: 1. Local volume averaging and large-scale averaging, Water Resour. Res., 24, 913-926.
55. Porter, M., F. Valdes-Parada, and B. Wood (2010), Comparison of theory and experiments for dispersion in homogeneous porous media, Adv. Water Resour., 33, 1043-1052.
56. Prude'Homme, R. K., and D. A. Hoagland (1999), Taylor-Aris dispersion arising from flow in a sinusoidal tube, AIChE J., 31, 236-244.
57. Rehfeldt, K., J. Boggs, and L. Gelhar (1992), Field study of dispersion in a heterogeneous aquifer: 3. Geostatistical analysis of hydraulic conductivity, Water Resour. Res., 28, 3309-3324. (Pubitemid 23379497)
58. Rosencrans, S. (1997), Taylor dispersion in curved channels, SIAM J. Appl. Math., 57, 1216-1241. (Pubitemid 127631482)
59. Sidle, R., B. Nilsson, M. Hansen, and J. Fredeicia (1998), Spatially varying hydraulic and solute transport characteristics of a fractured till determined by field tracer tests, Funen, Denmark, Water Resour. Res., 24, 2515-2527. (Pubitemid 28451052)
60. Silliman, S., and E. Simpson (1987), Laboratory evidence of the scale effect in dispersion of solutes in porous media, Water Resour. Res., 23, 1667-1673. (Pubitemid 17634263)
61. Silliman, S., L. Konikow, and C. Voss (1987), Laboratory experiment of longitudinal dispersion in anisotropic porous media, Water Resour. Res., 23, 2145-2154.
62. Tartakovsky, A., and S. Neuman (2008), Effects of Peclet number on porescale mixing and channeling of a tracer and on directional advective porosity, Geophys. Res. Lett., 35, L21401, doi:10.1029/2008GL035895.
63. Tartakovsky, D., and D. Xiu (2006), Stochastic analysis of transport in tubes with rough walls, J. Comput. Phys., 217, 248-259. (Pubitemid 44111679)
64. Tartakovsky, A. M., D. M. Tartakovsky, and P. Meakin (2008), Stochastic Langevin Model for Flow and Transport in Porous Media, Phys. Rev. Lett., 101, 044502, doi:10.1103/PhysRevLett.101.044502.
65. Taylor, G. (1953), Dispersion of soluble matter in solvent flowing slowly through a tube, Proc. R. Soc. London, Ser. A, 219, 186-203.
66. Valdes-Parada, F., M. Porter, K. Narayanaswamy, R. Ford, and B. Wood (2009), Upscaling microbial chemotaxis in porous media, Adv. Water Resour., 32, 1413-1428.
67. Wood, B. (2009), The role of scaling laws in upscaling, Adv. Water Resour., 32, 723-736.