Time evolution of mixing in heterogeneous porous media

Water Resources Research

Volumn 48, Issue 6, 2012, Pages

  De Dreuzy, J R ^a,b   Carrera, J ^a   Dentz, M ^a   Le Borgne, T ^b  

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

^b UNIVERSITÉ DE RENNES 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

DISPERSION PROCESS; GAUSSIAN PLUMES; GAUSSIANS; HETEROGENEOUS MEDIA; HETEROGENEOUS POROUS MEDIA; INTERFACIAL AREAS; LOCAL SCALE; LONGITUDINAL DISPERSIONS; MACRODISPERSION; MEAN CONCENTRATIONS; MIXING STATE; SCALING FORMS; SPATIAL DOMAINS; SPREADING RATE; TAYLOR DISPERSION; TIME EVOLUTIONS; TRANSPORT EQUATION; VARIANCE EQUATIONS; VELOCITY FLUCTUATIONS;

DIFFUSION; DISPERSIONS; POROUS MATERIALS;

MIXING;

CONCENTRATION (COMPOSITION); GAUSSIAN METHOD; HETEROGENEITY; INTERFACE; MIXING; NUMERICAL MODEL; PLUME; POROUS MEDIUM; TEMPORAL EVOLUTION; VELOCITY PROFILE;

EID: 84862235362     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2011WR011360     Document Type: Article

References (37)

1. Ababou, R., et al. (1989), Numerical simulation of three-dimensional saturated flow in randomly heterogeneous porous media, Transp. Porous Media, 4(6), 549-565.
2. Andricevic, R. (1998), Effects of local dispersion and sampling volume on the evolution of concentration fluctuations in aquifers, Water Resour. Res., 34(5), 1115-1129. (Pubitemid 28219542)
3. Beaudoin, A., et al. (2007), An efficient parallel tracker for advectiondiffusion simulations in heterogeneous porous media, Europar, Springer, Berlin.
4. Bolster, D., et al. (2011), Mixing in confined stratified aquifers, J. Contam. Hydrol., 120-121, 198-212.
5. Caroni, E., and V. Fiorotto (2005), Analysis of concentration as sampled in natural aquifers, Transp. Porous Media, 59(1), 19-45. (Pubitemid 40301156)
6. Chiogna, G., O. A. Cirpka, P. Grathwohl, and M. Rolle (2011), Transverse mixing of conservative and reactive tracers in porous media: Quantification through the concepts of flux-related and critical dilution indices, Water Resour. Res., 47, W02505, doi:10.1029/2010WR009608.
7. Cirpka, O. A., and P. K. Kitanidis (2000), Characterization of mixing and dilution in heterogeneous aquifers by means of local temporal moments, Water Resour. Res., 36(5), 1221-1236. (Pubitemid 30254882)
8. Dagan, G. (1989), Flow and Transport in Porous Formations, 465 pp., Springer, New York.
9. de Dreuzy, J.-R., et al. (2007), Asymptotic dispersion in 2D heterogeneous porous media determined by parallel numerical simulations Water Resour. Res., 43, W10439, 10.1029/2006WR005394. (Pubitemid 350210185)
10. Dentz,M., H. Kinzelbach, S. Attinger, and W. Kinzelbach (2000), Temporal behavior of a solute cloud in a heterogeneous porous medium, 2, Spatially extended injection, Water Resour. Res., 36(12), 3605-3614, doi:10.1029/ 2000WR900211. (Pubitemid 32039911)
11. de Simoni, M., J. Carrera, X. Sanchez-Vila, and A. Guadagnini (2005), A procedure for the solution of multicomponent reactive transport problems, Water Resour. Res., 41, W11410, doi:10.1029/2005WR004056. (Pubitemid 43041791)
12. Englert, A., J. Vanderborght, and H. Vereecken (2006), Prediction of velocity statistics in three-dimensional multi-Gaussian hydraulic conductivity fields, Water Resour. Res., 42, W03418, doi:10.1029/2005WR004014.
13. Fiori, A. (2001), The Lagrangian concentration approach for determining dilution in aquifer transport: Theoretical analysis and comparison with field experiments, Water Resour. Res., 37(12), 3105-3114. (Pubitemid 34108266)
14. Fiori, A., and G. Dagan (2000), Concentration fluctuations in aquifer transport: A rigorous first-order solution and applications, J. Contam. Hydrol., 45(1-2), 139-163.
15. Fiorotto, V., and E. Caroni (2002), Solute concentration statistics in heterogeneous aquifers for finite Peclet values, Transp. Porous Media, 48(3), 331-351. (Pubitemid 34735973)
16. Gelhar, L. W. (1993), Stochastic Subsurface Hydrology, Engelwood Cliffs, N.J.
17. Gelhar, L. W., and C. L. Axness (1983), Three-dimensional stochastic analysis of macrodispersion in aquifers, Water Resour. Res., 19, 161-180. (Pubitemid 14256049)
18. Grassberger, P., and I. Procaccia (1983), Characterization of strange attractors, Phys. Rev. Lett., 50(5), 346-349.
19. Jankovic, I., et al. (2003), Flow and transport in highly heterogeneous formations: 3. Numerical simulations and comparison with theoretical results, Water Resour. Res., 39(9), 1270, doi:10.1029/2002WR001721.
20. Kapoor, V., and L. W. Gelhar (1994a), Transport in three-dimensionally heterogeneous aquifers. 1. Dynamics of concentration fluctuations, Water Resour. Res., 30(6), 1775-1788. (Pubitemid 285247)
21. Kapoor, V., and L. W. Gelhar (1994b), Transport in three -dimensionally heterogeneous aquifers. 2. Predictions and observations of concentration fluctuations, Water Resour. Res., 30(6), 1789-1801. (Pubitemid 285248)
22. Kapoor, V., and P. K. Kitanidis (1998), Concentration fluctuations and dilution in aquifers, Water Resour. Res., 34(5), 1181-1193. (Pubitemid 28219546)
23. Kitanidis, P. K. (1994), The concept of the dilution index, Water Resour. Res., 30(7), 2011-2026, doi:10.1029/94WR00762. (Pubitemid 286134)
24. Le Borgne, T., J.-R. de Dreuzy, P. Davy, and O. Bour (2007), Characterization of the velocity field organization in heterogeneous media by conditional correlations, Water Resour. Res., 43, W02419, doi:10.1029/2006 WR004875.
25. Le Borgne, T., et al. (2010), Non-Fickian mixing: Temporal evolution of the scalar dissipation rate in heterogeneous porous media, Adv. Water Resour., 3(12), 1468-1475.
26. Le Borgne, T., et al. (2011), Persistence of incomplete mixing: A key to anomalous transport, Phys. Rev. E, 84(1), 015301.
27. Le Goc, R., et al. (2009), Statistical characteristics of flow as indicators of channeling in heterogeneous porous and fractured media, Adv. Water Resour., 33(3), 257-269.
28. Neuman, S. P., and Y.-K. Zhang (1990), A quasi-linear theory of non-Fickian and Fickian subsurface dispersion. 1. Theoretical analysis with application to isotropic media, Water Resour. Res., 26(5), 887-902.
29. Pannone, M., and P. K. Kitanidis (1999), Large-time behavior of concentration variance and dilution in heterogeneous formations, Water Resour. Res., 35(3), 623-634. (Pubitemid 29111794)
30. Pope, S. (2000), Turbulent flows, Cambridge Univ. Press, New York.
31. Rolle, M., et al. (2009), Enhancement of dilution and transverse reactive mixing in porous media: Experiments and model-based interpretation, J. Contam. Hydrol., 110(3-4), 130-142.
32. Salandin, P., and V. Fiorotto (1998), Solute transport in highly heterogeneous aquifers, Water Resour. Res., 34(5), 949-961. (Pubitemid 28219529)
33. Tartakovsky, A. M., et al. (2008), Stochastic Langevin model for flow and transport in porous media, Phys. Rev. Lett., 101(4), 4.
34. Tennekes, H., and J. L. Lumley (1972), A First Course in Turbulence, MIT Press, Cambridge, Mass.
35. Tonina, D., and A. Bellin (2008), Effects of pore-scale dispersion, degree of heterogeneity, sampling size, and source volume on the concentration moments of conservative solutes in heterogeneous formations, Adv. Water Resour., 31(2), 339-354. (Pubitemid 350246407)
36. Vanderborght, J. (2001), Concentration variance and spatial covariance in second-order stationary heterogeneous conductivity fields, Water Resour. Res., 37(7), 1893-1912. (Pubitemid 32632477)
37. Villermaux, J., and J. C. Devillon (1972), Représentation de la coalescence et de la redispersion des domaines de ségrégation dans un fluide par un modèle d'interaction phénoménologique, in Proceedings of the 2nd International Symposium of Chemical Reaction Engineers, pp. 1-14, Elsevier, New York.