A. Ahmadi, M. Quintard, and . Whitaker, Transport in chemically and mechanically hetero- 769 geneous porous media V. Two-equation model for solute transport with adsorption Advances 770 in Water Resources, pp.5986-771, 1998.

M. M. Aral and B. Liao, Analytical solutions for two-dimensional transport equation with 772 time-dependent dispersion coecients, Theorie de la speculation. Annales Scientiques de l'ENS, pp.773-2186, 1900.
DOI : 10.1061/(asce)1084-0699(1996)1:1(20)

O. Bakunin and J. Bear, Turbulence and diusion. Scaling versus equations Dynamics of Fluids in Porous Media, pp.775-776, 1972.

D. A. Benson, S. W. Wheatcraft, and M. M. Meerschaert, The fractional-order governing 777 equation of Lévy motion, Water Resour. Res, vol.36, issue.6, pp.14131423-778, 2000.

D. A. Benson, S. W. Wheatcraft, and M. M. Meerschaert, Application of a fractional ad- 779 vectivedispersion equation, Water Resour. Res, vol.36, issue.6, pp.14031412-780, 2000.

B. Berkowitz, H. Scher, and S. E. Silliman, Anomalous transport in laboratory-scale, het- 781 erogeneous porous media, Water Resour. Res, vol.36, issue.1, pp.149158-782, 2000.

B. Berkowitz, S. Emmanuel, and H. Scher, Non-Fickian transport and multiplerate mass 783 transfer in porous media, Water Resour. Res, vol.44, pp.784-785, 2008.
DOI : 10.1029/2007wr005906
URL : http://onlinelibrary.wiley.com/doi/10.1029/2007WR005906/pdf

C. Pentland, F. Cherblanc, A. Ahmadi, M. F. Quintard, A. Ahmadi et al., Pore-scale imaging and modelling Two-medium description of dispersion in 788 heterogeneous porous media: calculation of macroscopic properties Two-domain description of solute transport 791 in heterogeneous porous media: Comparison between theoretical predictions and numerical 792 experiments Anomalous transport in classical soil and sand columns, Advances in Water Resources Water Resour. Res. Advances in Water Resources, vol.5113, issue.30, pp.197-786, 2003.

. Sci, . Soc, C. Danquigny, P. Ackerer, and J. P. Carlier, 15391548 Laboratory tracer tests on threedimensional 796 reconstructed heterogeneous porous media Diusion equation with the inclusion of molecular velocity, J. J. Hydrol, vol.6815, issue.294, pp.795-809, 1934.

Y. Davit, M. Quintard, and G. Debenest, Equivalence between volume averaging and mo- 800 ments matching techniques for mass transport models in porous media, International Journal 801 of Heat and Mass Transfer, vol.53, issue.49854993, p.802, 2010.

D. Smedt, F. , P. J. Wierenga, M. Dentz, B. Berkowitz et al., A generalized solution for solute ow in soils with 803 mobile and immobile water Transport behavior of a passive solute in continuous time 805 random walks and multirate mass transfer On the movement of small particles suspended in a stationary liquid 807 demanded by the molecular-kinetic theory of heat On the theory of the Brownian movement, The elementary theory of the Brownian motion. Zeitung f??r Elektro- 810 chemie, pp.804-1111, 1905.

G. Gao, H. Zhan, S. Feng, G. Huang, and X. Mao, Comparison of alternative models 812 for simulating anomalous solute transport in a large heterogeneous soil column, Journal, p.813, 2009.

G. Gao, H. Zhan, S. Feng, B. Fu, Y. Ma et al., A new mobile-immobile model 815 for reactive solute transport with scale-dependent dispersion Solute transfer, with exchange 817 between mobile and stagnant water, through unsaturated sand A critical review of data on eld scale dispersion 820 in aquifers, Water Resour. Res. Soil Sci. Soc. Am. J. Water Resour. Res, vol.4625, issue.287, p.821, 1977.

H. H. Gerke and M. T. Van-genuchten, A dual-porosity model for simulating the pref- 822 erential movement of water and solutes in structured porous media, Water Resour. Res, vol.29, pp.823-305319, 1993.

H. H. Gerke and M. T. Van-genuchten, Evaluation of a rst-order water transfer term for 825 variably saturated dual-porosity ow models, Water Resour. Res, vol.29, pp.12251238-826, 1993.

H. H. Gerke, M. T. Van-genuchten, M. Quintard, F. Cherblanc, B. Zinn et al., Macroscopic representation of structural geometry 827 for simulating water and solute movement in dualporosity media Comparison of theory 830 and experiment for solute transport in highly heterogeneous porous medium Advances in 831, Adv. Water Resour, vol.19, issue.829, 1996.

F. Goler, M. Quintard, B. Wood, M. N. Goltz, and P. V. Roberts, Comparison of theory and experiment for solute 833 transport in weakly heterogeneous bimodal porous media Advances in Water Resources 34 Simulations of physical nonequilibrium solute transport 836 models: Application to a large-scale eld experiment, Magnetic resonance imaging of 838 paramagnetic tracers in porous media: quantication of ow and transport parameters. Water 839, pp.832-837, 1988.

. Resour, J. Gwo, P. Jardine, G. Wilson, G. Yeh et al., Using a multiregion model to study the eects 841 of advective and diusive mass transfer on local physical non-equilibrium and solute mobility 842 in a structured soil Mass transfer in structured porous media: Em- 844 bedding mesoscale structure and microscale hydrodynamics in a two-region model Multiple-rate mass transfer for modeling diusion and 847 surface reactions in media with pore-scale heterogeneity Evidence of one-dimensional scale-dependent fractional 850 advectiondispersion, Water Resour. Res. J. Hydrol. Water Resour. Res. {Practical Genetic Algorithms Journal of Contaminant Hydrology, vol.333536, issue.85, pp.14611473-840, 1995.

K. Huang, N. Toride, M. T. Van-genuchten, N. C. Irwin, M. M. Botz et al., Experimental investigation of solute 852 transport in large, homogeneous and heterogeneous, saturated soil columns, Transp. Porous 853 Media Experimental investigation of characteristic 855 length scale in periodic heterogeneous porous media Numerical solution of the dispersion equation using a 857 variable dispersion coecient: method and applications, Fractional Ensemble Average Governing Equations of 859 Transport by Time-Space Nonstationary Stochastic Fractional Advective Velocity and Frac- 860 tional Dispersion. I: Theory, pp.283302-854, 1984.

M. L. Kavvas, A. Ercan, and J. Polsinelli, Governing equations of transient soil water 862 ow and soil water ux in multi-dimensional fractional anisotropic media and fractional time, 2017.

J. Klafter, A. Blumen, and M. F. Shlesinger, Stochastic pathway to anomalous diusion. Phys, p.865
DOI : 10.1103/physreva.35.3081

N. Kumar, U. Harbola, and K. Lindenberg, Memory-induced anomalous dynamics: Emer- 867 gence of diusion, subdiusion, and superdiusion from a single random walk model, p.866, 1987.

M. Lévy and B. Berkowitz, Measurement and analysis of non-Fickian dispersion in hetero- 870 geneous porous media, Review E J. Contam. Hydrol, vol.82, issue.64, pp.869-871, 2003.

L. Li, D. A. Barry, P. J. Culligan-hensley, and K. Bajracharya, Mass transfer in soils with 872 local stratication of hydraulic conductivity, Water Resour. Res, issue.11, pp.30-28912900, 1994.

S. Majdalani, R. Angulo-jaramillo, D. Pietro, and L. , Estimating preferential water ow 874 parameters using a binary genetic algorithm inverse method. Environmental Modelling and 875 Software, pp.950-956, 2008.
DOI : 10.1016/j.envsoft.2007.12.002

S. Majdalani, C. Delenne, J. P. Chazarin, and V. Guinot, Solute transport in periodical 877 heterogeneous porous media: Importance of observation scale and experimental sampling, Journal of Hydrology, vol.878, issue.520, pp.52-60, 2015.

R. Metzler and J. Klafter, The random walk's guide to anomalous diusion: a fractional 880 dynamics approach, Phys. Rep, vol.33950, issue.177, pp.881-882, 2000.

L. F. Gladden, Determining NMR ow propagator moments in porous rocks without 883 the inuence of relaxation, Journal of Magnetic Resonance, vol.193, pp.218-225, 2008.

E. W. Montroll, G. H. Weiss, S. Niehren, and W. Kinzelbach, Random Walks on Lattices. II, Journal of Mathematical Physics, vol.6, issue.2, pp.167-181, 1965.
DOI : 10.1093/qmath/os-10.1.266

J. C. Parker, A. J. Valocchi, J. F. Pickens, and G. E. Grisak, Constraints on the validity of equilibrium and rst-order 889 kinetic transport models in structured soils Scale-dependent dispersion in a stratied granular aquifer, Water Resour. Res, vol.2254, issue.399407, pp.890-891, 1981.

J. F. Pickens, G. E. Grisak, J. E. Saiers, G. M. Hornberger, C. Hervey et al., Modeling of scale-dependent dispersion in hydrogeologic 893 systems Colloidal silica transport through structured, 895 heterogeneous porous media Quantitative 897 nuclear magnetic resonance measurements of preasymptotic dispersion in ow through porous 898 media, Water Resour. Res. Water Resour. Res. J. Hydrol. Phys Fluids, vol.17, issue.17, pp.11911211-892, 1981.

S. E. Silliman, E. S. Simpson, J. Skopp, W. R. Gardner, E. J. Tyler et al., Laboratory evidence of the scale eect in dispersion of 900 solutes in porous media Solute movement in structured soils: Two-region 902 model with small interactionA second-order semi-implicit hybrid scheme for one- 904 dimensional Boussinesq-type waves in rectangular channels, International Journal for Nu- 905 merical Methods in Fluids Laboratory observation of nonlocal 907 dispersion. Transp. Porous Media 23 Use of a variable-index fractional-derivative 909 model to capture transient dispersion in heterogeneous media. Journal of Contaminant Hy- 910 drology, pp.903-908, 1981.

T. Ngoc, T. D. Lewandowska, J. Vauclin, M. Bertin, H. Van-genuchten et al., Two-scale modeling of 912 solute dispersion in unsaturated double-porosity media: homogenization and experimental 913 validation Mass transfer studies in sorbing porous media: 915 II. Experimental evaluation with tritium (3H2O) Some exact solutions for solute trans- 917 port through soils containing large cylindrical macropores Dierential space An analytical solution for one-dimension transport in heterogeneous porous 920 media An analytical solution for one-dimensional transport in porous media with 922 an exponential dispersion function Solute movement through homogeneous and hetero- 924 geneous soil columns, Selim, H.M., 2002. A conceptual fractal model for describing time-dependent dis- 926 persivity, pp.914-916, 1923.