D. A. Benson and M. M. Meerschaert, A simple and efficient random walk solution of multi-rate mobile/immobile mass transport equations, Advances in Water Resources, vol.32, issue.4, pp.532-539, 2009.
DOI : 10.1016/j.advwatres.2009.01.002

D. A. Benson, R. Schumer, M. M. Meerschaert, and S. W. Wheatcraft, Fractional Dispersion, L??vy Motion, and the MADE Tracer Tests, Transport in Porous Media, pp.211-240, 2001.
DOI : 10.1007/978-94-017-1278-1_11

D. A. Benson, S. W. Wheatcraft, and M. M. Meerschaert, Application of a fractional advection-dispersion equation, Water Resources Research, vol.40, issue.11, 2000.
DOI : 10.1029/2000WR900031

B. Berkowitz, A. Cortis, M. Dentz, and H. Scher, Modeling non-Fickian transport in geological formations as a continuous time random walk, Reviews of Geophysics, vol.33, issue.5, pp.10-1029, 2006.
DOI : 10.1029/2005RG000178

B. Berkowitz and H. Scher, Theory of anomalous chemical transport in random fracture networks, Physical Review E, vol.57, issue.5, 1998.
DOI : 10.1103/PhysRevE.57.5858

B. Berkowitz, H. Scher, and S. Silliman, Anomalous transport in laboratory-scale, heterogeneous porous media, Water Resources Research, vol.146, issue.11, 2000.
DOI : 10.1029/1999WR900295

J. Carrera, X. Sánchez-vila, I. Benet, A. Medina, G. Galarza et al., On matrix diffusion: formulations, solution methods and qualitative effects, Hydrogeology Journal, vol.6, issue.1, 1998.
DOI : 10.1007/s100400050143

J. H. Cushman and T. R. Ginn, Fractional advection-dispersion equation: A classical mass balance with convolution-Fickian Flux, Water Resources Research, vol.12, issue.6, 2000.
DOI : 10.1029/2000WR900261

J. R. De-dreuzy, A. Rapaport, T. Babey, and J. Harmand, Influence of porosity structures on mixing-induced reactivity at chemical equilibrium in mobile/immobile Multi-Rate Mass Transfer (MRMT) and Multiple INteracting Continua (MINC) models, Water Resources Research, vol.38, issue.14, pp.8511-853010, 1002.
DOI : 10.1002/2013WR013808

URL : https://hal.archives-ouvertes.fr/hal-00914049

M. Dentz and B. Berkowitz, Transport behavior of a passive solute in continuous time random walks and multirate mass transfer, Water Resources Research, vol.12, issue.12, pp.111110-1029, 2003.
DOI : 10.1029/2001WR001163

M. Dentz, A. Cortis, H. Scher, and B. Berkowitz, Time behavior of solute transport in heterogeneous media: transition from anomalous to normal transport, Advances in Water Resources, vol.27, issue.2, pp.155-173, 2004.
DOI : 10.1016/j.advwatres.2003.11.002

D. Fernandez-garcia, G. Llerar-meza, and J. J. Gomez-hernandez, Upscaling transport with mass transfer models: Mean behavior and propagation of uncertainty, Water Resources Research, vol.39, issue.3, pp.10-1029, 2009.
DOI : 10.1029/2009WR007764

E. G. Flekkøy, A. Malthe-sørenssen, and B. Jamtveit, Modeling hydrofracture, Modeling hydrofracture, p.2151, 2002.
DOI : 10.1029/2000JB000132

H. Garnier, L. Wang, and P. Young, Direct Identification of Continuous-time Models from Sampled Data: Issues, Basic Solutions and Relevance, in Identification of Continuous-time Models from Sampled Data, pp.1-2910, 2008.

F. Golfier, M. Quintard, F. Cherblanc, B. A. Zinn, and B. D. Wood, Comparison of theory and experiment for solute transport in highly heterogeneous porous medium, Advances in Water Resources, vol.30, issue.11, pp.2235-2261, 2007.
DOI : 10.1016/j.advwatres.2007.05.004

F. Golfier, C. Zarcone, B. Bazin, R. Lenormand, D. Lasseux et al., On the ability of a Darcy-scale model to capture wormhole formation during the dissolution of a porous medium, Journal of Fluid Mechanics, vol.457, pp.213-25410, 2002.
DOI : 10.1017/S0022112002007735

H. Gotovac, V. Cvetkovic, and R. Andricevic, Flow and travel time statistics in highly heterogeneous porous media, Water Resources Research, vol.39, issue.3, 2009.
DOI : 10.1029/2008WR007168

P. Gouze, Y. Melean, T. Le-borgne, M. Dentz, and J. Carrera, Non-Fickian dispersion in porous media explained by heterogeneous microscale matrix diffusion, Water Resources Research, vol.93, issue.11, 2008.
DOI : 10.1029/2007WR006690

URL : https://hal.archives-ouvertes.fr/insu-00373705

R. Haggerty, Matrix diffusion -heavy-tailed residence time distributions and their influence on radionuclide retention, paper presented at 5th GEOTRAP Workshop on Radionuclide Retention in Geologic Media, p.75, 2001.

R. Haggerty, S. W. Fleming, L. C. Meigs, and S. A. Mckenna, Tracer tests in a fractured dolomite: 2. Analysis of mass transfer in single-well injection-withdrawal tests, Water Resources Research, vol.24, issue.8, 2001.
DOI : 10.1029/2000WR900334

R. Haggerty and S. M. Gorelick, Multiple-Rate Mass Transfer for Modeling Diffusion and Surface Reactions in Media with Pore-Scale Heterogeneity, Water Resources Research, vol.24, issue.8, pp.2383-240010, 1995.
DOI : 10.1029/95WR10583

R. Haggerty, C. F. Harvey, C. F. Von-schwerin, and L. C. Meigs, What controls the apparent timescale of solute mass transfer in aquifers and soils? A comparison of experimental results, Water Resources Research, vol.39, issue.3, pp.10-1029, 2004.
DOI : 10.1029/2002WR001716

R. Haggerty, S. A. Mckenna, and L. C. Meigs, On the late-time behavior of tracer test breakthrough curves, Water Resources Research, vol.33, issue.12, pp.3467-3479, 2000.
DOI : 10.1029/2000WR900214

R. A. Horn, Matrix analysis, 1985.

P. M. Jardine, W. E. Sanford, J. P. Gwo, O. C. Reedy, D. S. Hicks et al., Quantifying diffusive mass transfer in fractured shale bedrock, Water Resources Research, vol.145, issue.17, pp.2015-203010, 1029.
DOI : 10.1029/1999WR900043

M. Karimi-fard, B. Gong, and L. J. Durlofsky, Generation of coarse-scale continuum flow models from detailed fracture characterizations, Water Resources Research, vol.29, issue.3, 2006.
DOI : 10.1029/2006WR005015

I. Neretnieks, Diffusion in the rock matrix: An important factor in radionuclide retardation?, Journal of Geophysical Research: Solid Earth, vol.17, issue.SM1, pp.4379-4397, 1980.
DOI : 10.1029/JB085iB08p04379

S. P. Neuman and D. M. Tartakovsky, Perspective on theories of non-Fickian transport in heterogeneous media, Advances in Water Resources, vol.32, issue.5, pp.670-680, 2009.
DOI : 10.1016/j.advwatres.2008.08.005

B. Noetinger and T. Estebenet, Up-scaling of double porosity fractured media using continuous-time random walks methods, Transport in Porous Media, 2000.

K. Pruess, Brief Guide to the MINC -Method for Modeling Flow and Transport in Fractured MediaRep, Earth Sciences Division, 1992.

K. Pruess and T. N. Narasimhan, A Practical Method for Modeling Fluid and Heat Flow in Fractured Porous Media, Society of Petroleum Engineers Journal, vol.25, issue.01, pp.14-26, 1985.
DOI : 10.2118/10509-PA

O. Silva, J. Carrera, M. Dentz, S. Kumar, A. Alcolea et al., A general real-time formulation for multi-rate mass transfer problems, Hydrology and Earth System Sciences, pp.1399-1411, 2009.

A. Sornette, P. Davy, and D. Sornette, Fault growth in brittle-ductile experiments and the mechanics of continental collisions, Journal of Geophysical Research: Solid Earth, vol.123, issue.B7, pp.12111-12139, 1993.
DOI : 10.1029/92JB01740

E. A. Sudicky and E. O. Frind, Contaminant transport in fractured porous media: Analytical solutions for a system of parallel fractures, Water Resources Research, vol.17, issue.3, pp.1634-1642, 1982.
DOI : 10.1029/WR018i006p01634

D. H. Tang, E. O. Frind, and E. A. Sudicky, Contaminant transport in fractured porous media: Analytical solution for a single fracture, Water Resources Research, vol.1137, issue.219, pp.555-564, 1981.
DOI : 10.1029/WR017i003p00555

Y. W. Tsang, Study of alternative tracer tests in characterizing transport in fractured rocks, Geophysical Research Letters, vol.27, issue.2227, pp.1421-142410, 1995.
DOI : 10.1029/95GL01093

J. Villermaux, Chemical engineering approach to dynamic modelling of linear chromatography, Journal of Chromatography A, vol.406, issue.00, pp.11-2610, 1987.
DOI : 10.1016/S0021-9673(00)94014-7

J. E. Warren, P. J. Root, and M. Aime, The Behavior of Naturally Fractured Reservoirs, Society of Petroleum Engineers Journal, vol.3, issue.03, pp.245-255426, 1963.
DOI : 10.2118/426-PA

M. Willmann, J. Carrera, and X. Sanchez-vila, Transport upscaling in heterogeneous aquifers: What physical parameters control memory functions?, Water Resources Research, vol.38, issue.14, pp.10-1029, 2008.
DOI : 10.1029/2007WR006531