J. E. Aarnes, T. Gimse, and K. Lie, An introduction to the numerics of 1121 flow in porous media using matlab, in Geometric modelling, numerical simulation, 1122 and optimization, pp.265-306, 2007.

E. E. Adams and L. W. Gelhar, Field study of disperion in a heterogeneous 1124 aquifer 2. spatial moment analysis, Water Resour. Res, vol.28, pp.3293-3307, 1992.

G. K. Batchelor, An Introduction to Fluid Dynamics, 2000.

J. Bear, Dynamics of Fuids in Porous Media, 1972.

R. Benke and S. Painter, Modeling conservative tracer transport in fracture 1129 networks with a hybrid approach based on the boltzmann transport equation, p.1130, 2003.

, Water Resour. Res, vol.39, p.1324

B. Berkowitz and H. Scher, Anomalous transport in random fracture net-1132 works, Phys. Rev. Lett, vol.79, issue.20, pp.4038-4041, 1997.

B. Berkowitz, A. Cortis, M. Dentz, and H. Scher, Modeling non-fickian 1134 transport in geological formations as a continuous time random walk, Rev. Geo-1135 phys, vol.44, p.2003, 2006.

J. M. Boggs, S. C. Young, L. M. Beard, L. W. Gelhar, K. R. Rehfeldt et al.,

A. , Field study of dispersion in a heterogeneous aquifer 1. overview 1138 and site description, Water Resour. Res, vol.28, pp.3281-3291, 1992.

A. Comolli and M. Dentz, Anomalous dispersion in correlated porous media: 1140 a coupled continuous time random walk approach, The European Physical Journal, p.1141, 2017.

B. , , vol.90, p.166

V. Cvetkovic, H. Cheng, and X. Wen, Analysis of nonlinear effects on 1143 tracer migration in heterogeneous aquifers using Lagrangian travel time statistics, p.1144, 1996.

, Water Resour. Res, vol.32, issue.6, pp.1671-1680

V. Cvetkovic, A. Fiori, and G. Dagan, Solute transport in aquifers of ar-1146 bitrary variability: A time-domain random walk formulation, Water Resources 1147 Research, vol.50, pp.5759-5773, 2014.

G. Dagan, Solute transport in heterogenous porous formations, J. Fluid 1149 Mech, vol.145, pp.151-177, 1984.

G. Dagan, Flow and transport in porous formations, 1989.

G. Dagan, Solute plumes mean velocity in aquifer transport: Impact of injec-1152 tion and detection modes, Advances in Water Resources, vol.106, pp.6-10, 2017.

P. De-anna, T. L. Borgne, M. Dentz, A. M. Tartakovsky, D. Bolster et al., Flow intermittency, dispersion and correlated continuous time random 1155 walks in porous media, Phys. Rev. Lett, vol.1154, p.502, 2013.

,. De-dreuzy, A. Beaudoin, and J. Erhel, Asymptotic dispersion in 2d 1157 heterogeneous porous media determined by parallel numerical simulations, Water 1158 Resources Research, p.43, 2007.

M. Dentz, A. Cortis, H. Scher, and B. Berkowitz, Time behavior of solute 1160 transport in heterogeneous media, p.1161, 2004.

, Adv. Water Resour, vol.27, issue.2, pp.155-173

M. Dentz, T. L. Borgne, A. Englert, and B. Bijeljic, Mixing, spreading and 1163 reaction in heterogeenous media: a brief review, J. Cont. Hydrol, pp.1-17, 2011.

M. Dentz, P. K. Kang, A. Comolli, T. L. Borgne, and D. R. Lester, Continu-1165 ous time random walks for the evolution of lagrangian velocities, Physical Review 1166 Fluids, vol.1, issue.7, p.4, 2016.

L. Devroye, Non-Uniform Random Variate Generation, 1986.

, Physical and Chemical Hydroge-1169 ology, 1997.

Y. Edery, A. Guadagnini, H. Scher, and B. Berkowitz, Origins of anomalous 1171 transport in heterogeenous media: Structural and dynamic control, Water Resour, p.1172, 2014.

Y. Edery, S. Geiger, and B. Berkowitz, Structural controls on anomalous 1174 transport in fractured porous rock, locity correlation and distribution on transport in fractured media: field evidence 1228 and theoretical model, vol.52, pp.940-959, 2016.

P. K. Kang, M. Dentz, T. L. Borgne, S. Lee, and R. Juanes, Anomalous 1230 transport in disordered fracture networks: Spatial markov model for dispersion 1231 with variable injection modes, Adv. Water Resour, 2017.

A. Koponen, M. Kataja, and J. Timonen, Tortuous flow in porous media, Physical Review E, vol.54, issue.1, p.406, 1234.

L. Borgne, T. , J. R. De-dreuzy, P. Davy, and O. Bour, Characterization of 1236 the velocity field organization in heterogeneous media by conditional correlation, p.1237, 2007.

, Water Resour. Res, vol.43, p.875, 2006004.

L. Borgne, T. , M. Dentz, and J. Carrera, Spatial markov processes for model-1239, 2008.

, ing lagrangian particle dynamics in heterogeneous porous media, Phys. Rev. E, vol.78, p.110

M. Levy and B. Berkowitz, Measurement and analysis of non-fickian disper-1242 sion in heterogeneous porous media, Journal of Contaminant Hydrology, vol.64, issue.3-4, pp.1243-203, 2003.

D. W. Meyer and H. A. Tchelepi, Particle-based transport model with 1245, 2010.

, Markovian velocity processes for tracer dispersion in highly heterogeneous porous 1246 media, Water Resources Research, vol.46, issue.11

V. L. Morales, M. Dentz, M. Willmann, and M. Holzner, Stochastic dynam-1248 ics of intermittent pore-scale particle motion in three-dimensional porous media: 1249 Experiments and theory, Geophysical Research Letters, vol.44, issue.18, pp.9361-9371, 2017.

S. P. Neuman and D. M. Tartakovsky, Perspective on theories of anoma-1251 lous transport in heterogeneous media, Adv. Water Resour, vol.32, pp.670-680, 2008.

A. Niemi and J. , Geological Storage of CO2 in 1254, 2017.

, Deep Saline Formations

B. Noetinger, D. Roubinet, A. Russian, T. L. Borgne, F. Delay et al.,

D. Dreuzy and P. Gouze, Random walk methods for modeling hydro-1257 dynamic transport in porous and fractured media from pore to reservoir scale, pp.1-41, 1258.

S. Painter, Evidence for non-gaussian scaling behavior in heterogeneous 1260 sedimentary formations, Water Resources Research, vol.32, issue.5, pp.1183-1195, 1996.

S. Painter and V. Cvetkovic, Upscaling discrete fracture network simula-1262 tions: An alternative to continuum transport models, Water Resources Research, vol.1263, issue.2, p.41, 2005.

, Radionuclide Behaviour in the Natural 1265, 2012.

, Environment

D. Pollock, Semianalytical computation of path lines for finite-difference 1267 models, Ground Water, vol.26, issue.6, pp.743-750, 1988.

A. Puyguiraud, P. Gouze, and M. Dentz, Upscaling of anomalous pore-1269 scale dispersion, Transport in Porous Media, vol.128, pp.837-855, 2019.

K. R. Rehfeldt, J. M. Boggs, and L. W. Gelhar, Field study of dispersion in 1272 a heterogeneous aquifer: 3. geostatistical analysis of hydraulic conductivity, Water 1273 Resources Research, vol.28, pp.3309-3324, 1992.

H. Risken, The Fokker-Planck Equation, 1996.

Y. Rubin, Applied stochastic hydrogeology, 2003.

A. Russian, M. Dentz, and P. Gouze, Time domain random walks for hydro-1278 dynamic transport in heterogeneous media, Water Resources Research. 1279 conductivities in saturated groundwater flow, vol.44, 2016.

X. Sanchez-vila, A. Guadagnini, and J. Carrera, Representative hydraulic 1283 conductivities in saturated groundwater flows, Rev. Geophys, vol.44, p.3002, 2006.

M. Schlather, A. Malinowski, P. J. Menck, M. Oesting, and K. Strokorb, , p.1285, 2015.

, Analysis, simulation and prediction of multivariate random fields with package 1286 randomfields, Journal of Statistical Software, vol.63, issue.8, pp.1-25

M. Shlesinger, Asymptotic solutions of continuous-time random walks, 1974.

, Stat. Phys, vol.10, issue.5, pp.421-434

A. Tyukhova, M. Dentz, W. Kinzelbach, and M. Willmann, Mechanisms 1290 of anomalous dispersion in flow through heterogeneous porous media, Physical 1291 Review Fluids, vol.1, issue.7, p.2, 2016.

A. Zech, C. Angelo, S. Attinger, and A. Fiori, Revisitation of the dipole 1293 tracer test for heterogeneous porous formations, Advances in water resources, vol.115, pp.1294-198, 2018.

C. Zheng, M. Bianchi, and S. M. Gorelick, Lessons learned from 25 years of 1296 research at the made site, Groundwater, vol.49, issue.5, pp.649-662, 2011.