G. E. Grisak and J. F. Pickens, An analytical solution for solute transport through fractured media with matrix diffusion, Journal of Hydrology, vol.52, issue.1-2, pp.47-57, 1981.

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.17, issue.3, pp.555-564, 1981.

S. Feenstra, J. A. Cherry, E. A. Sudicky, and Z. Haq, Matrix Diffusion Effects on Contaminant Migration from an Injection Well in Fractured Sandstone, Ground Water, vol.22, issue.3, pp.307-316, 1984.

R. H. Nilson and K. H. Lie, Double-porosity modelling of oscillatory gas motion and contaminant transport in a fractured porous medium, International Journal for Numerical and Analytical Methods in Geomechanics, vol.14, issue.8, pp.565-585, 1990.

D. Blessent, P. R. Jørgensen, and R. Therrien, Comparing Discrete Fracture and Continuum Models to Predict Contaminant Transport in Fractured Porous Media, Groundwater, vol.52, issue.1, pp.84-95, 2013.

N. I. Robinson, J. M. Sharp, and I. Kreisel, Contaminant transport in sets of parallel finite fractures with fracture skins, Journal of Contaminant Hydrology, vol.31, issue.1-2, pp.83-109, 1998.

C. I. Steefel and P. C. Lichtner, Multicomponent reactive transport in discrete fractures: I. Controls on reaction front geometry, Journal of Hydrology, vol.209, issue.1-4, pp.186-199, 1998.

H. Yoshida, K. Yamamoto, S. Yogo, and Y. Murakami, An analogue of matrix diffusion enhanced by biogenic redox reaction in fractured sedimentary rock, Journal of Geochemical Exploration, vol.90, issue.1-2, pp.134-142, 2006.

D. Weatherill, T. Graf, C. T. Simmons, P. G. Cook, R. Therrien et al., Discretizing the Fracture-Matrix Interface to Simulate Solute Transport, Ground Water, vol.46, issue.4, pp.606-615, 2008.

J. P. Fairley, Fracture/matrix interaction in a fracture of finite extent, Water Resources Research, vol.46, issue.8, 2010.

J. C. Chambon, M. M. Broholm, P. J. Binning, and P. L. Bjerg, Modeling multi-component transport and enhanced anaerobic dechlorination processes in a single fracture?clay matrix system, Journal of Contaminant Hydrology, vol.112, issue.1-4, pp.77-90, 2010.

F. Chen, R. W. Falta, and L. C. Murdoch, Numerical analysis of contaminant removal from fractured rock during boiling, Journal of Contaminant Hydrology, vol.134-135, pp.12-21, 2012.

C. Liu and H. Yeh, Development of approximate solutions for contaminant transport through fractured media, Applied Mathematical Modelling, vol.39, issue.2, pp.438-448, 2015.

N. Joshi, C. S. Ojha, P. K. Sharma, and C. A. Madramootoo, Application of nonequilibrium fracture matrix model in simulating reactive contaminant transport through fractured porous media, Water Resources Research, vol.51, issue.1, pp.390-408, 2015.

K. Chen and H. Zhan, A Green's function method for two-dimensional reactive solute transport in a parallel fracture-matrix system, Journal of Contaminant Hydrology, vol.213, pp.15-21, 2018.

C. Doughty, Investigation of conceptual and numerical approaches for evaluating moisture, gas, chemical, and heat transport in fractured unsaturated rock, Journal of Contaminant Hydrology, vol.38, issue.1-3, pp.69-106, 1999.

Q. Hu, R. Salve, W. T. Stringfellow, and J. S. Wang, Field tracer-transport tests in unsaturated fractured tuff, Journal of Contaminant Hydrology, vol.51, issue.1-2, pp.1-12, 2001.

B. Berkowitz, Characterizing flow and transport in fractured geological media: A review, Advances in Water Resources, vol.25, issue.8-12, pp.861-884, 2002.

M. Hu, Y. Wang, and J. Rutqvist, On continuous and discontinuous approaches for modeling groundwater flow in heterogeneous media using the Numerical Manifold Method: Model development and comparison, Advances in Water Resources, vol.80, pp.17-29, 2015.

Q. Hu, T. J. Kneafsey, R. C. Trautz, and J. S. Wang, Tracer Penetration into Welded Tuff Matrix from Flowing Fractures, Vadose Zone Journal, vol.999, issue.999, pp.102-112, 2002.

Y. Wu, L. Pan, and K. Pruess, A physically based approach for modeling multiphase fracture?matrix interaction in fractured porous media, Advances in Water Resources, vol.27, issue.9, pp.875-887, 2004.

K. T. Macquarrie and K. U. Mayer, Reactive transport modeling in fractured rock: A state-of-the-science review, Earth-Science Reviews, vol.72, issue.3-4, pp.189-227, 2005.

C. I. Steefel and P. C. Lichtner, Diffusion and reaction in rock matrix bordering a hyperalkaline fluid-filled fracture, Geochimica et Cosmochimica Acta, vol.58, issue.17, pp.3595-3612, 1994.

E. R. Giambalvo, C. I. Steefel, A. T. Fisher, N. D. Rosenberg, and C. G. Wheat, Effect of fluid-sediment reaction on hydrothermal fluxes of major elements, eastern flank of the Juan de Fuca Ridge, Geochimica et Cosmochimica Acta, vol.66, issue.10, pp.1739-1757, 2002.

C. A. Appelo and P. Wersin, Multicomponent Diffusion Modeling in Clay Systems with Application to the Diffusion of Tritium, Iodide, and Sodium in Opalinus Clay, Environmental Science & Technology, vol.41, issue.14, pp.5002-5007, 2007.

M. Rolle, M. Muniruzzaman, C. M. Haberer, and P. Grathwohl, Coulombic effects in advection-dominated transport of electrolytes in porous media: Multicomponent ionic dispersion, Geochimica et Cosmochimica Acta, vol.120, pp.195-205, 2013.

C. Tournassat and C. I. Steefel, Ionic Transport in Nano-Porous Clays with Consideration of Electrostatic Effects, Reviews in Mineralogy and Geochemistry, vol.80, issue.1, pp.287-329, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01269893

C. Tournassat and C. I. Steefel, Reactive Transport Modeling of Coupled Processes in Nanoporous Media, Reviews in Mineralogy and Geochemistry, vol.85, issue.1, pp.75-109, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02154808

C. Tournassat, C. I. Steefel, and T. Gimmi, Solving the Nernst?Planck Equation in Heterogeneous Porous Media With Finite Volume Methods: Averaging Approaches at Interfaces, Water Resources Research, vol.56, issue.3, pp.2019-026832, 2020.
URL : https://hal.archives-ouvertes.fr/insu-02496420

C. Tournassat and C. I. Steefel, Modeling diffusion processes in the presence of a diffuse layer at charged mineral surfaces: a benchmark exercise, Computational Geosciences, pp.1-18, 2019.
URL : https://hal.archives-ouvertes.fr/insu-02280189

P. Wersin, T. Gimmi, M. Mazurek, P. Alt-epping, M. P?kala et al., Multicomponent diffusion in a 280?m thick argillaceous rock sequence, Applied Geochemistry, vol.95, pp.110-123, 2018.

M. A. Glaus, M. Birgersson, O. Karnland, and L. R. Van-loon, Seeming Steady-State Uphill Diffusion of 22Na+ in Compacted Montmorillonite, Environmental Science & Technology, vol.47, issue.20, pp.11522-11527, 2013.

M. Muniruzzaman, C. M. Haberer, P. Grathwohl, and M. Rolle, Multicomponent ionic dispersion during transport of electrolytes in heterogeneous porous media: Experiments and model-based interpretation, Geochimica et Cosmochimica Acta, vol.141, pp.656-669, 2014.

C. A. Appelo, A. Vinsot, S. Mettler, and S. Wechner, Obtaining the porewater composition of a clay rock by modeling the in- and out-diffusion of anions and cations from an in-situ experiment, Journal of Contaminant Hydrology, vol.101, issue.1-4, pp.67-76, 2008.

M. Muniruzzaman and M. Rolle, Impact of multicomponent ionic transport on pH fronts propagation in saturated porous media, Water Resources Research, vol.51, issue.8, pp.6739-6755, 2015.

B. J. Kirby, Micro- and Nanoscale Fluid Mechanics, 2009.

G. Miller and D. Trebotich, An embedded boundary method for the Navier?Stokes equations on a time-dependent domain, Communications in Applied Mathematics and Computational Science, vol.7, issue.1, pp.1-31, 2012.

M. Hu, Y. Wang, and J. Rutqvist, Development of a discontinuous approach for modeling fluid flow in heterogeneous media using the numerical manifold method, International Journal for Numerical and Analytical Methods in Geomechanics, vol.39, issue.17, pp.1932-1952, 2015.

C. A. Appelo, L. R. Van-loon, and P. Wersin, Multicomponent diffusion of a suite of tracers (HTO, Cl, Br, I, Na, Sr, Cs) in a single sample of Opalinus Clay, Geochimica et Cosmochimica Acta, vol.74, issue.4, pp.1201-1219, 2010.

C. Tournassat and C. A. Appelo, Modelling approaches for anion-exclusion in compacted Na-bentonite, Geochimica et Cosmochimica Acta, vol.75, issue.13, pp.3698-3710, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00597084

R. M. Tinnacher, M. Holmboe, C. Tournassat, I. C. Bourg, and J. A. Davis, Ion adsorption and diffusion in smectite: Molecular, pore, and continuum scale views, Geochimica et Cosmochimica Acta, vol.177, pp.130-149, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01368176

J. M. Soler, C. I. Steefel, T. Gimmi, O. X. Leupin, and V. Cloet, Modeling the Ionic Strength Effect on Diffusion in Clay. The DR-A Experiment at Mont Terri, ACS Earth and Space Chemistry, vol.3, issue.3, pp.442-451, 2019.

M. Muniruzzaman and M. Rolle, Multicomponent Ionic Transport Modeling in Physically and Electrostatically Heterogeneous Porous Media With PhreeqcRM Coupling for Geochemical Reactions, Water Resources Research, vol.55, issue.12, pp.11121-11143, 2019.

L. Onsager, Reciprocal Relations in Irreversible Processes. I., Physical Review, vol.37, issue.4, pp.405-426, 1931.

L. Onsager, Reciprocal Relations in Irreversible Processes. II., Physical Review, vol.38, issue.12, pp.2265-2279, 1931.

A. Einstein, Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen, Annalen der Physik, vol.322, issue.8, pp.549-560, 1905.

C. I. Steefel, C. A. Appelo, B. Arora, D. Jacques, T. Kalbacher et al., Reactive transport codes for subsurface environmental simulation, Computational Geosciences, vol.19, issue.3, pp.445-478, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01223868

J. A. Davis and D. B. Kent, CHAPTER 5. SURFACE COMPLEXATION MODELING IN AQUEOUS GEOCHEMISTRY, Mineral-Water Interface Geochemistry, vol.23, pp.177-260, 1990.

I. C. Bourg and G. Sposito, Molecular dynamics simulations of the electrical double layer on smectite surfaces contacting concentrated mixed electrolyte (NaCl?CaCl2) solutions, Journal of Colloid and Interface Science, vol.360, issue.2, pp.701-715, 2011.

H. M. Park, J. S. Lee, and T. W. Kim, Comparison of the Nernst?Planck model and the Poisson?Boltzmann model for electroosmotic flows in microchannels, Journal of Colloid and Interface Science, vol.315, issue.2, pp.731-739, 2007.

A. Revil and P. Leroy, Constitutive equations for ionic transport in porous shales, Journal of Geophysical Research, vol.109, issue.B3, 2004.

M. Birgersson and O. Karnland, Ion equilibrium between montmorillonite interlayer space and an external solution?Consequences for diffusional transport, Geochimica et Cosmochimica Acta, vol.73, issue.7, pp.1908-1923, 2009.

T. Gimmi and P. Alt-epping, Simulating Donnan equilibria based on the Nernst-Planck equation, Geochimica et Cosmochimica Acta, vol.232, pp.1-13, 2018.

G. Sposito, The surface chemistry of natural particles, 2004.

C. Tournassat, I. C. Bourg, C. I. Steefel, and F. Bergaya, Surface Properties of Clay Minerals, Natural and Engineered Clay Barriers, vol.6, pp.5-31, 2015.

C. Appelo, Solute transport solved with the Nernst-Planck equation for concrete pores with ?free? water and a double layer, Cement and Concrete Research, vol.101, pp.102-113, 2017.

C. I. Steefel and A. C. Lasaga, A coupled model for transport of multiple chemical species and kinetic precipitation/dissolution reactions with application to reactive flow in single phase hydrothermal systems, American Journal of Science, vol.294, issue.5, pp.529-592, 1994.

S. Balay, S. Abhyankar, M. Adams, J. Brown, P. Brune et al., PETSc Users Manual (Rev. 3.5), 2014.

J. Lund and C. Wright, Building Union Power Through the Supply Chain, Labor Studies Journal, vol.27, issue.4, pp.59-75, 2003.