Diffusion of ionic tracers in the Callovo-Oxfordian clay-rock using the Donnan equilibrium model and the formation factor

The transient diffusion of cationic and anionic tracers through clay-rocks is usually modeled with parameters like porosity, tortuosity (and/or constrictivity), sorption coefficients, and anionic exclusion. Recently, a new pore scale model has been developed by Revil and Linde [Revil A. and Linde N. (2006) Chemico-electromechanical coupling in microporous media. J. Colloid Interface Sci.302, 682–694]. This model is based on a volume-averaging approach of the Nernst–Planck equation. The influence of the electrical diffuse layer is accounted for by a generalized Donnan equilibrium model through the whole connected pore space that is valid for a multicomponent electrolyte. This new model can be used to determine the composition of the pore water of the Callovo-Oxfordian clay-rock, the osmotic efficiency of bentonite as a function of salinity, the osmotic pressure, and the streaming potential coupling coefficient of clay-rocks. This pore scale model is used here to model the transient diffusion of ionic tracers (22Na+, 36Cl−, and 35SO42-) through the Callovo-Oxfordian clay-rock. Speciation of SO42- shows that ∼1/3 of the SO4 is tied-up in different complexes. Some of these complexes are neutral and are therefore only influence by the tortuosity of the pore space. Using experimental data from the literature, we show that all the parameters required to model the flux of ionic tracers (especially the mean electrical potential of the pore space and the formation factor) are in agreement with independent evaluations of these parameters using the osmotic pressure determined from in situ pressure measurements and HTO diffusion experiments.