Multicomponent diffusion of a suite of tracers (HTO, Cl, Br, I, Na, Sr, Cs) in a single sample of Opalinus Clay

Diffusion experiments with HTO, ³⁶Cl⁻, Br⁻, I⁻, ²²Na⁺, ⁸⁵Sr²⁺ and ¹³⁴Cs⁺ at trace concentrations in a single sample of Opalinus Clay are modeled with PHREEQC’s multicomponent diffusion module. The model is used first in a classical approach to derive accessible porosities, geometrical factors (the ratio of pore tortuosity and constrictivity) and sorption behavior of the individual tracers assuming that the clay is homogeneous. The accessible porosity for neutral species and cations is obtained from HTO, the anion exclusion volume from ³⁶Cl⁻ and Br⁻, and the cation exchange capacity from ²²Na⁺. The homogeneous model works well for tritium, the anions and ²²Na⁺. However, the ⁸⁵Sr²⁺ and ¹³⁴Cs⁺ experiments show an early arrival of the tracer and a front-form that suggest a dual porosity structure. A model with 10% dead-end pores, containing 19% of the total exchange capacity, can satisfactorily calculate all the experimental data. The Cs⁺ diffusion model builds on a 3-site exchange model, constructed from batch sorption data. The excellent agreement of modeled and measured data contradicts earlier reports that the exchange capacity for Cs⁺ would be smaller in diffusion than in batch experiments.The geometrical factors for the anions are 1.5 times larger than for HTO, and for the cations 2-4 times smaller than for HTO. The different behavior is explained by a tripartite division of the porespace in free porewater, diffuse double layer (DDL) water, and interlayer water in montmorillonite. Differences between estimated and observed geometrical factors for cations are attributed to increased ion-pairing of the divalent cations in DDL water as a result of the low relative dielectric permittivity. Interlayer and/or surface diffusion contributes significantly to the diffusive flux of Cs⁺ but is negligible for the other solutes. The geometrical factors for anions are higher than estimated, because pore constrictions with overlapping double layers force the anions to take longer routes than HTO and the cations. Small differences among the anions can also be attributed to different ion-pairing in DDL water.     

Modelling approaches for anion-exclusion in compacted Na-bentonite

The accessible porosity for Cl⁻ in bentonite is smaller than the the total porosity due to anion repulsion (exclusion) by the surface of montmorillonite, the main mineral in bentonite. The accessible porosity is a function of the bentonite density and the salt concentration. Anion exclusion data were gathered from the literature, reprocessed in a coherent data set, and modelled using four different models. Very simple models, with or without anion access to the interlayer space, are successful in reproducing trends in anion exclusion in bentonite as a function of ionic strength in the external solution and montmorillonite bulk dry densities in the bentonite. However, a model that considers clay microstructure changes as a function of bentonite compaction and ionic strength is necessary to reproduce observed trends in the data for all experimental conditions within a single model. Our predictive model excludes anions from the interlayer space and relates the interlayer porosity to the ionic strength and the montmorillonite bulk dry density. This presentation offers a good fit for measured anion accessible porosities in bentonites over a wide range of conditions and is also in agreement with microscopic observations.