A Quantitative Model for Ion Diffusion in Compacted Bentonite

Compacted bentonite is a candidate backfill material for the disposal of radioactive waste. A correct understanding of the processes affecting diffusion in compacted bentonite is needed to predict radionuclide migration. Using distribution coefficients (K_d) obtained in batch experiments and geometric factors relevant for compacted bentonite, it is not possible to predict or explain the apparent diffusivities (D_a) typically observed. Here, an approach is presented that integrates mechanistic sorption and diffusion models in combination with thermodynamic data and bentonite characteristics in order to predict D_a for cesium. Key features of this approach are (i) to calculate the correct K_d value at high dry densities of the bentonite, and (ii) to calculate the correct constrictivity based on an electric double layer model. The integrated sorption-diffusion model present in this paper assigns exchangeable, immobile ions to the Stern layer, whereas ions located in the diffuse layer are considered mobile. Constrictivity is interpreted as the ratio of the average concentration of an ion in the diffuse layer to its concentration in the bulk solution. We show that in this way, the diffusion of Cs in Kunigel-V1 as well as Kunipia-F bentonite can be modeled successfully for a wide range of dry densities. Stern plane potentials calculated for these conditions also agree with measured zeta-potentials.