Advanced diffusion model in compacted bentonite based on modified Poisson-Boltzmann equations

Document available in extended abstract form only. Diffusion and sorption of radionuclides in compacted bentonite are the key processes in the safe geological disposal of radioactive waste. JAEA has developed the integrated sorption and diffusion (ISD) model for compacted bentonite by coupling the pore water chemistry, sorption and diffusion processes in consistent way. The diffusion model accounts consistently for cation excess and anion exclusion in narrow pores in compacted bentonite by the electric double layer (EDL) theory. The firstly developed ISD model could predict the diffusivity of the monovalent cation/anion in compacted bentonite as a function of dry density. This ISD model was modified by considering the visco-electric effect, and applied for diffusion data for various radionuclides measured under wide range of conditions (salinity, density, etc.). This modified ISD model can give better quantitative agreement with diffusion data for monovalent cation/anion, however, the model predictions still disagree with experimental data for multivalent cation and complex species. In this study we extract the additional key factors influencing diffusion model in narrow charged pores, and the effects of these factors were investigated to reach a better understanding of diffusion processes in compacted bentonite. We investigated here the dielectric saturation effect and the excluded volume effect into the present ISD model and numerically solved these modified Poisson-Boltzmann equations. In the vicinity of the negatively charged clay surfaces, it is necessary to evaluate concentration distribution of electrolytes considering the dielectric saturation effects. The Poisson-Boltzmann (P-B) equation coupled with the dielectric saturation effects was solved numerically by using Runge-Kutta and Shooting methods. Figure 1(a) shows the concentration distributions of Na+ as numerical solutions of the modified and original P-B equations for 0.01 M pore water, 800 kg m-3 dry density Kunipia-F (-0.129 C m-2 surface charge density). We used Booth equation and Malsh-Grahame equation as the dielectric permittivity dependent on electric field. In this condition field strength come to ∼ 109 V m-1 in the vicinity of the interface, then saturation effect by Booth equation is larger than Malsh-Grahame equation. Therefore Na+ is strongly eliminated from the interface by Booth equation than Malsh-Grahame equation. While Figure 1(b) shows salinity dependence of the effective diffusivity (De) of Sr2+/Cs+/I-, calculated by the modified ISD model incorporated the dielectric saturation effects with Booth equation and original one (present ISD model). For Cs+ as an example electrostatic potential term in Boltzmann factor of the modified model is larger than the original one, however hydration free energy term in Boltzmann factor cancel out this increment. Consequently De by the modified model was not mostly changed from the original model. For other ionic species we can be considered as well. The ISD model was modified considering the excluded volume effect which is caused by quantum mechanical short range repulsive force of inter-particle. We used the restricted primitive model for the sake of simplicity. Figure 2 shows the concentration distributions of Na+ as numerical solutions of the modified models incorporated the excluded volume effect and the original model, and salinity dependence of De (b). We used here the Stokes radius (=1.84 x 10-10 m) as ionic radius in a solution and crystal radius (= 1.16 x 10-10 m) on the interface. It can be said that the excluded volume effect influence hardly De as well as the dielectric saturation effects. As results of numerical analysis of the models the considered factors influence hardly De of Sr2+/Cs+/I-. Therefore it was concluded that the disagreements with experimental data observed in present ISD model cannot be improved by considered factors in this study, because ionic concentration distributions change but total charge are invariant in the interlayer. (authors)