Effect of Dry Density on Activation Energy for Diffusion of Strontium in Compacted Sodium Montmorillonite

Connecting the molecular scale to the continuum scale for diffusion processes in smectite-rich porous media

In this paper, we address the manner in which the continuum-scale diffusive properties of smectite-rich porous media arise from their molecular- and pore-scale features. Our starting point is a successful model of the continuum-scale apparent diffusion coefficient for water tracers and cations, which decomposes it as a sum of pore-scale terms describing diffusion in macropore and interlayer "compartments." We then apply molecular dynamics (MD) simulations to determine molecular-scale diffusion coefficients D(interlayer) of water tracers and representative cations (Na(+), Cs(+), Sr(2+)) in Na-smectite interlayers. We find that a remarkably simple expression relates D(interlayer) to the pore-scale parameter δ(nanopore) ≤ 1, a constrictivity factor that accounts for the lower mobility in interlayers as compared to macropores: δ(nanopore) = D(interlayer)/D(0), where D(0) is the diffusion coefficient in bulk liquid water. Using this scaling expression, we can accurately predict the apparent diffusion coefficients of tracers H(2)0, Na(+), Sr(2+), and Cs(+) in compacted Na-smectite-rich materials.

Diffusion of 22Na+, 85Sr2+, 134Cs+ and 57Co2+ in bentonite clay compacted to different densities: experiments and modeling

The diffusion of radionuclides in water-saturated porous media, such as compacted bentonite, is traditionally modeled assuming diffusion in the pore water and immobilization by adsorption on the clay surface. In reality there are several sorption mechanisms acting in the clay-water system. We have therefore carried out a careful diffusion study of the cations Na+, Sr2+, Cs+, which are predominantly sorbed by electrostatic interaction, and Co2+, for which the dominant sorption mechanism at pH > 7 is inner-sphere complexation and/or surface precipitation. The study has been performed at different densities of clay compaction (1.8, 1.6, 1.2, 0.8, 0.4 g cm−3) using a through diffusion technique. In each experiment, the apparent diffusivity and transport Kd were obtained by computer simulation of the experimentally measured cumulative flux through a plug of compacted bentonite and the concentration profile within the bentonite. Batch sorption experiments with Na+, Sr2+, Cs+ and Co2+ were also carried out. Measured batch Kd values were compared to diffusion-derived Kd values using the computer code ANADIFF. The obtained diffusivities of Cs+ and Sr2+ decreased as the density of bentonite increased. The diffusivity of Cs+ decreased from 1.5×10−7 to 1.1×10−8 cm2/s as the clay dry bulk density increased from 0.4 to 1.8 g/cm3 and the diffusivity for Sr2+ varied from 4.3×10−7 to 9.0×10−8 cm2/s. The diffusivities of Co2+ also decreased from 3.0×10−9 to 1.0×10−10 cm2/s in the same range of clay density. An interpretation of the diffusion data is proposed based on differences in porosity and tortuosity of the bentonite compacted to different densities, and on differences in binding energy, hydration energy, and hydrolysis constants for the cations studied.

Effect of silica sand on activation energy for diffusion of sodium ions in montmorillonite and silica sand mixture

The effect of silica sand on the diffusion of sodium ions in mixtures of montmorillonite and silica sand was studied by measuring the apparent diffusion coefficients, activation energies for diffusion, and the basal spacing of the mixed samples. These diffusion experiments suggest that the apparent diffusion coefficients of sodium ions in the mixed samples were almost the same as those of pure montmorillonite samples having the same partial dry densities of montmorillonite. The activation energy dependence for diffusion of sodium ions on the partial dry density was different between the mixed samples and the pure montmorillonite samples. The activation energy increased by adding silica sand at the partial dry density of 1.0 Mg m(-3), and decreased by adding silica sand at the partial dry densities higher than 1.2 Mg m(-3). A change in the XRD profile was observed after adding silica sand at the partial dry density of 1.6 Mg m(-3). Here, a three-water-layer hydrate state of montmorillonite was found in the mixed sample whereas only a two-water-layer hydrate state was observed in the pure montmorillonite sample. These experimental results suggest that silica sand changed the montmorillonite microstructure in the mixed samples, which then altered the sodium-ion diffusion process.

Modeling diffusion and adsorption in compacted bentonite: a critical review

The current way of describing diffusive transport through compacted clays is a simple diffusion model coupled to a linear adsorption coefficient (K(d)). To fit the observed results of cation diffusion, this model is usually extended with an adjustable "surface diffusion" coefficient. Description of the negative adsorption of anions calls for a further adjustment through the use of an "effective porosity". The final model thus includes many fitting parameters. This is inconvenient where predictive modeling is called for (e.g., for waste confinement using compacted clay liners). The diffusion/adsorption models in current use have been derived from the common hydrogeological equation of advection/dispersion/adsorption. However, certain simplifications were also borrowed without questioning their applicability to the case of compacted clays. Among these simplifications, the assumption that the volume of the adsorbed phase is negligible should be discussed. We propose a modified diffusion/adsorption model that accounts for the volume of the adsorbed phase. It suggests that diffusion through highly compacted clay takes place through the interlayers (i.e., in the adsorbed phase). Quantitative prediction of the diffusive flux will necessitate more detailed descriptions of surface reactivity and of the mobility of interlayer species.

Apparent diffusion coefficients and chemical species of neptunium (V) in compacted Na-montmorillonite

Diffusion of neptunium (V) in compacted Na-montmorillonite was studied through the non-steady state diffusion method. In this study, two experimental attempts were carried out to understand the diffusion mechanism of neptunium. One was to establish the diffusion activation energy, which was then used to determine the diffusion process in the montmorillonite. The other was the measurement of the distribution of neptunium in the montmorillonite by a sequential batch extraction. The apparent diffusion coefficients of neptunium in the montmorillonite at a dry density of 1.0 Mg m-3 were from 3.7 x 10(-12) m2 s-1 at 288 K to 9.2 x 10(-12) m2 s-1 at 323 K. At a dry density of 1.6 Mg m-3, the apparent diffusion coefficients ranged between 1.5 x 10(-13) m2 s-1 at 288 K and 8.7 x 10(-13) m2 s-1 at 323 K. The activation energy for the diffusion of neptunium at a dry density of 1.0 Mg m-3 was 17.5 +/- 1.9 kJ mol-1. This value is similar to those reported for diffusion of other ions in free water, e.g., 18.4 and 17.4 kJ mol-1 for Na+ and Cl-, respectively. At a dry density of 1.6 Mg.m-3, the activation energy was 39.8 +/- 1.9 kJ mol-1. The change in the activation energy suggests that the diffusion process changes depending on the dry density of the compacted montmorillonite. A characteristic distribution profile was obtained by the sequential extraction procedure for neptunium diffused in compacted montmorillonite. The estimated fraction of neptunium in the pore water was between 3% and 11% at a dry density of 1.6 Mg m-3 and at a temperature of 313 K. The major fraction of the neptunium in the montmorillonite was identified as neptunyl ions sorbed on the outer surface of the montmorillonite. These findings suggested that the activation energy for diffusion and the distribution profile of the involved nuclides could become powerful parameters in understanding the diffusion mechanism.

An integrated sorption-diffusion model for the calculation of consistent distribution and diffusion coefficients in compacted bentonite

A thermodynamic sorption model and a diffusion model based on electric double layer (EDL) theory are integrated to yield a surface chemical model that treats porewater chemistry, surface reactions, and the influence of charged pore walls on diffusing ions in a consistent fashion. The relative contribution of Stern and diffuse layer to the compensation of the permanent surface charge represents a key parameter; it is optimized for the diffusion of Cs in Kunipia-F bentonite, at a dry density of 400 kg/m3. The model is then directly used to predict apparent diffusivities (Da) of Cs, Sr, Cl-, I- and TcO4- and corresponding distribution coefficients (Kd) of Cs and Sr in different bentonites as a function of dry density, without any further adjustment of surface chemical and EDL parameters. Effective diffusivities (De) for Cs, HTO, and TcO4- are also calculated. All calculated values (Da, De, Kd) are fully consistent with each other. A comparison with published, measured data shows that the present model allows a good prediction and consistent explanation of (i) apparent and effective diffusivities for cations, anions, and neutral species in compacted bentonite, and of (ii) Kd values in batch and compacted systems.