Diffusion of Cs, Np, Am and Co in compacted sand-bentonite mixtures: evidence for surface diffusion of Cs cations^†

During the storage of high-level radioactive waste in a deep geological isolation systems, long-lived ¹³⁵Cs (half life: 2.3 × 10⁶ years) may leach from the waste packages and subsequently move through the surrounding buffer materials to the geosphere. Thus, the buffer materials are expected to form a low-permeability barrier against groundwater flow and to retard the migration of ¹³⁵Cs by sorption. For this purpose, compacted sand-bentonite mixtures are considered as candidate buffer materials. Water permeability in sand-bentonite mixtures is so low that diffusion is the only possible mechanism for ¹³⁵Cs transport.

Fick’s 1^st law of diffusion was applied to the diffusion of ions in sand-bentonite mixtures. Two diffusivities, apparent diffusivity (D_a) and effective diffusivity (D_e), are used to describe the diffusive transport of radionuclides through engineered and natural barriers in radioactive waste management. When the concentration gradient is defined on the basis of the amount of diffusing species per unit volume of porous material, the proportional constant between the flux and the concentration gradient is called D_a. On the other hand, when the definition is based on the concentration of diffusing species in pore water, the proportional constant is D_e.

The driving force behind cation diffusion in bentonite mixtures is well known for Sr²⁺. Eriksen & Jansson (1996) showed positive correlation between D_e and distribution coefficient (K_d), which is evidence for the contribution of surface diffusion or diffusion in the sorbed state. For Cs, on the other hand, plausible data on the driving force for diffusion in bentonite mixtures are not available. On the basis of the results of a through-diffusion experiment, Muurinen et al. (1987) reported that surface diffusion is the predominant Cs diffusion mechanism in compacted bentonite. In their experiment, however, steady state was not reached, and the results and conclusion are questionable. Yu & Neretnieks (1997) conducted a literature review, proposed diffusion coefficients of elements in compacted bentonite, and concluded that surface diffusion effects are found for Cs, Pa and Sr in low-ionic-strength waters. Their discussion was, however, based on the effective diffusivity that was indirectly estimated from D_a and K_d data. Okamoto et al. (1999) hinted at the contribution of surface diffusion by showing that the D_a of Cs is independent of K_d. The scarce information on Cs is mainly because of the difficulties encountered in through-diffusion experiments or the extremely long times required for reaching steady-state diffusion.

In this study, through-diffusion experiments for Cs in compacted sand-bentonite mixtures were performed under several water compositions, expecting that the variation in the water composition can lead to variations in Cs sorptivity and in the driving force of diffusion. We examined whether the apparent diffusivity or the effective diffusivity was the fixed constant, namely the proportional constant between the diffusive flux and the concentration gradient driving diffusion. For comparison, the diffusivities of ²³⁷Np(IV), ²⁴¹Am(III), and ⁶⁰Co(II) in the mixtures were also determined under 0.3/0.03 mol l^–1 (NH₄)₂CO₃/Na₂S₂O₄ conditions through multitracer diffusion experiments.

Through-diffusion experiments were carried out at various solution compositions. The acrylic diffusion cell used in this study is shown in Fig. 1. The experimental conditions are summarized in Table 1. The employed bentonite material was Kunigel V1 (Kunimine Industries Co. Ltd.), with 46–49 wt.% Na-montmorillonite (Ito et al., 1993). In the experiments, mixtures of Kunigel V1 and silica sand were compacted to an acrylic diffusion column of 20 mm in diameter and 10 mm in thickness. The mixture ratio of Kunigel V1 and silica sand was 7:3 by dry weight and the density of the mixed specimens was 1600 kg m^–3; these are specified as the reference buffer material in Japan (JNC, 2000). Each side of the sand-bentonite mixture was covered with sintered stainless steel, 1-mm-thick filters of 40% porosity in order to prevent the expansion of bentonite in the reservoirs.

A multitracer through-diffusion experiment was performed by using the diffusion cell following a diffusion experiment for HTO. A 0.01 mol l^–1 NaCl solution was employed to simulate fresh groundwater. The diffusion cell was soaked in the solution under vacuum to remove all air from the pores in the specimen. The two reservoirs of the diffusion cell were then filled with 1.1 × 10^–1 l of the solution. The diffusion experiment was started by adding HTO to the solution in one of the reservoirs (high-concentration reservoir). At intervals of seven days, 1.0 × 10^–3 l aliquot was taken from the low-concentration reservoir, and 1.0 × 10^–4 l aliquot from the high-concentration reservoir for radiometric analysis. The 1.0 × 10^–3 l aliquot removed from the low-concentration reservoir was replaced by an equal volume of 0.01 mol l^–1 NaCl solution to maintain the water levels in the two reservoirs. This balancing act prevents the development of a pressure difference that can lead to advective transport from the high-concentration to low-concentration reservoir. The concentrations of HTO in both reservoirs were determined by liquid scintillation counting (LS-6500, Beckman Coulter, Inc.). After the diffusion of HTO reached a steady state, the solution was replaced by one containing Cs, I, Ni, Sr, Nb, Sn and Pb in order to allow the elements to diffuse. The solutions were sampled, using a similar procedure to that in the HTO experiment, for 363 days. The concentrations of the elements were determined by using inductively coupled plasma-mass spectrometry (ICP-MS, JMS-PLASMAX2, JEOL Ltd.). The initial concentrations of HTO, Cs, I, Sr, and Sn were 100 kBq l^–1, 1 × 10^–4 mol l^–1, 1 × 10^–4 mol l^–1, 3 × 10^–3 mol l^–1, and 6 × 10^–5 mol l^–1, respectively. Because the concentrations of Ni, Nb and Pb were lower than the detection limit, diffusivities were not obtained for these elements. The diffusion experiments were performed at room temperature under Ar (O₂ < 1 ppm) to avoid oxidation of I^–.

A 0.5 mol l^–1 NaCl solution was employed to simulate saline groundwater. The procedure of the diffusion experiments was similar to that of the series-1–1 experiments.

A 0.5 mol l^–1 NaOH solution was employed to simulate the highly alkaline groundwater conditions induced by cementitious materials in the radioactive waste repositories. The procedure of the diffusion experiments was similar to that of the series-1–1 experiments. In this series, the initial concentrations of HTO, Cs, I, Sr, Sn and Pb were 100 kBq l^–1, 1 × 10^–4 mol l^–1, 2 × 10^–4 mol l^–1, 1 × 10^–3 mol l^–1, 1 × 10^–4 mol l^–1 and 9 × 10^–4 mol l^–1, respectively. The concentrations of Ni and Nb were lower than the detection limit, so the diffusivities were not determined.

A 0.3 mol l^–1 (NH₄)₂CO₃ solution was used to simulate groundwater rich in ammonium, a reduction product of $NO3−$ released from transuranic (TRU) waste. The diffusion cells were soaked in distilled-deionized water under vacuum to remove air from the pores of the specimens. Three diffusion cells (runs 1, 2 and 3) were filled with a 1.1 × 10^–1 l (NH₄)₂CO₃/Na₂S₂O₄ mixed solution, whose total ammonia concentration, total carbonate concentration and dithionite concentration were 6.0 × 10^–1 mol l^–1, 3.0 × 10^–1 mol l^–1 and 3.0 × 10^–2 mol l^–1, respectively. A diffusion cell without bentonite was used in a blank test to check the adsorption of radionuclides on the cell walls. The diffusion cells were transferred into an atmosphere-controlled glove box and left for 30 days to condition the specimens in the solution. The starting solution was prepared by combining a 5.5 × 10^–1 l of (NH₄)₂CO₃/Na₂S₂O₄ solution, a 1.0 × 10^–5 l ¹³⁷Cs stock solution, a 9.0 × 10^–4 l ⁶⁰Co stock solution, a 1.0 × 10^–4 l ²⁴¹Am stock solution and a 1.5 × 10^–3 l Np(IV) stock solution in a polypropylene bottle. The concentrations of $NH4+$⁠, $HCO3−$⁠, $S2O42−$⁠, ¹³⁷Cs, ⁶⁰Co, ²⁴¹Am, and ²³⁷Np in the starting solution were 0.6 mol l^–1, 0.3 mol l^–1, 0.03 mol l^–1, 5.5 × 10¹ kBq l^–1, 5.5 × 10¹ kBq l^–1, 1.35 × 10² kBq l^–1 and 1.36 × 10² kBq l^–1, respectively. The pH and E_H (redox potential against normal hydrogen electrode) of the solutions were measured with electrodes. Aliquots of the solutions were withdrawn to determine the concentrations of radionuclides by γ-spectrometry. The diffusion runs started by replacing the solution in one of the reservoirs with a 1.1 × 10^–1 l starting solution and a blank test with a 2.2 × 10^–1 l starting solution. At intervals of three weeks, the solutions in the high- and low-concentration reservoirs were sampled. The sampling procedure was similar to the series-1 experiments.

After performing series-2 diffusion runs for 363 days, a series of post-experimental analyses were performed for the diffusion tests and the blank test. The pH and E_H were measured with electrodes, and the ratio of Np(IV) to the total dissolved Np was determined using the thenoyltrifluoroacetone (TTA) extraction technique (Yamaguchi et al., 2007). Np(IV) is extracted by TTA, while the other oxidation states of Np remain in the aqueous phase (Foti & Freiling, 1964) in 1 mol l^–1 HCl. We filtered 4.0 × 10^–4 l aliquots of the solution through four types of filters, a 0.45 μm durapore (PVDF, polyvinylidene fluoride) filter, a regenerated cellulose filter with 100 k and 30 k nominal molecular weight limit (NMWL), and polyether sulphon filters with 10 k and 5 k NMWL in series to analyse the colloidal Np in the solution. The filters were preconditioned by filtering a 4.0 × 10^–4 l aliquot of the solution before use to avoid any change in the Np concentration during filtration. The remainder of the solution was removed from the reservoir and the diffusion cell was disassembled. Each reservoir was rinsed with 1.0 × 10^–2 l deionized water three times, and then rinsed with 1.0 × 10^–2 l of 1.0 × 10¹ mol l^–1 HNO₃ to analyse the amount of Np adsorbed on the acrylic walls. The sand-bentonite mixture was pushed out from the acrylic frame one millimeter at a time by using a screw presser and sliced with a steel blade to reveal the distribution of radionuclides in the sand-bentonite mixture specimens. Because the periphery of the slice seemed to be disturbed from pushing the sample out of the acrylic frame, the centre of the slice with a 14 mm in diameter was cut using a polypropylene tube. The specimen was dried, weighed, and analysed for radionuclides by γ-spectrometry.

Then, D_a becomes the ratio of the diffusive flux to the concentration gradient of the species adsorbed on the diffusion medium (ρ·K_ddc/dx). Yu & Neretnieks (1997) defined this ratio as surface diffusivity.

We also applied the above-mentioned method to analyse the Cs diffusion data in a similar diffusion experiment using a 0.3/0.03 mol l^–1 NaHCO₃/Na₂S₂O₄ solution by Yamaguchi et al. (2007), and re-estimated D_e and D_a.

The changes in the concentrations of Cs in the high- and low-concentration reservoirs are shown in Fig. 3. The concentration of Cs in the low-concentration reservoir was first detected after 20–40 days, then gradually increased, and finally reached equilibrium about 150 days later. The concentrations of radioactive Cs have been compensated for radioactive decay in series-2. The distribution coefficients and diffusivities of Cs estimated using the exact solution are summarized in Table 1. The distribution coefficients of Cs⁺ in 0.01 mol l^–1 NaCl solution, 0.5 mol l^–1 NaCl solution, 0.5 mol l^–1 NaOH solution, 0.3/0.03 mol l^–1 (NH₄)₂CO₃/Na₂S₂O₄ solution and 0.3/0.03 mol l^–1 NaHCO₃/Na₂S₂O₄ solution were obtained as 1.0 m³ kg^–1, 0.080 m³ kg^–1, 0.067 m³ kg^–1, 0.064 m³ kg^–1 and 0.25 m³ kg^–1, respectively. The distribution coefficients of Cs⁺ decreased with increasing ionic strength.

At high ionic strength (series-1–2, series-1–3, series-2, and Yamaguchi et al., 2007), the effective diffusivities through the column, including the filters, were corrected for the filter effect to obtain effective diffusivity through the specimens using equation 8. On the other hand, the effective diffusivity through the column for low ionic strength (series-1–1) was higher than the value expected when only the filter was placed in the column (2.4 × 10^–9 m² s^–1), and could not be corrected using equation 8. The D_eb of Cs in series-1–1 shown in Table 1 is a minimum value.

Effective diffusivities of Cs⁺ in 0.01 mol l^–1 NaCl, 0.5 mol l^–1 NaCl, 0.5 mol l^–1 NaOH, 0.3/0.03 mol l^–1 (NH₄)₂CO₃/Na₂S₂O₄ and 0.3/0.03 mol l^–1 NaHCO₃/Na₂S₂O₄ solutions were obtained as > 5.9 × 10^–9 m² s^–1, (7.8±2.8) × 10^–10 m² s^–1, (7.8±4.0) × 10^–10 m² s^–1, (5.6±1.6) × 10^–10 m² s^–1 and (1.0±0.4) × 10^–9 m² s^–1, respectively. The effective diffusivities of Cs⁺ were higher than those of HTO, which ranged from 1.5 to 2.0 × 10^–10 m² s^–1 (JAEA, 2006).

The apparent diffusivities of Cs⁺ in 0.01 mol l^–1 NaCl, 0.5 mol l^–1 NaCl, 0.5 mol l^–1 NaOH, 0.3/0.03 mol l^–1 (NH₄)₂CO₃/Na₂S₂O₄ and 0.3/0.03 mol l^–1 NaHCO₃/Na₂S₂O₄ solutions were obtained as (3.7±1.1) × 10^–12 m² s^–1, (5.3±1.3) × 10^–12 m² s^–1, (6.2±2.0) × 10^–12 m² s^–1, (5.1±0.8) × 10^–12 m² s^–1 and (2.1±0.4) × 10^–12 m² s^–1, respectively. The apparent diffusivities obtained in this study were close to those reported by Sato et al. (1992) and by Kozaki et al. (1999) from indiffusion experiments using compacted montmorillonite. At the same effective montmorillonite density (montmorillonite gel density; Sawaguchi et al., 2006) and temperature as in this study, their values were 8.0 × 10^–12 m² s^–1 and 4.8 × 10^–12 m² s^–1, respectively.

The diffusivities, D_e and D_a, as a function of K_d are shown in Figs 4 and 5, respectively. D_e values of 4.7 × 10^–10 to 5.9 × 10^–9 m² s^–1 were obtained with somewhat large variation. The variation is not caused by the variation in the geometry of the diffusion pathways because the density and mixture ratio of the sand-bentonite mixture specimens were the same in all diffusion runs. D_a values, on the other hand, varied less from 2.0 × 10^–12 to 6.2 × 10^–12 m² s^–1. The results indicate that the diffusive flux is proportional to the apparent concentration gradient of Cs⁺ in the compacted sand-bentonite mixtures rather than the gradient of the Cs⁺ concentration in pore water. Because the apparent concentration gradient in the mixture is nearly equal to the gradient of adsorbed Cs⁺, the diffusion of Cs⁺ in the mixtures is probably dominated by the concentration gradient of the Cs⁺ adsorbed on the mixtures. As shown in Fig. 4, the D_e of Cs⁺ is not constant but positively correlated to K_d, which may be explained if surface diffusion is dominant at high K_d and its contribution decreases as K_d decreases at high ionic strength. Figure 4, however, shows that the contribution of surface diffusion is almost equal to that of pore diffusion in 0.5 mol l^–1 solutions (series-1–2 and series-1–3), which are equivalent to saline groundwater.

In series-2, Np was prepared as Np (IV) at the start of the diffusion and TTA extraction was 99% at the termination of the diffusion runs. Np (IV) is extracted by TTA, while the other oxidation states of Np remain in the aqueous phase. The pH, E_H, and total carbonate concentrations were 8.8, –312 mV vs. normal hydrogen electrode (NHE) and 3.0 × 10^–1 mol l^–1, respectively, at the termination of each diffusion run. These facts ensured that Np was mainly in the +IV state throughout the diffusion runs. The filtration analysis showed that (97%± 6%) of Np passed through the 5 k NMWL filter, which ensured that Np was not present in the solution as colloidal particles. Speciation calculations using a thermodynamic database (Yamaguchi, 2000) show that the carbonatohydroxo complex of $NpIV(CO3)2(OH)22−$ accounts for most ratios of Np under the experimental conditions.

The concentrations of ²³⁷Np in the high-concentration reservoirs decreased throughout the experimental period of 363 days, as shown in Fig. 6. Np diffusion in the specimens reached a steady state after 300 days. The effective diffusivities of Np in series-2 were estimated using the exact solution (Table 1), and the analytical results reproduced well the experimental results in both reservoirs.

The effective diffusivities of HTO, I, Ni, Sr, Nb, Sn and Pb in the series-1 experiments are described elsewhere (JAEA, 2006). Further investigation is necessary to identify the driving force behind the diffusion of elements other than Cs and Sr.

The driving force for the diffusion of Cs⁺ through compacted sand-bentonite mixtures was studied using the through-diffusion method under different aqueous compositions. The variation in effective diffusivity values was somewhat large, while that in the apparent diffusivity values was small. The results indicated that the diffusion of Cs in the adsorbed state would be the main Cs diffusion mechanism in the mixtures.

The authors acknowledge Messrs M. Kizaki, S. Miyata, Y. Kawasaki and F. Itonaga for performing the long-term experiments at the Waste Safety Testing Facility (WASTEF) of the Japan Atomic Energy Agency. Messrs N. Ito, S. Inagaki and T. Kawamura are acknowledged for the caesium concentration analyses by ICP-MS. Professor Ivars Neretnieks and an anonymous referee are acknowledged for reviewing the manuscript and making helpful comments.