Introduction

China has the biggest reservation of bentonite in the world. Considering the mining scale, quality, economic limitation and location, Gaomiaozi (GMZ) bentonite was chosen as the potential backfilling materials for the HLW repository. It is in the northern Chinese Inner Mongolia autonomous region. There are 160 million tons with 120 million tones Na-bentonite reserves in the deposit and the mine area is about 72 km2. The deposit is formed in the late Jurassic [1, 2]. Compared to relatively well studies reference bentonite, such as such as MX-80 (USA, Switzerland and Sweden), Fo-Ca (France), FEBEX (Spain) and Kunigel V1 (Japan), the mineralogy composition of GMZ bentonite is different, whereas the chemical composition is similar to Kunigel-V1 [3]. The main composition is montmorillonite, which is built from layers of oxygen atoms and cations in tetrahedral–octahedral–tetrahedral (TOT) coordination. The structure has an excess of negative charge due to isomorphic substitution of Al for Si in tetrahedral layers and Mg for Al, or Li for Mg in octahedral layer. The negative surface is compensated by cations between the clay layers in the interlayer space [4]. It has been widely accepted that diffusion of anions in compacted bentonite is predominantly governed by pore water diffusion and anion exclusion effect. Anion exclusion was ineffective when the compacted dry density above 1,800 kg/m3 [5].

99Tc is a radioactive fission product of 235U and 239Pu and an important radionuclides related to repository safety assessment due to its long half-life (2.1 × 105 year), high environmental mobility and it possible uptake into the food chain [6]. 99Tc speciation, solubility and sorption behavior is strongly dependent on its valence state [7]. Under oxic and suboxic environments, the dominant form of Tc(VII) is pertechnetate (TcO4 −), which is highly solubility in water and essentially nonadsorptive properties toward sediment minerals. However, under anoxic conditions, Tc(VII) can be reduced to technetium(IV) hydrous oxides, i.e., TcO2·nH2O, which is sparingly soluble in water under circumneutral pH conditions [8]. Tc(VII) can be reduced to Tc(IV) by ferrous iron as either aqueous (Fe2+) or solid [Fe(II)], which is associated with solid minerals such as magnetite, hematite, goethite, etc. [9–11].

Diffusion coefficient is an important parameter for transport modeling in evaluating the safety of repository. The apparent diffusion coefficient in bentonite of Tc(VII) is in the range of 10−10–10−11 m2/s, whereas Tc(IV) is 10−12–10−14 m2/s [12–14]. The Fe(II)-bearing minerals like magnetite in granite could markedly slow the mass transport of 99Tc by reduction of Tc(VII) to Tc(IV), the apparent diffusion coefficient (D a) was decreased from 2.0 × 10−11–1.9 × 10−13 m2/s [15]. Whether this applies also to GMZ bentonite, which contains 0.29 % FeO [3], the diffusion behavior of 99Tc(VII) was investigate for the first time by through- and out-diffusion methods.

Materials and methods

Through- and out-diffusion experiments were carried out under atmospheric condition using GMZ bentonite (contains 75.4 wt% montmorillonite) from Beijing research institute of uranium geology without further processing. GMZ bentonite powder was pressed into a cylinder about 2.54 ± 0.01 cm diameter and 0.87 ± 0.01 cm thick. The dry densities were 1,600 and 1,800 kg/m3, respectively. All experiments were carried out in artificial pore water of Gansu Beishan at room temperature. 0.003 M NaN3 was added in the pore water to stop bacterial growth.

The diffusion set-up and experimental procedure were the same as that of used for through- and out-diffusion experiments [16]. For through-diffusion experiment, NH4 99TcO4 was put in a source reservoir with 200 mL, whereas the target reservoir had a volume 20 mL. Both out-reservoirs had a volume 20 mL for out-diffusion. The samples were measured by liquid scintillation counting (Perkin Elmer Tri-Carb 3170 TR/SL). 5 mL of sample was placed in a 20 mL polyethylene counting vial and 13 mL scintillation cocktail (Packard LLT USA) was added. The counting efficiency was 100 ± 0.05.

The experimental and theoretical data processing in through- and out-diffusion methods has been described previously [17]. A house-made computer code compiled by mathematica 6.0 named fitting for diffusion parameters (FDP) was used for the experimental and modeling data processing [16, 18].

Results and discussion

Figure 1 showed the accumulated activity (A cum) as a function of diffusion time obtained by through-diffusion experiments at 1,600 and 1,800 kg/m3 dry densities, respectively. A cum were increased with time relatively slow at the transient states, becoming a linear function of time at the steady phase. A cum were increased faster at 1,600 kg/m3 than that at 1,800 kg/m3. D e and rock capacity factor (α) were obtained by fitting the experimental data of A cum versus t including both transient and steady-state phases.

Fig. 1
figure 1

Measured (symbols) and fit (lines) A cum versus time at 1,600 and 1,800 kg/m3 compacted bentonite by through-diffusion methods, respectively

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Table 1 summarized the parameters used to fit the diffusion profile and the diffusion parameters results. V 0,dead and V l,dead are the dead volumes at the source- and out-reservoir sides, respectively. They contained the volume of the tubings, the grooves in the end plates and the filter pore space. D w (m2/s) is the bulk water diffusion coefficient. D w values was 1.95 × 10−9 m2/s [19]. K d, D a and geometrical factor (G) were calculated by following equations:

$$ \alpha = \varepsilon_{\text{tot}} + \rho \cdot K_{\text{d}} , $$
(1)
$$ D_{\text{a}} = \frac{{D_{\text{e}} }}{\alpha }, $$
(2)
$$ G = \frac{\varepsilon \cdot \delta }{{\tau^{2} }} = \frac{{D_{\text{e}} }}{{D_{\text{w}} }}, $$
(3)

where εtot (−) is the total porosity obtained from the diffusion results of HTO in GMZ bentonite [16]; ρ (kg/m3) is the bulk dry density; δ is the constrictivity factor, which represents the reduction in diffusivity due to the pore narrowing; τ is the tortuosity factor, which represents the reduction of diffusivity due to the path lengthening [20]. Because of the anion exclusion, K d values were less than zero. It was higher at 1,600 kg/m3 than that of at 1,800 kg/m3. εacc, D e and D a decreased with the increasing of dry density. The D e values were 10−11–10−12 m2/s, indicating that the dominating species was soluble TcO4 −. D e and G values were about 10 and 7 times higher at 1,600 kg/m3 than that at 1,800 kg/m3. Similar results can be found elsewhere [21]. It indicated that the pore was narrowed or the path of TcO4 − was lengthened when GMZ bentonite was pressed, because εacc decreased only three times, δ might decreased or τ might increased when the dry density increased from 1,600 to 1,800 kg/m3.

Table 1 Diffusion parameters for 99Tc in GMZ bentonite
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Figure 2 showed flux as a function of diffusion time. The flux increased with diffusion time at the transient phase and became constant at the steady phase. The experimental data of flux as a function of diffusion time were in good agreement with the modeled data. It showed that flux of 99Tc was higher at 1,600 kg/m3 than at 1,800 kg/m3. It took circa 3 days to reach the steady state at 1,600 kg/m3, while it took longer time (circa 7 days) to reach it at 1,800 kg/m3.

Fig. 2
figure 2

Measured (symbols) and expect (lines) flux versus time at 1,600 and 1,800 kg/m3 compacted bentonite by through-diffusion methods, respectively

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Figure 3 showed the flux as a function of diffusion time obtained by the out-diffusion experiments. The shaded area represented the uncertainty of the calculated curve. The first experimental data did not fit well with the modeled data at out-reservoir sides because of the activity in dead volume, the uncertainty of the solution volume and the measurement. At low-concentration side, the experimental and theoretical data were agreed with each other well, whereas the experimental data were systematically higher than theoretical data at high-concentration side. The slow release of 99Tc resulted in the higher diffusive flux. Since the high dry density of bentonite was employed in the experiments, the heterogeneous porosity at the clay boundaries can be neglect [22]. It can be explained that that the species 99Tc may be changed during the diffusion processing. Because the GMZ bentonite used in the experiments were untreated, it may contain Fe-bearing minerals. Some 99TcO4 − could be transformed to insoluble TcO2·nH2O. Similar results can be found the in situ diffusion experiments of 99TcO4 − in borehole laboratory [23]. However, the reactions happed in this procedure is unclear, further investigation is underway to clarify this phenomenon.

Fig. 3
figure 3

Out-diffusion of 99Tc in GMZ bentonite at 1,600 and 1,800 kg/m3 dry density, respectively

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Figure 4 showed the D e as a function of εacc. Here, εacc equals α for anion. For a given type of porous medium, D e can be related to D w and εacc by an empirical relationship analogous to Archie’s law [21, 24]:

$$ D_{\text{e}} = D_{\text{w}} \cdot \varepsilon_{\text{acc}}^{n} , $$
(4)

where n is the cementation factor and has a constant value related to a given type of porous medium. Our literatures search showed that a few studies of 99Tc diffusion in bentonite were focused on both D e and εacc. The diffusion behavior of 99Tc were compared between GMZ and Czech R-bentonite [25] in order to study the relationship of D e and εacc. It could be described by Archie’s law with exponent n = 1.2–2.8 in bentonite, whereas n was equal to 2.4 in GMZ bentonite.

Fig. 4
figure 4

The effective diffusion coefficient of 99Tc as a function of accessible porosity

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Previously research showed that an exponential relationship could be described between D a and dry density for 99Tc [14]. Figure 5 showed the relationship of the D a as a function of dry density in GMZ and other types of bentonite. D a and dry density could be described as the exponential relationship with intercept = 5.61 × 1010 and slope = −2.91 × 10−13. The linearly dependent coefficient R 2 was equal to 0.629. Then, it was showed that 99Tc had similar diffusion behavior in GMZ and other types of bentonite like MX-80, Avonlea etc. [13, 25–28], except that the species could be changed by Fe(II)-bearing minerals in the GMZ bentonite. However, little investigation was mentioned in other bentonite. Therefore, the diffusion parameters (D e and D a) of 99Tc in other bentonite could be proposed in the safety assessment for Chinese repository when there is lack of experimental results of GMZ bentonite.

Fig. 5
figure 5

The apparent diffusion coefficient of 99Tc as a function of dry density

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Conclusions

The diffusion behavior of 99Tc in GMZ bentonite was investigated by through- and out-diffusion methods at dry density of 1,600 and 1,800 kg/m3. D e and α were obtained by modeling both through- and out-diffusion experimental data with a computer code FDP. D e, D a and εacc were decreased with the increasing of dry density. Out-diffusion results showed that the experimental data were higher than that of theoretical data at the source-reservoir side. It could be explained that the species of 99Tc may be changed when they were diffused in Fe(II)-bearing minerals in the GMZ bentonite.

The relationship of D e and εacc can be explained by Archie’s law with exponent n = 2.4 for 99Tc diffusion in GMZ bentonite. The effective diffusion coefficient of anion can be estimated from the knowledge of both εacc and the corresponding exponent n. Furthermore, the relation between D a and ρ was exponential. 99Tc had similar diffusion behavior in GMZ and other types of bentonite like MX-80, Avonlea, Kunigel V1, etc.