Matrix diffusion and sorption of Cs+, Na+, I- and HTO in granodiorite: Laboratory-scale results and their extrapolation to the in situ condition

Dynamics of radionuclide electromigration in intact granite: An kinetic adsorption-advection-dispersion model and its application

Granite, as the natural barrier for the disposal of high-level radioactive waste, plays an important role in ensuring environmental and public safety. The safety assessment of the repository depends on the reliable migration parameters of radionuclides in granite. In this study, we developed a kinetic adsorption-advection-dispersion model based on first-order adsorption kinetics. It introduces a first-order adsorption rate coefficient to describe the kinetics of adsorption process and accounts for other crucial mechanisms affecting the migration of radionuclide ions, namely, the electromigration, electroosmosis, and dispersion. This model is then applied to interpret the experimental results of electromigration of tracer ions in intact granite. The results show that for the weakly adsorbed radionuclides studied, iodide and selenite, the effective diffusion coefficients and formation factors calculated by this model are in constant with those derived from the classical advection-dispersion model based on linear adsorption equilibrium. By contrast, for the moderately or strongly adsorbed tracer ions studied, including cobalt, cesium, and strontium, the migration parameters calculated by this model exhibit significantly less uncertainty than those obtained from the advection-dispersion model simulations. The advection-dispersion model based on the first order adsorption kinetics introduces the first order adsorption rate coefficient, and considers the influence of electromigration, electroosmosis and dispersion mechanism, which helps to explain the migration mechanism of nuclide ions in intact granite more accurately.

Diffusion and Sorption Studies of Cs, Sr and Co in Intact Crystalline Rock

Three cationic tracers, Sr2+, Co2+ and Cs+ were tested with a modified electromigration device by applying 2V, 3V and 4V voltage gradients over an intact Grimsel granodiorite rock sample. An ideal plug-flow model and an advection-dispersion model were applied to analyze the breakthrough curves. Matrix characterization by C-14-PMMA autoradiography and scanning electron microscopy showed that in the centimeter scale of Grimsel granodiorite rock, the interconnected matrix porosity forms a well-connected network for diffusion. Micrometer-scale fissures are transecting biotite and chlorite minerals, indicating sorption of the studied cations. The ideal plug-flow model indicated that the effective diffusion coefficients (De values) for Sr2+, Co2+ and Cs+ tracer ions within the Grimsel granodiorite rock were 3.20 × 10−13 m2/s, 1.23 × 10−13 m2/s and 2.25 × 10−12 m2/s, respectively. De values were also derived from the advection-dispersion model, from which 2.86 × 10−13 m2/s, 1.35 × 10−13 m2/s and 2.26 × 10−12 m2/s were calculated. The diffusion speed for the tracers was in the sequence of Cs+ > Sr2+ > Co2+ that is in the same sequence as their diffusion in diluted water. The distribution coefficients (Kd values) calculated from the models covered the range of two magnitudes (from 10−7 m3/kg to 10−5 m3/kg). The result indicated that the sorption process of the studied elements did not reach equilibrium during the electromigration process, mainly due to the too much acceleration of the migration speed by the voltage gradients applied over the rock sample.

Development and application of an advection-dispersion model for data analysis of electromigration experiments with intact rock cores

An advection-dispersion model was developed for interpreting the experimental results of electromigration in granitic rock cores. The most important mechanisms governing the movement of the tracer ions, i.e. electromigration, electroosmosis and dispersion were taken into account by the advection-dispersion model, but the influence of aqueous chemistry was ignored. An analytical solution in the Laplace domain was derived and then applied to analyze the measured results of a series of experiments, performed in an updated experimental device using different applied voltages. The modelling results suggested that both studied tracers, i.e. iodide and selenite, are effectively non-sorbing in the intact rock investigated. The effective diffusivities and formation factors evaluated from the model were also found to be in good agreement with data reported in literature and the associated uncertainties are much smaller than those obtained from the classical ideal plug-flow model, which accounts only for the dominant effect of electromigration on ionic transport. To explore further how the quality of parameter identifications would be influenced by neglect of aqueous chemistry, a reactive transport model was also implemented, which may be regarded as a multi-component version of the advection-dispersion model. The analysis showed that the advection-dispersion model works equally well as the reactive transport model but requires much less computational demand. It can, therefore, be used with great confidence to interpret the experimental results of electromigration for studies of diffusion and sorption behavior of radionuclides in intact rock cores.

A modification of the electromigration device and modelling methods for diffusion and sorption studies of radionuclides in intact crystalline rocks

To determine the diffusion and sorption properties of radionuclides in intact crystalline rocks, a new electromigration device was built and tested by running with I^- and Se(IV) ions. By introducing a potentiostat to impose a constant voltage over the studied rock sample, the electromigration device can give more stable and accurate experimental results than those from the traditional electromigration devices. In addition, the variation in the pH of the background electrolytes was minimised by adding a small amount of NaHCO₃ as buffers. To interpret the experimental results with more confidence, an advection-dispersion model was also developed in this study, which accounts for the most important mechanisms governing ionic transport in the electromigration experiments. Data analysis of the breakthrough curves by the advection-dispersion model, instead of the traditional ideal plug-flow model, suggest that the effective diffusivities of I^- and Se(IV) are (1.15 ± 0.06) × 10^-13 m²/s and (3.50 ± 0.86) × 10^-14 m²/s, respectively. The results also show that I^- is more mobile than Se(IV) ions when migrating through the same intact rock sample and that their sorption properties are almost identical.

Sorption of selenium species onto phlogopite and calcite surfaces: DFT studies

Sorption of Se(IV) and Se(VI) species onto Mg-rich biotite (phlogopite) and calcite surfaces was investigated using molecular modelling techniques. A CASTEP code implemented into Materials Studio was used to calculate the periodic systems, site densities and site types on the phlogopite and calcite surfaces. According to the results, the Se oxyanions attach to both edge and basal surfaces of phlogopite via an oxygen atom. However, calculated sorption energies indicate that surface complexation reactions via hydrogen bonding happen on the edge surfaces of phlogopite while cation exchange reactions happen on the basal surfaces of phlogopite. These reactions occur on the so-called weak sites according to the PHREEQC modelling. On the calcite surface, only cation exchange reactions are possible, and only for neutral Se species which do not occur in low saline groundwater conditions with pH 8-10. Biotite which is an abundant mineral in crystalline rock works fairly well as a sorbent but calcite which often exists on fracture surfaces of bedrock does not act as a sorbent for Se species.

Batch sorption experiments of cesium and strontium on crushed rock and biotite for the estimation of distribution coefficients on intact crystalline rock

The distribution coefficient (K_d) of radionuclides on bedrock is one of the key parameters used in the safety analysis of spent nuclear fuel repositories. Typically, distribution coefficients have been determined using crushed rock. However, recent studies have shown that crushing of the rock increases considerably the distribution coefficient compared with the values of intact rock. This study aimed to test if batch sorption experiments using different grain sizes (i.e. mean diameter of grains) can be used to evaluate the K_d of strontium (Sr) and cesium (Cs) on intact crystalline rock, which would decrease the needed experimental time compared with transport experiments. Here we report the results of the batch sorption experiments with crushed rocks and compare the results with those from a recent study performed using electromigration experiments with intact drill core samples (Puukko et al., 2018). The batch sorption experiments were done for rock samples from Olkiluoto, Finland, as a function of grain size and of Cs and Sr concentration. Furthermore, the specific surface areas of the same rock samples with different grain sizes were determined. It was shown that Cs distribution coefficients correlate with specific surface areas of the studied rocks and biotite, the correlation coefficient being 0.95. The Cs distribution coefficient was highest for biotite at about 0.1 m³/kg at 10⁻⁴ M cesium concentration and increased systematically to about 1 m³/kg at 10⁻⁸ M. Distribution coefficients for rocks were up to about two orders of magnitude lower, being lowest with the rock with the lowest biotite content (3.3%). The distribution coefficient of Sr varied from 0.04 m³/kg to 0.007 m³/kg and behaved in a different manner: it remained constant in two out of three studied rocks in the concentration range of 10⁻⁸-10⁻⁴ M and only in the case of one rock a decreasing trend was seen at the higher concentration range. It was also shown that batch sorption experiments overestimate the distribution coefficient in respect to intact rock. The decrease of the distribution coefficient as a function of grain size can be estimated using a power law function. It was also shown that estimation of distribution coefficients of Cs and Sr for intact rock by extrapolation of distribution coefficients determined for different grain sizes is not possible without increasing grain size, but in that case diffusion into the grains would also affect the results. A new method was developed for estimating the fraction of the inner surface area of the total surface area of crushed grains. For the mean grain sizes of 0.25 mm and 0.75 mm the fraction of the inner surface was found to be 35–70% and 60–90%, respectively. The inner specific surface area was highest with biotite at 1.2 m²/g and lowest with the rock with lowest biotite content (3.3%) at 0.07 m²/g. The surface area analysis revealed that crushing creates and/or allows access to additional inner surface area that is not measured in intact rock. Furthermore, it was demonstrated that sorption of Cs on crushed rock was dominated by mica minerals in multiple concentrations while the effect of mica minerals on the K_d of Sr was not as straightforward.

Through diffusion experiments to study the diffusion and sorption of HTO, 36Cl, 133Ba and 134Cs in crystalline rock

The spent nuclear fuel in Finland will be deposited in crystalline granitic rock in Olkiluoto, Finland. As a part of the safety assessment of the repository, series of extensive in-situ sorption and diffusion experiments and supplementary laboratory work has been done in the Olkiluoto site. Through Diffusion Experiment in a laboratory (TDElab) aims to provide applicable data for the ongoing in-situ experiment in Olkiluoto. This laboratory scale experiment resembles the in-situ experiment and aims to gain information on possible effects in values of distribution coefficients, effective diffusion coefficient and porosity that are caused by differences in laboratory and in-situ conditions. The through diffusion and sorption of tracer solution with known activities of HTO, ³⁶Cl, ¹³³Ba and ¹³⁴Cs were studied in a decimeter scale sample of veined gneiss, which is one of the main rock types in Olkiluoto. The measured breakthrough curves were modeled taking into account the porosity of the rock and diffusion and sorption of the radionuclides using Time-Domain Random Walk (TDRW) simulations. The porosities of 0.7-0.8% were determined for the rock and effective diffusion coefficients of (3.5 ± 1.0) × 10^-13 m²/s and (3.0 ± 1.0) × 10^-13 m²/s were determined for HTO and ³⁶Cl, respectively. The porosity and effective diffusion coefficients were found to be in agreement with previous results for veined gneiss. Furthermore, distribution coefficients of (1.0 ± 0.3) × 10^-4 m³/kg and (2.0 ± 0.5) × 10^-3 m³/kg were determined for ¹³³Ba and ¹³⁴Cs, respectively, using information about the effective diffusion coefficient determined for HTO. The distribution coefficients were found to be significantly smaller than the ones determined for crushed rock in previous studies and slightly smaller than the ones from previous in-diffusion experiments.

Electromigration experiments for studying transport parameters and sorption of cesium and strontium on intact crystalline rock

This study aims to determine upscaling factors for the radionuclides' distribution coefficients (K_d) on crushed rocks to intact rock for the safety analysis of radionuclide migration from spent nuclear fuel in bedrock towards biosphere. Here we report the distribution coefficients for intact rock determined by electromigration sorption experiments and compare the results with those from recently performed batch sorption experiments. In total 34 rock samples, representing three typical rock types from Olkiluoto Finland, were studied in order to determine distribution coefficients, effective diffusion coefficients and porosities using the electromigration sorption experiments, formation factor experiments and porosity measurement. The parameters determined represent the three main parameters of geosphere used in the safety assessment of spent nuclear fuel disposal. The distribution coefficients of cesium and strontium on intact rock varied between (0.12-26.2) × 10^-3 m³/kg and (1.4-13.3) × 10^-3 m³/kg, respectively, whereas recent results for crushed rock varied between (2-57) × 10^-3 m³/kg and (17-40) × 10^-3 m³/kg, respectively. This implies that crushing increases the distribution coefficient significantly and upscaling factors from 3 to 33 were determined for scaling the distribution coefficients of crushed rock to ones of intact rock. The determined distribution coefficients of cesium and strontium for intact rock can be directly applied in the safety assessment whereas the upscaling factors can be used to convert distribution coefficients determined for crushed rock into ones for intact rock. Based on the results for porosities and effective diffusion coefficients it was concluded that they do not seem to correlate with sorption parameters. However, an alteration state, heterogeneity and mineral content seem to be important factors affecting the distribution coefficients and upscaling factors.

The diffusion of 75Se(IV) in Beishan granite – temperature, oxygen condition and ionic strength effects

To explore the diffusion behavior of 75Se(IV) in Beishan granite (BsG), the influences of temperature, oxygen condition and ionic strength were investigated using the through-diffusion experimental method. The effective diffusion coefficient D e of 75Se(IV) in BsG varied from 4.21×10−14 m2/s to 3.19×10−13 m2/s in our experimental conditions, increased with increasing temperature. The formation factor F f of BsG was calculated to be nearly constant in the range of temperatures investigated, suggesting that the inner structure of BsG had no significant change in the temperature range of 20–55°C. Meanwhile, the D e values of 75Se(IV) in BsG under anaerobic condition was significantly larger than that under aerobic condition, which may be attributed to the difference in the sorption characteristics and species distribution of Se and pH values. Moreover, the diffusion of 75Se(IV) was promoted with ionic strength increased from 0.01 M to 0.1 M, and then decreased at 0.5 M, mainly due to the combined effects of reduced double layers with increased ionic strength and increase of the solution viscosity at higher ionic strength.

Effects of Mineral Compositions on Matrix Diffusion and Sorption of 75Se(IV) in Granite

Exploring the migration behaviors of selenium in granite is critical for the safe disposal of radioactive waste. The matrix diffusion and sorption of ⁷⁵Se(IV) (analogue for ⁷⁹Se) in granite were systematically studied to set reliable parameters in this work. Through-diffusion and batch sorption experiments were conduct with four types of Beishan granite. The magnitudes of the obtained apparent diffusion coefficient (D_a) values are of the following order: monzogranite > granodiorite-2 > granodiorite-1, which is opposite to the sequence of the K_d values obtained from both the diffusion model and batch sorption experiments. The EPMA results of the granitic flakes showed that there was no obvious enrichment of Se(IV) on quartz, microcline and albite. Only biotite showed a weak affinity for Se(IV). Macroscopic sorption behaviors of Se(IV) on the four types of granite were identical with the sequence of the granitic biotite contents. Quantitative fitting results were also provided. XPS and XANES spectroscopy data revealed that bidentate inner-sphere complexes were formed between Se(IV) and Fe(III). Our results indicate that biotite can be representative of the Se(IV) sorption in complex mineral assemblages such as granite, and the biotite contents are critically important to evaluate Se(IV) transport in granite.

Behavior of Cs in Grimsel granodiorite: sorption on main minerals and crushed rock

In this study the sorption of cesium was investigated on four different minerals; quartz, plagioclase, potassium feldspar and biotite as well as granodiorite obtained from the Grimsel test site in Switzerland. The experiments were conducted in the presence of the weakly saline Grimsel groundwater simulant by determining the distribution coefficients using batch sorption experiments and PHREEQC-modelling across a large concentration range. In addition, the purity of the minerals was measured byXRDand the specific surface areas by BET method using krypton. The distribution coefficients of cesiumwere largest on biotite (0.304±0.005 m3/kg in 10-8 M). Furthermore, the sorption of cesiumon quartzwas found to be negligibly small in all investigated concentrations and the sorption of cesium on potassium feldspar and plagioclase showed similar behavior against a concentration isotherm with distribution coefficients of 0.0368±0.0004 m3/kg and 0.18±0.04 m3/kg in 10-8 M. Finally, cesium sorption behavior on crushed granodiorite followed the trend of one of its most abundant mineral, plagioclase with distribution coefficient values of 0.107±0.003 m3/kg in 10-8 M. At low concentrations (<1.0·10-6 M) cesiumwas sorbed on the frayed edge sites of biotite and once these sites are fully occupied cesium sorbs additionally to the Type II and Planar sites. As a consequence, the sorption of cesium on biotite is decreased at concentrations >1.0·10-6 M. Secondly cesium sorption on potassium feldspar and plagioclase showed similar non-linear behavior with varying concentration. The results were used to assist the interpretation of cesium diffusion process in the 2.5 year in-situ experiment carried out in the underground laboratory at Grimsel test site in Switzerland (2007–2009).

Reconstruction of in-situ porosity and porewater compositions of low-permeability crystalline rocks: Magnitude of artefacts induced by drilling and sample recovery

Geological site characterisation programmes typically rely on drill cores for direct information on subsurface rocks. However, porosity, transport properties and porewater composition measured on drill cores can deviate from in-situ values due to two main artefacts caused by drilling and sample recovery: (1) mechanical disruption that increases porosity and (2) contamination of the porewater by drilling fluid. We investigated the effect and magnitude of these perturbations on large drill core samples (12-20 cm long, 5 cm diameter) of high-grade, granitic gneisses obtained from 350 to 600 m depth in a borehole on Olkiluoto Island (SW Finland). The drilling fluid was traced with sodium-iodide. By combining out-diffusion experiments, gravimetry, UV-microscopy and iodide mass balance calculations, we successfully quantified the magnitudes of the artefacts: 2-6% increase in porosity relative to the bulk connected porosity and 0.9 to 8.9 vol.% contamination by drilling fluid. The spatial distribution of the drilling-induced perturbations was revealed by numerical simulations of 2D diffusion matched to the experimental data. This showed that the rims of the samples have a mechanically disrupted zone 0.04 to 0.22 cm wide, characterised by faster transport properties compared to the undisturbed centre (1.8 to 7.7 times higher pore diffusion coefficient). Chemical contamination was shown to affect an even wider zone in all samples, ranging from 0.15 to 0.60 cm, in which iodide enrichment was up to 180 mg/kg water, compared to 0.5 mg/kg water in the uncontaminated centre. For all samples in the present case study, it turned out that the magnitude of the artefacts caused by drilling and sample recovery is so small that no correction is required for their effects. Therefore, the standard laboratory measurements of porosity, transport properties and porewater composition can be taken as valid in-situ estimates. However, it is clear that the magnitudes strongly depend on site- and drilling-specific factors and therefore our results cannot be transferred simply to other locations. We recommend the approach presented in this study as a route to obtain reliable values in future drilling campaigns aimed at characterising in-situ bedrock properties.

Comparative modeling of an in situ diffusion experiment in granite at the Grimsel Test Site

An in situ diffusion experiment was performed at the Grimsel Test Site (Switzerland). Several tracers ((3)H as HTO, (22)Na(+), (134)Cs(+), (131)I(-) with stable I(-) as carrier) were continuously circulated through a packed-off borehole and the decrease in tracer concentrations in the liquid phase was monitored for a period of about 2years. Subsequently, the borehole section was overcored and the tracer profiles in the rock analyzed ((3)H, (22)Na(+), (134)Cs(+)). (3)H and (22)Na(+) showed a similar decrease in activity in the circulation system (slightly larger drop for (3)H). The drop in activity for (134)Cs(+) was much more pronounced. Transport distances in the rock were about 20cm for (3)H, 10cm for (22)Na(+), and 1cm for (134)Cs(+). The dataset (except for (131)I(-) because of complete decay at the end of the experiment) was analyzed with different diffusion-sorption models by different teams (IDAEA-CSIC, UJV-Rez, JAEA) using different codes, with the goal of obtaining effective diffusion coefficients (De) and porosity (ϕ) or rock capacity (α) values. From the activity measurements in the rock, it was observed that it was not possible to recover the full tracer activity in the rock (no activity balance when adding the activities in the rock and in the fluid circulation system). A Borehole Disturbed Zone (BDZ) had to be taken into account to fit the experimental observations. The extension of the BDZ (1-2mm) is about the same magnitude than the mean grain size of the quartz and feldspar grains. IDAEA-CSIC and UJV-Rez tried directly to match the results of the in situ experiment, without forcing any laboratory-based parameter values into the models. JAEA conducted a predictive modeling based on laboratory diffusion data and their scaling to in situ conditions. The results from the different codes have been compared, also with results from small-scale laboratory experiments. Outstanding issues to be resolved are the need for a very large capacity factor in the BDZ for (3)H and the difference between apparent diffusion coefficients (Da) from the in situ experiment and out-leaching laboratory tests.