Through-diffusion Method Research Articles

Predicting anion diffusion in bentonite using hybrid machine learning model and correlation of physical quantities

Radionuclide diffusion will be influenced by numerous factors. Establishing a model that can elucidate the internal correlation between mesoscopic diffusion and the microscopic structure of bentonite can enhance the comprehension of radionuclide diffusion mechanisms. In this study, a light gradient boosting machine (LightGBM) was employed to predict the effective diffusion coefficients of HCrO4−, I−, and CoEDTA2− in bentonite. The model's hyperparameters were optimized using the particle swarm optimization (PSO) algorithm. Several correlated physical quantities, such as mesoscopic parameters (total porosity, rock capacity factor, and ion molar conductivity) and microscopic parameters (ionic radius and montmorillonite stacking number) were incorporated to develop a machine learning model that incorporated micro- and meso-scale features. The predictive performance of PSO-LightGBM was verified using diffusion experiments, which investigated the diffusion of HCrO4−, I−, and CoEDTA2− at compacted dry densities of 1200–1800 kg/m3 using a through-diffusion method. Spearman correlation and Shapley additive explanation analyses revealed that the compacted dry density, ionic diffusion coefficient in water, ionic radius, and total porosity were the top-four influencing factors among the 16 input features. Partial dependence plot analysis elucidated the relationship between the effective diffusion coefficient and each input feature. The analysis results were consistent with the experimental findings, demonstrating the reliability of machine learning. Due to the incorporation of multi-scale features, the PSO-LightGBM model demonstrated enhanced predictive accuracy, linking the microstructure of bentonite to radionuclide diffusion, and providing a comprehensive interpretation of the diffusion mechanism.

Analysis of the Role of Water Saturation Degree in HTO, 36Cl, and 75Se Diffusion in Sedimentary Rock

The aim of this study was to analyze HTO, 36Cl, and 75Se(IV) diffusion behavior in a sedimentary rock, which was obtained from the site initially selected for the emplacement of centralized temporal disposal of radioactive waste in Spain. Different experimental methodologies were used to analyze radionuclide diffusion in this rock: the through-diffusion (TD) method and the instantaneous planar source (IPS) methods. For the conservative tracers HTO and 36Cl, the effective diffusion coefficients, De, were obtained by the TD method, which was applied to the consolidated material taken at different orientations with respect to the bedding plane (parallel and normal). This revealed a negligible anisotropy of the rock. To analyze the effect of the water saturation degree, the IPS method was used, which was shown to be very suitable for evaluating these effects. For these tests, the samples were crushed, adequately hydrated, and compacted. The apparent diffusion coefficient, Da, was determined for all the tracers at five different water saturation degrees. For each of the tracers investigated, the results indicated that, when the water saturation decreased from 100% to 60%, the Da also decreased by at least one order of magnitude: for HTO, this decrease was from 1.5 × 10−9 to 2.3 × 10−10 m2/s; that for 36Cl was from 4.6 × 10−10 to 2.8 × 10−11 m2/s; and that for 75Se was from 3.6 × 10−11 to 8.3 × 10−13 m2/s. The experimental diffusion profiles of HTO and 36Cl could be satisfactorily fitted considering a unique diffusion coefficient, whereas the profiles of 75Se could not. This behavior is related to the existence of different species of selenium in the system, or to different retention mechanisms.

Restriction of Re(VII) and Se(IV) diffusion by barite precipitation in compacted bentonite

The diffusion of anionic radionuclides in bentonite buffers for a high-level radioactive waste repository is only minimally retarded due to the anion exclusion effect and the low sorption onto the bentonite. In this study, barite precipitates in compacted barium-modified bentonite (Ba-bentonite) were used to study the restriction of the diffusion of Re(VII) and Se(IV). To this end, a synthetic porewater containing sulfate was placed in contact with compacted Ba-bentonite so that the sulfate ions could diffuse in the pores and produce barite precipitates. The Ba-bentonite and the bentonite with barium sulfate (BBS) retained the original interlayer structure based on X-ray diffractometer (XRD) analysis. Scanning electron microscopy (SEM) analysis revealed that the barite precipitates were formed in the inter-aggregate pores. A through-diffusion method was employed to measure the effective diffusion coefficient and the rock capacity factor of Re(VII) and Se(IV) in compacted Gaomiaozi (GMZ) bentonite, Ba-bentonite, and BBS. The effective diffusion coefficient decreased with increasing the compacted dry density of the three bentonites, and it decreased with increasing the amount barite precipitates in the BBS. The diffusive flux was completely stopped by the formation of high amounts of barite precipitates. The relationship between the effective diffusion coefficient and the accessible porosity could be described by Archie's law. The cementation factor of BBS was 2.9 for Re(VII) and 3.2 for Se(IV). Compared to the GMZ and Ba-bentonites, the high cementation factor of the BBS indicated a low connectedness and/or a high tortuosity. It had a better clogging effect on anion diffusion than the Ba- and GMZ bentonites.

Porosity investigation of compacted bentonite using through-diffusion method and multi-porosity model

The diffusion behavior of ReO4− and HSeO3− in low-grade bentonites was firstly investigated under different compacted dry densities. The effective diffusion coefficient, the accessible porosity, and the rock capacity factor were measured by a through-diffusion method. The effective diffusion coefficient was approximately three times in Zhisin bentonite with 36.8 wt% of montmorillonite than that in GMZ bentonite with 74.5 wt% of montmorillonite. The porosity distribution of the compacted bentonite was analyzed by a multi-porosity model. The effects of the compacted dry density, the ionic strength, and the stacking number on porosities were discussed. The compacted dry density had obvious influence on the accessible porosity, the diffuse double layer porosity, and the interlayer porosity. The effects of ionic strength and stacking number were mainly on the diffuse double layer porosity, leading to the alteration of the accessible porosity and the effective diffusion coefficient. Moreover, the multi-porosity model could successfully predict the trend of effective diffusion coefficient in compacted bentonite combined with Archie law, which provides a useful tool to understand the relationship between the microstructure of montmorillonite and the diffusion of radionuclide anions.

Investigating diffusion mechanism for HTO and Se(IV)/Se(VI) in compacted Tamusu clay rock with different column lengths

Abstract Due to continuous self-sealing and good mechanical properties, the Tamusu clay rock of Inner Mongolia has been identified as the pre-selected site for high-level radioactive waste geological disposal site in China. The study of chemical behaviors related to Tamusu clay rock, such as nuclide migration, will be an important content of the performance assessment and safety assessment of the disposal repository in the future. The diffusion behavior of HTO and Se(IV)/Se(VI) with different compacted column lengths in Tamusu clay rock is discussed by the through-diffusion method. The diffusion coefficient, rock capacity factor, effective porosity, and other diffusion parameters closely related to nuclide migration are calculated, and the mechanism of nuclide diffusion is preliminarily discussed. The results show that D a (6.23 × 10−11∼17.96 × 10−11 m2 s−1), D e (1.62 × 10−11∼4.67 × 10−11 m2 s−1) for HTO increase with the increase of the compacted column length, and it is proposed that the diffusion process of HTO is affected by the change of geometrical factor and path tortuosity. D a (7.29 × 10−13∼1.74 × 10−13 m2 s−1), D e (5.15 × 10−12∼2.15 × 10−12 m2 s−1) for Se(IV), D a (3.11 × 10−12∼1.09 × 10−12 m2 s−1), D e (2.53 × 10−12∼1.09 × 10−12 m2 s−1) for Se(VI), which decrease with the increase of the compacted column length, it is mainly due to the existence of anion repulsion effect.

Thermodiffusion of ions in nanoconfined aqueous electrolytes

Understanding of thermal effects on ion transport in porous media is very important for environmental applications. The movement of ions along a temperature gradient is named thermophoresis or thermodiffusion. In nanoporous media, where the interaction of ions with solid–liquid interfaces has a significant influence on their migration, the theoretical understanding of thermodiffusion is still incomplete. Herein, we present experimental results for the thermodiffusion of cations in saturated nanoporous silica by the through-diffusion method. Both the experimental data and theoretical analysis indicate that the temperature-induced polarization of surface charges strongly influences ionic transport. Stated simply, the electric field in a liquid electrolyte confined in nanopores changes when the applied temperature gradients are altered, thereby affecting the motion of the nanoconfined ionic species. By applying an external temperature field, the gradient of the surface charge density leads to the charged aqueous species exhibiting strong temperature gradient-dependent electrophoretic mobility. When the thickness of the electrical double layer is comparable to the size of the nanopores, the theory used herein indicates that this kind of nonisothermal ionic mobility is up to one order of magnitude larger than classical thermophoretic mobility. This study improves the understanding of the underlying mechanisms that govern the transport of ions in nanoporous media, which could set the stage for diffusional metamaterials induced by specific thermal fields.

Investigation of Re(VII) diffusion in Tamusu clayrock core by through-diffusion method

Abstract Tamusu area is the primary pre-selection site of clayrock disposal repository for high-level radioactive waste (HLW) in China. However, the research on the migration behavior of nuclides in Tamusu clayrock is still in its infancy. For the first time in laboratory, the diffusion behavior of Re(VII) in Tamusu clayrock core was studied by means of through-diffusion method. The effects of pH, ionic strength and humic acid on the diffusion behavior of Re(VII) in clayrock were studied. The effective diffusion coefficient, apparent diffusion coefficient and rock capacity factor value were obtained. All the experimental conditions of Re(VII) diffusion in Tamusu clayrock are compared with other geological samples under the same conditions in literature data. The diffusion mechanism of radionuclide in Tamusu clay is discussed, which can provide experimental data for site selection and safety assessment of high-level radioactive waste repository in China. The experimental results showed an effective application and reference for the countries disposed HLW in mudrocks or clayrocks, such as France, Belgium etc. in Europe. Moreover, this research can provide the original data support for the metallogenic regularity and prospecting prognosis of rare element rhenium in different geological environments.

Diffusion behavior of Se(IV) in Tamusu clayrock core by through-diffusion method

Diffusion behavior of Se(IV) in Tamusu clayrock core by through-diffusion method

Anion exclusion and sorption effect for compacted bentonite: the dependency of diffusion coefficients and capacity of HTO and Se(IV)

Quantitative calculation based on the joint action of anion exclusion and sorption has not been reported. This article studies the diffusion behavior of Se(IV) in MX-80 bentonite fills in different lengths by the through-diffusion method. The anion exclusion and sorption are simultaneously considered and quantitatively calculated. The results show that the effective diffusion coefficient of Se(IV) decreases with the increasing lengths of bentonite plug, because of the joint action of anion exclusion and sorption. On this basis, the anion exclusion and sorption are first quantitatively calculated, then a new theory for calculation is proposed in this article. The calculation results show that the ratio of anion exclusion and sorption. In groundwaterenvironments and seawaterenvironments, the weight of sorption is lower than anion exclusion in diffusion process.

Diffusion of Re(VII) and Se (IV) in compacted GMZ bentonite in the presence of Bacillus spp.

The effect of Bacillus spp. on Re(VII) and Se(IV) diffusion in compacted GMZ bentonite was investigated by a through-diffusion method. Bacillus spp. had no significance effect on the effective diffusion coefficient (De) and the accessible porosity (eacc) of Re(VII), whereas a decrease of De and an increase of distribution coefficient (Kd) were observed for Se(IV). Moreover, Archie’s law and an exponential decay equation were employed to fit the De value of Re(VII) and Se(IV).

The influence of pH on diffusion of 75Se(IV) in Beishan granite

The through-diffusion method and batch sorption experiments were used to explore the influence of pH on the diffusion behavior of 75Se(IV) in matrix Beishan granite (BsG). In the pH range of 2.0–8.5, the De values of 75Se(IV) in BsG decreased first and then increased with pH increasing, while the changing trend of Kd was nearly opposite. It was speculated that the influence of pH on the diffusion of 75Se(IV) in BsG was due to the joint effects of different species distribution of Se, change in surface charge of BsG and change in ionic strength at various pH values.

Investigation of Re(VII) diffusion in bentonite by through-diffusion and modeling techniques

Abstract The interlayer cation of bentonite has obviously influence on the diffusion behavior of radionuclides. The diffusion behavior of Re(VII) in Na+- and Ca2+-bentonites was investigated by a through-diffusion method at bulk dry densities from 1000 kg/m3 to 1800 kg/m3. A modified multi-porosity model (APM), which subdivided the porosity into the interlayer porosity (eil), the diffuse double layer porosity (eddl) and free layer porosity (efree) in compacted bentonite, is employed to describe the distribution of the three porosities as a function of the bulk dry density and to explain the lower effective diffusion coefficient (De) and accessible porosity (eacc) of Re(VII) in Na+-bentonite compared to that in Ca2+-bentonite. With increasing bulk dry density, eacc decreased, leading to a decrease of De for Re(VII). eddl and eil are both related to the montmorillonite bulk dry density. Moreover eddl is also related to the external surface area (Aext) and the ionic strength. APM was successful in reproducing trends of eacc data for Re (this work), 35Cl and 125I (data from the literature) as a function of the bulk dry density. Compared to Ca2+-bentonite, Na+-bentonite had higher eil and eddl at the same compaction, indicating a less proportion of large pores. After combing with Archie's law, the dependency of De on bulk dry density was reproduced with a cementation factor of 2.2 and 2.6 for Na+- and Ca2+-bentonites, respectively.

Water Mobility within Compacted Clay Samples: Multi-Scale Analysis Exploiting 1H NMR Pulsed Gradient Spin Echo and Magnetic Resonance Imaging of Water Density Profiles.

1H NMR pulsed gradient spin echo attenuation and water density profile analysis by magnetic resonance imaging are both used to determine the mobility of water molecules confined within a porous network of compacted kaolinite clay sample (total porosity of ∼50%). These two complementary experimental procedures efficiently probe molecular diffusion within time scales varying between milliseconds and few hours, filling the gap between the time scale of diffusion dynamics measured by traditional quasi elastic neutron scattering and through-diffusion methods. Furthermore, magnetic resonance imaging is a nondestructive investigation tool that is able to assess the effect of the local structure on the macroscopic mobility of the diffusing probe.

Mobility of chloride through cement-based materials under partially saturated conditions

This work presents two complementary techniques to study 36Cl and stable chloride diffusion through unsaturated cement-based materials for saturation degrees (Sw) ranging from 0.18 to 1. The first technique is based on steady-state through-diffusion method where suction (up to 9 MPa) is controlled using osmosis process. In the second technique, in-diffusion experiments are performed by putting into contact a spiked-fresh-cement paste with a CEM-V/A-hardened-cement paste (HCP) sample (initial water to cement ratio of 0.4) having a given water saturation imposed by saline solution method. After a controlled diffusion time, the 36Cl activity profiles within the samples are acquired by means of the abrasive peeling method and 36Cl activity is determined by liquid scintillation counting (LSC) technique. The application of the first technique resulted in data showing a sharp decrease of the effective diffusion coefficient (De) (by a factor of ten) between the experiments done on the fully-saturated HCP sample and the HCP sample at Sw = 0.85. Moreover, duplicate in-diffusion experiments carried out on HCP samples partially-saturated at Sw = 0.86 provided 36Cl De range well bracketing the one determined by the first approach at Sw = 0.85. Four other in-diffusion experiments were thus performed on HCP samples with saturation degrees down to 0.18. Interpretation of the experimental results showed a very small decrease of De values for Sw from 0.74 to 0.41 and a sharp decrease for Sw from 0.41 to 0.18. Lastly, comparison with the diffusive behavior of tritiated water (HTO) through unsaturated CEM V/A HCP samples clearly indicated that diffusion of chloride was more affected by desaturation than HTO. Its ionic form would restrict chloride to the liquid phase whom continuity is broken when dehydration is strong enough.

Comparison of experimental methods for estimating matrix diffusion coefficients for contaminant transport modeling

Diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating effective matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of effective matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged from 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than effective matrix diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields effective matrix diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.

Diffusion of Re(VII) in gamma-irradiated bentonite: effect of compacted dry density and pH

The diffusion behavior of Re(VII) in γ-irradiated Gaomiaozi bentonite was investigated by a through-diffusion method at different dry densities and pH values. The dependency of effective diffusion coefficient (D e) on the dry density could be described by an exponential decay function, and the relationship of D e and accessible porosity (e acc) followed Archie’s law. Generally, radiation-induced effect resulted in no obvious difference in Re(VII) diffusion.

Barrier properties of crystalline rocks in radionuclide migration

The parameters of the diffusion–sorption interaction of rocks with Sr, Cs, U, Np, Pu, and Am isotopes dissolved in simulated groundwater were determined by in- and through-diffusion methods for monolithic rock samples (gneisses, dolerites, lamprophyres) from the Yeniseisky site of the Nizhnekansy massif. Despite heterogeneous mineral composition and structure of the rocks, these parameters mainly depend on the physicochemical properties of the element and on the open porosity of the rock. The effective diffusion coefficients D e vary in the order Sr = Cs ≫ U > Np > Am ≥ Pu, dividing these elements into two groups, the difference between which is 1.5–2 orders of magnitude. With respect to the apparent diffusion coefficient D a, the elements are also subdivided into two groups, Sr = Cs > Np ≥ U ≫ Am > Pu, differing by 5 orders of magnitude because of different sorbability of the elements: Pu > Am ≫ Cs = Sr > U > Np. The end members of this series differ in the sorption capacity coefficient of the rocks, α = D e/D a, by 4.5 orders of magnitude.

Salt effects on Re(VII) and Se(IV) diffusion in bentonite

The through-diffusion method was employed to investigate the effect of the salt concentration on the diffusion behaviour of Re(VII) and Se(IV) in compacted bentonite. The accessible porosity, εacc, of Re(VII) increased from 0.25 to 0.38 with an increase of the ionic strength from 0.1 to 1.0mol/L. The dependency of the accessible porosity εacc on the salt concentration could be described approximately by a first-order decay exponential function. The interlayer porosity of GMZ bentonite was 21% of the total porosity at a bulk dry density of 1600kg/m3 at 12°C. The De values of Re(VII) and Se(IV) increased from 2.6×10−11 to 6.1×10−11m2/s and from 1.6×10−11 to 4.7×10−11m2/s in GMZ bentonite with an increase of the ionic strength from 0.1 to 1.0mol/L, respectively. In the case of Se(IV), the adsorption showed a different ionic strength dependency in GMZ bentonite and montmorillonite. The ionic strength has no significant effect on the adsorption (Kd=1.8×10−4m3/kg) on GMZ bentonite, indicating the formation of inner-sphere surface complexes. In the case of synthetic montmorillonite, the Kd values increased with increasing ionic strength. This can be explained by the fact that the electric potential of surface sites becomes less negative with increasing ionic strength resulting in an increase in the adsorption of Se(IV) at a pH above the point of zero salt effect (PZSE). The De values of both Re(VII) and Se(IV) increased with increasing salt concentration. Both anions are totally excluded from the interlayer space and partially from the diffuse double layer. Ionic strength alters the effective diffusion coefficient of anions by controlling the thickness of the diffuse double layer. Anion diffusion data from the literature (effective and apparent diffusion coefficients) were satisfactorily evaluated by Archie's relation.

Diffusion behavior of Re(VII) in compacted illite-, hematite- and limonite-montmorillonite mixtures

A through-diffusion method was used to investigate the Re(VII) (as a surrogate to 99Tc(VII)) diffusion in compacted illite-, hematite- and limonite-montmorillonite mixtures. The effective diffusion coefficient De values were in the range of (4.29–6.71) × 10−11 m2/s at pH 3.0 and (3.44–5.72) × 10−11 m2/s at pH 9.0, respectively. Compared to montmorillonite, both De and α values enhanced at least three-folds in montmorillonite mixtures, indicating that the impurities changed the diffusion path. Interestingly, the Kd values of (0.63–3.94) × 10−4 kg/m3 were found in montmorillonite mixtures. However, the change of Da value was less than two-folds, indicating that the illitization and iron corrosion of a back-fill material had no obvious influence on Re(VII) diffusion velocity.

PH effect on Re(VII) and Se(IV) diffusion in compacted GMZ bentonite

In a high-level radioactive waste (HLW) repository, pH has an impact on the solubility, migration, and adsorption of radionuclides. Thus, understanding the effects of pH on the diffusion of radionuclides is essential for long-term disposal of HLW. In this work, the diffusion behaviors of Re(VII) and Se(IV) in compacted Gaomiaozi (GMZ) bentonite at different pH have been investigated by a through-diffusion method. The effective diffusion coefficient, i.e., De values of Re(VII) and Se(IV) were in the range of (1.0–2.4) × 10−11 m2/s at pH 3.0–10.0 and (0.38–2.3) × 10−11 m2/s at pH 3.0–9.0. In the case of Re(VII), the De values remained almost unchanged probably because ReO4− was the dominant species in the pH range of 3.0–10.0. In the case of Se(IV), whose predominant species were HSeO3− at pH < 9.0 and SeO32− at pH ≥ 9.0, the De values decreased by a factor of 3–6 at pH 9.0, i.e., De (pH < 9.0)/De (pH 9.0) ≈ 3–6, implying that the species with a higher valence state had a stronger anion exclusion effect. The decrease in De values can be explained by the diffusion species of Se(IV). Additionally, the rock capacity factor α decreased with the increase of pH. HSeO3− was absorbed on GMZ bentonite with distribution coefficient Kd values in the range of (1.0–2.5) × 10−4 m3/kg at pH ≤ 8.0, whereas SeO32− was negligibly sorbed at pH > 8.0.