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

Assessment of natural radionuclide transfer factors and partition coefficients in some Syrian soils

Transfer factors of radium 226(²²⁶Ra), lead 210(²¹⁰Pb), polonium 210 (²¹⁰Po), uranium 238 (²³⁸U) and thorium 234(²³⁴Th) from five different agricultural soils in Syria to coriander, parsley and mint were investigated in a pot culture experiment. Geometric means of transfer factors (TF)were²²⁶Ra (0.13),²¹⁰Pb(0.03), ²¹⁰Po (0.02) and ²³⁸U (1.76) were within worldwide values, while TF values for ²³⁴Th (1.35) were higher than those recorded globally. The available transfer factor (ATF) values ranged between 0.03 and 1.45, 0.33 and 3.2, 0.10 and 3.36, 1.30 and 16.2 and 1.0 and 6.95 for²²⁶Ra,²¹⁰Pb,²¹⁰Po, ²³⁸U and ²³⁴Th, respectively. However, it is worth mentioning that the data from pot experiments may not represent field conditions. Liquid/solid partition coefficients (K_d)of ²²⁶Ra, U, ²¹⁰Pb and ²¹⁰Po for55 soils representing the dominant types of soils in Syria were also determined. Geometric means of K_d values ranged from 280 to1200, 750 to1600, 350to 4800 and 100-120 L kg^-1 for ²²⁶Ra, ²³⁸U, ²¹⁰Pb and ²¹⁰Po, respectively at pH = 4.0, and from 200 to 6700, 670 to 2400, 150 to 2100 and 100 to 160Lkg^-1at pH = 5.5, and from 370 to 790, 130 to 550, 60 to 330 and370 to 920Lkg^-1at pH = 7.0. The effects of soil mineral content, CEC, ECE, pH and soluble ions on the K_d values were investigated. In general, there were logarithmic relationships between the activity concentrations in soil and the K_d values (R² ranged from 0.59 to 1.00 at pH 4.0). There were no relationships between the K_d values and soil pH.

Some aspects of the adsorption of glyphosate and its degradation products on montmorillonite

The most worldwide used herbicide is glyphosate, phosphonomethylglycine (PMG). Consequently, a significant amount of PMG, its metabolites (sarcosine, SAR, and aminomethylphosphonic acid, AMPA) and the degradation product, methylphosphonic acid (MPA), reaches the soil, which acts as final sink. Because clays are one of the most reactive components of soils, expansive clays such as montmorillonite (Mt) are used to retain agriculture contaminants with some success. In this work, as a preliminary step for the evaluation of the risk that PMG, SAR, AMPA, and MPA occurrence could have on the environment, their adsorption on Mt surface was performed. The adsorption process was analyzed at constant adsorbate concentrations and two pH values to take into account the different protonation states of the amino group. DTA, XRD, zeta potential measurements, and XPS were used to identify the interactions or association mechanisms with the clay surface, the entry of adsorbates into the Mt interlayer, and electric charge changes on the Mt surface, and evaluate the acid-base surface complex constants, respectively. The interlayer thickness in acid media indicated that adsorbates are able to enter the interlayer in planar form. Besides, for the Mt-PMG sample, some PMG molecules could be also inserted as a bilayer or with a tilt angle of 52.4° in the interlayer. However, in alkaline media, the interlayer thickness indicated that the adsorbate arrangement differed from that of acidic media where PMG and MPA could have more than one orientation. The surface complex deprotonation constants were determined for the =NH+2 ⇆ =NH+H+ process, being 3.0, 5.0, and 7.3 for PMG, AMPA, and SAR, respectively.

Decreasing Kd uncertainties through the application of thermodynamic sorption models

Radionuclide retardation processes during transport are expected to play an important role in the safety assessment of subsurface disposal facilities for radioactive waste. The linear distribution coefficient (Kd) is often used to represent radionuclide retention, because analytical solutions to the classic advection-diffusion-retardation equation under simple boundary conditions are readily obtainable, and because numerical implementation of this approach is relatively straightforward. For these reasons, the Kd approach lends itself to probabilistic calculations required by Performance Assessment (PA) calculations. However, it is widely recognised that Kd values derived from laboratory experiments generally have a narrow field of validity, and that the uncertainty of the Kd outside this field increases significantly. Mechanistic multicomponent geochemical simulators can be used to calculate Kd values under a wide range of conditions. This approach is powerful and flexible, but requires expert knowledge on the part of the user. The work presented in this paper aims to develop a simplified approach of estimating Kd values whose level of accuracy would be comparable with those obtained by fully-fledged geochemical simulators. The proposed approach consists of deriving simplified algebraic expressions by combining relevant mass action equations. This approach was applied to three distinct geochemical systems involving surface complexation and ion-exchange processes. Within bounds imposed by model simplifications, the presented approach allows radionuclide Kd values to be estimated as a function of key system-controlling parameters, such as the pH and mineralogy. This approach could be used by PA professionals to assess the impact of key geochemical parameters on the variability of radionuclide Kd values. Moreover, the presented approach could be relatively easily implemented in existing codes to represent the influence of temporal and spatial changes in geochemistry on Kd values.

Measurement and modelling of reactive transport in geological barriers for nuclear waste containment

Unit cell illustrating potential diffusion paths (bonds, yellow and red) in the neighbourhood of central particle (green); these join neighbouring cell faces and show where elongated pores may be assigned to the experimental pore system information.

Radionuclide interaction with clays in dilute and heavily compacted systems: a critical review

Given the unique properties of clays (i.e., low permeability and high ion sorption/exchange capacity), clays or clay formations have been proposed either as an engineered material or as a geologic medium for nuclear waste isolation and disposal. A credible evaluation of such disposal systems relies on the ability to predict the behavior of these materials under a wide range of thermal-hydrological-mechanical-chemical (THMc) conditions. Current model couplings between THM and chemical processes are simplistic and limited in scope. This review focuses on the uptake of radionuclides onto clay materials as controlled by mineral composition, structure, and texture (e.g., pore size distribution), and emphasizes the connections between sorption chemistry and mechanical compaction. Variable uptake behavior of an array of elements has been observed on various clays as a function of increasing compaction due to changes in pore size and structure, hydration energy, and overlapping electric double layers. The causes for this variability are divided between "internal" (based on the fundamental structure and composition of the clay minerals) and "external" (caused by a force external to the clay). New techniques need to be developed to exploit known variations in clay mineralogy to separate internal from external effects.

Diffusion of Cesium and Iodine in Compacted Sodium Montmorillonite Under Different Saline Conditions

Diffusion and sorption of cesium (Cs) and iodine (I) were investigated in a purified and moderately compacted sodium montmorillonite (dry density of 800 kg m-3) saturated with 0.01, 0.1 and 0.5M NaCl solutions. The effective diffusivity (De) and capacity factor (α) for Cs and I were measured by through-diffusion experiments, coupled with multiple curve analyses, including tracer depletion, breakthrough and depth concentration curves, which could be fitted with a conventional diffusion model using only one set of parameters. The De values obtained for Cs were of the order of 10-9-10-10 m2 s-1 and decreased as salinity increased, and those for I were of the order of 10-11-10-12 m2 s-1 and showed the opposite dependency. The distribution coefficient (Kd) of Cs decreased from the order of 100 to 10-2 m3 kg-1 as salinity increased. Diffusion and sorption parameters for Cs were also obtained by in-diffusion and batch sorption experiments and showed good agreement with those obtained by the through-diffusion experiments. The diffusion model, based on homogeneous pore structure and electrical double layer (EDL) theory, predicted the salinity dependence of De reasonably well, showing the effect of cation excess and anion exclusion as a function of salinity. The apparent diffusivity (Da), which includes sorption effects, was also interpreted by a coupled sorption model.

Diffusion and sorption of neptunium(V) in compacted montmorillonite: effects of carbonate and salinity

Diffusion and sorption of radionuclides in compacted bentonite/montmorillonite are key processes in the safe geological disposal of radioactive waste. In this study, the effects of carbonate and salinity on neptunium(V) diffusion and sorption in compacted sodium montmorillonite were investigated by experimental and modeling approaches. Effective diffusion coefficients (De) and distribution coefficients (Kd) of237Np(V) in sodium montmorillonite compacted to a dry density of 800 kg m−3were measured under four chemical conditions with different salinities (0.05/0.5 M NaCl) and carbonate concentrations (0/0.01 M NaHCO3).Devalues for carbonate-free conditions were of the order of 10−10–10−11 m2s−1and decreased as salinity increased, and those for carbonate conditions were of the order of 10−11–10−12 m2s−1and showed the opposite dependence. Diffusion-derivedKdvalues for carbonate-free conditions were higher by one order of magnitude than those for carbonate conditions. Diffusion and sorption behaviors were interpreted based on mechanistic models by coupling thermodynamic aqueous speciation, thermodynamic sorption model (TSM) based on ion exchange, and surface complexation reactions, and a diffusion model based on electrical double layer (EDL) theory in homogeneous narrow pores. The model predicted the experimentally observed tendency ofDeandKdqualitatively, as a result of the following mechanisms; 1) the dominant aqueous species are NpO2+and NpO2CO3−for carbonate-free and carbonate conditions, respectively, 2) the effects of cation excess and anion exclusion result in opposite tendencies ofDefor salinity, 3) higher carbonate in solution inhibits sorption due to the formation of carbonate complexes.

Diffusive transport of neptunium and plutonium through compacted sand-bentonite mixtures under anaerobic conditions

Diffusive transport of neptunium, plutonium, tritiated water (HTO), Cs+and I-in compacted sand-bentonite mixtures was studied by a through-diffusion method. Experiments for Np were performed in the presence of carbonate where Np is stable as NpIV(CO3)2(OH)22-and those for Pu in the presence of fulvic acid where the Pu is stable as fulvic complexes. These experiments were performed under Ar (pO2< 10-6atm). Effective diffusivity (De) values of (1.81 ± 0.03) × 10-10, (1.8 ± 0.8) × 10-10, (5.1 ± 0.8) × 10-11and (9.0 ± 4.1) × 10-11m2s-1were obtained for HTO, Cs+, I-and Np(CO3)2(OH)22-, respectively. The ratio of theDeto the diffusivity in bulk of the water was around 0.1 for Np(CO3)2(OH)22-, HTO and Cs+, which is consistent with the pore diffusion model. Observed diffusive transport of Pu was much smaller than those of HTO, Cs+, I-and Np(CO3)2(OH)22-probably because Pu was present as colloidal forms and that confined pore space in the compacted sand-bentonite mixtures does not allow diffusive transport of colloidal plutonium.

New best estimates for radionuclide solid-liquid distribution coefficients in soils. Part 1: radiostrontium and radiocaesium

Best estimates for the solid-liquid distribution coefficients (K(d)) of radiostrontium and radiocaesium for various soil types, were derived from geometric means (GM) calculated from grouping soils by texture and organic matter content, and also using soil cofactors governing soil-radionuclide interaction. The K(d) (Sr) GM for Sand, Loam, Clay and Organic groups were similar, although the value for the Sand group was significantly lower. The Sr cofactor approach, based on the ratios of cation exchange capacity (CEC) to Ca and Mg concentrations in the soil solution, leads to K(d) (Sr) GM with a lower variability, from which best estimates could be proposed. The K(d) (Cs) GM for Sand and Organic groups differed, although similar values were obtained for Loam and Clay groups. Grouping the K(d) (Cs) according to the Radiocaesium Interception Potential (RIP) and the RIP divided by the K concentration in the soil solution also allows to suggest K(d) (Cs) best estimates with a lower variability.

Long-term geochemical evolution of the near field repository: insights from reactive transport modelling and experimental evidences

The KBS-3 underground nuclear waste repository concept designed by the Swedish Nuclear Fuel and Waste Management Co. (SKB) includes a bentonite buffer barrier surrounding the copper canisters and the iron insert where spent nuclear fuel will be placed. Bentonite is also part of the backfill material used to seal the access and deposition tunnels of the repository. The bentonite barrier has three main safety functions: to ensure the physical stability of the canister, to retard the intrusion of groundwater to the canisters, and in case of canister failure, to retard the migration of radionuclides to the geosphere. Laboratory experiments (< 10 years long) have provided evidence of the control exerted by accessory minerals and clay surfaces on the pore water chemistry. The evolution of the pore water chemistry will be a primordial factor on the long-term stability of the bentonite barrier, which is a key issue in the safety assessments of the KBS-3 concept. In this work we aim to study the long-term geochemical evolution of bentonite and its pore water in the evolving geochemical environment due to climate change. In order to do this, reactive transport simulations are used to predict the interaction between groundwater and bentonite which is simulated following two different pathways: (1) groundwater flow through the backfill in the deposition tunnels, eventually reaching the top of the deposition hole, and (2) direct connection between groundwater and bentonite rings through fractures in the granite crosscutting the deposition hole. The influence of changes in climate has been tested using three different waters interacting with the bentonite: present-day groundwater, water derived from ice melting, and deep-seated brine. Two commercial bentonites have been considered as buffer material, MX-80 and Deponit CA-N, and one natural clay (Friedland type) for the backfill. They show differences in the composition of the exchangeable cations and in the accessory mineral content. Results from the simulations indicate that pore water chemistry is controlled by the equilibrium with the accessory minerals, especially carbonates. pH is buffered by precipitation/dissolution of calcite and dolomite, when present. The equilibrium of these minerals is deeply influenced by gypsum dissolution and cation exchange reactions in the smectite interlayer. If carbonate minerals are initially absent in bentonite, pH is then controlled by surface acidity reactions in the hydroxyl groups at the edge sites of the clay fraction, although its buffering capacity is not as strong as the equilibrium with carbonate minerals. The redox capacity of the bentonite pore water system is mainly controlled by Fe(II)-bearing minerals (pyrite and siderite). Changes in the groundwater composition lead to variations in the cation exchange occupancy, and dissolution-precipitation of carbonate minerals and gypsum. The most significant changes in the evolution of the system are predicted when ice-melting water, which is highly diluted and alkaline, enters into the system. In this case, the dissolution of carbonate minerals is enhanced, increasing pH in the bentonite pore water. Moreover, a rapid change in the population of exchange sites in the smectite is expected due to the replacement of Na for Ca.

Obtaining the porewater composition of a clay rock by modeling the in- and out-diffusion of anions and cations from an in-situ experiment

A borehole in the Callovo-Oxfordian clay rock in ANDRA's underground research facility was sampled during 1 year and chemically analyzed. Diffusion between porewater and the borehole solution resulted in concentration changes which were modeled with PHREEQC's multicomponent diffusion module. In the model, the clay rock's pore space is divided in free porewater (electrically neutral) and diffuse double layer water (devoid of anions). Diffusion is calculated separately for the two domains, and individually for all the solute species while a zero-charge flux is maintained. We explain how the finite difference formulas for radial diffusion can be translated into mixing factors for solutions. Operator splitting is used to calculate advective flow and chemical reactions such as ion exchange and calcite dissolution and precipitation. The ion exchange reaction is formulated in the form of surface complexation, which allows distributing charge over the fixed sites and the diffuse double layer. The charge distribution affects pH when calcite dissolves, and modeling of the experimental data shows that about 7% of the cation exchange capacity resides in the diffuse double layer. The model calculates the observed concentration changes very well and provides an estimate of the pristine porewater composition in the clay rock.

Modeling cation diffusion in compacted water-saturated sodium bentonite at low ionic strength

Sodium bentonites are used as barrier materials for the isolation of landfills and are under consideration for a similar use in the subsurface storage of high-level radioactive waste. The performance of these barriers is determined in large part by molecular diffusion in the bentonite pore space. We tested two current models of cation diffusion in bentonite against experimental data on the relative apparent diffusion coefficients of two representative cations, sodium and strontium. On the "macropore/nanopore" model, solute molecules are divided into two categories, with unequal pore-scale diffusion coefficients, based on location: in macropores or in interlayer nanopores. On the "surface diffusion" model, solute molecules are divided into categories based on chemical speciation: dissolved or adsorbed. The macropore/nanopore model agrees with all experimental data at partial montmorillonite dry densities ranging from 0.2 (a dilute bentonite gel) to 1.7 kg dm(-3) (a highly compacted bentonite with most of its pore space located in interlayer nanopores), whereas the surface diffusion model fails at partial montmorillonite dry densities greater than about 1.3 kg dm(-3).

Multicomponent diffusion modeling in clay systems with application to the diffusion of tritium, iodide, and sodium in Opalinus Clay

The hydrogeochemical transport model PHREEQC was extended with options to calculate multicomponent diffusion in free pores and in the diffuse double layer (DDL). Each solute species can be given its own tracer diffusion coefficient. The composition of the DDL is calculated with the Donnan approximation. With these options, solute species can be transported in coexisting charged and uncharged regions as may exist in clays and membranes. The model was developed to simulate in-situ tracer diffusion experiments in Opalinus Clay with tritium, iodide, and sodium. Tritium gives the formation's tortuosity factor, which applies in principle for all the neutral species. Half of the porosity is not accessible for iodide due to anion exclusion, and assumed equal to the amount of DDL-water. With this assumption, the tortuosity factor for iodide is 1.4 times higher than that for tritium. The sodium data can be matched by reducing the tortuosity factor 1.6 times relative to tritium, and by distributing the cation exchange capacity over the DDL and fixed sites that are spread heterogeneously over the model domain. The physical origin of the variable tortuosity for differently charged species is discussed.

A multiscale approach to ion diffusion in clays: Building a two-state diffusion–reaction scheme from microscopic dynamics

The mobility of particles is generally lowered by the presence of a confining medium, both because of geometrical effects, and because of the interactions with the confining surfaces, especially when the latter are charged. The water/mineral interface plays a central role in the dynamics of ions. The ionic mobility in clays is often understood as an interplay between the diffusion of mobile ions and their possible trapping at the mineral surfaces. We describe how to build a two-state diffusion-reaction scheme from the microscopic dynamics of ions, controlled by their interaction with a mineral surface. The starting point is an atomic description of the clay interlayer using molecular simulations. These provide a complete description of the ionic dynamics on short time and length scales. Using the results of these simulations, we then build a robust mesoscopic (Fokker-Planck) description. In turn, this mesoscopic description is used to determine the mobility of the ions in the interlayer. These results can then be cast into a diffusion-reaction scheme, introducing in particular the fraction of mobile ions, or equivalently the distribution coefficient Kd. This coefficient is of great importance in characterizing electrokinetic phenomena in porous materials.

Sorption kinetics of strontium in porous hydrous ferric oxide aggregates II. Comparison of experimental results and model predictions

In a previous paper, we introduced the Donnan diffusion model to describe cation diffusion into microporous solids with variably charged surfaces, such as hydrous ferric oxides (HFO). Here, we present experiments investigating slow diffusion and sorption of strontium by HFO aggregates with well-characterized porosity. Adsorption of protons and strontium at the HFO surface was evaluated by acid-base titration and batch adsorption experiments with dispersed HFO. The experimental data were fitted with a 1-pK basic Stern model including surface ion pair formation of Na(+) and NO(3)(-) and charge distribution for Sr surface complexes. Sorption-diffusion experiments were conducted in flow-through columns at controlled flow rates and at two different pH values, pH 4 and 7. Wet HFO aggregates, which were synthesized using a freezing and thawing method, were packed into chromatographic columns, pre-equilibrated to reach a constant pH, and then Sr breakthrough curves for adsorption and desorption of Sr were recorded. Strong retardation of Sr indicated that diffusion was sufficiently fast in a fraction of pores, so that sorption sites in these pores were rapidly accessible. Based on the analysis of NaNO(3) breakthrough curves, this rapidly accessible pore fraction was estimated to be 37% of the total aggregate pore volume at pH 4.0 and 72% at pH 7.0, respectively. Taking this into account, the Donnan diffusion model gave a good description of the experimental Sr breakthrough curves. Cation exclusion was correctly predicted at pH 4.0. At pH 7, the strong tailing of Sr breakthrough curves due to Sr diffusion into the smallest pores was very well simulated. The Donnan diffusion model proved adequate for pore sizes between approximately 2 and 5 nm, depending on pH and ionic strength. This category of pores was dominant in the HFO aggregates used in this work.

Sorption kinetics of strontium in porous hydrous ferric oxide aggregates

Sorption of ions by hydrous ferric oxide (HFO) often shows a fast initial sorption reaction followed by a much slower sorption process. The second step is diffusion-controlled and can continue for days or months before equilibrium is reached. In this paper, we demonstrate that the diffusion rate may be explained by electrostatic interactions. The internal and external surfaces of HFO are generally positively charged and therefore repel cations. This can result in extremely low cation concentrations in pores, and therefore a significant reduction in pore diffusion rate. The theory is demonstrated here for sorption of Sr(2+) in HFO aggregates. The ion concentrations in the pore space are calculated using a Donnan model and diffusion is calculated from the Donnan concentration and potential gradients. This diffusion model is compared with nonelectrostatic pore diffusion, which does not take electrostatic interactions into account. The Donnan model predicts very low concentrations of Sr(2+) in the pores and diffusion rates that are up to 8000 times lower than predicted with a nonelectrostatic model.

Sensitivity analysis of radionuclide migration in compacted bentonite: a mechanistic model approach

Mechanistic model calculations for the migration of Cs, Ra, Am and Pb in compacted bentonite have been carried out to evaluate sensitivities with respect to different parameter variations. A surface chemical speciation/electric double layer model is used to calculate: (i) porewater composition and radionuclide speciation in solution and at the bentonite surface, yielding the distribution of mobile and sorbed species and (ii) interaction of diffusing species with negatively charged pore walls to obtain diffusion parameters. The basic scenario considers the interaction of compacted bentonite with a fresh-type groundwater; variations include the presence of bentonite impurities and saline groundwater. It is shown that these scenarios result in significant variations of porewater composition that affect migration via three mechanisms that can partly compensate each other: (1) effects on sorption through radionuclide complexation in solution, and competition of major cations for surface sites; (2) changes in radionuclide solution speciation leading to different diffusing species under different conditions; (3) effects on diffusion through changes in the electric double layer properties of the clay pores as a function of ionic strength.

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.