Methodology for diffusion coefficient determination was applied on sandstone samples, using conservative non sorbing tracer.
The results proved that methodology, through-diffusion cell design and GoldSim diffusion module can be used for sandstone
samples in order to determine important migration parameters, necessary for transport model input. However, rock heterogeneity
factor has to be taken into account in any case as it can potentially change rock properties, even within centimeter scale.
Effective diffusion coefficient De for rock samples was determined. The values fell into the range of 1.0–6.17 × 10−10 m2 s−1. Discrepancies in measured and simulated porosity were observed. Statistical analyses revealed that values of diffusion coefficient
De were in close interrelation to primary mineral (quartz) and cement forming minerals (kaolinite and organic matter).
Repositories for radioactive wastes are sited in the environment with very low permeability. One of the most important processes
leading to the release of radionuclides to the environment is therefore diffusion of radionuclides in both natural and engineered
barriers. Data for its description are crucial for the results of safety assessment of these repositories. They are obtained
usually by comparison of the results of laboratory diffusion experiments with analytical and/or numerical solution of the
diffusion equation with specified initial and boundary conditions. Results of the through-diffusion experiments are obviously
evaluated by the “time-lag” method that needs for most of sorbing species unfortunately very long time of the experiment duration.
In this paper a modified approach is proposed for the evaluation of diffusion data for safety assessment, which decreases
the influence of propagation uncertainties using incorrect data and reduces time for acquiring data for safety assessment.
This approach consist in the following steps: (i) experimental measurement of material diffusion parameters under various
conditions using non-sorbing tritiated water or chlorine for which it is easy to reach conditions under which the “time-lag”
method of evaluation of the result of the through-diffusion experiment is applicable—this step provides well established diffusion
characteristics of materials for neutral species and anions, then (ii) to evaluate sorption isotherms for sorbing radionuclides
from batch experiments under conditions corresponding to composition of material pore water, (iii) to assess the values of
effective and apparent diffusion coefficients for sorbing radionuclides from well-defined diffusion coefficients of species
in free water and (iv) to verify the obtained results using relatively short-term diffusion experiments with sorbing radionuclides,
which will be evaluated using the time dependent decrease of the concentration in the input reservoir of the diffusion cell.
A numerical model of the diffusion cell can model the decrease of concentration of species. The code, which we used for this
type of evaluation of diffusion experiment, is based on the same approach to modelling that we use for modelling of the diffusion
transport in performance assessment studies. The advantage of this approach consists in the compatibility of the approaches
used for both evaluation and verification of the laboratory diffusion experiments and performance assessments and in considerable
less time needed for experiments.
Authors:K. Štamberg, J. Škrkal, P. Beneš, K. Chalupská, and D. Vopálka
A surface complexation model, the so-called diffuse double layer model (DLM), was used in the description of the multicomponent
system consisting of Czech sodium bentonite SABENYL and synthetic granitic water spiked with233U(VI). The experimental data were evaluated and the characteristic parameters, e.g., the equilibrium constants of all the
reactions considered, were obtained and used for the numerical simulation of sorption selectivity of the uranium in relation
to the total carbonate concentration. The values of separation factors indicate that the selectivity of uranium sorption in
such multicomponent systems can depend not only on the pH and composition of both phases, but also on the phase ratio and
starting concentrations of participating components.
Authors:K. Štamberg, P. Beneš, J. Mizera, D. Vopálka, and Š. Procházková
The kinetics of complexation (C) and decomplexation (D) reactions between Eu(III) and Aldrich humic acid (HA) was investigated as a function of pH (pH 4, 5, 6, 7 and 8) in the system Eu(III) - HA - Amberlite IR-120(Na) (I = 0.1). The derivation of the kinetic differential equations was based on the reactions of Eu3+ with, so called, strong (HAS) and weak (HAW) carboxylic groups of HA formulated in accordance with the new complexation model.1 The differential equations determining d[EuaHAS]/dt and d[EubHAW]/dt have the classical form applicable for reversible reactions where the forward reaction is the C-reaction and the reverse one is the D-reaction. Kinetic model used for the evaluation of experimental data includes these differential equations and the film diffusion model of sorption of Eu3+ on Amberlite IR-120(Na).
Authors:P. Beneš, K. Štamberg, D. Vopálka, L. Široký, and Š. Procházková
Kinetics of Eu sorption on sandy sediment from Gorleben, Germany, containing humic substances, was studied by radiotracer method in batch experiments at very low europium concentration (3.4.10-8 mol/l), with the aim to find kinetic parameters suitable for modeling Eu migration in bed of the sediment and to elucidate the mechanism of the sorption. Experiments were evaluated using a new simplified method taking into account simultaneous sorption/desorption of Eu on the walls of sorption vessel. Five kinetic functions were tested, of which that describing diffusion in inert surface layer of sorbent proved most suitable. The effects of pH (3.0-8.8) by addition of Aldrich humic acid (10 mg/l), addition of hydrogencarbonates (5.10-3 mol/l) and preequilibration of the sediment with solution or of Eu with solution were examined. From the results it has been concluded that the kinetics and mechanism of the sorption strongly depend on pH. At pH 4.8 Eu is sorbed mainly as humate complex from the solution of humic acid. The addition of humic acid accelerates the sorption. Carbonate complexes of Eu are the probable forms sorbed at pH 8.8. The presence of humic substances in the slightly alkaline solutions suppresses the rate of the sorption due to slow dissociation of Eu-humate complexes.
Authors:K. Štamberg, P. Beneš, J. Mizera, J. Dolanský, D. Vopálka, and K. Chalupská
A general model, the so called Mean Molecular Weight Model (MMWM), of complexation of metal cations (Mez+) with macromolecular polyanions of humic acid (HAp-) is proposed. The model is based on the results of previous studies of the electrophoretic mobility of humate complexes and assumes that the complexation proceeds by consecutive neutralization of the dissociated carboxyl groups of the central polyanion HAp- with Mez+ cations. It reflects the macromolecular character of humic acid, applies molar concentrations of reacting components with equations for stability constants and incorporates also the mean charge of humic macromolecules. The model has been verified with experimental data obtained in the study of complexation of Eu(III) with Aldrich humic acid using ion exchange (Amberlite IR-120), over a broad range of [Eu] to [HA] ratio, at pH 4 and 7.
Authors:G. Lujanienė, P. Beneš, K. Štamberg, K. Jokšas, D. Vopalka, E. Radžiūtė, B. Šilobritienė, and J. Šapolaitė
Sorption–desorption behaviour of 137Cs in the Baltic Sea and the Curonian Lagoon was studied in 1997–2009 with the aim to better understand processes responsible
for redistribution and sink of 137Cs in the system. Data obtained from several sampling campaigns were analyzed and short and long-term kinetic tracer experiments
using natural water and bottom sediments were carried out with particles of various sizes from 0.2 to 50 μm. Samples of suspended
particles and bottom sediments collected during two sampling campaigns were fractionated according to the size, and association
of 137Cs with solid phase was studied using sequential extraction. The difference in 137Cs behaviour observed between expeditions in 1999 and 2001 was attributed to seasonal variations in chemical composition of
suspended particles entering the system and consequent differences between the sorption (in 1999) and the desorption (in 2001)
of 137Cs in sea water. Data obtained from tracer kinetic sorption experiments with 134Cs and bottom sediment fractions of different grain size were used for finding a suitable kinetic sorption model, kinetic
constants and the corresponding equilibrium Kd values. It has been found that the modelled data best conform to the mechanism of ion diffusion through the so-called inert
layer on the surface of the sediment particles.
Authors:G. Lujanienė, P. Beneš, K. Štamberg, J. Šapolaitė, D. Vopalka, E. Radžiūtė, and T. Ščiglo
Sorption of Cs, Pu and Am on natural clay of complex composition was studied to better understand the sorption mechanisms.
It was found that cesium sorption to natural clay was affected by its coatings and by the ionic strength of solution. The
sorption of Pu and Am on the clay was compared with that on synthetic goethite, hematite and magnetite, representing components
of the clay coatings. The sorption was quantitatively interpreted using models assuming ion exchange and/or complex formation
on the “layer sites” and “edge sites” of the clay and its coatings. Constants characterizing properties of the sites and sorption
equilibria were determined.