Intercomparison of determining diffusion coefficients of I− in compacted bentonite using various mathematical models of through-diffusion experiments in the laboratory

2021 ◽  
Author(s):  
Tsuey-Lin Tsai ◽  
Shih-Chin Tsai ◽  
Der-Ming Chang ◽  
Wen-Hsi Cheng
Keyword(s):  
Mathematical Models ◽  
Diffusion Coefficients ◽  
Compacted Bentonite ◽  
Through Diffusion

scholarly journals Measurement on Diffusion Coefficients and Isotope Fractionation Factors by a Through-Diffusion Experiment

Minerals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 208
Author(s):  
Takuma Hasegawa ◽  
Kotaro Nakata ◽  
Rhys Gwynne
Keyword(s):  
Groundwater Flow ◽  
Diffusion Coefficients ◽  
Isotope Fractionation ◽  
Free Water ◽  
Effective Porosity ◽  
Diffusion Experiment ◽  
Fractionation Factor ◽  
Through Diffusion ◽  
Geological Formations ◽  
Fractionation Factors

For radioactive waste disposal, it is important that local groundwater flow is slow as groundwater flow is the main transport medium for radioactive nuclides in geological formations. When the groundwater flow is very slow, diffusion is the dominant transport mechanism (diffusion-dominant domain). Key pieces of evidence indicating a diffusion-dominant domain are the separation of components and the fractionation of isotopes by diffusion. To prove this, it is necessary to investigate the different diffusion coefficients for each component and the related stable isotope fractionation factors. Thus, in this study, through-diffusion and effective-porosity experiments were conducted on selected artificial materials and natural rocks. We also undertook measurements relating to the isotope fractionation factors of Cl and Br isotopes for natural samples. For natural rock samples, the diffusion coefficients of water isotopes (HDO and H218O) were three to four times higher than those of monovalent anions (Cl−, Br- and NO3−), and the isotope fractionation factor of 37Cl (1.0017–1.0021) was slightly higher than that of free water. It was experimentally confirmed that the isotope fractionation factor of 81Br was approximately 1.0007–1.0010, which is equivalent to that of free water. The enrichment factor of 81Br was almost half that of 37Cl. The effective porosity ratios of HDO and Cl were slightly different, but the difference was not significant compared to the ratio of their diffusion coefficients. As a result, component separation was dominated by diffusion. For artificial samples, the diffusion coefficients and effective porosities of HDO and Cl were almost the same; it was thus difficult to assess the component separation by diffusion. However, isotope fractionation of Cl and Br was confirmed using a through-diffusion experiment. The results show that HDO and Cl separation and isotope fractionation of Cl and Br can be expected in diffusion-dominant domains in geological formations.

Direct Determination of Transport Parameters in Repository Materials

1992 ◽  
Vol 294 ◽  
Author(s):  
J. L. Conca ◽  
M.J. Apted ◽  
R.C. Arthur
Keyword(s):  
Diffusion Coefficients ◽  
Direct Determination ◽  
Advective Transport ◽  
Transport Parameters ◽  
Centripetal Acceleration ◽  
Compacted Bentonite ◽  
Diffusion Limited ◽  
Gradient Measurements ◽  
Time Required ◽  
Host Rocks

ABSTRACTA new flow technology has been developed that significantly decreases the time required to obtain transport data on saturated and unsaturated porous/fractured media. This technique is based on open-flow centrifugation and was developed to measure steady-state transport properties in most geologic materials within a matter of hours. Centripetal acceleration does not induce artificial effects in samples i.e., fracturing, collapse of interlayer structures, structural dewatering, compaction, chemical changes, etc., that occur with high-pressure methods. Using this technique, hydraulic conductivities (K) and diffusion coefficients (D) for compacted bentonite and four host rocks have been measured and re-interpreted. Based on these new data, K for compacted bentonite is less than 10−14 m/s, a factor of 1000 lower than previous pressure-gradient measurements, providing further assurance that radionuclide transport through bentonite backfill will be diffusion limited. Measured K for mudstone (1.8 × 10−12 m/s) indicates diffusion-limited far-field transport, while advective transport should occur for granite, basalt, and tuff, with expected matrix diffusion coefficients (correlated to measured D values) of 8.3 × 10−13 and 2.5 × 10−12 m2/s for fractured granite and basalt, respectively.

Migration from plastic packages into their contents. I. The role of mathematical models

1995 ◽  
Vol 350 (1694) ◽  
pp. 379-406 ◽  
Keyword(s):  
Mass Transfer ◽  
Mathematical Models ◽  
Diffusion Coefficients ◽  
Unit Area ◽  
Detailed Examination ◽  
Diffusion Equations ◽  
Legal Regulations ◽  
Successful Model ◽  
Plastic Packages

Materials contained in plastic packages can transfer (migrate) into the contents. In some circumstances, such as packages of food, drink or medicine, the consequences of this migration can be unpleasant or even harmful. Many countries, and the European Community, have adopted legal regulations designed to limit the amount of migration. It is shown, partly by discussing one example in some detail, that certain quantitative criteria in such regulations are unsatisfactory. The reasons include ( a ) improper recognition of the importance of package geometry, ( b ) invalid assumptions about a correspondence between concentrations in the contents and mass transfer per unit area of the package-contents interface and ( c ) failure to account, in an adequate manner, for the inevitable variability between nominally identical package systems. The principal theme of the paper is that these faults could have been, and can be, substantially ameliorated by proper use of mathematical models. Common shortcomings in the previous (but very limited) use of mathematics are exposed partly by detailed examination of a recent research paper. The paper discusses the requirements of a successful model and considers the simplest type, namely diffusion equations with diffusion coefficients that are independent of the concentrations of the migrant in either the plastic or the contents. Particular solutions are chosen to illustrate faults in existing legislation and practice, and because they are thought to be good candidates for testing against data. It is argued that future experiments would be more successful and more useful if they were planned and conducted in teams involving mathematicians.

Distribution Coefficients and Apparent Diffusion Coefficients of Cesium in Compacted Bentonites

1999 ◽  
Vol 556 ◽  
Author(s):  
Akiko Okamoto ◽  
Kazuya Idemitsu ◽  
Hirotaka Furuya ◽  
Yaohiro Inagaki ◽  
Tatsumi Arima
Keyword(s):  
Diffusion Coefficients ◽  
Distribution Coefficients ◽  
Dry Density ◽  
Apparent Diffusion Coefficients ◽  
Compacted Bentonite ◽  
Apparent Diffusion ◽  
Tracer Solution ◽  
Cesium Concentration ◽  
Penetration Profile ◽  
Very High

AbstractDistribution coefficients and apparent diffusion coefficients of cesium in some compacted bentonites were determined by the penetration profile method. Cylindrical compacted bentonites with the dry density of 0.8 to 1.6 Mg/m3 were contacted with tracer solutions containing 1000, 100 or 10 ppm of cesium. The apparent diffusion coefficients were obtained from the concentration profiles of cesium in compacted bentonites. The distribution coefficients were obtained concurrently by dividing the intercepts of the profiles by the concentration of the tracer solution. The apparent diffusion coefficients of cesium in compacted bentonite were obtained in the range of 0.42 to 9.6· 10−12 m2/s. The apparent diffusion coefficients in the compacted bentonite contacted with three different concentrations of cesium tended to decrease with increasing dry density of the specimen; but, they had no dependence on cesium concentration within a factor of 3 at the same dry density. The distribution coefficient of cesium for the specimens contacted with three different concentrations of cesium were obtained in the range of 0.3 to 90 L/kg and had little dependence on dry density. The distribution coefficients obtained in the compacted bentonites were dependent on pH of the solution rather than concentration of cesium. These distribution coefficients obtained in the compacted bentonites were 10 to 1000 times smaller than those obtained by batch experiments. The data suggest that not all sorption sites for cesium are available in highly compacted bentonite. It is necessary to consider surface diffusion as a significant migration mechanism of cesium through the compacted bentonites at very high pH condition such as 12.

Evaluation of the Sorption Properties of a Self-Adhesive Hydrogel Wound Dressing

2019 ◽  
Vol 821 ◽  
pp. 10-16
Author(s):  
Javier Kristina Mutya ◽  
Nadura Riscia ◽  
Jim Clarence Rengel ◽  
Terence Tumolva
Keyword(s):  
Layer Thickness ◽  
Diffusion Coefficients ◽  
Wound Dressing ◽  
Adhesive Layer ◽  
Sorption Properties ◽  
Hydroxyethyl Cellulose ◽  
Swelling Kinetics ◽  
Hydrogel Formulation ◽  
Through Diffusion

A novel self-adhesive wound dressing product was developed using a hydroxyethyl cellulose (HEC) hydrogel layered with a TAPE-gelatin bioadhesive. This wound dressing was then evaluated for its sorption properties through diffusion and swelling tests, and the parameters analyzed were hydrogel formulation, wound dressing thickness and adhesive layer thickness. Results showed that the wound dressing produced using 6% NaOH/5% thiourea in the crosslinking solution, with 2.5 mm hydrogel thickness, and 0.2 mm TAPE-gelatin thickness had the highest water absorbed. Lastly, analysis on swelling kinetics based on a previous study was conducted to determine the diffusion coefficients for the composite wound dressing.

Some Methodological Modifications of Determination of Diffusion Coefficients in Compacted Bentonite

2006 ◽  
Vol 932 ◽  
Author(s):  
Dušan Vopálka ◽  
Helena Filipská ◽  
Antonín Vokál
Keyword(s):  
Diffusion Coefficients ◽  
Effective Porosity ◽  
Diffusion Method ◽  
Dry Density ◽  
Diffusion Cell ◽  
Compacted Bentonite ◽  
Method Of Evaluation ◽  
Exclusion Effect ◽  
Positively Charged

ABSTRACTThe results of 3H, 36Cl and 137Cs diffusion experiments through compacted bentonite using a new design of diffusion cell and a new methodology of diffusion coefficients evaluation are presented. The diffusion cell was made from the stainless steel and enables to connect it directly to the input and/or output reservoirs without any tubing. The evaluation of diffusion coefficients utilizes a compartmental model developed in the environment of the GoldSim transport code. It enables to determine diffusion coefficients for various types of boundary conditions, including also input and output filters. The influence of the diffusion through filters on the determined values of both effective (De) and apparent (Da) diffusion coefficients was numerically demonstrated for the through diffusion method. This effect is most important for Da, the value of which would be underestimated using standard ways of evaluation for neutral and positively charged species, mainly in the case of high effective porosity.The comparison of standard and the newly developed method of evaluation of diffusion coefficients showed a significant influence of diffusion in filters for HTO. Contrary to the standard method of evaluation, the evaluation taking into account filters showed here no difference between total and effective porosity. The effect of filter resistance was negligible for Cl-, especially at high dry density of compacted bentonite, due to the anion exclusion effect. The numerical model developed enabled to determine Da values of Cs+ from the concentration change in the inlet reservoir.

Analysis of Uranium Diffusion Coefficients in Compacted FEBEX Bentonite

2003 ◽  
Vol 807 ◽  
Author(s):  
M. García-Gutiérrez ◽  
J. L. Cormenzana ◽  
T. Missana ◽  
M. Mingarro ◽  
U. Alonso
Keyword(s):  
Radioactive Waste ◽  
Diffusion Coefficients ◽  
Solid Phase ◽  
Dry Density ◽  
Compacted Clay ◽  
Spent Fuel ◽  
Apparent Diffusion Coefficients ◽  
Theoretical Approaches ◽  
Through Diffusion ◽  
High Level

ABSTRACTIn the Spanish concept of a high level radioactive waste (HLRW) repository, the canister with the spent fuel would be surrounded by a layer of FEBEX bentonite (Ca-Mg smectite clay) compacted to a dry density of 1.65 g/cm3. Since the permeability of the compacted bentonite is very low, the main mechanism for radionuclide transport in the clay barrier is expected to be diffusion, retarded by the sorption on the solid. Since the mayor component of the radioactive waste is uranium it is very important to study its diffusion behaviour in the compacted clay.Generally, effective (De) and apparent (Da) diffusion coefficients are obtained from "through-diffusion" and "in-diffusion" experiments, respectively. The obtention of both parameters in the same sample is a very interesting issue because the former includes the information on the porous medium structure (connectivity, constrictivity, tortuosity) and the latter takes into account the sorption on the solid phase. In this work, through-diffusion experiments were carried out for studying uranium diffusion and both effective and apparent diffusion coefficients were estimated, from the same experiment, by using different theoretical approaches.

The Dependence of the Diffusion Coefficients of 3H and Cs on Grain Size in Compacted Montmorillonite

1997 ◽  
Vol 506 ◽  
Author(s):  
Mamoru Nakajima ◽  
Tamotsu Kozaki ◽  
Hiroyasu Kato ◽  
Seichi Sato ◽  
Hiroshi Ohashi
Keyword(s):  
Grain Size ◽  
Diffusion Coefficients ◽  
Dry Density ◽  
Formation Factor ◽  
Apparent Diffusion Coefficients ◽  
Compacted Bentonite ◽  
Buffer Material ◽  
Apparent Diffusion ◽  
Different Grain Size ◽  
High Level

ABSTRACTCompacted bentonite is a candidate buffer material in geological disposal of high-level radioactive waste. The transport of radionuclides in compacted bentonite is dominated by diffusion, because of its very low permeability. In this study, we focused on the grain size of clay mineral, which is considered to be closely related to the formation factor in the pore water diffusion model[1,2]. The apparent diffusion coefficients (Da) of HTO and cesium ions in compacted clays were determined using montmorillonite samples with different grain size and dry density, and the effect of the grain size on diffusion behavior was discussed.

Mathematical Modeling of Biofilms

1997 ◽  
Vol 11 (1) ◽  
pp. 127-132 ◽  
Author(s):  
George H. Dibdin
Keyword(s):  
Mathematical Modeling ◽  
Complex System ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Mathematical Models ◽  
Diffusion Coefficients ◽  
Theoretical Basis ◽  
Reversible Reaction ◽  
Mathematical Equations ◽  
Insight Into

A set of mathematical equations constitutes a mathematical model if it aims to represent a real system and is based on some theory of that system's operation. On this definition, mathematical models, some very simple, are everywhere in science. A complex system like a biofilm requires modeling by numerical methods and, because of inevitable uncertainties in its theoretical basis, may not be able to make precise predictions. Nevertheless, such models almost always give new insight into the mechanisms involved, and stimulate further investigation. The way in which diffusion coefficients are measured for use in a model, particularly whether they include effects of reversible reaction, is a key element in the modeling. Reasons are given for separating diffusion from reversible reaction effects and dealing with them in a separate subroutine of the model.

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