In order to investigate in more detail the relation between the size of diffusing molecules and their diffusion coefficients (and geometric factors), diffusion experiments with gases of different size and tritiated water (HTO) have been performed on different clayey samples (Boom Clay, Eigenbilzen Sands, Opalinus Clay, Callovo-Oxfordian Clay, and bentonite with different dry densities). We observed that, for unreactive gases in clayey materials, the effective diffusion coefficient varies with the size of the diffusing molecule and this variation can be described by an exponential or a power law function. The variation of the geometric factor can also be described by an exponential function. The observed experimental relations can be used to estimate diffusion coefficients; by measuring experimentally in clay the effective diffusion coefficient of two unreactive dissolved gases with a different size, the diffusion coefficients of other dissolved gases (with a size in between the two measured gases) can be estimated by using the fitted exponential relationship.
Clay-based materials are considered by many countries in their concepts for the safe disposal of high- and intermediate-level radioactive waste, either as the material of choice in the engineered barrier system or because of the choice of argillaceous formations to host the repository. Examples of European countries where argillaceous formations are being explored as potential host formations are Belgium, Switzerland, and France [
In Belgium, no formal decision has been taken yet on a host formation, but for R&D purposes, the Belgian Radioactive Waste Management Organization (ONDRAF/NIRAS) considers Boom Clay (BC) as a potential host formation for a geological disposal facility. In France, the National Agency for Radioactive Waste Management (Andra) selected the Callovo-Oxfordian Clay Formation in the east of France as a potential host formation [
In the context of nuclear waste disposal, the transport of dissolved gases in compacted clays is an area, which receives a high amount of interest. First, the production of gas within a geological repository is unavoidable. Mainly anaerobic corrosion of metals will lead to the production of hydrogen. If the rate of gas generation is larger than the diffusive flux into the clay, a free gas phase will form, which might have a negative effect on the performance of the barriers. In order to compute a comprehensive and reliable balance between gas generation versus gas dissipation, correct estimates for gas diffusion coefficients of dissolved gases are essential. Moreover, the produced hydrogen may be converted to other gases like CH4 due to, for example, microbial activity. Thus, also the diffusion coefficient of methane needs to be established.
Secondly, naturally occurring noble gases such as He and Ar can act as natural tracers whose profiles can be used to constrain transport properties on the scale of the formation [
Measuring reliable diffusion coefficients of gases is not evident [
In case of hydrogen, Jacops et al. [
When performing scoping calculations on the diffusive mobility and possible build-up of dissolved gases in a geological repository or in a geological formation, reliable gas diffusion coefficients obtained from laboratory experiments are often not available. Hence, these diffusion coefficients are often estimated from measured values of other species like HTO. In case of hydrogen, the diffusion coefficient for helium is often used as a surrogate. In this approach, it is implicitly assumed that the geometric factor of the formation (a factor which describes the effect of the porous network on diffusion and for which the value obtained for HTO is used) is equal for all other gases and species considered (e.g., [
Different approaches for estimating the geometric factor exist: for example, (i) from diffusion experiments (mostly with HTO [
In clay, a relation between the size of the diffusing molecule (expressed by the kinetic diameter) and its diffusion coefficient has been observed [
For mortars with a different sand content, the measured geometric factors for Li+, Cl−, and HTO are relatively similar, leading to the conclusion that the formation factor can be used to determine the order of magnitude of the effective diffusion coefficient of other diffusion species [
The main objective of this paper is to investigate in more detail the relation between the size of the diffusing gas molecules and their diffusion coefficients and hence geometric factors in different clayey materials. We also investigate whether this relation can be used to estimate diffusion coefficients of gases, based on their size.
This objective is achieved by performing diffusion experiments with gases of different size, on different clayey samples (Boom Clay, Eigenbilzen Sands, Opalinus Clay, Callovo-Oxfordian Clay, and bentonite (Volclay KWK with different dry densities)).
The Boom Clay is a marine sediment that was deposited in the early Oligocene (Rupelian), 29 to 32 million years ago in the North Sea Basin, at water depths between 50 and 100 m [
One of the topics under investigation is the effect of variations in the clay and silt/sand content on the diffusion parameters [
Overview of used samples with the SCK ID, core number, type, and orientation with respect to the bedding.
Material | SCK ID | Core # | Type | Orientation |
---|---|---|---|---|
Boom Clay | K2 | ON-Mol-1 84b | Clay | ⊥ |
Boom Clay | K4 | ON-Mol-1 127b | Clay | // |
Eigenbilzen Sands | K14 | ON-Mol-1 36a | Clayey sand | // |
Eigenbilzen Sands | K15 | ON-Mol-1 37b | Clayey sand | // |
Eigenbilzen Sands | K16 | ON-Mol-1 35b | Clayey sand | ⊥ |
Eigenbilzen Sands | K17 | ON-Mol-1 39b | Clayey sand | ⊥ |
Volclay KWK | Bentonite 1.4 | Dry density 1.4 g/cm3 | ||
Volclay KWK | Bentonite 1.6 | Dry density 1.6 g/cm3 | ||
Callovo-Oxfordian Clay | COX | EST 49109 | Claystone | ⊥ |
Opalinus Clay | OPA | Schlattingen 860.32 m depth | Claystone | ⊥ |
All samples from the Boom Clay and Eigenbilzen Sands used in this study are taken from the ON-Mol1 borehole which was drilled in 1997, in the town of Mol, in the northeast of Belgium (Lambert coordinates
The Callovo-Oxfordian Clay (COX) is an indurated, Middle Jurassic mudstone from marine origin, which was deposited 150–160 million years ago. It has been intensively studied by Andra on a 250 km2 area. In this area, Andra has performed several drilling campaigns and constructed an Underground Research Laboratory (URL) in Bure, at a depth of 490 m in the COX layer. The thickness of the COX formation is about 135 m at the URL. The COX consists mainly of clay minerals (illite, interstratified smectite/illite, and others), calcite, dolomite/ankerite, quartz, feldspars, and minor amounts of accessory phases, such as pyrite [
The Opalinus Clay is a fine-grained sedimentary rock, which was deposited 172 million years ago. The latter consists mainly of clay minerals (illite, illite/smectite, kaolinite, and others), calcite, dolomite/ankerite, quartz, feldspars, pyrite, and organic matter. Research on the Opalinus Clay is mainly performed in the Mont Terri Underground Research Lab, located in the canton Jura. The studied sample was, however, taken from the Schlattingen borehole (Northeast of Switzerland, canton Thurgau), at a depth of 860.32 m below surface. As the burial history for the Mont Terri site and Schlattingen is different, with deeper burial in Schlattingen [
The Volclay KWK (a MX 80 type bentonite) is a fine-grained sodium bentonite with montmorillonite as the main component [
For the experimental setup of the design of the diffusion cell, see Jacops et al. [
As Callovo-Oxfordian Clay and Opalinus Clay contain lower proportions of swelling clay minerals, their swelling capacity/plasticity is therefore much lower compared to the Boom Clay. Hence, the samples had to be embedded in a resin (Sikadur 52 Injection Normal) in order to seal the interface clay sample-cell. The embedded samples (80 mm diameter and 25 mm height for Opalinus Clay and 70 mm diameter and 30 mm height for the Callovo-Oxfordian Clay) were placed between an upper and lower flange, and subsequently the flanges were welded to the diffusion cell (confinement with constant volume). As the flanges were provided with a circulation loop, good contact between the water containing the dissolved gas and the clay sample was ensured. More information on the preparation of these samples can be found in Jacops et al. [
The Volclay KWK was compacted to two different dry densities, that is, 1.4 and 1.6 g/cm3. Prior to the compaction, the water content of the batch was measured by drying at 105°C for at least 24 hours. The correct amount of bentonite was compacted into a cylinder of 20 by 20 mm. Next, the compacted samples were saturated with a synthetic pore water of 0.05 M NaClO4.
For mineralogical analyses samples were grinded first with mortar and pestle and afterwards (after adding ethanol) in a McCrone Micronizing Mill. After drying, the residue was crushed again with mortar and pestle and finally it was packed in the sample holder [
The specific surface area was measured by nitrogen adsorption at 77 K in a TriStar 3020 (Micromeritics), using the Brunauer-Emmett-Teller theory. Prior to the measurement, ca. 3 g sample was degassed at 110°C. Next, the pressure of N2 was gradually increased and the amount of adsorbed gas was measured as a function of the relative pressure, which plots the adsorption isotherm.
Once the diffusion experiments ended, the porosity was determined by drying the samples at 105°C until the mass was stable. Based on the mass loss during drying and the density, the porosity could be calculated [
Hydraulic conductivity was measured prior to the diffusion experiment. The used technique is based on Darcy's law and applies a constant pressure difference [
The methodology of through-diffusion experiments has been described in detail in Jacops et al. [
Sampling of the gas phase was performed on a regular basis (generally once per week) until 10 data points were obtained in the regime of approximately constant outlet flux of the diffusion process. The gas composition was analysed with a CP4900 micro GC (equipped with a Molsieve 5A and a Pora Plot U column and TCD detectors, Agilent, USA) or a CG4 Compact GC (equipped with a RT-Qbond column, a Molsieve 5A column and TCD detectors, Interscience, The Netherlands). Both GCs were operated with the EZChrom CDS software.
The experiment was performed in a temperature-controlled room (21 ± 2°C).
The diffusion experiments with several gases on the same sample were performed consecutively: the content of the inlet and outlet vessel was replaced each time while the sample remained in the same position.
In order to allow comparison of our results with available results in literature, diffusion experiments with HTO were performed with a setup similar to the one used to measure through-diffusion of dissolved gases. A more detailed description can be found in Jacops et al. [
The theoretical aspects of diffusion are discussed in detail in Jacops et al. [
In general, two transport parameters can be obtained from diffusion experiments: the apparent diffusion coefficient
From these two basic parameters, one can calculate the effective diffusion coefficient
The geometric factor
Grathwohl [
Due to the single pore size approximation in the
Poiseuille's law gives the flow
If
The size of a diffusing molecule can be characterized in several ways. As it would be not appropriate to use values which have been determined from diffusion measurements (hence leading to circular reasoning), some extra clarification on the selection of the kinetic diameters is given in this paragraph. The most widely used measure for the size of a (small) gas molecule is the kinetic diameter
The potential
However, the selected kinetic diameters are representative for dilute gas mixtures and are thus only an approximation for gases dissolved in water. More information on this topic can be found in [
Empirically, the gas diffusion coefficients
Similar to the diffusion coefficient
A similar combination as (
A detailed description on the modelling approach can be found in Jacops et al. [
The diffusion experiments are modelled by fitting the solutions of the diffusion equation with the appropriate boundary and initial conditions. For both the gas diffusion and the HTO diffusion experiments, the diffusion equation is solved by COMSOL coupled with MATLAB for optimization.
A through-diffusion experiment allows fitting both the apparent diffusion coefficient
The water content of a core was measured at the end of the diffusion experiments, and if this information was not available, a reference value obtained from literature was used (see also Table
As discussed above, confining filters are used in the diffusion experiments. As discussed by Glaus et al. [
Diffusion coefficients of dissolved gases in the filters are not available and therefore only the value of HTO could be used as an approximation. As this would introduce a large uncertainty into the model and given the large length of the samples (35 mm) compared to the length of the filters (2 × 2 mm), the effect of the filter on diffusion is not taken into account in the experiments with dissolved gases.
Both the Boom Clay and the Eigenbilzen Sands are mainly composed of quartz and 2 : 1 clay minerals. As shown in Table
Quantitative mineralogical composition of the different samples (in mass%) and the specific surface area (m2/g). Minerals which were below the detection limit are indicated with BD.
Boom Clay |
Eigenbilzen Sands | Bentonite | COX | OPA | |||||
---|---|---|---|---|---|---|---|---|---|
Core 84b K2 | Core 127b K4 | Core 36a K14 | Core 37b K15 | Core 35b K16 | Core 39b K17 | ||||
Quartz | 31 | 28 | 59 | 58 | 60 | 54 | 3 | 24 | 28 |
K-feldspar | 8 | 5 | 8 | 9 | 10 | 8 | BD | 5 | 3 |
Plagioclase | 3 | 1 | 6 | 6 | 5 | 5 | 3 | 3 | BD |
Calcite | 0.2 | 2 | BD | BD | BD | BD | BD | 21 | 8 |
Ankerite/dolomite | BD | BD | BD | BD | BD | BD | BD | 4 | BD |
Pyrite | 2 | 2 | 0.6 | 0.5 | 1 | 0.5 | BD | 1 | 0.6 |
|
0.6 | 0.5 | 1 | 1 | 0 | 0 | BD | BD | BD |
Anatase | 0.6 | 0.7 | BD | BD | BD | BD | BD | BD | BD |
Kaolinite | 8 | 9 | 2 | 4 | 2 | 3 | BD | 0 | BD |
2 : 1 Al clay | 34 | 41 | 20 | 18 | 21 | 27 | 93 | 39 |
|
Muscovite | 9 | 8 | BD | BD | BD | BD | BD | BD | BD |
Chlorite | 2 | 2 | 3 | 3.5 | 0 | 2.5 | BD | 3 | BD |
Opal A | 2 | 1 | BD | BD | BD | BD | BD | BD | BD |
Specific surface area | 38 | 45 | 14 | 12 | 8 | 20 | + | 28 | 21 |
HTO Diffusion coefficients, fitted capacity factor, and total porosity assuming fixed filter transport parameter values (Fixed Filter, FF).
Material |
Core |
|
|
|
| |
---|---|---|---|---|---|---|
(m2/s) | (-) | (m2/s) | ||||
Boom Clay | 84b (K2) | ⊥ |
|
|
|
|
Boom Clay | 127b (K4) | // |
|
|
|
|
Eigenbilzen Sand | 36a (K14) | // |
|
|
|
|
Eigenbilzen Sand | 37b (K15) | // |
|
|
|
|
Eigenbilzen Sand | 35b (K16) | ⊥ |
|
|
|
|
Eigenbilzen Sand | 39b (K17) | ⊥ |
|
|
|
|
Bentonite 1.4 |
|
|
|
|
||
Bentonite 1.6 |
|
|
|
|
||
COX | ⊥ | NM | NM |
|
NM | |
OPA | OPA 1 | ⊥ |
|
|
|
|
The composition of the COX sample corresponds well to the reference values presented in [
The hydraulic conductivity
Overview of measured hydraulic conductivity and diffusion coefficients
Kinetic diameter |
He | HTO | Ne | H2 | Ar | CH4 | Xe | C2H6 | ||||
2.58 | 2.75 | 2.79 | 2.97 | 3.42 | 3.82 | 4.06 | 4.42 | |||||
7.28 | 2.20 | 4.03 | 5.11 | 2.44 | 1.84 | 1.47 | 1.38 | |||||
|
||||||||||||
Core | Code |
|
|
|
|
|
|
|
|
|
| |
(m/s) | (-) |
|
|
|
|
|
|
|
|
|||
|
||||||||||||
BC 84b | K2 | ⊥ |
|
0.4 |
|
|
|
NM |
|
|
|
|
BC 127b | K4 | // |
|
0.38 |
|
|
|
|
|
|
|
|
BC 36a | K14 | // |
|
0.37 |
|
|
|
NM | NM |
|
NM |
|
BC 37b | K15 | // |
|
0.40 |
|
|
|
NM | NM |
|
NM |
|
BC 35b | K16 | ⊥ |
|
0.41 |
|
|
|
NM | NM |
|
NM |
|
BC 39b | K17 | ⊥ |
|
0.40 |
|
|
|
NM | NM |
|
NM |
|
Bent 1.4 | Bent 1.4 |
|
0.47 |
|
|
|
NM | NM |
|
NM |
|
|
Bent 1.6 | Bent 1.6 |
|
0.40 |
|
|
|
NM | NM |
|
NM |
|
|
COX 1 | COX 1 | ⊥ |
|
|
|
NM |
|
NM |
|
|
NM |
|
OPA 1 | OPA 1 | ⊥ |
|
0.096 |
|
|
|
NM |
|
|
|
|
Assuming that a soil consists of spherical grains, the pores largely consist of the space between the grains. In a very rough approximation, the pore size is related to the grain size and the sorting of the sedimented particles. Because the grain size of sand is larger than that of clay grains, according to expression (
As described above, the HTO experiments are fitted by using fixed filter (FF) values. The results are shown in Table
For the capacity factors, there is for some samples a considerable difference between the fitted capacity factors and the total porosity
All measured effective diffusion coefficients and the corresponding geometrical factors for dissolved gases and HTO are reported in Tables
Geometrical factors obtained from the aqueous and effective diffusion coefficients from Table
Core | Code |
|
He | HTO | Ne | H2 | Ar | CH4 | Xe | C2H6 | |
---|---|---|---|---|---|---|---|---|---|---|---|
|
|||||||||||
BC 84b | K2 | ⊥ | 0.4 | 6.2 | 4.7 | 9.2 | 14.1 | 7.6 | 9.6 | 11.9 | |
BC 127b | K4 | // | 0.38 | 3.7 | 3.0 | 6.7 | 3.8 | 6.4 | 4.5 | 8.4 | 8.9 |
BC 36a | K14 | // | 0.37 | 4.0 | 2.5 | 4.4 | 2.9 | 3.6 | |||
BC 37b | K15 | // | 0.4 | 3.5 | 2.0 | 4.0 | 2.6 | 3.6 | |||
BC 35b | K16 | ⊥ | 0.41 | 4.0 | 2.7 | 4.7 | 2.0 | 4.1 | |||
BC 39b | K17 | ⊥ | 0.4 | 5.0 | 2.9 | 5.3 | 3.0 | 6.2 | |||
Bent 1.4 | Bent 1.4 | 0.47 | 19.3 | 6.6 | 18.4 | 30.7 | 60.3 | ||||
Bent 1.6 | Bent 1.6 | 0.4 | 10.8 | 10.9 | 18.5 | 79.9 | 161.7 | ||||
COX 1 | COX 1 | ⊥ | 0.18 | 16.1 | 34.6 | 60.2 | 131.1 | ||||
OPA 1 | OPA 1 | ⊥ | 0.096 | 10.2 | 17.5 | 62.1 | 54.0 |
Opalinus Clay has the lowest porosity of all the samples used in this paper. It is evidently the first candidate showing possible percolation transition problems. These occurred for all gases larger than Argon: CH4, Xe, and C2H6: For CH4 the measurements were scattered and all below 100 ppm. As 100 ppm is the lower limit for reliable CH4 peak detection and measurement, all measurements contain a significant portion of noise and are therefore considered nonsignificant. For Xe, no breakthrough was measured which could also be related to the detection limit of 100 ppm. For C2H6, where the detection limit is only 5 ppm, a clear breakthrough curve was detected, but it could not be fitted by a simple diffusion model (see Figure
Evolution of the outlet concentration versus time in the C2H6 diffusion experiment in Opalinus Clay. A clear breakthrough after a couple of days, leading to a quasi-stationary state is followed by an sudden unexplained increase after more than 150 days.
When comparing the measured diffusion coefficients in the Boom Clay samples and the samples from the Eigenbilzen Sands, one can observe that despite a comparable porosity, the diffusion coefficients in the Eigenbilzen Sands are slightly higher than in Boom Clay. This agrees with previous results from pulse injection experiments [
Also, note that, for the samples from the Eigenbilzen Sands and for the Boom Clay samples, the diffusion coefficients for HTO and Ne (two molecules with a nearly equal kinetic diameter) are about the same. Due the very different values for the HTO and Ne aqueous diffusion coefficients (
Table
Parameter values obtained by fitting the effective diffusion coefficient versus molecular size by the exponential expression (
Water |
|
|
||||||||
(m2/s) | (m−1) | |||||||||
|
|
|||||||||
|
||||||||||
Code |
|
|
|
|
|
|
|
|
|
|
(-) | (m2/s) | (m−1) | ( ) | (m) | (m) | (m/s) | (m/s) | |||
|
||||||||||
K2 | ⊥ | 0.4 |
|
|
11.1 |
|
|
|
|
0.0002 |
K4 | // | 0.38 |
|
|
3.7 |
|
|
|
|
0.92 |
K14 | // | 0.37 |
|
|
8.4 |
|
|
|
|
212 |
K15 | // | 0.4 |
|
|
6.4 |
|
|
|
|
28 |
K16 | 0.41 |
|
|
8.0 |
|
|
|
|
4397 | |
K17 | ⊥ | 0.4 |
|
|
5.9 |
|
|
|
|
10.1 |
Bent 1.4 | 0.47 |
|
|
4.0 |
|
|
|
|
0.31 | |
Bent 1.6 | 0.4 |
|
|
0.5 |
|
|
|
|
0.76 | |
COX 1 | ⊥ | 0.18 |
|
|
4.3 |
|
|
|
|
3.4 |
OPA 1 | ⊥ | 0.096 |
|
|
55.0 |
|
|
|
|
0.010 |
Effective diffusion coefficients for dissolved gases in Boom Clay (a) and other clayey materials (b), fitted with expression (
Most of the fits of Table
For all Boom Clay and Eigenbilzen Sands samples, the exponential factor
As discussed earlier, for gases, the geometric factor
Geometric factors for dissolved gases in Boom Clay (a) and other clayey materials (b).
From Figure
For the Eigenbilzen Sands samples, the geometric factor is rather a constant value. This can also be deduced from the exponential factors of the fit of
For the other clayey samples, the geometric factor clearly increases quite spectacularly with the kinetic diameter: the
From the fits in Table
According to expression (
When the diffusing molecules are not small compared to the pore size, the pore size becomes more important. When, in this case, the size of the diffusing molecule increases, the geometric factors in the different clays diverge, and the geometric factor for different gases in a single sample is not constant. For both bentonites and COX, both fitted
Despite the enormously simplifying assumption to replace a whole pore distribution by just one pore size in both the hydraulic conductivity model and the effective diffusion coefficient versus diffusing molecule size model, both models lead to similar values for the typical pore size. Using the fitted
The effective diffusion coefficients can also be fitted as a function of size by using the power law expression (
Parameter values obtained by fitting the effective diffusion coefficient versus size of the diffusing molecule by the power law expression (
Water |
|
|
||||
(m2/s) | ( ) | |||||
|
|
|||||
|
||||||
Code |
|
|
|
|
|
|
(-) | (m2/s) | (m−1) | ( ) | ( ) | ||
|
||||||
K2 | ⊥ | 0.4 |
|
|
8.4 | 0.2 |
K4 | // | 0.38 |
|
|
3.1 | 0.7 |
K14 | // | 0.37 |
|
|
10.0 |
|
K15 | // | 0.4 |
|
|
6.6 |
|
K16 | ⊥ | 0.41 |
|
|
8.3 |
|
K17 | ⊥ | 0.4 |
|
|
5.5 |
|
Bent 1.4 | 0.47 |
|
|
2.8 | 1.9 | |
Bent 1.6 | 0.4 |
|
|
0.2 | 4.5 | |
COX 1 | ⊥ | 0.18 |
|
|
1.9 | 2.8 |
OPA 1 | ⊥ | 0.096 |
|
|
94.2 |
|
Based on the results presented in this work, one can state that the approach of using one geometric factor for estimating
A more correct way to estimate diffusion coefficients would be by using the exponential or power law relation between
Ratios between the experimentally determined
Core | Code | He | Ne | H2 | Ar | CH4 | Xe | C2H6 |
---|---|---|---|---|---|---|---|---|
Ratio Exp/Fit (-) | ||||||||
BC 84b | K2 | 2.3 | 1.0 | 0.7 | 1.4 | 1.1 | 1.1 | |
BC 127b | K4 | 2.0 | 0.8 | 2.1 | 1.0 | 1.6 | 0.9 | 1.1 |
BC 36a | K14 | 1.4 | 0.8 | 1.1 | 1.0 | |||
BC 37b | K15 | 1.4 | 0.8 | 1.2 | 1.0 | |||
BC 35b | K16 | 1.4 | 0.8 | 1.6 | 0.9 | |||
BC 39b | K17 | 1.3 | 0.8 | 1.5 | 0.9 | |||
Bent 1.4 | Bent 1.4 | 1.1 | 0.9 | 1.1 | 1.0 | |||
Bent 1.6 | Bent 1.6 | 1.7 | 0.8 | 0.8 | 1.2 | |||
COX 1 | COX 1 | 2.4 | 0.9 | 0.9 | 1.2 | |||
OPA 1 | OPA 1 | 7.8 | 0.9 | 1.1 | ||||
Average | 1.7 | 0.8 | 2.1 | 0.9 | 1.3 | 1.0 | 1.0 | |
Standard deviation | 0.4 | 0.1 | 0.2 | 0.3 | 0.2 | 0.1 |
Predicting the gas effective diffusion coefficients of sample K4 after measuring the Ne and C2H6 (both in italic) effective diffusion coefficients. In a first phase, the prediction is based only on expression (
He | Ne | H2 | Ar | CH4 | Xe |
| ||
---|---|---|---|---|---|---|---|---|
Kinetic diameter |
( |
2.58 |
|
2.97 | 3.42 | 3.82 | 4.06 |
|
|
( |
74.7 |
|
51.2 | 14.5 | 15.5 | 6.6 |
|
|
|
27.2 |
|
19.7 | 13.6 | 9.7 | 8.0 |
|
Ratio |
( ) | 2.7 |
|
2.6 | 1.1 | 1.6 | 0.8 |
|
Correction factor | ( ) | 1.7 | 0.8 | 2.1 | 0.9 | 1.3 | 1.0 | 1.0 |
|
( |
45.8 | 41.2 | 12.2 | 12.4 | 7.7 | ||
Ratio |
( ) | 1.6 | 1.2 | 1.2 | 1.2 | 0.9 |
By using this approach, the diffusion coefficient of, for instance, H2 (which is difficult to measure due to microbial activity [
Summarizing, for unreactive gases in clayey materials, the effective diffusion coefficient varies with the size of the diffusing molecule and this variation can be described by an exponential or a power law function. Besides, the geometric factor can be described by a decreasing exponential function of the ratio between the size of the diffusing molecule and a characteristic pore size
By measuring experimentally the effective (or apparent) diffusion coefficient of two unreactive gases in clay, the remaining diffusion coefficients can be estimated by an exponential (or alternatively a power law) relationship.
The authors declare that they have no conflicts of interest.
This work is partly performed in close cooperation with and with the financial support of ONDRAF/NIRAS, the Belgian Agency for Radioactive Waste and Fissile Materials, as part of the programme on geological disposal that is carried out by ONDRAF/NIRAS. This work has been performed with the support of Tom Maes, Marc Van Gompel, Dorien Verhaegen, Serge Labat, Joan Govaerts, Lander Frederickx, Mieke de Craen, Rieko Adriaens, and Nancy Weyns.