Technical Report NTB 12-03
Effective Diffusion Coefficients and Porosity Values for Argillaceous Rocks and Bentonite: Measured and Estimated Values for the Provisional Safety Analyses for SGT-E2
In Stage 2 of the Sectoral Plan for Deep Geological Repositories so-called provisional safety analyses have to be performed. Among other input data, geochemical parameters to describe the transport and retardation of radionuclides in the argillaceous rocks considered and in compacted bentonite are required. In the present report, a comprehensive set of diffusion parameters for all clay host rocks, confining units and compacted bentonite is derived.
Diffusion of tritiated water (HTO), 36Cl- and 22Na+ was studied on samples from Effingen Member, 'Brauner Dogger', Opalinus Clay and Helvetic Marls using the through-diffusion technique described in detail by Van Loon & Soler (2004). Earlier measurements on Opalinus Clay are also shortly summarised in this report. The diffusion measurements gave values for effective diffusion coefficients and diffusion accessible porosities. The general observed trend NaDe > HTODe > ClDe is in agreement with the expected behaviour of the three species in clay materials (Glaus et al. 2010), i.e. ion exchanging cations show an enhanced mobility due to surface diffusion effects (Gimmi & Kosakowski 2011) and anions are slowed down due to anion exclusion, i.e. due to the negatively charged clay surfaces, anionic species are repelled from these surfaces resulting in an accessible porosity that is smaller than the total porosity as measured with HTO (Van Loon et al. 2007).
The effect of porewater composition on the diffusion of HTO, 36Cl- and 22Na+ in Opalinus Clay was investigated. For ionic strength (IS) values between 0.17 M and 1 M (0.17 M ≤ IS ≤ 1.07 M), no significant effect on the effective diffusion coefficient could be observed. In the case of 36Cl-, no effect on the accessible porosity was observed. The anion diffusion accessible porosity equals 50 – 60 % of the total porosity, independent on the ionic strength of the porewater. For the other host rocks no experimental data are available. However, it is assumed that also for the other host rocks, no significant effect can be expected. Further investigations will be performed.
The diffusion parameters were compared with other data taken from the literature and measured on a series of sedimentary rocks such as chalk, clay and limestone rocks. All data could be described by one single modified version of Archie's relation (extended Archie's relation). For values of the porosity greater than ca. 0.1, the classical Archie relation was valid. For porosity values smaller than 0.1, the data deviated from the classical Archie relation, i.e. the decrease of De with porosity, was less fast. This phenomenon can be explained by additional changes of tortuosity with porosity values. At high porosity values, which can be found in low density rocks, the microfabric of the clay rock is of a house-of-cards type. With increasing density, the randomly oriented clay platelets become more and more oriented in a specific direction perpendicular to the direction of compaction. As soon as the platelets are more or less horizontally oriented, further decrease of the porosity has no longer an effect on the orientation and consequently on the tortuosity. The rock bulk dry density threshold value is ca. 2500 kg m-3, representing a porosity value of 0.1.
The extended version of Archie's relation (e-Archie) is the basis for a procedure for estimating effective diffusion coefficients to be used in safety analyses. Important input parameters are the diffusion coefficient of the radionuclides in free bulk water and the transport relevant porosity. Although each radionuclide has its own free water diffusion coefficient, radionuclides were subdivided into two main groups with a free water diffusion coefficient of (20.0 ± 2.5) × 1010 m2 s-1 and (7.5 ± 2.5) × 10-10 m2 s-1. The porosities to be used were given by Nagra and were derived mainly from drilling core samples of the host rocks. The total porosity was based on measurements of the bulk and grain density of the rocks. The values for anion accessible porosities were based on the observation that for most clay rocks ca. 50 % of the total porosity is accessible to anions.
In case of cations undergoing ion exchange, correction for surface diffusion was made using the method developed by Gimmi & Kosakowski (2011). A correction factor CF was calculated using the surface mobility of the cation and the sorption values (Kd) as calculated by Baeyens et al. (2014). The reference values of the effective diffusion coefficients, and their upper and lower bounding values, were multiplied with these correction factors. For most clay rocks investigated, the correction factors used ranged from 1 to at most 30, depending on the sorption value of the cation. The largest values were calculated for Cs+, which is known to be affected by surface enhanced diffusion in argillaceous rocks (Appelo et al. 2010, Melkior et al. 2005, Melkior et al. 2007). In case of Helvetic Marls, the correction factors were between 30 and 400. This is caused by the much larger capacity ratio (κ) values, which are directly proportional to the reciprocal transport porosity of the clay rocks.
As the depth of the host rocks varies notably in the siting regions, it is not possible to define a unique temperature value for the considered formations. Instead, a temperature range was defined for each potential host rock. Effects of temperature on diffusion were evaluated using the Arrhenius equation with an average activation energy for diffusion of 22.9 kJ mol-1 (Van Loon et al. 2005a).
For each host rock, a table with effective diffusion coefficients was compiled. The tables contain a reference value at 25 °C that was calculated for the reference porosity using the master e-Archie's curve. Upper and lower values were estimated by combining the upper e-Archie's curve with the upper value for porosity, and the lower e-Archie's curve with the lower value for porosity. Only the effect for the maximum temperature boundary was considered. To this end, a combined uncertainty on porosity and temperature was estimated by error propagation. The calculated uncertainty was added to the reference value at 25 °C.