A modified version of Archie’s law to estimate effective diffusion coefficients of radionuclides in argillaceous rocks and its application in safety analysis studies

• We measured the diffusion of HTO, 36Cl− and 22Na+ in several clay rocks.
• De was related to porosity by an extended version of Archie’s law (e-Archie).
• De values for performance assessment were estimated by e-Archie.
• A correction procedure for surface diffusion of ion exchanging cations was developed.

Because of the very low hydraulic conductivity of clay rocks, molecular diffusion is the main process responsible for the transport of radionuclides released from the waste matrix into the host rock. Diffusion values are thus important input parameters in safety analyses. Because diffusion measurements are very time consuming, it is impossible to measure diffusion coefficients for all radionuclides of interest. It is therefore important to develop procedures for doing reliable estimates of diffusion coefficients.Diffusion data of mainly tritiated water (HTO) and anions (I−, Cl−) measured in different sedimentary rocks were taken from the literature. The effective diffusion coefficient could be related to the transport porosity by an extended version of Archie’s law (e-Archie): De=Dw·εm1+B·εm2De=Dw·εm1+B·εm2. The extended version deviates from the classical law at porosity values below ca. 0.1.Effective diffusion coefficients of HTO, 36Cl− and 22Na+ were measured for a series of Swiss clay rocks (“Brauner Dogger”, Effingen Member, Opalinus Clay and Helvetic Marls) and for one Hungarian rock (Boda Claystone Formation) and could be satisfactorily described by the extended version of Archie’s law, bounded by an upper and a lower curve.A method was developed based on e-Archie for estimating effective diffusion coefficients for a series of radionuclides. Important input parameters are the accessible porosity of the rock and the diffusion coefficient of the radionuclide in water. In case of cations showing surface diffusion, a correction term was introduced based on the work of Gimmi and Kosakowski (2011).

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