Surrogate models for the estimation of spatial and temporal scales of the maximum breakthrough of radionuclides in low-permeability porous media

Representative preliminary safety analyses in the site selection procedure for high-level radioactive waste repositories or the subsequent safety assessments require the analysis of the transport regime of radionuclides in e.g. the geological and geotechnical barrier. This can be done (i) using sophisticated, but time consuming numerical models on unstructured grids representing complex geological systems or (ii) using more efficient simple models such as analytical, process- or grid-simplified numerical models that are e.g. calculating in a lower-dimensional space, or simple equations based on e.g. dimensionless numbers.

The present study employs an analytical model of the solute transport equation with linear sorption and decay and a numerical simulator in order to reproduce physical through-diffusion experiments. The same set of transport parameters are used to predict temporal and spatial scales of radionuclide diffusion in low-permeability porous media. The results are then used to develop surrogate models for the estimation of timescales and maximum breakthrough distances of radionuclides. We demonstrate that an expression based on the 2^nd Damköhler number can be used for the calculation of the maximum breakthrough distance for the non-sorbing radionuclides. This expression is calculated using the effective diffusion coefficient, the diffusion-effective porosity, the physical half-life and a dimensionless number. Further, we show that the timescale for reaching the maximum breakthrough distance can be roughly estimated and is two orders of magnitude larger than the physical half-life.