Effect of Spatial Variability on uranium diffusion in the three facies of the Opalinus Clay at Mont Terri

In this contribution the influence of spatial variability on uranium diffusion in clay is investigated by means of 2D reactive transport simulations at the host rock scale. The Opalinus Clay at the Mont Terri underground laboratory displays three main facies: a sandy and carbonate-rich facies, with porosity ranging from 6% to 14%, and a shaly facies with porosity from 10% to 25%. Geostatistical unconditional simulations of porosity were generated with different variogram parameters (correlation length, anisotropy of the variogram, anisotropy ratio) matching the available ranges for each facies, assuming a spherical variogram. The generated gaussian porosity was than employed to compute the tortuosity and hence a spatially variable effective diffusion coefficient. Reactive transport simulations up to 10⁶ years were performed with the POET code using PHREEQC as geochemical engine, considering cation exchange and surface complexation as retention mechanisms, assuming otherwise chemically homogeneous medium. The considered simulation grid is a square with side of 50 m discretized in 100x100 elements and imposing constant boundary condition for uranium concentration at 10^-6 molal along one whole side.

Ten independent geostatistical simulations of porosity were generated for a spherical isotropic semivariogram with correlation lengths of 5, 10, and 20 meters. We also considered anisotropic cases, with main axis of anisotropy parallel and orthogonal to the diffusion direction respectively and anisotropy ratios (ratio between the maximum and minimum correlation lengths) of 4 and 10, with a fixed range of 20 m.

The average migration length of around 22.3 meters after 1 million years is very similar to the one obtained for the spatially homogeneous, reference case. In the isotropic case, larger correlation lengths cause a more relevant spreading of the uranium profiles after 1 million years, achieving a maximum migration length of 23.66 meters with a correlation length of 20 m for the sandy facies, which is around 6 % longer than the homogeneous case. This can be taken as a rough estimate of the uncertainty of the maximum migration length due to spatial variability. Anisotropy of the variogram does not result in a significant difference in terms of covered distance.

These preliminary results highlight moderate effects of spatial variability, which is however largely unknown und needs to be estimated for each possible site. In future work more realistic geometries and facies alternance as well as spatial variability of the mineral fractions and hence the chemical retention potential of the formation will be considered.