Evaluation of Solute Transport through a Fracture by Considering the Spatial Distributions of Retardation Effect in Grain Scale

The retardation effect of radionuclides (RNs) is a key factor to comprehend the performance of the geological disposal system. Since natural rock includes various minerals, the physical and chemical properties are not spatially uniform. However, in general, the performance assessments ignore such heterogeneity. This study focused on the grain size of each mineral in granite, to consider the spatial distribution of retardation coefficients. In a grain size, the retardation coefficient was assumed to be uniform in this study. Through such heterogeneous media, the transport rates of cesium-135 ( $2.1\times {10}^6$ $y$ in half-life) have been numerically examined, using two-dimensional advection-dispersion equations. Here, the sorption data of each mineral in granite were quoted from the past report. The conclusions are summarized as follows: (1) Since the flow test limits the sorption onto biotite (taking the highest sorption-coefficient in the minerals of granite) in the flow paths, the flow test showed less sorption, compared to that expected from the result of batch test for the same material of granite. In other words, because in the batch test the RNs are forcibly sorbed onto a specific mineral, it is possible that the sorption distribution coefficient of granite obtained from batch test is overestimated. (2) When a spatial size of mineral grain boundary is assumed to be a unit size (a few square millimeters), the surface area more than $30\times 30$ unit size at least is needed to obtain the characteristic transport rate for the rock matrix. (3) When the heterogeneity of both sorption efficiency and permeability exists spatially, the assumption of the homogeneity for these distributions yields a conservative result in the breakthrough curve of RNs, compared to the two-dimensional analysis considering the heterogeneity.