Modeling of a dipole matrix diffusion test at the Grimsel Test Site. What explains the different slopes of the tails of the breakthrough curves?

Within the framework of the LTD project (NUMO - Japan, SURAO - Czech Rep., NAGRA – Switzerland, BASE - Germany), a dipole tracer test was performed in the GAM shear zone at the Grimsel Test Site. The granitic rock at Grimsel is characterized by the presence of ductile shear zones with thicknesses ranging up to meter scales, which in turn include intensely deformed mylonitic bands with thicknesses up to several tens of centimeters. Brittle fractures (mm scale) developed in late stages of deformation, mainly in the mylonite bands, and are partially filled by a highly porous fault gouge.

The experimental setup included two boreholes (injection and extraction) which intersected the shear zone. The distance between the two boreholes along the shear zone was 1.2 m. In the first part of the experiment, Grimsel groundwater containing the tracers was injected at 1 mL/min during 20 hours, followed a long period (> 1 year) of injection of groundwater without tracers. Extraction in the second borehole was continuously performed at the same rate of 1 mL/min together with monitoring of tracer concentrations. The tracers were ³H as HTO (conservative), ²²Na (weakly-sorbing) and uranine (only for early on-line monitoring).  In the second part of the experiment, not discussed here, injection was repeated using strongly sorbing ¹³⁴Cs and ¹³³Ba, together with uranine. Overcoring for rock sampling took place shortly after the end of the second tracer injection.

The breakthrough curves (btc) for HTO and ²²Na showed very well defined tails, with different slopes in log-log space for HTO (-2.0) and ²²Na (-1.5). While the slope for ²²Na is that typical for diffusion from the rock matrix back to the fracture, the one for HTO could in principle be attributed to heterogeneous advection. To check this hypothesis, the tests were modeled accounting for fractures with different apertures within the shear zone. First, an analytical solution for the one-dimensional advection-dispersion equation was used to model the results for HTO. Calculations were performed for twenty different fracture apertures following a truncated Pareto distribution. Flow in the fractures was distributed according to the cubic law, with a fixed total flow rate of 1 mL/min.

Once the results for HTO could be reproduced with the analytical model, it was applied in a numerical 2D model, including flow along the fractures and diffusion in the rock matrix. The slope of the tails of the btc’s could be then explained by the addition of the individual btc’s from the different types of fractures. For HTO, the peaks of the individual btc’s have a much stronger weight than the tails, due to the small rock capacity factors (non-sorbing tracer), resulting in the overall slope of -2.0. For ²²Na the tails have much stronger weights (larger concentrations), due to the larger capacity factors, producing the overall slope of -1.5 typical of matrix diffusion.