Diffusion in Thin Slits with Variable Aperture

Abstract: This project aims to evaluate and improve the design of an experimental setup for visualization and experimental verification of the Q-equivalent model.   The Q-equivalent model by Neretnieks (1979) is used (by SKB in Sweden) to assess mass transport of radionuclides from a broken copper canister at a repository for nuclear waste to water seeping in the host rock fractures, and the same model can be used to assess the mass transport of corrosive agents from the water to the canister. To verify and visualize the model an experimental setup has been designed by Neretnieks (KTH). This setup is what this work will evaluate and try to improve.   Experiments were made by determining the aperture in thin slits (150x150mm) made from wavy glass (simulated rock fractures) by filling it and a calibration slit with a dye and measuring the light extinction. Dyes used for the experiments were copper sulphate, carminic acid and uranine. In a second step, dye from a reservoir was allowed to diffuse in to the same slit filled with pure water. It was photographed daily, for about 2-4 months. From this, together with the known aperture the evolution of the concentration can be determined. The diffusion in the same slit is simulated with a finite volume discretization of Fick’s second law in two dimensions. By fitting the simulation results to the experimental results the dyes diffusion coefficient can be determined. It is then compared with values found in literature. Similar experiments with an advective flow where also conducted, with a slit volume of ~9 ml and a flow with a slit residence time of 5.3 days.   The experiments gave varying results for the different dyes used; uranine gave results varying with a factor 2 and carminic acid a factor 10 lower than the expected diffusion coefficients. For the setup with advective flow steady state set after ~16 slit volumes. All dyes displayed some unsuitable properties during the experimental runs.   Results where diffusion coefficients vary with a factor 2 from expected data as obtained for uranine, can be seen as satisfactory if it was not for its unpredictable behaviour during filling. The results of the experiments with carminic acid are not within satisfactory bounds; this can be an effect of dye degradation or possible effect of mass transfer resistance in the filter, which should be further investigated. The setup with advective flow did not give an expected profile, because the dye was able to diffuse in to the setups decompression chambers; if this problem can be reduced the profile should approach the theoretical.   The experimental design has good prospects to visualize and verify the Q-equivalent model if the current issues, such as finding a stable and predictable dye and hindering diffusion in to the decompression chambers, can be eliminated.