A method for determining both diffusion and sorption coefficients of rock medium within a few days by adopting a micro-reactor technique

Migration properties characterized by physico-chemical factors such as distribution coefficient (K_d) and diffusion coefficient (D_e) are of great concern in performance assessment of high-level radioactive waste disposal in a deep geologic environment. These coefficients are normally obtained with different sample geometries using conventional methods, i.e., crushed samples by the batch sorption method for K_d determination and block samples by the through-diffusion method for D_e. A size dependence on both K_d and D_e has been reported and an additional correction due to size difference is required to maintain consistency of the data set. A fast method was developed, hereafter referred to as the micro-channel method, to determine both the sorption coefficient (R_d) and D_e using non-crushed rock sample by adopting the micro-reactor technique. In this method, a radionuclide solution is injected into a micro-channel (20 mm length, 4 mm width, 160 μm depth), which is in contact with a plate-shaped rock sample. A part of the injected radionuclide can diffuse into the rock matrix and/or adsorb on the rock surface and this results in an inlet-outlet concentration difference. A breakthrough curve is easily obtained with a short observation period because the injection amount is extremely small and is comparable to that escaping by diffusion into the matrix. The breakthrough curve is analyzed by a two-dimensional diffusion-advection equation to evaluate R_d and D_e.In the present study, tritiated water (specific activity, 1.2 × 10⁴ Bq/mL; pH, 6) was injected into the micro-channel, and the breakthrough curve of ³H obtained. A series of experiments was carried out by changing the flow rate of the tritiated water (2.6 × 10⁻⁵–7.7 × 10⁻⁴ m/s). Rock samples were biotite granite from the Makabe area, Japan. The diffusion coefficient evaluated by least squares fitting to the numerical solutions (D_e = 1.5 × 10⁻¹¹ m²/s) agreed well with that obtained by the through-diffusion method (1.3 × 10⁻¹¹ m²/s). The breakthrough curve of Cs ([Cs] = 1.0 × 10⁻⁷ mol/L, pH 6) labeled with ¹³⁴Cs (specific activity adjusted to 4.9 × 10¹ Bq/mL) was also obtained. A nearly constant R_d value (5.5 × 10⁻² m³/kg) was found when the flow rate was less than 2.5 × 10⁻⁴ m/s. This implied that the sorption equilibrium is reached and K_d is obtained by the present method. This value was almost identical to K_d obtained by the batch sorption method (5.0 × 10⁻² m³/kg), but the testing period was very different; 1 day and 7 days, respectively. It is concluded that application of the micro-channel method provided advantages when compared with the conventional methods.