Determination of Diffusion Parameters by a Computer Code (FDP) Based on Mathematica 6.0

A computer code named Fitting for Diffusion Parameters (FDP) based on Mathematica 6.0 has been developed for modeling through- and out-diffusion experiments. FDP was used to determine the diffusion coefficients (D_e) and the rock capacity factors (α) for tritiated water (HTO) and ²²Na⁺ and the distribution coefficient (K_d) of ²²Na⁺ in Opalinus Clay (OPA). The values for D_e and α were obtained by fitting the results of experimental data of both transient and steady-state phases to the analytical solution of accumulated activity. The quality of the parameters D_e and α was tested by using them as input parameters in the equation of flux. Moreover, the diffusion parameters of HTO and ²²Na⁺ were determined also by out-diffusion experiments. Under ambient condition at pH 7.6, the D_e value of (1.5 ± 0.1) × 10⁻¹¹ m²/s for HTO is lower than that of (1.9 ± 1.1) × 10⁻¹¹ m²/s for ²²Na⁺, which could be explained by the electrostatic attraction between the negative surface charge of OPA and the sodium cations. For the non-sorbing species HTO, α was 0.15 ± 0.01. For the weakly sorbing species ²²Na⁺, α was 0.50 ± 0.02 and K_d equaled (1.5 ± 0.3) × 10⁻⁴ m³/kg. The obtained diffusion parameters for HTO and ²²Na⁺ in OPA are in good agreement with previous results by Van Loon et al. [1, 2]. FDP developed in this study has been used successfully to determine the parameters D_e and α for the diffusion of ²³⁷Np(V) in OPA [3].