Why tracer migration experiments with a pressure gradient do not always allow a correct estimation of the accessible porosity in clays

Abstract

For assessing the radionuclide transport parameters, the apparent diffusion coefficient and the rock capacity factor ηR (being the product of the accessible porosity η and the retardation factor R) in host rocks used for nuclear waste disposal, mainly two classes of experiments are used: pure diffusive experiments e.g. through-diffusion, and experiments where next to a concentration gradient also a pressure gradient is applied e.g. pulse injection experiments. In Boom Clay, through-diffusion and pulse injection experiments lead to similar values for the accessible porosity of tritiated water (HTO), while for another unretarded tracer, iodide, significantly higher values are obtained by pulse injection. Similarly, in recompacted Na-illite, for chloride (another unretarded anion), lower accessible porosity values are observed by through-diffusion than by pulse injection. The difference increases while lowering the ionic strength.The reason for the discrepancy lies in the models used for analysing the migration experiments with a pressure gradient. Experiments with a pressure gradient allow fitting the apparent velocity Vapp of a tracer. The rock capacity factor is estimated as the ratio VDarcy/Vapp of the Darcy velocity VDarcy and Vapp. This is correct for HTO, but not for anions because the water flow through anion inaccessible porosity is neglected. Making a correct water flow mass balance by taking the water flow through inaccessible porosity into account, demonstrates that the rock capacity factor is given by the product FVVDarcy/Vapp with FV the fraction (0 ≤ FV ≤ 1) of the Darcy velocity flowing through tracer accessible porosity. Previously determined ηR values are in reality the ratio ηR/FV and overestimate ηR. In agreement with the experimental results, a lower ionic strength leads for (unretarded) anions to a lower accessible porosity η and consequently a lower FV and more overestimation of η. Besides charge related inaccessible porosity, porosity can also be inaccessible because of the size of the transported species: the accessible porosity becomes zero in case the particle size approaches the pore throat.Because the intention of experiments with a pressure gradient is to know ηR, we propose two models, which are basically two tracer distributions over a pore, for estimating FV. Considering Poiseuille flow, we calculate a typical pore radius, the hydraulic conductivity and for both distributions the accessible porosity, the fraction FV and the fitted ratio ηR/FV. Application to experimental data shows anisotropy in the pore radius, corresponding to the observed anisotropy in hydraulic conductivity. For anion exclusion, the model describes qualitatively the experimentally observed evolution as a function of double layer width.Because also for cations there is presently no valid relation between Vapp and ηR, migration experiments with a pressure gradient only provide a reasonable estimate for the rock capacity factor ηR in case of small (with respect to the average pore size) neutral particles like HTO.