Lab-scale and pore-scale study of low-permeability soil diffusional tortuosity

Abstract

Diffusion coefficients for Na+ was measured in low-permeability samples (diameter of 3 cm and average length of 7 cm) from the deep disposal site of the Siberian Chemical Combine (SCC) using the end-diffusion technique. The direction of diffusion was perpendicular to the direction of bedding. Special equipment was designed and constructed for the experiment. Two types of concentration observations were used. For non-sorbing Na+, EC sensors and the length distribution of sorbed elements were used. The synthetic solution used in the experiments was a model of the low-activity contaminant of the SCC and consisted of NaNO3 (25 g/L) and nitrate compounds of Cs+, Ni2+, Co2+, and Sr2+ (100 mg/L each). The measured values of the effective diffusion coefficients De for Na+ from 1.92 × 10−11 to 1.70 × 10−10 m2/s. The microstructure was studied with X-ray microtomography for the same cores. Image shooting was performed on undisturbed microsamples with a size of 0.913 mm (7003 vox). Spatial correlation analysis was performed after the binarization of each obtained 3-D structure. This analysis showed that the spatial correlation scale of the indicator variogram is considerably smaller than the microsample length. Then, a numerical simulation of the Laplace equation with binary coefficients for each microsample was performed. The results were analysed in the form of a plot of the tortuosity versus the porosity. Pore-scale simulations show a nonlinear decrease in the tortuosity with decreasing porosity. Exponential values in the range between 1.8 and 2.4 were found by fitting this graph with Archie's model. Anisotropic tortuosity is also detected in the horizontal and vertical directions. The diffusion coefficients of non-sorbing Na+ measured in this study agree with those of the pore-scale diffusion simulation of the microtomography data.