Characterization of structure and diffusion in geological materials

Abstract

This work deals with two important factors of the element transport in geological materials. Firstly, element diffusion is an important migration process in geological materials, especially when considering transport next to water conducting fractures and shear zones. Secondly, the structure of the pore network forms an environment for migration of elements to take place. These two factors are important when considering radionuclide transport in geological materials in which all affecting processes are not fully understood yet. Therefore further information and development of analysis methods are needed. First of all, a semi-analytical solution for advection-matrix diffusion equations in the case of a well-mixed flow past a porous matrix was developed. Solution is based on a Laplace transform of the equation and on using appropriate dimensionless variables. The matrix-diffusion models considered here include the effects of a finite depth of the matrix, varying aperture of the flow channel, the shape of the input pulse, and longitudinal diffusion and Taylor dispersion of the element in the flow channel as well as a non-zero initial element concentration in the matrix. In order to validate the developed solutions, a measuring system was constructed. Matrix diffusion was illustrated by observing the migration of KCl-tracer in the water flowing through a channel facing a porous matrix. Migration of K+ and Cl− ions was monitored by measuring the electrical conductivity of the solution. The experimental system allowed also measurement of the concentration profile inside the porous matrix, but the focus was here on the input and output (breakthrough) curves. The effects of a finite depth of the matrix and non-zero initial concentration of tracer, predicted by semi-analytical solutions, were successfully validated by the experiments. Secondly, a method to characterize pore network and mineral distribution of geological materials was developed using X-ray micro computed tomography (X-μCT), 14C-labeled-polymethylmethacrylate (14C-PMMA) method, and scanning electron microscopy (SEM). As an example a sample of altered Sievi tonalite was used. X-μCT was used to create 3D density maps of the samples from which different minerals and pores were segmented. From these density maps mineral abundances, porosity, connectivity, porosity distribution and pore size distribution were determined, together with qualitative information about the structure of minerals and pores. X-μCT offers information only of structures whose size is above the detection limit. In order to get information below this limit, the 14C-PMMA method and SEM were applied. Different minerals in the sample were identified by SEM, after which these minerals were linked to different components observed in the X-μCT images. The 14C-PMMA method gives a 2D porosity map of imaged rock surface in which porosity of each pixel represents the averaged porosity over its area, and thus it offers information even from nanometer scale. Further, this information was used to determine the intragranular porosities by superimposing the 2D porosity map with stained and segmented image of the corresponding rock surface and then averaging the pixel porosities over each mineral. Finally, 3D porosity maps of the samples were constructed by combining intragranular porosities and segmented tomographic images. Thirdly, these research issues above were combined by modeling diffusion in tomographic images using time domain diffusion (TDD) simulations. The TDD method is a fast particle tracking method which allows to model diffusion in 3D heterogeneous media when local porosities and diffusion coefficients are known. The method was first validated in various cases including comparison to analytical and numerical solution of the diffusion equation. In addition, the results produced by the method were compared to ones by discrete-time random-walk simulations. TDD simulations were first applied to analyzing a diffusion experiment of tritiated water (HTO) in altered Sievi tonalite and to determine the apparent diffusion coefficient. Then the TDD method was applied to study the effect of material heterogeneity on diffusion processes using a sample of altered Sievi tonalite. This study was done by comparing simulated in-diffusion profiles in samples with heterogeneous and homogeneous distribution of porosity and known diffusion coefficients. In the case of altered Sievi tonalite, inclusion of heterogeneity in the porosity increased the apparent diffusion coefficient by 16%. The method was also found to be suitable when considering the effects of different mineral components and diffusion direction.