Multi-scale micro-structure generation strategy for up-scaling transport in clays

Clays and claystones are used as backfill and barrier materials in the design of waste repositories, because they act as hydraulic barriers and retain contaminants. Transport through such barriers occurs mainly by molecular diffusion. There is thus an interest to relate the diffusion properties of clays to their structural properties. In previous work, we have developed a concept for up-scaling pore-scale molecular diffusion coefficients using a grid-based model for the sample pore structure. Here we present an operational algorithm which can generate such model pore structures of polymineral materials. The obtained pore maps match the rock’s mineralogical components and its macroscopic properties such as porosity, grain and pore size distributions. Representative ensembles of grains in 2D or 3D are created by a lattice Monte Carlo (MC) method, which minimizes the interfacial energy of grains starting from an initial grain distribution. Pores are generated at grain boundaries and/or within grains. The method is general and allows to generate anisotropic structures with grains of approximately predetermined shapes, or with mixtures of different grain types. A specific focus of this study was on the simulation of clay-like materials. The generated clay pore maps were then used to derive upscaled effective diffusion coefficients for non-sorbing tracers using a homogenization technique. The large number of generated maps allowed to check the relations between micro-structural features of clays and their effective transport parameters, as is required to explain and extrapolate experimental diffusion results. As examples, we present a set of 2D and 3D simulations and investigated the effects of nanopores within particles (interlayer pores) and micropores between particles. Archie’s simple power law is followed in systems with only micropores. When nanopores are present, additional parameters are required; the data reveal that effective diffusion coefficients could be described by a sum of two power functions, related to the micro- and nanoporosity. We further used the model to investigate the relationships between particle orientation and effective transport properties of the sample.

Influence of Smoothing on Voxel-Based Mesh Accuracy in Micro-Finite Element

The interest in automatic volume meshing for finite element analysis (FEA) has grown more since the appearance of microfocus CT (μCT), due to its high resolution, which allows for the assessment of mechanical behaviour at a high precision. Nevertheless, the basic meshing approach of generating one hexahedron per voxel produces jagged edges. To prevent this effect, smoothing algorithms have been introduced to enhance the topology of the mesh. However, whether smoothing also improves the accuracy of voxel-based meshes in clinical applications is still under question. There is a trade-off between smoothing and quality of elements in the mesh. Distorted elements may be produced by excessive smoothing and reduce accuracy of the mesh. In the present work, influence of smoothing on the accuracy of voxel-based meshes in micro-FE was assessed. An accurate 3D model of a trabecular structure with known apparent mechanical properties was used as a reference model. Virtual CT scans of this reference model (with resolutions of 16, 32 and 64 μm) were then created and used to build voxel-based meshes of the microarchitecture. Effects of smoothing on the apparent mechanical properties of the voxel-based meshes as compared to the reference model were evaluated. Apparent Young’s moduli of the smooth voxel-based mesh were significantly closer to those of the reference model for the 16 and 32 μm resolutions. Improvements were not significant for the 64 μm, due to loss of trabecular connectivity in the model. This study shows that smoothing offers a real benefit to voxel-based meshes used in micro-FE. It might also broaden voxel-based meshing to other biomechanical domains where it was not used previously due to lack of accuracy. As an example, this work will be used in the framework of the European project ContraCancrum, which aims at providing a patient-specific simulation of tumour development in brain and lungs for oncologists. For this type of clinical application, such a fast, automatic, and accurate generation of the mesh is of great benefit.