Microstructure-based characterization of permeability using a random walk model

Quantitative transport properties of materials are analysed using a random walk model, based on the microscopic compositional distribution of compositions in the materials. A material sample is defined on a simple-cubic lattice, with volume fractions specified for each composition on every volume pixel (voxel). The quantitative relation between bulk permeability and fine-scale anisotropy is investigated by assuming fully anisotropic and fully isotropic voxel morphology. Such a study has prompted an analytic approximate formulation to predict bulk permeability range for a heterogeneous multi-component system that lacks detailed microstructure information. The numerical approach is verified on synthetic structures with known permeability. The analysis technique is applied to a real-world rock sample, as illustrated by a case study detailed in this paper. The investigations show that the bulk permeability is affected significantly by fine length scale anisotropy.