The study of fluid flow in porous media is important in many fields from oil recovery and carbon sequestration to fuel cells. An important area still under investigation is the relationship between the porous microstructure and the permeability of a material since accurate permeability estimations are required for predictive continuum models of flow and mass transport through porous media. Tortuosity is another important parameter used in continuous permeability relationships to relate permeability to porosity and other microstructural properties of porous media such as pore connectivity. The focus of this research is to provide foundational tools to characterize porous media flow transport properties such as permeability and tortuosity. To achieve this goal, this thesis is divided into two parts:​ First, a numerical-based approach (lattice-Boltzmann model) was developed in-house to simulate fluid flow in porous media. This numerical tool was used to determine the permeability of two structured simulated porous domains. The lattice-Boltzmann model was also used in a stochastic model to investigate the impact of the geometric properties of the grains (such as grain aspect ratio) on the tortuosity-porosity relationships in porous media. In the second part, an analytical approach was proposed and used to investigate the tortuosity-porosity relationships in fractal geometries.

From the permeability study, it was found that the predictability of the Kozeny-Carman equation (a commonly-used permeability relationship) can be improved with a modified KC parameter that is an algebraic function of porosity. From the numerical stochastic tortuosity study, it was found that tortuosity exhibits an inverse relationship with the porosity that can be expressed in logarithmic form. Furthermore, the adjusting parameters (a and b) were calculated in the tortuosity-porosity correlation of τ=a-b.ln⁡(ϕ). It was found that tortuosity increases with increasing grain aspect ratio. From the analytical tortuosity study, it was found that the analytical tortuosity-porosity relationships in the studied fractal geometries are linear and the tortuosity has an upper bound at the limiting porosity (ϕ=0 for the Sierpinski carpet). These tools and observations provide the capability for predicting continuous permeability and tortuosity correlations that can be used in large-scale continuum modelling of fluid flow in porous media.