Mass Transport in Heterogeneous Porous Granular Materials

Abstract

In this thesis, the impact of the particle size distribution and spatial correlations in porous granular material structures on fluid permeability is systematically investigated. A goal is to complement the existing versions of the Kozeny-Carman equation, relating the material properties fluid permeability, porosity and specific surface, with an explicit spatial dependence. Including such a dependence would make it possible to distinguish between materials with different degree of heterogeneity, i.e. granular structures in which the granules are uniformly distributed and in which the they tend to create clusters. An in silico (simulation-based) approach is employed, where virtual material structures based on monodisperse, lognormal and bidisperse size distributions of granules are generated using Monte Carlo-based algorithms. The spatial correlations in the structures are characterized using two types of microstructural descriptors, the pore size distribution and the two-point probability function. Fluid dynamics simulations, from which the fluid permeability is obtained, are performed using a lattice Boltzmann method-based software. The results suggest that there is a linear relationship between the fluid permeability and the squared mean of the pore size distribution. This relationship holds for isotropic structures. As the degree of isotropy decreases, the permeability becomes dependent on the flow direction. It is also shown that the two-point probability function may be used to investigate the order and correlations in the structures, as well as to characterize clustering.