The analysis of the 3D microstructure of porous materials is of importance in multiple disciplines, such as reservoir engineering and environmental science. We have developed a suite of methods to characterize the geometry and topology of pore systems from 3D images of samples, allowing us to extract pore network representations for use in network flow models that predict single-/multi-phase fluid flow properties. Using these methods, we have investigated geometric and topological factors that have a major impact on the flow prediction. The parameters that describe the geometric and topological characteristics are directly related to the fluid flow properties of the medium. By arbitrarily and independently altering the pore sizes and the connectivity, we show that pore connectivity is the most important influence on the permeability, with the pore size also being important. The work reported here has general relevance in the prediction of properties from 3D images, because of the issue of image artifacts, since mis-assignment of solid/pore can lead to significant changes in predicted properties, especially for coarse-resolution images.