We study the structural and transport properties of two model porous membranes made by compaction of spherical monosize gamma -alumina particles. A ballistic deposition process of spherical particles has been employed as a process-based representation method for accurately simulating the pore structure of the membranes. Comparison between the computed and experimental permeability values obtained in the Knudsen regime shows very good agreement for both membranes and indicates that sufficient representation of the original pore structure is achieved with the random sphere packs. In a further step, a medium with the same porosity and autocorrelation function as the sphere pack has been stochastically reconstructed. Comparison between the structural properties of the random sphere pack system (process-based model) and the stochastically reconstructed medium (statistical model) shows nearly identical correlation functions and pore chord length distributions but widely different mass chord length distributions. This is reflected to a significant difference in the prediction of a dynamic property like the Knudsen permeability by a factor of about 4. The results suggest that matching of the porosity and the two-point correlation function alone is not always adequate when pursuing an accurate representation of the structure of a porous material. In such cases, higher order statistical properties of the material contained in the chord length distribution of both pore and solid phase should be satisfied as well. It is also found that proper account of the formation process in the reconstruction of a porous material (process-based model) leads to representations of its structure more accurate than those of statistical reconstruction models.