Pore network as a model of porous media: Comparison between nonhierarchical and hierarchical organizations of pores

A pore network is used as a model of a porous medium with hierarchical and single level organization of the pores. A microscopic diffusion or adsorption process is introduced that permits the study of both temporal evolution and effective properties of transport. The relationships between the model parameters and the measurable quantities are derived. The transport in media with a hierarchical organization of pores is shown to be qualitatively different from that in media lacking this organization. The question of experimental distinction between the two types of pore organization is also studied. We show that mercury intrusion porosimetry (MIP) measurements furnish valuable information about the pore organization in a sample, but that the exact deconvolution of the real pore size distribution from the experimental data is not straightforward. Our work provides indications for a correct interpretation of MIP results. Qualitative comparison with experiments show the pertinence of hierarchical models.