Physically representative network models of transport in porous media

We calculate permeabilities for a class of granular porous media derived from a real, disordered packing of equal spheres. The entire structure, including pore space, of these media is completely specified by the radii and spatial locations of the constituent grains. When geometric nearest neighbor grains are grouped together, the structure may be subdivided into pore bodies and pore throats in a natural and unambiguous way. From this subdivision we can establish a network of flow paths whose geometry and topology are completely specified, so that permeability and other transport coefficients can be calculated directly and without any adjustable parameters. The calculations focus on processes that form porous media, rather than on specific examples of such media. Hence, the approach is essentially predictive, rather than correlative. No additional measurements (such as capillary pressure data or pore system data from thin sections) are required, and correlations between permeability and other properties are not used. Predicted permeabilities match measurements on sandstone samples similar to the model perous media studied here over a wide range of porosity. Geometrical attributes of the network representation of the pore space of the model media are found to be spatially correlated. This departure from randomness significantly affects permeability. The agreement between predictions and measurements suggests that spatial correlation is inherent in granular porous media and that uncorrelated network models are therefore unlikely to be physically representative of such media.