On the ability of a class of random models to portray the structural features of real, observed, porous media in relation to fluid flow

The description of transport processes is practically accomplished at the macroscopic scale compatible with our ability to observe, and measure processes. The macroscopic description requires to faithfully account for the effects of the detailed inter-phase boundaries on the microscopic level (the micro-structure) in the expression for macroscopic transport coefficients such as permeability. Herein, the porous descriptors held to express macroscopic coefficients are the porosity and the autocorrelation function (ACF) measured directly on a 2-D finite digital image of the porous material. The flow-relevance of the selected porous descriptors will be eventually demonstrated if synthetic porous media generated through a random model from measured porosity and ACF yield the same transport properties than the actual media. Towards that goal, synthetic 2-D numerical porous micro-structures are generated from measured porosity and ACF on two types of natural mechanical aggregates: an Upper Shoreface and a Tidal Channel Sandstone. The achieved synthetic porous media are shown to include all the geometrical features of the real, observed, natural aggregates. Such agreement between synthetic and actual media is demonstrated to be the consequence of: (1) the richness of the structural information carried out by the ACF and, (2) a structural noise produced by the "practical use" of the random model. The requirement to account for the impact on macroscopic physics of this structural noise is emphasized. Extension of the approach to artificial aggregates such as cement, mortars or concrete is shown to be a promising avenue.