Permeability, conductivity, and pore geometry of sandstone

Using Bruggeman's effective medium theory, the hydraulic permeability and dc electrical conductivity of sandstone are both expressed in terms of the ratio of two microscopic lengths, which are the dimensions of a characteristic pore throat and pore chamber, respectively. The theory is consistent with Kozeny‐Carman formulas in the limit of a perfectly microscopically homogeneous pore structure. Based on the effective medium approximation, the transport properties of Fontainebleau sandstone are predicted from a quantitative study of the pore space morphology. A series of epoxy‐impregnated thin sections of Fontainebleau sandstone was prepared from cores with porosity ranging between 5 and 22%. Using an image analyzer, throat and pore size distributions were constructed from the digitized and segmented microsections. For each sample the transport coefficients are calculated from the characteristic lengths, which are estimated directly from the experimental size histograms. The changes of both permeability and conductivity are predicted within a factor of 3 over the whole range of porosity. The variations of transport coefficients with porosity are interpreted from the contrasting evolution of pores and throats during diagenesis. Large pore chambers alternate with narrow passages in Fontainebleau sandstone. With decreasing porosity, some of the large pores remain stable, while the throats gradually shrink and are finally eliminated. The microscopic inhomogeneity of the pore geometry of Fontainebleau sandstone implies that its flow properties deviate from Kozeny‐Carman predictions.