Statistical analysis of the porous microstructure as a method for estimating reservoir permeability

Back-scatter scanning electron microscope images of cross-sections of several porous rocks were analyzed to determine the statistical properties of the porous microstructure. For statistically homogeneous media these properties are the porosity and autocorrelation function. A length scale (integral correlation scale), characteristic of the spatial distribution of porosity, was obtained as the integral of the autocorrelation function. The permeability of a wide variety of rock samples, including those investigated by Coskun and Wardlaw (1993), was adequately described by an empirical equation of the form k proportional to phi(a)I(S)(b), where phi is the porosity and I-S is the integral correlation scale. The results obtained have useful application in the estimation of reservoir permeability from samples not amenable to experimental testing (e.g., drill cuttings) and provide support for the use of statistical methods for the generation of 3-D model porous media.