Using two-point correlation functions to characterize microgeometry and estimate permeabilities of sandstones and porous glass

We have developed an image processing method for characterizing the microstructure of rock and other porous materials and to provide a quantitative means for understanding the dependence of physical properties on the pore structure. Our method is based upon the statistical properties of the microgeometry as observed in scanning electron micrograph (SEM) images of cross sections of porous materials. This method uses a simple statistical measure of microstructure called the spatial correlation function. We formulate a two-point spatial correlation function and Show how it can be used to estimate porosity, specific surface area, and other microstructural features such as pore and grain sizes. The porosity arid specific surface area are of special interest as they can lie used in a Kozeny-Carman relation to predict permeability of porous materials. We explore the Kozeny-Carman relation and show how it incorporates a characteristic microstructural length parameter similar to that used in other analyses of permeability. We analyze SEM images of several different porous glasses and natural sandstones using the two-point correlation function, discuss the importance of image resolution, and show for the sandstones studied here how the appropriate choices of image resolution can be made so the measured parameters are consistent with those used in a simple flow model for computation of permeability. Estimates of permeabilities for several different porous glasses and natural sandstones are presented. Comparison of these estimates to laboratory measurements shows good qualitative agreement and quantitative agreement within about a factor of 2 for most samples and 3 for all samples.