Morphology and physical properties of Fontainebleau sandstone via a tomographic analysis

We present a study of the morphology and bulk physical properties of a Fontainebleau sandstone via an X ray tomographic analysis. Synchrotron-based X ray tomographic techniques provide us with a high-resolution (7.5 μm), three-dimensional digitized representation of the sandstone that leaves the sample intact and unaltered. To estimate a wide spectrum of bulk properties of the Fontainebleau sandstone specimen, we extract from this image a number of different correlation functions that statistically characterize the pore-space morphology and relevant pore-space length and time scales. These statistical measures are obtainable from lineal, plane, and/or volume measurements and include the porosity, specific surface, two-point and three-point probability functions, lineal-path function, chord-length distribution function, pore-size distribution function, and coarseness. The pore-size distribution function, in particular, contains a certain level of connectedness information and accordingly can only be obtained from a three-dimensional representation of the sample. Many bulk properties of the sandstone, such as the mean survival time τ (obtainable from Nuclear Magnetic Resonance relaxation studies), fluid permeability k, effective electrical and thermal conductivities, and effective elastic moduli, can be estimated using the aforementioned statistical correlation functions. Specifically, the electrical conductivity (or, equivalently, the formation factor F), mean survival time, and fluid permeability are determined using rigorous bounds. The mean survival time and fluid permeability are also found using direct simulation techniques and cross-property relations, respectively. One such cross-property relation for k depending on τ and F gives a permeability estimate that is within a factor of 2 of the experimental result.