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We use scanning electron microscopy and optical data to show that the pore spaces of several sandstones are fractal geometries and we use the fractal statistics to predict the correct porosity.Steady-state crystal growth during rock formation is a plausible cause of the self-similar geometry.The fractal-dimension values and a systematic analysis of rock conductivity data both mediate against percolation models as suitable models of rock pore-space geometry.PACS numbers: 91.60.pn, 05.60.+w We present experimental evidence indicating that the pore spaces of a set of sandstone samples are fractals' and are self-similar over 3 to 4 orders of magni-0 tude in length extending from 10 A to over 100 p, m.The measured values of the fractal dimensions are greater than those expected for a three-dimensional, random mixture near the percolation threshold, which suggests that percolation theory does not describe the pore-space geometry.The fractal dimension varies from sample to sample with extreme values of 2.57 to 2.87. This range of values suggests that the pore formation processes do not fall within a single universality class.The density-density correlation function of the pore space is constant over length scales greater than a characteristic length l2, which is approximately the size of sand grains in a sandstone (typically 100 p, m across). For length scales l & l2, we expect the transport coefficients to be constant and characteristic of the macroscopic properties of the rock. At length scales I& & l (l 2, we show that the pore-space -rock interface is a self-similar manifold with a well-defined fractal dimension, D, and a lower limit of selfsimilarity, l &.We further argue that the pore volume is a fractal with the same fractal dimension as the pore-rock interface. This conclusion is supported by correctly predicting the porosity from the fractal parameters and by directly showing that the fractal dimension measured by autocorrelation of pores on thin sections agrees with that measured on fracture surfaces.We also show that self-similar pore-space geometries can arise naturally from crystal growth in pore spaces under quasi -steady-state conditions and that the resulting fractal dimensions can assume a continuous range of values that depend on chemical kinetic parameters. Self-similarity in rock pore spaces leads naturally to an explanation of Archie's law for the conductivity. We find that the literature conductivity data cannot be used to draw any conclusions regarding the presence (or absence) of a percolation threshold.Measurements of the electrical conductivity of rocks play an important role in oil and mineral exploration and production. For many sandstones saturated with saline solution, the electrical conductivity follows the empirical Archie formula, 3 o-= o-"@,where o-is the rock conductivity, o-is the conductivity of the pore fluid, @ is the porosity, and m is an exponent, which is traditionally defined by log-log plots of ovsArchie's law depends on the geometry of the pore space, but there exists no d...

We show that mercury injection can be used to characterize the portions of rock pore space that dominate both the electrical conductivity and the absolute permeability. The resulting new expression for the conductivity formation factor is fundamentally different from the classical Archie's law but will appear similar to it in some circumstances. The predictions of our theory for both conductivity and permeability agree with the experimental measurements within expected errors. The results indicate that the absolute permeability and the conductivity formation factor can be predicted from mercury injection measurements with no adjustable parameters.

An automatic technique has been developed to measure precisely the fractal dimension of the microstructure of sandstones from scanning-electron-microscope (SEM) images of fracture surfaces.The technique involves digitizing the images, filtering, counting geometrical features as a function of feature size, and fitting feature histograms. The magnification of the SEM is changed to cover 2.5 orders of magnitude in feature sizes. A po~er-law model, which includes the resolution of the digital filter, accounts for the feature size distributions for all magnifications and the scaling from magnification to magnification. Results have been obtained for a dozen sandstones, and the fractal dimension is observed to range from 2.55 to 2.85. The precision for averaged images is +0.01. In addition, a long-length limit to the fractal regime is defined and measured.

A new electrochemical technique is described that involves applying a series of constant potential steps to an electrochemical cell. On each potential step the cell is permitted to attain quasi open-circuit conditions by letting the current decay to a small, but finite, value. When small voltage steps are made, the voltage-charge relation is a highly precise and accurate approximation to the thermodynamic properties of the cell. Application to the Li-TiS2 couple shows that the charge accumulated on each voltage step resembles an electrochemical potential spectrogram that provides evidence for the structural ordering of lithium in Li~TiS2. The technique may be used to study the potential-dependent cell kinetics, the thermodynamzcs of adsorption on surfaces, and the phase diagrams of cathode materials.Recent reports (1, 2) have shown that high energy density lithium batteries can be based on the inter-, Electrochemical Society Active Member.