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- Fractal dimension (1)
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- Permeability (1)
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- Spectral induced polarization (1)
Permeability estimation from induced polarization (IP) measurements is based on a fundamental premise that the characteristic relaxation time τ is related to the effective hydraulic radius reff controlling fluid flow. The approach requires a reliable estimate of the diffusion coefficient of the ions in the electrical double layer. Others have assumed a value for the diffusion coefficient, or postulated different values for clay versus clay-free rocks. We have examined the link between a widely used single estimate of τ and reff for an extensive database of sandstone samples, in which mercury porosimetry data confirm that reff is reliably determined from a modification of the Hagen-Poiseuille equation assuming that the electrical tortuosity is equal to the hydraulic tortuosity. Our database does not support the existence of one or two distinct representative diffusion coefficients but instead demonstrates strong evidence for six orders of magnitude of variation in an apparent Diffusion coefficient that is well-correlated with reff and the specific surface area per unit pore volume Spor. Two scenarios can explain our findings:
(1) the length scale defined by τ is not equal to reff and is likely much longer due to the control of pore-surface roughness or
(2) the range of diffusion coefficients is large and likely determined by the relative proportions of the different minerals (e.g., silica and clays) making up the rock. In either case, the estimation of reff (and hence permeability) is inherently uncertain from a single characteristic IP relaxation time as considered in this study.
The pore size distribution provides a suitable description of the pore space geometry that can be used to investigate the fractal nature of the pore space or to determine a fractal dimension. Fractal dimension describes the size of geometric objects as a function of resolution. It can be integrated into models of permeability prediction. We investigated the fractal dimension of the pore volume of 11 Eocene sandstone samples from China. This study describes an approach to use spectral induced polarisation spectra to estimate the pore size distribution and to determine the fractal dimension of the pore volume. Additionally, the fractal dimension was derived from data of the capillary pressure curves from mercury intrusion and the transversal relaxation time distribution of nuclear magnetic resonance. For samples with an effective pore radius larger than 1 μm, good agreement exists between the values of fractal dimension derived from the three different methods, which implies the identification of similar pore structures. Spectral induced polarisation can be a non-invasive laboratory technique for the estimation of the pore size distribution, but the application of the methodology for field measurements remains a challenging problem considering the limited frequency range.