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The relationship between low-frequency electrical properties and hydraulic permeability of rocks has been the focus of geophysical investigations for a long time because it offers a possibility for an in situ and noninvasive permeability estimation of rocks. We examined the hydraulic and low-frequency [Formula: see text] electrical properties as well as the anisotropic properties of low-permeability sandstones from a tight gas reservoir. Single-frequency electrical properties were found to be of low value for the determination of permeability for the studied samples, whereas a strong link between the spectral-induced polarization (SIP) response and permeability was found. The SIP response was transformed into a relaxation-time distribution using a Debye decomposition procedure. We observed a strong positive correlation in form of a power law between median relaxation time of the distribution and permeability, suggesting that relaxation time is a good measure of the effective hydraulic length scale. From a comparison of our results with published relationships between relaxation time and permeability, it becomes evident that the corresponding function is formation specific, requiring a separate calibration for each formation. Nevertheless, SIP offers a high potential for in situ permeability determination because estimation of permeability from relaxation time seems to be applicable for very different lithologies.

[1] The possibility to estimate permeability from the electrical spectral induced polarization (SIP) response might be the most important benefit offered by SIP measurements. It can thus be deduced that, in the future, SIP measurements will be carried out more frequently at the field scale or in a well-logging context to estimate permeability. In the shallow subsurface, however, the temperature generally exhibits seasonal variability, and in the deeper subsurface, it usually increases with depth. Hence, knowledge about the dependence of the SIP response on temperature is necessary in order to avoid possible misinterpretation of datasets impacted by thermal effects. In our study, we present a semiempirical framework to describe the temperature dependence of the SIP response. We briefly introduce the SIP response and its relation to permeability in terms of an electrochemical polarization mechanism and combine this formulation with relationships for the dependence of ionic mobility on temperature. We compare the predictions of our formulation with the experimental data from SIP measurements performed on sandstone at temperatures from 0°C to 80°C. The measured SIP response was transformed into a relaxation time distribution, using the empirical Cole-Cole model and a regularized Debye decomposition procedure. The SIP response was found to be in good agreement with the theoretical model. The temperature dependence of both direct current conductivity and relaxation time is controlled mainly by the dependence of ionic mobility on temperature, and the shape of the relaxation time distribution of the investigated sandstone is almost independent of temperature. The temperature effect on the SIP response can therefore be easily corrected.Citation: Zisser, N., A. Kemna, and G. Nover (2010), Dependence of spectral-induced polarization response of sandstone on temperature and its relevance to permeability estimation,

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We have carried out spectral induced polarization (IP) measurements at three different hydrogeological test sites (Hasloh, Lüdingworth and Kappelen) and estimated hydraulic conductivity using empirical equations previously derived from laboratory measurements. We also reviewed previously published data from another site (Krauthausen). The intention was to explore the potential and practical limitations when applying the method at the field scale. The test sites cover a lithological spectrum from gravel to silt, with a variation in hydraulic conductivity (K) over three orders of magnitude. At each site, hydraulic conductivity was estimated from the real and imaginary conductivity resulting from 2D inversion. We applied the constant phase angle model, where only one frequency, typically around 1 Hz is being used. The uncertainty in K-estimates arising from inversion ambiguity was assessed by exploring the model space with a control parameter that permits a transition from smooth to blocky models and by using different starting models. At the Kappelen site, this uncertainty is larger than four orders of magnitude but a reasonable lower limit for K can be obtained. At the other three sites, the uncertainties are typically one order of magnitude.The IP-based hydraulic conductivity estimates were compared with K-values obtained from grain size analyses and pumping tests. At the Hasloh and Lüdingworth sites the results agree within one order of magnitude and at the Kappelen site the derived lower boundary for K is consistent with grain size information. At the Krauthausen site, the difference between IP-based data and the values derived from grain size and pumping tests is significantly larger than the estimated uncertainties, which is probably due to the non-uniform grain size distribution. The overall results indicate that order of magnitude K-estimates from IP data at the field scale are realistic targets. However, sites with significant deviations from the empirical equations can exist, emphasizing the recommendation to use a priori information whenever possible. (Mazac et al. 1985;Purvance and Andricevic 2000). Spectral induced polarization (IP) measures the complex, frequencydependent electrical conductivity. Physical considerations and laboratory measurements support the idea that the imaginary part of complex conductivity strongly depends on the geometrical characteristics of the pore space and thus might considerably improve quantitative hydraulic conductivity estimation.A number of laboratory measurements of unconsolidated sediments suggest that the phase of the complex conductivity is constant over a broad frequency range . The measured spectra may be described by the constant phase angle model and measurements of a single frequency (i.e., IP measurements) are sufficient to describe the spectra. Empirical equations