Spectral induced polarization (SIP) measurements explore the variation of the complex conductivity (σ*) of a material with frequency. Much of this variation results from polarization effects associated with the electric double layer on the surfaces of pore spaces. The consequent dependence of the SIP signature on pore structure thus has the potential to provide a link to the hydraulic properties of the material, which have a similar dependence. We report here on the variation of the SIP signature of unconsolidated sands, typical of those found in coastal aquifers in New Zealand, with the conductivity of the pore fluid. The SIP parameters of the measurements are modelled in terms of a Cole‐Cole model and demonstrate the independence of relaxation time on fluid conductivity. The contribution of surface conductivity to the overall conductivity is calculated and the variation of the imaginary part of the surface conductivity with fluid conductivity is tested against two models for the origin of surface conductivity. The measured hydraulic conductivity is also compared with estimates provided by three proposed equations relating hydraulic properties to structural and electric properties.
Laboratory measurements of the permeability and spectral-induced polarization (SIP) response of samples consisting of unconsolidated sands typical of those found in New Zealand aquifers have been made. After correction of measured formation factors to allow for the fact that some were measured at only one fluid conductivity, predictions of permeability from the grain size (d) of the samples are found to agree well with measured values of permeability. The Cole-Cole time constant (derived from the SIP measurements) is found, as expected, to depend upon d 2 , but can be affected by the inclusion of smaller grains in the sample. Measurements made on samples comprising of mixtures of grain sizes show that inclusion in a sample of even 10% of smaller grains can significantly reduce both the Cole-Cole time constant (s CC ) and the permeability, and support theoretical derivation of how the permeability of a mixture of grain sizes varies with the content of the mixture. Proposed relationships for using s CC as a predictor for permeability are tested and found to be crucially dependent on the assumed relationship between the dynamic pore radius and grain size. The inclusion of a multiplicative constant to take account of numerical approximations results in good predictions for the permeability of the samples in this study. It seems unlikely, however, that there is a single global expression for predicting permeability from SIP data for all samples.
<p>Spectral Induced Polarization (SIP) is a geophysical technique that measures the frequency dependence of the electrical conductivity of a material. This thesis is an attempt to investigate the potential of using SIP as a proxy to predict the hydraulic conductivity of New Zealand shallow coastal aquifers. SIP measurements were made on sand samples that are typical of New Zealand coastal aquifers with a custom built impedance spectrometer and sample holder allowing the measurement of a phase difference as small a milliradian. Even though the relaxation time shows a small dependence on pore fluid conductivity, especially at lower pore fluid conductivities, this variation is not serious enough to affect the hydraulic conductivity estimation at the field scale, but could be significant in the investigation of mechanisms that cause polarization in porous media. Measurements on sieved fractions of sand established that there is an excellent correlation between the Cole-Cole relaxation time constant and grain size. The Cole-Cole relaxation time constant is very sensitive to the grain size distribution. Hydraulic conductivity predictions were attempted using various existing models. While the results are encouraging, it looks like there may not be a single universal model to predict hydraulic conductivity using SIP response. When a correction term in the form of a multiplication constant is used, all the tested models seem to make very good predictions. But the constants calculated by fitting to the measured data could be applicable only to the type of materials studied. The dependence of the existing models on quantities like counterion diffusion coefficient, electrical formation factor and porosity makes hydraulic conductivity prediction challenging as these quantities are difficult to measure accurately in a field setting. Nevertheless it is concluded that SIP can be successfully applied to study hydraulic conductivity of New Zealand shallow coastal aquifers.</p>
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