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- Diffusion (2)
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Over the last 15 years significant advancements in induced polarization (IP) research have taken place, particularly with respect to spectral IP (SIP), concerning the understanding of the mechanisms of the IP phenomenon, the conduction of accurate and broadband laboratory measurements, the modelling and inversion of IP data for imaging purposes and the increasing application of the method in near-surface investigations. We summarize here the current state of the science of the SIP method for near-surface applications and describe which aspects still represent open issues and should be the focus of future research efforts. Significant progress has been made over the last decade in the understanding of the microscopic mechanisms of IP; however, integrated mechanistic models involving different possible polarization processes at the grain/pore scale are still lacking. A prerequisite for the advances in the mechanistic understanding of IP was the development of improved laboratory instrumentation, which has led to a continuously growing data base of SIP measurements on various soil and rock samples. We summarize the experience of numerous experimental studies by formulating key recommendations for reliable SIP laboratory measurements. To make use of the established theoretical and empirical relationships between SIP characteristics and target petrophysical properties at the field scale, sophisticated forward modelling and inversion algorithms are needed. Considerable progress has also been made in this field, in particular with the development of complex resistivity algorithms allowing the modelling and inversion of IP data in the frequency domain. The ultimate goal for the future are algorithms and codes for the integral inversion of 3D, time-lapse and multi-frequency IP data, which defines a 5D inversion problem involving the dimensions space (for imaging), time (for monitoring) and frequency (for spectroscopy). We also offer guidelines for reliable and accurate measurements of IP spectra, which are essential for improved understanding of IP mechanisms and their links to physical, chemical and biological properties of interest. We believe that the SIP method offers potential for subsurface structure and process characterization, in particular in hydrogeophysical and biogeophysical studies.
The results from several laboratory studies of the relationships between electrical polarization and physical properties of porous media have prompted interest in the potential use of low-frequency electrical spectra to qualitatively or quantitatively map variation in hydrogeologic properties in the field. Compiling several published and unpublished data sets, supported by new measurements, we have examined the low-frequency electrical spectra of a range of natural and artificial porous media to assess the generality of proposed relationships between electrical and physical properties. Our work confirms a significant positive correlation between the magnitude of electrical polarization (quantified as imaginary conductivity at a specific frequency) and the surface-area/pore-volume ratio Spor. Analyzing the parameters of ageneralized Cole-Cole resistivity relaxation model fitted to many electrical spectra, we observe two apparent controls on the electrical relaxation. For samples with abundant relatively large pore throats, we observe a distinct increase in the time constant of the model with modal pore-throat size, in accordance with classical electrical relaxation models. However, for media with pore structures dominated by small pore throats, the diffusion-length scales do not appear to be controlled by modal pore-throat size. We conclude that for such media, the microstructure of the network of small pores leads to some connectivity of diffusion paths; thus, these samples exhibit relatively large time constants. There is potential value in addition to limitations when using electrical spectra to estimate physical properties of porous media, and we see the need for more appropriate generalized theories of electrical polarization in hydrogeologic media.
A number of recent investigations have highlighted the potential value of using relaxation times derived from electrical spectra to infer key physical properties of permeable rocks. To date, most studies have assumed a grain size or pore throat as a measure of the length scale of the ionic diffusive process, although this has been challenged in recent experimental investigations. We compare the electrical spectra of three sandstones, adopting a new approach in which the temperature of the rock samples is perturbed and the relaxation time measured as a function of temperature. Our results suggest that, for the sandstones tested here, the effective diffusion coefficient should be considered as a function of the electrical tortuosity. These findings may help explain the apparent long relaxation times observed in low-permeability rocks in recent experimental studies. We also highlight the need to account for temperature in related studies of electrical spectra.