In this study, spectral induced polariza on (SIP) spectra were generated numerically to be er understand how actual rock microstructure and electrolyte proper es in rock pores aff ect the spectral pa ern, i.e., the characteris c relaxa on me of polariza on as well as the polariza on strength of a rock pore system. The dynamics of charge carriers in threedimensional pore systems were simulated using a frequency-dependent formula on of the Nernst-Planck-Poisson (NPP) ion-transport equa ons. Basically, a pore-system model of alterna ng stacked cylinders of two diff erent sizes was studied considering the electrical double layer (EDL). A reduced ca onic mobility-resul ng from increased adsorp on of these ca ons at the rock-water interface-was assumed within the EDL. By solving the NPP equa ons using the fi nite element method, complex resis vity phase spectra were generated. Subsequently, the eff ect of pore structural proper es and electrolyte conduc vity on the magnitude and frequency posi on of the characteris c resis vity phase minimum of rocks was studied. The following results were found: First, regarding pore geometry, the characteris c frequency of the phase minimum f min decreases with increasing pore length of the large pore. Second, both small pores having a radius of a few Debye lengths combined with larger pores are needed to ensure detectable phase amplitudes. Third, with regard to electrolyte concentra on, the phase amplitude is inversely propor onal to the concentra on, whereas f min remains constant. Because the studied model does not provide a direct and exclusive link between the simulated electrical proper es and pore throat size, further research is needed here to specify a convincing SIP interpreta on method for improved permeability es ma on.Abbrevia ons: EDL, electrical double layer; SIP, spectral induced polariza on; SNP, short narrow pore.In geophysics, frequency-dependent complex resistivity measurements are a typical noninvasive method for fi eld-and laboratory-scale applications. Th is method is called spectral induced polarization (SIP) or the complex resistivity method, fi rst discovered by Schlumberger (1920). In other fi elds, it is known as impedance spectroscopy. Estimating permeability by such noninvasive electrical measurements has been extensively studied since the 1950s (e.g., Carman, 1956, Ch. 1) and is still a current fi eld of research (e.g., Binley et al., 2005;Titov et al., 2010). To achieve this estimation, one can take advantage of the dependence of both hydraulic and complex or frequency-dependent electric conductivity on microstructural rock properties. A simple model with respect to permeability k is given by the Kozeny-Carman (Carman, 1956, Ch. 1) and related equations (e.g., Katz and Th ompson, 1986). Th ese state a dependence of k on porosity φ and the surface area to volume ratio S por , which in turn can be linked to the electrical formation factor F and a characteristic hydraulic length scale l of the pore space. Th ere are several approaches to obtaining these ...

Impedance Spectroscopy (IS) measurements allow to study a wide range of polarization mechanisms associated with different frequency ranges. Experimental devices usually cover limited frequency ranges with sufficient accuracy. We propose (a) a combination of four-electrode and two-electrode devices and (b) a data combination and mutual verification procedure using the actual sample under test. Hereby, we cover a frequency range from 1 mHz to 10 MHz. The data combination relies on the precondition that any dispersive disturbance decayed at some mutual point within an overlapping frequency range between 1 Hz and 45 kHz. We validate our data combination procedure by IS measurements on simple reference systems and comparison with widely accepted model functions, e.g. the complex refractive index model (CRIM) for high frequency behavior and Kramers-Kronig relations in terms of data consistency. In this respect, our suggested processing approach is superior to two selected alternative approaches. We successfully adapt typical empirical model functions, e.g. multi-Cole-Cole, to the resulting wideband data to show that they are fully applicable for further data analysis.

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