# Evaluation of low-frequency rock polarization models using wide-band impedance spectroscopy on porous sintered glass samples

Aachen (2016) [Dissertation / PhD Thesis]

Page(s): 1 Online-Ressource (vi, 117 Seiten) : Illustrationen, Diagramme

Abstract

Recently, significant progress has been made in understanding low-frequency complex conductivity measurements of rocks. The relevant publications study this method in two different ways: On the one hand, petrophysical interpretation has been improved in terms of theoretical approaches. These approaches are either modificationsof pore size related membrane polarization concepts or rely on grain size related polarization models in combination with semi-empirical model function parametrizations.On the other hand, extensive petrophysical studies provide insight in dependencies of parameters of frequency dependent complex conductivity on structural and electrochemical rock properties. I aim at assessing the results of published theoretical and experimental findings for a reference system, consisting of sintered porous glass samples. Thereby, I benefit from well characterized samples, which allow for direct tests of theoretical predictions and empirical relations.In order to achieve this aim, I improve reliability of my data analysis by a preceded method development step. In particular, this thesis provides the means to conduct wide-band Impedance Spectroscopy measurements of rocks. Since experimental devices usually cover limited frequency ranges with sufficient accuracy, I propose (a) a combination of four-electrode and two-electrode devices and (b) a data combination and mutual verification procedure using the current sample under test. Hereby, I 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 anoverlapping frequency range between 1 Hz and 45 kHz. I verify my data combination procedure by IS measurements on simple reference systems and comparison with widely accepted model functions, i.e. the “complex refractive index model” (CRIM) for high-frequency behavior and Kramers-Kronig relations in terms of data consistency. In this respect, my suggested processing approach is superior to two selected alternative approaches. I successfully adapt typical empirical model functions, e.g. Multi-Cole-Cole, to the resulting wide-band data to show they are fully applicable forfurther data analysis. Using the newly developed method, I find the following results for the reference samples: (1) The correlation $\sigma'' \sim S_{\text{m}}$ is stronger than $\sigma'' \sim S_{\text{por}}$ for a wide range of fluid conductivities and frequencies above 1 Hz. (2) Coefficients of determination for the imaginary conductivity to inner surface area relations are strongly frequency dependent. (3) Normalized chargeability, obtained by fitting a Cole-Cole model to the spectral data, provides a fair alternative to single frequency information. (4) Correlation breaks down for disturbed fluid-surface interaction by wettability manipulation. (5) Salinity dependence of proportionality factors ${a_1 = S_{\text{m}}/\sigma''}$ and $a_2 = S_{\text{por}}/\sigma''$ due to a salinity dependent partition coefficient is confirmed qualitatively. Quantitative theoretical predictions of $a_1$ or $a_2$ fail due to the assumption of non-reduced Stern layer mobility for clay free silica. (6) Earliest grain size related models provide the best quantitative estimate of time constant. (7) Results agree well with published data for sands and sandstones with respect to (i) quantitative estimates of $a_1$ or $a_2$ and (ii) influences of rock structural parameters on time constant.

### Identifier

• URN: urn:nbn:de:hbz:82-rwth-2016-052992
• REPORT NUMBER: RWTH-2016-05299