Abstract
4-electrode setups are usually used to measure the dielectric response (complex conductivity) of sandstones, as it is known that 2-electrode systems are sensitive to unwanted electrode polarization at low frequency. Moreover, electrode polarization (EP) occurs in the frequency range where the characteristic relaxation associated to the grain size also occurs, which can therefore theoretically be assessed using 4-electrode setups. Nonetheless, we find that other parameters of interest (porosity, salinity) can easily be extracted from the frequency range ∼ 1–10 kHz, beyond the one affected by EP using a 2-electrode setup. An additional unwanted effect (“pseudo-inductance”) is observed in the frequency range 10 kHz–1 MHz during our experiments. Even though the origin of this effect remains unknown, it is shown to be correlated with the ionic strength of the system and the electrode separation. The bulk polarization region, i.e., the region of intermediate frequencies devoid of EP and pseudo-inductance polarizations, is the one of interest, as the complex conductivity of the system is there only dependent on material parameters such as the porosity of the sandstone and the conductivity of the electrolyte. We demonstrate that in the bulk region the model predicts the complex conductivity response, when these porosity and ionic strength are known. The model has been validated using laboratory measurements on a Bentheim sandstone saturated with five different NaCl concentrations: 5, 10, 100, 170, and 540 mM.
Highlights
Frequency dependent electrical measurements have been widely used during the last decades for environmental and engineering studies [e.g., 1–4]
The capacitance is given by Cep = Aκεepε0/2 and the impedance corresponding to Electrode polarization (EP) and bulk polarization of the electrolyte is given by Ztheo = Zep + Ze
We have demonstrated that the dielectric response of a porous sandstone saturated with NaCl solutions of different concentrations measured with a 2-electrode setup can correctly be modeled using the theory presented in this article
Summary
Frequency dependent electrical measurements have been widely used during the last decades for environmental and engineering studies [e.g., 1–4]. Dielectric Response of Saturated Sandstones by electromagnetic pseudo-inductance effects which produce inductive loops yielding positive values in the phase spectra at high frequencies. These loops can be triggered by the wiring of the measurement system [10]. We compare the data with the response of an equivalent circuit model that is built as a sum of three complex impedances Two of these impedances are directly linked to the theoretical complex conductivities of EP and bulk, and are, only dependent on the system parameters (fluid, grain and electrode properties). In the first section we formulate theoretical descriptions of electrode polarization, bulk polarization, and pseudo-inductance complex conductivities as functions of the system parameters, i.e., porosity, conductivity and dielectric permittivity of water and grains. In the fourth section we test the new model by predicting the desired bulk properties from the measured electrokinetic response of a fully saturated reservoir rock for 5 different NaCl solution concentrations
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