PhotonIcs and Electromagnetics Research Symposium,
also known as Progress In Electromagnetics Research Symposium
PIERS Proceedings
Published: 2015-07-09
Effect of the Rock/Water/Air Interaction on the Complex Dielectric Permittivity and Electromagnetic Waves Attenuation in Water-saturated Sandstones
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Proceedings of 2015 Photonics & Electromagnetics Research Symposium, Prague, July 6 - 9,Page(s)1877-1880
Abstract
The results of the experimental measurements of the complex relative permittivity (CRP) of the water-saturated powders of the quartz granules of different size and solid sandstones are given in the frequency range from 0.1 kHz to 1 GHz. It is shown that when the water content decreases in the powders of the fine granules and solid sandstones at the determined frequency band the increasing of the real part and decreasing of the imaginary part of the CRP are observed. This leads to the significant increasing of the skin layer, that reaches the highest values at the water content of about 60–80% of the full saturation. In the literature, for example in [1], the properties of elastic waves in the water-saturated sand- stones, particularly the dispersion and attenuation, were described in details, but the properties of electromagnetic waves were described insufficiently. It is known that the real part of complex relative permittivity (CRP) of sedimentary rocks containing clay roughly increases at frequencies below 1 GHz [2–4]. The reason is in the multifrequency relaxation processes. In completely satu- rated sandstones the real part of complex relative permittivity (CRP) depends on the porosity and it remains almost constant in the frequency range of 1 MHz to 1 GHz. At frequencies below 1 MHz observed abrupt increase due to the relaxation of the double layer at the rock-water interface. It is usually assumed that reduction of water content in the rock reduces the real part of CRP. Though there are a number of works which shows the deviations from the tendency in some cases [5– 7]. We measured CRP of water-saturated powders of the quartz granules and solid sandstones with a porosity from 7% to 40% in the frequency range from 100 Hz to 1 GHz by using the method described in [8]. The measurement error at different frequencies was from 0,2 to 3% for ε0 and ε00 . The schematic illustration of the experimental setup is given in Fig. 1. The complex dielectric permittivity was measured in the frequency range from 0.1 kHz to 1 GHz with Rohde & Schwarz ZNB8 vector network analyzer (VNA) and the LCR-meter 3532-50 Hioki HiTESTER. Depending on the measured frequency range, the same cell was either directly connected to the VNA (for measuring in the range from 100 MHz to 1 GHz) or included into the break of the central conductor of a coaxial line of a large cross section (for measuring in the range from 300 kHz to 100 MHz). At frequencies below 1 MHz, the cell admittance was measured ordinary by the LCR meter. CRP of the solid samples was measured in the range of frequencies from 100 Hz till 100 MHz The characteristics of the investigated samples are in the Table 1. Table 1: The characteristics of the investigated samples. The characteristics The average The d RMSE The dry density No. The porosity of the samples diameter d, (µm) (µm) (g/cm3 ) 1 1,35 0,42 0,434 1,50 2 Powders of the 29,6 11,9 0,327 1.58 3 quartz granules 54,5 11,6 0,420 1.57 4 71,5 17,6 0,392 1.60 5 0.173 2.21 Solid sandstones 6 0.068 2.27 The results of the measurements of the real part of the CRP of the completely deionized water- saturated samples that are shown in the table are given at Fig. 2. The temperature here and furthermore is 25◦ C. At frequencies upper 1 MHz the values of ε0 of the large granules powders (samples 2–4) don’t almost depend on frequency and they are determined by general porosity. Sample 1 consisting 1878 PIERS Proceedings, Prague, Czech Republic, July 6–9, 2015 of fine granules contains the considerable part of bound water on the rock-water interface. At frequencies higher than 100 MHz, the dielectric permittivity of this form of water is determined by oriental polarization of water molecules and it is significantly less than the free water has [8]. At frequencies below 1 MHz the main role plays the polarization in the double layer at the rock-water interfaces, that is why the more the specific surface area (the less the pore size) the higher the ε0 . In the solid samples the porosity is far less therefore the dielectric permittivity ε0 is less at frequency of 100 MHz. For all the samples except the sample 1 there is dependence between general porosity and ε0 and the square of the correlation coefficient (R2 = 0.97) that is close to linear. The increasing of the ε0 while decreasing of the frequency begins earlier than in the powders of the quartz granules and obeys another law. Evidently the defining role plays not only the pore size but their form. The CRP frequency dependence of the samples at different saturation levels is similar to the dielectric relaxation, described by the models of Debye or Cole-Cole. At certain frequency range the real part of CRP is bigger than the one of the completely saturated samples, but the imaginary part of ε00 sharply decreases. It is necessary to note that experimental results that could be treated as the result of the dielectric relaxation were given earlier in works [4–6] as a rule at limited frequency range. The frequency dependencies for ε0 and ε00 for different saturation levels of the quartz granules powders are shown at the Figs. 2, 3. At high frequencies about 1 GHz within the water saturation level KW increasing the values of ε’ are monotonically raising. At the same time the values of ε0 and ε00 in powders of granules of different size for the relevant values of KW are almost identical. In the samples containing the fine granules (r ≤ 54.5 µm) at frequencies of 100 kHz–20 Hz there is a strong influence of relaxation process when KW is between 0.2 and 0.9. The values of ε0 are much bigger than at the completely saturation (Fig. 2), but the values of ε00 are much smaller. The reason of the relaxation process is in interlayer polarization at the water-air bound. While increasing the size of granules (and consequently the size of pores) the relaxation process area moves down the frequency. Thus the rising of ε0 at the decreasing of water saturation level is at frequency range of 50 kHz–12 MHz in the sample No. 2, and at the same frequency range there is only the upper bound of relaxation process in the sample No. 4 at frequency about 20 kHz (Fig. 2). Unfortunately the theoretical dependence of the relaxation time on the pore size wasn’t found yet.
Citation
Pavel Petrovich Bobrov, Anastasiya Sergeevna Lapina, and Andrey V. Repin, "Effect of the Rock/Water/Air Interaction on the Complex Dielectric Permittivity and Electromagnetic Waves Attenuation in Water-saturated Sandstones," Proceedings of 2015 Photonics & Electromagnetics Research Symposium, Prague, July 6 - 9,Page(s)1877-1880
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