Dielectric Dispersion Measurements Research Articles

The Effect of Salt Concentration on Dielectric Permittivity and Interfacial Polarization in Carbonate Rocks with Complex Pore Structure

Summary Broadband dielectric dispersion measurements are attractive options for the assessment of water-filled porosity. Dielectric permittivity is influenced by salinity as well as other rock/fluid properties. However, the effect of salinity on Maxwell-Wagner polarization (i.e., interfacial polarization) and dielectric permittivity in rock samples with complex pore structures requires further investigation. The objectives of this work are (a) to perform frequency-domain dielectric permittivity numerical simulations on 3D pore-scale rock samples at different salt concentration levels, (b) to quantify the effect of salinity on dielectric permittivity and interfacial polarization in the frequency range between 20 MHz and 5 GHz, and (c) to quantify the critical frequency (i.e., the frequency at which the relative permittivity becomes frequency-independent). We first perform pore-scale frequency domain dielectric permittivity simulations in fully water-saturated carbonate samples with complex pore structures to obtain the complex dielectric permittivity in the frequency range of 0.01–5 GHz and at different salinity levels. Next, we numerically create partially water/hydrocarbon-saturated water-wet samples and perform simulations at different salinity and water saturation levels to investigate the combined effect of salinity and water saturation on dielectric permittivity. Finally, we investigate how reliable conventional mixing models, such as the complex refractive index model (CRIM) and Hanai-Bruggeman (HB), are in the assessment of water saturation at different salinity levels. We used 3D pore-scale rock samples with complex pore structures from Austin Chalk, Estaillades Limestone, and Happy Spraberry formations. The increase in salinity from 2 to 50 parts per thousand (PPT) resulted in the relative permittivity to increase by 18% at 20 MHz. Similarly, an increase in salinity from 2 PPT to 50 PPT resulted in electrical conductivity to increase by 15 times at 20 MHz. However, at 5 GHz, the difference between the relative permittivity of the samples at different salinities was negligible. We demonstrated that the critical frequency was above 1 GHz. Thus, if complex dielectric permittivity at 1 GHz is being used, an accurate salinity assumption is required in the interpretation of conventional dielectric mixture models in carbonate formations. Finally, we observed 52% and 42% average relative errors in water saturation quantification when applying CRIM and HB models at all the frequencies of interest, respectively. The results also indicated that conventional models should not be used in the presence of uncertainty in salinity at lower frequencies. The results of this work quantified the frequency at which the water-filled pore volume rather than the Maxwell-Wagner polarization controls the relative permittivity of rock samples saturated with a wide range of brine salinity. Moreover, the results demonstrated that the relative permittivity of the rock samples with complex pore structures may still be significantly affected by the interfacial polarization even at 1 GHz. Moreover, the results suggested that the conventional mixture methods cannot reliably take into account the salt concentration of formation water, and this can lead to significant errors in reserves assessment.

Electrorheological Properties of α-Bi2O3 and Bi2O2CO3

Abstract—We have synthesized needle- and platelike α-Bi2O3 and Bi2O2CO3 nanoparticles. The bulk density of the α-Bi2O3 and Bi2O2CO3 powders is 8.5 and 6.9 g/cm3. The dielectric permittivity of α-Bi2O3 and Bi2O2CO3 has been calculated using dielectric permittivity and dielectric loss tangent dispersion measurements in the frequency range from 2.5 × 101 to 1 × 106 Hz for 40% suspensions (0.05 and 0.08 volume fractions of α-Bi2O3 and Bi2O2CO3, respectively) in PMS-300 polydimethylsiloxane. The value of e∞ has been found to be 5.4 for α-Bi2O3 and 4.9 for Bi2O2CO3. Dielectric spectra of the suspensions have been shown to exhibit no relaxation behavior in the frequency range studied. We have compared the effects of the shape and dielectric permittivity of the particles on the magnitude of the electrorheological effect in them. Using a simple polarization model, we have analyzed the effect of the dielectric characteristics of the filler material on the yield stress τ0 of the suspensions in electric fields from 0 to 4 kV/mm. Using a combination of rheometric and direct microscopic observations, we have explained the effect of the type of filler on the electrorheological effect: the Bi2O2CO3-based ERFs have higher shear and compressive yield stresses, whereas the α-Bi2O3-based ERFs have a higher tensile yield stress.

Joint petrophysical inversion of multifrequency conductivity and permittivity logs derived from subsurface galvanic, induction, propagation, and dielectric dispersion measurements

Borehole-based subsurface electromagnetic (EM) measurements, namely, galvanic resistivity (laterolog), induction, propagation, and dielectric dispersion logs, are commonly used for water-saturation estimation in hydrocarbon-bearing formations. EM logs exhibit frequency dependence due to the interfacial polarization (IP) effects arising from clay-grain surfaces, conductive minerals, and charge blockage in pore throats. IP effects in shale formations adversely affect the log-derived water-saturation estimates, especially when there is low porosity, high salinity, the presence of pyrite disseminations, and high clay concentration. Conventional EM log-interpretation methods estimate water saturation in shale formations by separately interpreting the galvanic, induction, propagation, and dielectric dispersion logs using various empirical models or mixing laws. This approach leads to significant variations and uncertainties in petrophysical estimations. We have developed an inversion-based joint petrophysical interpretation of multifrequency effective electrical conductivity and dielectric permittivity logs derived from various combinations of the four aforementioned downhole EM logs acquired in clay- and pyrite-rich shale formations. The proposed joint-interpretation method uses a single mechanistic model that accounts for the IP effect arising from clay and conductive mineral grains, thereby generating physically consistent water-saturation estimates in shales. The proposed inversion-based interpretation also generates estimates of formation brine conductivity, surface conductance of clay, and average radius of clay and conductive mineral grains. The proposed method is applied to one field case and three synthetic geologic formations, with varying clay type, conductive mineral properties, and water saturation. Further, the sensitivity of inversion-derived estimates to the presence of various types of noise in the EM logs is investigated. The joint petrophysical inversion algorithm is applied to field broadband dispersion EM data acquired in an organic-rich shale formation. Water saturation, brine conductivity, surface conductance of clay, and radius of clay were consistently estimated in the shale formation using various combinations of available EM logs.

Advanced logging and analytical methods unlock producibility potential in fresh formation water — A case study from offshore West Africa

The sedimentary basins of West Africa encompass a vast diversity of geologic depositional settings, in and from which hydrocarbons are being explored and produced. The siliciclastic rock units can be structurally heterogeneous, the reservoirs distribution and quality is highly variable, and formation waters have changing salinity values. The fresh to very fresh formation water diminishes the contrast to hydrocarbon complicating any salinity-based measurement technique, such as resistivity. As a result, the reservoir potential might be under- or overestimated by conventional methods; hence, an intelligent petrophysical evaluation and a fit-to-purpose solution become essential to enable the most appropriate development and production strategy. As part of an extended portfolio of wireline logging technology, dielectric dispersion measurement is a critical contribution to the logging programs across the region. The advanced measurement provides dielectric permittivity and conductivity at multiple depths of investigation through the use of multiple frequencies, receiver spacing, and polarizations that are adequately fit into an innovative mandrel design. Robust inversion of all measurements enables solving for salinity, invasion profile, water fraction, shallow zone resistivity, and saturation even when it is hard to distinguish oil from freshwater. We have developed a remarkable example of intelligent logging assessment in highly complex reservoir units where the novel dielectric dispersion measurement is combined with high-resolution magnetic resonance for improved formation evaluation and reservoir management. An integrated data analysis workflow enables fast determination of pay zones and movable fluids independently from and to support saturation equation and input parameters setting. Comparison of the results from well testing confirms the improvement in reservoir description with additional advanced logging measurements (at an early stage of reservoir development) into reservoir models. The information provided is vital to guide perforation and completion designs.

Thermal and dielectric properties of K3Nd(PO4)2 prepared by Pechini and solid state method

• The K 3 Nd(PO 4 ) 2 powders built of nanometric sized crystals have been obtained. • The polymorphic transition β/α depends strongly on preparation method. • The activation energy of active dipoles in K 3 Nd(PO 4 ) 2 has been determined. The binary neodymium–potassium phosphate β-K 3 Nd(PO 4 ) 2 was obtained by the ceramic and modified Pechini methods. The obtained powders were studied using TGA/DSC, XRD, FTIR and BET techniques. The materials obtained by the Pechini method show a strong tendency towards agglomeration. The average crystallite size of β-K 3 Nd(PO 4 ) 2 obtained at 480 °C amounts to about 30 nm. The temperature and enthalpy of the β/α-K 3 Nd(PO 4 ) 2 polymorphic transition were determined. In the case of the materials obtained by the Pechini method, the polymorphic transition occurs at 1181 °C and it is assisted by one endothermic effect with the Δ H ph.tr. = 58 ± 9 kJ mol −1 . For powders obtained by ceramic technique the β/α polymorphic transition takes place in a temperature range of 1148–1180 °C and is accompanied by two endothermic effects with the total enthalpy change of 53 ± 15 kJ mol −1 . The effect of the synthesis method and that of the size of the phosphate crystallites on the mechanism of polymorphic transition have been discussed. The electric permittivity and dielectric loss measurements were carried out, too. The activation energy of active dipoles in K 3 Nd(PO 4 ) 2 was determined on the basis of the electric permittivity and the dielectric dispersion and absorption measurements. The activation energy amounts to 149.8 kJ mol −1 .

Static and dynamic critical behaviours in de Vries liquid crystals

Measurements of dielectric dispersion have been carried out on two liquid crystal compounds 8422[2F3] and 8O23[7F8-], showing non-layer-shrinkage (NLS) behaviour through the smectic-A (Sm-A)–smectic-C (Sm-C) transition. The critical exponent γ for the susceptibility determined from the data lies in the range 1.9–2.0 for 8422[2F3] and 1.1–1.2 for 8O23[7F8-]. While the former agrees with the general trend reported so far for this group of liquid crystals, the latter result is distinct from them, the γ value being definitely smaller. These observations indicate that the Sm-A–Sm-C transition with NLS behaviour can exhibit quasi two-dimensional Ising critical behaviour under certain conditions. The critical exponent Δ for the relaxation frequency has also been obtained as Δ = 2.0–2.1 for 8422[2F3] and 1.2–1.3 for 8O23[7F8-]. The results support the general expectation Δ > γ rather than the conventional behaviour Δ = γ.

Study of Dielectric Dispersion in Non-Layer-Shrinkage Liquid Crystal Compounds

Measurements of dielectric dispersion have been carried out on two liquid crystal compounds 8422[2F3] and 8O23[7F8-], showing non-layer-shrinkage (NLS) behavior through the smectic-A(Sm-A)-smectic-C (Sm-C) transition. The critical exponent γ determined from the data lies 1.5–1.9 for 8422[2F3], and 1.1–1.2 for 8O23[7F8-]. These results indicate that the Sm-A-Sm-C transition with NLS behavior can exhibit quasi two-dimensional Ising critical behavior under a certain condition.

An interpretation of fluctuations in enzyme catalysis rate, spectral diffusion, and radiative component of lifetimes in terms of electric field fluctuations

Time-dependent fluctuations in the catalysis rate (deltak(t)) observed in single-enzyme experiments were found in a particular study to have an autocorrelation function decaying on the same time scale as that of spectral diffusion deltaomega(0)(t). To interpret this similarity, the present analysis focuses on a factor in enzyme catalysis, the local electrostatic interaction energy (E) at the active site and its effect on the activation free energy barrier. We consider the slow fluctuations of the electrostatic interaction energy (deltaE(t)) as a contributor to deltak(t) and relate the latter to deltaomega(0)(t). The resulting relation between deltak(t) and deltaomega(0)(t) is a dynamic analog of the solvatochromism used in interpreting solvent effects on organic reaction rates. The effect of the postulated deltaE(t) on fluctuations in the radiative component (deltagamma(r)(-1)(t)) of the fluorescence decay of chromophores in proteins also is examined, and a relation between deltagamma(r)(-1)(t) and deltaomega(0)(t) is obtained. Experimental tests will determine whether the correlation functions for deltak(t), deltaomega(0)(t), and deltagamma(r)(-1) are indeed similar for any enzyme. Measurements of dielectric dispersion, epsilon(omega), for the enzyme discussed elsewhere will provide further insight into the correlation function for deltaE(t). They also will determine whether fluctuations in the nonradiative component gamma(nr)(-1) of the lifetime decay has a different origin, fluctuations in distance for example.

Structure and properties of tris(tetramethylammonium) nonabromodiarsenate(III),[(CH3)4N]3[As2Br9

The new tetramethylammonium bromoarsenate(III) crystal[(CH3)4N]3 [As2Br9] has been synthesized and its phase behaviour established by differential scanningcalorimetry and dilatometry. Three phase transitions are found: at 346/346 K , at 165/171 K and at 157/165 K on cooling/heating. Single-crystal x-ray diffraction studies of phases I (at370 K) and II (at 298 K) have shown that the structure comprises discrete[As2Br9]3− anions anddisordered [(CH3)4N]+ cations. Phase II crystallizes in the polar space groupP31c; its polar nature was confirmed by pyroelectric measurements. Phase I has higher symmetry,P63mc or . Dielectric dispersion measurements revealed a relaxation process in the crystal. Theferroic (ferroelastic) properties were found below 165 K (the transition). The NMR studies indicate the subtle change in the motional state of thetetramethylammonium cations through all observed phase transitions.

Domain dynamics of 2-aminopyridyne phosphate crystal in ferroelectric phase

Measurements of dielectric dispersion in the ferroelectric phase of a 2-APP crystal in the frequency range 200 Hz–1 MHz were carried out. Data points were stored for different amplitudes of measuring field. The dielectric spectra were analysed using the Cole–Cole equation. In this frequency range, one relaxation process was found. The temperature dependence of the relaxation time of this process was calculated. The activation energy of this process was obtained according to the Arrhenius equation, and two amplitudes of the measuring field, 2.8 and 2.1 kV m−1, yielded the following two values: 0.0383± 0.003 and 0.0350± 0.003 eV.

Structure and properties of [(CH3)4P]3[Sb2Cl9] and [(CH3)4P]3[Bi2Cl9

Two new phosphonium chloroantimonate(III) and chlorobismuthate(III) crystals([(CH3)4P]3[Sb2Cl9] (PCA)and [(CH3)4P]3[Bi2Cl9] (PCB)) have been synthesized and their structure determined by means ofsingle-crystal x-ray diffraction. The structure of the title compounds contains discrete[M2Cl9]3− anions in generalpositions and disordered [(CH3)4P]+ cations. The two compounds are isomorphous in the roomtemperature phase and crystallize in the polar trigonal space group,P31c. The phase situation in PCA and PCB is established on the basis of differential scanningcalorimetry and dilatometric studies. Two phase transitions are found: at 534/534 K() and at 135/138 K () for PCA and at 550/550 K () and at 151/155 K () for PCB (on cooling/heating). The values of the transition entropies(ΔStr) obtained suggest that the transitions are of the order–disorder type. The dielectric dispersion measurements haverevealed a relaxation process in the PCB crystal. The pyroelectric measurements of bothcompounds have confirmed the polar nature of the low temperature phase (III). The ferroic(ferroelastic) properties were found over phase III for both crystals.

Water Structures of Differing Order and Mobility in Aqueous Solutions of Schizophyllan, a Triple-Helical Polysaccharide as Revealed by Dielectric Dispersion Measurements

Dielectric dispersion measurements were made on aqueous solutions of a triple-helical polysaccharide schizophyllan over a wide concentration range 10-50 wt % at -45 to +30 degrees C. In the solution state, three different water structures with the different relaxation times tau were found, namely, bound water (taul), structured water (taus), and loosely structured water (tauls) in addition to free water (tauP). Structured water is less mobile and loosely structured water is nearly as mobile as free water, but bound water with taul is much less mobile, thus taul >> taus >> tauls greater, similar tauP. The order-disorder transition accompanies the conversion between structured water and loosely structured water. However, the species with taus remains even in the disordered state and constitutes part of bound water in the entire temperature range. In the frozen state, in addition to bulk water formed by partial melting, two mobile species existed, which were assigned to liquidlike bound water and found to be a continuation of bound water in the solution state. These relaxation time data are discussed in connection with the entropy levels of the four structures deduced from heat capacity data (cf. Yoshiba, K.; et al. Biomacromolecules 2003, 4, 1348-1356).

Broadband Dielectric Spectra of Spheroidal Hematite Particles

In this paper, we contribute new data on the dielectric dispersion of suspensions of two kinds of spheroidal hematite particles (α-Fe2O3). One of the samples consisted of nearly spherical particles, and the other included almost spindle-like particles. We intended to demonstrate the unique potential applications of dielectric dispersion measurements on the characterization of the electrical double layer of nonspherical particles. Thus, we show that while the electrophoretic velocity is practically the same for both systems, the dielectric spectra differ very significantly from each other. In addition to analyzing the role of axial ratios on the electrokinetic behavior, we have also focused on the effect of pH and of the frequency range in which experiments are performed. Thus, two relaxations can be identified in the suspensions: the so-called α-relaxation (typically in the kilohertz region), related to the polarization of the electrical double layer, and the Maxwell−Wagner−O'Konski relaxation (of the or...

Time-resolved measurements of the dynamics of the photoinduced smectic-C* alpha-smectic-A transition.

We present the study of the dynamics of the recently reported photoinduced smectic-C(*)(alpha)-smectic-A transition. High resolution time-resolved dielectric dispersion measurements carried out during the photoisomerization process demonstrate that the magnitude of the uv intensity mimics the role played by temperature in determining the behavior of the soft mode relaxation. We also show that the uv intensity dependence of the soft mode relaxation frequency f(R) in the photoinduced smectic-A phase can be described with a functional form similar to that derived for the temperature dependence of f(R) and compare the experimentally determined critical exponent with the theoretically predicted for the Ising and three-dimensional XY universality classes. Our study illustrates an interesting feature, namely, the magnitude of light intensity can be treated like a thermodynamic variable such as temperature and pressure to study phase transitions in general.

Photoinduced effects in the vicinity of the smectic-C(*)(alpha)-smectic-A transition.

We report the first results of photoinduced effects near the smectic-C(*)(alpha)-smectic-A transition in a binary liquid crystalline material. Dielectric dispersion measurements show that the softening of the tilt fluctuation mode in the vicinity of the transition gets enhanced in the presence of the UV light.

Dielectric Properties of Ethyethlenediamine Cobalt Nitrate (ECN) Single Crystals

Dielectric properties of [Co(H 2 N(CH 2 ) 2 NH 2 ) 3 ](NO 3 ) 3 (ethylenediamine cobalt nitrate, ECN) single crystals have been investigated. Dielectric constants measured at 10 kHz exhibited anomalies around 110 K and 140 K in addition to a tiny anomaly at 250 K. Dielectric dispersion measurements in the frequency range from 100 Hz to 1 MHz have been performed between room temperature and 20 K to investigate the mechanism of the dielectric anomalies. Two Debye-type relaxation modes with rather long relaxation times were found. The temperature dependence of the dielectric strengths, relaxation times, indices for distribution of relaxation time was determined.

Single semicircular response of dielectric properties of diamond films

Diamond films were synthesized by a microwave plasma-enhanced chemical vapor deposition method using H 2/CH 4 gas mixtures. A Fluke PM6306 RCL Meter was used to study the dielectric properties of the diamond films deposited. The dielectric dispersion measurement yielded the real and imaginary parts of impedance of diamond films in the form of a depressed semicircle in a complex plane. A Cole–Cole plot was observed at frequencies from 50 Hz to 1 MHz. The result was found to fit the theoretical resistor–capacitor parallel circuit model. The structure and quality of diamond films were analyzed by scanning electron microscopy, X-ray diffraction and Raman spectroscopy.

Rheological and Electrokinetic Properties of Sodium Montmorillonite Suspensions: II. Low-Frequency Dielectric Dispersion

Because of their particular electric surface properties and crystal structure, most clay minerals possess a very high ion exchange capacity. Furthermore, the surface charge distribution is anisotropic: while faces of the laminar clay particles have a negative, pH-independent charge, edges may be positive or negative, depending on pH. In this work, we propose to contribute new data on particle–particle interaction and charge distribution, by means of measurements of the low-frequency dielectric dispersion (LFDD) of the clay suspensions. Because of the nonspherical shape of clay particles, there are no theoretical models capable of explaining the experimental relaxation spectra. Hence, we limit ourselves to obtaining indirect information by comparing LFDD spectra in different experimental conditions. The quantities of interest in LFDD are the value of the low-frequency dielectric constant, ϵ′r(0), and the characteristic or relaxation frequency, ωcr. These two parameters were measured varying the weight fraction, φ, of clay (0.5, 1, and 1.5% w/v) and the pH of the dispersion medium (5, 7, and 9), while maintaining the ionic strength constant ([NaCl]=10−4 M). It was found that the characteristic relaxation frequency of the dielectric constant was pH-dependent, with a significant minimum at pH 7 in all cases. The results are interpreted as the superposition of two independent relaxation phenomena, associated with edges and faces. With respect to the weight fraction influence, we have found a linear behavior of ϵ′r(0) with φ at pH 9, indicating the existence of no significant interaction between particles. However, at pH 7 a slight deviation of linearity is observed, and at pH 5 we observe a clearly nonlinear behavior, indicating a stronger degree of interaction between particles. This is in good agreement with the initial assumption that at acid pH values, the electric surface charge of faces is negative, whereas the edges possess a positive charge, thus favoring attractive face-to-edge interaction.

Dielectric relaxation and defect analysis of Ta2O5 thinfilms

The presence of defects in thin-film dielectrics often leads todielectric relaxation as a function of frequency, in which the dielectricconstant decreases and the loss tangent increases with increasingfrequency. Dielectric relaxation results in charge storage capacityreduction under dynamic random access memory operating conditions. In thiswork, the dielectric relaxation behaviour of dc reactive sputtered Ta2O5 thin film was investigated. Using dielectric dispersionmeasurements as a function of frequency (100 Hz⩽f⩽10 MHz) and temperature (27 °C⩽T⩽150 °C),we determined the dielectric relaxation and defect quantity of the filmsand propose an equivalent circuit on the basis of complex capacitance,admittance and impedance spectral studies.

Dielectric behaviour of suspensions of non-spherical colloidal particles

In this paper, we explore the possibility of using low-frequency dielectric dispersion (LFDD) measurements in suspensions of non-spherical particles. We present results on the LFDD of clay suspensions, with laminar, non-homogeneously charged particles, and of monodisperse spheroids of haematite (iron III oxide). The heterogeneous surface of the clay (montmorillonite) is manifested in dielectric measurements, since two relaxation times (one associated with faces and the other with edges) can be separated. Furthermore, it is found that the latter is absent at pH 7, thereby directly confirming that the edges of the clay platelets are uncharged at such pH. Experiments conducted with monodisperse haematite spheroids allow a preliminary check of existing theories for the LFDD in such geometries. Comparison of the zeta potentials deduced from dielectric and electrophoresis measurements confirm the validity of the models, and suggest that haematite could be a model spheroidal colloid, to which standard electrokinetic theories are applicable.