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. 2019 Jan 22;4(1):1810–1815. doi: 10.1021/acsomega.8b02802

High Water Content Prediction of Oil–Water Emulsions Based on Terahertz Electromagnetically Induced Transparency-like Metamaterial

Yan Song †,‡,∥, Honglei Zhan ‡,§,∥,*, Chen Jiang ⊥, Kun Zhao †,‡,§,∥,*, Jing Zhu §, Ru Chen §, Shijie Hao ∥, Wenzheng Yue †
PMCID: PMC6648462  PMID: 31459435

Abstract

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This work aims to investigate the electromagnetically induced transparency-like (EIT-like) metamaterial for high water cut emulsions’ detection in the terahertz band. The electromagnetic responses of the selected metamaterial covering emulsions exhibit red-shifted resonant frequency with increasing water volume from 60 to 98%. Three numerical models coinciding with theory analysis were built based on the extracted resonant frequencies at the transmission peak and dips to predict water concentration. The results show that the built models accurately predicted the water content with absolute errors less than 0.26, 0.41, and 0.24%, respectively. The EIT-like resonance is introduced by coupled bright and dark modes, making it similar to a weakened plasma resonance. Consequently, the permittivity-dependent frequency would help develop both economically feasible and socially beneficial sensors for high water content prediction.

1. Introduction

Determining the water content is significant in evaluating crude oil dehydration, logging, refining, and exportation.1,2 So far, many conventional approaches have been employed to determine the water content of oil–water emulsions in different situations according to specific needs, such as the microwave technique, the ray, the capacitance, the Karl Fischer titration method, and near-infrared spectroscopy.3−7 In recent years, requirements for accurate high water content measurement in oil have been more and more exigent and attracted widespread attention in theoretical and experimental work. An open measurement method was proposed to accurately measure water content using a suitable electromagnetic wave with the right wavelength based on Rayleigh scattering, which was further proved to be applicable to oil-wells whose water content is more than 80%.8 An all-optical detection method based on a noncontact laser source and receiver was introduced to measure water content from 0 to 100% in crude oil. The theoretical values of the effective medium model agreed with the experimental results.9 In addition, terahertz (THz) spectroscopy, as a new noncontact technique, has been proposed for predicting subtle changes of water in emulsions owing to the sensitivity of the THz wave to the fluctuations of water dipole moments occurring on the picosecond (ps) timescale.10−14 THz time-domain spectroscopy has been used to measure the water content ranging from 50.05 to 100% in crude oil and to characterize the distribution of oil, air, and water simultaneously.1 Subsequently, combined with 3D printing technology, oil–water mixtures with water content from 1.8 to 90.6% were measured and analyzed with the THz parameters.15 However, THz waves are strongly attenuated by a water layer, which is a practical limitation in detecting water content for high water cut emulsions. As a result, to accurately detect high water cut emulsions in the THz range, a sensing system without suffering large attenuation effects in the polar liquids is required.

Metamaterials are a new type of artificially fabricated material with exotic properties such as super lensing, negative refraction, cloaking, and sensitive sensing.16,17 These properties are mostly derived from their ability to support resonance, which is mainly determined by geometrical parameters. Recently, metamaterials have been employed as sensitive sensors for chemical and biological detection because their spectral resonance frequency substantially depends on the dielectric condition of surrounding media,18−20 which provides a new solution for us to overcome the limitation mentioned above in oil–water emulsion measurement by THz spectroscopy. Despite these advances, they still suffer from low quality factors (Q-factors) because of the existing radiative losses, which is less than 10 typically.21−23 Thus, their wider utilization in many aspects is limited by the sensing capabilities and filter performance.

In the past few years, the phenomenon of electromagnetically induced transparency (EIT), as a concept of quantum mechanics, has been introduced to metamaterial design to overcome the radiative loss problem and become a fascinating research topic.24,25 EIT is a well-known quantum interference effect that bases on extraordinary dispersive properties of an atomic medium in three-level atomic systems. This phenomenon leads to an extremely narrow band transparency window in the original absorption spectrum by dramatically changing the dispersion properties of the system. As EIT stems from coupled resonances, analogous effects can be realized using classical oscillator systems such as spring-mass or RLC oscillators (capacitance-inductance-resistance coupled oscillators). Thus, considerable attention has been paid to the EIT-like effect in plasmatic metamaterials, whose spectral response can be explained as being either the result of engaging “trapped mode” resonances or by the destructive interference between the so-called bright and dark mode resonances. These metamaterials can overcome the limitation and realize an EIT-like effect in normal environment where a significant difference in Q-factors or full width at half-maximum (fwhm) of the two resonance modes is required in developing the analogy to the EIT effect.26 Recently, research studies on EIT-like metamaterials have been performed by introducing a graphene layer in the metamaterials and achieve independent amplitude modulation of the transmission peaks in the THz regime.27−30

As a consequence, focusing on the high water cut oil–water emulsion, a method was introduced in this paper to detect the water content of oil–water emulsions using a THz metamaterial sensor. To gain the EIT-like effect, a planar symmetric metamaterial sensor was first designed and simulated without varying the lateral distance between the resonators. As the sensing performance of the metamaterial depends strongly on the relative spacing position between the two modes, the simulated transmission spectra with varying spacing distances were investigated to choose the optimum parameter for the designed sensor. It is shown that, because of the coupling strength modulation of the bright and dark modes, the sensing performance can be significantly impacted by the altering separation between the two modes. In addition, analyses of the electromagnetic responses with 5 μm thick oil–water emulsion overlayers on the selected metamaterial were made to demonstrate the sensing ability of water concentration. The THz transmission data illustrate the resonance shifting effects as water concentration increasing from 60 to 98%, from which the numerical expression used to predict the water content with high accuracy was then extracted. The results pave an avenue for THz metamaterials in terms of high water concentration sensing.

2. Results and Discussion

The sensitivity (Δf/Δn) and Q-factors of the EIT-like metamaterial sensor, associated with the coupling degree between the radiative and dark modes, can be also determined by their spatial separation.34,35 Δf and Δn represent the shift of resonance frequency and the change of the refractive index resulted from the covering thin layers, respectively. Here, the transmission spectra of the designed metamaterial were simulated by displacing the U-shaped resonators (USRs) gradually from d = 0 to 40 μm as depicted in Figure 1a. It is clear that the coupling strength between the USR and I-shaped cut-wire (ICW) diminishes with the decreasing d, leading the fading EIT-like response to less transparency. When the USR moves downward from d = 40 to 10 μm, the transparency window gradually shrinks without a notable frequency shift. However, from d = 10 to 0 μm, the transparency window changes with a notable frequency shift. During the simulating, the surrounding environmental materials were selected as air (εair = 1) and oil (εoil = 2.33), respectively, making Δn remain constant and thus sensitivity is proportional to frequency shifts (Δf) between the two surroundings. Then, the frequency shifts and the corresponding Q-factors were evaluated to explore the effect of d on the sensing parameters of THz metamaterials. The sensitivity of the metamaterials becomes higher first and then keeps stable when d increases from 0 to 40 μm. The Q-factors, rather, exhibit a downward tendency with an increase of d. Considering the abovementioned two parameters, metamaterial with d = 14 μm acted as the sensor to investigate the responses of oil–water emulsions in the next section.

Figure 1.

Figure 1

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(a) Simulated transmission spectra of coupled USR and ICW with different spacing distances. (b) Frequency shifts with surrounding environments of air and oil, respectively, and Q-factors vs the distance between the coupled USR and ICW.

A series of simulated THz transmission spectra of oil–water emulsions with high water cut for analysis have been shown in Figure 2. As the water content is gradually raised from 60 to 98%, the simulated EIT resonance is observed to shift lower in frequency because of the change in the dielectric configuration of the surrounding area and the amplitude of the transmission peak is also found to decrease as a result of changes in the resonant matching conditions.

Figure 2.

Figure 2

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Simulated transmission spectra of the designing structure covered by 5 μm thick oil–water emulsions whose water content varies from 60 to 98%.

The resonant frequency (f) with the covering emulsions can be calculated by f = f0(εeff/ε0)−1/2 where f0 is the resonant frequency without the target material while εeff and ε0 are the effective dielectric constants with and without the target material in the metamaterial sensor, respectively. The total effective dielectric constant can be given by εeff = ε1 + Aε + ε3, which is made up of three parts: ε1 is the dielectric constant due to flux within the substrate, Aε should be due to flux within the overlayer, and ε3 is the fringing flux in air where A is a scaling constant. Assuming ε1 and ε3 do not change by the addition of the overlayer, then f can be further given as: f = f0((ε1 + Aε + ε3)/(ε1 + Aεair + ε3))−1/2.17,36 Thus, the red shift of the EIT peak is due to the increase of the ambient dielectric constant.

The extracted resonant frequencies f at the transmission peak and dips from the FDTD (Finite-Difference Time-Domain) simulation results, as well as the corresponding emulsion water contents α, for the characterized emulsions are shown in Figure 3a, indicating that the emulsions’ resonant frequencies can be characterized as functions of water concentration (solid line). Then, the water concentration of the oil–water mixture can be deduced from the resonant frequencies of the EIT peak as well as dips with the following formula

2.

where the corresponding values of a, b, c for the predicting models built by the frequencies at transmission peak and dips are presented as a table in Figure 3a and all the correlation coefficients (R) exceeded 99.9%. Moreover, to verify the predicting accuracy of the model, the transmission spectra were simulated for emulsions with a water content range of 62–99%, from which the frequencies of EIT-like resonant peak and dips were derived. As indicated in Figure 3b, the predicted water concentrations were then calculated using the models built above and were listed as Table 1.

Figure 3.

Figure 3

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(a) Resonance frequencies at the EIT-like peak (ω2) and two transmission dips (ω1, ω3) as functions of water content (α) in different concentrations of oil–water emulsions extracted from simulated THz transmission spectra; the table in the figure includes the paraments of the corresponding predicting models. (b) Predicted data on water content compared with true values and the corresponding absolute errors at ω1, ω2, and ω3.

Table 1. Correlation Coefficients of Each Predicting Model and the Water Contents in the Actual and Predicted Sets.

  actual (%)
predicted (%) 62 67 72 77 81 83 87 89 91 93 97 99 R (%)
ω1 61.917 66.936 72.06684 76.966 80.814 83.016 86.869 88.893 90.995 92.744 97.067 98.86582 99.995
ω2 62.07 66.973 71.9754 77.067 81.168 82.957 87.08 89.051 91.094 92.793 96.971 99.40556 99.996
ω3 61.757 66.842 72.00029 76.913 80.833 82.879 86.797 89.038 90.975 92.988 96.953 99.19702 99.995
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Meanwhile, the absolute errors of the approach are presented in Figure 3b as well, where the horizontal axis and the vertical axis represent the true water content in simulation and the water content predicted by the EIT-like metamaterial sensor, respectively. Agreement is shown between the predicting and the standard data with absolute errors less than 0.26, 0.41, and 0.24% for predicting models at ω1, ω2, and ω3, respectively. These data illustrate that THz EIT-like metamaterial has a higher detecting performance on comparing with the ultrasound method whose detection error is 0.5%.37 The results demonstrate that the THz EIT-like metamaterial can work as an efficient sensor for high water concentration measurement of oil–water emulsions.

In order to understand the predicting models further, the distribution of induced currents at ω1, ω2, and ω3 are shown in Figure 4a. The ICW element is directly excited by the external field, whereas the USR is further excited by the near-field coupling of the ICW. The resonances of USR at ω1 and ICW at ω3 are caused by the interaction between the induced currents in the two coupling units. However, at the resonance ω2, both the USR and ICW are simultaneously excited because of the resonance detuning and result in the strong EIT-like effect. The radiation ability of the whole system was weakened because of the out-of-phase current oscillation, which lead to the sharp transparency window in the transmission spectra.38

Figure 4.

Figure 4

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(a) Distribution of induced currents at ω1, ω2, and ω3, respectively. (b) Fitted curves of frequency and dielectric constant for oil–water emulsions at ω1, ω2, and ω3. (c) Plot of the dielectric constant and water content of the emulsions.

It has been known that the resonant frequency at the transmission peak and dips, f, is related to ε by f = f0((ε1 + Aε + ε3)/(ε1 + Aεair + ε3))−1/2. The extracted resonant frequencies for the transmission peak and dips are shown in Figure 4b as functions of dielectric constant, which agree with the fitting line. The frequencies decrease with the augment of dielectric constant, which depends on the water concentration of the emulsions. The nonlinear relationship between the dielectric constant and water concentration is shown in Figure 4c and can be written as the following formulation39

2.

Accordingly, combining the above equations, the formulas to predict water concentration of oil–water mixtures with high accuracy can be obtained as follows

2.
2.
2.

In brief, our results demonstrate the feasibility of performing characterization of water content in oil–water emulsions with high water cut using THz EIT-like metamaterials, overcoming the current limitations imposed by the strong attenuation of THz waves by polar liquids.

3. Conclusions

In summary, because of the unique properties of metamaterials whose resonance frequencies are sensitive to the changes in permittivity in the surrounding environment, simulations of 5 μm thick oil–water emulsions containing 60–98% water were performed using THz metamaterial, whose Q-factors substantially reduce, whereas sensing sensitivity amplifies with increasing distance between the bright and dark modes. A red shift of the EIT-like resonant frequency is observed with increasing water volume for the 5 μm thick oil–water emulsion as the sample material. In addition, the resonance frequencies at the transmission peak and dips are on a downward trend with increasing water concentration of emulations, which is closely related to the dielectric constant. The numerical expressions whose predicting absolute errors are less than 0.26, 0.41, and 0.24% in the actual water content range of 60–99% have been built about the resonance frequencies and particular water content at ω1, ω2, and ω3, respectively. The results verify the ability of this approach to accurately determine the water content of emulsions for high water cut emulsions without suffering large attenuation effects in water in the THz regime. Furthermore, the metamaterial could be potentially coupled with a microfluidic system for in situ sensing for oil–water two-phase flow.

4. Methods

The THz metamaterial was first designed in this work. The dark mode is similar to a metastable energy level, which is necessary for the realization of an EIT medium in an atomic system.31,32 The EIT-like THz metamaterial consisting of a coupled symmetrical USR and ICW resonator has been proposed and designed as shown in Figure 5b, in which 3 μm quartz (relative permittivity εquartz = 3.75) and 0.1 μm lossy gold with a conductivity of δgold = 4.56 × 107 s/m were selected as the substrate and covering material. The geometric parameters a, b, w, m, g, l, and t are 30, 50, 10, 17, 31, 90, and 5 μm, whereas the periodicity in the x and y directions is Px = Py = 100 μm in free space. The spacing of the two coupling elements is denoted as d (d = 14 here), which will be discussed in the next section. Meanwhile, the electric wall, magnetic wall, as well as open boundary conditions in the x, y, and z directions were utilized. During the simulating, the hexahedral grids with an accuracy of −60 dB in the time domain solver were applied to create an improved mesh.

Figure 5.

Figure 5

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(a) Simulated transmission spectra of the designed EIT-like metamaterial as well as the coupling units (90-USR, USR, and ICW) and the illustration of a unit cell schematic is shown in (b). (c–f) show the distribution of induced currents at resonance frequencies of 90-USR, USR, ICW, and EIT-like, respectively.

The transmission spectra of the designed EIT-like metamaterial and the coupling unit cells were simulated by CST Microwave Studio and are shown in Figure 5a. As expected, when a plane wave with its electric orientation parallel to the y axis normally irradiates on the metamaterials along the z axis, the 90° rotating USR (90-USR) and ICW are excited strongly by incident light and inspire a strong plasmon resonance at 1.098 and 1.118 THz, whereas there is no resonance peak for USR between 0.1 and 1.6 THz. Although the spectral resonant frequencies of 90-USR and ICW elements are similar, the Q-factors of the USR are much different from that of ICW, which lays the foundation of the achieving of EIT-like metamaterial. When the USR substructure is combined with the ICW structure, it demonstrates two splitting transmission dips (denoted as ω1 and ω3) as well as a sharp transmission peak (denoted as ω2) in the transmission spectrum and an EIT-like transparency window with 56.95% transmission appears at 1.132 THz in the transmission spectrum. The fwhm of the EIT-like resonance peak is 0.034 THz, and the corresponding quality factor (Q = ω2/fwhm) reaches 33.3.

As depicted in Figure 5c,d, to interpret the discrepant resonance characteristics, the distribution of the induced surface currents in the 90-USR and ICW resonator elements was plotted at their resonant frequencies. The current in the 90-USR structure is circulating current, while it is the dipole current in the ICW structure. However, owing to the equal length of the top and bottom arms of 90-USR, the symmetrical currents in the two arms cancel each other, making the net dipole moment excited from the external E-field, which is mainly contributed from the left arm of 90-USR. Thus, the effect length of the left arm of the 90-USR element is slightly shorter than that of the ICW one, leading the 90-USR to a thinner fwhm of resonance because the radiation damping increases with the particle size.33 The distribution of induced surface currents of USR at 1.098 THz is presented in Figure 5e where no circulating currents form. Therefore, there is no direct electrical dipole coupling with the incident wave, and it can be considered as a dark mode, whereas the ICW which is excited strongly by propagating waves could serve as the bright mode. The concomitant circulating currents and dipole moment in Figure 5f reveal the simultaneous excitation of both USR and ICW for the designed structure. The LC resonance in the dark mode is excited by the constructive interference between electrical and magnetic surface currents whose coupling strength depends on the phase difference between the magnetic and the electric excited in the ICW.34

The media used in simulations were 5 μm thick oil–water emulsions whose water content ranged from 60 to 98%. The density and dielectric constant of water are 1000 kg/m3 and 78, respectively, whereas they are 920 kg/m3 and 2.33 for oil.

Acknowledgments

This work was supported by the National Nature Science Foundation of China (grant nos. 11574401 and 11804392), the Beijing Natural Science Foundation (no. 1184016), and the Science Foundation of China University of Petroleum, Beijing (nos. 2462017YJRC029, 2462018BJC005 and yjs2017019).

The authors declare no competing financial interest.

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