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Abstract

Herein, the microwave transmission method is proposed that demonstrates such advantages as non-invasiveness, excellent penetration performance, and fast detection. As a key component of the microwave method water content measurement instrument, the antenna is required to have a smaller radiation size than the inner diameter of the oil pipe. To address this technical challenge, a small-sized microwave projection method based on water content measurement antenna is designed in this study for the water content measurement of oil-water mixtures in downhole pipelines. Also, the half-cut antenna with a size of $17 \times 45 m m^{2}$ is proposed to operate in the frequency band of 2–6 GHz (The measured gain of the antenna varies from 2.48 dBi to 4.98 dBi). Then, the designed half-cut antenna is applied to the established water-content test environment for analysis as to the relationship between water content and the variation in transmission coefficient of the half-cut antenna. According to the test results, the relative water content error is about 0.31% between the simulation and measured results for the transmission coefficient $S_{21}$ in the range of 0%–30%, while that is about 0.16% for the transmission coefficient $S_{21}$ in the range of 40%–100%. The experimental results can be extended to the measurement of the part with high water content of the oil-water mixture in the pipeline, which provides a practical reference for field tests and basic research.

Keywords

Microwave transmission method water content measurement half-cut surface antenna compact antenna design

Introduction

Due to the long-standing routine of using the water injection-based extraction method, most oil fields in China have entered the stage of high water content development.¹ With the increase of water content in the output fluid of oil wells, the significant parameter of water content is proposed in the process of oil-field extraction, so as to facilitate the measurement.² The accurate measurement of this parameter is essential for determining the water output of a well and its location, estimating the production of the oil-water mixture, performing intelligent stratification of oil recovery, and predicting the development life, etc.³

At present, there are various methods proposed for the measurement of water content at home and abroad. In general, these methods can be divided into four types according to their rationales: density method, conductivity method, ray method, and microwave method. Alternatively, the above measurement methods can be divided into two categories: contact measurement methods and non-contact measurement methods. The density and conductivity methods require physical contact, while the ray and microwave methods do not.⁴ Besides, the density method is suitable mainly for measuring the water content of less than 5%. There is a single sampling volume that is small and the sampling period is long.⁵ As for the conductivity method, it is easy to scale on the sensor surface during long-term service.⁶ RF method is costly and not suitable for large-scale promotion.⁷ Microwave measurement method, according to the object to be measured on the microwave radiation or transmission and other characteristics microwave sensor sensitive to non-electricity is applied to convert the non-electrical quantity of the substance to be measured into electrical parameters.⁸ The microwave measurement method is advantaged by no requirement for physical contact, the capacity to penetrate non-metal objects, a wide band, high transmission, the resistance to low-frequency interference, and other characteristics.⁹ Besides, it enables loss-free, real-time, and rapid measurement online. Comparatively, microwave measurement technology is relatively mature, showing such merits as no contact, no damage, no toxicity, the ease of operation, high safety performance, low cost, etc. To sum up, it has promising prospects for practical application.¹⁰

The microwave measurement method can be divided into the trans-missive method and resonant cavity method. Since the resonant cavity method is commonly used for oil-water mixture with low water content, and the transmission method has a wider measurement range, this paper chooses to use the microwave transmission method for water content measurement. The microwave transmissive method is based on the different absorption rates of microwave signals by oil-water mixture with different dielectric constants for water content measurement.¹¹ According to the characteristics of the electromagnetic wave transmission, the microwave sensor plays the most important part in the measurement system. Besides, as for the accuracy and range of the water content measurement of the oil-water mixture, they are determined largely by the performance of the sensor.⁹ Given the confined downhole space of oil wells and the small inner diameter of pipes, it is essential to minimize the size of oil-water mixture water content measurement instruments, especially microwave sensors. The sensor proposed for water content measurement by 12 is a microwave spiral antenna, the size of which is designed to be $40 \times 40 m m^{2}$ . In the pipe with an internal diameter of 110 mm, the measurement frequency is 3.80 GHz. The sensor proposed by 13 for water content measurement is a microwave resonant cavity antenna with a measurement frequency of 3.25 GHz, which is relatively low. Using a pipe with an internal diameter of 150 mm, the antenna is sized $86 \times 43 m m^{2}$ . In the study of 14, the sensor used for water content measurement is a microstrip antenna. When the measurement frequency reaches 5.35 GHz, the antenna is $38 \times 35 m m^{2}$ and the inner diameter of the pipe is 110 mm. Through a review of the above literature, it can be found out that the size of the microwave sensor is relatively high at low frequency, and the sensor can be applied to the pipes with larger inner diameters. At a high frequency, the size of the microwave sensor is relatively small. However, this places a more demanding requirement on the moisture content device for the microwave transmission method. Besides, the higher the operating frequency, the more cost the instrument incurs.¹²

Herein, a miniaturized antenna is designed as a microwave sensor that takes into account the process of antenna installation for the downhole water content meter and other measurement devices to occupy the center channel of the pipe. According to literature,^13–16 the maximum inner diameter of the pipe is 150 mm. This paper is aimed to design a miniaturized antenna according to the above pipe size. Since the designed antenna has a size that is much smaller than the inner diameter of the pipe, the optimized antenna is characterized by the simplicity of structure, wide band, and compactness, thus meeting the experimental requirements.

Principle of water content measurement by microwave transmission method

Relationship between dielectric constant and water content

In general, the mixed media consist of a mixture of substances that vary in dielectric constants, which is one of the most significant parameters required for measuring the water content of oil-water mixture. Wiener¹³ put forward an empirical formula for the dielectric constant of two-component mixed media^14,16:

\frac{ε_{r} - 1}{ε_{r} + m} = w (\frac{ε_{n 1} - 1}{ε_{n 2} + m}) + (1 - w) (\frac{ε_{n 2} - 1}{ε_{n 2} + m}),

(1)

where $w$ represents water content, $ε_{r}$ indicates the complex permittivity of the mixed media, $ε_{n 1}$ denotes the homogenous uniform dielectric constant, and $ε_{n 2}$ refers to the non-uniform dielectric constant.

When pure water is one of the substances in the mixed medium, the constant denoted as $m$ is often taken as $0$ . In this case, $ε_{r}$ is often expressed as equation (2)¹⁷

\sqrt{ε_{r}} = w \sqrt{ε_{n 1}} + (1 - w) \sqrt{ε_{n 2}},

(2)

where $ε_{r}$ represents the relative dielectric constant of the oil-water mixture, $ε_{n 1}$ indicates the dielectric constant of pure water, and $ε_{n 2}$ denotes the dielectric constant of pure oil. According to equation (2), the change in water content of the oil-water mixture will cause the relative dielectric constant of the oil-water mixture to vary.

The relationship between oil-water absorption of microwave and water content

As polar molecules, water molecules tend to be polarized into dipoles when electric field force is exerted. With the increase in frequency of the external electric field, the dipole will keep changing direction with the change in direction of the electric field. Besides, collisions will occur during the change of direction, which diminishes electric field energy.¹⁷ Usually, the complex permittivity denoted as $ε$ can be expressed as:

ε = ε' - j ε ″,

(3)

where $ε$ indicates the ability of the medium to store electromagnetic fields, $ε'$ denotes the ability of the medium to emit thermal energy,⁹ $ε ″$ refers to the loss factor, and the loss of electric field energy $(\tan δ)_{r}$ can be expressed as:

(\tan δ)_{r} = ε ″ / ε',

(4)

From equations (3) and (4), equation (5) is deduced as:

ε = ε_{r} [1 - j {(\tan δ)}_{r}],

(5)

According to equations (2)–(5), both the relative permittivity of oil-water mixed media and the relative loss angle tangent are related to the water content. Also, the relative loss angle tangent can be expressed as equation (6).

\sqrt{{(\tan δ)}_{r}} = w \sqrt{{(\tan δ)}_{n 1}} + (1 - w) \sqrt{{(\tan δ)}_{n 2}} .

(6)

where $(\tan δ)_{r}$ , $(\tan δ)_{n 1}$ , and $(\tan δ)_{n 2}$ represent the tangents of the relative loss angles of oil-water mixture, pure water and pure oil respectively, and $w$ (%) refers to the volume percentage of water. According to study of 12, the relative permittivity $ε_{r}$ and relative loss Angle tangent $(\tan δ)_{r}$ of oil-water mixed media at room temperature and under normal pressure are obtained, as shown in Table 1.

Table 1.

Relationship between relevant parameters of the oil-water mixture and the water content.

$w$ (%)	$ε_{r}$	$(\tan δ)_{r}$
0	2.30	0.0001
10	5.10	0.0019
20	9.01	0.0060
30	14.02	0.0123
40	20.14	0.0209
50	27.36	0.0318
60	35.68	0.0449
70	45.10	0.0603
80	55.63	0.0779
90	67.26	0.0978
100	80.00	0.1200

According to Table 1, at room temperature and under normal pressure, the water content of the oil-water mixture varies between 0 and 100%. Meanwhile, the relative permittivity shows an upward trend, varying between 0 and 80. With the continuous increase in the water content of the oil-water mixture, the loss tangent angle increases as well, varying between 0 and 0.12. According to study of 15 and that of 18, the complex permittivity of general materials is $ε' < 10, ε ″ < 0.1$ , which is much higher compared to general materials. Therefore, the water content of the oil-water mixed medium determines the dielectric permittivity of the medium at microwave frequencies. That is to say, the measurement of the water content of the oil-water mixture can be performed by measuring the dielectric constant of water.

Microwave transmission method of moisture content measurement principle

The principle followed to perform measurement under the microwave transmission method is based on the loss of energy caused when the microwave signal passes through the measured object to detect the water content of the measured material.¹⁵ Figure 1 shows the microwave transmission method as adopted when a uniform plane wave approaches the measured medium in a vertical incidence.

Figure 1.

Schematic diagram of microwave measurement.

As shown in Figure 1, when the microwave passes through the measured medium, the change to the dielectric constant of the measured medium will lead to the attenuation of the microwave signal. When the oil-water mixture is filled with the medium under test, the electromagnetic wave complex propagation constant falls within the range of 10 and 11:

γ = α + j β = jw \sqrt{μ_{r} ε_{r}},

(7)

where $γ$ represents the electromagnetic wave complex propagation constant; $ε_{r}$ denotes the relative permeability of the measured material; $w$ indicates the water content. Known commonly used, combined with equation (5) to simplify equation (7) and substitute it into $μ_{r} = 1$ , the attenuation constant of the oil-water mixture is obtained as:

γ = α + j β = jw \sqrt{μ_{r} ε_{r}},

(8)

When $\tan δ << 1$ , the following approximation can be performed.

α \approx w \sqrt{ε_{r}} (\tan δ)_{r},

(9)

Thus, the attenuation of the microwave signal $ϕ$ caused by the oil-water mixture, and the change $Δ ϕ$ in the amount of attenuation is:

ϕ = \int_{0}^{l} α (l) dl,

(10)

S_{21} = Δ ϕ = w ε_{r} (\tan δ)_{r} .

(11)

where $(\tan δ)_{r}$ represents the relative loss angle tangent, $ϕ$ indicates the attenuation of the microwave signal, and $Δ ϕ$ denotes the attenuation variable of the microwave signal. From equation (11), it can be known that the attenuation variable of the oil-water mixture to the microwave signal is related to the relative permittivity and the relative loss tangent of the oil-water mixture. Both $ε_{r}$ and $(\tan δ)_{r}$ associated with the water content. Therefore, when the attenuation variable can be measured (generally expressed as the transmission coefficient $S_{21}$ when the test is conducted with a vector network analyzer), the water content can be calculated in combination with the relative permittivity and relative loss tangent of the oil-water mixed medium, as shown in Table 1.

Antenna design of microwave transmission method water content measurement instrument

The microwave sensor is applied to deal with electromagnetic wave transmission and reception. Besides, the performance of the antenna has an immediate impact on the accuracy of the test.¹⁸ Herein, by taking into account the requirement of miniaturization, the analysis of various antennas is conducted, with the half-cut antenna selected as the detection sensor for water content under the microwave transmission method.

Microwave transmission method of water content measurement principle

The full-wave 3D electromagnetic simulator CST Studio suite is adopted to design and optimize the half-cut antenna proposed in this study. By optimizing the characteristics of impedance, reflection coefficient, antenna gain, and other parameters of the antenna, the performance of the antenna can be improved. Considering a variety of influencing factors and the requirements on the performance of the designed antenna, the material used to build the dielectric layer of the antenna is determined as FR-4 (epoxy board with high mechanical properties and dielectric properties), and the dielectric constant of the dielectric layer is 4.3. The basic radiating patch antenna of the antenna design is shown in Figure 2(a), the designed half-cut antenna is illustrated in Figure 2(b), the physical diagram of the designed antenna is illustrated in Figure 3, and the related characteristics are shown in Figure 4. The selected reference antenna is a microstrip antenna with a $50 Ω$ and center frequency of 2.45 GHz, the geometry and dimensions of which are shown in Table 2.

Figure 2.

Evolution of the proposed Antenna: (a) detailed structure diagram of the antenna and (b) half-section antenna treated by dichotomy.

Figure 3.

Physical view of the antenna.

Figure 4.

Correlation characteristic curve of antenna: (a) the $S_{11}$ curves of the front and rear antennas are processed by dichotomy method and (b) voltage standing wave ratio VSWR curve of half-cut antenna.

Table 2.

Structural dimensions of the antenna.

Parameter	L	W	h	r1	r2	w1	l1	l2
Value (mm)	45	34	1	16	2	2	12	11

where L, W, and h represent the length, width and thickness of the dielectric layer of the antenna, respectively. r1, r2, w1, l1 represent the outer diameter, inner diameter, length, width of the metal layer of the antenna, respectively. l2 represents the length of the metal layer of the opposite antenna.

The basic antenna size is sized $34 \times 45 m m^{2}$ . As shown in Figure 2(a), the ground plane and the circular patch are on different sides of the ground plane. The entire microstrip antenna has a left-right symmetric structure, and size reduction is achieved using the dichotomy method, where the current in the left half of the antenna is symmetric to the right half because the antenna has structural symmetry along the X-axis.¹⁹ With the imaging principle, the right half of the antenna is removed, and Figure 2(a) and (b) illustrate the design graphics before and after modification. The size of the known synthetic antenna is $17 \times 45 m m^{2}$ , which is reduced by 50% compared to the reference antenna. Figure 3 shows the physical drawing of the designed half-cut antenna. The $S_{11}$ curves of the two antennas before and after the dichotomous treatment are shown in Figure 4(a), and the proposed voltage VSWR of the half-cut antenna is shown in Figure 4(b).

As shown in Figure 4(a), the bandwidth of the basic antenna before the dichotomy is 3.04 GHz, and the bandwidth of the half-cut antenna after processing is 3.06 GHz. Compared with the basic antenna, the bandwidth is basically unchanged. And from the observation of the transmission coefficient $S_{11}$ curve of the half-section antenna after processing in Figure 4(a), it can be seen that the $S_{11}$ curve has two resonance frequencies, that is, the antenna has two resonance points in the working frequency band of 2–6 GHz, which are 3.25 and 4.77 GHz, respectively. The two resonance points are set in the far-field region, as shown in Figure 5.

Figure 5.

Far-field setup: (a) radiation direction diagram of 2.45 GHz, (b) radiation direction diagram of 3.25 GHz and (c) radiation direction diagram of 4.77 GHz.

As shown in Figure 5, the antenna is an omnidirectional antenna, and the gain of this antenna is 2.61 dBi in the far-field region of 3.25 GHz, the gain in the far field area of 4.77 GHz is 4.27 dBi. Since the frequency places requirements on the equipment, and the lower the frequency, the larger the antenna size. Considering the size and gain of the antenna, the selected frequency is about 3.25 GHz. Simulation of the test results to take into account the actual measurement effect, the following through the actual measurement to find the highest measurement accuracy between 2.25 and 3.25 GHz frequency point. The measurement results show that the measurement linearity is better at 2.45 GHz. As shown in Figure 4(b), the voltage VSWR is less than 2 at 2.45 GHz, and the known standard of VSWR, VSWR<2. It is known that the designed antenna bandwidth meets the experimental requirements.

Antenna characterization

For the design of the antenna, an analysis is conducted as to the impact caused by the thickness of the dielectric plate and the width of the microstrip line on the performance of the antenna. Besides, the design of the miniaturized antenna can be worked out easily by analyzing the performance of the parameters. Figure 6 shows the relationship between the thickness of the dielectric plate h and the width of the ground plate w1 and the ultra-wideband performance when other parameters are unchanged.

Figure 6.

The effect of two parameters on the reflection coefficient $S_{11}$ of the antenna: (a) curve of the effect of dielectric plate thickness h on the reflection coefficient $S_{11}$ and (b) influence curve of the width w1 of the ground plate on the reflection coefficient $S_{11}$ .

As shown in Figure 6, when the thickness is 1.5 mm, the antenna bandwidth range of $S_{11}$ <-10 dB is 2.8 to 3.6 GHz and 4.5–5.5 GHz, and the $S_{11}$ curve at 2.45 GHz is −12.57 dB. When the thickness is 1.2 mm, the bandwidth range of $S_{11}$ <-10 dB is 2.35 to 5.35 GHz. When the thickness is 1 mm, the bandwidth range of $S_{11}$ <-10 dB is 2.35 to 5.39 GHz. The comparative analysis shows that the antenna bandwidth is 3.04 GHz at 2.45 GHz when the thickness is 1 mm, which is the largest. In this case, the outcome of simulation is better.

Antenna performance test of microwave transmission method water content meter

Construction of an experimental environment

Figure 7 illustrates the water content test model of the oil-water mixture. The oil-water mixture exists in a metal pipe with a height of 110 mm, an inner diameter of 50.30 mm, and a wall thickness of 1 mm. In order to make the electromagnetic waves emitted by the antenna penetrate the metal pipe, holes are drilled on both sides of it and then filled with the materials resistant to high temperature and pressure. This ensures the wave transmission expected. Then, the designed transmitting and receiving antennas are installed on both sides of the metal pipe. The antenna used in the experiment is a half-section antenna. The $S_{21}$ parameters of the oil-water mixture with varying water content in the metal pipeline are measured through the transceiver antennas on both sides of the pipeline.

Figure 7.

Water content model of oil-water.

Simulation analysis of the effect of antenna transmission coefficient on water content

For the CST solution, the antenna operating band is set to 2–6 GHz, the half-cut antenna on the left is set as the transmitting antenna, and the half-cut antenna on the right is treated as the receiving antenna. This is to study the change of transmission coefficient $S_{21}$ when water content varies, with the transmission coefficient denoted as $S_{21}$ , and to describe the change of water content according to the attenuation value of transmission coefficient $S_{21}$ after the introduction of different oil-water mixtures.^19,20

Experiments were conducted to measure the water content of the oil-water mixture from 0% to 100%, with the interval of measurement set to 10% for each test. For this reason, the experimental test was conducted on diesel. The results of experimental measurements are shown in Figure 8. When water content is in the range of $0 % ~ 30 %$ water content, the decay curve of each water content shows irregularity. Besides, the decay does not increases continuously with the increase of water content. This is because, when water content is in the range of $0 % ~ 30 %$ , the oil-water mixture contains more oil and less water content, the effective dielectric constant of the oil-water mixture can be obtained. According to equation (2), the effective dielectric constant of the oil-water mixture is relatively small, and the electromagnetic waves in the $2 ~ 6 GHz$ band $λ_{2.45 GHz} \ \sqrt{ε_{mix}}$ , which is comparable to the diameter of the pipe and even in excess of it. Therefore, the transmission mode of the electromagnetic waves in the pipe is different from the mode of far-field transmission. Consequently, the attenuation of each frequency point in the case of different water content shows non-monotonicity and irregularity.

Figure 8.

Antenna transmission coefficient curve when the water content varies from 0% to 30%.

Figure 9 shows the curve of changes in the transmission coefficient $S_{21}$ with the water content. It can be seen from the figure that when the antenna operating frequency is 2.45 GHz and the water content is in the range of $40 % ~ 100 %$ , the transmission coefficient $S_{21}$ of the antenna changes with the water content increase, $S_{21}$ gradually decreased. When the water content of the oil-water mixture is 40%, the transmission coefficient $S_{21}$ of electromagnetic waves in pure oil is −25.08 dB. When the water content of the oil-water mixture is 100%, that is, pure water, the transmission coefficient $S_{21}$ of electromagnetic waves in pure water is −64.73 dB. According to the simulation results, it can be found that the curve presents a linear change trend.

Figure 9.

Antenna transmission coefficient curve when the moisture content varies from 40% to 100%.

Figure 10 shows the simulation results of water content from 0% to 100%, with the frequency set to 2.45 GHz for the system. To further elaborate on the relationship between transmission coefficient $S_{21}$ and water content in the range of 0% to 100%, and to verify equation (11), the simulated curve of oil-water mixture was fitted linearly, and the variation curve was fitted with the fitted function as follows:

y = - 0.50 x - 6.45

(12)

where $x$ (%) represents the water content and $y$ (dB) represents the transmission coefficient $S_{21}$ .

Figure 10.

Water content simulated curve from 0% to 100%.

As shown in Figure 10, the fitting degree of the trend line $R^{2} = 0.958$ , and the fitting curve obtained by the fitting function is clearly consistent with the simulation curve at low water contents. However, such a consistency is slightly compromised at a water content ranging from 0% to 100%. By incorporating the simulation results of the oil-water mixture into the fitting relationship, the corresponding water content can be obtained.

Measured analysis of the effect of antenna transmission coefficient on water content

The $S_{21}$ transmission characteristics of electromagnetic waves were analyzed through simulation at varying water contents. At a 2.45 GHz operating frequency, a linear change occurs between the water content and the transmission coefficient $S_{21}$ in the range of 0%–100%. The applicability of the half-cut antenna as the front-end sensor of the microwave transmittance water content meter was verified experimentally. Figure 11 shows the block diagram of the microwave transmittance water content meter.

Figure 11.

Block diagram of microwave transmittance water content meter.

When the vector network analyzer is used to measure the water content of crude oil in the system, the experimental system is developed according to the measurement principle as shown in Figure 11. The data of transmission coefficient were tested by the vector network analyzer at a water content ranging from 0% to 100%, and an analysis is conducted on the relationship between water content and transmission coefficient. That is to say, the transmission coefficient varies with a continuous increase in the water content of crude oil. Figure 12 illustrates, a vector network experimental test on the microwave crude oil with a water content of 80%.

Figure 12.

Experimental setup in actual measurement.

The measured medium is placed in a glass container with a diameter of 50.30 mm. Then, the variation in the transmission coefficient $S_{21}$ of antenna 1 and antenna 2 is analyzed in real time by using a vector network analyzer, so as to determine the relationship between the water content and the transmission coefficient. The comparison of measured and simulated data of $S_{21}$ with water content at 2.45 GHz is shown in Figure 13. It can be found out that in both the measured and simulated curves of water content, the transmission coefficient $S_{21}$ showed monotonic changes with the increase in water content. As shown in Table 3, the trends of the relationship curves between the transmission coefficient $S_{21}$ and water content in the range of 0%–100% are basically the same for both curves, indicating that the tongue-side results are in good agreement with the simulation data. However, there is a difference of about 6 dB between actual and measurement results for the transmission coefficient $S_{21}$ in the range of $0 % ~ 30 %$ , while that is about 9 dB for the transmission coefficient $S_{21}$ in the range of $40 % ~ 100 %$ . This is due to the loss caused by the motor during the test, the transmission path loss of the transmitting and receiving antennas, and the difference loss of cables and adapters.

Figure 13.

Simulated and measured comparison of water content from 0% to 100%.

Table 3.

Simulation results and relative error of transmission coefficient $S_{21}$ .

$w$ (%)	$y$ (dB)	$y_{1}$ (dB)	$E_{1}$ (dB)	$E_{2}$ (%)
0	−10.58	−15.27	4.69	0.31
10	−13.21	−19.01	5.8	0.31
20	−16.09	−21.44	5.35	0.25
30	−20.46	−26.12	5.66	0.22
40	−25.08	−29.58	4.5	0.15
50	−27.40	−33.01	2.61	0.08
60	−29.79	−38.09	6.3	0.17
70	−36.65	−45.01	8.36	0.19
80	−42.61	−47.85	4.24	0.11
90	−50.23	−51.56	−0.27	0.03
100	−64.73	−56.04	−8.69	0.16

In the microwave transmission method water content testing system, in order to verify whether the loss error of the oil-water mixture within the range of $0 ~ 100 %$ water content meets the experimental requirements, specific analysis can be conducted on the loss error of the transmission coefficient $S_{21}$ under simulation measurement and experimental measurement, as shown in Table 3.

where $x$ (%) represents the water content, $y$ (dB) refers to the Simulated measurement transmission coefficient $S_{21}$ , and $y_{1}$ (dB) stands for the Vector network measurement transmission coefficient $S_{21}$ , $E_{1}$ (dB) represents the absolute error (y− $y_{1}$ ), $E_{2}$ (%) represents the relative error $| (y - y_{1}) / y_{1} | \times 100 %$ .

Based on the comparison of transmission coefficient $S_{21}$ between simulated and experimental measurements under water content in Table 3, the following conclusions are drawn.

(1) When the percentage of water content in crude oil is lower than 30%, the absolute error difference between the analog measurement and the loss measured by vector network analyzer is small; When the water content of crude oil is higher than 30%, there is a small difference between the loss measured by analog measurement and that measured by vector network analyzer. The main reason is that when the water content of crude oil is higher than 30%, it can be seen from equations (1) and (2) that the dielectric constant of water begins to play a dominant role in the measurement of the dielectric constant of oil-water mixtures. According to equation (8), the loss on antenna 2 is directly proportional to the dielectric constant of oil-water mixtures. In addition, as the water content of crude oil increases, the oil-water mixture changes from a weakly conductive medium to a strongly conductive medium. Therefore, when the water content of crude oil exceeds 30%, Due to the insensitivity of the antenna in a high water content state, the absolute error between the percentage of water content between the two will gradually increase.

(2) If the transmission coefficient $S_{21}$ is used as the water content measurement standard. When the water content of crude oil is 0%–30%, the relative error of the experimental measurement system is below 0.31%, the measurement error of the water content of 90% is 0.03%, the measurement error in pure water is 0.31%, and the measurement error of the water content of 0%–10% is relatively large. The main reason is that this is caused by the loss of the motor during the testing process, the transmission path loss of the transmitting and receiving antennas, and the differential loss of the cable and adapter. However, overall, the consistency between the simulated measurement system used under high water content conditions and the experimental values is good, which meets the experimental requirements.

We added a comparison of the proposed scheme with the state of the art in the literature, as shown in Table 4. And the corresponding textual description of Table 4 is provided.

Table 4.

Performance comparison with the state of the art in literature.

Ref. No	Size (mm³)	Water content	Measurement frequency (GHz)	Bandwidth	Peak gain (dBi)
Ping et al.²	45 × 167 × 2	NA	2~3	6%	1.7
Huang¹⁰	40 × 45.2 × 0.5	50%–100%	2~6	4.5%	4.4
Zeng et al.¹⁵	82.4 × 62.5 × 1	0%–100%	8.2~12.4	5%	NA
McKerricher et al.²¹	56.75 × 25 × 1.5	5%–50%	1~2.5	5%	2.65
Sheila-Vadde et al.²²	NA	60%–100%	2~2.4	2.5%	1.7
Elwi²³	100 × 50 × 1	17%–73%	2~3	3%	3.4
Tayyab et al.²⁴	60 × 279.3 × 0.1016	20%–40%	0.2~0.3	0.74%	1.7
Liu et al.²⁵	75 × 40 × 0.5	75%–100%	1.7~2	−5% & 5%	1.67
Abdulsattar et al.²⁶	50 × 50 × 1.6	3%–76%	1~2.5	−0.66%	4.4
Yang et al.²⁷	70 × 75 × 2	10%–85%	2.5~8	7%	4.4
This work	17 × 45 × 1.2	0%–100%	2~6	0.31%	4.3

Table 4 compares the performance and characteristics of the proposed water content with the most advanced water content-related performance reported in the literature. Some important features proposed are as follows:

(a) The proposed antenna was developed on a microwave laminate with a thickness of 1 mm. As is well known, the bandwidth of the antenna decreases as the thickness of the microwave laminate decreases. However, in the proposed technology, a broadband bandwidth of 3.04 GHz was achieved. This makes the antenna suitable for measuring microwave water content in the 2.25–5.29 GHz spectrum. Therefore, the implementation bandwidth of the proposed miniaturized antenna is greater than the bandwidth reported in refs.^2,10,21–26

(b) Unlike the research reported in refs.,^2,15,21,22 the proposed miniaturized antenna is implemented on microstrip patch antennas to achieve ultra-wideband high gain antennas.

(c) The research in refs.^2,25 focuses on developing spiral antennas with high-precision water content. However, antennas are suitable for narrow ranges and are not suitable for experimental measurements across the entire range.

(d) Different from refs.,^{21–24,26,27} the proposed antenna is essentially broadband and does not use complex electromagnetic structures such as metamaterial to achieve miniaturization.

(e) The measurement of crude oil water content is conducted at lower frequencies, which is one of the limiting factors for achieving antenna miniaturization. Unlike the work reported in refs.,^10,21,26 the antenna for water content measurement tends to be miniaturized and has relatively low frequencies.

(f) Although the minimum operating frequency of the antenna reported in refs.^21–23,25 is lower than 2.45 GHz, the relative error of the antenna’s water content is relatively high, higher than the relative error of 3% water content.

(g) Although the reported water content error in refs.^24,26 is comparable to the proposed error, the applicable range of water content for antennas is narrow and the size is large. On the other hand, the dielectric constant of the antenna reported in Abdulsattar et al.²⁶ is 4.4.

(h) Although the antenna size reported in Abdulsattar et al.²⁶ is physically equivalent, the antenna is limited by antenna frequency and relative dielectric constant.

(i) Although the antenna bandwidth reported in refs.^15,27 is greater than 4 GHz, the antenna is limited by antenna size and frequency size.

(j) Although the physical size of 10 is comparable to the proposed slot antenna, the proposed antenna is electrically smaller due to its minimum operating frequency of 3.8 GHz.

Conclusion

This paper proposed a new type of circular slot antenna with a 50% size reduction. The size reduction is realized by exploiting the structural symmetry along the principal planes of the antenna. The reference circular slot antenna reduces its size while achieving broadband impedance and radiation characteristics. Studied the impact of miniaturization on bandwidth and radiation characteristics, and provided results. The proposed miniaturized antenna covers wide bandwidth with broadband ranging from 2.25 to 5.29 GHz and gain ranging from 2.61 to 4.27 dBi. The radiation pattern is omnidirectional making the antenna suitable for broadband applications. By analyzing the relationship between the water content and the transmission coefficient $S_{21}$ as shown in Table 3, it can be found out that the relationship curves between the transmission coefficient $S_{21}$ and water content in the range of 0%–100% show almost the same trend, indicating that the measurement results are highly consisted with simulation results. However, there is a relative error of about 0.31% between the water content range of 0%–30%, and the relative error is about 0.16% between the actual and measured results for the water content range of 40%–100%.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported in part by the Xi’an Science Foundation, Shaanxi Province, China, Grant No. 21XJZZ0058, and by the Postgraduate Innovation and Practice Training Program of Xi’an Shiyou university, No.YCS21213209.

ORCID iDs

Huiqin Jia

Dan-dan Wan

Jia-Cheng Zhou

Yi Wei

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