Design of Microwave Antenna Array for Imaging of Multiphase Flows in Polypropylene Pipes

'e oil and gas industry requires accurate sensors to control fluid flow in pipelines during the production process from horizontal and near horizontal wells. 'e extracted crude oil is usually a multiphase mixture of oil, water, and gas, and the accurate measurement of the ratio of each multiphase within the pipeline is an important parameter to manage wells efficiently by maximizing the hydrocarbons that can be extracted. Various methods have been developed for determining the phase ratio including mechanical, optical, X-ray or gamma ray, ultrasound, nuclear magnetic resonance (NMR), and rarely microwave techniques. However, these methods do not permit the knowledge of the real-time evolution of the phase ratio and are less precise. Here, we propose and develop by simulation two microwave systems, in horizontal and vertical polarizations, to choose the optimal configuration for crude pipeline imaging applications. First, the pipeline containing crude oil wasmodeled and its thermal and dielectric properties are proposed. 'en, the antennas array performances were optimized and assembled to the pipeline. Different numbers of antenna elements were successfully investigated using CST simulation in both vertical and horizontal polarizations to find the optimal number of antenna elements for the pipeline applications.


Introduction
Multiphase and three-phase flow (oil, water, and gas) are the main components while drilling oil. e exact proportion of multiphase flow components is a challenging problem to solve due to the differences in geological conditions, such as temperature, pressure, flow dynamics, and salinity. Some techniques based on gamma ray [1,2] and X-ray [3] were used; however, these techniques require long measurement time and are based on ionizing radiations. e reduction of measurement time requires intense sources, which increases the cost and causes safety concerns [4]. In addition, the salinity variation of the water phase in the pipeline affects and introduces a significant source of error during the measurement procedure [5]. Another technique based on electrical impedance consists of measuring the impedance between two electrodes inserted in the oil-water-gas mixture flow.
However, the measured parameters (resistance and capacitance) depend highly on the dielectric properties (permittivity and conductivity) of the three phases (oil, water, and gas), their fractions, the flow regime, and the operating frequency [6]. is high dependence on many parameters leads to large errors in measurements. Ultrasound Doppler velocimetry was employed to measure the liquid velocity, where the velocity is used to realize real-time flow regime identification with the help of machine learning [7]. Recently, the use of microwave attenuation and phase shift appeared as an emerging technique used to overcome some deficiencies related to the previous techniques. To overcome the problem of high sensitivity of measurement, the pulsed neutron activation (PNA) technique was proposed. is technique uses a high-energy source of neutrons to irradiate the flowing mixture. e emitted gamma radiation is used to determine the chemical composition and phase fractions of the mixture, but this technique is expensive and uses ionizing radiation. Another technique was developed and utilized, the nuclear magnetic resonance (NMR), by applying a magnetic field to the flow of the mixture to align spin states of the nuclei [8]. e spin realignment may be related to the chemical composition and hence the phase fractions of the flow. Again, this technique is heavy and expensive. e microwave technique was performed by measuring the permittivity and conductivity of the flowing mixture at different microwave frequencies by determining both the amplitude and phase of transmission coefficients to the electromagnetic waves that passed through the flow [9], or by determining the frequency shift of a resonating cavity carrying the fluid flow [10]. However, the resonant technique suffers from two main limitations: single frequency measurement and the presence of water which may introduce a high perturbation of electromagnetic fields in the cavity due to its conducting behavior [11]. However, although microwave methods require more complex excitation and detection circuitry than impedance methods, they have been successfully utilized in a number of three-phase flow meters [11]. e main applications of UWB antennas array are medical imaging [12][13][14], through-wall imaging [15], ground penetration radar (GPR) [16], and indoor geolocation and positioning [17]. Tapered slot antennas are widely known either by elliptical proles [18] or exponential profiles [19]. 3-D circular connected Vivaldi elements are proposed in [20], where they used an array of 10 elements with an elliptical taper profile for near-field radar imaging applications. Antenna array with 16 elements is proposed to achieve an omnidirectional UWB horizontal polarization antenna [21]. In this work, we propose and develop by simulation a new 3-D microwave imaging system based on circular array antennas to determine the real-time phase ratio of crude oil within the pipeline. e array antennas will scan one cylindrical section of the pipeline and produce 2-D images, in which it will quantify the localization of the oil in the pipeline and its ratio. us, better real-time monitoring of the well production could be successfully realized. e proposed antennas array consists of a circular ring of 32 UWB Vivaldi antennas operating over a band of 1 GHz to more than 7 GHz. e array will be a part of a complete microwave system based mainly on a 16/32 MIMO system based on software defined radio (SDR) technology or 8-port vector network analyzer with a switching network and software for analysis of all signals and generation of the scanned images.

Pipeline Model Assumption
e pipeline is represented by its main three components of oil, water, and gas and a combination of a cylinder of water in blue color (6 cm diameter, 10 cm height) and a cylinder of oil in black color (6 cm diameter, 10 cm height). Both cylinders are surrounded by air (gas representation). e pipeline tube material is defined as polyether ether ketone (PEEK) which is a technical plastic. e outer diameter of PEEK tube is set to 20 cm, with 0.3 cm thickness and 10 cm height. Table 1 summarizes the thermal and electromagnetic properties used in the CST thermal transient solver for water, oil [22], and PEEK (polymide) materials ( Figure 1).

Design of a 3-D Single Vivaldi Element.
e unit element for the microwave imaging system is shown with its parameters in Figure 2, where A is the antenna length, B is the antenna width, R is the cavity diameter, Lg is the distance between the ground plan and the bottom of the circular cavity, and C is the aperture width. e single element is designed using CST (computer simulation technology, GmbH) microwave studio simulation tools [22]. Time-domain solver will be used to simulate the different structures. A ground plan of 0.5 cm thickness is added to hold the antenna properly. e antenna material is set to aluminum. e type of taper profile is exponential.

Design of the Microwave System.
In this section, we will present the advantages of the horizontal and vertical Vivaldi antennas and then choose the best configuration in terms of antenna bandwidth, S 21A average (add up all transmission coefficients of S 21 values divided by how many S 21 numbers), miniaturization, and number of elements. From the antenna point of view, lower S 21 leads to less mutual coupling between antennas, which has less impact on the embedded radiation patterns and input impedance [23].

Design of a 3-D Circular Array in Horizontal
Polarization. 3-D circular arrays of three different configurations with 8, 16, and 32 Vivaldi elements in horizontal polarization (HP) are proposed, developed, and simulated, as shown in Figure 3. e single element parameters are reported in Table 2 for each configuration. e 32-element case shown in Figure 3(c) was performed by fixing the dimensions of the single element of 16-element case, producing 32 array dimensions with 89.6 × 89.6 cm 2 .
However, the simulation time will be increasing dramatically. Optimizing such a large array is difficult to achieve by CST time-domain solver due to the huge number of mesh cells to solve. Some numerical methods could be applied to reduce the simulation time such as array scanning method (ASM) [24]. Figure 4(a) shows the array bandwidth of 8element array between 1.47 GHz up to more than 7 GHz. e distance between antennas and PEKK is 3.1 cm. Since there is enough space between the array elements, the mutual coupling is relatively low. e S 21A average gives −21.5 dB. Figures 4(b) and 4(c) present the antenna array performance of 16-element case, and it shows a bandwidth from 1.45 GHz to more than 7 GHz below −10 dB criterion. e transmission coefficient average S 21A of 16 elements is higher than 8 elements due to the shorter distance between the radiating elements. S 21A average value gives −16.7 dB.

Design of a 3-D Circular Array in Vertical Polarization.
e main advantage of vertical element configuration is the possibility of arranging higher number of elements in an array compared with the horizontal configuration. ree different configurations with 8, 16, and 32 Vivaldi elements 2 International Journal of Antennas and Propagation in vertical polarization (VP) are proposed, as shown in Figure 5. e single element parameters are reported in Table 3 for each configuration. e proposed large antenna array design of 32 elements is shown in Figure 5(c). e 32 array dimension is 68.3 × 68.3 cm 2 , which is less than the horizontal design by 24%. Figure 6(a) shows the array bandwidth of 8-element array between 1.28 GHz up to more than 7 GHz. e distance between antennas and PEKK is 7 cm. e space between the array elements is 16 cm, which produces S 21A average of −23.15 dB. As presented in Figures 6(b) and 6(c), the antenna array performance in terms of reflection and transmission coefficients shows less than −10 dB for a bandwidth range from 1.17 GHz to more than 7 GHz. e S 21A average of 16 elements is slightly higher than 8 elements due to the shorter distance between the radiating elements. S 21A average value records −21.19 dB. e antenna bandwidth starts from 1.17 GHz up to more than 7 GHz. e distance between antennas and PEKK is 13.1 cm. S 21A average value records −18.6 dB. Table 4 summarizes the performance of horizontal and vertical polarizations. For 8element configuration case, both designs are similar in terms of array dimensions and the lower cut-off frequencies.
However, the vertical polarization design exhibits lower S 21A value. Also, it is noticed that the VP array configuration has lower S 21A than HP ones for 16-element case. e optimized 32-element array design has a satisfactory result in terms of antenna bandwidth, array size, and system complexity.

Thermal Analysis
e following is a study of the temperature variation over the entire structure based on thermal losses in the conductors and dielectric materials. ese thermal losses are computed using the frequency electromagnetic solver at 2.45 GHz.

3.1.
e Electromagnetic ermal Model. Simulating the heating process of pipelines is technically challenging to be achieved since there is no report so far that has been studied their thermal properties, especially the PEEK. e complexity of finding the pipeline heating transfer coefficients is due to nonlinear functions of thermal model parameters that relay on temperature and water content. erefore, the following case study will consider tabulated data as well as the default properties mentioned above. According to the technical data sheet [25], each element can handle an input power level of 350 W, in which it will produce 5.6 kW as nominal power. e exposure duration and ambient temperature are set to 450 seconds and 25°C, respectively. e maximum temperature distribution is rescaled to 50°C to detect the water component inside the pipeline, as shown in Figure 7(a), and rescaled to 29°C to distinguish between the oil component and ambient temperature. erefore, the water is clearly detected among the oil and air inside the pipeline due to its large dielectric constant compared to oil. Also, the close section of PEEK tube is affected by water heating. e oil model is mostly heated at 26.5°C, whereas the section close to water is heated to 29°C. It is noticed that the central section of oil is heated more than 26.5°C due to focus radiated power at the pipeline center. As the oil real part of permittivity is close to air value, it is challenging to distinguish between both materials by their response to microwave heating.      Figure 4: e horizontal scattering matrix of (a) 8 elements, (b) 16 elements: S1,1-S2,1-S3,1-S15,1-S16,1, and (c) 32 elements: S1,1-S2,1-S3,1-S31,1-S32,1.

Conclusion
e antenna vertical polarization is advantageous over the horizontal polarization due to the relatively small size in the case of using large number of antenna elements. e large number of antenna elements has major advantages of providing more information about the pipeline components, which is an essential element for accurate pipeline image reconstruction algorithms. For 8-and 16-element array configurations, VP array shows lower S 21A values, which express lower mutual coupling. Both HP and VP arrays show similar proportion for their dimensions and lower cut-off frequencies. For 32-element case, VP is preferable over the HP configuration due to its compact size and acceptable S 21A value. e thermal analysis presents the pipeline components at different temperatures, where the water can be seen at 50°C, oil at 26.5°C, and gas at ambient temperature of 25°C.

Data Availability
e results of this study are available from the corresponding author.

Conflicts of Interest
e authors declare that they have no conflicts of interest. International Journal of Antennas and Propagation 7