Design and numerical simulation of a microwave antenna with coaxial slots for preventing secondary formation of gas hydrate

. Gas hydrate is a new clean energy resource with polar molecule. However due to the change of temperature and pressure during extraction process, there will be secondary formation of gas hydrate, which usually occurs in reservoirs or pipelines near the wellhead. It is significance to prevent secondary formation of hydrate because of safety issues or production rate reduction caused by it. Theoretically, microwave heating can accelerate the decomposition of gas hydrate. Therefore, it is possible to use microwave radiation to prevent secondary formation of hydrate. In this paper, a microwave antenna with special shaped coaxial-slots was designed. Based on electromagnetics and antenna transmission theories, the key parameters of the coaxial-slot antenna were calculated. The frequency is 2.45 GHz, the impedance is 50 ohms, and ratio of outer to inner conductor radius is 3.32. The slots were designed as ‘H’-shape with the width is 2 mm, the radial length is 12mm, the axial length is 14 mm and the interval is 35 mm. Teflon was used as filling material and the radome. Then the software HFSS and ANSYS were used to analyze the electromagnetic field and temperature field to further optimize the parameters. It will be proved that the microwave antenna can heat gas hydrate and prevent the secondary formation.


Introduction
Natural gas hydrate is a non-stoichiometric crystalline solid, which is formed by water and small molecular gases (such as H 2 , CH 4 , H 2 S, etc.) under low temperature and highpressure conditions [1]. At present, depressurization is one of the commonly used methods for producing natural gas hydrate. Studies have shown that in the early (late) stages of gas hydrate decomposition by depressurization, heat transfer and kinetics are the control mechanisms for hydrate decomposition. In the later stage, the heat supply will be insufficient due to the large amount of decomposition and heat absorption of the hydrate in the early stage. Because of the Joule-Thomson effect, there will be secondary formation of gas hydrate in the gas production channels, wellbores, blowout preventers (BOP), and other parts under low temperature and high-pressure conditions. Severe blockage will affect the rate of gas migration or even block gas production channels, causing the risk of reducing gas production rate or even production shutdown [2][3][4][5][6][7]. In order to eliminate or suppress the secondary hydrate plug in the depressurization process, the supply of heat can restore the gas production efficiency theoretically. The traditional heating method has a slow heating rate and large heat loss. In contrast, the electromagnetic heating method can quickly heat as needed, and it has demonstrated its effectiveness in heavy oil [8][9][10][11][12][13][14][15][16][17][18][19].
Electromagnetic heating can be divided into high frequency (microwave, radio frequency) heating, medium frequency induction heating, and low frequency resistance heating according to different frequencies. Microwaves are ultra-high frequency electromagnetic waves with frequencies between 300 to 300000 MHz. The microwave frequencies between 2450 and 915 MHz are commonly used for heating in the industry. Because microwaves will be absorbed when interacting with some polar substances or molecules to produce thermal effects, microwave heating is widely used in food, industry, agriculture, medical treatment, and the exploitation of unconventional oil and gas resources (oil shale, heavy oil, and oil sands) [20][21][22][23].
Natural gas hydrate is a kind of polar molecule. In theory, its molecular motion is disturbed and blocked under the changing electromagnetic field, which will produce an effect similar to friction. And a part of the microwave energy is converted into the energy of the chaotic thermal movement to intensify the movement of the polar molecules, thereby increasing the temperature and solving the problem of insufficient heat supply in the later stage of depressurization [24][25][26][27]. Moreover, microwave heating is a kind of body heating, which does not depend on the power system. It means that the temperature can be increased in a short time so that the energy conversion rate is high and the heat loss is small. In this case, the thermodynamic power required for the decomposition of hydrates can be provided, which is beneficial to inhibit the secondary formation of hydrates or promote the decomposition of secondary hydrates, and ultimately improve productivity [28][29][30][31].
In the application of microwave heating, the microwave energy generated by the microwave generator is conducted to heat the object through the microwave transmission line. In actual high-power transmission applications, coaxial lines or waveguides are often used as microwave transmission lines, and antenna as a kind of transmission media has the function of radiating microwave energy in a certain direction [22]. At present, the researchers are mainly focused on heating mechanism of heavy oil and gas hydrate by microwave antenna. On the contrary, there are few studies related to the structure design of the antenna for microwave heating of hydrate. For instance, in the case study reported by Kasevich et al. [32], they used antenna to heat a small sample of heavy oil. A microwave antenna with a special protective cover was designed by Matteo et al. [33], which was used to heat the heavy oil. Possibility and capability of gas pipelines used as microwave transmission waveguides was studied and calculated by Wang Yulong [34] and Meng Xiaofeng et al. [35].
The antenna design for heating hydrate is different from that for heating heavy oil because of the different conditions in the process. In this paper, a microwave antenna with coaxial slots suitable for the frequency of 2.45 GHz is designed to prevent the secondary formation of hydrate. The antenna can transmit the high-power microwave energy to the place where the secondary hydrate is easy to form, and radiate microwaves energy in a certain range to heat the secondary hydrate. In addition, it can ensure the normal operation of the antenna while irradiating high microwave power under the conditions of low temperature and high pressure. Through the numerical simulation of the HFSS software, the electromagnetic field and temperature field of the secondary gas hydrates was analyzed. The dimension of antenna was optimally designed, which provides a theoretical basis for the removal of secondary hydrates during the exploitation of natural gas hydrates.

Mathematical calculations
The antenna can radiate effective microwave energy in a specific direction. Monopole antenna is one of the most basic categories and can be used as an omnidirectional antenna. Its basic structure is that the inner conductor of the coaxial cable protrudes from the outer conductor in an appropriate length relative to. Theories and experiments show that the backward heating effect of the monopole antenna is serious, and it will produce a narrow ablation zone with a long tail. In contrast, the heating area formed by the coaxial slot antenna is more ideal. The antenna with coaxial slots is the antenna with some slots on the surface of outer conductor. According to the dimension of the slots, the slots can be divided into radiating slots and non-radiating slots [36][37][38].
The basic structure of the antenna with coaxial slots designed in this paper is shown in Fig. 1. The antenna is composed of a hollow outer conductor 1 and a solid inner conductor 4. The inner conductor at the top protrudes from the outer conductor with a proper length. The outer conductor is cut to form the slots with H-shaped structure. These radiation slots can cut the microwave line and establish excitation microwave electromagnetic field. The material of the outer conductor 1 can be made by stainless steel in consideration of corrosion resistance, workability and strength. The surface of the outer conductor 1 is uniformly arranged with multiple H-shaped slots in the radial direction to expand the radiation direction range of microwave heating. Copper should be selected as the material of the inner conductor 4 considering its excellent performance in the electronic field. The filler 3 between the inner and outer conductor should be made of low dielectric loss, insulating and impermeable material Teflon. Because of its good pressure resistance, it can also be used as an antenna shell to protect the antenna.  Studies have shown that the dielectric properties of hydrates in the microwave frequency range are similar to those of ice and dry sand [39]. The extension length of the inner conductor is related to the effective wavelength in the filler, while the effective wavelength is related to the microwave frequency and relative permittivity. The calcul ation formula is as follows [39]: where λ eff -the effective wavelength, m; c -the speed of light in vacuum, c = 3·10 8 m/s; fthe frequency of microwave radiation, Hz; ε r -the relative permittivity.
There are transmission electromagnetic waves and cutoff electromagnetic waves due to different frequencies. The frequency determined by the critical state between transmission and cutoff is called cutoff frequency. The wavelength corresponding to this frequency is called cut-off wavelength [39]. When the working wavelength exceeds the cut-off wavelength, only one mode of electromagnetic wave can be transmitted. If it does not exceed this wavelength, multiple modes of waves can be propagated. Since the single-mode transmission is farther than that of multi-mode [34], and the coaxial line is mainly TEM mode. It is necessary to ensure that only the TEM mode is transmitted in the coaxial media, considering the actual long-distance transmission in the actual design.
The calculation of the diameter of the inner and outer conductors of the coaxial slit antenna mainly considers the following two factors [39].
1. The working wavelength must fit the following conditions: where λ c -the working wavelength, m; a -the radius of the inner conductor, mm; b -the radius of the outer conductor, mm. 2. The antenna should have a large power capacity and a small attenuation coefficient. According to experience, the characteristic impedance can be selected as 50 Ω. The ratio of the characteristic impedance to the inner and outer conductor diameters is calculated as follows: 60 ln where Z c -the characteristic impedance, Ω; ε r -the relative permittivity of the filler, F/m. The theoretical value of the slot's length is related to the effective wavelength and relative permittivity. The calculation formula is as follows: where l -the length of slots, mm. The theoretical value of the gap distance is also related to the effective wavelength, and needs to fulfill the requirements of constant amplitude and in-phase feeding. The general calculation formula is as follows: where G -the gap distance, mm. The distance (G 2 , mm) from the center of the first slot to the microwave input end is usually taken a quarter of the waveguide wavelength: The antenna needs to be able to work under certain pressure conditions, thus the wall thickness of the outer conductor can be simply calculated by the following formula: where t -the wall thickness of outer conductor, mm; K -the safety factor, K = 2; P -the working pressure that needs to be met, Pa; D -the diameter of the outer conductor, m; σ -the allowable stress of the material selected for the outer conductor, Pa. The calculation results of main parameters of the antenna are shown in Table 1. The schematic diagram of the size of antenna with coaxial slot is shown in Figs. 2 and 3.

Results of simulation and discussion
According to preliminary calculation, using software HFSS and ANSYS to simulate the electromagnetic field and temperature field of the antenna in the process of heating the secondary hydrate. Based on the principle of microwave heating and actual situation of hydrate exploitation [34][35][36][37][38][39][40][41], 2.45 GHz frequency is selected and the remote end of antenna with coaxial slots serves as wave port. The material to be heated is hydrate, which the relative permittivity is 3 and dielectric loss tangent is 0.0006. The length of antenna is 1000 mm. The radiation area is a cylinder, which the radius is 50 mm and length is 2000 mm. The model of antenna is showed in Fig. 4. Tn antenna with coaxial slots mainly relies on the slots opened on the coaxial line and coaxial port to radiate microwave energy to heat hydrate. Under the condition of 2.45 GHz, the far-field radiation pattern and 3D polarization plot of the designed antenna are showed in Fig. 5. It can be seen that antenna has a better radiation in all direction, which also proves that the antenna will irritate microwaves through slots to hydrate in all around.  Considering the thermal properties of hydrates, the temperature field and electric field in the heating process are different. In the heating process, a series of issues such as heat conduction, heat diffusion, and heat dissipation of the cavity need to be considered. Therefore, using software HFSS and ANSYS as a joint simulation. As shown in Fig. 6, solutions of HFSS software are imported into ANSYS to analyze the steady-state thermal and transient thermal of using the antenna heating secondary hydrate. In ANSYS, the energy absorption of each part of the simulation can be seen (Fig. 7). Cylinder 1 is the model of the heated hydrate. The input power is 300 w. Since the field and dissipation inside the metal are not calculated in HFSS software, this value is better than the real situation. From the Steady-State thermal simulation (Fig. 8), it shows that the antenna can heat the secondary hydrate to 24℃. According to the hydrate phase equilibrium theory model, the decomposition condition of hydrate can be satisfied.  As shown in Fig. 9, it can be found that the heating rate and temperature uniformity of the antenna to hydrate are effective, which shows that the antenna can achieve the purpose of inhibiting the secondary formation of hydrate.

Conclusions
The special antenna with coaxial slots which is used to heat secondary hydrates is calculated and designed according to related theories, such as dielectric theory, waveguide theory and slot antenna theory, etc.
The antenna is designed with several 'H'-shaped slots based on frequency of 2.45 GHz, and the diameter of outer conductor is 30 mm, which makes it can be easily lowered into the gas producing channel to prevent the secondary formation of hydrate.
From the simulation results of far-field radiation in HFSS software, the antenna has good omnidirectional radiation. Then combining software HFSS and ANSYS to simulate the heating effect of the antenna on the secondary hydrate. It can be discovered that the secondary hydrate can be heated from -3.8 to 17.8℃ within 1800 s. While in 3600 s, the hydrate can be heated from -3.4 to 27.3℃. According to the model of hydrate phase equilibrium, hydrate can be decomposed under this condition. Therefore, based on simulations, it has been demonstrated that the antenna can effectively radiate microwaves to heat hydrates and prevent the secondary formation of hydrates.