###### Abstract  
In the environment of oil and gas wells, the shielding effect of metal casing increases the difficulty of applying wireless electromagnetic wave transmission technology in such wells. This paper constructs a theoretical model of downhole electromagnetic helical loop transmission based on the finite element method. The magnetic loop is equated with the helical loop antenna in the model. By means of simulation calculations, this study deeply investigates the impact of various factors, such as working frequency within the cased well, drilling fluid resistivity, formation resistivity, drill string dimensions, and electrical conductivity, on the attenuation pattern of the helical loop antenna. The results show that low-frequency signals experience relatively less attenuation underground, while high-frequency signals demonstrate better transmission effects over shorter distances. Moreover, drilling fluids with low resistivity are more suitable for short-distance transmission, whereas high resistivity can effectively reduce signal attenuation and improve transmission distance. The variation in formation resistivity has a relatively small impact on signal transmission and can be considered negligible. In terms of drill string characteristics, as the electrical conductivity of the drill collars increases, signal attenuation gradually decreases, and the amplitude of the received signal is enhanced. With the inner and outer diameters of the drill collars remaining the same, a finer inner diameter of the casing aids electromagnetic wave short-distance transmission, whereas a thicker casing can reduce electromagnetic wave attenuation. Theoretical and practical results are in good agreement through field trial comparative analysis. Measurement While Drilling (MWD); helical loop antenna; finite element simulation; short-range wireless transmission; metal casing shielding +
Footnote †: journal: Applied  
in Measurement While Drilling (MWD) work [4; 5]. Electromagnetic wave transmission in wells is affected by various factors such as the transmission frequency, dimensions of the drill string and casing, and the resistivity of the formation and drilling fluid. To accurately control and optimize the propagation characteristics of electromagnetic signals, it is crucial to consider these factors comprehensively and select the appropriate excitation method. There are three common methods of motivation as shown in Figure 1.  
The first method involves installing an insulating sub between two drill pipes to form an asymmetric dipole antenna. Although this requires high standards of insulation performance and mechanical strength, with the development of high-performance insulated subs, this model has been widely applied in various scenarios. The second method is to wind a helical coil on the drill pipe without severing it, which has superior mechanical strength, low costs, simplicity of manufacturing, and convenience in operation. Although its excitation effect is slightly inferior compared with the other two methods, it can still play a key role in specific situations. The third method is achieved by slipping a magnetic core helical loop over the drill pipe. The generated field is similar to the first method, but the effect is better than the second method. Despite being influenced by various factors such as the number of coil turns, size, and magnetic permeability of the core, it is cost-effective, less prone to damage, and has good stability. Therefore, it has a wide range of applications in multiple domains, such as short-range transmission and relay transmission [6]. [PERSON] [7] described in detail the working principle of the relay station and compared the attenuation characteristics of magnetic excitation and electrical excitation. The study found that magnetic excitation attenuated more quickly, and [PERSON] [7] also conducted an in-depth analysis of the position of the relay.