Research on extremely low frequency electromagnetic wave model and simulation in wellbore communication

Over recent years, as digitalization and intelligence in oil wellbore have increased, so have the stricter requirements for wireless communication technology in terms of distance, accuracy, and portability. As a result, it's necessary to rely on more advanced and efficient wireless communication technologies to meet the industry's needs. However, traditional communication technologies such as cables and optical fibers have inherent shortcomings in construction, data interpretation, and cost. ELF electromagnetic waves are an ideal solution for communication in complex wellbore conditions due to long-distance communication and strong penetration capabilities, making it a highly effective option. Based on the theory of network splitting, this paper establishes a polygonal multiple-delays uncertainty coupled complex network model of ELF electromagnetic waves propagating through the casing in layered media and designs a controller, including expressions for the intensity of the magnetic and electric fields in different directions, and the propagation and distribution characteristics in different media. We determined that the optimal transmitting frequency of ELF electromagnetic waves under general conditions is 12.7 Hz. Based on field experiments, we verified that ELF electromagnetic waves can enable wireless wellbore communication within 1500 m without relays. We also analyzed the impact of casing thread deformation on ELF electromagnetic wave propagation due to high-temperature and high-pressure environments. We used simulation experiments to solve the distribution relationship between the electric and magnetic fields of the solenoids through casing and strata, as well as the coupling coefficients between the transmitting and receiving solenoids, and explore how different transmitting frequencies affect the efficiency of signal propagation. Both theories and experiments have verified the correctness of the model, and have also demonstrated the reliability and continuity of using ELF electromagnetic waves to achieve wireless wellbore communication, which provides a theoretical basis and feasibility for subsequent engineering applications.