The Electromagnetic Field Analytical Solution Analysis to Downhole Current Injection Ranging

As the final crucial line of defense against well blowout accidents, the implementation of the relief well scheme facilitates the swiftest possible rescue of the target well, thereby minimizing economic losses and enhancing production efficiency. Among them, the relative distance and orientation determination between the relief well and the accident well becomes the key to the rapid intersection and connection of the two wells. However, the inaccessibility of the accident well due to safety factors makes it challenging to accurately determine the relative position of the two wells. The current injection method has now been proved to be able to achieve relief well detection, and some signal processing methods are necessary for optimizing the detection performance. In the process of signal characterization, analytical methods show many advantages due to their direct relevance to the principles of electromagnetic theory. To provide an effective theoretical basis for the optimization of relief well detection methods, this paper proposes an analytical solution to the corresponding electromagnetic field distribution for current injection detection scheme. Based on the principle of the current injection detection, the signal model is constructed, and the electromagnetic distribution expression is deduced. Then, the adaptability of the analytical solution obtained under different physical parameters is investigated. Moreover, the reliability and validity of the proposed analytical solution are validated by comparing the results with those obtained from finite element numerical simulations, thus providing a theoretical basis for subsequent signal processing and method optimization.