Accurate ranging of adjacent well using compressive sensing-based current injection with a uniform sensor array

Drilling a relief well provides a last resort option in the event the blowout wellbore is inaccessible, where one of the most key points is to determine the distance of the target before uncertainty ellipsoids overlap, so as to guide the relief well to intersect with the target well. As the only commercially applicable technique presented by Haliburton, the current injection method has been proven to be effective for adjacent well ranging. However, the detection process is implemented by an openhole logging tool after pulling out of hole, where the logging tool is probably stuck especially in such a directional relief well. To realize an accurate measurement of the well spacing when the downhole tool is stuck, this paper proposes a compressive sensing (CS)-based ranging method for the adjacent well using current injection with a uniform sensor array. On the basis of the current injection signal model, the influences of the stuck tool on the detection signal with a magnetic sensor are analyzed. It is shown that the error term corresponding to the tool being stuck and the target term related to the well spacing are coupled in the received magnetic signal. In order to reduce the influence of the stuck error, we use the Gauss-Legendre quadrature to separate the error term and the target term in the detection signal with the uniform sensor array, so that the target vector can be extracted with the dimension reduction property of the CS technique. Moreover, an iterative CS-based ranging algorithm is proposed for the extracted target vector to accurately determine the distance between two wells by searching for the optimal solution in each iteration. Finally, simulation and experiment data are shown to verify the effectiveness of the proposed method, and the results show that this method can achieve accurate ranging, even in the case of a stuck logging tool.