Borehole transient electromagnetic (TEM) techniques have been proven to be efficient for nondestructive evaluations (NDEs) of metal casings using eddy-current properties. However, physical limitations and bad borehole conditions restrict the use of eddy-current sensors, which makes downhole casing inspections very different from those of conventional NDE systems. In this paper, we present a uniform linear multi-coil array-based borehole TEM system for NDEs of downhole casings. On the basis of the borehole TEM signal model, a numerical multi-coil array approach using the Gauss–Legendre quadrature is derived. The TEM response can be divided into two independent parts related to the transmitting-receiving distance (TRD) and the observation time and casing thickness. Using this property, the signal received by the multi-coil array is weighted to cancel the influence of the TRDs of the different array elements to obtain the optimal response according to the linearly constrained minimum variance criterion, which can be shown to be identical to that of achieving the maximum signal-to-noise ratio. The effectiveness of the proposed method was verified by applying the uniform linear multi-coil array to a borehole TEM system for NDEs of oil-well casings. Field experiments were conducted, and the results demonstrate the effectiveness of the proposed method.

In this article, we address the problem of synthesized magnetic field focusing (SMF) of the pulsed eddy-current (PEC) technology for the non-destructive testing (NDT) of oil and gas well casing pipes. The electromagnetic response excited by multiple transmitters was derived using the signal model of downhole PEC system. The magnetic field was shown to be adjustable by modifying the currents of the multiple transmitting array. Based on this property, magnetic fields were synthesized with the mean squared error (MMSE) criterion to be focused on the center of the transmitting array, and a weighted MMSE (WMMSE)-based SMF was also proposed to achieve an optimal synthetic magnetic field. Furthermore, the primal-dual interior-point method was used to solve the WMMSE optimization problem with the total and single transmit power constraints for the practical application. Simulations and experimental results showed that the SMF with the PEC array effectively focuses the eddy-current field on the center of the transmitting array.

Borehole transient electromagnetic (TEM) array has proven to be efficient for the downhole nondestructive testing (NDT) of metal casings through the eddy-current property. However, restricted by bad downhole conditions, the simple increase of the receiving array is not sufficient enough for improving the downhole NDT performance. In this paper, we present a multiple-transmit focusing (MTF)-based borehole TEM system for the NDT of downhole casings. On the basis of the borehole TEM signal model, the response of the multiple-transmit array is derived by employing the matrix form of the borehole TEM response. It was shown that the excited magnetic field by the multiple-transmit array can be focused by weighting the current of each transmitter. Using this property, a modified linear constrained minimum variance-based multiple-transmitting array weighting method was proposed to realize the MTF. Moreover, a subarray partition approach was proposed to simplify the MTF realization, where the subarray weighting and mean square error were also analyzed. The MTF method performance was verified by applying it to a borehole TEM system for the NDTs of downhole casings. Finally, simulations and experiments were conducted, and the results demonstrated the effectiveness of the proposed method.

Transient electromagnetic (TEM) techniques are widely used in the field of geophysical prospecting. In borehole detection, the nondestructive inspection (NDI) of a metal pipe can be performed efficiently using the properties of eddy currents. However, with increasing concern for safety in oil and gas production, more than one string of pipe is used to protect wellbores, which complicates data interpretation. In this paper, an auxiliary sensor-based borehole TEM system for the NDI of multipipe strings is presented. On the basis of the characteristics of the borehole TEM model, we investigate the principle behind the NDI of multipipe strings using multiple time slices of induced electromotive force (EMF) in a single sensor. The results show that the detection performance of NDI is strongly influenced by eddy-current diffusion in the longitudinal direction. To solve this problem, we used time slices of the induced EMF in both the main and auxiliary sensors. The performance of the proposed system was verified by applying it to an oil well with a production casing and liner. Moreover, field experiments were conducted, and the results demonstrate the effectiveness of the proposed method.

In this article, we present a space–time pulsed eddy current (PEC) array for nondestructive testing (NDT) of wellbore casings using a multiple-input multiple-output (MIMO) technique. On the basis of a multilayered cylindrical wellbore model, an MIMO-PEC model is developed according to the phase shift characteristics of the PEC response corresponding to different transmitting–receiving (TR) distances. To achieve a more significant number of TR channels than in a traditional receiving array to reduce the complexity of the TR structure, a space–time transmission scheme is proposed to recover multiple TR channels. Moreover, a specific space–time MIMO array structure is designed to maximize the number of independent TR channels. The effectiveness of the proposed method is verified by applying the proposed MIMO array to a borehole PEC system for NDT of wellbore casings. The simulation and experimental results demonstrate that using the array structure and space–time transmission scheme proposed in this article, an MIMO structure consisting of ${M}$ transmitters and ${N}$ receivers can be equivalent to a transceiver system with a single transmitter and ${M}\,\,\times \,\,{N}$ receivers. Thus, MIMO technique can be effectively applied to PEC-NDT systems and drastically reduce the cost and complexity of the PEC system.