Electromagnetic logging is a technique used to probe differences in electric conductivity around a measurement device. Electromagnetic logging while drilling can contribute to proactive geosteering to improve well placement in reservoirs because such measurements can serve as an indication for the structure of the surrounding geology. We have developed a novel way of predicting the 3D conductivity distribution around a drilling tool, based on the contrast-source inversion method, in which we have replaced the full integral-equation approach by the single spherical scatterer (SSS) approximation. The approximation took into account the dominant features of the diffusive electromagnetic field. This allowed for a substantial gain in computational speed and storage of the inversion method for reconstruction of the conductivity distribution. In view of the limited range of the electromagnetic probing, the overall reconstruction can be segmented in several local windows. This reduced the computational speed requirements and the storage requirements dramatically, while safeguarding the overall 3D character of reconstruction. We have synthesized 3D electromagnetic logging data using synthetic models and conductivity maps from a hydrocarbon North Sea reservoir model. Reconstructions were made for multiple source frequencies, and the results were compared with the results obtained from the Born approximation. We have observed that reconstruction based on the SSS approximation was superior to the one based on the Born approximation. Our algorithm helped us determine the feasibility of producing reconstructions of reservoir sections in a short time frame, which allows for real-time decision making during drilling operations.
Over many years, induction logging systems have been used to create well formation logs. The major drawback for the utilization of these tools is the long simulation time for a single forward computation. We proposed an efficient computational method based on a contrast-type of integral-equation formulation, in which we applied an approximation for the 3D electromagnetic field. We assumed that the dominant contribution in the integral equation is obtained by the contribution around the singularity of Green's kernel. It is expected that the approximation yields reliable results when the (homogeneous) background conductivity around the logging tool is close to the actual conductivity at the location of the tool. We have developed a data-driven method to determine this background conductivity from the dominant part of the measured coaxial magnetic fields, which are mainly influenced by the conductivity at the tool sensors. For a synthetic model, the results were compared to the ones of a rigorous solution of the integral equation and show a good simulation response to small-scale variations in the medium. Further, the method was used to simulate the response of a realistic reservoir model. Such a model is created by a geological modeling program. We concluded that our approximate method was able to improve the approximation results in highly heterogeneous structures compared to the Born approximation and provide an effective medium-gradient around the tool. Our method, based on the wavefield approximation, also estimates the error, and hence yields a warning when the method becomes unreliable.
Over many years, induction logging systems have been used to create well formation logs. The major drawback for the utilization of these tools is the long simulation time for a single forward computation. We proposed an efficient computational method based on a contrast-type of integral-equation formulation, in which we applied an approximation for the 3D electromagnetic field. We assumed that the dominant contribution in the integral equation is obtained by the contribution around the singularity of Green's kernel. It is expected that the approximation yields reliable results when the (homogeneous) background conductivity around the logging tool is close to the actual conductivity at the location of the tool. We have developed a data-driven method to determine this background conductivity from the dominant part of the measured coaxial magnetic fields, which are mainly influenced by the conductivity at the tool sensors. For a synthetic model, the results were compared to the ones of a rigorous solution of the integral equation and show a good simulation response to small-scale variations in the medium. Further, the method was used to simulate the response of a realistic reservoir model. Such a model is created by a geological modeling program. We concluded that our approximate method was able to improve the approximation results in highly heterogeneous structures compared to the Born approximation and provide an effective medium-gradient around the tool. Our method, based on the wavefield approximation, also estimates the error, and hence yields a warning when the method becomes unreliable.
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