An approximate 3D inversion method for inversion of single-well induction-logging responses

Abstract

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.