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An Efficient and Effective Algorithm for Mapping Reservoir Boundaries

An efficient and effective algorithm is developed for real-time inversion interpretation for bed-boundary mapping in proactive geosteering. The algorithm is tailor-made for an electromagnetic tool to detect reservoir boundaries of up to ten meters from wellbore and at the same time also to account for the presence of thin beds in the volume of investigation. The algorithm focuses on three main objectives, namely, to delineate a remote target location and the boundaries between the tool and the target, to perform the processing in real-time anywhere on a portable computer, and most critically to achieve a reliable solution. The consideration of thin-beds is especially important to the oilfields where reservoir bed-thickness is in the range of less than one meter to several meters. The tool-configuration is designed with optimized coil-spacings, coil-orientations and a range of operating frequencies. The multitude of operating frequencies is designed to cover the entire range of distance with minimal number of coils and tool length to lower the burden on the tool’s hardware design. The data inversion algorithm performs the computation at a speed required by the fastest drilling applications on a laptop computer. Geologic constraints on inversion parameters are also built into the inversion process. Another critical feature is to maintain the interpretation reliability by synthesizing an integrated cross-sectional display to account for potential multi-solution scenarios. To achieve computational efficiency, the first step is to cast the mathematic formulation into an efficient expression by computing simultaneously all coil-combinations. The second step accomplishes algorithm-parallelization over various operating-frequencies and on all sampling points in each inversion segment. The third significant speed-up is from developing a hybrid Jacobian matrix evaluation, integrating the derivative computation with the Broyden method. The hybrid approach offers acceptable Jacobian accuracy while saving large amount of computation. The fourth scientific contribution made is the selection of inversion seeds for simultaneous inversion on models of varying complexity. The fast inversion algorithm generates formation resistivity profile above and below the borehole. As resistivity is related to lithology and fluid types, a geosteering engineer can intuitively carry out quantitative steering task and can optimize drilling trajectory based on the inverted curtain-section together with other measurements. The developed fast and robust inversion algorithm enables mapping correctly the bed-boundaries around the wellbore.