High-Performance Stochastic Inversion for Real-Time Processing of LWD Ultradeep Azimuthal Resistivity Data

Logging-while-drilling (LWD) ultradeep azimuthal resistivity (UDAR) tools become an essential part of well placement because they are deep enough to explore the reservoir as a whole and expose it in a similar scale with seismic sections. Due to the increased formation volume being investigated, UDAR measurements depend on many formation parameters and require multilayer models to be interpreted, as well as effective inversion approaches. Stochastic inversion algorithms have many advantages and are used extensively in field applications. Working with multiparametric models, these algorithms might become time consuming, which limits their applicability to real-time data processing, especially while drilling with high penetration rates. This paper presents an advanced stochastic algorithm with sufficient performance to invert UDAR data in real time. The proposed inversion supports all existing UDAR tools with coaxial, tilted, or orthogonal antennas and has a flexible interface for adding new tools with arbitrary types of measurements. Besides that, there is an option to consider the modular configurations of UDAR tools by setting the number of transmitter/receiver subs and the distances between them. The inversion utilizes a 1D layer-cake formation model and enables simultaneous processing of resistivity data logs by intervals. The algorithm is based on the stochastic Monte Carlo method with reversible jump Markov chains and can be launched automatically without prior assumptions about the reservoir structure. The algorithm automatically adjusts model complexity through the data fitting based on the detection and resolution capabilities of tool responses. Finally, inversion provides an ensemble of unbiased formation models, their probabilities, and uncertainty estimates of the recovered model parameters. Working in high-dimensional parameter space, stochastic inversion algorithms might not be effective due to the limitation of sampling procedures that often do not consider relations between model parameters and their influence on tool responses. To guarantee real-time results, the proposed algorithm employs a Metropolis-adjusted Langevin technique that evaluates the gradient of the posterior probability density function and generates proposals being accepted as very likely. Additionally, a special semi-analytical solver is utilized to compute the gradient simultaneously with tool responses with almost no extra computational costs. The presented algorithm has two concurrency levels to ensure near-optimal speedup for all stages of the geosteering job. First, the computation is parallelized over inversion intervals that are independent of each other and can be processed concurrently without any computational losses. This level is important for both pre- and post-well stages when a lot of inversion intervals are processed at once. At the second level, which is crucial for the real-time stage with only a few intervals being processed at a time, the parallelization is implemented over Markov chains with the necessity to synchronize computational threads to enable exchanging states between different chains and eventually avoid sticking in local optima. The workflow was adjusted specially to enable inversion running on computers with 32 and more cores by reducing both memory fragmentation and the number of requests from computational threads to the operating system to prevent its overload and eliminate possible deadlocks. The paper will demonstrate both inversion capabilities and performance estimated on a series of industry-adopted benchmarks and field data sets. Presented high-performance inversion may help oilfield operators to improve their understanding of full-scale reservoir structure while drilling, delineate pay zones better, and eventually achieve higher reservoir contact by making more informed geosteering decisions.