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

Logging-while-drilling (LWD) ultradeep azimuthal resistivity (UDAR) tools became an essential part of well placement technology because they are deep enough to explore the reservoir as a whole and map it on a similar scale to seismic sections. Due to the large formation volume being investigated, UDAR measurements depend on many formation parameters and require complex multilayer formation models used in the interpretation as well as new, effective inversion approaches. Stochastic inversion algorithms have many advantages and are used extensively in borehole field applications. Working with multiparametric models, these algorithms could become time consuming, which limits their applicability in real time, especially while drilling with high rates of penetration. This paper presents both a new, advanced high-performance stochastic algorithm and specially developed software allowing for inverting UDAR data in real time. The inversion software 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. It includes an option to account for the modular configurations of UDAR tools by setting the number of transmitter/receiver subs and the distances between them. The inversion uses a one-dimensional (1D) layer-cake formation model with arbitrary borehole trajectory 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 without prior assumptions about the reservoir structure. The algorithm automatically adjusts model complexity by increasing the number of layers based on the data fitting and analyzing 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 multiparametric space, stochastic inversion algorithms might not be effective due to the limitations of sampling procedures that often do not consider the sensitivities of the model parameters. To enable real-time results, the developed algorithm employs the Metropolis-adjusted Langevin technique that evaluates the gradient of a posterior probability density function and generates proposals with higher probability. Additionally, a special semi-analytical solver is used to compute the Jacobean simultaneously with tool responses with almost no extra computational costs. The presented algorithm has two concurrency levels to ensure maximum speedup for all stages of the geosteering job. First, the computations are parallelized over inversion intervals that are independent of each other and can be processed concurrently with very slight computational losses. This level is important for both pre- and post-well stages when many inversion intervals are processed at once. The second level is crucial for the real-time stage, when only a few intervals are processed at a time. At this level, parallelization is implemented across Markov chains, requiring synchronization of computational threads to facilitate state exchanges between chains and prevent sticking in local optima. The algorithm was adjusted specially to enable inversion running on computers with 32 or 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. This paper demonstrates the resolution and performance of the new inversion software on a series of industry-adopted benchmarks and on the field data sets. The developed high-performance inversion software may help oilfield operators improve their understanding of full-scale reservoir structures while drilling, delineate pay zones better, and, eventually, achieve better production by making more informed geosteering decisions.