Reservoir Mapping with Vendor-Independent Gradient-Based Stochastic Inversion of LWD Ultra-Deep Azimuthal Resistivity Data

Abstract

Logging-while-drilling (LWD) ultra-deep resistivity technology can explore the reservoir on a similar scale to seismic, so interpreted resistivity models can be combined with seismic sections to enable oil field operators to delineate pay zones better, improve reservoir understanding, and eventually achieve higher reservoir contact value by proactive geosteering. Currently, there is no industry-adopted processing software which supports different ultra-deep tools. This paper presents the first vendor-independent, gradient-based stochastic approach for ultra-deep data inversion while drilling. Industry literature review was performed to determine parameters of ultra-deep tools, investigate their responses, and add them to the list of supported devices. Inversion algorithm is based on stochastic Monte Carlo method with reversible jump Markov chains and can be launched automatically without prior assumptions about the reservoir structure. Finally, it provides an ensemble of unbiased 1D formation models explaining the measurements as well as uncertainty estimates of model parameters. Parallel running of several Markov chains on multiple CPUs with both gradient-based sampling and exchanging their states makes the algorithm computationally effective and helps to avoid sticking in local optima. The proposed approach enables gathering of ultra-deep tools from different vendors under a common interface, along with other resistivity tools, joint processing various resistivity data with the same inversion workflow, and representation of inversion deliverables in unified format. Due to the large formation volume being investigated, the ultra-deep readings become complex. To be interpreted, such responses require multi-layer models as well as special multi-parametric inversion software. Working in high-dimensional parameter space, stochastic Monte Carlo inversion algorithms might not be effective due to the limitation of sampling procedure that usually generates new samples through the random perturbation of the few model parameters and does not consider their relations with other model parameters. This may lead to a high rate of proposal rejections and a lot of unnecessary calculations. To overcome this issue and guarantee real-time results, the presented approach employs Metropolis-adjusted Langevin technique which evaluates the gradient of posterior probability density function and generates proposals with a higher posterior probability of being accepted. Additionally, a special fast semi analytical solver is utilized to compute the gradient simultaneously with tool responses, with almost no extra computational costs. Application of the developed software is shown on synthetic scenarios and case studies from Norwegian natural gas and oil fields. The presented approach is identified as the first vendor-independent gradient-based inversion algorithm operating with any measurements of ultra-deep and deep azimuthal resistivity tools available on the market. The algorithm is high-performance and ensures real-time inversion results even in case of multi–layer formation models required to interpret ultra-deep measurements. The software may help oil field operators to resolve reservoir structure at a larger scale and pursue a more informed reservoir development strategy thus making more confident geosteering decisions.