Application of Automatic Stochastic Inversion for Multilayer Reservoir Mapping while Drilling Measurements
Authors: Dong Cindy , Dupuis Christophe , Morriss Chris , Legendre Emmanuel , Mirto Ettore , Kutiev Georgi , Denichou Jean-Michel , Viandante Mauro , Seydoux Jean , Bennett Nicholas , Zhu Qingfeng , Zhong Xiaoyan 
Published: November 2015

Abstract
The data delivered by a new reservoir mapping while drilling (RMWD) tool provides more geological information than that from any other logging-while-drilling (LWD) technology previously available in the oil field. Its answer product images the surrounding formation structure, and the resulting maps can be used by the geoscientists to improve their understanding of the subsurface, the well placement and the reservoir.
To take advantage of the richness of the measurements and deep depth of investigation across multiple formation boundaries, an automatic stochastic inversion has been developed that combines approximately a hundred phase and attenuation measurements at various frequencies and transmitter-to-receiver distances. This efficient Bayesian model-based stochastic inversion runs in parallel with multiple independent search instances that randomly sample hundreds of thousands of formation models using a Markov chain Monte Carlo method. All samples above a quality threshold over the solution space are used to generate the distribution of formation models that intrinsically contain the information for model uncertainties.
RMWD is a highly nonlinear problem; inverting for a unique solution is analytically difficult due to the well-known local minima issue. The stochastic method addresses that by sampling thousands of possible formation models and outputting a distribution of layered models that are consistent with the measurements. Statistical distributions are displayed for formation resistivity, anisotropy and dip at each logging point. Additionally, the median formation models for resistivity are shown along the well trajectory as a curtain section plot. This provides an intuitive interpretation for the entire reservoir formation around the tool. The inversion curtain section plot can be overlaid with the seismic formation model for combined interpretation. Furthermore, the curtain plot provides graphical information for dip and distance to boundary, which are critical for field applications such as landing, geosteering, remote fluid contact identification, etc. The stochastic-sampling-based answer product has been intensively field tested and has proven to provide reliable estimation of the formation geometries and fluid distributions in many locations and geological environments worldwide.
Field applications and simulated examples of the stochastic inversion include remote detection of the reservoir to enable accurate landing, navigating multilayered reservoirs, remote identification of fluid contacts and reservoir characterization in the presence of faults.
The stochastic inversion samples the formation properties randomly and provides the distribution of formation properties based on a large number of samples, instead of providing only the most likely solution as is typical for deterministic inversions. A statistical method of presenting inversion results in formation space provides an instant and intuitive understanding of the formation surrounding the tool. Quantifying the non-uniqueness of the inverted formation models gives geologists a more robust insight into what the formation scenarios may be, and helps with the steering decision-making and reservoir mapping interpretation.