Systematic Uncertainty Analysis of Reservoir Image from New Generation LWD Azimuthal Resistivity Measurements
Authors: Shen Qiuyang , Chen Jiefu , Wang Hanming 
Published: October 2018

Abstract
A new generation of logging-while-drilling (LWD) azimuthal resistivity tools has emerged in the market since a few years ago. With the depth-of-detection (DoD) more than 100 feet, the application of the new service widely ranges from well placement, reservoir mapping, geo-stopping, landing fault detection to salt edge detection, etc. The azimuthal propagation resistivity tools all use the concept of multi-spacings, multi-frequencies, and multi-components. The measurements acquired by the new generation tools are much richer than those by the conventional azimuthal resistivity LWD tools with DoD around or less than 20 feet. However, due to the complexity of the measurement physics and data interpreting process, without a thorough understanding of the uncertainty of the measurements, the operators do not have sufficient confidence in this service as much as expected from service providers.
To promote the understanding of the technology, in this paper, we evaluate the ultra-deep azimuthal resistivity tool by systematic sensitivity study, and uncertainty quantification on reservoir image using a new statistical method. The sensitivity of the measurements to the dip angle, the anisotropy, the layer boundaries, and the formation resistivity is essential to assess the capability of the technology for practical applications. A group of studies are conducted to evaluate the sensitivity under several common situations including homogeneous isotropy formation, homogeneous anisotropy formation, and layered formation. The information content of the measurements and the proper use of the measurements are clearly demonstrated.
The interpretation of ultra-deep azimuthal resistivity measurements stresses on the search of true earth model parameters within DoD from borehole. The unique solution can hardly be found due to local minima problem. The statistical methods governed by Bayesian theorem can search for the statistical distribution, hence, tell the uncertainty of interpreted model. Additionally, a novel statistical analysis, the trans-dimensional Markov Chain Monte Carlo (tMCMC) method is proposed in this paper to handle multi-model uncertainty quantification problem. A set of 1D formation models, proposed by SPWLA Resistivity Special Interest Group (RtSIG) chapter, are used to quantify the uncertainty of the bed boundary position, the formation resistivity, the dip angle through. The probability maps of the boundary interface and the distributions of the resistivity profile can be extracted from the statistical characteristics of the posterior predictive distribution (PPD). The exercise of the statistical solver on the formation models recommended by SPWLA RtSIG demonstrates that the uncertainty quantification techniques can be crucial to assess the azimuthal propagation resistivity technology. A field example from a subsea gas well of Wheatstone liquefied-natural-gas project in Western Australia is used to confirm the importance of the uncertainty quantification in evaluating the capacity of the azimuthal propagation resistivity measurements.