Wellbore Stability Uncertainty Quantification Using a Bayesian Machine Learning Framework

Abstract One of the major challenges in wellbore stability analysis is to quantify the uncertainty of the mud weight window and provide probabilities of breakouts and drilling induced tensile fractures for a given mud weight. Modeling the safe drilling window requires many geomechanics inputs, such as: rock strength, elastic properties, in-situ stresses, pore pressure, etc. Most of these inputs are calculated using empirical correlations based on limited test data; or calculated using simple elastic equations and calibrated with limited data points. Uncertainties in test and calibration data combined with uncertainties in correlations make it exceedingly difficult to correctly assess the uncertainty of the resulting safe drilling window. An accurate quantification of measurement and other input uncertainties and correct propagation of uncertainty throughout the modeling process can improve decision quality and wellbore instability related non-productive time and drilling costs. Geomechanics modeling of a complex physical system requires a solid understanding of fundamental physics and domain expertise. However, current uncertainty methods often lack a mathematically rigorous framework that can integrate both physics and domain expertise into the modeling process. To address the challenges mentioned above, a Bayesian machine learning framework has been adopted as the foundation of our physics-based uncertainty workflow, which allows to incorporate prior information from domain knowledge and fundamental physics, to integrate collected lab and field measurement data into the modeling process, and to improve the model using an iterative workflow. The resulting workflow can account for the complex interrelationships and interactions between different components in the geomechanics system; specifically, the capability to model and calibrate the uncertainties for several essential components underlying the one-dimensional wellbore stability model. These components include geomechanical core tests and stress measurements (such as Leak-off Test (LOT), Extended Leak-off Test (XLOT), Diagnostic Fracture Injection Tests (DFIT), etc.), as well as drilling performance (such as mud weight used, appearance of breakout and drilling induced tensile fractures, etc.). This workflow provides a systematic and consistent framework for evaluating uncertainty in building a 1D Mechanical Earth Model (1DMEM) which is a crucial step in ensuring a safe and efficient drilling process. We will demonstrate this uncertainty quantification workflow and its application for estimating the safe drilling windows with a case study.