Stochastic Inversion of Wellbore Stability Models Calibrated with Hard and Soft Data

Abstract

ABSTRACT: Wellbore stability models are used in well-planning to determine the safe mud-weight window for drilling. More generally, calibration of wellbore stability models against observations (such as image logs, caliper measurements, and general drilling observations) is an essential step in constructing reliable 1D and 3D Mechanical Earth Models (MEMs) which are used to design safe drilling, completion, and production strategies. However, such calibration usually produces non-unique results, partly because most common types of calibration data impose only soft (inequality) constraints on wellbore stability models. Such non-uniqueness can be represented using probability density functions (PDFs). In this paper we show the results of stochastic inversion for stress parameters performed by drawing samples from these PDFs using a Markov Chain Monte Carlo procedure. Most types of calibration data (e.g., breakouts, drilling-induced fractures) produce a wide range of possible solutions for the stress parameters. However, the uncertainty reduces dramatically as data from an increasing number of depth locations is simultaneously inverted. The results also illustrate how including depths where breakouts and drilling-induced fractures are absent produces a powerful constraint on inferred stress parameters. 1. INTRODUCTION Mechanical Earth models (MEMs) encompass the parameters needed to predict deformation and failure of rocks such as rock mechanical properties and in situ stresses. They constitute an essential tool for predicting safe mud weight windows while drilling and are used to inform the well planning process. Traditional methods for calibrating MEMs are tedious, due to their subjective nature, as they rely entirely on the judgement and experience of the analyst. Calibration of MEMs also requires cumbersome and time-consuming fine-tuning of a large number of parameters and computational options. These problems can potentially be addressed through the implementation of automatic search schemes. To this end, we have developed a Bayesian inversion scheme to search for tectonic strain parameters, εxx, εyy, that control the magnitudes of the minimum (σh), and maximum (σH) horizontal stresses derived from a poroelastic stress model (Thiercelin and Plumb, 1991): (Equation)