Journal of Petroleum Engineering

Volume 2016, Article ID 3472158, 13 pages

http://dx.doi.org/10.1155/2016/3472158

## Probabilistic Approach in Wellbore Stability Analysis during Drilling

Department of Petroleum and Chemical Engineering, Sultan Qaboos University, Muscat, Oman

Received 20 April 2016; Accepted 21 July 2016

Academic Editor: Alireza Bahadori

Copyright © 2016 Mahmood R. Al-Khayari et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In oil industry, wellbore instability is the most costly problem that a well drilling operation may encounter. One reason for wellbore failure can be related to ignoring rock mechanics effects. A solution to overcome this problem is to adopt* in situ* stresses in conjunction with a failure criterion to end up with a deterministic model that calculates collapse pressure. However, the uncertainty in input parameters can make this model misleading and useless. In this paper, a new probabilistic wellbore stability model is presented to predict the critical drilling fluid pressure before the onset of a wellbore collapse. The model runs Monte Carlo simulation to capture the effects of uncertainty in* in situ* stresses, drilling trajectories, and rock properties. The developed model was applied to different* in situ* stress regimes: normal faulting, strike slip, and reverse faulting. Sensitivity analysis was applied to all carried out simulations and found that well trajectories have the biggest impact factor in wellbore instability followed by rock properties. The developed model improves risk management of wellbore stability. It helps petroleum engineers and field planners to make right decisions during drilling and fields’ development.

#### 1. Introduction

Drilling is one of the most important and costly operations in oil industry due to the fact that if the wellbore stability cannot be accomplished, drilling will lead to higher than necessary costs. So, maintaining a stable wellbore is one of the main challenges encountered during drilling, whether a well is being drilled with overbalanced or underbalanced techniques [1].

The possible mechanical wellbore failures (rock failures) can be grouped in two main types: tensile failure and shear failure. The tensile failure represents a hydraulic fracture within the formation which normally leads to a loss in system circulation during drilling, whereas the shear failure can be simply described as the collapse of the borehole wall which may result in stuck pipe and, in severe cases, a loss of the open hole section [2]. The upper limit of the mud weight is the maximum mud weight before the onset of tensile failure (fracturing). It can be obtained by conducting a leak off test. On the other hand, the minimum allowable mud pressure is the critical pressure before a wellbore collapse.

The most common well failure during drilling is borehole collapse. The method of analyzing this case involves the use of wellbore stability modeling consisting of a constitutive model coupled with a failure criterion. The constitutive model describes the deformation properties of the rock and the failure criterion determines the limits of the deformation [3].

This paper presents a model that accounts for uncertainties of rock properties and* in situ* stresses as well as wellbore trajectories in order to estimate the critical mud pressure during drilling. Unlike conventional stability models that deal with static values, this probabilistic model uses Monte Carlo simulation method in order to study the impact of uncertainties on wellbore instability [4]. It was developed by utilizing a linear elastic and isotropic constitutive model in conjunction with the Mogi-Coulomb rock failure law.

Al-Ajmi and Al-Harthy [4] have developed a probabilistic borehole model to study the influence of uncertainty of input variables in vertical borehole stability. This paper discusses a probabilistic model to predict the collapse pressure for nonvertical wellbores (horizontal and deviated wells) as well as vertical wellbores during drilling. That will be done by applying Monte Carlo simulation to the stability model developed by Al-Ajmi and Zimmerman [5, 6].

For nonvertical wellbores, there is no closed-form analytical solution to calculate collapse pressure in order to prevent borehole instability. To solve this problem, an excel program was developed to conduct stability analysis in vertical and nonvertical boreholes and perform risk analysis in wellbore instability.

##### 1.1. Stresses around Boreholes

A constitutive model is a set of equations needed to determine the stress state of a borehole and describe its behavior. Different models have been developed and widely studied; however, linear elastic analysis is the most common approach due to its ease of application [7] and its requirements of fewer input parameters compared with the rest of complicated models.

The stress components in cylindrical coordinates can be represented by where , , and are called radial, tangential, and axial stress components in a cylindrical coordinate system, respectively, while the virgin formation stresses in () coordinate system before excavation can be expressed as Equation (2) represents the virgin formation stresses which are denoted by the superscript “” on the stresses. The virgin* in situ* stresses will be altered by excavation. In cylindrical coordinates, the complete stress solution around an arbitrary oriented wellbore can be represented by the following:where “” is the radius of the wellbore, is the internal wellbore pressure, and is Poisson’s ratio. The angle is measured clockwise from -axis, as shown in Figure 1.