Uncertainty Analysis of Wellbore Instability: Impact of Parameters Interdependence on Drilling Decisions

Uncertainty in input parameters and inconsistencies in wellbore stability analysis methods can lead to costly consequences. While the impact of uncertain parameters on wellbore stability has been widely discussed, the interdependence of these parameters and their influence on decision-making is rarely explored. This paper provides a consistent uncertainty analysis of wellbore stability considering uncertainty in input parameters and shows how the correlation of input parameters affects drilling decisions. A quantitative uncertainty analysis, decision analytics, and Monte Carlo simulations were used. The impact of uncertainty in input parameters and their interdependence on predicting the safe mud window was evaluated. The traditional approach of Montecarlo simulation and single factor sensitivity analysis, which assumes independent parameters, was compared to the proposed approach considering correlated parameters. The effect of parameter correlations was assessed using a matrix of correlation coefficients. A reliable limit of a safe mud window was determined, and the consequences of the best- and worst-case scenarios were estimated within their likelihood of occurrence. The findings reveal that the impact of parameter correlations on the reliability of wellbore stability should not be overlooked, primarily when decisions are based on percentiles, such as P10 and P90, rather than the central value. Accounting for correlations enhances the prediction of fracture and wellbore collapse pressures and, consequently, the drilling decisions. The correlation of input parameters in collapse pressure prediction indicates that the upper and lower bounds range widens when no correlation is considered compared to when strong correlations are applied. This impact on fracture pressure is more significant than the collapse pressure. Additionally, singlefactor sensitivity analysis ranks parameters differently than sensitivity analysis with parameter interdependence. In wellbore collapse pressure, T remains in the leading position regardless of correlation changes, while the other parameters exhibit varying sequences as the correlation coefficient changes. In fracture pressure, ch remains in the leading position within independent parameters and a small correlation coefficient of 0.2. In contrast, the pore pressure exhibits the most significant impact on fracture pressure as the correlation coefficient increases to 0.6 and 0.8. Compared to the other correlated parameters, the correlation between cohesive strength and maximum horizontal stress has the greatest effect on collapse pressure. In contrast, the correlation between minimum horizontal stress and pore pressure more significantly influences fracture pressure than other correlated parameters. The proposed decision-based analysis of wellbore instability supports decision-making during the planning stage and improves decision quality.