Uncertainties associated with wellbore stability analyses lead to wellbore issues despite the accurate measures taken prior to operations. Uncertainties of the input parameters result in inaccuracy in estimation of circulation loss gradient, collapse gradient and downhole pressure estimations. In the present work a novel approach towards uncertainty assessment of wellbore stability analyses is presented. Analytical models used for borehole stability studies combined with input uncertainties are taken into account to provide a model for uncertainties of borehole stability in terms of input variances. Results highlight the importance of accuracy in mud density measurements and pore pressure estimation as well as wellbore diameter and horizontal stress.
Stability of boreholes is one of the major aims of drilling fluid design prior to operations. Ideally, the drilling fluid forms a thin firm impermeable mud cake over the formation rapidly while maintaining downhole pressure within a safe range. One of the main purposes of stability analyses is to estimate the upper and lower pressure limits. There is a wide range of parameters which are required to perform accurate studies while most of these variables are associated with uncertainties to some extent and sometimes hard to measure or estimate. In addition borehole stability analytical models contribute to the output inaccuracies since they suffer from simplifying assumptions. Numerical models on the other hand consider the prevailing conditions in more detail and exhibit more flexibility. However the inevitable drawback of numerical errors exists.
Deterministic studies resulting in deterministic outputs lack reliability in terms of considering spatial variations and uncertainties embedded in the influential parameters. Application of uncertainty assessment methods was initiated in recent decades leading to more reliable informed decisions with respect to pressure limit estimations. Figure 1 shows the schematic of contribution of different factors in the ultimate uncertainty of a borehole stability analysis. Morita  published the first study on the effects of uncertainties in input parameters on wellbore stability analyses. He also investigated the shortcomings of model and discussed his approach to modify them and reduce the uncertainties. He considered circulation loss and collapse prediction in his analysis and applied a derivative based uncertainty assessment method. He also carried out a sensitivity analysis of critical pressure limits on input parameters uncertainties and came up with some recommendations to decrease the uncertainties of borehole stability analyses. Dumans  completed his dissertation on quantification of effects of uncertainties on the reliability of wellbore stability model predictions. He applied Monte – Carlo simulation and Fuzzy sets methodology to estimate the uncertainty of the outputs which were critical pressures for collapse and tensile failure. Later, Ottesen  presented his model for assessment of uncertainties in collapse pressure prediction which was mostly based on operationally tolerable limits. Liang  presented a complete scheme of risk analysis in wellbore stability studies. He presented the formulation of estimation of uncertainties and associated risks. He considered tensile failure as the upper limit and pore pressure as the lower limit of downhole pressure.