Various geomechanical-modeling approaches, which cover a wide range of techniques and complexity, have been developed to assess the stability of a borehole and/or the integrity of well casing. The ability to confidently use these models can be limited, however, because they generally do not allow the model user to consider the "real-world" variability of the input parameters defined in the models. Often, these geomechanical models do not adequately accommodate the innate variability of the rock properties (mechanical and petrophysical) of the target reservoirs. Consequently, this deterministic approach too often results in uncertainty about the "correct" value of a critical parameter to use and insecurity in the model results. Decisions based on these results can later, not surprisingly, be found to be incorrect. Model users attempting to overcome the limitations noted above have tried various techniques. Subjective estimation, arbitrary "minimums", grading techniques, and stepwise estimation have all been commonly used.
Recently, more powerful techniques such as Monte Carlo simulation and decision analysis have come into popular use. Over the past decade these two techniques have been extensively used in the petroleum industry to evaluate and solve a wide range of analytical problems in reservoir engineering and the geosciences. In this paper, the application of these techniques to a number of generalized geomechanical problems will be illustrated. A Monte Carlo simulation enables the user to identify, measure or estimate, and evaluate uncertainties in the problems being analyzed. The simulation models the random behavior of the input variables much like in a game of chance. That is, the variables have an uncertain value within a known range for any particular time or event. Numerical model and software packages are developed based on the Green's function for a nucleus of strain in the reservoir. The model is coupled with reservoir simulations to evaluate pressure maintenance and reservoir development schedule effect on casing integrity, fault stability via sensitivity studies. The geomechanics solutions would be coupled with both commercial or in-house developed reservoir simulators. The results of multiple simulations, done to determine the most likely outcome of various wellbore solution options, are reported in the current paper.