Petroleum is one of the most important sources of energy in the world. The increasing demand for this energy source would be met by exploring and drilling new reservoirs. Problems associated with drilling could reduce the production and impose extra costs to the projects. An issue that is critical to drilling process is wellbore stability. This becomes more important once the trajectory of the wells is not vertical and deviations are needed in well route to access the reservoir or increase the production. Parameters that dominate the instability of the wellbores are rarely controllable. The well-trajectory plan and the mud weight are two important constituents that can be controlled and are useful in minimizing the wellbore instability. In order to determine the well trajectory and mud weight it is required to recognize the state of stress in the ground and determine the parameters of the study area. In this research, the required parameters to construct the earth’s geomechanical model were obtained and then using experimental equations a safe mud window was determined. For this purpose, three failure criteria including: Mohr-Coulomb, Mogi-Coulomb, and Hoek-Brown criteria have been employed. The results showed that the Mogi-Coulomb failure criterion was the most reliable and realistic one amongst these three criteria. However, the uncertainties associated with data could have negative effects on determination of parameters and ultimately could cause errors in designing of the mud weight. Calculating and quantifying uncertainties and considering them in calculations could greatly reduce errors. For this purpose, Monte Carlo simulation is used to in this research and the safe mud window was determined by using distribution functions and using existing equations. The resulting mud weight from above techniques were compared with mud weights resulted from numerical method of finite element and also the point estimation method. For this purpose, the simulation was done for each zone of a well assuming lithological and mechanical homogeneity inside every zone. The results of these simulation presented the amounts of displacements and also distribution of the plastic zone around the wellbore. The results delivered the optimum mud weight by which minimum displacement in wellbore and the smallest plastic zone could take place. By using combination of the aforementioned methods, the optimal mud weight window could be determined more accurately.
