Quantitative risk analysis and parameter sensitivity evaluation of wellbore instability in poroelastic media considering uncertainty of geomechanical parameters

The randomness and fuzziness of geomechanical parameters make it difficult to directly determine the wellbore collapse and fracture pressures, and thus show significant influence on the risk assessment of drilling operations. Therefore, to effectively analyze the risk of wellbore instability in deep formation, this paper develops the evaluation models of wellbore stability for the vertical well drilled through the poroelastic rock formation subjected to borehole stresses under different time domains, including the instantaneous, modified instantaneous, short-time, long-time, and elastic ones. Meanwhile, based on the Monte Carlo method, one compares the difference between Taylor expansion and the Rosenbluth method in quantifying the uncertainty of the evaluation models. One analyzes the risk of wellbore instability under the condition that the geomechanical parameters satisfy the uniform, triangular, and normal distribution characteristics. In addition, different from the single factor sensitivity evaluation in previous uncertainty analysis, one introduces Morris and Sobol methods to conduct the comprehensive analysis of local and global sensitivity of geomechanical parameters. The main results show that the collapse pressure determined by the different cases of borehole stresses presents in descending order of short-time, long-time, and instantaneous. However, the fracture pressure shows in ascending order of long-time, instantaneous, and short-time cases. Besides, the different distribution characteristics of geomechanical parameters lead to the relationship of safe mud weight window in descending order of normal distribution, triangular, uniform distributions, and the uncertainty characteristics caused by the normal distribution of geomechanical parameters can be effectively quantified by Taylor expansion and Rosenbluth method. The strong sensitivity parameters affecting wellbore collapse and fracture are the maximum and the minimum horizontal in situ stresses, respectively. These two parameters present a strong difference in global sensitivity and local sensitivity analysis, which is manifested by the comprehensive effect of global parameters. The influence of the maximum horizontal in -situ stress on borehole collapse is weakened to a certain extent, while wellbore tensile fracturing is strengthened. On the contrary, the minimum horizontal in -situ stress is characterized by enhancing the borehole collapse whereas weakening the tensile fracturing. Besides, the influence degree increases with the increasing of parameter uncertainty.