Combined effect of anisotropy and uncertainty on the safe mud pressure window of horizontal wellbore drilled in anisotropic saturated rock

The investigation of safe mud pressure window of horizontal wellbore drilled in the saturated rock by accounting for the combined effect of anisotropy and uncertainty is the main purpose of this work. To this aim, the deterministic solution of collapse and fracture initiation pressures are firstly presented in three cases that describe the behavior of wellbore: (1) immediately after drilling (i.e., undrained problem); (2) at long term due to the steady-state fluid flow (permeable boundary case) and (3) by neglecting the variation of initial pore pressure (i.e., impermeable boundary condition case). Based on these deterministic solutions, the key parameters of different sources of anisotropy (initial stress state, poro-elastic and strength properties of rock mass) are highlighted through sensitivity analysis. Then, the famous Monte Carlo Simulation (MCS) is undertaken to quantify the uncertainty effect on the probability of success of safe mud pressure window of the wellbore. We also present an adaptation of the Kriging metamodeling technique to study the stability of wellbore. In comparison with the referent solution of MCS, the Kriging metamodel provides a high accuracy and can be used as a performant tool for the probabilistic assessment of wellbore. The consideration of anisotropy combined with uncertainty, and the hydraulically boundary condition around wellbore in this work allows us to complete the contributions in the literature and confirm their strong effect on the design of wellbore.