Sensitivity Analysis of the Anisotropy Degree of Elastic Parameters on Breakdown Pressure in Transversely Isotropic Shale

Shale formations commonly develop bedding structures and micro-fractures and exhibit strong elastic anisotropy; however, existing wellbore breakdown pressure models are mostly based on isotropic assumptions. We hypothesize that the elastic modulus anisotropy ratio vE = Eh/Ev dominates wellbore breakdown pressure, while the Poisson’s ratio anisotropy ratio vν = νh/νv plays a secondary but non-negligible role through lateral-deformation coupling. To test this hypothesis, a three-dimensional wellbore stress model for transversely isotropic (VTI) shale is developed using VTI constitutive equations and the Lekhnitskii complex-variable framework. The model is combined with Biot poroelastic theory and the minimum principal stress tensile-failure criterion, and the breakdown pressure is solved by a numerical iterative method. The effects of vE and vν are then systematically analyzed. The results show that vE is the controlling factor: as vE increases from 0.1 to 3, the breakdown pressure evolves non-monotonically, first increasing and then decreasing, with a peak at vE = Eh/Ev = 0.3. Changing vE to 0.5 or 2 significantly shifts the magnitude and extreme-value region of the breakdown pressure. In contrast, under vE = 1, varying vν from 0.1 to 3 produces a slightly nonlinear monotonic decrease in breakdown pressure, with an absolute reduction of less than 10%, indicating that vν mainly redistributes tangential and axial stresses by modifying lateral deformation compatibility. Coupled vE–vν effects are synergistic or antagonistic: they increase the local gradient and asymmetry of the breakdown-pressure response surface and can cause nonlinear responses or trend reversals under extreme anisotropy. Elastic anisotropy also distorts the breakdown pressure versus deviation angle, creating local minima or abrupt changes and narrowing the safe drilling fluid density window. The research findings provide a theoretical basis for wellbore fracture pressure prediction, which can assist in determining the upper limit of the safe drilling fluid density window and provide some reference for wellbore trajectory optimization in shale formations.