Poroelastodynamic solution for an incline borehole subjected to non-hydrostatic stress field

When the dynamic load is applied on the borehole, such as sudden excavation or impact load, the inertia effect cannot be neglected, and dynamic theory should be introduced. Traditional theories of wellbore stability neglect the inertial effects of solid-fluid system and they are not suitable for studying wellbore stability under dynamic loads. This paper deals with the wellbore stability of an inclined borehole induced by the drilling and the pressurization. In order to analyze the transient response and discover the main factors which influence the wellbore stability, the Biot’s poroelastic theory is extended to characterize the dynamic behavior of the wellbore subjected to non-hydrostatic stress field. By considering the superposition principle, mode decomposition and Laplace transform, the analytical solutions of stress and pore pressure are obtained. The results suggest that it is of great importance to incorporate the inertia effects of solid-fluid system, which results in the wave-diffusion behavior in the early times. The poroelastodynamic solutions can be served to analyze the transient response of an inclined wellbore when passing though different type of faults, which can help to understand the complex accidents during the drilling process.