In the air drilling process, the pre-bent pendulum bottom hole assembly (PBP-BHA) has excellent performance in controlling the well deviation and improving the wellbore quality, but the mechanism that is closely related to the dynamics of the PBP-BHA has not been ascertained. In this paper, an effective technique combining the weighted residuals method with the finite element method is presented to study the PBP-BHA lateral vibration. First, a three-dimensional nonlinear static model of pre-bent BHA is established under small deformation condition and solved by the weighted residuals method and optimization method, so as to define the tangent point according to the deformation characteristics of the PBP-BHA. This tangent point determines the end of the effective PBP-BHA length that starts from the drill bit. Subsequently, the finite element model of PBP-BHA is established to solve the lateral natural frequencies and mode shapes of the PBP-BHA. After considering the borehole wall constraint, the modal superposition technique is used to obtain the steady dynamic responses of the PBP-BHA. Meanwhile, the dynamic performance of the PBP-BHA used in the actual air drilling process is calculated to obtain its critical speeds and working status chart. The critical speeds of the PBP-BHA are 80 r/min and 190 r/min, which are far away from the surface rotary speed in the actual drilling site. Through comparing with the dynamic characteristics of regular BHA with the same structural parameters, it is discovered that the bend angle in the PBP-BHA plays a crucial role in improving the dynamic performance of the PBP-BHA. Moreover, the technique presented in this study can be used to make a reasonable design of BHA configuration and optimize drilling parameters.
