Dynamic model for 3D motions of a horizontal oilwell BHA with wellbore stick-slip whirl interaction

Failure of horizontal oilwell drilling equipment, in particular the bottom-hole-assembly, is very costly. Vibration causes tool joint failure, twist-off, and bit-damage, and has motivated extensive research on understanding and predicting the dynamic shock-loading response of the bottom-hole-assembly. This paper presents a model to analyze the dynamics of a horizontal oilwell bottom-hole-assembly. A nonlinear three-dimensional multibody shaft model has been verified and extended to include stick-slip whirl phenomena due to the contact between the rotating bottom-hole-assembly and wellbore. The model has been verified with a dynamic finite element analysis through comparisons of the response of an enclosed shaft under axially compressive load rotating inside the wellbore. Finally, a complete deviated drillstring has been simulated by combining the bottom-hole assembly model with a model of the drill pipe and collars. The pipe and collars are modeled using a lumped-segment approach that predicts axial and torsional motions. The model can predict how axial and torsional bit-rock reactions are propagated to the surface, and the role that lateral vibrations near the bit play in exciting those vibrations and stressing components in the bottom-hole-assembly. The proposed model includes the mutual dependence of these vibrations, which arises due to bit-rock interaction and friction dynamics between the drillstring and wellbore wall. A force excitation source, which simulates an axially-vibrating downhole tool, has been implemented in the horizontal section of the virtual drillstring. Simulations show a better weight transfer to the bit due to the tool, with a low frequency and high amplitude force excitation giving best performance but potentially increasing the severity of lateral shock. The model, implemented using the bond graph formalism, is a useful tool for design and sensitivity analysis due to its physically meaningful parameters and low simulation times on a personal computer.