Directional drilling technology provides more flexibility in the selection of rig locations than conventional vertical drilling. It significantly increases drilling efficiency by avoiding undesirable rock formations. In addition, it maximizes production efficiency by increasing the exposed area of a reservoir and grouping multiple reservoirs. In drilling operations, the analysis of drillstring dynamics is critical to circumvent undesirable vibrations and to improve performance. Linear modeling methods are insufficient to describe the system dynamics because directional drilling, unlike vertical drilling, causes the drillstring and the bottomhole assemble (BHA) to bend with a large curvature. In this paper, a model, based on the finite element method (FEM), is established to characterize the dynamics of a directional drill-string. High computational efficiency is achieved by separating the overall displacement into an initial displacement representing the nonlinear bending and a small deformation linear dynamic model. The proposed model is verified against two case studies from the literature, and the comparisons show accurate results. To demonstrate the utility of the proposed model, a BHA force model is included, which considers bit-rock collision, hydraulic damping of the mud, and the eccentricity of the BHA. The simulation results show the capabilities of the model in describing typical drilling vibrations.

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