Study on Vibration of Directional Drill String with Affecting the Important Parameters with Energy Considering

A vibrant model for drill string in inclined well drilling is presented. Also, the effects of weight on bit, drilling mud flow rate and vibration of the drill string are analyzed analytically. The vibrations of drill string may bind optimizing the power and advantages of drill string that is an important problem for optimization and design of it. Dynamic equation of the model is introduced with consider of the axial displacement and lateral bending geometric nonlinear coupling. The effect of drilling mud flow is modeled using Paidoussis formulations considering energy formulation. Equation of the motion for the rotating drill string is derived utilizing Lagrangian technique and implementing FEM to analyze and solve these equations. The obtained outcomes show the nonlinear effects are important on the obtained results and findings. The effects of the drilling mud flow rate and weight on bit on the natural frequencies and time responses are evaluated. Improvement and development of the drilling mud flow rate results in decreasing of natural frequencies and vibrational amplitude, while increasing the weight on bit, leads to reduce of the natural frequencies and enhance the vibration amplitude clearly.

Keywords: Energy formulation; Vibration; Instability; Drill string and mud

Highlights:

• Study on vibration of directional drill string

• Energy considering for analyzing the nonlinear vibration

• Modeling using Paidoussis formulations