The Effect of Drilling Mud on Nonlinear Instability Threshold of Drill String

The main goal of this research is to analyze the effect of drilling mud and WOB on instability threshold of drill string. To this end, the kinetic and potential energy of an element of drill string for axial and lateral vibration is written in an integral form. The effect of geometrical shortening is considered in potential energy. The effect of drilling mud is modeled by the Paidoussis model. The works done by external forces are calculated. The finite element method is employed to discretize the system. The effects of stabilizers are modeled by dropping the nodes coincided with them. Flutter instability analysis is employed to analyze drill string’s instability threshold. By this procedure, the instability threshold of drill string is obtained for different WOB and drilling mud flow. Also, the effects of stabilizers numbers and arrangements are also illustrated. These results may be used for choosing the safe domain of drilling process.