Influence of drilling fluid on natural frequency of drill string lateral vibration

In order to study the vibration modal and dynamic properties of drill string system, the influence of drilling fluid in and out of the drill string on natural frequency of drill string lateral vibration was studied based on the dynamic theory. By introducing the additional mass factor and linear hypothesis, the relation among the additional mass factor, drilling fluid displacement and the ratio between outer diameter of drill string and well diameter was obtained through Laplace transform. The results show that the natural frequency of drill string lateral vibration drops compared with inexistence of drilling fluid. The mechanism of drilling fluid in and out of the drill string for the natural frequency of drill string lateral vibration is different. The influence of drilling fluid in the annulus on natural frequency of drill string lateral vibration is larger than ordinary estimation results.