The Effect of Drilling Mud Flow on the Lateral and Axial Vibrations of Drill String

Abstract

In this research, the effects of drilling mud flow and WOB force on the lateral vibration of drill string are investigated. To this goal, the kinetic and potential energy of drill string for axial and lateral vibrations are written in an integral equation. In potential energy equation, the effect of geometrical shortening, which causes nonlinear coupling between axial and lateral vibration, is considered. Drilling mud forces are modeled by Paidoussis formulations. The works done by WOB force, weight of drill string and drilling mud forces are calculated. The mode summation method is employed to convert the continuous system to a discrete one. Dropping and considering third and fourth order tensor of potential energy lead to linear and nonlinear system, respectively. The effects of stabilizers are modeled by a linear stiff spring. The wall contact is modeled by Hertzian contact force. Lagrange equation is employed for finding the equations of motions. First and second natural frequencies of drill string are found for different WOB and drilling mud flow. Also the effects of drilling mud and nonlinear terms on lateral vibration of drill string are investigated. The effect of drilling mud on the post buckling vibration of drill string is also delivered. This formulation can be used for optimization of drilling mud flow, WOB and the number and positions of stabilizer so that the lateral vibration of drill string is minimized.

Effects of Drilling Fluid Rheology on Nonlinear ALTC Vibration Response Characteristic of Rotary Drill String

“…Drilling fluid has a great influence on the vibration behaviors of drill string [2], [3], which attracts the attention of scholars. Kazemi et al [4], Jafari et al [5] and Taheran et al [6] used Paidoussis formulations to model drilling mud forces and investigated the effects of drilling mud flow on the lateral vibration of drill string, and found that the increase of drilling mud flow resulted in the decrease of natural frequency and amplitude of vibration. Ma et al [7] considered the effects of drilling fluid on drill string as viscous damping, established a longitudinal vibration model of drill string, and found that the increase of drilling fluid damping would lead to a linear decrease in vibration amplitude.…”