In this research, optimum arrangements of drill string’s stabilizers are investigated. The optimum arrangement leads to biggest WOB without buckling. So the penetration rate of the drill bit can be increases. To this goal, the potential energy of drill string for axial and lateral vibration is written in an integral equation. In this equation, the effect of geometrical shortening, which causes nonlinear coupling between axial and lateral vibration, is considered. The work done by WOB force and weight of drill string is calculated. The mode summation method is employed to convert the integral potential energy of the continuous system to a discrete one. The effects of stabilizers are modeled by linear springs with large stiffness constant. Dropping and considering third and fourth order tensor of potential energy lead to linear and nonlinear stability analysis, respectively. Taking first and second order derivatives of discrete potential energy, the stability of drill string can be analyzed. Repeating this procedure for different numbers and positions of stabilizers, the optimum arrangement of stabilizers can be found. This method is employed to find the best arrangement of one and two stabilizers, by linear and nonlinear method.

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