Analysis of critical whirling velocity of drill string

Abstract

ABSTRACT During the drilling process, the whirling motion often occurs, which will cause the drill string to vibrate violently, accelerate the fatigue damage of the drill string, and eventually cause the bottom hole assembly to fail. But the existing research rarely focuses on the critical whirling velocity of drill string. To solve this problem, the whirl differential equation of drill string was set up based on the D’Alembert principle, and the critical whirling speed equation of drill string was deduced according to separation variable method. Reference to actual downhole conditions, the influence of drill stem wall thickness, tension, drilling depth, drilling fluid flow rate, and other factors on the critical whirling speed of drill string are considered. Research results indicate that when n ≤ 8324, drill string has a critical whirling speed, and when n > 8324, there is no critical whirling speed. And under different orders, as drill string wall thickness and drilling depth increase, the critical whirling velocity decreases. In general, the drill string rotation rate is 0–150 rad/min. When the drilling depth is 0–500 m, the critical speed is not considered. However, as drilling depth exceeds 500 m, the critical whirling velocity is within the general range of drill string speed. Therefore, drill string velocity should be chosen reasonably to avoid resonance. When the tension increases, critical whirling velocity increases. As the drilling fluid flow rate increases, the critical whirling velocity of drill string decreases. But when drilling fluid velocity is close to 120 L·s−1, increasing the drilling fluid velocity hardly affects the critical whirling velocity of drill string. In a word, research results of this paper have certain guiding significance to drilling engineering.