钻柱共振是引起深井钻具失效的主要原因之一,钻柱工作在井下一个高温的环境下,温度的升高必然使钻柱的固有频率发生变化。分析了井下温度对钻柱轴向振动固有频率的影响,推导出了井下任意温度时钻柱轴向振动固有频率的计算公式。通过实际算例,分析了井下温度对钻柱轴向振动固有频率的影响。计算结果表明:钻柱轴向振动固有频率随着温度的升高而降低,其降低的幅度随着钻杆长度的增大而增大;当井下温度不超过200℃时,钻柱轴向固有频率的变化幅度不会超过常温下计算值的6.7%。任意温度时钻柱轴向振动固有频率与温度成近似线性关系,可以根据常温下的计算值和温度值通过一个简单的一次函数来计算。
Drilling string resonance is the main reason of the drilling tools' failure. The drilling string is at the high temperature condition, the natural frequency of drill string must be changed when the downhole temperature rises. Effects of the downhole temperature on axial vibration natural frequency of drill string in deep wells is investigated. The calculation formulas of axial vibration natural frequencies of drill string is derived. The effect of the downhole temperature of deep wells on natural frequencies are illustrated by numerical exampies. It is shown that the frequency decrease gradually with the rise of the downhole temperature, the larger the length of drill string, the larger of temperature influence on the frequency. When the downhole temperature is below 200 ℃, the decrease of the natural frequency is less than 6.7%. The natural frequency of drill string vary linearly approximately with the downhole temperature, the natural frequency can be calculated by a simple linear function through downhole temperature and normal natural frequency value.