钻柱力学三原理及定性模拟实验

Three principles of drill string mechanics and qualitative simulation experiments

在一般力学中,系统都要遵循平衡原理、最小势能原理和最小耗散功率原理。钻柱力学也遵循这三原理。钻柱的任何一点、任何时刻,都必须满足力学平衡方程;若出现多解,先用最小势能原理判断;若还存在多解,则用最小耗散功率原理判断。用钻柱失稳问题说明了最小耗散功率原理不包含最小势能原理;不可用最小耗散功率原理取代最小势能原理。实验发现:1杆柱的转速越高,其挠度越小,越靠井筒中心。2存在涡动状态转换临界转速。当转速低于此临界转速时,随着转速的增加,耗散功率增加;当转速高于此临界转速时,随着转速的增加,耗散功率先迅速降低并且杆柱的挠度突然减小,然后随着转速的增加,耗散功率又增加。3液体的黏度越大,涡动状态转换临界转速越小;轴向载荷越大,涡动状态转换临界转速越小。钻柱力学三原理为复杂的钻柱动力学问题的多解性判别提供了新的判据。

In general mechanics,the system must follow the principles of equilibrium,minimum potential energy and minimum power dissipation rate;these three principles are also followed by the drill string mechanics.Any point of drill string at any time must meet the mechanical equilibrium equation.In case of multiple solutions,initial judgment is made using the principle of minimum potential energy.If multiple solutions still exist,secondary judgment is conducted using the principle of minimum power dissipation rate.The problem of drill string instability illustrates the principle of minimum power dissipation rate excludes the principle of minimum potential energy,and the former principle is unable to be adopted to replace the latter one.It has been found from the experiments that：（1）the higher the rotating speed of the rod string is,the smaller its deflection will be,and the closer to the wellbore center it will be;（2）the transition critical speed under whirling state exists.When the rotating speed is less than this critical speed,the power dissipation rate increases with the rotating speed;when the rotating speed is higher than this critical speed,the power dissipation rate first decreases rapidly and the deflection of rod string abruptly decreases,and then power dissipation rate increases;（3）the greater the viscosity of the liquid is,the smaller the transition critical speed under whirling state will be;the greater the axial load is,the smaller the transition critical speed in whirl state will be.Three principles of drill string mechanics provide a new criterion for judging the multiple solutions of complex drill string dynamics problems.