径向井转向器滑道导入段阻力模型及其多项式解

Modeling and polynomial resolutions of resistance on introduction slide in whipstock of ultra-short radius radial system

径向井滑道导入段是径向井转向器滑道的组成部分。当钻杆初始通过转向器时,导入段诱导钻杆发生弯曲。当钻头离开导入段后,导入段与钻杆不再接触。导入段轨迹设计要求导入段对钻杆的阻力小,阻力波动小。通过分析钻杆在导入段的受力,建立了钻杆导入段阻力与导入段轨迹之间的微分方程,采用多项式函数逼近该一阶非线性微分方程真解的方法,研究了直线型、抛物型及三次多项式导入轨迹的阻力特性。研究结果表明,导入段轨迹设计应以抛物型或三次型曲线为主;运用局部坐标法设计的三次型导入轨迹,可以达到实际操作对导入轨迹阻力波动的要求。

The introduction slide is part of the slide in whipstock of uhra-short radius radial system （URRS）. As drill pipe passes through the slide initially, the introduction slide leads the drill pipe to be bent. After the drill pipe passing through the slide, they will not touch each other again. The locus design of the introduction slide aims to decrease the drill pipe resistance to introduction slide, and to decrease the fluctuation of the resistance. A differential equation between resistance factor and the locus of introduction slide was built by analyzing loads on drill pipe during being guided, Polynomial functions were used to approach the solution of the nonlinear differential equation. The results show that parabolic or cubic curves shall be the main in the locus design of introduction slide based on the analysis of their resistance factors of linear, parabolic and cubic curves, and cubic curves with local coordinator system can fit the demand of resistance fluctuation for field drilling.