旋转导向系统底部钻具组合力学计算新方法

A New Method for Mechanical Calculation of Bottom Hole Assembly in Rotary Steerable System

底部钻具组合(Bottom Hole Assembly,BHA)的力学计算是进行旋转导向系统钻具组合设计和井眼轨迹控制的基础.本文在纵横弯曲法、加权余量法和有限元法的基础上,提出了一种基于管柱单元组合的BHA力学求解方法.该方法以保持微分方程特解相同的条件作为管柱单元划分依据,对底部钻具组合进行单元划分;将管柱单元的挠曲线通解替代传统加权余量法的试函数,结合单元节点类型和组合关系,构建出包含边界条件和通解系数的线性方程组.对于边界条件未知问题,以支点反力符号条件为约束条件,以挠曲线越界程度、切点处弯矩平衡条件为目标函数,建立了以边界条件未知量为变量的多目标优化数学模型.应用多目标优化算法求解出边界变量,进而得出通解系数;最后,得出管柱单元内各点位移和载荷.以推靠式旋转导向系统BHA力学计算为案例,对比本文方法与加权余量法的计算结果,发现两者计算结果相差较小,表明本文方法可用于旋转导向系统底部钻具组合的力学计算.

The mechanics analysis of Bottom Hole Assembly(BHA)is the foundation for the BHA design of the rotary steerable system(RSS)and the wellbore trajectory control.In this paper,a BHA mechanics analysis method based on the string element combination is proposed on the basis of the beam-column method,the weighted residual method and the finite element method.In this method,the BHA is discretized with the string elements according to the criteria of keeping the same special solution for the differential equation.By replacing the trial function of the traditional weighted residual method with the general solution of the deflection curve of the elastic tube,the linear equations of the string element combination including the boundary conditions and the general solution coefficients are constructed based on the element node types and the combination relations.For unknown boundary conditions,a multi-objective optimization mathematical model with unknown boundary conditions was established with the sign of the fulcrum reaction force as the constraint condition,and the extent of beam deflection out of bounds and the bending moment balance condition at the tangent point as the objective function.The boundary variables are solved by the multi-objective optimization algorithm,and the general solution coefficients are obtained.Finally,the displacements and loads of each node in the string elements are obtained.Taking the BHA mechanics calculation of the Push-the-bit RSS as an example,the results of the proposed method are compared with those of the weighted residual method.It is found that the relative error between the two results is small,indicating that the proposed method is suitable for the mechanics calculation of BHA of RSS.