自然曲线井眼轨道设计模型及反演求解方法

Natural Curve Wellbore Trajectory Model and Its Inversion Solution Method

针对自然曲线模型复杂度较高,无解析解,需要求解复杂的隐式方程,容易遇到迭代发散的问题,重点探讨两种约束条件下的自然曲线反演求解算法,设计了稳定的迭代求解流程,并根据坐标增量求解新的井斜角,通过迭代计算快速确定最终结果。为确保计算过程的稳定性和计算结果的可靠性,计算过程中针对模型求解过程中可能出现的除以零的特殊情况,在特殊临域内采用极限值代替数值计算。将该算法的计算结果与国外知名的商业软件计算结果进行对比,评价计算的精度。结果表明:对于定点问题,该算法在相同条件下,计算结果与约束条件误差为2.0×10^(-5),商业软件的误差为1.13×10^(-3);对于垂深对齐问题,该算法和商业软件在1.0×10^(-5)精度范围内无误差,精度一致。

The natural curve model has high complexity and no analytical solution.It is easy to encounter iterative divergence when solving complex implicit equations.Therefore,this paper focuses on the inversion algorithms of natural curve under two constraints.Stable iterative solution processes are designed,the new well deviation angle issolved according to the coordinate increment,and the final result is quickly determined through iterative calculation.In order to ensure the stability of the calculation process and the reliability of the calculation results,for the special case of dividing by zero that may occur in the process of solving the model,the numerical calculation is replaced by using the limit value in the special domain.The calculation accuracy of the algorithm is evaluated by comparing the calculation results of the algorithm with those of foreign well-known commercial software.The results show that for the fixed-point problem,under the same conditions,the error between the calculation result of this algorithm and the constraint is 2.0×10^(-5),while the error with the commercial software is 1.13×10^(-3);For the vertical depth alignment problem,there is no error between the calculation results of the algorithm and the commercial software within the accuracy range of 1.0×10^(-5),and the accuracy is consistent.