给定井眼方向的修正轨道设计模型的解析解

Analysis Solutions for Correcting Trajectory Design Model of Given Trajectory Direction

限定井眼方向的修正井眼轨道设计模型是一个非线性代数方程组,通常需要使用数值迭代方法进行求解。利用这个方法能够将这个非线性代数方程组最终化简成一个一元至多24次代数方程和两个一元2次代数方程。通过求一元代数方程的全部正实数解的数值算法,能够得到井眼轨道设计模型的全部真实解。求解过程中可以正确判断模型有解或无解。数值求解过程没有初值依赖性,具有很好的数值稳定性。

The drilling planning model of modified well--path with desired direction is a non--linear equation group. It requires the numeral iteration to get the solutions. Current existing methods can＇t well deal with the problems of iterative convergence, initial dependence, the existence of the solution and multi--solutions. A new method is given in this paper. It simplifies the non--linear equations to an algebra equation of at most power 24 and two quadratic equations of one variable. By using the numerical algorithms to solve the algebra equations of one variable, it can get all the real solutions. It can tell whether the model has solutions or not. Numerical algorithms process doesn＇t depend on initial. It has good numerical stability.