三维圆弧型井眼轨道模型的完全解

All Solutions of 3D ArcTyped WellPath Planning Model

摘要:

限定了目标点井眼方向的三维圆弧型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.提出了一个消元化简方法，能够将其化简成一个一元至多22次代数方程和两个一元至多二次代数方程.通过求一元代数方程的全部非负实数解的数值算法，能够判断设计模型是否有解、有解时求出全部真实解.

关键词:井眼轨道; 数学模型; 圆弧; 消元法; 钻井设计

Abstract:

The drilling planning model of wellpath with desired direction is a nonelinear equations.The numeral iteration is requested to get the solutions.The paper presents an elimination method,which can simplify the nonelinear equations to an algebra equation,and can tell whether the equation has solutions and get all the solutions by using the numerical algorithms.

Key words:wellpath; mathematical model; arc; elimination; drilling planning