井眼轨迹位移插值计算的解析法

井眼轨迹的位移插值计算在定向井轨迹监控、中靶分析、水平井靶心距计算和井眼轨迹三维图形实时显示等许多问题中都有很重要的应用。位移插值计算是要根据井段两个端点的井眼轨迹参数从实钻井眼轨迹上给定点的视平移计算出该点的其他井眼轨迹参数；前人在井段曲线为圆柱螺线的假设下提出了逐次位移法实现位移插值计算，但需要反复多次迭代才能求出近似数值解。从空间解析几何学有关公式出发，推导出了圆柱螺线备件下的位移插值解析计算公式并通过算例验证了其正确性。与逐次位移法相比，解析计算公式可以极大地提高井眼轨迹位移插值计算的速度和精度，能够应用于井眼轨迹实时监控、三维图形显示、中靶分析、水平靶心距计算等问题中。

An Analytical Method for Interpolation Calculation of Well Trajectory Displacement

The Interpolation calculation of the well trajectory displacement is very important in directional well trajectory monitoring,target-hitting analysis,calculation of horizontal well's target distance,and real-time 3D display of the trajectory.Displacement interpolation calculation is to calculate other wellbore parameters of a point based on the parameters of the two ends of an interval using apparent translation of that given point on wellbore trajectory.Previous researchers proposed a method of successive displacement for displacement interpolation calculation by assuming that the curve of the internal is cylindrical helix,while this method needs multiple iterations to obtain an approximate numerical solution.Starting with related equations of analytical geometry,an analytical equation to calculate the displacement interpolation for cylindrical helix curve of the internal was derived and verified by the calculation examples.Compared with the successive displacement method,the analytical method can improve the calculation speed and the precision greatly and can be applied in the wellbore trajectory real-time monitoring,3D display,target-hitting analysis and the calculation of horizontal well's target distance.