Abstract: The shape and change of a wellbore trajectory vicinal to a given point were researched.A universal equation for the wellbore trajectory within a survey interval was obtained.This equation can be used to objectively describe and calculate drilled wellbore trajectories.The well curvature and torsion of a given point can determine the shape of wellbore trajectory in space within neighbor area,and the 3-D local coordinate area can be expressed as linear,conic and thrice functions of curved length away from the given point,respectively.The wellbore spline functions were constructed to determine the wellbore curvature and torsion on the basis of expounding theoretical foundation.The method for simulating inclination and azimuth functions and the formula for calculating wellbore trajectory parameters were given.The more accurate and stable results can be obtained in the calculation.The structure parameters of wellbore trajectory can objectively express the actual wellbore trajectories.

Key words: directional drilling, wellbore trajectory, inclinometry calculation, wellbore spline function, mathematical model

摘要： 通过研究井眼轨迹上某测点邻近的结构形状及其变化规律,得到了测段内井眼轨迹的一般性方程,从而可以客观地描述和计算实钻井眼轨迹。研究结果表明:井眼轨迹上某点的井眼曲率和井眼挠率决定了邻近区域内井眼轨迹的空间形状,其局部三维坐标可分别表示为曲线长度的一次、二次和三次函数。为了确定井眼曲率和井眼挠率,在充分阐述其理论依据的基础上构造出了井眼样条函数,给出了井斜函数和方位函数的模拟方法以及井眼轨迹参数的计算公式。利用井眼轨迹结构参数来描述和计算井眼轨迹更具有普遍性,而且具有很高的计算精度和稳定性,可以客观地描述出井眼轨迹的实际形状。

关键词: 定向钻井, 井眼轨迹, 测斜计算, 井眼样条函数, 数学模型