最小曲率法计算中的数值方法

最小曲率法是测斜计算、井眼轨道设计中最常用的方法之一,在井眼轨迹计算中有广泛的应用。研究了最小曲率法计算机数值计算中的几个细节问题,给出了零井斜角测点的方位角定义,阐述了零井斜角测点方位角的二义性。分析了坐标增量计算过程,给出了减小三角函数计算次数的算法。对小弯曲角情形的坐标计算使用高精度近似公式代替容易产生除法溢出的直接计算,提高了计算过程的稳定性和计算精度。对水平投影长度的计算给出了使用Gauss数值积分法的精确计算方法。文中提出的方法可以用于使用最小曲率法时的井眼轨道计算的计算机软件开发,提高计算机软件的计算稳定性和计算精度。对涉及井眼轨迹计算的其他实际问题如定向井中靶分析预测、井眼轨迹控制、井身质量检查等都有一定的参考价值。

Numerical Methods of Calculation Minimum-curvature

The minimum-curvature method is one of the most basic methods in the inclinometry calculation and the wellpath design, it has been widely used in the trajectory calculation. In this paper, the computer numerical calculation using minimum-curvature method has been researched, the azimuth definition and its ambiguity were elaborated when the deviation angle was zero. Secondly, the process of coordinate incremental calculation and the method to reduce the number of trigonometric calculation were analyzed. In the situation of small bending angle, the coordinate computation using high accuracy approximate formula replaced the direct calculation which was easily lead to division overflow, which enhanced the stability and the computational accuracy of computational process. Thirdly, in terms of the calculation to the length of horizontal projection, the Gauss numerical integration method has been used. Besides, the proposed methods can be used to the computer software development in the trajectory calculation using minimum-curvature method.