井眼轨道模型中的数值积分计算

Numerical Integral Calculation in Borehole Trajectory Model

为了提高钻井设计软件中所使用定积分的计算速度,从井眼轨道模型的基本公式出发,经过积分参数变换,将恒工具面法北东坐标定积分中的被积函数需要7次三角函数和1次对数函数的运算减少为3次三角函数和1次对数函数的运算,将空间圆弧法水平投影长度定积分的被积函数中的三角函数运算简化掉,从而提高定积分的计算速度;使用变步长Simpson数值积分公式,计算恒工具面法北东坐标定积分和空间圆弧法水平投影长度定积分,可将计算精度控制到任意精度。算例计算表明,本文算法除了提高了计算速度,计算精度还与公开数据完全相同。本文给出的算法是对井眼轨道计算的进一步改进和完善,可应用于钻井软件开发中。

In order to improve calculation speed of the definite integrals in the drilling design software,the basic formula of the borehole trajectory model and the integral parameter conversion were adopted.The calculation of seven trigonometric and one logarithmic functions was reduced to that of three trigonometric and one logarithmic functions required by the integrand of the definite integral in the north and east coordinates by the constant tool face method.The trigonometric functions in the integrand of the definite integral with a horizontal projection length by the space arc method were simplified,so as to improve the calculation speed of the definite integral.Using the variable step size Simpson numerical integration formula to calculate the above two kinds of definite integrals,the calculation accuracy can be controlled to arbitrary precision.The calculation shows that the new algorithm in this paper not only improves the calculation speed but also has the same calculation accuracy as the public data.The algorithm given in this paper is further improves and refines of the borehole trajectory calculation and can be applied in the software development of drilling.