大位移井侧位抛物线剖面设计的数值计算

侧位抛物线剖面是大位移井轨道设计中常用的剖面类型。对侧位抛物线剖面设计求解过程中的求侧位抛物线初始点井斜角的数值方法和从段长求井斜角的数值方法进行了分析,指出其关键是求解侧位抛物线初始点井斜角所满足的一个三角函数方程。用倍角公式可将该三角函数方程转化成一个四次代数方程,然后用求根公式直接求出解析解。用解析解可简化侧位抛物线剖面设计过程,减少计算工作量,提高计算速度。侧位抛物线井段参数计算中需要通过段长公式来反求井斜角,给出了反求井斜角的二分法。本文的算法可应用于大位移井轨道设计的软件开发。

Numerical Calculation of Lateral Parabolic Profile Design of the Extended Reach Well

Lateral parabolic profile is common used in orbital design of the extended reach well.During the lateral parabolic profile was computed ,numerical methods of calculating angle of inclination on initial point of the lateral paracurve and calculating angle of inclination based on interval length were analyzed.It is pointed out that the key of the lateral parabolic profile design is a circular function equation which can be applied to solving the angle of inclination on initial point of the lateral paracurve.Double angle formula can transform the circular function equation to a biquadratic algebraic equation,and the analysis solution can be solved by extract equation directly.After the analysis solution was known,the process of the lateral parabolic profile design may be simplified,computational effort may be decreased and computation speed can be improved.During the parameter calculation of lateral parabolic interval, segment length equation may be used to solve the angle of inclination ,so the corresponding dichotomy was given.The computational method given in this paper can be applied to computer software development of orbital design of the extended reach well.