定向井方位漂移轨道设计问题的数值算法

Numerical algorithm of directional well position drifting track design

方位漂移是实际钻井过程中普遍存在的现象,常规的轨道设计方法没有考虑方位漂移的影响,增加了钻井施工过程中的井眼轨迹控制的难度。考虑方位漂移影响的轨道设计方法采用井段的自然曲线模型,能够较好地反映地层自然造斜和方位漂移规律。所产生的约束方程组为三元非线性方程组,通常使用的数值迭代方法不易给定迭代初始值、迭代收敛性能差、收敛速度慢。推导出了用稳斜井段井斜角来表示的初始方位角和稳斜段长的解析公式,将三元方程组的求解问题归结为以稳斜井段井斜角为未知数的一元非线性方程方程的求解问题,并给出了求解该一元非线性方程的数值迭代算法。理论分析和大量实际算例表明,文中新算法具有收敛速度快、迭代初值相关性小、全局范围收敛等良好性质。

The position drifting commonly existed in the actual well drilling process.In the conventional track design,the position drifting influence had not been considered,which increased difficulty to the well trajectory control in the well drilling construction process.The track design method of considering the position drifting influence uses the well section natural curve model,which can reflect the stratum natural deviation and the position drifting rule as well. The produced restraint equation set is ternary nonlinear equation,The usually used numerical iterative method is not easy to assign iterative initial value, convergence performance is bad, the convergence rate is slow. Analytic formula of initial directional angle and section length expressed by steady inclined section deviation angle is inferred, which make ternary equation solution to unary equation with unknown steady inclined section deviation angle and gave numerical iterative algorithm to the equation.The theoretical analysis and the massive actual examples indicated that the new algorithm in the article has good natures of quick convergence rate, small iterative initial value relevance, overall convergence and so on.