最小二乘法在定向钻进中的数据拟合

Data fitting with least square in directional drilling

向军文

XIANG Junwen

中国地质大学地球物理与信息技术学院，北京　100083

College of Geophysics and Information Technology, China University of Geo-sciences, Beijing 100083, China

定向钻进成功的关键在于按设计要求，较好地控制预定井段的井斜角和方位角。而目前使用的计算方法不能快速准确地预测井底轨迹参数。通过对井斜角、方位角、造斜率、井段长与造斜工具角的数据分析，采用最小二乘法原理，拟合出快速计算井底井斜角和方位角计算公式。结合实例，与通用定向井计算公式相比，井斜角最大误差为-0.036°，方位角最大误差为+0.02°。该计算式只涉及到初始角、井段长、钻具造斜率及定向工具角，且计算精度高，现场应用较为方便，提高了井底轨迹预测速度和防止定向钻进失误率，可指导定向钻井现场快速准确地预测井底参数。

To control precisely the inclination and the azimuth over the assumed well portion as required by the design is key to directional drilling. The existing calculation method is not conducive to give a quick prediction of the situation of the well bottom. With the least square principle, the inclination and azimuth calculation formula are fitted out through analysis of inclination, azimuth, build-rate, length of well portion, and toolface data. The field cases have demonstrated that compared with the conventional formula, the methods give the maximum inclination error of 0.036° and maximum azimuth error of +0.02°over 12 m well length. The formula involves only the starting angle, length of well portion, build-rate, and toolface, thus, providing high precision, easy use, quick prediction of well bottom trajectory, less directional drilling failure, and important guidance to quick site prediction for directional drilling.