Abstract: From the assumption that within a survey interval the rates of inclination change and azimuth change remain constant, this paper derives formulae for calculating the course coordinates and puts forward to a new mathematical method of modeling and calculating the wellbore trajectory——Natural Parameter Method. The new method has several advantages. First, the model is simple and relatively reasonable. Second, the calculated results are stable. Third, interpolation calculation can be easily achieved for wellbore trajectory. Therefore, it is very convenient for oil field application. The calculated results of two typical curves employed to verify its correctness and advantages above showed that Natural Parameter Method is superior to Cylinder Helix Method (Radius of Curvature Method) and Minimum Curvature Method which are most commonly used today, and it is suitable for both rotary system and steerable system.

Key words: drilling theory, mathematical model, wellbore trajectory, directional drilling, horizontal drilling

摘要： 在线性井斜函数的假设条件下,推导出了测段内坐标增量的计算公式,提出了计算井眼轨迹的自然参数法.该方法的描述模型比较合理,具有计算公式简单、计算稳定性好、对井眼轨迹的插值计算容易实现等特点,便于现场应用.经两种典型理论曲线的验证表明:自然参数法优于目前普遍采用的圆柱螺线法和最小曲率法等测斜计算方法,并且对于转盘钻进井段和导向钻具定向钻进井段都可以得到较好的计算结果.

关键词: 钻井理论, 数学模型, 井眼轨迹, 定向钻井, 水平钻井