均角全距法钻孔轨迹一般计算公式的缺陷修正

Modification of the General Formula of the Average-angle Method for Drilling Trace Calculation

均角全距法是定向钻孔轨迹计算最常用的方法之一;但均角全距法一般计算公式存在一个缺陷:当临近两测点的方位角差值大于180°时,按均角全距法一般公式计算的方位角算术平均值方向与模型假设的实际平均方位方向正好相反;如果忽视此问题往往会造成水平向坐标增量出现较大的计算误差,进而影响钻孔定位精度。针对该问题,首先讨论了实际平均方位与方位角算术平均值的关系;然后通过严格的几何计算推导出了全新的均角全距法修正公式;最后采用一般公式、SY/T5088—2008《钻井井身质量控制规范》(下简称《规范》)算法、修正公式三种方法进行算例对比分析。计算结果显示:修正公式与《规范》算法的计算结果完全一致,证明了修正公式的正确性;当相邻两测点方位角差值大于180°,一般计算公式与修正公式的水平向坐标增量Δx、Δy正负异号,表明修正公式正好克服了一般公式方位算反的缺陷。总的说来,修正公式成功地解决了一般公式的缺陷,同时克服了《规范》算法需分类讨论的缺陷,建议推广使用。

The average-angle method is one of the most generally-used methods for drilling trace calculation.However,there＇s a defect in the general formula of the average-angle method. When the azimuth difference between two adjacent measuring points exceeds 180°,the corresponding direction of the arithmetic average of azimuth angles used in the general formula is opposite to the actual average azimuth orientation. If we ignore this defect,it may lead to a relatively big calculation error of the horizontal coordinate increments,which may directly affect the borehole positioning accuracy. To solve the defect of the general formula,this paper discussed the relationship between the actual average azimuth orientation and the corresponding direction of the arithmetic average of azimuth angles,and then derived the modified formula from rigorous geometric calculations,and finally use the general formula,the calculation method in ＂Drilling Borehole Quality Control Specification＂（ SY/T 5088—2008）,the modified formula to calculate a certain example respectively. Through the analysis of the calculation results by three methods,we concluded： the modified formula is exactly the same as the Specification method in calculation results,which proved the correctness of the modified formula; when the azimuth difference between two adjacent measuring points is greater than 180°,the horizontal coordinate increments calculated by the general formula and the modified formula are just opposite,which just verifies the effectiveness of the modified formula＇s correcting the defect of the general formula. In summary,the modified formula perfectly corrects the defect of the general formula,and overcomes the shortcomings of the Specification method which requires classified discussion meanwhile,which is well worth being popularized.