底部钻具组合两维分析的新算法

NEW ALGORITHM OF 2-D ANALYSIS OF BOTTOM HOLE ASSEMBLY

过去在对底部钻具组合 (BHA)进行力学分析时 ,全是依靠手工进行公式的推演 ,不但费时费力 ,而且容易出错。而在计算轴向力时 ,只是简单地用钻压值减去井底到所算跨中点的BHA轴向重量 (浮重 ) ,并假设BHA轴向力与井眼轴线方向一致 ,没有考虑稳定器处支反力对轴向力的影响 ,这样处理必然给计算结果带来一定的误差。文章应用MatLab的符号运算功能对二维底部钻具组合分析权余法 (MWR)的消除残值方程和边界条件方程构成的方程组进行直接求解 ,使得求解过程更为简单和准确 ;同时 ,假设BHA轴向力与BHA变形线轴线方向一致 ,并考虑稳定器处支反力对轴向力的影响 ,将钻压作为目标函数对BHA单跨轴向力进行迭代求解 ,进一步提高了计算精度。

In the past, the mechanical analysis of bottom hole assembly (BHA) was all dependent on deducing the formulas by hand, which not only took both time and effort but also often led to the error; and when the axial force was calculated, it was only simply regarded as the result of subtracting the weight on bit and the BHA axial weight from bottom hole to calculated span neutral point, the BHA axial force consistent with the direction of borehole axial line was assumed and the influence of the bearing reaction foroce at stabilizer on the axial force wasn't considered, because of which the calculating result was bound to fall into error. In the paper, it is proposed that the equation group being composed of the boundary condition equation and residual-relieving equation in the analysis of the method of weighted residuals of BHA may be directly solved with the help of the Symbolic Math Toolbox of MatLab, which makes the solving process more simple and the result more accurate; meanwhile, if the BHA axial force is consistent with the direction of BHA deformation axial line and in consideration of the influence of the bearing reaction force at stabilizer on the axial force, the iteration solving of the BHA single-span axial force may be carried out by taking the weight on bit as the object function, thus raising the calculation accuracy.