小参数高阶项对射孔段套管屈曲摄动解的影响

Effect of high-order small parameter on buckling perturbation solution for perforated casing

采用摄动法求解射孔套管的屈曲临界压力时,一般仅取小参数ε的一次项,忽略其高阶项必然对计算结果产生一定的影响。针对此问题,建立了考虑小参数二阶项影响的射孔段套管弹性屈曲近似控制方程,给出了含有ε2项影响的射孔段套管屈曲问题摄动解的一般形式;分析了小参数变化时,ε2项对射孔段套管抗挤能力系数的影响。数值计算结果表明,计算孔眼的轴向最大尺寸、布孔格式和孔密度发生变化对小参数及射孔段套管抗挤能力都有直接的影响。当计算孔眼的轴向最大尺寸小于30mm、孔密度小于40孔/m时,仅考虑ε一次项可以给出满意的结果,而不必考虑小参数高阶项的影响。

The neglect of second and higher orders of small parameter ε will result in some errors when calculating the collapsing pressure of the perforated casing by using perturbation method. The elastic collapses governing differential equation and general formula for collapse resistance coefficient solved by perturbation method were given, in consideration of the influence of the second order of small parameter ε~2. The influence of term with ε~2 on the collapse resistance coefficient in changing the small parameter was analyzed. The results indicate that small parameter and collapse resistance coefficient vary with the maximum axial diameter d_0 of equivalent hole, perforation phase angle and shot density D_n. When d_0 is less than 30 mm and D_n is less than 40 shots per meter, the terms of second and higher orders of ε have no effect on the collapsing pressure.