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对于立井井筒,其受到的水平不均匀压力,按公式p(θ)=p2(1-β2cos 2θ)拟合效果比p(θ)=p1·(1+β1sinθ)更好。为比较二者对井筒内力计算结果的影响,为井筒截面设计提供依据,将立井井筒简化成环形线弹性杆件,应用卡氏第二定理,并结合平衡方程分别解出了2种表达式作用下井筒圆环的弯矩、轴力和剪力的表达式。结合工程实例,采用有限元数值分析的方法,比较了2种表达式形式对弯矩、轴力和剪力计算结果的影响。结果表明:根据2种表达式计算出的内力,其结果有一定的差别。在相同地压作用下,弯矩最大相对差值约为9.57%,轴力最大相对差值较为接近,不大于2.23%,剪力最大相对差值约为14.36%。由于按照公式p(θ)=p2(1-β2cos 2θ)的压力拟合效果更好,因此推荐采用基于该式推导的轴力和弯矩表达式作为井筒截面设计的计算公式。
For vertical wellbores, the horizontal pressure to which it is subjected is better than p (θ) = p1 · (1 + β1sinθ) according to the formula p (θ) = p2 (1- β2 cos 2θ). In order to compare the influence of the two on wellbore internal force calculation and provide the basis for wellbore cross section design, the vertical wellbore is simplified into a ring-shaped elastic rod. Two kinds of expressions are respectively solved by applying the second Karlsruhe’s theorem and the equilibrium equation The expression of bending moment, axial force and shear force of downhole ring. Combined with engineering examples, the influence of two kinds of expressions on the calculation results of bending moment, axial force and shear force was compared by using the method of finite element numerical analysis. The results show that the internal forces calculated by the two expressions have some differences. Under the same pressure, the maximum relative difference of bending moment is about 9.57%, the maximum relative difference of axial force is close to no more than 2.23% and the maximum relative difference of shear force is about 14.36%. As the pressure fitting according to the formula p (θ) = p2 (1 - β2 cos 2θ) is better, it is recommended to use the formulas of axial force and bending moment deduced from this formula as the calculation formula of wellbore section design.