采用俞茂宏统一强度理论求解套管的极限外压强

Solving Ultimate Outer Pressure of Casing by Yu's Unified Strength Theory

充分考虑拉压强度比和中间主应力系数,根据俞茂宏统一强度理论推导出在外压强下闭端、开端和平面应变套管弹塑性极限外压强的统一算法。数值仿真显示:随拉压强度比的减小和中间主应力系数的增大,弹性极限外压强增大;开端套管的弹性极限外压强最大,平面应变套管的次之,闭端套管的最小;塑性区的半径随外压强的增大而增大;当外压强增大时,套管由弹性状态进入弹塑性状态,塑性区的半径逐渐从内半径扩展到外半径;塑性极限外压强随拉压强度比的减小而增大;随外内半径比的增大,在同样的统一强度理论参数下,闭端、开端和平面应变的塑性极限外压强之间的差异增大,且塑性极限外压强大于弹性极限外压强;塑性极限外压强的计算值与试验测试值之间的相对误差为-4%^-9%,而国际标准化组织样板数据与试验测试值之间的相对误差为-12%^-25%,美国石油协会推荐数据与试验测试值之间的相对误差为-17%^-30%,表明文中的套管塑性极限外压强公式更接近试验值。

With due consideration of the tensile to compressible strength ratio and intermediate principal stress coefficient, a unified algorithm of elastic and plastic ultimate outer pressures for the casing with close end, open end or plane strain under the outer pressure is obtained following Yu＇es unified strength theory. Numerical simulation reveals that the elastic ultimate outer pressure increases with the decreasing tensile to compressible strength ratio and the increasing intermediate principal stress coefficient. The elastic ultimate outer pressure of the open end casing reaches the maximum, that of the close end casing reaches the minimum, and that of the plane strain casing is between the extremums. The plastic zone radius increases due to the increase of the outer pressure. When the outer pressure increases, the casing diverts from elastic state to elastoplastic state, and the plastic zone radius expands gradually from the inner radius to the outer radius. The plastic ultimate outer pressure increases with the decrease in the tensile to compressible strength ratio. The plastic ultimate outer pressure differences among close end, open end and plane strain casings increase with the increasing outer to inner radius ratio for the same unified strength theory parameters, and the plastic ultimate outer pressure of casing is greater than the elastic one. The relative error between the computational value of plastic ultimate outer pressure and the measured one lies within the range from -4% to -9% the relative error between ISO template datum and the measured value lies between- 12% and -25%, and the relative error between the commendatory datum from American Petroleum Institute and the measured value lies between 17% and 30%. These comparisons show that the present plastic ultimate outer pressure equation for casing is closer to the experimentally measured value than those in other references.