一种固定远场法向位移的水泥环弹塑性应力解

An elastoplastic stress solution of cement based on fixed farfield normal displacement

为更精确分析水泥环应力,针对目前水泥环应力解远场边界不固定的问题,把水泥环当作理想弹塑性材料,固定地层无限远场法向位移,结合Mohr-Coulomb准则,利用待定系数法建立了一种套管水泥环地层组合体受均匀内外压的位移和应力分布弹塑性修正解。对比套管外壁载荷弹性解和弹塑性解,并对不同套管内压和水泥环力学参数条件下的水泥环力学完整性进行敏感性分析。分析结果表明1)当套管内压超过弹性极限内压时,套管外壁载荷的弹塑性解大于弹性解,且随着套管内压增大套管外壁载荷增加幅度变大,最大增幅为4.05%。2)随着套管内压增加,水泥环弹性模量增加,泊松比降低,水泥环塑性区增加,由4.29 mm增加到最大19.54 mm。径向应力始终为压应力,但套管内压较高时,周向应力有转变为拉伸应力的风险。3)以渤海一口直井为例进行分析,计算得到水泥环弹性极限内压为29.8 MPa,套管最大内压为22.8 MPa,小于水泥环弹性极限内压,现场测定固井质量合格。工程上应控制最高套管内压不超过弹性极限内压,避免水泥环发生塑性变形,导致“微环空”形成。研究成果对水泥浆体系设计和力学完整性分析提供理论指导。

In order to analyze the stress of the cement ring more accurately,in view of the current problem that the stress of the cement ring is not fixed in the far field boundary,the cement ring is regarded as an ideal elastoplastic material to fix the normal displacement of the infinite far field of the formation,combined with the Mohr-Coulomb criterion,an elastoplastic modified solution for the displacement and stress distribution of a casing-cement ring-stratum composite body subjected to uniform internal and external pressure is established by using the method of undetermined coefficients.Compare the elastic solution and the elastoplastic solution on the casing outer wall,and conduct a sensitivity analysis of the mechanical integrity of the cement ring under different casing internal pressure and cement ring mechanical parameters.The results of analysis indicate that:1)When the casing internal pressure exceeds the elastic limit internal pressure,the result of the elastoplastic solution of the casing external wall load is greater than the elastic solution.As the internal pressure of the casing increases,the load on the outer wall of the casing increases,and the maximum increase is 4.05%.2)With the internal pressure of the casing increasing,the elastic modulus of the cement ring increasing,and the Poisson’s ratio decreasing,the plastic zone of the cement ring increases,from 4.29 mm to a maximum of 19.54 mm.The radial stress is always compressive,but when the casing internal pressure is relative high,the circumferential stress may be transformed into tensile.3)Taking a vertical well in Bohai as an example for analysis,the calculated cement ring elastic limit internal pressure is 29.8 MPa,and the casing maximum internal pressure is 22.8 MPa,which is less than the cement ring elastic limit internal pressure,and the cementing quality measured on site is qualified.In engineering,the maximum casing internal pressure should not exceed the elastic limit internal pressure to avoid plastic deformation of the cement ring,resulting in the formation of“micro annulus”.The research results provide the oretical guidance for cement slurry system design and mechanical integrity analysis.