膨胀水泥环空界面径向应力理论解及实验验证

为了确定固井水泥凝固过程中套管和水泥环初始载荷状态,综合考虑水泥凝固过程中体积膨胀和材料参数的变化规律,推导出水泥凝固过程中环空界面的径向应力理论解。在理论解推导过程中,将水泥环的凝固过程分为多个时间步长,在每一个时间步长中,先计算水泥环无载荷状态下的原始半径,然后依据套管、膨胀后的水泥环和地层3者的协调变形条件,计算出变形后的径向应力,并将其和变形后的半径值一起作为下一步计算的初始数据。通过室内实验测量了套管和地层在水泥凝固过程中的环向应变,实验结果证明了理论解的正确性。计算和实验结果表明,水泥环在凝固过程中,内外两个界面的径向应力均为压应力,其绝对值随着井壁岩层弹性模量的增加而增加。水泥环的弹性模量越大,其凝固过程中对井壁产生的径向压应力越大,而对套管外壁产生的径向压应力反而越小。故对不同弹性模量的地层应采用适宜弹性模量的水泥固井,以达到使系统载荷均衡的目的。

The theoretical radial stress solution and its experimental verification of expansion cement at annulus interfaces

To determine the initial loading state of the casing and cement sheath during cement setting, the theoretical solution of radial stresses at the annulus interfaces during cement setting is derived based on volume expansion and material parameter variation. During the theoretical derivation, cement setting is divided into many time steps. In each step, the original radii of cement sheath without loading are calculated and the radial stresses are calculated according to the compatible deformation condition among the casing, cement sheath after free expansion and the stratum in this time step. The current radial stresses and radii of the cement sheath are used as initial data for the next step. The circumferential strains of casing and stratum are measured during cement setting process. The experimental result verifies the correctness of the theoretical solution. The calculated results and experimental data show that the radial stresses on both inner and outer boundaries of cement sheath are compressive stresses during the cement setting process, and their absolute values increase as the elastic modulus of the rock around the well increases. The higher the cement elastic modulus is, the larger the radial compressive stress on the wellbore will be. The radial compressive stress on the outer boundary of the casing will decrease on the contrary. The cement material with appropriate elastic modulus should be adopted according to different elastic modulus of stratum, so as to realize loading equilibrium of the oil and gas well structural systems.