# A Study on the Stress Field Around an Elliptical Wellbore with an Eccentric Casing in Deep Wells
## 3 Result Analysis and Discussion
### Stress Distribution of Casing Under Different Eccentricities
#### 3.1.3 Shear Stress Distribution on the Outer Wall of the Casing  
Figure 8 shows the distribution cloud map of casing shear stress under different eccentricities. By observing the graph, we can conclude that an increase in eccentricity leads to an uneven distribution of shear stress in the casing. As the eccentricity increases, a concentration of high-stress areas appears on one side of the thick cement sheath, and the area of the high-stress area gradually decreases, ultimately positioning on the inner wall of the casing.  
The specific changes in cementing are as follows. When eccentricity is 0.0, the shear stress distribution is symmetrical about the T-Z plane. The high-stress zone, 20\({}^{\circ}\) to 80\({}^{\circ}\) and 100\({}^{\circ}\) to 160\({}^{\circ}\), is on the outer wall of the casing.  
When eccentricity is 0.3, the high-stress zone moves towards the thick cement ring side. The distribution area expands from the outer wall to the inner wall of the casing.  
When eccentricity is 0.6, the area of the high-stress zone decreases. The distribution zone concentrates towards the thick cement sheath and the inner wall of the casing.  
When eccentricity is 0.9, the area of the high-stress zone further decreases. The high-stress zone is located on the inner wall of the casing.  
Figure 9 displays a line graph of casing outer wall shear stress at different eccentricities, with the data representing absolute values of the stresses at corresponding positions on the casing. From the graph, the following conclusions can be drawn. (1) As the eccentricity increases, the non-uniformity of shear stress distribution increases, the direction of shear stress changes, and the stress values show significant increments. The specific changes are shown in Table 6. It can be observed that increasing eccentricity significantly increases the non-uniformity of shear stress distribution. (2) Based on Figure 9, it can be concluded that as the eccentricity increases, the distribution of the shear stress on the casing's outer wall becomes more non-uniform, with changes in the direction of the shear stress and significant  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(\varepsilon\)**=0.0** & \(\varepsilon\)**=0.3** & \(\varepsilon\)**=0.6** & \(\varepsilon\)**=0.9** \\ \hline \(\sigma_{\text{Max,c}}/\text{MPa}\) & 235.31 & 235.95 & 236.14 & 235.37 \\ \(\sigma_{\text{Minc}}/\text{MPa}\) & 179.26 & 168.69 & 136.09 & 93.73 \\ \(K\) & 1.31 & 1.4 & 1.75 & 2.56 \\ \hline \hline \end{tabular}  
* Footnotes: \(\sigma_{\text{Max,c}}\) is the maximum circumferential stress value, \(\sigma_{\text{Min,c}}\) is the minimum circumferential stress value, and K is the stress non-uniformity coefficient.  
\end{table}
Table 5: Maximum circumferential stress and stress non-uniformity coefficient under different eccentricities.  
Figure 8: The distribution of casing shear stress under different eccentricity ratios. Shear stress cloud map at eccentricities: (**a**) \(\varepsilon=0.0\), (**b**) \(\varepsilon=0.3\), (**c**) \(\varepsilon=0.6\), and (**d**) \(\varepsilon=0.9\).  
increases in stress values. Additionally, the orientation of the maximum shear stress is typically closer to the side with a thicker cement sheath.