# A Study on the Stress Field Around an Elliptical Wellbore with an Eccentric Casing in Deep Wells
## 4 Conclusions  
This article mainly analyzes the computational results of the elliptical wellbore casing-cement sheath-formation model under different eccentricities using numerical simulation methods. The main conclusions are as follows:  
1. Under an elliptical wellbore configuration, eccentricity significantly influences the stress distribution within the casing. As eccentricity increases, the non-uniformity of casing stress distribution becomes more pronounced. Concurrently, an increase in eccentricity results in a reduction in the high-stress zone area and an expansion of the low-stress zone.  
Figure 14: Maximum stress distribution on the outer wall of the casing under different Poisson’s ratios of cement sheath: (**a**) maximum radial stress distribution, (**b**) maximum circumferential stress distribution, (**c**) maximum shear stress distribution, (**d**) maximum equivalent stress distribution.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(\varepsilon\)**=0.0** & \(\varepsilon\)**=0.3** & \(\varepsilon\)**=0.6** & \(\varepsilon\)**=0.9** \\ \hline \(\Delta\sigma_{\text{r}}/\text{MPa}\) & \(-3.01\) & \(-3.38\) & \(-7.92\) & \(-16.38\) \\ \(\Delta\sigma_{\text{c}}/\text{MPa}\) & \(-26.93\) & \(-28.66\) & \(-29.86\) & \(-30.75\) \\ \(\Delta\tau/\text{MPa}\) & \(-3.21\) & \(-5.26\) & \(-8.56\) & \(-12.45\) \\ \(\Delta\sigma_{\text{e}}/\text{MPa}\) & \(-21.38\) & \(-22.82\) & \(-23.67\) & \(-24.36\) \\ \hline \hline \end{tabular}
\end{table}
Table 9: Reduction in casing stress under different eccentricities when the Poisson ratio of cement sheath increases.  
2. When eccentricity is held constant, an increase in the non-uniformity of geostress leads to a greater rise in equivalent stress and circumferential stress. Compared to radial stress and shear stress, equivalent and circumferential stresses exhibit higher sensitivity to variations in geostress non-uniformity. Moreover, the larger the eccentricity, the higher the stress values, even when the degree of geostress non-uniformity remains unchanged.
3. The stress within the casing exhibits a trend of initially increasing and subsequently decreasing with changes in the elastic modulus of the cement sheath. Notably, stress values under a high elastic modulus are greater than those under a low elastic modulus. Furthermore, the presence of eccentricity amplifies the stress values within the casing.
4. A high Poisson ratio is advantageous for improving the stress conditions of the casing, with casing stress continuously decreasing as Poisson's ratio increases.  
This article only uses numerical simulation methods to analyze the stress distribution of elliptical wellbore casing under eccentric conditions, and the results may contain certain errors. In order to obtain more accurate analysis results, future research can use theories such as complex variables to derive analytical expressions for casing stress distribution and compare and analyze them with finite element results.  
Software, C.W.; Formal analysis, C.W.; Investigation, Y.X. ([PERSON]), Y.X. ([PERSON]) and B.Z.; Resources, X.Z., B.H., Y.X. ([PERSON]) and C.W.; Writing--original draft, X.Z. and Y.X. ([PERSON]); Writing--review & editing, X.Z.; Supervision, Y.X. ([PERSON]) and B.Z.; Funding acquisition, Y.X. ([PERSON]). All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
Author [PERSON] was employed by the company CNPC Tianjin Bo-Xing Engineering Science & Technology Co., Ltd. Author [PERSON] was employed by the company China Oilfield Services Limited. The remaining authors declare that the re-search was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.