# Analysis of Cement Sheath-Rock Damage Mechanism--A Case Study on Water Injection Wells
## 4 Numerical Simulation Analysis of Water Channeling outside Casing in Water Injection Wells  
### Bonded Interface Rock Model outside Casing in Water Injection  
Water channeling in the casing of water injection wells is caused by the progressive advancement of injected water along the bonded surface rock. The primary cause of external water channeling in the casing is the damage to the bonded surface rock induced by fluid-solid coupling. COMSOL simulation software, a widely utilized and powerful tool for multi-physics field simulations, is capable of effectively handling coupled problems in multiple physical domains. Moreover, its numerical algorithms offer high precision, and the obtained numerical solutions have undergone extensive testing and verification. In this study, a model of the bonded surface rock outside the casing of a water injection well was established using COMSOL software to simulate the evolution of damage under the influence of fluid-solid coupling. The model comprises a square shape measuring 2 m \(\times\) 2 m and features a central crack with a length of 1 m, as shown in Figure 6. The crack experiences a pressure loading rate of 0.5 MPa/s. The parameters utilized in the model can be found in Table 4.  
The experimental setup includes a cylindrical specimen with dimensions of 50 mm (width) \(\times\) 100 mm (height). The specimen's material strength follows a Weibull distribution \begin{table}
\begin{tabular}{c c c} \hline \hline
**Material Parameters of Rock and Cement Ring** & **Numerical Value** & **Unit** \\ \hline Density of rock \(\rho_{\text{m}}\) & 2600 & kg/m\({}^{3}\) \\ Density of cement ring \(\rho_{\text{y}}\) & 2000 & kg/m\({}^{3}\) \\ Young’s modulus of rock E1 & 50 & GPa \\ Young’s modulus of cement ring E2 & 10 & GPa \\ Poisson’s ratio of rock \(\mu\)1 & 2.012 & \\ Poisson’s ratio of cement ring \(\mu\)2 & 2.341 & \\ Permeability of rock k1 & \(1\times 10^{-16}\) & m\({}^{2}\) \\ Permeability of cement ring k2 & \(1\times 10^{-14}\) & m\({}^{2}\) \\ \hline \hline
**Rock Material Parameters of the Bonding Surface** & **Numerical Value** & **Unit** \\ \hline Tensile strength ft & 10 & MPa \\ Compressive strength fc & 60.1 & MPa \\ Initial porosity \(\Phi_{0}\) & 0.15 & \\ Residual porosity \(\Phi_{\text{r}}\) & 0.03 & \\ Biot’s coefficient \(\alpha\) & 0.5 & \\ Density \(\rho_{\text{w}}\) & 930 & kg/m\({}^{3}\) \\ Viscosity \(\theta_{\text{w}}\) & \(1.2\times 10^{-4}\) & Pa-s \\ Compressibility \(c_{\text{w}}\) & \(4.1\times 10^{-10}\) & Pa\({}^{-1}\) \\ Fracture energy per unit area \(\Psi\)i & 300 & J/m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Numerical simulation parameters of the bonding interface rock. Figure 6: Schematic diagram of the bonded interface rock outside the casing in a water injection well. with a shape parameter (m) of 2.34 and a characteristic strength (F0) of 60.1 MPa. In the process of validating fluid-solid coupling, a constant water pressure of 3 MPa is exerted on the top surface of the specimen. The specimen is loaded uniformly with a loading rate of 0.5 mm/s to ensure a gradual loading progression. ### Bonded Interface Rock Model outside Casing in Water Injection  
Based on oilfield water injection development practices, the progression of water injection time and the advancement of adjacent formations in the injection zone contribute to the dynamic changes in reservoir pressure. The confining pressure on the bonded rock surfaces fluctuates with the dynamic changes during water injection well production. These fluctuations in confining pressure lead to different damage profiles on the bonded surfaces based on specific operational conditions. In addition, the variation in wellbore diameter during the drilling of water injection wells leads to different widths of bonded rock surfaces, which consequently results in diverse damage patterns. The performance and quality of the cement slurry utilized during the cementing process contribute to discrepancies in the Young's modulus of the cement sheath.