## 4 Result
### Domain Knowledge Embedding
By comparing Figure 9c,d, similar conclusions can be drawn, confirming that the power-law model consistently outperforms the Bingham model across different temperature conditions, providing a more accurate description of the rheological properties of cement slurry. Additionally, the rheological curve fitting results for cement slurry from other wells are presented in Appendix A, further validating this conclusion. Therefore, this study recommends using the power-law model to calculate the rheological properties of cement slurry for a more precise characterization of its flow behavior. During the actual cementing process, there are significant temperature variations at different depths of the wellbore. If the rheological parameters are not corrected for temperature, it may lead to inaccurate predictions of the cement slurry's flow behavior throughout the wellbore [33; 34]. In this study, the power-law equation was modified to account for temperature effects, resulting in the corrected formula shown in Equations (12)-(14). Based on this corrected model, the rheological properties of the second-stage and third-stage cementing slurries for this well were fitted, with the results presented in Figure 10.  
\[\tau=k(T)\dot{\gamma}^{n(T)} \tag{12}\]  
\[k(T)=k_{0}\times e^{-C_{k}(T-25)} \tag{13}\]  
\[n(T)=n_{0}\times e^{-C_{n}(T-25)} \tag{14}\]  
where the following are used:  
\(T\): temperature (\({}^{\circ}\)C);  
\(C_{k}\), \(C_{n}\): temperature influence coefficient;  
\(k_{0}\), \(n_{0}\): fitted parameter. In Figure 10a,b, the experimental data (red/blue points) show a high degree of fit with the temperature-corrected power-law model (dashed lines), with \(R^{2}\) values close to 1. This indicates that the temperature-corrected power-law equation can accurately describe the rheological properties of cement slurry at different temperatures. In the power-law fluid Equation (12), the consistency coefficient \(k\) and the flow behavior index \(n\) are key parameters representing the flow characteristics of the fluid. To verify whether temperature correction affects the relationship between cement slurry flow parameters and cementing quality, this study calculated the consistency coefficient and  
Figure 9: Rheological equation fitting results of cement slurry: (**a**) Second-stage cementing slurry at **25**\({}^{\circ}\)C. (**b**) Second-stage cementing slurry at 76 \({}^{\circ}\)C. (**c**) Third-stage cementing slurry at 25 \({}^{\circ}\)C. (**d**) Third-stage cementing slurry at 93 \({}^{\circ}\)C.  
flow behavior index both with and without temperature correction based on Equation (2) and analyzed their correlation with the interface bond quality between the cement sheath and formation, as well as between the casing and cement sheath. The corresponding results are presented in the form of bar charts, as shown in Figure 11.  
The uncorrected consistency coefficient \(k\) and flow behavior index \(n\) exhibit relatively weak correlations with both the casing-cement sheath interface and the cement sheath-formation interface quality, with Spearman correlation coefficients of 0.1512, 0.1625, and 0.2342, 0.2037, respectively. However, after incorporating temperature effects, the corrected parameters \(k(T)\) and \(n(T)\) show significantly improved correlations, reaching 0.3175, 0.3284, and 0.4192, 0.4013, respectively. This enhancement indicates that the temperature-corrected consistency coefficient and flow behavior index more accurately reflect the actual rheological behavior of the cement slurry under downhole conditions. Therefore, to achieve more reliable predictions of cement bond quality, it is recommended to adopt temperature-corrected rheological parameters as input indicators. Figure 11: Comparison of Spearman correlation coefficients between rheological parameters and interface bond quality with and without temperature correction. \[\tau=\tau_{y}+\mu_{p}\hat{\gamma} \tag{10}\]0 Cement slurry rheology fitting results: (**a**) Third-stage cementing slurry. (**b**) Second-stage cementing slurry.