## 3 Results and Discussion
### Impact of Drilling Fluid
#### 3.2.5 Comprehensive Parameter Sensitivity Analysis  
The influence of fluid parameters on SFED and TREE is summarized in Table 3. Based on the aggregated data, a sensitivity analysis of SFED and TREE was conducted using the range normalization method. To eliminate discrepancies in dimensional units and variation ranges among parameters, a normalized sensitivity index (Equation (25)) was employed to quantify the impact of each parameter on output metrics (SFED and TREE). Furthermore, the relative importance ranking of parameters was calculated via weight Equation (26). A high-sensitivity zone was defined to identify critical thresholds where SFED and TREE exhibited strong responses to fluid parameter variations, with thresholds determined by Equation (27).  
\[S_{n}(p)=\frac{\Delta I(p)}{\Delta p/p_{\text{mid}}} \tag{25}\]  
where \(p\) represents the parameters for analysis (Q, \(\eta\) and \(\rho\)), \(\Delta I\) (\(p\)) is the absolute variation in the evaluation index (SFED and TREE) over the parameter range \(\Delta p\), and \(p_{\text{mid}}\) is the mid-range value.  
\[\omega(p)=\frac{S_{n}(p)}{\sum_{k=1}^{N}S_{n}(p_{k})}\times 100\% \tag{26}\]  
where the denominator \(\sum\) represents the sum of all parameter-normalized sensitivity indexes. \(N\) represents the total number of parameters. In this study, \(N=3\).  
\[\Gamma=\mu_{Y}+k\cdot\sigma_{Y} \tag{27}\]  
Figure 34: SFED and TREE versus density of drilling fluid.  
where \(Y\) represents the absolute values of the rate of change in the indicators caused by all parameters. \(\mu_{Y}\) and \(\sigma_{Y}\) represent the arithmetic mean and standard deviation of the absolute values of the rate of change in SFED or TREE, respectively. \(k\) represents the engineering safety factor. In this study, \(k\) is set to 1.3.  
The final sensitivity analysis results are illustrated in Figure 35. The SFED and TREE values under no-drilling-fluid conditions were used as baseline references, while reductions in SFED and TREE due to drilling fluid parameters are represented as negative values. As shown in the figure, a higher viscosity (9 \(\times\) 10\({}^{-5}\) m\({}^{2}\)/s) resulted in a maximum reduction of 44.0% for SFED, whereas at a lower viscosity (2.5 \(\times\) 10\({}^{-5}\) m\({}^{2}\)/s), the TREE reduction reached 49.1%. Additionally, when the density was set at 1400 kg/m\({}^{3}\), the SFED reduction exceeded 40%, reaching 42.5%, indicating that higher viscosities and densities significantly reduce both SFED and TREE. On the other hand, sensitivity analysis revealed that SFED is most sensitive to variations in density; thus, controlling density is crucial for reducing SFED. Conversely, TREE exhibits the highest sensitivity to flow rate changes, making flow rate control essential for minimizing TREE. However, viscosities exceeding 2.5 \(\times\) 10\({}^{-5}\) led to an increase in TREE, suggesting that viscosity should be maintained below this threshold.  
The high-sensitivity region thresholds for SFED and TREE were 20.05% and 23.92%, respectively. These values indicate that within typical drilling fluid parameter ranges, both SFED and TREE exhibit pronounced responses to parameter variations.  
Figure 35: Sensitivity analyses of SFED and TREE.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Parameter Range**} & \multicolumn{2}{c}{**Response Range of Reduction**} \\ \cline{3-4}  & & **SFED** & **TREE** \\ \hline Flow rate \(Q\) (L/min) & 30–70 & \(-\)16.43–32.79\% & \(-\)21.56–34.6\% \\ Kinematic viscosity \(\eta\) (m\({}^{2}\)/s) & \(1\times 10^{-6}\)–9 \(\times\) 10\({}^{-5}\) & \(-\)24.28–44.02\% & \(-\)27.41–49.06\% \\ Density \(\rho\) (kg/m\({}^{3}\)) & 1000–1400 & \(-\)24.28–42.5\% & \(-\)27.41–30.26\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Summary of the influence of fluid parameters on SFED and TREE.