# Research on Intelligent Optimization of Wellbore Trajectory in Complex Formation
## 5 Results
### Actual Application Analysis  
The constraints listed in Tables 4 and 5 are based on engineering requirements in actual drilling operations. Wellbore trajectory design must meet the following key constraints. Kickoff point (KOP): The KOP location must ensure a gradual increase in well inclination to avoid sudden curvature changes that could destabilize the borehole wall. Deviation angle: Excessive inclination can increase drill string friction and reduce drilling efficiency, while \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Function** & **Evaluating Indicator** & **NSGAII** & **MOGWO** & **MOLPB** & **MOPSO** & **New\_MOPSO** \\ \hline \multirow{4}{*}{Schaffer} & IGD\_score & 0.0044786 & 0.0027075 & 0.0029799 & 0.011328 & 0.00248 \\  & (Lower is better) & & & & \\  & HV\_score & 0.68306 & 0.684 & 0.7128 & 0.67968 & 0.86038 \\  & (Higher is better) & & & & & \\  & Spacing\_score & 0.0031164 & 0.0013585 & 0.0015345 & 0.006672 & 0.00157 \\  & (Lower is better) & & & & & \\  & IGD\_score & 0.00539 & 0.0030685 & 0.0031977 & 0.03456 & 0.0030041 \\ \multirow{4}{*}{Kursawe} & HV\_score & & & & & \\  & (Higher is better) & 0.43218 & 0.4218 & 0.43956 & 0.408 & 0.50421 \\ \multirow{4}{*}{ZDT6} & Spacing\_score & & & & & \\  & (Lower is better) & 0.002793 & 0.0015105 & 0.0018018 & 0.0014784 & 0.0014957 \\ \multirow{4}{*}{ZDT6} & IGD\_score & & & & & \\  & (Lower is better) & 0.003822 & 0.0027455 & 0.0029205 & 0.0024672 & 0.0020447 \\ \multirow{4}{*}{ZDT3} & HV\_score & & & & & \\  & (Higher is better) & 0.58604 & 0.56905 & 0.594 & 0.576 & 0.63572 \\ \multirow{4}{*}{ZDT3} & Spacing\_score & & & & & \\  & (Lower is better) & 0.0033026 & 0.001824 & 0.0020097 & 0.0029568 & 0.0022616 \\ \multirow{4}{*}{ZDT3} & IGD\_score & & & & & \\  & (Lower is better) & 0.27048 & 0.027835 & 0.037917 & 0.50784 & 0.002601 \\ \multirow{4}{*}{ZDT3} & HV\_score & & & & & \\  & (Higher is better) & 0.4018 & 0.0028025 & 0.66924 & 0.16224 & 0.25023 \\ \multirow{4}{*}{(Higher is better)} & Spacing\_score & & & & & \\  & (Lower is better) & 0.013622 & 0.0093385 & 0.0050688 & 0.011616 & 0.0040176 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Algorithm function index comparison. a small inclination may cause trajectory deviation from the target formation. Azimuth angle: In horizontal well design, azimuth angle variations must align with reservoir trends to optimize hydrocarbon recovery. Build angle rate: A high build rate may cause drill string fatigue, reducing tool lifespan, thus requiring a reasonable limit. Length of stable inclined section: This parameter directly affects the maneuverability and cost-effectiveness of the wellbore trajectory; a short length may increase operational difficulty, while an excessively long length may reduce trajectory adjustment flexibility. In this study, these constraints were set based on industry standards and validated across various geological environments. The table below presents the constraint conditions for well parameters in a three-stage well trajectory design, ensuring feasibility and operational efficiency. Table 6 presents the planning results of the three-stage wellbore trajectory, detailing key parameters and optimized values for each stage to achieve an efficient and feasible trajectory design. To validate the robustness of the proposed algorithm, additional field tests were conducted in two contrasting geological environments: a fractured sandstone formation and a high-stress shale reservoir. The results showed consistent improvements in trajectory length reduction and complexity minimization compared to traditional methods, further highlighting the algorithm's adaptability. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Scope of Initial Values** \\ \hline KOP(m) & \(200<D_{kop}<500\) \\ Deviation angle & \(30<R_{i}<45\) \\ Azimuth & \(0<a_{i}<110\) \\ Build angle rate & \(2.15<\varphi_{i}<2.35\) \\ Length of stable inclined section & \(0<L_{\text{bc}}<2200\) \\ \hline \hline \end{tabular}
\end{table}