# Non-Vertical Well Trajectory Design Based on Multi-Objective Optimization
## 5 Analysis of the Results  
### Experimental Results  
The DR-NSGA-III-MGA algorithm is used to optimize the three-stage wellbore trajectory. The model is validated against historical data from three horizontal wells in the Daqing Oilfield (provided by Northeast Petroleum University's drilling database). For Well DQ-01 (target depth 2100 m), the optimized trajectory by DR-NSGA-III-MGA shows a 92% match with the actual drilling path, with friction/torque values within 5% of field measurements. Consultation with two senior drilling engineers (with 15+ years of experience) confirmed that the selected metrics (length, friction, torque, etc.) align with real-world priorities: Target accuracy and torque are the top concerns in shale gas wells. The well depth structure data are shown in Table 1, and the trajectory is displayed in 3D and 2D projections, as shown in Figure 8. Key input parameters for the simulation are based on practical drilling scenarios. Geological conditions: shale formation with a pressure of 35 MPa, consistent with typical shale gas reservoir characteristics. Drilling tools: 215.9 mm bit diameter (standard for horizontal wells), drill string weight of 25 kg/m (commonly used in field operations), and a friction coefficient of 0.25 (typical for shale-steel contact). Target parameters: 2100 m target depth and 1500 m horizontal section length, aligned with common design specifications for domestic shale gas wells. It can be seen from the chart that the DR-NSGA-III-MGA algorithm shows good optimization ability and engineering adaptability in wellbore trajectory design. Validation using field data from a shale gas well in the Songliao Basin (well depth 2150 m, target layer thickness 5 m) shows that the trajectory optimized by DR-NSGA-III-MGA deviates by \(\leq\)0.8 m from the actual drilling path, with 12.3% lower friction and torque than the field scheme, confirming applicability in complex geological conditions. The three-dimensional trajectory diagram clearly shows the whole process of the smooth transition of the trajectory from the starting point to the target point. Each section is naturally connected, which is  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Serial Number** & **North** & **East** & **Height** & **Serial Number** & **North** & **East** & **Height** \\ \hline
1 & 0 & 0 & 0 & 18 & 319.99 & 262.92 & 776.75 \\
2 & 1.38 & 1.14 & 412.66 & 19 & 375.20 & 308.29 & 778.  
in line with the typical configuration of the deflecting-stabilizing section and has strong construction feasibility. In the horizontal projection diagram, the trajectory is close to the straight line and the azimuth control is accurate, indicating that DR-NSGA-III-MGA has strong stability in horizontal orientation and can effectively avoid the risk of horizontal deviation. It can be seen from the north and east projections that the trajectory deflection transition is gentle, there is no mutation, and the vertical control is proper, reflecting the effective control ability of the algorithm to the trajectory curvature change, which is conducive to improving the stability and safety of the wellbore trajectory. The DR-NSGA-III-MGA algorithm can not only realize the compression of the total length of the wellbore in the multi-objective optimization design of the wellbore trajectory, but also control the curvature change and trajectory smoothness, which significantly improves the trajectory quality and constructability, and has good practical application potential. Table 1 shows the results of the key parameters obtained by the DR-NSGA-III-MGA algorithm for wellbore trajectory optimization. The vertical depth of the build-up point is 374.79 m, indicating that the DR-NSGA-III-MGA algorithm can quickly complete the transition of the vertical section in the early stage and control the trajectory in advance. It is helpful to improve the flexibility of the trajectory design and provide a more sufficient adjustment space for subsequent segments.