## 3 Analysis of the Individual Factors Affecting the Stability of the Skid-and-Mud-Return Line  
### Effect Analysis of Drilling Ship Motion  
The effect of drilling ship motion on the stability of the skid-and-mud-return line is analyzed in consideration of the effect of sea wind and current flow. Based on the \begin{table}
\begin{tabular}{c c} \hline
**Rotational Speed (rpm)** & **Reverse Torque (N-m)** \\ \hline
0 & \(-\)320.4 \\
300 & 224.75 \\
600 & 669.83 \\
900 & 1343.63 \\
1200 & 2328.65 \\
1500 & 3620.28 \\ \hline \end{tabular}
\end{table} 
Table 1: Reverse torque at 6 different rotational speeds. \begin{table}
\begin{tabular}{c c c c} \hline
**Number** & **Rotational Speed (rpm)** & **Torque (N-m)** & **Amplitude (mm)** \\ \hline
1 & 0 & 4546.54055 & 2.2229 \\
2 & 300 & 5796.57208 & 2.3618 \\
3 & 600 & 7240.85487 & 2.5285 \\
4 & 900 & 8735.65304 & 2.6466 \\
5 & 1200 & 10,590.07644 & 2.7322 \\
6 & 1500 & 0 & 0.00129 \\ \hline \end{tabular}
\end{table} 
Table 2: Analysis data for 6 sets at voltage Un. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Variables** & **Wind Recurrence** & **Wind Direction** & **Sea Recurrence** & **Water Flow Attack Angle** & **Voltage** & **Rotational Speed** \\ \hline \multirow{4}{*}{Value} & 1 year & 0\({}^{\circ}\) & 1 year & 0\({}^{\circ}\) & 60\%Un & 0 rpm \\  & 5 years & 45\({}^{\circ}\) & 5 years & 45\({}^{\circ}\) & 80\%Un & 300 rpm \\  & 10 years & 90\({}^{\circ}\) & 10 years & 90\({}^{\circ}\) & 90\%Un & 60 rpm \\  & 25 years & 135\({}^{\circ}\) & 25 years & 135\({}^{\circ}\) & Un & 900 rpm \\  & 180\({}^{\circ}\) & & 180\({}^{\circ}\) & 110\%Un & 1200 rpm \\ \hline \end{tabular}
\end{table} 
Table 3: Relevant variables for each analysis factor. Figure 4: Effects of drilling vessel motion on the stability of the skid-and-mud-return line with different attack angles in a 5-year recurrence period: (**a**) equivalent stress, (**b**) displacement, (**c**) rotation angle, and (**d**) bending moment. Figure 5: Effects of drilling vessel motion on the stability of the skid-and-mud-return line with different attack angles in a 10-year recurrence period: (**a**) equivalent stress, (**b**) displacement, (**c**) rotation angle, and (**d**) bending moment. The analysis results indicate that the equivalent stress of the skid-and-mud-return line increases sequentially with the attack angles of 0\({}^{\circ}\), 180\({}^{\circ}\), 135\({}^{\circ}\), 45\({}^{\circ}\), and 90\({}^{\circ}\). The equivalent stress increases less at 0\({}^{\circ}\) and 180\({}^{\circ}\) and increases more from 45\({}^{\circ}\) to 135\({}^{\circ}\). The equivalent stress reaches its peak at a depth of 100 m, as shown in Figure 3a. The displacement of the skid-and-mud-return line also increases sequentially with the attack angles of 0\({}^{\circ}\), 180\({}^{\circ}\), 135\({}^{\circ}\), 45\({}^{\circ}\), and 90\({}^{\circ}\), with a significant increase from 45\({}^{\circ}\) to 135\({}^{\circ}\). The displacement increases with a decrease in the depth of the skid-and-mud-return line, with a lesser increase between 2000 m and 250 m or so. It increases sharply between 250 m and the sea surface. The maximum displacement occurs at the sea surface. This indicates that the main displacement of the skid-and-mud-return line occurs between 250 m and the sea surface, as shown in Figure 3b. With attack angles of 0\({}^{\circ}\), 180\({}^{\circ}\), 135\({}^{\circ}\), 45\({}^{\circ}\), and 90\({}^{\circ}\), the rotation angle of the skid-and-mud-return line increases sequentially. The rotation angle remains almost unchanged between 2000 m and 500 m or so and significantly increases from around 500 m. The maximum rotation angle occurs at the sea's surface, as shown in Figure 3c. The maximum bending moment of the skid-and-mud-return line decreases sequentially with the attack angles of 0\({}^{\circ}\), 180\({}^{\circ}\), 135\({}^{\circ}\), 45\({}^{\circ}\), and 90\({}^{\circ}\).