## 3 Results and Discussion
### Safety Evaluation of Surface Vibrated Drill-String  
The introduction of vibration in drilling can reduce the friction between the drill-string and the wellbore wall and improve the load transfer efficiency, and a higher exciting amplitude or frequency is good for improving friction reduction and load transfer effectiveness. However, vibration of the drill-string will simultaneously increase the internal stress and the failure risk of the drill-string. Therefore, the increase in the exciting amplitude and frequency must be restricted by the dynamic safety of the drill-string. The methods for evaluating the drill-string's safety mainly include the safety factor method and the real-time monitoring of downhole tools. Drill stem design and operation [32] indicates that overload or fatigue are the two main reasons for drill-string failure. In the process of drill-string design, the safety factors in the stretch and torsional direction are 1.0 to 1.3, which guarantee the real stress of the drill-string is lower than the allowable stress. However, the safety factor method does not consider the effect of induced vibration on drill-string safety. A large number of statistical results of drill-string failure indicate that drill-string vibration will result in a dramatic change in the drill-string stress on the premise that the drill-string stress is lower than the allowable stress, which will influence the safety of the drill-string. Based on the above considerations, several petroleum technology service corporations have developed underground vibration monitoring systems (such as the VSS system of Baker Hughes, MVC system of Schlumberger, and TVM system of Weatherford; the installation methods of these systems are different) to control the vibration and decrease the dynamic stress level of the drill-string by adjusting the drilling parameters in the drilling process. We adopted the method of Baker Hughes (see Table 1[33]) to evaluate the safety of the drill-string axial vibration at the surface technology proposed in this paper. Figure 6: WOB changes during surface vibration drilling. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Grade** & **Vibration Level in Axial Direction RMS(g)** & **Color Marking** & **Evaluation Result** \\ \hline \(0\) & [0.0, 0.5) & green & safe \\ \(1\) & [0.5, 1.0) & green & safe \\ \hline \(2\) & [1.0, 2.0) & yellow & caution \\ \(3\) & [2.0, 3.0) & yellow & caution \\ \hline \(4\) & [3.0, 5.0) & & \\ \(5\) & [5.0, 8.0) & & \\ \(6\) & [8.0, 15.0) & red & danger \\ \(7\) & [15.0, \(\infty\)) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Vibration level classification (Baker Hughes INTEQ company). Figure 7: _Cont._  
acceleration, a lower value is obtained at 5 Hz and 10 Hz and the highest value is obtained at 0.5 Hz in the vertical section, while a lower value is obtained at 10 Hz to 30 Hz and the highest value is obtained at 0.5 Hz to 5 Hz in the horizontal section. For RMS acceleration, a lower value is obtained at 0.5 Hz to 5 Hz and the highest value is obtained at 20 Hz to 30 Hz in the vertical section, while a lower value is obtained at 10 Hz to 30 Hz and the highest value is obtained at 0.5 Hz to 5 Hz in the horizontal well section. Therefore, we can see that the RMS acceleration shows an opposite trend in the vertical and horizontal sections. When the frequency equals 10 Hz, the differences in the RMS between the different well sections are small and the RMS acceleration of the whole drill-string has a lower value. Therefore, 10 Hz is the optimum value for drill-string safety under the conditions set by the given parameters. According to the vibration level classification method shown in Table 1, the safety grades along the drill-string under different exciting parameters are shown in Table 2. From Table 2, the  
Figure 8: Maximal and root mean square acceleration along the drill-string under different exciting force amplitude. (**a**) Max: 10 kN. (**b**) RMS: 10 kN. (**c**) Max: 20 kN. (**d**) RMS: 20 kN. (**e**) Max: 30 kN. (**f**) RMS: 30 kN.