## 3 Results and Discussion  
### Advantages of Surface Vibrating Technology  
Nominal WOB equals the vector sum of the hook load \(F_{top}\), the gravity of the drill-string, the real WOB, and the static friction between the drill-string and the borehole in the axial direction of the drill-string. A nominal constant WOB is applied and we expect to obtain a constant real WOB and ROP in conventional slide drilling. However, the real WOB and ROP are variational because of the existence of friction between the drill-string and the borehole wall and the stick-slip motion of the drill-string. We choose a representative horizontal well to analyze its load transfer characteristics. The well profile is shown in Figure 2. The well depth is 4200 m, and the kickoff point and landing point are 1290 m and 2190 m, respectively, and the build-up rate is 0.0524 rad/30 m. The drill-string is made up of \(\mathcal{O}\)127 mm drill pipe, whose inner diameter, density, and elasticity modulus are 108.6 mm, 7850 kg/cm\({}^{3}\), and 210 GPa, respectively. Other calculating parameters are as follows: the static and dynamic frictional coefficient are equal to 0.3 and 0.25 (static coefficient is always 1.2 times of dynamic coefficient [6]), respectively. The time step is 0.00005 s and the space step is 5 m. The exchange critical velocity of static friction and dynamic friction is 0.01 m/s. A binary model of the ROP and the WOB is adopted (see Equation (13)), in which \(WOB_{cri}=20\) KN, \(\text{a}=1\), and \(K^{\prime}=5\times 10^{-5}\). Under such circumstances, the static friction and dynamic friction of the whole drill-string are 173 kN and 144 kN, respectively. Therefore, the maximal friction released by vibration equals 29 kN. The increase in the WOB also includes the exciting force and inertia force of the drill-string.  
Figure 3 shows the variations in the real WOB and ROP with a different nominal WOB. From Figure 3, although the nominal WOB applied at the surface is constant, the real WOB and ROP at the bottom are fluctuant because of the static-d  
stick-slip. Moreover, the real WOB transmitted to the bit increases with the increase in the nominal WOB. The amplitude and frequency of real WOB fluctuation decrease with the increase in the nominal WOB because of the continuous and steady motion of the drill-string under a high nominal WOB.  
Even though under a certain nominal WOB, the load transfer efficiency decreases in a well with a longer horizontal section and higher friction coefficients. As can be  
Figure 3: Variations in real WOB and ROP with different nominal WOB. (**a**) Real WOB; (**b**) ROP.  
Figure 2: Well profile of a horizontal well. (**a**) Vertical projection view. (**b**) Horizontal projection view.  
seen in Figures 4 and 5, the amplitude of the downhole WOB fluctuation increases and the frequency decreases with the increase in the horizontal section length and friction coefficients when the nominal WOB equals 100 kN, which means that the load transfer becomes worse.  
As can be seen from Figure 3, the WOB fluctuates severely under a lower WOB, and the drill-string cannot move continuously under 60 kN WOB. The reason for this is the stick-slip phenomenon of the drill-string caused by the static-dynamic friction switch between the drill-string and the borehole wall. If we apply an axial exciting force with an amplitude of 20 kN and a frequency of 10 Hz on the drill-string at the surface, will the load transfer be improved? Figure 6 shows the WOB changes during typical slide drilling and surface vibration drilling. From Figure 6, the real WOB and ROP improve significantly after applying vibration at the surface, and the WOB curve becomes smoother, which is beneficial for the drilling operation.