## 1 Introduction  
Drilling complex structural wells (such as directional, horizontal, and extended reach wells) is essential for the successful exploitation of petroleum and natural gas reserves. These types of wells ensure optimal formation exposure and increase the chances of hitting the pay zone. Moreover, these wells are suitable for future stimulation techniques, which can significantly improve well production efficiency and final recovery rates. Directional drilling realized by combining a positive displacement motor (PDM) and measurement while drilling (MWD), which is known as slide drilling, is an effective well trajectory control method and is widely used worldwide. This technology has its drawbacks, as the lack of rotation in the drill-string creates significant friction with the borehole wall. As a result, the transfer of axial load to the bit decreases, leading to a reduction in both the rate of penetration (ROP) and the extended-reach limit. Meanwhile, the stick-slip phenomenon of the drill-string is further intensified by the frequent transform between static and dynamic friction force. Reducing the amount of resistance between the drill-string and the borehole wall and enhancing the effectiveness of load transfer during directional drilling are essential objectives with significant importance in petroleum drilling that have been given attention for several years [1]. Two main approaches are typically employed in friction reduction research, namely reducing the normal contact force and decreasing the coefficient of friction. To decrease the normal contact force, one can optimize the well track and make use of a lightweight drill pipe. To reduce the friction coefficient, it is possible to develop a high-performance lubricant, utilize a cylindrical roller sub, and incorporate a nonrotating protective joint. Adding vibrators to the drill-string was first proposed by [PERSON] in 1983 as a means of reducing friction between the drill-string and the borehole wall. Although categorized as passive methods of friction reduction, these techniques have limited effectiveness [2]. In the past, the concept of utilizing a vibrator for petroleum drilling technology was not extensively researched. However, in recent years, various technology service companies have started conducting application studies on this idea and concentrated their efforts towards enhancing the vibrator's development [3; 4]. Axial vibration friction reduction tools were first developed and widely used, represented by Agitator of National Oilwell Varco [5; 6]. Then lateral vibration friction reduction tools were developed, represented by Xcite. The research concluded that axial vibration tools provide significantly more effective friction reduction in horizontal wells [7]. Axial and lateral vibration friction reduction patterns are realized by adding downhole tools in the drill-string, which will consume hydraulic energy. Moreover, drillers need to trip out and reassemble the makeup of the string when the well depth goes to a deeper extent. Contrary to the aforementioned vibration technologies, the automatic surface rocking technology utilizes the top drive to rotate the drill-string to the right limit and then to the left limit by a predetermined amount, without relying on any downhole tool. This innovative technique is exemplified by the \"Slider\" [8] and \"DSCS\" [9] systems. However, it is sometimes difficult to control the real-time tooface orientation because of dynamic reactive torque from bit-rock interaction. After weighing the pros and cons of the aforementioned vibration methods, our proposition is to apply axial vibration on the drill-string at the surface. This will reduce the friction between the drill-string and the borehole wall while enhancing the efficiency of load transfer. The excitation means may be displacement or force.