## 3 Results and Discussion
### Impact of Formation and Friction  
In shale gas exploitation, variations in formation depth and reservoir properties result in a wide range of Young's modulus values for wellbore walls. The dynamic response of the drill string to different formations directly impacts wellbore stability and drilling parameter selection. Figure 36 illustrates the contact force in formations with varying Young's modulus. The collision contact force exhibits a pronounced periodic variation trend, with both its amplitude and frequency increasing as Young's modulus increases. A higher Young's modulus indicates higher formation hardness; during drill string-wellbore collisions, elevated contact stiffness leads to larger normal contact forces, stronger rebound effects, and intensified perturbations on the wellbore wall. In softer formations, the drill string will not experience excessive rebound. However, the damping effect of softer formations can also have a hysteresis effect on the movement of the drill string, which is not conducive to the elastic recovery of the deformed drill string to a certain extent. As illustrated in Figure 37, the kinetic energy of the drill string increases sharply with the elevation of the formation Young's modulus, reaching a maximum of 1384.69 J. This phenomenon primarily arises because, in harder formations, the drill string undergoes significant rebound due to contact impact forces, whereas in softer formations, a substantial portion of the energy is absorbed by the formations, thereby suppressing random vibrations. Consequently, when drilling through hard formations, particular attention should be paid to mitigating drill string vibrations to prevent wellbore instability and drill string failure. Figure 36: Contact force in formations with varying Young’s modulus. Figure 37: Kinetic energy of drill string in formations with varying Young’s modulus. Figure 38 illustrates the influence of the friction coefficient between the drill string and the wellbore wall on annular velocity distribution. The friction coefficient primarily affects annular velocity by altering the drill string's dynamic behavior. When the friction coefficient is 0.07, the drill string deflects leftward by 5.66\({}^{\circ}\) due to the dynamic pressure effect of the fluid in the right clearance. However, the fluid velocity in the right clearance remains higher than that in the left clearance, influenced by the drill string's rotation direction. At a friction coefficient of 0.15, the leftward deviation angle reduces to 0.58\({}^{\circ}\). As the friction coefficient increases further, the drill string gradually shifts rightward, reaching a maximum deviation angle of 20.83\({}^{\circ}\) at a friction coefficient of 0.5. Although the drill string exhibits leftward deviation under low friction coefficients, the rotational motion of the drill string induces a tendency to climb upward along the right side of the wellbore. Consequently, the leftward deviation angle remains small, reducing the probability of asymmetric cuttings' accumulation in the annulus. As previously analyzed, drilling fluid viscosity significantly influences the deviation angle of the drill string. To mitigate excessive lateral displacement, adjusting the drilling fluid viscosity can help keep the drill string in the optimal position. Specifically, when the formation exhibits low friction coefficients, reducing the kinematic viscosity of the drilling fluid can minimize leftward deviation. Conversely, in formations with high friction coefficients, the addition of drag reducers and increased kinematic viscosity can effectively improve the deviation of the drill string. To enhance field performance based on FSI insights, the following adaptive strategies may be considered: (1) During pump pressure escalation (0.5-8 MPa), prioritize real-time monitoring of low-order vibration modes to enable prompt mitigation measures against resonance.