## 3 Results and Discussion
### Dynamic Response Under Drilling Parameters
Although the increase in feed pressure will intensify the squeezing between the drill string and the wellbore wall, it has no effect on the wall force of the fluid. Figure 18 clearly reveals the significant influence of different rotational speeds (400 rpm, 600 rpm, and 800 rpm) on the annular velocity field distribution under conditions of constant drilling fluid parameters: a flow rate of 50 L/min, a kinematic viscosity of 1 \(\times\) 10\({}^{-6}\) m\({}^{2}\)/s, and a density of 1000 kg/m\({}^{3}\). Due to the eccentric positioning of the drill string within the wellbore (located in the lower-right region of the annulus), a narrow annular gap is formed between the drill string and the wellbore wall in this area. Observational results indicate a highly non-uniform fluid velocity distribution within the annulus. Specifically, in the narrow annular region of the lower-right, due to eccentricity, a distinct high-velocity zone is formed owing to the strong shearing and dragging action  
Figure 16: Effect of rotational speeds on drill string dynamics considering annular fluid interaction. Figure 17: Effect of feed pressure on drill string dynamics considering annular fluid interaction. of the rotating drill string (i.e., mechanical disturbance); this high velocity is attributed to the acceleration effect on the fluid within the narrow channel and the direct momentum transfer from the rotating drill string. Critically, as the drill string's rotational speed increases (from 400 rpm to 800 rpm), this high-velocity zone not only expands significantly in the circumferential direction but also experiences an evident increase in its internal fluid velocity magnitude (e.g., at 800 rpm, the area covered by orange and red, representing higher velocities in the lower-right region, is considerably larger than at 400 rpm, with velocities approaching 3.0 m/s). The expansion and velocity intensification of this high-velocity zone are crucial for the efficient transport of cuttings in horizontal wells, significantly enhancing cuttings carrying capacity and improving wellbore cleanliness. This, in turn, optimizes subsequent hydraulic fracturing efficiency by reducing flow resistance and minimizing formation damage. Concurrently, given the relatively narrow annular clearance and the low kinematic viscosity of the drilling fluid, the fluid flow is predominantly characterized by circumferential and axial components, resulting in an insignificant radial velocity gradient. Figure 19 investigates the effect of different feed pressures (10, 13, and 15 kN) on the annular velocity field at a specific rotational speed and with the same drilling fluid parameters as in Figure 18. The results clearly indicate that despite an increase in feed pressure, the overall distribution of the annular velocity field--including the morphology, location, and velocity magnitude of the high-velocity zone--exhibits no significant changes. This demonstrates that the flow field characteristics are insensitive to variations in feed pressure. This insensitivity is presumably because the macroscopic annular flow field is primarily governed by hydrodynamic factors such as drill string rotation and drilling fluid circulation rate, whose effects substantially outweigh minor perturbations to local contact conditions from feed pressure changes. Concurrently, under the drill string parameters of this study (a length of 20 m), variations in feed pressure are unlikely to cause significant alterations in the drill string's macroscopic posture or the annular geometry, and the associated energy may be dissipated through other mechanical interactions (such as drill bit-rock interaction). Therefore, feed pressure has a minor impact on the main annular velocity distribution, a finding relevant for optimizing drilling parameters. Figure 18: Annular velocity field under different rotational speeds: (**a**) 400 rpm; (**b**) 600 rpm; (**c**) 800 rpm.