## 3 Results and Discussion
### Impact of Drilling Fluid
#### 3.2.3 Impact of Kinematic Viscosity  
Figure 26 shows the distribution patterns of annular velocity under varying kinematic viscosity. The deviation angle was defined as the angle between the vertical direction and the line connecting the drill string center to the wellbore center, quantifying lateral displacement. As shown in the analysis, variations in kinematic viscosity significantly enhance the coupling effects between drilling fluid and the drill string. At a kinematic viscosity of \(1\times 10^{-6}\) m\({}^{2}\)/s, the drill string deviates to the right by approximately 10.7\({}^{\circ}\). With increasing drilling fluid viscosity, the drill string gradually shifts from rightward to leftward deflection within the borehole, with a critical viscosity threshold of \(2.5\times 10^{-5}\) m\({}^{2}\)/s. At a viscosity of \(9\times 10^{-5}\) m\({}^{2}\)/s, the leftward deflection angle reaches 56.99\({}^{\circ}\). A higher viscosity induces greater internal shear stress in the fluid, enabling the rotating drill string to more effectively drive fluid into the right-side annular clearance. Additionally, increased viscosity significantly amplifies the dynamic pressure effect of the annular fluid, pushing the drill string toward the left borehole wall. Figure 26 further demonstrates that elevated viscosity enlarges radial velocity gradients, with fluid velocities near the wellbore wall notably lower than those adjacent to the drill string. This phenomenon arises because higher viscosity suppresses internal momentum transfer within the fluid, while axial flow cancels out rotational momentum induced by the drill string before it can propagate radially. Figure 25: Distribution patterns of annular velocity under varying drilling fluid flow rates: (**a**) 30 L/min; (**b**) 50 L/min; (**c**) 70 L/min. Figure 27 shows the trend of annular pressure variation. An increase in kinematic viscosity significantly alters the circumferential pressure distribution: as more fluid is entrained into the right-side clearance channel, the pressure in this region gradually rises to a maximum of approximately 6000 Pa. Conversely, the pressure in the left-side clearance channel decreases substantially, reaching a minimum of about 51 Pa. In heterogeneous shale formations, uneven circumferential pressure distribution can induce localized stress concentration, elevating the risk of wellbore collapse and affecting the transformation of the reservoir. Consequently, the use of high-kinematic-viscosity drilling fluids should be avoided during drilling operations to mitigate these risks. Furthermore, Figure 28 illustrates the axial velocity distribution in the left annular clearance. At lower kinematic viscosities, the fluid velocity exhibits a relatively uniform axial distribution. However, as the kinematic viscosity increases, the flow regime gradually transitions to laminar flow, with a critical value of \(2.5\times 10^{-5}\) m\({}^{2}\)/s. The narrowing of the clearance due to drill string lateral displacement leads to an expansion of high-velocity fluid zones. The emergence of laminar flow implies that cuttings in the bottom-hole region struggle to be transported upward via circumferential flow. Additionally, the leftward deflection of the drill string further inhibits the removal of bottom-hole cuttings. During shale gas drilling operations, the persistent retention of bottom-hole cuttings can impair fracturing efficiency if not effectively removed, thereby reducing shale gas production rates. Therefore, drilling fluids with a kinematic viscosity higher than \(2.5\times 10^{-5}\) m\({}^{2}\)/s should be used with caution to prevent the occurrence of laminar flow. Figure 29 shows the effect of kinematic viscosity on friction torque. Compared to direct contact between the drill string and wellbore wall, the presence of drilling fluid effectively reduces friction torque. With the increase in kinematic viscosity, the friction torque continuously decreases, with the maximum reduction reaching 58.31%.