## 3 Results and Discussion
### Flow Characteristics in the Differential Motion Assembly
To further study the drilling fluid velocity distributions at the vortex area, we extracted the velocity at a monitoring line 220 mm away from the flow inlet, as shown in the inset illustration of Figure 7. The velocity distributions at the monitoring line with different inlet flow rates are shown in Figure 7. Along the radial direction, the flow area could be divided into the central jet area and vortex area according to the flow characteristics of the drilling fluid. In the central jet area, the velocity was stable at a larger value in the area with a radius less than 7 mm, such as 64 m/s for the inlet flow rate of 0.04 m\({}^{3}\)/s. As the inlet flow rate decreased from 0.04 to 0.01 m\({}^{3}\)/s, this velocity value gradually decreased to 16 m/s. With increasing radius, the velocity started to decrease and then gradually entered the vortex area where the velocity gradually decreased to nearly 0 m/s with increasing radius and then increased slowly. This trend conformed to the typical characteristics of the vortex. Near the wall with a diameter of 90 mm, the velocity of the vortex was relatively slow, less than 7.3 m/s. As the inlet flow rates decreased from 0.04 to 0.01 m\({}^{3}\)/s, the velocity near the wall decreased from 7.3 to 1.9 m/s. At low velocity and small impact angles, the particles in the drilling fluid could still remove material from the wall with a diameter of 90 mm by plowing, which resulted in erosion [47]. As the flow rate increased from 0.01 to 0.04 m\({}^{3}\)/s, although the size of the vortex area did not increase, the vortex velocity near the wall increased by 3.8-fold, which may lead to more severe surface erosion. Figure 6: Velocity streamlines in the differential motion assembly with different inlet flow rates (0.01\(\sim\)0.04 m\({}^{3}\)/s); the fluid viscosity was set as 100 mPa-s.  
Figure 7: Velocity distributions at the monitoring line with different inlet flow rates; the fluid viscosity was set as 100 mPa-s.  
Pressure contours in the differential motion assembly with different inlet flow rates are shown in Figure 5.0 There was an obvious pressure drop when the drilling fluid flowed through the differential motion assembly. In this study, the outlet pressure was set to 30 MPa during the calculation. With an increase in the inlet flow rate from 0.01 to 0.04 m\({}^{3}\)/s, the inlet pressure increased from 30.1 to 31.4 MPa, and the pressure drop \(\Delta P\) between the inlet and outlet of the differential motion assembly increased by 14-fold. Due to the greater pressure drop of 1.4 MPa when the inlet flow rate was 0.04 m\({}^{3}\)/s, under the long-term impact of the drilling fluid, there is a risk of cutting the pins before the ball is dropped, which may trigger the differential motion assembly at the wrong time and result in the failure of the IPP-Coring process. Therefore, when a deep oil and gas IPP-Coring operation is conducted under large pump displacement, it is necessary to replace the pins with those of greater shear strength or diameter. In addition, the lowest pressure of 28.3 MPa (inlet flow rate 0.04 m\({}^{3}\)/s) occurred at the inlet of the ball seat of the differential motion assembly where the flow velocity was extremely fast, up to 65 m/s. Therefore, severe erosion may occur in this zone due to the complex flow characteristics. In general, there was a severe vortex area in the differential motion assembly due to the presence of the ball seat and, with the increase in inlet flow rate, the velocity of the drilling fluid and the pressure drop between the inlet and outlet increased remarkably. These conditions may increase the erosion rate on the inner surface of the differential motion assembly and the risk of cutting the pin at the wrong time, which would damage the differential motion assembly and lead to the failure of the IPP-Coring process.