# Sand Removal Mechanism of a High-Speed Roller Bit with Helical Sealing
## 3 Methods  
### Numerical Simulation  
This study uses FLUENT 15.0 (ANSYS, Inc. Canonsburg, PA, USA) to simulate the flow field distribution of helical sealing. In the actual working conditions at the bottom of the well, the temperature of all fluid boundaries is the same, and the movement of the fluid is not affected by the temperature. Therefore, the assumption in the simulation solution process is that the thermal coupling was not considered. After discovering and confirming the bottom hole gas overflow, it is necessary to carry out relevant operations to prevent the bottom hole gas from overflowing before drilling can continue. Therefore, when the roller bit is working, there is almost no gas in the bottom mud, the gas overflow from the bottom hole was not considered. Due to the certain gap between the spiral seal ring and the bearing, the spiral seal ring does not collide with the bearing to cause deformation when the roller bit is working. Since the material of the spiral sealing is metal, the deformation caused by the temperature is small and negligible. Therefore, the deformation of the metal spiral seal was not considered. The simulation model in this paper was generated by modeling software. In this process, the actual roller bit model was solved by Boolean operation, and the cavity model of the roller bit, that is, the flow channel model in Figure 2 was obtained. The mesh generation is an important step in flow field simulation. The mesh types are mainly divided into structured and unstructured grids. The structured grids are homogenous and are difficult to construct for the complex shape. The spatial distribution of unstructured grids is random with no specific structural characteristics and adaptability and can adapt well to a complex shape. An unstructured mesh was generated in this paper because the helical structure is complex and small in size. The generated mesh had a cell number of 219,122, and the number of nodes was 54,262. Both the inlet and outlet were set as pressure boundary conditions. A shallow well with a depth of 940 m was studied in this paper. The mud density was 1200 kg/m\({}^{3}\) and the mud viscosity was 0.2 Pa\(\cdot\)S. Additionally, the pressure at the mud inlet was 11 MPa. Because the theoretical pressure difference between the inside and outside of the sealing chamber is 0.3-0.7 MPa, the actual pressure difference was greater than the theoretical pressure difference. Moreover, the safety factor was 1.5, and the pressure difference between the inside and outside was set at 1.05 MPa. The outlet pressure was 12.05 MPa [33]. The wall boundary condition was used for simulation, and a non-slip wall was set. The inner wall was set as a rotating wall, which comprises an inner roller hole and helical sealing ring. The rotational speeds of the roller and sealing ring were the same. Other walls were set as static walls with zero velocity [34], and the rotational speed of the bit was 200 r/min. Figure 2: Boundary conditions. It was assumed using the discrete phase model in FLUENT that the second phase (i.e., the particle phase) was thin, such that the interaction between debris pieces and the effect of the particle volume fraction on the continuous phase need not be considered. This assumption means that the volume fraction of the discrete phase must be low, generally less than 12 percent. The drilling bit parameters were an 8 1/2-inch drilling bit; i.e., \(d=216\) mm. The mudflow rate was \(V=30\)L/s and the drilling rate was 6 m/h. The volume of rock debris per second \(V_{Y}\) was  
\[ \begin{array}{ll}V_{Y}&=\pi\left(\frac{d}{2}\right)^{2}\times h=3.14\times \left(0.108\right)^{2}\times\frac{6}{3600}\\ &=0.00006104\text{m}^{3}/\text{s}\\ &=0.06104\text{L}/\text{s}\end{array} , \tag{4}\]  
The volume fraction of rock debris per second was  
\[\frac{V_{Y}}{V}=\frac{0.06104}{30}=0.002047=0.2047\%\leq 10\%. \tag{5}\]  
The calculation results show that the volume fraction of rock debris is far less than 10%-12%.