## 3 Simulation and Analysis
In the process of constructing the model, in the upper water phase, the oil droplets with the same radius of 0.2 mm were randomly distributed in different axial and radial cross sections. The initial number of oil droplets was 200. The water cut was changed by changing the quantity of oil droplets. Because of the uneven distribution of oil droplets, the mesh model was encrypted. Figure 8a shows the relative position of the oil droplet to the center electrode, and Figure 8b is the 2D model of the XOY section under the DO/W&W flow pattern. Figure 9 shows the static responses of the CCS, CYS, and COS for the DO/W&W flow pattern under different water cuts. Obviously, with the increase of the water cut, all response values showed a downward trend. From the analysis of the figure, the sensor resolution of the COS was the largest among the three sensors. The resolution of the CCS was greater than that of the CYS under the DO/W&W flow pattern. The variety of sensor response values was due to the oil droplets that attached to the electrode led to the variety of the thickness of the insulating layer between the sensor electrodes, so the response value of the sensor was changed. Moreover, the CCS had two electrodes to contact fluids, and oil droplets were more likely to attach to the sensor electrodes, which resulted in higher resolution of the CCS than that of the CYS. In addition, the non-smooth response curve of the sensor was mainly caused by the random distribution of the oil bubble, which better reflects the real situation of the actual measurement. Figure 8: Mesh model of the CCS for the dispersion of oil in water and water flow (DO/W&W) flow pattern (**a**) 3D; (**b**) XOY section. Figure 7: The static responses of the CCS, CYS, and COS for the ST&MI flow pattern. For the O/W flow pattern, the mesh model was constructed as shown in Figure 10, where the water cut is 0.795. The model was constructed similar to that of the DO/W&W flow pattern. The difference was that oil droplets of the same radius were also randomly distributed in the lower layers of the fluid. The initial number of oil droplets was 400. The water cut was changed by changing the quantity of oil droplets. The grid of the model was also encrypted. Figure 10a shows the relative position of oil droplets and the center electrode, and Figure 10b is the 2D model of the XOY section under the O/W flow pattern. The static responses of the CCS, CYS, and COS for the O/W flow pattern under different water cuts are shown in Figure 11. It can be seen from the figure that the response result of the DO/W&W flow pattern is similar to that of the O/W flow pattern. Likewise, the CCS and the COS have greater resolution than the CYS for the O/W flow pattern. Because of the complexity of the DW/O&DO/W flow pattern, the simplified model was used to simulate the DW/O&DO/W flow pattern. Figure 12 shows the finite element model for the DW/O&DO/W flow pattern with a water cut of 0.5543. The upper part of the runner was evenly distributed in the continuous oil phase, and the lower part of the flow runner was distributed in the continuous water phase. The oil-water interface was composed of sinusoidal curves with a peak value of 1 mm. By changing the oil droplet size in the continuous water phase and the water droplet size in the continuous oil phase, the capacitance value of the CCS for the DW/O&DO/W flow pattern  
Figure 10: Mesh model of the CCS for the oil in water emulsion (O/W) flow pattern (**a**) 3D; (**b**) XOY section. Figure 9: The static responses of the CCS, CYS, and COS for the DO/W&W flow pattern. can be measured under different water cut conditions. Figure 12a shows the relative position of the lower layer to the oil droplets with a radius of 1 mm, in which the number of radial sections of the droplets was 20, each radial segment consisted of four oil droplets, and the total number of droplets in the continuous water phase was 80.