## 3 Simulation and Analysis
In order to obtain the response characteristics of CCS under different flow patterns, the finite element models of six flow patterns, including stratified flow (ST), stratified flow with mixing at the interface (ST&MI), dispersed flow that includes dispersion of oil in water and water flow (DO/W&W), oil in water emulsion (O/W), dispersion of water in oil and oil in water flow (DW/O&DO/W), and water in oil emulsion (W/O), which were proposed by [PERSON] et al. [9], were constructed. For ST flow patterns, the meshed model of the CCS is shown in Figure 4, where the blue color represents the oil phase and the area outside the annular runner represents the water phase for the ST flow pattern. In Figure 4, the water cut is 0.6. In order to better analyze the static response characteristics of the CCS, the sensors CYS and COS were modeled and simulated. Because the CCS is the combination of the CYS and the COS, the CYS and the COS were simulated with the same structural parameters and simulation conditions as the CCS. Using COMSOL simulation software, the static response curves of the CCS, CYS, and COS under the ST flow pattern were calculated by the finite element method as shown in Figure 5, where the math of the CCS represents the results calculated by the measurement principle of the CCS. As can be seen from the figure, the static response values of the CCS were basically consistent with the results obtained through the mathematical model, and the \(\rm C_{N}\) decreased with the increase of the water cut. The reason for the slight difference between the simulation results and the results calculated by the mathematical model is that in the mathematical model of the CCS, the capacitance C3 and C4 introduced by the boundary effect near the oil-water interface were approximately calculated. Compared with the CYS, the slope of the result curve of the CCS in the water cut range 0-0.4 and 0.6-1 increases obviously, which indicates that the resolution oil of the CCS was better under an ST flow pattern. The COS has no response when the water cut was greater than 0.63. The reason is that when the oil-water interface exceeds the center electrode, the oil phase cannot contact the electrode, so the response value of the COS will not change. The results show that the CCS has better resolution abilities compared with the CYS and the COS for the ST flow pattern. Figure 4: Mesh model of the CCS for the stratified flow (ST) flow pattern (a) 3D; (b) XOY section. Figure 6 shows the mesh model of the CCS for the ST&MI flow pattern, where the water cut is 0.5058, the blue color represents oil, and the area outside the annular runner represents water. In order to construct the ST&MI flow pattern, the wave of flow pattern was represented by a sinusoidal curve with a peak value of 1 mm, which represents the wave height of the interface. The static response curves of the CCS, CYS, and COS under an ST&MI flow pattern were calculated as shown in Figure 7. As observed from the figure, the variation trends of the three sensors are approximately the same as the response curves under an ST flow pattern. With the increase of the water cut, the response values decreased. Due to the structural characteristics of fluid fluctuations for the ST&MI flow pattern, the response curve is slightly less smooth than the ST flow pattern. Compared with the response values of the CYS and the COS, the CCS had better response characteristics, which shows that the combined capacitance sensor has a good resolution ability for ST&MI flow patterns with different water cuts. Figure 5: The static responses of the CCS, the cylindrical capacitance sensor (CYS), and the coaxial capacitance sensor (COS) for the ST flow pattern. Figure 6: Mesh model of the CCS for a stratified flow with mixing at the interface (ST&MI) flow pattern (**a**) 3D; (**b**) XOY section. The mesh model of the CCS for the DO/W&W flow pattern is shown in Figure 8, where the water cut is 0.8907.