## 4 Experiments and Analysis
### Analysis of Dynamic Experiment Results  
In order to obtain a reliable measurement value, the output response of the instrument under different flow rates and water cuts was recorded. The output frequency value was used to reflect the capacitance value of the CCS, and the capacitance value had a certain relationship with the water cut. Thus, the frequency was used to calibrate the water cut. The frequency values obtained from the CCS in the pure water phase and the pure oil phase are listed in Table 5. It can be seen that the frequency value obtained from the CCS in the pure oil phase is larger than that in the pure water phase, which is consistent with the results of the simulation as shown in Figure 5.  
The frequency signal from the CCS with the flow rate of 30 m\({}^{3}\)/d varies with time as shown in Figure 21. As observed from the figure, the frequency values decrease with the increase of the water cut, which was consistent with the simulation results of the CCS. In addition, it can be seen preliminarily that the higher the water cut, the more stable the frequency. Figure 21: Frequency signal obtained from the CCS with a flow rate of 30 m\({}^{3}\)/d. Figure 20: Flow pattern map of oil-water two-phase flow. (**a**) Flow pattern map based on flow rate and water cut; (**b**) flow pattern map based on oil and water flow velocity. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Pure Water Phase** & **Pure Oil Phase** \\ \hline Frequency values (Hz) & 224 & 1918 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Frequency values obtained from the CCS under conditions of a pure water phase and a pure oil phase. In order to be more conducive to the comparison of values, the output frequency of the instrument was standardized by that of the pure oil phase and the pure water phase to obtain the standardized response. Figure 22 shows the response law of the instrument under different flow rates and water cuts. It can be seen from the figure that when the flow rate is 3-60 m\({}^{3}\)/d, and the water cut is 0-1, the instrument has a response characteristic. When the water cut is less than 0.2, the trend of the CCS response curve is relatively smooth. When the water cut reaches 0.3, the response values of the CCS become larger, especially when the flow rate is greater than 40 m\({}^{3}\)/d. This is because when the water content is greater than 0.3, the height of the oil-water interface reaches the boundary of the central electrode rod of the CCS. In this case, the capacitance of the sensor was more easily affected by the electrode rod, which was consistent with the simulation results. When the flow rate increased, the oil-water interface at the central electrode rod became more unstable. Additionally, the more susceptible the CCS was to the electrode rod, the greater the change of response value. The CCS was designed to measure the water cut under different flow rates. When measuring the water cut with the CCS, the flow rate of fluid is known. According to the flow rate of the fluid and the response value of the CCS as shown in Figure 22, the water cut of the fluid can be obtained. Thus, for a certain flow rate, the CCS has response characteristics under different water cuts, which indicates that the CCS can effectively measure the water cut. Although the resolution decreases below 10 m\({}^{3}\)/d and decreases to the minimum at 3 m\({}^{3}\)/d, it still has resolution and is better than the conventional coaxial and cylindrical capacitance sensors. In addition, because different flow patterns will appear at a certain flow rate in the dynamic experiments, it is difficult to obtain the corresponding flow pattern and the result curve of the simulation experiment. Nevertheless, it can be seen from the figure that for different flow patterns, the CCS has a good resolution, which shows that the calibration results of the CCS were consistent with the simulation results.