## 5 Experiments and Discussion
### Effect of the Correction for the Impact of Carbon Dioxide  
Due to the significant impact of carbon dioxide on ultrasonic methane detection, it was necessary to correct the impact of carbon dioxide on the measurement results. In order to verify the corrective effect of the system with respect to carbon dioxide, three concentrations (i.e., 0.5%, 1%, and 1.5%) of CO\({}_{2}\)-air mixtures were prepared as background gases, and gas mixtures composed of CH\({}_{4}\), CO\({}_{2}\), and air with CH\({}_{4}\) concentrations of 0%, 2%, and 4% were prepared according to a volume ratio.  
We first tested the measured values before correction for each methane concentration using a mixture of carbon dioxide and air as the background gas; we then tested the corrected measured values at each methane concentration and compared the measured values before and after carbon dioxide correction. Figure 6 shows the results of the methane concentration measurements before and after carbon dioxide correction.  
Figure 6a shows the actual measured values of methane concentrations with different carbon dioxide concentrations, and the deviations shown in Figure 6b are the difference between the measured value and the actual value. The dotted line represents the measured value before correction and the solid line represents the measured value after correction. A measurement result is marked with * if the measured dual-channel phase difference was converted into a negative value. In the measurement results, there was a large deviation before carbon dioxide correction, and the measured values decreased as the concentration of carbon dioxide increased. As shown in Figure 6a, if the methane concentration was zero, the measured values were all negative. This was because the sound velocity of carbon dioxide is lower than that of air, and the phase of the measuring acoustic tube signal lags behind the phase of the reference acoustic tube signal. When there was only carbon dioxide in the gas mixture with no methane present, or the concentration of methane was quite low, the measured value obtained after the calculation was a negative value. It can be seen  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methane** & **Measured Value/\%** & **Absolute Error/\%** & **Relative Error/\%** \\
**Concentration/\%** & & & \\ \hline
1.00 & 1.02 & +0.02 & 2.0 \\
2.00 & 2.05 & +0.05 & 2.5 \\
4.00 & 4.06 & +0.06 & 1.5 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Test results of methane–air mixtures with concentrations of 1%, 2%, and 4%.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**CO\({}_{2}\) Concentration/\%** & **Measured Value/\%** & **Absolute Error/\%** & **Relative Error/\%** \\ \hline
0.20 & 0.21 & +0.01 & 2.5 \\
0.50 & 0.49 & \(-\)0.01 & 2.0 \\
1.00 & 1.02 & +0.02 & 2.0 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Test results for CO\({}_{2}\)–air mixtures with concentrations of 0.2%, 0.5%, and 1%.  
that the system exhibited good correction with different carbon dioxide concentrations and that the measurement results were more accurate after carbon dioxide correction, thus achieving the requirements for methane gas concentration detection at higher carbon dioxide concentrations.