# An Analytical Method for Gas Flow Measurement Using Conservative Chemical Elements
## 3 Results and Discussion
### Validation of Gas Flow Measurement Using a Conservative Element  
To check the reliability of the proposed method (Method II), we compared the measurement using an MFM and verified the gas flow for a continually flowing single gas or a mixture of two gases (N\({}_{2}\): CO\({}_{2}\) = 33:66), as shown in Figure 3. Although the gas was injected at a constant rate (300 mL/min), the flow rate of the MFM showed a significant change. In addition, we observed high flow rates in the section where the internal temperature of the reactor remained high (850 \({}^{\circ}\)C), despite the loading of the fixed flow at 300 mL/min from the beginning. This reflected the temperature-induced gas expansion characteristics, and the gas flow was dependent on the internal temperature because this experiment was carried out under atmospheric pressure. Interestingly, the fluctuation of the gas flow measured by the MFM decreased gradually until the internal temperature of reactor reached 850 \({}^{\circ}\)C. When heating the furnace, the temperature of the furnace did not rise with the set point at an ideal constant ramping rate. As shown in Figure 3, temperature fluctuation was derived from the degree of heater power, which appeared to be the result of gas flow fluctuation. Moreover, gas flow measured by both the MFM and a conservative element gradually decreased immediately after reaching the reaction temperature of 850 \({}^{\circ}\)C. According to the ideal gas equation (PV = nRT), temperature and pressure are the only factors that control the volumetric expansion of gas. Considering that our experiments were conducted in an open system in which the pressure was negligible, the tendency for the gas flow to decrease even at the constant temperature of 850 \({}^{\circ}\)C is difficult to understand. These patterns were observed in experiments applied to both single and mixed gases. Nevertheless, the gas flow rates identified only for the single gas using the MFM and those using Method II were consistent (Figure 3a). By comparison, when a mixed gas of N\({}_{2}\) and CO\({}_{2}\) was injected, there was a significant difference depending on the measuring method (Figure 3b). Even considering the gas conversion factor from the injected gas mixing ratio, the gas flow measured using the MFM differed from the injection flow. Unlike that of the MFM, the flow using Method II was consistent with the total injected flow rate (300 mL/min), although this was limited within the measuring interval. This suggests flow measurement using a conservative element is superior to that undertaken using mechanical devices such as an MFM.  
Figure 2: Gas flow rate measured by an MFM with changes in CH\({}_{4}\) mixing ratio.  
We also estimated the reaction paths by precisely measuring the gas flow rate. Figure 4 illustrates the changes in each gas composition identified via the gas analysis. In terms of flow rate contribution, the flow rate with N2 as a conservative element was consistent with the injection flow (200 mL/min). This result demonstrates the high reliability of the gas flow measurement using the conservative element (Method II). However, CO2 showed a flow rate lower than the injection flow (100 mL/min) in a certain section (620-850 \({}^{\circ}\)C). In the above section of lower CO2 flow, the opposite result was found for CO, and the flow rate value was also the same as the flow reduction of CO2. Although CO was not injected in this experiment, it appears that the injected CO2 was converted to CO in a certain section by the Boudouard reaction (CO2(g)+C(s)+2 CO(g) at over 700 \({}^{\circ}\)C) [10].