# A Study on the Effect of O\({}_{2}\) Diffusion on the Retention Time of Inert Agents
## 4 Results
### Experiment Analysis
From this figure, it can be seen that the interface descending velocity \(\partial\dot{H}_{i}/\partial t\) descends in the z-direction at a constant velocity. This shows the same result regardless of the type of inert agent used. However, the interface descending velocity \(\partial\dot{H}_{i}/\partial t\) is different for each agent. This can be attributed to the difference between the outflow volumetric flow \(\dot{V}_{o}\) and diffusion flux \(J_{d}\). The outflow volume flow \(\dot{V}_{o}\) is expected to be similar because the densities of IG-55 and IG-541 are almost the same. Therefore, the advection velocity \(v_{a}\) is expected to be similar according to Equation (3). However, as the interface slope \(\alpha\) is larger for IG-55 than for IG-541, the diffusion velocity \(v_{d}\) is expected to be larger for IG-55. Therefore, the interface descending velocity \(\partial\dot{H}_{i}/\partial t\) for IG-55 is greater than that for IG-541. In addition, because IG-01 has a higher density than IG-55, the advection velocity \(v_{a}\) will be greater for IG-01. However, because the diffusion velocity \(v_{d}\) of IG-55 is large, the interface descending velocities \(\partial\dot{H}_{i}/\partial t\) for IG-01 and IG-55 show small differences. As shown in Figure 10b, this tendency is also the same when the outflow volume flow \(\dot{V}_{o}\) increases. The retention time for each agent was measured. It was measured at a specified height of 1.5 m, based on an O\({}_{2}\) concentration of 0.15. This is shown in Figure 11.  
Figure 7:0 Comparison of the experimental results of the interface descending velocity \(\partial\dot{H}_{i}/\partial t\) when the O\({}_{2}\) concentrations were 0.15: (**a**) Comparison of 8 holes; (**b**) comparison of 12 holes. Figure 11 shows a comparison of O\({}_{2}\) concentrations for the three agents with 8 and 12 leakage areas. In Figure 11, the retention time is the fastest for IG-01 and the slowest for IG-541. When compared, the retention time of IG-55 was about 260 s faster than that of IG-541. However, IG-55 and IG-541, on the other hands, have almost the same density. That is, there is no difference in outflow volume flow \(\dot{V}_{o}\), i.e., advection flow \(J_{a}\). Therefore, it is determined that the difference in retention time between the two agents is ultimately caused by the difference in diffusion flux \(J_{d}\). As IG-55 has a larger \(J_{d}\) than IG-541, even though \(J_{a}\) is the same, the retention time appears faster. Moreover, there is a minor difference between the retention times of IG-01 and IG-55. The diffusion flux \(J_{d}\) is greater for IG55 than for IG-01, but the retention time is faster for IG-01. This can be explained by the difference in the advection flux \(J_{a}\) due to the difference in density between the agents. The density of IG-01 is 1.399 kg/m\({}^{3}\), which is approximately 8.3% greater than the density of IG-55, 1.292 kg/m\({}^{3}\). As a result, it can be seen from Equation (4) that the outflow volumetric flow \(\dot{V}_{o}\) is larger for IG-01 than for IG-55. Therefore, the difference in retention time between the two agents is reduced, and it is determined to have similar values. The experimental data measured and the data calculated using the proposed equation are summarized in Figure 7:1 In Table 5, the retention time theoretically calculated using the measured and calculated factors is compared to the measured retention time. The experiment was performed using three types of inert agents. In this experiment, the interface slope \(\alpha\) was the smallest with IG-541 (\(\alpha_{541}=0.062\)), it was \(\alpha_{01}=0.071\) for IG-01, and it was the largest at \(\alpha_{55}=0.083\) for IG-55. The retention time of IG-541 with the smallest interface slope \(\alpha_{541}\) was the longest. The edge of the interface \(H_{i}\) at an O\({}_{2}\) concentration of 0.15 of the specified height \(H_{e}\) can be  
Figure 7:2 Change in the O\({}_{2}\) concentration over time for each inert agent: (a) 8 holes; (b) 12 holes.