# A Study on the Effect of O\({}_{2}\) Diffusion on the Retention Time of Inert Agents
## 3 Methodology  
### Experiment Study  
All experiments were conducted to validate the species diffusion for an inert agent. The enclosure used in the experiment was 1 m \(\times\) 1 m \(\times\) 2 m in height. A schematic diagram of the enclosure is shown in Figure 5.  
A hole with a diameter of 0.01 m was drilled at an offset of 0.01 m from the floor and the ceiling. The low leakage factor F was set to 0.5, which is the worst condition. That is, the leakage areas at the top and bottom were set identically. The worst condition of F is defined in NFPA 2001 [6]. In order to control the total flow rate of the inflow and outflow, holes were removed or reopened using a vacuum adhesive. The enclosure was placed inside a room with temperature and humidity control, which allowed the external ambient conditions to be controlled. A sensor (OXY-GEN oxygen monitor, \(\Delta\Omega\)) was placed inside the enclosure to measure the ambient temperature, humidity, and O\({}_{2}\) concentration. In this experiment, the O\({}_{2}\) concentration for 10 points was measured at 0.1 m intervals from 1 to 1.9 m from the bottom to analyze the interface descending velocity \(\partial\dot{H}_{i}/\partial t\) and interface characteristics. The O\({}_{2}\) concentration at each point was measured at 5 s intervals.  
The difference between the outside and inside temperatures of the enclosure was within 1 K. This was done to minimize the effect of temperature. However, it was not possible to control the humidity inside the enclosure. Therefore, the humidity prior to the injection of the inert agent to the enclosure was set to a constant so that the humidity under experimental conditions could be matched as much as possible. Three types of inert agents were used. The experimental initial conditions inside and outside the enclosure are listed in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & **Total Leakage** & **Inert** & **Temperature** & **Initial Humidity** & **Inside Pressure** \\  & **Area (cm\({}^{2}\))** & **Agent** & **In/Out (K)** & **In/Out (\%)** & **(hPa)** \\ \hline
1-1 & 6.28 & IG-01 & 292.5/293.4 & 20/50 & 1014 \\
1-2 & 6.28 & IG-55 & 293.3/293.2 & 21/51 & 1014 \\
1-3 & (Hole 8 ea) & IG-541 & 292.8/293.3 & 19/50 & 1013 \\ \hline
2-1 & 9.42 & IG-01 & 292.7/293.4 & 21/50 & 1014 \\
2-2 & (Hole 12 ea) & IG-55 & 293.3/293.3 & 20/51 & 1014 \\
2-3 & (Hole 12 ea) & IG-541 & 293.1/293.4 & 19/51 & 1013 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Initial conditions inside and outside the enclosure.  
Figure 5: Schematic diagram of test enclosure and measuring equipment.  
The experiment was repeated 5 times for each case, and the measured data were used to calculate the interface slope \(\alpha\) and diffusion velocity \(v_{d}\). As in previous studies, agent discharge was intentionally omitted [3,4,15,16]. In this study, the design O\({}_{2}\) concentration in the air-agent mixture gas was set to 0.12, and the O\({}_{2}\) concentration that determines the retention time was set to 0.15. The inert agent was injected into the enclosure at a pressure of 1.2 MPa to thoroughly mix the air and agent. Therefore, the initial O\({}_{2}\) concentration according to the height of the measurement could be set to \(0.12\pm 1\times 10^{-3}\).