## 2 Materials and Methods
### Selection of the Chemical Accident Content for Training
#### 2.2.2 Derivation of Changes to the Facility Status due to a Chemical Accident  
Based on the selected cases, leakage-source modeling was used to numerically calculate changes in leakage amounts, reactor pressure, and liquid levels. This was performed in accordance with the Center for Chemical Process Safety guidelines [35]. Gradual changes in the liquid levels and pressure of the reactor were achieved by calculating them according to the procedure outlined in Figure 3. The liquid levels and pressure of the reactor measured one second after the start of the leak were calculated by determining the leakage rate at zero seconds, after which the result was inserted in the leakage rate equation. Each case was calculated after one second, and repeated until \(h\) equaled 0. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case No.** & **Scenario** & **Situation** & **Response** & **Leakage Model** \\ \hline
1 & Piping failure 1 & Leakage from a flange gap due to & Close the valve and shut off & Liquid leakage from the pipe \\  & & gasket aging. & the pump. & Gas leakage from the pipe \\
2 & Piping failure 2 & Leakage due to corrosion of the & Close the valve connected to & Gas leakage from the pipe \\  & & hydrochloric acid supply pipe. & the reactor. & Block the inflow and outflow \\
3 & Level gauge leakage & Leakage at the bottom of the & by closing the valve connected & Liquid leakage from the vessel \\  & & reactor due to poor welding. & to the reactor. & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Accident scenarios for training. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Division** & **Chemical Formula** & **CAS No.** & **Boiling Point (\({}^{\circ}\)C)** & **Vapor Pressure (mmHg)** \\ \hline Hexamethyldisilane & Si\({}_{2}\)C\({}_{6}\)H\({}_{18}\) & 1450-14-2 & 113 & 20.8 \\ Hydrogen chloride & HCl & 7647-01-0 & \(-85.05\) & 35.42 \\ Trimethylsilane & C\({}_{3}\)H\({}_{10}\)Si & 993-07-7 & 6.7 & 594 \\ Trimethylchlorosilane & C\({}_{3}\)H\({}_{9}\)SiCl & 75-77-4 & 57 & 200 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Design and operation specifications for the pilot plant. iquid leakage from the pipe system (case 1) is calculated as follows:  
\[\mathbf{Q}= \begin{cases}\frac{A\rho_{L}\left(Re\sqrt{f}\right)\sqrt{\frac{D}{2 Lp}\left[ \frac{\varepsilon\left(P-P_{0}\right)}{\rho_{L}}+gh\right]}}{16}&\left(Re\sqrt{ f}\leq 180\right)\\ -4A\rho_{L}log_{10}\left[\frac{1}{37}\left(\frac{\varepsilon}{D}\right)+ \frac{1.255}{Re\sqrt{f}}\right]\sqrt{\frac{D}{2 Lp}\left[\frac{\varepsilon \left(P-P_{0}\right)}{\rho_{L}}+gh\right]}&\left(Re\sqrt{f}\geq 525\right)\end{cases}  \tag{1}\]  
where \(Re\) denotes the Reynolds number, \(f\) denotes the friction coefficient, \(A\) denotes the area of the leakage source, \(D\) denotes the inner diameter of the pipe, \(L_{P}\) denotes the distance between the vessel and the leakage point, \(P\) denotes the pressure of the pipe system, \(P_{CF}\) denotes the critical flow pressure, \(P_{a}\) denotes the atmospheric pressure, \(h\) denotes the height difference between the leakage point and liquid in the facility, and \(\varepsilon\) denotes the pipe roughness. Gas leakage from the pipe system (case 2) is calculated as  
\[Q=AMaP_{1}\sqrt{\frac{\gamma g_{C}M_{W}}{RT_{1}}} \tag{2}\]  
where \(\gamma\) denotes the specific heat coefficient from the database embedded in Aspen Plus, \(M_{W}\) denotes the molecular weight of the leaking substance, \(R\) denotes the gas constant,  
Figure 3: Calculation flowchart for \(\mathbf{Q}\), \(\mathbf{h}\), and \(\mathbf{P}\). denotes the initial temperature of the pipe, and \(Ma\) denotes the Mach number calculated using Excel's Solver tool. Liquid leakage from the vessel (case 3) is calculated using  
\[Q=C_{D}A\rho_{L}\sqrt{\left[\frac{2g_{c}(P-P_{a})}{\rho_{L}}+2 gh\right]}\, \tag{3}\]  
where \(C_{D}\) is the leakage coefficient calculated with respect to the flow state. Subsequently, the liquid levels and pressure of the reactor are calculated based on the leakage rate in each case using Equations (1)-(3).