## 2 Materials and Methods
### Modeling
#### 2.3.2 Modeling of OAR System  
Modeling of OAR system includes the evaporator, open generator, absorber, and SAHEXs and CWHEXs. \begin{table}
\begin{tabular}{l c} \hline \hline
**Parameters** & **Triple-Stage** \\ \hline Components of feed air & Nitrogen 0.7812; Oxygen 0.2095; Argon 0.0093 \\ Feed air mass flow rate (kg/h) & 340,439.85 \\ Product (kg/h) & \\ Liquid O2 (0.3 MPa, \(-183\)\({}^{\circ}\)C) & 2992.78 \\ Gas O2 (2.82 MPa, \(20\)\({}^{\circ}\)C) & 71,381.73 \\ Liquid N2 (0.6 MPa, \(-189.3\)\({}^{\circ}\)C) & 2499.67 \\ N2 (0.524 MPa, \(20\)\({}^{\circ}\)C) & 56,240.97 \\ N2 (0.114 MPa, \(20\)\({}^{\circ}\)C) & 31,245.44 \\ N2 (1 MPa, \(40\)\({}^{\circ}\)C) & 56,242.79 \\ Outlet pressures of compressors (kPa) & 200 \\ Compressor II & 360 \\ Compressor III & 635 \\ Isentropic efficiency of compressors & 85\% \\ Pressure drop of each inter and after coolers (kPa) & 8 \\ Outlet temperatures of intercoolers and aftercooler (\({}^{\circ}\)C) & 40 \\ Intercooler II & 40 \\ Aftercooler I & 40 \\ Variables & 40 \\ Inlet air temperature of feed air (\({}^{\circ}\)C) & 13.8–25 \\ Inlet air mass fraction of water (kg/kg) & 0.06–0.016 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Processed parameters in the triple-stage air compression section. (1) Evaporator and absorber  
The evaporator and absorber are both considered as shell-and-tube heat exchangers. Chilled water for the evaporator and cooling water for the absorber flow through the tube side. Makeup water evaporation and water vapor absorption occur at the shell side. It is solved by the simple effectiveness-number of transfer units (\(\varepsilon\)-\(NTU\)) model:  
\[NTU_{eva}=(UA)_{eva}/\left(m_{clw}c_{p,clw}\right) \tag{5}\]  
\[\varepsilon_{eva}=1-\exp(-NTU_{eva}) \tag{6}\]  
\[\varepsilon_{eva}=(t_{clwin}-t_{clwout})/(t_{clwin}-t_{eva}) \tag{7}\]  
The same calculation method is adopted for the absorber. The evaporation rate of the makeup water gives a direct measure of the cooling capacity of the OAR. The energy conservation equation is given:  
\[m_{mw}(h_{mwin}-h_{mwout})=m_{clw}(h_{clwin}-h_{clwout}) \tag{8}\]  
where \(U\) represents the heat transfer coefficient, W/(m\({}^{2}\cdot\)K); A represents heat transfer area, m\({}^{2}\); \(c_{p}\) represents the specific heat capacity, J/(kg\(\cdot\)K); subscripts \"\(clw\)\" and \"\(mw\)\" represent chilled-water and makeup water, respectively. Mass and energy conservation equations for the absorber are given as:  
\[\left(mx\right)_{ssin}=\left(mx\right)_{ssout} \tag{9}\]  
\[m_{ssin}+m_{mw}=m_{wsout} \tag{10}\]  
\[\left(mh\right)_{mwin}+\left(mh\right)_{ssin}-\left(mh\right)_{usout}=m_{cw}( h_{cwout}-h_{cwin}) \tag{11}\]  
where \(x\) represents mass fraction of solvent in the solution, %; subscripts \"\(ws\)\",\"\(ss\)\" and \"\(cw\)\" represent weak solution, strong solution, and circulating cooling water, respectively. (2) SAHEXs and CWHEXs  
A shell-and-tube heat exchanger is used here, in which solution flows through the tube side, while air flows through the shell side. Air and solution temperatures are also solved by the counterflow \(\varepsilon\)-\(NTU\) model:  
\[NTU_{SAHEX}=(UA)_{SAHEX}/\min(m_{us}c_{p,ms},m_{a}c_{pa}) \tag{12}\]  
\[\varepsilon_{SAHEX}=\frac{1-\exp\left((-NTU_{SAHEX})\left(1-\frac{\min(n_{ac _{pa},m_{us}c_{pms}})}{\max(m_{ac_{pa},m_{us}c_{pms}})}\right)\right)}{1-\frac {\min\left(m_{a}c_{pa},m_{us}c_{pms}\right)}{\max(m_{a}c_{pa},m_{us}c_{pms})} \left((-NTU_{SAHEX})\left(1-\frac{\min\left(m_{a}c_{pa},m_{us}c_{pms}\right)} {\max(m_{a}c_{pms},m_{us}c_{pms})}\right)\right)} \tag{13}\]  
\[NTU_{eva}=(UA)_{eva}/\left(m_{clw}c_{p,clw}\right) \tag{5}\]0  
The energy conservation equation is given as:  
\[NTU_{eva}=(UA)_{eva}/\left(m_{clw}c_{p,clw}\right) \tag{5}\]1  
The same calculation method is adopted for CWAHEXs. It is worth noting that pressure drops of SAHEXs and CWAHEXs are all assumed to be 4 kPa due to the similar patterns.