## 2 Materials and Methods
### Modeling
#### 2.3.4 Economic Analysis  
Economic calculation of the proposed ACS-OAR is also conducted to evaluate its profitability. Economic evaluation is based on the dynamic payback period (\(DPP\)), which is widely used for financial evaluation of investment.  
The calculation of \(DPP\) is based on the annualized cost of system (\(C_{acs}\)), which is comprised of annualized capital cost, maintenance cost, management cost, and operation cost:  
\[C_{acs}=C_{acc}+C_{ama}+C_{amg}+C_{aop} \tag{34}\]  
where, annualized capital cost of the system is calculated as:  
\[C_{acc}=C_{dec}\cdot\alpha=C_{dec}\frac{i(i+1)^{n}}{{{(i+1)}^{n}}+1} \tag{35}\]  
where \(\alpha\) represents capital recovery ratio, also known as the amortization ratio, which is a function of the interest rate \(i\) and estimated lifetime of the proposed system \(n\). \(C_{dec}\) is the direct capital cost. It is worth noting that economic analysis is conducted based on the increased capital cost of the ACS caused by the coupling of OAR compared with conventional ACS. Accordingly, \(C_{dec}\) is calculated as:  
\[C_{dec}=(C_{dec})_{ACS-OAR}-(C_{dec})_{CACS}=\sum_{i=1}^{k}(C_{i})_{ACS-OAR}- \sum_{i=1}^{k}(C_{i})_{CACS} \tag{36}\]  
Direct capital costs of the ACS includes purchase costs of the main equipment, pipes and fittings, control devices, and so on. Purchase cost of the main equipment, such as the evaporator, open generator, and heat exchangers, are usually estimated by the production capacity index approach. Equations and references adopted are given in Table 3.  
The management cost is considered annually as 20% of the operating labor cost. The maintenance cost is set annually as 4.63% of the capital investment cost [33]. Annualized operation cost in the ACS-OAR mainly consists of fresh water, electricity, and labor cost.  
Based on the annualized capital cost, \(DPP\) is calculated as:  
\[NPV=-C_{dec}+\sum_{t=0}^{DPP}\frac{(P_{r}-C_{acs})(1-T_{r})}{{{(1+D_{r})}^{t}}}=0 \tag{37}\]  
where \(NPV\) (net present value) is the present value of the current and future benefit minus the present value of the current and future costs, which is a base calculation for the \(DPP\); \(T_{r}\) and \(D_{r}\) are the tax rate and discounted annual rate, respectively, %. \(P_{r}\) is the project revenue, which refers to the value created by the energy saving caused by the coupling  
\begin{table}
\begin{tabular}{l l} \hline \hline Absorber & **Equation** \\ Evaporator & \(C_{hex}=f_{m}\cdot 1192\cdot(A_{hex})^{0.71}\) \\ Solution heat exchanger & \(A_{hex}=\frac{O_{ave}}{U_{hex}(LMTD)_{hex}}\) \\ SA-HEX1/2 & \(f_{m}\): Material factor \\ CWA-HEX1/2 & \(LMTD\): Mean logarithmic temperature difference \\ Intercooler & \(U_{hex}\): overall heat transfer coefficient \\ Aftercooler & \(C_{pump}=2100\left(\frac{W_{pump}}{10}\right)^{0.26}\left(\frac{1-T_{pump}} {\eta_{h,pump}}\right)^{0.5}\) \\ Compressors & \(C_{comp}=71.1\left(\frac{W_{pump}C_{HC}}{0.01}\right)ln(CR)\) \\ Expansion valves & \(C_{ep}=114.5\cdot m_{ep}\) \\  & \(c_{lower}=\) \\ Air-cooling tower & \(1780H^{0.87}d^{1.23}[2.86+1.694f_{m}(10.01-7.408 lnP+1.395(lnP)^{2})]\) \\ Water-cooling tower & \(H\): Height of the column; \(d\): Diameter of column \\  & \(f_{m}\): Material factor; \(P\): Column mean pressure \\ \hline \hline \end{tabular}
\end{table}
Table 3: Calculation of initial capital cost of the main system equipment [35; 36; 37; 38].  
of the OAR in the ACS, USD. The energy saving mainly refers to the electricity saving of compressors. The value of electricity saving is calculated as:  
\[P_{r}=\Delta W_{com}\cdot wh\cdot EP \tag{38}\]  
where \(\Delta W_{com}\) is the electricity saving, kW; \(wh\) is the working hours of the system, h; \(EP\) is the electricity purchase price, USD/kWh.