## 2 Materials and Methods
### Advanced Exergo-Environmental Analysis  
Advanced exergo-economic analysis separates effective environmental components and exergy destruction into unavoidable/avoidable and endogenous/exogenous parts and compounds them in different possible modes, [PERSON] and [PERSON] (2016). The environmental impact of the exogenous exergy destruction rate (\(\dot{B}^{EX}_{D,K}\)) was affiliated with the relations between the components, while the environmental impact of the endogenous exergy destruction rate (\(\dot{B}^{EN}_{D,K}\)) was affiliated with irreversible environmental impacts of the component itself. Moreover, the environmental impact of exergy destruction rate was categorized into unavoidable (\(\dot{B}^{UN}_{D,K}\)) and avoidable (\(\dot{B}^{AV}_{D,K}\)) parts. Categorizing the environmental impact of exergy destruction into improvable and un-improvable sections was assumed as well. The four parts of the environmental impact of the exergy destruction rate were avoidable endogenous environmental impact of the exergy destruction rate (\(\dot{B}^{AV,EN}_{D,K}\)), unavoidable endogenous environmental impact of the exergy destruction rate (\(\dot{B}^{UN,EN}_{D,K}\)), avoidable exogenous environmental impact of the exergy destruction rate (\(\dot{B}^{AV,EX}_{D,K}\)) and unavoidable exogenous environmental impact of the exergy destruction rate (\(\dot{B}^{UN,EX}_{D,K}\)), [PERSON] and [PERSON] (2016). See Table 7 for all equations correlated to the advanced exergo-environmental analysis of the proposed system, [PERSON] et al. (2011), [PERSON] et al. (2013). \begin{table}
\begin{tabular}{l c} \hline \hline
**Definition of Cost Rate** & **Equations** \\ \hline The cost of the kth component that is called the endogenous cost, [PERSON] and [PERSON] (2016) & \(\dot{C}^{EN}_{D,K}=\ c_{F,K}\dot{E}^{EN}_{D,K}\) (31) \\ The exogenous cost of kth component, & \(\dot{C}^{EX}_{D,K}=\dot{C}_{D,K}-\dot{C}^{EN}_{D,K}\) (32) \\ Unavoidable cost of exergy destruction, & \(\dot{C}^{UN}_{D,K}=\ c_{F,K}\dot{E}^{UN}_{D,K}\) (33) \\ Avoidable cost rate, [PERSON] (2016) & \(\dot{C}^{AV}_{D,K}=\ c_{F,K}\dot{E}^{AV}_{D,K}\) (34) \\ Unavoidable cost rate of kth component associated with the operation of the component itself, [PERSON] et al. (2013) & \(\dot{C}^{UN,EN}_{D,K}=\ c_{F,K}\dot{E}^{UN,EN}_{D,K}\) (35) \\ Unavoidable cost rate of kth component caused by the remaining components, [PERSON] and Dincer (2016) & \(\dot{C}^{UN,EX}_{D,K}=\dot{C}^{UN}_{D,K}-\dot{E}^{UN,EN}_{D,K}\) (36) \\ Avoidable cost rate of kth component associated with the operation of the component itself, [PERSON] et al. (2013) & \(\dot{C}^{AV,EN}_{D,K}=\dot{C}^{EN}_{D,K}-\dot{E}^{UN,EN}_{D,K}\) (37) \\ Avoidable cost rate of kth component caused by the remaining components, [PERSON] et al. (2013) & \(\dot{C}^{AV,EX}_{D,K}=\dot{C}^{EX}_{D,K}-\dot{E}^{UN,EX}_{D,K}\) (38) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Equations for the advanced exergo-economic analysis of the proposed system. \begin{table}
\begin{tabular}{l c} \hline \hline
**Description** & **Equations** \\ \hline Endogenous exergy destruction rate & \(\dot{B}^{EN}_{D,K}=\ b_{F,K}\dot{E}^{EN}_{D,K}\) (39) \\ Exogenous exergy destruction rate & \(\dot{B}^{EX}_{D,K}=\ b_{F,K}\dot{E}^{EX}_{D,K}\) (40) \\ Unavoidable exergy destruction rate & \(\dot{B}^{UN}_{D,K}=\ b_{F,K}\dot{E}^{UN}_{D,K}\) (41) \\ Avoidable exogenous exergy destruction rate & \(\dot{B}^{AV}_{D,K}=\ b_{F,K}\dot{E}^{AV}_{D,K}\) (42) \\ Unavoidable endogenous exergy destruction rate & \(\dot{B}^{UN,EN}_{D,K}=\ b_{F,K}\dot{E}^{EN}_{D,K}\) (43) \\ Unavoidable exogenous exergy destruction rate & \(\dot{B}^{UN,EX}_{D,K}=\ b_{F,K}\dot{E}^{UN}_{D,K}\) (44) \\ Avoidable endogenous exergy destruction rate & \(\dot{B}^{AV,EN}_{D,K}=\ b_{F,K}\dot{E}^{AV}_{D,K}\) (45) \\ Avoidable exogenous exergy destruction rate & \(\dot{B}^{AV,EX}_{D,K}=\ b_{F,K}\dot{E}^{AV}_{D,K}\) (46) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Equations for the advanced exergo-environmental analysis of the proposed system, [PERSON] et al. (2011), [PERSON] et al. (2013).