## 3 System Modelings
### Exergoeconomic Model  
On the basis of the mass, energy and exergy balances above, the exergoeconomic analysis can be conducted to obtain the cost per unit exergy of product streams and to assess the combined systems. Firstly, all energy and exergy values should be determined, which has been achieved in the above section. Then, the fuel-production definition for the energy conversion system should be determined. For the sCO\({}_{2}\)/AHP system and sCO\({}_{2}\)/DH system in this study, the definitions are shown in Table 2. Finally, the cost balance equations can be constructed for all components. For the \(k\)th system component, the cost balance can be expressed with Equations (31)-(34) [32; 33],  
\[\sum\dot{C}_{out,k}+\dot{C}_{w,k}=\sum\dot{C}_{in,k}+\dot{C}_{q,k}+\dot{Z}_{k} \tag{31}\]  
in which,  
\[\dot{C}=c\cdot E \tag{32}\]  
\[\dot{C}_{q,k}=c_{q,k}\cdot E_{q,k} \tag{33}\]  
\[\dot{C}_{w,k}=c_{w,k}\cdot W \tag{34}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**System Components** & **sCO\({}_{2}\)/AHP System** & **sCO\({}_{2}\)/DH System** \\ \hline reactor & \(E_{\text{core}}+E_{4}=E_{5}+I_{\text{core}}\) & \(E_{\text{core}}+E_{4}=E_{5}+I_{\text{core}}\) \\ sCO\({}_{2}\) turbine & \(E_{5}=E_{6}+W_{\text{tur}}+I_{\text{tur}}\) & \(E_{5}=E_{6}+W_{\text{tur}}+I_{\text{tur}}\) \\ HTR & \(E_{3}+E_{6}=E_{4}+E_{7}+I_{\text{HTR}}\) & \(E_{3}+E_{6}=E_{4}+E_{7}+I_{\text{HTR}}\) \\ LTR & \(E_{2}+E_{7}=E_{3a}+E_{8}+I_{\text{LTR}}\) & \(E_{2}+E_{7}=E_{3a}+E_{8}+I_{\text{LTR}}\) \\ main compressor & \(E_{1}+W_{\text{mcom}}=E_{2}+I_{\text{mcom}}\) & \(E_{1}+W_{\text{mcom}}=E_{2}+I_{\text{mcom}}\) \\ recompression compressor & \(E_{8b}+W_{\text{recom}}=E_{3b}+I_{\text{recom}}\) & \(E_{8b}+W_{\text{recom}}=E_{3b}+I_{\text{recom}}\) \\ cooler & \(E_{10}=E_{1}+I_{\text{cooler}}\) & \(E_{10}=E_{1}+I_{\text{cooler}}\) \\ DHE & \(E_{9}+E_{\text{H}4}=E_{10}+E_{\text{H}5}+I_{\text{DHE}}\) & \(E_{8a}+E_{\text{H}4}=E_{10}+E_{\text{H}6}+I_{\text{DHE}}\) \\ generator & \(E_{8a}+E_{A4}=E_{9}+E_{A7}+E_{\text{A8}}+I_{\text{Gen}}\) & / \\ absorber & \(E_{\text{A}1}+E_{\text{A5}}+E_{\text{H}1}=E_{\text{A2}}+E_{\text{H2}}+I_{\text{ Abs}}\) & / \\ SHE & \(E_{\text{A}3}+E_{A7}=E_{\text{A4}}+E_{\text{A6}}+I_{\text{SHE}}\) & / \\ condenser & \(E_{\text{A8}}+E_{\text{H2}}=E_{\text{A9}}+E_{\text{H3}}+I_{\text{Cond}}\) & / \\ Evaporator & \(E_{\text{A}10}+E_{13}=E_{\text{A1}}+E_{\text{I4}}+I_{\text{Eva}}\) & / \\ Pump & \(E_{\text{A2}}+W_{\text{Pump}}=E_{\text{A3}}+I_{\text{Pump}}\) & / \\ Valve1 & \(E_{\text{A9}}=E_{\text{A10}}+I_{\text{Valve1}}\) & / \\ Valve2 & \(E_{\text{A6}}=E_{\text{A5}}+I_{\text{Valve2}}\) & / \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Exergy balance equations for the sCO\({}_{2}\)/AHP system and sCO\({}_{2}\)/DH system. where \(\dot{C}\) is the cost rate of the stream, while \(\dot{C}_{q}\) and \(\dot{C}_{w}\) are the cost rate of the heat transfer and power, respectively. \(\dot{Z}_{k}\) represents the total cost rate of capital investment, operation and maintenance, which can be obtained as Equation (35),  
\[\dot{Z}_{k}=\dot{Z}_{k}^{\text{CI}}+\dot{Z}_{k}^{\text{OM}}. \tag{35}\]  
where \(\dot{Z}_{k}^{\text{CI}}\) denotes the annual levelized capital investment and \(\dot{Z}_{k}^{\text{OM}}\) denotes the annual levelized operation and maintenance cost. They can be obtained with Equations (36) and (37) [32],  
\[\dot{Z}_{k}^{\text{OM}}=\gamma_{k}Z_{k}/\tau \tag{36}\]  
\[\dot{Z}_{k}^{\text{CI}}=\Big{(}\frac{CRF}{\tau}\Big{)}Z_{k} \tag{37}\]  
where \(CRF\), \(\tau\) and \(\gamma\) represent the capital recovery factor, operating hours, and the maintenance factor, respectively. \(CRF\) is relative to the bank interest rate, which can be expressed as Equation (38),  
\[CRF=\frac{i_{r}(1+i_{r})^{n}}{(1+i_{r})^{n}-1} \tag{38}\]  
where \(i_{r}\) is the interest rate, and \(n\) is the number of operation years.