## 2 Methodology
### Exergo-Economic Analysis  
#### 2.4.1 Economic Analysis  
To estimate the total production cost (TPC) of the WHR systems, the total capital invested (TCI) and the operation and maintenance costs (O&M) are considered, as shown in Equation (6) [50]. \[\text{TPC}=\text{TCI}+\text{O\&M} \tag{6}\]  
where the TCI of the SORC systems is calculated by means of Equation (7) [51]. \[\text{TCI}=\text{FCI}+\text{ other }\cos\text{ts} \tag{7}\]  
where the fixed cost investment (FCI) of the system is a function of the direct cost (CD) and indirect costs (CI), according to Equation (8). \[\text{FCI}=\text{CD}+\text{CI} \tag{8}\]  
In addition, the other costs (SUC) are related to the start-up costs of the devices, the initial working capital of the thermal system (WC), the costs related to the research and development actions (LRD), \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Component** & **SORC** & **Component** & **SORC** \\ \hline Heat Exchanger (ITC1) & \(\dot{\text{Q}}_{\text{G}}=\dot{\text{m}}_{\text{10}}\text{C}_{\text{P10}}( \text{T}_{\text{10}}-\text{T}_{\text{11}})\) & Turbine 1 (T1) & \(\eta_{\text{T1}}=\frac{\text{h}_{\text{H}_{\text{O}RC}}-\text{h}_{\text{B} \text{O}RC}}{\text{H}_{\text{O}RC}-\text{h}_{\text{B}\text{O}RC}}\) (A.7) & \\  & & & \(\dot{\text{W}}_{\text{T1}}=\dot{\text{m}}_{\text{O}RC}+\dot{\text{h}}_{\text{O}RC }\) (\(\text{h}_{\text{O}RC}-\text{h}_{\text{B}\text{O}RC}\)) \\  & & Zone E (Coiling) & \\  & & & \(\dot{\text{Q}}_{\text{ZE}}=\dot{\text{m}}_{\text{ORC}}\big{(}\text{h}_{\text{2 0}\text{R}\text{C}}-\text{h}_{\text{2 0}\text{R}\text{C}}\big{)}\) \\ Pump 1 (B1) & \(\eta_{\text{B1}}=\frac{\text{v}_{\text{J}AT}(\text{h}_{\text{J}AT})}{\text{h}_{ \text{J}AT}-\text{h}_{\text{J}AT}}\) & Heat Exchanger (ITC3) & \(=\dot{\text{m}}_{\text{A}}\big{(}\text{h}_{\text{2A}}-\text{h}_{\text{1g}}\big{)}\) \\  & & (ITC3) & Zone C (Condenser) \\  & & & \(\dot{\text{Q}}_{\text{ZC}}=\dot{\text{m}}_{\text{ZC}}\big{(}\text{h}_{\text{2 0}\text{R}\text{C}}-\text{h}_{\text{3 0}\text{R}\text{C}}\big{)}\) \\  & & & \(=\dot{\text{m}}_{\text{A}}\big{(}\text{h}_{\text{1g}A}-\text{h}_{\text{1A}}\big{)}\) \\  & Zone 1 (Preheating) & & \\  & \(\dot{\text{Q}}_{\text{Z1}}=\dot{\text{m}}_{\text{A}T}(\text{h}_{\text{A}T}-\text {h}_{\text{2 AT}})\) & & \\  & \(=\text{m}_{\text{ORC}}\big{(}\text{h}_{\text{4 ORC}}-\text{h}_{\text{4 ORC}}\big{)}\) & & \\ Heat Exchanger 2 (ITC2) & \(\dot{\text{Q}}_{\text{Z2}}=\dot{\text{m}}_{\text{A}T}\big{(}\text{h}_{\text{A}T }-\text{h}_{\text{A}T}\big{)}\) & Pump 2 (B2) & \(\eta_{\text{B2}}=\frac{\text{v}_{\text{J}OC}(\text{P}_{\text{ORC}}-\text{P}_{ \text{ORC}})}{\text{h}_{\text{O}RC}-\text{h}_{\text{B}\text{O}RC}}\) (\(\dot{\text{W}}_{\text{B2}}=\dot{\text{m}}_{\text{ORC}}(\text{h}_{\text{4 ORC}}- \text{h}_{\text{30}\text{R}\text{C}})\) \\  & Zone 3 (overheating) & & \\  & \(\dot{\text{Q}}_{\text{Z3}}=\dot{\text{m}}_{\text{A}T}\big{(}\text{h}_{\text{1 AT} }-\text{h}_{\text{A}T}\big{)}\) & & \\  & \(=\dot{\text{m}}_{\text{ORC}}\big{(}\text{h}_{\text{10}\text{R}\text{C}}-\text{h}_{ \text{4}\text{6}\text{ORC}}\big{)}\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Energy balances for the components of simple organic Rankine cycle (SORC) configuration. and the costs related to the provision of resources in the construction phase (AFUDC), as shown in in Equation (9). \[\text{Other}\,\cos\text{ts}=\text{SUC}+\text{WC}+\text{LRD}+\text{AFUDC} \tag{9}\]  
The purchase cost of the heat exchangers (evaporator and condenser), the pump, and the turbine used correlations depending on the output power of the turbine, the power of the pump, and the area of the heat exchanger, considering commercial data from manufacturers [52; 53; 54]. The purchase cost equation for the turbine is given by Equation (10) [52; 54; 55].