## 2 Methods
### Economic Indicators and Calculations  
The investment in ORC includes two parts: equipment investment and working fluid investment. Equipment investment includes investment in evaporator, condenser, expander, and pump. The calculations of investment in evaporator and condenser are based on their heat exchanger areas. The calculations of investment in pump and expander are based on their capacity. The working fluid investment is calculated by the quality of working fluid that can be accommodated by the evaporator and condenser chamber and the system piping.  
The purchased cost of heat exchanger can be estimated by the following equation [54].  
\[\mathrm{lg}C_{\mathrm{p}}=K_{1}+K_{2}\mathrm{lg}A+K_{3}(\mathrm{lg}A)^{2}, \tag{17}\]  
The purchased cost of pump and expander can be estimated by the following equation [54].  
\[\mathrm{lg}C_{\mathrm{p}}=K_{1}+K_{2}\mathrm{lg}W+K_{3}(\mathrm{lg}W)^{2}, \tag{18}\]  
In Equations (17) and (18), \(C_{\mathrm{p}}\) is basic purchased cost. Bare module cost of equipment after material and pressure corrections is estimated by  
\[C_{\mathrm{BM}}=C_{\mathrm{P}}(B_{1}+B_{2}F_{\mathrm{M}}F_{\mathrm{P}}), \tag{19}\]  
where \(F_{\mathrm{M}}\) is material factor and \(F_{\mathrm{P}}\) is pressure factor.  
Pressure factor can be calculated by  
\[\mathrm{lg}F_{\mathrm{P}}=C_{1}+C_{2}\mathrm{lg}p+C_{3}(\mathrm{lg}p)^{2}, \tag{20}\]  
In the above equations, \(K_{1}\), \(K_{2}\), \(K_{3}\), \(B_{1}\), \(B_{2}\), \(C_{1}\), \(C_{2}\), and \(C_{3}\) are all correction factors. Their values for purchased cost calculation of heat exchanger are listed in Table 3. Those values for pump and expander are listed in Table 4. The uncertainty was quantified via a scenario analysis [54].  
To consider the effects of inflation on equipment costs, the Chemical Engineering Plant Cost Index (CEPCI) was adopted for all inflation adjustments. Therefore, bare module cost of equipment in 2016 can be estimated by  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Correction Factors** & **Value for Pump** & **Value for Expander** \\ \hline \(K_{1}\) & 3.4771 & 2.2476 \\ \(K_{2}\) & 0.135 & 1.4965 \\ \(K_{3}\) & 0.1438 & \(-\)0.1618 \\ \(C_{1}\) & \(-\)0.25832 & 0 \\ \(C_{2}\) & 0.259016 & 0 \\ \(C_{3}\) & \(-\)0.01363 & 0 \\ \(B_{1}\) & 1.89 & 0 \\ \(B_{2}\) & 1.35 & 0 \\ \(F_{\mathrm{M}}\) & 1.4 & 0 \\ CEPCI\({}_{1996}\) & 382 & 382 \\ CEPCI\({}_{2016}\) & 606 & 606 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Correction factors for purchased cost of pump and expander [54].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Correction Factors** & **Value** & **Correction Factors** & **Value** \\ \hline \(K_{1}\) & 3.2138 & \(B_{1}\) & 1.8 \\ \(K_{2}\) & 0.2688 & \(B_{2}\) & 1.5 \\ \(K_{3}\) & 0.0796 & \(F_{\mathrm{M}}\) & 1.25 \\ \(C_{1}\) & \(-\)0.0650 & CEPCI\({}_{1996}\) & 382 \\ \(C_{2}\) & 0.0503 & CEPCI\({}_{2016}\) & 606 \\ \(C_{3}\) & 0.0147 & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Correction factors for purchased cost of heat exchanger [54].  
\[C_{\text{BM,2016}}=C_{\text{BM,1996}}\frac{\text{CEPCI}_{\text{2016}}}{\text{CEPCI }_{\text{1996}}}, \tag{21}\]  
The bare module cost of working fluid is estimated by  
\[C_{\text{BM,w}}=p_{\text{w}}\cdot M_{\text{w}}, \tag{22}\]  
where \(p_{\text{w}}\) is the unit price of working fluid. \(M_{\text{w}}\) is the mass of working fluid and it is obtained by multiplying the volume of working fluid determined by the heat exchanger chamber and the system piping by the density of working fluid. In this work, the unit price of R123 was 17.967 $/kg, R245 fa was 14.81 $/kg.