## 2 Methodology
### Economic Analysis  
An economic analysis of a waste heat recovery system from any source by means of an ORC system is based on knowing the total production cost (\(E_{TPC}\)), as indicated by Equation (22), is calculated \begin{table}
\begin{tabular}{l c} \hline \hline
**Component** & **Exergy Balance** \\ \hline Evaporator & \(\left(\mathbf{1}-\frac{\mathbf{T}_{a}}{T_{n}}\right)\dot{Q}_{in}+\dot{E}_{F}= \dot{E}_{P}+\dot{E}_{d,~{}equ}\) \\ Turbine & \(\dot{E}_{F}=\dot{E}_{P}+\dot{w}_{turb}+\dot{E}_{d,~{}turb}\) \\ Pump & \(\dot{w}_{P}+\dot{E}_{F}=\dot{E}_{P}+\dot{E}_{d,pum}\) \\ Condenser & \(\dot{E}_{F}=\dot{E}_{P}+\dot{E}_{d,cond}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Balance of exergy in components. by means of the total capital to be invested (\(E_{TCI}\)) and the maintenance and operation costs (\(E_{O\in M}\)) as follows:  
\[E_{TPC}=E_{TCI}+E_{O\in M} \tag{22}\]  
The total capital to be invested in an ORC system is determined by knowing the investment of fixed assets (\(E_{FCI}\)) of the system and additional costs. The calculation of the \(E_{TCI}\) is made using Equation (23) as follows:  
\[E_{TCI}=E_{FCI}+Additional\ costs \tag{23}\]  
The investment of fixed assets is quantified with the direct costs (\(E_{DC}\)) and the indirect costs (\(E_{IC}\)), by means of the Equation (24) as follows:  
\[E_{FCI}=E_{DC}+E_{IC} \tag{24}\]  
Equation (25) shows the costs that make up the additional costs, where \(E_{SUC}\) is the start-up cost, i.e., the commissioning of the equipment, \(E_{WC}\) refers to the initial working capital of the system, \(E_{LRD}\) is associated with the development and research costs, and finally \(E_{AFUDC}\) is the cost attributed to the provision of funds during construction, as follows:  
\[Additional\ costs=E_{SUC}+E_{WC}+E_{LRD}+E_{AFUDC} \tag{25}\]  
As mentioned before, the investment in fixed assets is made up of direct and indirect costs, where the direct costs represent the acquisition of equipment, piping and accessories, installation and assembly, electronic equipment, instrumentation and control, and the materials corresponding to the system, work area, and civil work. To estimate the cost of equipment acquisition (EPEC), equations proposed by [38; 50; 51] are used, where correlations are used as a function of the energy of the equipment, specifically, the turbine and pump, and the area in the case of the exchanger; data from manufacturers are collected and costs are calculated in US dollars. From this model, we have Equation (26) for the turbine as follows:  
\[log_{10}Y=2.6259+1.4398\cdot log_{10}\dot{W}_{t}-0.1776\cdot\left(log_{10} \dot{W}_{t}\right)^{2} \tag{26}\]  
For the pump, is obtained Equation (27) as follows:  
\[log_{10}Y=3.3892+0.0536\cdot log_{10}\dot{W}_{p}-0.1538\cdot\left(log_{10} \dot{W}_{t}\right)^{2} \tag{27}\]  
Finally, for the heat exchanger, the cost of acquisition is calculated using Equation (28) as follows:  
\[Y=10000+324\cdot\left(B^{0.91}\right) \tag{28}\]  
The costs associated with the installation and assembly are related to the transportation and nationalization of the equipment, in addition to the costs generated by the working fluids during the start-up of the thermal cycle, and they are calculated taking, as a reference, between 20% and 90% of the acquisition cost of the equipment [52]. Pipes and accessories are the investments required during the conformation of the project and they are estimated between 50% and 70% of the acquisition cost of the equipment [52]. With respect to instrumentation and control, which is necessary to achieve the most optimal operation of the system, the range is between 6% and 20% of the acquisition cost of the equipment [53]. The electrical equipment and materials are the costs related to the materials and installation of electrical energy distribution lines and the required connections, which also refers to the control centers and equipment to automate the security systems, are estimated between 10% and 15% of the cost of acquisition of equipment [52].