## 2 Materials and Methods
### Exergy Analysis  
An exergy analysis, which is based on the second law of thermodynamics, can be performed to determine the thermodynamic irreversibility in the components. Exergy rates are generally composed of four elements: physical (\(\dot{E}^{ph}\)), chemical (\(\dot{E}^{ch}\)), kinetic (\(\dot{E}^{ke}=\frac{1}{2}\dot{m}V^{2}\)) and potential (\(\dot{E}^{pe}=\dot{m}gz\)). Specific exergy can be given as, [PERSON] et al. (2019), [PERSON] et al. (2010).  
\[\dot{E}=\dot{E}^{ph}+\dot{E}^{ch}+\dot{E}^{pe}+\dot{E}^{ke} \tag{4}\]  
The formula for calculating the physical exergy rate is as follows, [PERSON] et al. (2019):  
\[\dot{E}^{ph}=\dot{m}[(\mathrm{h_{i}-h_{o}})-\mathrm{T_{O}}(\mathrm{s_{i}-s_{o} })]. \tag{5}\]  
The formula for calculating the chemical exergy rate is expressed as follows, [PERSON] et al. (2019):  
\[\dot{E}^{ch}=\dot{m}[\sum_{i=1}^{n}x_{i}e_{0,i}^{ch}+RT_{0}\sum_{i=1}^{n}x_{i} ln(x_{i})] \tag{6}\]  
where (n) represents the number of moles of the component in the inorganic matter, in mol.kg-1. \(e_{0,i}^{ch}\) and \(x_{i}\) are the standard chemical exergy and mole fraction of components(i) in inorganic matter, respectively. R is the universal gas constant, 0.0083145 kJ. (mol.K)\({}^{-1}\), [PERSON] et al. (2019).  
One of the most important concepts of exergy analysis is calculating the fuel and the product streams for each component. Every component needs a driver to continue working which is defined as  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Parameters** & **Value** \\ \hline The flow rate of geothermal fluid (kg\(\cdot\)s\({}^{-1}\)) & 100 \\ The pressure of the geothermal fluid (bar), & 10 \\ The temperature of the geothermal fluid (\({}^{\circ}\)C) & 150 \\ A minimum temperature of returned geothermal fluid (\({}^{\circ}\)C) & 100 \\ The temperature of inlet of turbine (\({}^{\circ}\)C) & 130 \\ Temperature of ambient (\({}^{\circ}\)C) & 15 \\ Efficiency of the turbine & 0.85 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The design parameters of present study, [PERSON] et al. (2016), [PERSON] et al. (2019), [PERSON] (2017).  
the fuel stream of the equipment and every component has an output and goal to produce which is the product stream of that component.  
See Equation (7) for the specific flow rates of exergy. After calculating fuel and product of the equipment, [PERSON] et al. [42], further outputs of exergy analysis, i.e., exergy destruction (\(\dot{E}_{D}\)) and exergetic efficiency (\(\psi_{k}\)) of each component can be determined from Equations (8) and (9).  
\[\dot{E}_{k}=\ \dot{m}_{k}\text{-}e_{k} \tag{7}\]  
\[\dot{E}_{D}=\dot{E}_{F}-\dot{E}_{P}=\sum\dot{E}_{in}-\sum\dot{E}_{out}+\sum \dot{\mathcal{Q}}\Big{(}1-\frac{T_{0}}{T}\Big{)}+\sum\dot{W} \tag{8}\]  
\[\psi_{k}\ =\frac{\dot{E}_{P,k}}{\dot{E}_{F,k}} \tag{9}\]  
where \(e_{k}\) is the specific exergy of the streams, \(\dot{E}_{in}\) and \(\dot{E}_{out}\) are the exergy of heat input and work output. The \(\dot{E}_{P,k}\) and \(\dot{E}_{F,k}\) are the exergy rates associated with the product and fuel of each component, [PERSON] et al. [43]. The definition of input-output is applied to a traditional exergetic analysis, where the input is the amount of exergy that enters a component to produce an amount of product. Similarly, the product exergy is defined as the amount of exergy left by a component converted by the fuel exergy that previously entered the same component. For the specific case of the component under study \(k\), the exergy rate of fuel (\(\dot{E}_{F}\)), product (\(\dot{E}_{p}\)) and destruction (\(\dot{E}_{D}\)) is given by Equation (8). The exergetic efficiency (\(\psi_{k}\)) of each component can be determined from Equation (9).