## 2 Methodology
### Traditional Exergetic Analysis  
Exergetic analysis takes into account the second law of thermodynamics, implying that exergetic analysis requires temperature and pressure in the environment where the process under consideration operates. Therefore, the entropy balance for the ORC system with recuperator for the steady state energy process is obtained from Equation (13) [49] as follows:  
\[\dot{s}_{gen.i}=\sum\dot{m}_{out}\cdot s_{out}-\sum\dot{m}_{in}\cdot s_{in}- \sum\frac{\dot{Q}}{T} \tag{13}\]  
where \(\dot{Q}\) represents the heat rate in kW, \(s\) shows the specific entropy for the fluid in kJ/kg\(\cdot\)K, \(\dot{m}\) is the mass flow in kg/s, a \(\dot{S}_{gen}\) refers to the generation of entropy. With this, the exergy of the thermomechanical flow is defined with Equation (14) as follows:  
\[\varepsilon_{i}=\left(h_{i}-h_{0}\right)-T_{0}\cdot\left(s_{i}-s_{0}\right) \tag{14}\]where \(h_{0}\) and \(s_{0}\) represent enthalpy and entropy in the dead state at temperatures and pressures (\(T_{0}\) and \(P_{0}\)), respectively. Therefore, the exergetic efficiency (\(\eta_{ox}\)) for the thermal system is denoted in Equation (15) as a function of output exergy (\(\dot{E}_{P}\)) and the inlet exergy (\(\dot{E}_{F}\)) for the system or device as follows:  
\[\eta_{ox}=\frac{\dot{E}_{P}}{\dot{E}_{F}} \tag{15}\]  
In Table 2, the balance of exergy by component is presented, where the term (\(\dot{E}_{d,~{}env}\)) represents the evaporator destroyed exergy, (\(\dot{E}_{d,~{}turb}\)) is the turbine destroyed exergy, (\(\dot{E}_{d,pum}\)) refers to the pump destroyed exergy, and (\(\dot{E}_{d,cond}\)) is the condenser destroyed exergy.  
For the calculation of the performance indicators for the WHR of an ORC system with a recuperator, the thermal efficiency in the cycle (\(\eta_{ll,~{}c}\)) is calculated by Equation (16), the efficiency of the heat recovery (\(\varepsilon_{hr}\)) represented in Equation (17), the energy conversion efficiency in overall system (\(\eta_{ll,~{}overall}\)) shown in Equation (18) and the absolute increase in thermal efficiency is determined by Equation (19), which relates the energy of the fuel to the net power output of the ORC. This indicator establishes the improvement in the performance of the ICE when an ORC-WHR type recovery system is used and is calculated as follows:  
\[\eta_{l,~{}c}=\frac{\dot{W}_{net}}{\dot{Q}_{G}} \tag{16}\]  
\[\varepsilon_{hr}=\frac{\dot{Q}_{G}}{\dot{m}_{10}C_{\rm P10}(T_{10}-T_{0})} \tag{17}\]  
\[\eta_{l,~{}overall}=\eta_{l,~{}c}\cdot\varepsilon_{hr} \tag{18}\]  
\[\Delta\eta_{thermal}=\frac{\dot{W}_{net-ORC}}{\dot{m}_{fuel}\cdot LHV} \tag{19}\]  
The improvement of the measurement of thermal efficiency, is calculated by improving the thermal efficiency by means of Equation (20) as a function of net work (\(\dot{W}_{net}\)) and the mass flow rate (\(\dot{m}_{fuel}\)). Fuel specific consumption (BSFC) is displayed in Equation (20), and the total specific reduction in fuel consumption as a result of the WHR is shown in Equation (21) as follows:  
\[BSFC_{ORC-engine}=\frac{\dot{m}_{fuel}}{\dot{W}_{engine}+\dot{W}_{net}} \tag{20}\]  
\[\Delta BSFC=\frac{\left|BSFC_{ORC-engine}-BSFC_{engine}\right|}{BSFC_{engine} }\cdot 100 \tag{21}\]