## 2 Material and Methods
### ORC Modeling  
Through the heat recovery system, the thermal oil transfers heat to the organic medium. The heat recovery device consists of the economizer, the evaporator, and the superheater, where the fluid is converted to saturated liquid, saturated vapor, and superheated vapor, respectively. The pinch point (PP) in the inlet of the evaporator is assumed at 10 K [26] and the superheating (\(\mathrm{\Delta T_{sh}}\)) of 5 K [13] is considered. The heat recovery system modeling is illustrated in Figure 2. To make this diagram clear, it is important to state that \(\mathrm{T_{3}}\), \(\mathrm{T_{33}}\), and \(\mathrm{T_{34}}\) are the organic medium temperature levels at the entrance of the economizer, evaporator, and superheater, respectively, while \(\mathrm{T_{4}}\) is the temperature level when the organic fluid exits the superheater.  
To avoid the two curves coming close, a minimum and a maximum heat recovery system inlet temperature (\(\mathrm{T_{s,in}}\)) are considered by the following expressions taking into account the pinch point and the ORC fluid saturation temperature (\(\mathrm{T_{sat}}\)) [13].  
\[\mathrm{T_{s,in,min}=T_{sat}+PP+\Delta T_{sh}} \tag{6}\]  
\[\mathrm{T_{s,in,max}=T_{3}+PP+(T_{sat}-T_{3}).\frac{(h_{4}-h_{3})}{(h_{33}-h_{ 3})}} \tag{7}\]  
Based on these two values above, a dimensionless parameter (b) is assumed to define the inlet temperature as below [13]:  
\[\mathrm{b}=\frac{T_{s,in}-T_{s,in,min}}{T_{s,in,max}-T_{s,in,min}} \tag{8}\]  
Figure 2: ORC heat recovery system modeling.  
The parameter b is considered to be equal to zero, because the ORC achieves higher energy and exergy efficiency in this case, according to Ref. [13]. The heat input to the organic Rankine cycle (Qin) is given as follows:  
\[\mathrm{Q_{in}}=\dot{\mathrm{m}}_{\mathrm{ORC}}\cdot(\mathrm{h_{4}}-\mathrm{h_{ 3}})=\dot{\mathrm{m}}_{\mathrm{s}}\cdot\mathrm{c}_{\mathrm{p,oil}}\cdot( \mathrm{T}_{\mathrm{s,in}}-\mathrm{T}_{\mathrm{s,out}}) \tag{9}\]  
Moreover, the ORC high-pressure (Phigh), is considered as a share of the organic medium critical pressure (Pcrit). The parameter (\(\alpha\)) is a ratio that compares the high pressure with the critical pressure and is defined below [26]:  
\[\alpha=\frac{\mathrm{P}_{\mathrm{high}}}{\mathrm{P}_{\mathrm{crit}}} \tag{10}\]  
The electricity demand of the ORC pump is defined as:  
\[\mathrm{P}_{\mathrm{pump}}=\frac{\dot{\mathrm{m}}_{\mathrm{ORC}}\cdot(\mathrm{ h_{2}}-\mathrm{h_{1}})}{\eta_{\mathrm{motor}}} \tag{11}\]  
The electricity production of the ORC turbine is defined as:  
\[\mathrm{P}_{\mathrm{turb}}=\eta_{\mathrm{Ing}}\cdot\dot{\mathrm{m}}_{\mathrm{ ORC}}\cdot(\mathrm{h_{4}}-\mathrm{h_{5}}) \tag{12}\]  
The net ORC electricity product is calculated as:  
\[\mathrm{P}_{\mathrm{el,ORC}}=\mathrm{P}_{\mathrm{turb}}-\mathrm{P}_{\mathrm{ pump}} \tag{13}\]  
The ORC thermal efficiency is equal to:  
\[\mathrm{\eta}_{\mathrm{ORC}}=\frac{\mathrm{P}_{\mathrm{el,ORC}}}{\mathrm{Q}_{ \mathrm{in}}} \tag{14}\]  
Table 1 includes all the ORC parameters of the ORC [13; 26]. Taking into consideration the heat source's possible temperature levels, organic working fluids with critical temperatures in a range from 200 to 300 \({}^{\circ}\)C are selected. Toluene, MDM, cyclohexane, n-heptane, and n-octane are examined as high-efficient and commonly-used fluids, according to Refs. [11; 13].