## 4 Modeling of the System Components
### Evaporator and Condenser
#### 4.3.1 Hydraulic Modeling  
The pressure drop in the evaporator and the condenser of the ORC unit was modeled in the refrigerant stream using the retuned empirical correlations, while it was neglected in the hot fluid stream in the evaporator and the cold fluid stream in the condenser. Hydraulic modeling of the PHEs was preliminarily performed to better assess their thermal performances afterward. Indeed, pressure drop mainly influences the calculated degree of subcooling in the condenser and of the superheating in the evaporator.  
In addition, solving a PHE using moving boundary or finite volume methods requires the resolution of the pressure distribution inside the PHE. Indeed, a specific calculation of the total pressure drop can result from infinite combinations of the pressure distribution in the channel, which in turn affects the thermal modeling. If a pressure drop correlation that depends on the local thermal resolution is adopted, the thermal and hydraulic correlations become coupled, and an iterative solver is needed for each zone/cell of the PHE consequently. However, since the mechanistic hydraulic modeling of the PHEs is out of the scope of the present work, an estimation of the pressure drop distribution was obtained using the relevant empirical models to obtain the hydraulic resolution independently from the thermal solver and make them decoupled.  
The pressure drop model is inspired by [22], suggested for single-phase flows in PHEs and used for boiling pressure drop modeling in PHEs by [PERSON] et al. [23] as in Equation (32).  
\[\Delta P_{i}=a\frac{G^{2}}{2\rho_{i}} \tag{32}\]  
where \(G\) is the mass flux (kg/m\({}^{2}\cdot\)s), \(\rho_{i}\) is the average zone/cell density (kg/m\({}^{3}\)), and \(a\) is the empirical coefficient to be found by minimization of the objective function (\(f\)) defined as the sum of the square of the relative deviation between the calculated pressure drop and the measured values as presented in Equation (33):  
\[f=\sum_{i=1}^{n}\left(\frac{\Delta P_{cal,i}-\Delta P_{meas,i}}{\Delta P_{meas,i}}\right)^{2} \tag{33}\]  
The results of the model and the pressure distribution in the condenser for one data point are presented in Figure 16. The root mean square error (RMSE) of the results is low, showing good agreement between the model results and the experimental data. The pressure distribution shows that the significant share of the total pressure drop is accounted for in the gas zone despite its marginal enthalpy change. In the gas zone, the fluid velocity is higher than the liquid and the two-phase zones; thus, pressure drop increases.  
Figure 16: Calculated and measured pressure drop of the condenser (**left**) and pressure drop resolution in different heat transfer zones in the condenser (**right**).  
The results for the evaporator are presented in Figure 17, showing even higher accuracy (lower RMSE) compared to the evaporator results. The lower accuracy of the results of the evaporator is due to the higher deviation of the evaporator experimental data around the mean value. The inlet pressure of the evaporator is directly affected by the pulses of the plunger pump and the variations of the heat source temperature as well. On the contrary, the plunger pump pulses were almost damped at the condenser inlet, and the water inlet temperature was much more stable due to the high mass flow rate of the cooling circuit.  
Finally, it should be noted that this approach should be taken with caution for general models of the heat exchangers especially if the pressure resolution is particularly important. However, for this work, a compromise between the accuracy and the computational speed was considered. The obtained empirical coefficients for the evaporator and condenser are reported in Table A1.