## 3 Data Processing
### Thermodynamic Investigation
#### 3.2.1 Performances Analysis and Calculation  
The performances of this ORC, with the pure fluid and the zeotropic mixture, were screened considering two different aspects: on the one hand, the expansion component; and on the other hand, the performances of the overall ORC system.  
The turbine performances, which were analyzed according to the variation in the pressure ratio as defined by Equation (2), were studied according to two different approaches: firstly, with a dimensionless parameter of the turbine as defined by Equation (3); and secondly, with the overall electrical efficiency of the turbine, which includes the expansion element and the generator as defined by Equation (4).  
\[\pi_{tur}=\ \frac{P_{in,wf,tur}}{P_{out,wf,tur}} \tag{2}\]  
\[\tilde{\Lambda}=\ \frac{\dot{m}_{wf}}{S_{in,tur}\cdot p_{0,in,tur}\cdot c_{0,in,tur} \left(\frac{2}{\gamma+1}\right)^{\frac{\gamma+1}{S(\gamma-1)}}} \tag{3}\]  
\[\eta_{tur}=\ \frac{\dot{W}_{el,tur}}{\dot{W}_{is,tur}}=\frac{\dot{W}_{el,tur}}{ \dot{m}_{wf}\left(\dot{h}_{in,wf,tur}-h_{is,wf,tur}\right)} \tag{4}\]  
Regarding the dimensionless parameter \(\tilde{\Lambda}\) in Equation (3)'s definition, the polytropic coefficient is involved. To be more realistic to the real transformation and not to consider the pure fluid or the mixture as a perfect gas, the equivalent \(\gamma\) model was used, which is supposed to be an accurate model for dense gas. This model is quite similar to the ideal one, with the difference that the gas goes through a polytropic transformation, assuming the relationship defined in Equation (5):  
\[\frac{P_{in,wf,tur}}{\rho_{in,wf,tur}}=\frac{P_{out,wf,tur}}{\rho_{out,wf,tur}} \tag{5}\]  
The polytropic coefficient, whose value can be less than 1, is evaluated by exploiting the linearity of Equation (5). Thanks to this definition, the polytropic coefficient is obtained for the experimental data, is expressed as the logarithmic relationship \(log\frac{P_{in}}{P_{out}}=\ \gamma\cdot log\frac{\dot{min}}{P_{out}}\), and treated as the slope of the linear regression. Figure 2a,b illustrate and confirm this interpretation.  
Figure 2: The polytropic coefficient in accordance with (**a**) Pure fluid; (**b**) Mixture.  
The overall electrical turbine efficiency, corresponding to the highest electrical gross production obtained during the experimental tests, is also compared with the other expansion technologies according to the available literature, for the power production range of 1-10 kW [23].  
To analyze the overall performances of the installation, the thermal efficiency of the ORC, as defined by Equation (6), and the second law efficiency of the ORC, as defined by Equations (7) and (8), are studied according to the electricity production. Two comparisons of the tests conducted in pure fluid and mixture are presented. The first one covers all the tests, and the second one compares the pure fluid tests with the mixture tests with the same operating parameters.  
\[\eta_{th,net}=\ \frac{\dot{W}_{el,tur}-\dot{W}_{el,ps}}{\dot{Q}_{heat}}=\ \frac{\dot{W}_{el,tur}-\dot{W}_{el,ps}}{\dot{m}_{hf} \big{(}h_{in,hf,eup}-h_{out,hf,pre}\big{)}} \tag{6}\]  
\[\eta_{ll,net}=\ \frac{\dot{W}_{el,tur}-\dot{W}_{el,ps}}{\dot{E}_{in,hf,eup}-\dot{E}_{ out,\ hf,pre}} \tag{7}\]  
\[\dot{E}_{x}=\dot{m}_{x}\big{(}h_{x}-h_{ref}-T_{ref}\big{(}s_{x}-s_{ref}\big{)} \big{)} \tag{8}\]  
As with the turbine, the performances of the ORC are compared with the literature data. To be analyzed with the available data, the ORC performances are taken as their gross efficiencies.  
The influence of the variation in the high pressure of the cycle with the mixture is also studied.