## 2 Materials and Methods
### Thermodynamic Analysis
#### 2.2.1 Energy Analysis  
Based on the assumptions made, the mass and energy balances of the control volume are given by Equations (1)-(3) below:  
\[\sum\dot{m}_{in}=\sum\dot{m}_{out} \tag{1}\]  
\[\sum\dot{E}n_{in}=\sum\dot{E}n_{out} \tag{2}\]  
\[\dot{E}n_{air}+\dot{E}n_{fuel}=\dot{E}n_{W}+\dot{E}n_{exh}+\dot{E}n_{loss} \tag{3}\]  
where \(\dot{m}_{in}\) and \(\dot{m}_{out}\) are respectively the inlet and outlet mass flow rates, \(\sum\dot{E}n_{in}\) and \(\sum\dot{E}n_{out}\) represents respectively the total energy inlet and outlet rates of the control volume, \(\dot{E}n_{air}\) is the inlet energy rate of air, \(\dot{E}n_{fuel}\) is the inlet energy rate of the fuel, \(\dot{E}n_{W}\) is the energy rate by work, \(\dot{E}n_{exh}\) is the energy outlet rate by the exhaust, and \(\dot{E}n_{loss}\) is the energy loss rate of the control volume. Because the intake air stream is at the same temperature as the reference state, the amount of energy inlet into the control volume can be neglected [45].  
The rate of energy inlet from the fuel (\(\dot{E}n_{fuel}\)) to the control volume is calculated using the fuel mass flow (\(\dot{m}_{fuel}\)) and the fuel lower heating value (\(\dot{L}HV\)) as shown in Equation (4) below, where \(i\) represents the different fuels that composed the blend.  
\[\dot{E}n_{fuel}\ =\ \sum_{i=1}^{3}\dot{m}_{fuel_{i}}\cdot\dot{L}HV_{fuel_{i}} \tag{4}\]  
Figure 2: Control volume of the engine.  
The work rate (\(\dot{E}n_{W}\)) was considered as the indicated power of the engine, which is expressed by Equation (5) below:  
\[\dot{E}n_{W}=\frac{IMEP\cdot V_{d}\cdot N}{n_{R}\cdot 60\cdot 10^{3}} \tag{5}\]  
where \(N\) (rpm) is the engine speed, \(V_{d}\) (m\({}^{3}\)) represents the displaced volume, IMEP is the indicated mean effective pressure and \(n_{R}\) is the number of crank revolutions for each power stroke per cylinder (e.g., \(n_{R}\) is 2 for a four-stroke engine). The IMEP is calculated only from the cylinder pressure to represent the average pressure over a cycle of the engine.  
The outlet exhaust energy rate (\(\dot{E}n_{exh}\)) of the control volume is determined as in Equation (6):  
\[\dot{E}n_{exh}\ =\ \sum_{i}\dot{m_{i}}\cdot h_{i} \tag{6}\]  
where \(\dot{m_{i}}\) is the mass flow rate and \(h_{i}\) is the enthalpy of each gaseous species in the engine exhaust, respectively.  
Then, the energy loss rate (\(\dot{E}n_{loss}\)) of the control volume consists of all energy heat losses involved, which includes the heat transfers from cylinder walls (combustion chamber and piston), by coolant, and by the oil, except for the exhaust losses. In this work, the \(\dot{E}n_{loss}\) is calculated as the difference between the energy inlet rate and the energy outlet rate (work and exhaust gases) from the control volume, such as in [26; 46], as shown in Equation (7) below:  
\[\dot{E}n_{loss}=\dot{E}n_{fuel}-\dot{E}n_{W}+\dot{E}n_{exh} \tag{7}\]  
Finally, the energy efficiency (\(\eta\)) of the control volume, based on the First Law of Thermodynamics (i.e., thermal efficiency), is defined as the work outlet ratio to the fuel energy inlet is shown in Equation (8).  
\[\eta=\frac{\dot{E}n_{W}}{\dot{E}n_{fuel}} \tag{8}\]