## 2 Materials and Methods
### Fundamentals of the Combustion and Thermodynamic Models
#### 2.3.5 Energy Distribution and Emissions Processing  
The engine inlet heat energy (\(\dot{Q}_{int}\)) is defined based on the fuel mode, which can be entirely liquid using pure gasoline or oxygenated fuel blends with ABE as indicated in Equation (25), or alternately liquid-gaseous fuel, which constitutes the dual-fuel operation mode given by Equation (26).  
\[\dot{Q}_{int}=\dot{m}_{fuel}\bullet LHV_{f} \tag{25}\]  
\[\dot{Q}_{int}=\dot{m}_{fuel}\bullet LHV_{fuel}+\dot{m}_{HHO}\bullet LHV_{HHO} \tag{26}\]where the subscripts fuel refers to the fuel mixture and HHO represents the hydroxy gas. Similarly, the model defines the exhaust gas energy as follows:  
\[\dot{Q}_{exh}=\dot{m}_{exh}\bullet C_{p,exh}\bullet T_{exh} \tag{27}\]  
where \(C_{p,exh}\) represents the specific heat capacity of the combustion gases at constant pressure. On the other hand, the mechanical efficiency of the engine according to the fuel mode is defined as follows.  
Liquid fuel standalone operation:  
\[\eta_{mech}=\frac{PW}{\dot{m}_{fuel}\bullet LHV_{fuel}}\bullet 100 \tag{28}\]  
Dual-fuel mode:  
\[\eta_{mech}=\frac{PW}{\dot{m}_{fuel}\bullet LHV_{fuel}+\dot{m}_{HHO}\bullet LHV _{HHO}}\bullet 100 \tag{29}\]  
where \(PW\) is the power output of the engine calculated according to Equation (30).  
\[PW=\frac{2\bullet\pi\bullet\omega\bullet T_{r}}{60\bullet 1000} \tag{30}\]  
where \(T_{r}\) is the torque condition, and \(\omega\) refers to the engine angular speed. Lastly, this section concludes with the calculation of the unit conversion of the overall emissions.  
On the other hand, the measuring instrumentation for emissions levels is commonly reported in ppm and %vol, which are the default characteristics of gas analyzers. However, it is necessary to apply further processing to display these results according to the international standards (i.g. European legislation) that describe pollutants in terms of g \(\bullet\) km\({}^{-1}\) for light-dutty and passenger vehicles and g \(\bullet\) kWh\({}^{-1}\) for heavy-duty vehicles [38]. Therefore, the study converts the output data from the gas analyzers into g \(\bullet\) kWh\({}^{-1}\) according to the empirical correlations proposed by [PERSON] and [PERSON] [39]. The relevance of the emissions above processing is that they assist in relating emissions and fuel metrics, facilitating comparison. The correlation for emissions processing is based on the following formulation:  
\[EP_{i}=EV_{i,dry}\bullet\left(\frac{M_{i}}{M_{exh,dry}}\bullet k_{d}\right)= EV_{i,wet}\bullet\left(\frac{M_{i}}{M_{exh,wet}}\bullet k_{w}\right) \tag{31}\]  
where \(EP_{i}\), \(EV_{i,dry}\) and \(EV_{i,wet}\) represents the pollutant mass in the power unit (g \(\bullet\) kWh\({}^{-1}\)), exhaust emissions on a dry basis and wet basis, respectively. The term \(M_{i}\) accounts for the molecular mass, while \(M_{exh,d}\) and \(M_{exh,w}\) relates to the molecular mass of exhaust emissions on a dry and wet basis, respectively. Finally, the terms \(k_{dry}\) and \(k_{wet}\) are empirical constants with a value of \(3.873\) g \(\bullet\) kWh\({}^{-1}\) and \(4.160\) g \(\bullet\) kWh\({}^{-1}\), respectively, and relate the power unit and the exhaust emissions on a dry basis and wet basis, respectively. The conversion of the three primary pollutants treated in experimental evaluation is described in Equation (32) to (34) [39].  
\[CO\left[\frac{g}{kWh}\right]=3.591\bullet 10^{-3}\bullet CO(\% vol) \tag{32}\]  
\[NOx\left[\frac{g}{kWh}\right]=6.636\bullet 10^{-3}\bullet NOx(ppm) \tag{33}\]  
\[HC\left[\frac{g}{kWh}\right]=2.002\bullet 10^{-3}\bullet HC(ppm) \tag{34}\]