## 2 Materials and Methods
### The Methodology of the Combustion Process  
The analysis of the combustion process and energy transformations were performed using the thermodynamic engine cycle and gas exchange simulation software AVL BOOST(tm) and its utility BURN. When simulating the combustion process, the first law of thermodynamics is applied for calculations to determine the thermodynamic state of the cylinder [44]:  
\[\frac{d(m_{c}\cdot u)}{d\alpha}=-p_{c}.\frac{dV}{d\alpha}+\frac{dQ_{F}}{d\alpha }-\sum\frac{dQ_{w}}{d\alpha}-h_{BB}.\frac{dm_{BB}}{d\alpha} \tag{1}\]  
where \(\frac{d(m_{c}\cdot u)}{d\alpha}\)--the total energy change in the cylinder; \(p_{c}\frac{dV}{d\alpha}\)--the work by the piston; \(\frac{dQ_{F}}{d\alpha}\)--the amount of heat in the fuel; \(\sum\frac{dQ_{w}}{d\alpha}\)--heat loss to the cylinder walls; \(h_{BB}.\frac{dm_{BB}}{d\alpha}\)--blowing due to piston rings. The mass inside the cylinder varies over time due to the continuous inflow and outflow of mass. This variation can be calculated by summing the mass entering and subtracting the mass leaving the cylinder:  
\[\frac{dm_{c}}{d\alpha}=\sum\frac{dm_{i}}{d\alpha}-\sum\frac{dm_{e}}{d\alpha} -\frac{dm_{BB}}{d\alpha}; \tag{2}\]  
where \(\frac{dm_{c}}{d\alpha}\)--the total mass inside the cylinder; \(\sum\frac{dm_{i}}{d\alpha}\)--the mass entering the cylinder; \(\sum\frac{dm_{e}}{d\alpha}\)--the mass going out from the cylinder. The single-zone Vibe function is used to approximate MFB, which is used to calculate ROHR with the subsequent equation:  
\[\frac{dQ_{B}}{d\alpha}=Q_{BT}\frac{a}{\Delta\alpha_{c}}\cdot(m+1)\cdot y^{m}.e^{-a\cdot y^{(m+1)}}; \tag{3}\]  
\[y=\frac{\alpha-\alpha_{0}}{\Delta\alpha_{c}}; \tag{4}\] \begin{table}
\begin{tabular}{c c c} \hline
**Properties** & **Gasoline (E10)** & **Natural Gas** \\ \hline Density, [kg/m\({}^{3}\)] & 753.7 * & 0.7609 \\ Lower heating value, [M]/kg] & 41.79 & 49.22 ** \\ Research octane number (RON) & 97.1 & \(\sim\)120 \\ Methane number (MN) & - & \(\sim\)77 \\ Stoichiometric A/F ratio, [kg/kg] & 14.24 & \(\sim\)17.1 \\ Fuel composition, [\%vol.] & Gasoline 90.3 & Methane (CH\({}_{4}\)) 94.3124 \\  & Ethanol 9.7 & Ethane (C\({}_{2}\)H\({}_{6}\)) 4.2309 \\  & Propane (C\({}_{3}\)H\({}_{8}\)) 0.6631 \\  & i-Butane (C\({}_{4}\)H\({}_{10}\)) 0.0766 \\  & n-Butane (C\({}_{4}\)H\({}_{10}\)) 0.1405 \\  & neo-Pentane (C\({}_{5}\)H\({}_{12}\)) 0.0015 \\  & i-Pentane (C\({}_{5}\)H\({}_{12}\)) 0.0098 \\  & n-Pentane (C\({}_{5}\)H\({}_{12}\)) 0.0043 \\  & C\({}_{6}\) plus (C\({}_{6+}\)) 0.0015 \\  & Nitrogen (N\({}_{2}\)) 0.4446 \\  & Carbon dioxide (CO\({}_{2}\)) 0.1155 \\ Hydrogen (H), [\%Mass] & 13.89 & 24.34 \\ Carbon (C), [\%Mass] & 82.5 & 74.69 \\ Oxygen (O), [\%Mass] & 3.61 & - \\ H/C ratio & 1.87/1 & 3.88/1 \\ Physical state & Liquid & Compressed gas \\ \hline \end{tabular}  
* at 15 \({}^{\circ}\)C measurement temperature; ** at 0 \({}^{\circ}\)C measurement temperature, 25 \({}^{\circ}\)C combustion temperature, and 1.01325 bar pressure.  
\end{table} 
Table 3: The properties of the fuels. where \(\frac{dQ_{B}}{da}\)--ROHR per crankshaft angle; \(Q_{BT}\)--total heat released during combustion; \(\alpha\)--Vibe function parameter related to the burn rate; \(\Delta\alpha_{\text{c}}\)--the combustion duration (CD) in terms of crank angle; \(m\)--Vibe function parameter influencing the shape of the burn curve, \(y\)--combustion progress, \(e\)--Euler's number. A numerical model of an SIE was implemented in AVL BOOST(tm) software (Figure 2), and the necessary input parameters were sourced from the manufacturer's specifications (Table 1) and fuel properties (Table 3). Combustion analysis, the reverse process of the combustion calculations performed in AVL BOOST(tm), is conducted using the BURN utility. This analysis leverages measured cylinder pressure data to derive the ROHR, a key indicator of combustion characteristics. To perform this, BURN requires input parameters encompassing engine and fuel specifications, cylinder geometry, and operating conditions (Table 4).