## 2 Materials and Methods
### Fundamentals of the Combustion and Thermodynamic Models  
The fundamental formulation implemented in this paper represents a simplified model of the physical phenomena due to required modeling assumptions. First, all combustion gases in all stages follow ideal gas behavior [30]. Moreover, the flame propagation speed is considered to operate below the supersonic condition, assuming a uniform pressure in the combustion chamber [31]. The combustion reactants are assumed in stoichiometric amounts, considering that a significant part of the combustion results from diffusion \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Units** & **ABE5** & **ABE10** \\ \hline LHV & (MJ \(\bullet\) kg\({}^{-1}\)) & 42.79 & 42.20 \\ Density & (kg \(\bullet\) mg\({}^{-3}\)) & 740.38 & 743.76 \\ Latent Vaporization heat & (kJ \(\bullet\) kg\({}^{-1}\)) & 451.77 & 463.54 \\ Autoignition & (\({}^{\circ}\)C) & 304.36 & 308.73 \\ Laminar flame velocity & (cm \(\bullet\) s\({}^{-1}\)) & 33.49 & 33.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Properties of the ABE blends. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Units** & **Gasoline** & **Acetone** & **Butanol** & **Ethanol** \\ \hline Chemical formula & - & C\({}_{4}-C_{12}\) & C\({}_{3}\)H\({}_{6}\)O & C\({}_{4}\)H\({}_{9}\)OH & C\({}_{2}\)H\({}_{5}\)OH \\ LHV & (MJ \(\bullet\) kg\({}^{-1}\)) & 43.4 & 29.6 & 33.1 & 26.8 \\ Density & (kg \(\bullet\) m\({}^{-3}\)) & 737 & 788 & 810 & 789 \\ Vaporization latent heat & (kJ \(\bullet\) kg\({}^{-1}\)) & 440 & 518 & 716 & 904 \\ Autoignition & (\({}^{\circ}\)C) & 300 & 465 & 343 & 420 \\ temperature & (cm \(\bullet\) s\({}^{-1}\)) & 33 & 34 & 48 & 39 \\ Laminar flame speed & (cm \(\bullet\) s\({}^{-1}\)) & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Properties of the fuels used in this study [28]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Test** & **RPM** & **Load (\%)** & **Fuel Mixture Composition** & **Symphology** \\ \hline
1 & & & 100\% Gasoline & G \\
2 & & & 95\% Gasoline + 5\% ABE & ABE5 \\
3 & & 50 & 90\% Gasoline + 10\% ABE & ABE10 \\
4 & & & 95\% Gasoline + 5\% ABE + 0.04 LPM Hydrology & ABE5 + HFO \\
5 & & & 90\% Gasoline + 10\% ABE + 0.04 LPM Hydrology & ABE10 + HFO \\
6 & & & 100\% Gasoline & G \\
7 & & & 95\% Gasoline + 5\% ABE & ABE5 \\
8 & 2400 & 75 & 90\% Gasoline + 10\% ABE & ABE10 \\
9 & & & 95\% Gasoline + 5\% ABE + 0.04 LPM Hydrology & ABE5 + HFO \\
10 & & & 90\% Gasoline + 10\% ABE + 0.04 LPM Hydrology & ABE10 + HFO \\
11 & & & 100\% Gasoline & G \\
12 & & & 95\% Gasoline + 5\% ABE & ABE5 \\
13 & & 100 & 90\% Gasoline + 10\% ABE & ABE10 \\
14 & & & 95\% Gasoline + 5\% ABE + 0.04 LPM Hydrology & ABE5 + HFO \\
15 & & & 90\% Gasoline + 10\% ABE + 0.04 LPM Hydrology & ABE10 + HFO \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Nomenclature and composition of fuels. interactions. Similarly, reactant's properties are calculated using an average temperature in the combustion chamber, which entails thermal stabilization as a result of the diffusion process. Finally, the model accounts for heat exchange interactions in the cylinder liner to reinforce the model prediction capabilities. As a first insight, the model establishes the first law of thermodynamics for an open system, which constitutes the combustion chamber. In essence, this model enables the characterization of the heat release curves as a function of the engine operating conditions. Accordingly, Equation (4) gives an energy balance for the control volume neglecting macroscopic effects [32]:  
\[\frac{dU}{d\theta}=\frac{dQ}{d\theta}-\frac{dW}{d\theta}+\sum_{i}\frac{dH_{i}} {d\theta} \tag{4}\]  
where \(U\) refers to internal energy, \(Q\) and \(W\) represent heat and mechanical work, respectively. \(H\) refers to the system enthalpy, and \(\theta\) relates to the crank angle.