## 4 Conclusions  
The paper describes a numerical study on the combustion of several methane-based fuels in a Controlled Auto Ignition engine. The authors studied pure methane and methane enriched with hydrogen at 10% and 20% of H\({}_{2}\), and for the first time, we also focused on three biogases. The biogases investigated are a conventional one with 66% of methane and 33% of carbon dioxide, and two innovative ones obtainable from digestion processes where the hydrogen yield is maximized. The latters are mixtures of methane, hydrogen, and carbon dioxide with methane/hydrogen ratio equal to 9:1 and 8:2, respectively. Due to the stoichiometry of the digestion process, the larger is the amount of hydrogen in the innovative biogas, the smaller will be the ratio Fuel/CO\({}_{2}\). Being Chemkin, the modelling environment, a single cylinder CAI engine was modelled to predict engine performance, comparing the fuels in terms of indicated mean effective pressure, engine efficiency, and NOx emissions. For the sake of simplicity, we used a single-zone model for CAI engines that is known to underestimate CO and HC emissions, whose analysis is here consequently neglected. The authors adopted the GRI-Mech 3.0 detailed radical chain reactions mechanism that, though derived for the combustion of a natural gas, it is appropriate to also study the combustion of all fuels investigated in this paper. In fact, all the elementary equations required to model the combustion of hydrogen are already present in the mechanism, as well as those involving CO\({}_{2}\). The comparison among the different fuels is performed by adjusting the CAI engine to obtain a constant maximum Indicated Mean Effective Pressure, impe, which is limited, in the CAI engine, by mechanical and thermal loads. The parameters were the initial gas temperature and the equivalence ratio. We can summarise main results as follows:  
* Methane-hydrogen mixtures require lower equivalence ratio (ER = 0.38) than methane (ER = 0.4) to deliver the same impe;
* Hydrogen addition to methane reduces the initial gas temperature requirement: In the optimal operating conditions with methane the initial gas temperature must be 468 K and drops to 448 K with the addition of 10% of hydrogen in CH4H2_1 blend and to 443 K with the addition of 20% of hydrogen in CH4H2_2 blend;
* Biogas 1 made of 66% methane and 33% carbon dioxide requires higher equivalence ratio (ER = 0.42) than methane (ER = 0.4) to deliver the reference impe due to the presence of CO\({}_{2}\) in the fuel. The initial gas temperature requirement also increases to 478 K;
* For the innovative biogas 2, with a CH\({}_{4}\)/H\({}_{2}\) ratio equal to 9:1, the required initial temperature decreases to 457 K with an ER = 0.4; \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Fuel** & **ER** & **T\({}_{\text{in}}\)** & **impe** & **\(\eta_{\text{i}}\)** & **NO\({}_{\text{x}}\)** \\  & **[-]** & **[K]** & **[bar]** & **[\%]** & **[g/kWh]** \\ \hline CH4 & 0.40 & 468 & 8.4 & 47.6 & 0.0249 \\ \hline CH4H2\_1 & 0.38 & 448 & 8.5 & 48.0 & 0.0120 \\ \hline CH4H2\_2 & 0.38 & 443 & 8.6 & 48.1 & 0.0113 \\ \hline Biogas 1 & 0.42 & 478 & 8.4 & 47.1 & 0.0275 \\ \hline Biogas 2 & 0.4 & 457 & 8.4 & 47.5 & 0.0112 \\ \hline Biogas 3 & 0.4 & 453 & 8.4 & 47.3 & 0.0089 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: ER, initial gas temperature and NOx emissions in optimal conditions. * For the innovative biogas 3, with a \(\rm CH_{4}/H_{2}\) ratio equal to 8:2, the required initial temperature further decreases to 448 K with an ER = 0.4;
* Hydrogen enrichment of methane reduces NOx emissions due to a lower initial gas temperature requirement in comparison with pure methane. The higher the hydrogen molar fraction, the smaller the NOx emissions. * For the innovative biogas NOx emissions decrease by increasing the amount of H\({}_{2}\) in the biogas. Additionally, in this case, this is due to a lower initial gas temperature requirement in comparison with both pure methane and the conventional biogas.