## 3 Results and Discussion
### Plasma-Catalytic Conversion of Biogas  
As indicated in Figure 3, no conversion of CH\({}_{4}\) or CO\({}_{2}\) takes place in the \"catalyst only\" run without any plasma discharge in the system, which uses the 5 Ni-5 Fe/Al\({}_{2}\)O\({}_{3}\) catalyst. This lack of reaction can be attributed to the relatively low reaction temperature (<100 \({}^{\circ}\)C). Nevertheless, upon applying NTP, the conversion of both CH\({}_{4}\) and CO\({}_{2}\) enhances substantially, resulting in the production of gas, liquid, and coke by-products, according to Table 3. The major gas products, hydrogen (H\({}_{2}\)) and carbon monoxide (CO), are detected by the micro-GC, while the incondensable hydrocarbons (C\({}_{x}\)H\({}_{y}\)) are mainly composed of C\({}_{2}\)H\({}_{6}\), along with trace amounts of C\({}_{2}\)H\({}_{4}\), C\({}_{3}\)H\({}_{8}\), and C\({}_{4}\)H\({}_{10}\). The liquid products collected were analyzed using GC-MS, and the results identified them as C\({}_{1}\)-C\({}_{3}\) oxygenates, including methanol, ethanol, formaldehyde, propaneic acid, acetic acid, and isopropanol, as shown in Figure S1. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Catalyst**} & **Weak (<250 \({}^{\circ}\)C)** & **Medium and Strong** & **Total Acid Sites** \\  & **mmol/g** & **(>250 \({}^{\circ}\)C) mmol/g** & **(mmol/g)** \\ \hline Al\({}_{2}\)O\({}_{3}\) & 0.31 & 0.59 & 0.90 \\ Ni/Al\({}_{2}\)O\({}_{3}\) & 0.35 & 0.13 & 0.48 \\ Fe/Al\({}_{2}\)O\({}_{3}\) & 0.32 & 0.11 & 0.43 \\ Ni-Fe/Al\({}_{2}\)O\({}_{3}\) & 0.33 & 0.09 & 0.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: NH\({}_{3}\)-TPD surface acidity of the fresh catalysts. Figure 3: Feed analysis in plasma-catalytic experiments for biogas conversion. In the \"plasma only\" run without using any catalyst powder in the reactor, the conversion rates for CH\({}_{4}\) and CO\({}_{2}\) are 30.3% and 15.4%, respectively. Due to the lower dissociation energy of CH\({}_{4}\) (4.57 eV) in comparison with CO\({}_{2}\) (5.52 eV) [14], the conversion of methane is higher than that of carbon dioxide. However, a significant drawback of this purely plasma-driven process was the complete absence of any condensable liquid products, coupled with a substantial formation of solid carbonaceous deposits, or coke, which reached a yield of 44.1%. This high coke formation posed a significant limitation to the practical application of the plasma-only process. In stark contrast, the introduction of metal-supported catalysts, namely 10 Fe/Al\({}_{2}\)O\({}_{3}\), 10 Ni/Al\({}_{2}\)O\({}_{3}\), 2.5 Ni-7.5 Fe/Al\({}_{2}\)O\({}_{3}\), 7.5 Ni-2.55 Fe/Al\({}_{2}\)O\({}_{3}\) and 5 Ni-5 Fe/Al\({}_{2}\)O\({}_{3}\), into the plasma discharge region profoundly altered the reaction pathway. These catalytic interventions not only enabled the formation of liquid products but also dramatically mitigated the undesirable deposition of coke. Notably, the CH\({}_{4}\) conversion rates exhibited a consistent increase across the catalytic series, reaching 31.6% for 10 Fe/Al\({}_{2}\)O\({}_{3}\), 33.1% for 10 Ni/Al\({}_{2}\)O\({}_{3}\), and culminating at 34.8% for the bimetallic 5 Ni-5 Fe/Al\({}_{2}\)O\({}_{3}\) catalyst. Similarly, CO\({}_{2}\) conversion rates demonstrated a corresponding upward trend, registering 15.9%, 17.5%, and 19.7% for the respective catalysts. Moreover, the yields of liquid products also showed a progressive enhancement, attaining values of 30.9%, 34.0%, and 38.6% for 10 Fe/Al\({}_{2}\)O\({}_{3}\), Ni/Al\({}_{2}\)O\({}_{3}\), and Ni-Fe/Al\({}_{2}\)O\({}_{3}\), respectively. The observed superiority of the bimetallic 5 Ni-5 Fe/Al\({}_{2}\)O\({}_{3}\) catalyst, characterized by the highest liquid product yield and the lowest coke formation, can be rationalized by considering its surface acidity. High surface acidity promotes coke formation by facilitating undesired side reactions, such as methane cracking and polymerization of hydrocarbons.