## 2 Methodology
### Life-Cycle Inventory  
According to ISO 14044 [33], the life-cycle inventory (LCI) involves the compilation and quantification of inputs and outputs of the system under study throughout its life-cycle. This work includes a detailed description of the hydrogen recovery process, the energy production in the HT PEM fuel cell, and the management of the residual gas stream obtained during the hydrogen separation. The corresponding data inventory was prepared to quantify the energy and material flow that enter and leave the systems. Resource consumption and emissions were considered in the analysis. Primary data were obtained from own calculations, material and energy balances, and experimental data. Secondary data were collected from the GaBi database [49] and Ecoinvent [51]. The LCI comprised the determination of flowrates and compositions of the APG and COG streams, the energy requirements and materials flow in the separation of hydrogen, and the inventory of the fuel cell. The LCI showed in Table 2 includes the material balances of the residual gas streams. The inventory data has been obtained by developing material and energy balances for each process unit, based on the flows and compositions of the input gas streams.  
The separation of hydrogen from the gas streams was considered as a basis to assess the required energy demand and the corresponding mass flows. To determine these energy requirements, shown in Table 3, the minimum work required to achieve a 99.97% H\({}_{2}\) flow was calculated, which is the purity necessary to operate the fuel cell according to the standard ISO 14687-2 [35]. The same operation is performed for the separation of 50% methane in the APG stream. The necessary calculations and equations are included in Section S1 in Supplementary Materials.  
In the case of the outputs, various calculations must be performed to know the energy obtained from the combustion engine, which is shown in Section S2 in Supplementary Materials, and the energy obtained from the HT PEM fuel cell stack (experimental data provided by a collaborating institution were employed). The emissions generated from the processes were calculated by the stoichiometry of the combustion of the compounds. Nonetheless, depending on the scenario under consideration, the energy inputs and outputs of the system varied, so Table 3 presents a summary of the main flows for each alternative.  
As expected, the fuel cell itself constituted a relevant input to the system. This device is made of different basic elements, which comprise the membrane electrode assembly (MEA). These MEAs comprise carbon (19.46 g), platinum (1.5 g), etc. Nevertheless, the end plates, the bipolar plate, and the collectors were excluded from this study. The detailed information about the compositions of the anode, the cathode, and the membrane is provided in Section S3 in Supplementary Materials, together with the operating conditions and main characteristics of the fuel cell.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Gas Stream**} & \multicolumn{2}{c}{**Flow Rate**} & \multicolumn{4}{c}{**Molar Composition**} & \\  & **(kg/h)** & **H\({}_{2}\)** & **N\({}_{2}\)** & **CH\({}_{4}\)** & **CO\({}_{2}\)** & **CO** \\ \hline COG & 1566 & 0.602 & 0.047 & 0.262 & 0.021 & 0.068 \\ APG & 137 & 0.610 & 0.220 & 0.170 & 0.000 & 0.000 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Flowrates and compositions of the APG and COG streams.  
To obtain the consumptions and emissions associated with each process, the environmental impact of the complete system was evaluated using the LCA software GaBi 9.2. The GaBi [49] and Ecoinvent databases [51] were used for the background system. Since several processes and products were not available, proxy processes were created mainly based on the stoichiometry of the reactions.