## 2 Methodology
### Alternative Based on Electrochemical Reduction CO\({}_{2}\)
Life Cycle Inventory (LCI) and LCA (cradle-to-gate analysis) were performed based on the experimental conditions used in three different approaches of ER of CO\({}_{2}\) to formate/formic acid that were found in the literature. The selected references and their corresponding conditions are summarized in Table 2. Data for A1.1 was obtained within the research group of the authors [15]. This work represents a relevant advance compared to previous results due to the high concentrations obtained. A1.2 and A1.3 are, to the best of our knowledge, the performing champions in terms of FA concentration. This way, it is possible to establish a benchmark for further developments as later discussed. A1.2 and A1.3 [14] alternatives were selected because of their demonstrated capability of producing FA concentrations of 10.0% wt. and 20.5% wt., respectively. Main difference between A1.2 and A1.3 is their mode of operation, being single pass in the case of A1.2 (as in the case of A1.1) and recirculated mode in the case of A1.3. Electrolyte flowrate used in A1.1 reference is an order of magnitude higher than A1.2 and A1.3. Differences in electrode and membrane materials can be also observed. They share mainly the cathode material in the form of Sn nanoparticles (Sn NPs) deposited over a carbonaceous GDE. Regarding FE, A1.1 shows a higher value than A1.3 but is lower than A1.2. \begin{table}
\begin{tabular}{c c} \hline \hline
**Cathodic Reaction** & **Anodic Reaction** \\ \hline CO\({}_{2}\) + H\({}_{2}\)O + 2e\({}^{-}\)\(\rightarrow\) HCOO\({}^{-}\) + OH\({}^{-}\) & H\({}_{2}\)O \(\rightarrow\) 2H\({}^{+}\) + 2e\({}^{-}\) + 1/2 O\({}_{2}\) \\ \hline Overall reaction & \\ CO\({}_{2}\) + 2H\({}_{2}\)O \(\rightarrow\) HCOOH + O\({}_{2}\) + H\({}_{2}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main and side reactions. Catalytic electrode materials, reactor design, hydrodynamic conditions, current density, supporting electrolyte, etc., could be potentially combined to yield the best FE. The detailed LCIs for required materials and energy corresponding to each set of experimental data were calculated by means of a sequence of energy and mass balances. More details can be found in the supplementary data published in a previous study [26]. Mass balances were performed in each unit, ensuring that there were no mass losses for any element. This methodology ensures that each CCU-ER alternative is treated equally; thus, the results are directly comparable. The electricity needed in the process, such as the electricity demanded in the reduction of CO2 to FA, the electricity for the pumps within the reactor cell, and the electricity needed for liquefying both O2 and H2, was assumed to come from the surplus production of renewable energy in the form of photovoltaic solar energy (PV). Alternatively, wind power could be also considered. Surplus energy derives from avoiding curtailment of PV solar or wind farms due to the possibility of injecting excess power in the CCU facility. The periods in which the electricity generation exceeds the demand create a problem of \"surplus production\", which can help at the ER of CO2. This selection determines the CF of each unit of electricity used for the process, which in this case was 0.03 kg\(\cdot\)kWh\({}^{-1}\)[31]. The use of other high-carbon source for the electricity consumption will make no sense for ER purposes [26]. Pumping needs are derived from the need to overcome the pressure drop inside the reactors. Heat, as steam, is a utility used in the distillation unit. The source for this steam is natural gas and the CF per unit of steam used is 0.277 kg\(\cdot\)kg\({}^{-1}\), which was obtained from Ecoinvent data [27].