## 2 Methodology
### Alternative Based on Electrochemical Reduction CO\({}_{2}\)  
To estimate the CF of the ER alternatives A1.1, A1.2, and A1.3, the LCA system framework was set as in Figure 2. As it can be seen, there are three main steps: the ER of CO\({}_{2}\), the distillation of the products, and the compression of parallel obtained byproducts such as H\({}_{2}\) and O\({}_{2}\) in a liquid form ready to transport. Energy consumption is in the form of electricity or steam according to the nature of each individual process. Mass balances are based on the reaction of the CO\({}_{2}\) ER shown in Table 1, assuming neutral to alkaline conditions [29; 30]. CO\({}_{2}\) and water are injected in the cathode. As solubility of CO\({}_{2}\) is assumed to be very high, the soluble CO\({}_{2}\) reaches the cathode surface. CO\({}_{2}\) is reduced to formate (HCOO\({}^{-}\)) and H\({}_{2}\)O to hydroxide ions (OH\({}^{-}\)) in the presence of the correspondent electrolyte in the cathodic compartment of the ER cell. Simultaneously, the formation of oxygen (O\({}_{2}\)) and protons (H\({}^{+}\)) is considered as the only reaction taking place in the anodic compartment. Both the formate ions and hydroxide ions migrate to the centre compartment through the membrane, where they balance the protons produced in the anode to form FA (HCOOH) and water (H\({}_{2}\)O). In an ideal ER reactor, an excellent electrode would lead to a value of 100% for the faradaic current efficiency (FE). This would  
Figure 1: System frameworks: (**a**) alternative A\({}_{\text{ER}}\) (scenarios A1.1, A1.2 and A1.3), (**b**) alternative A\({}_{\text{JBC}}\), and (**c**) conventional A\({}_{\text{CONV}}\). Figure 2: CCU system framework. correspond to the formation of pure HCOOH in the cathode and pure O\({}_{2}\) in the anode. However, a part of the applied current density is deviated to other parallel/parasitic reactions [30], reducing the FE to FA production. In this study, H\({}_{2}\) evolution reaction (HER) is assumed as the unique parallel reaction. It is considered that water is the chemical compound that is consumed regardless of the pH in the half-cell being acid or basic. The O\({}_{2}\) evolution reaction (OER) is the only reaction taking place in the anode. A purification process in the form of a distillation is required to increase the FA concentration at the outlet of ER to the accepted commercial concentration value at 85% wt. Therefore, cooling and heating are needed. The distillation process was simulated in a previous study carried out by the authors [26]. The simulation considers only presence of water (obtained as a head product) and FA (obtained as the bottom product) at the required concentration. Distilled water is recirculated and reinjected to the inlet freshwater stream to the cathode. Then, net water consumption is the difference between water in the inlet stream and water that is recirculated. The pure O\({}_{2}\) produced as a secondary product, mainly by the anodic reaction, is separated, liquefied, and recovered, as well as H\({}_{2}\), which is produced by the competing reaction, and it is assumed to be pure. Finally, a summary of additional hypothesis that was taking into account in this work is listed next:  
1. A CO\({}_{2}\) valorisation plant is in the same site of the CO\({}_{2}\) source (no transport is required). 2. The feed of CO\({}_{2}\) to the plant is assumed to be pure and with a suitable pressure for the ER process. 3. The feed of CO\({}_{2}\) to the plant is assumed to be free of environmental burdens. The feedstock CO\({}_{2}\) sourced to the plant is for free, so 100% of the burdens are allocated to the product that directly releases the CO\({}_{2}\), e.g., electricity forms a coal-fired power plant. 4. The vapour steam needed for FA purification exists in dry saturated conditions. 5. Electrolytes used in the ER process can be perfectly separated and they are considered to be avoided products. 6. The lifetimes of the electrode materials and catalysts are long enough to neglect their carbon footprint.