## 4 How Should We Treat the Multifunctionality of a Carbon Supply Chain in the LCA?
For these two cases, a valuable product such as electricity, ammonia, bio-ethanol, etc., is co-produced in a production process in addition to the feedstock carbon dioxide. In another case, if carbon dioxide is captured by air, then no other products are obtained because the scope is only to capture carbon dioxide from the ambient air. In the first case, positive carbon dioxide emissions are present, while in other cases, carbon dioxide emissions can be positive or negative. Then, the upstream processes of a carbon supply chain contain many co-products that should be considered inside system boundaries and then in the life cycle assessment. If carbon dioxide is used in the supply chain, two products are present: the product at the source that is co-produced with carbon dioxide and the carbon dioxide product in the utilization section. Overall, the carbon supply chain system is multifunctional. However, if carbon dioxide is captured from the air, the supply chain is mono-functional. In the case of multifunctionality, if the scope allows a joint evaluation, it is possible to operate by applying a system expansion methodology with the relative functional unit. In fact, the system expansion methodology is suggested by ISO due to the equivocal characteristic of allocation methodology. On the other hand, the allocation methodology will be used if system expansion is impossible because it should include the entire chemical industry or product-specific results are required, finding the emissions produced by a single product. It is important to underline that for a product-specific calculation, the avoided burden is not suggested for a carbon supply chain because the environmental benefit is totally assigned to a single product [10]. Furthermore, it is possible to use an economic allocation when prices are known: an economic allocation is suggested as a baseline method, and results can be verified with a sensitivity analysis. In order to understand the differences between these methods, these methodologies are applied and compared to measure the environmental impact of a carbon capture and utilization supply chain with methanol synthesis through carbon dioxide hydrogenation, capturing carbon dioxide from a power plant. Figure 7 shows the application of the system expansion methodology for the considered supply chain with and without methanol synthesis. If system expansion is applied, the functional unit considers both the production of 1000 kg of methanol and 1273 kW of electricity from the power plant. The total global warming potential impact is 153 (from the power plant) + 418 (from methanol synthesis) + 188 (from the eolic plant for electricity production and water electrolysis) = 759 kgCO2 eq, while for the conventional system, the global warming potential impact is 1090 (from the power plant) + 745 (from methanol synthesis) = 1835 kgCO2 eq. Emissions are reduced by 59% and the environmental benefit of the carbon supply chain is evident. The system expansion methodology allows a simple evaluation overcoming equivocal doubts raised with the multifunctionality. Figure 6: Classification of carbon dioxide sources: (**a**) carbon dioxide capture from non-biogenic point sources includes capture from power plants and industrial processes; (**b**) carbon dioxide from biogenic point sources includes biomass production; (**c**) carbon dioxide capture from ambient air [Modified after [PERSON] (2020)]. For a product-specific analysis, with the avoided burden applied to the considered supply chain, Figure 8 can be considered, where two products such as electricity (1273 kW) and methanol (1000 kg) are present. The main function of the system can be either electricity (considering the electricity producer point of view), as in Figure 7b, or methanol (considering the methanol producer point of view), as in Figure 7a. From a methanol perspective in the system, a surplus of electricity is present that can be avoided by a coal power plant without carbon dioxide capture. The same consideration is when electricity is the main function.