## 3 Implementation  
### Overview of the Process and the Amine Solvents  
For completeness, a brief overview of the process and solvents is provided in this work, with all details reported in [PERSON] et al. (2018). The flowsheets for the phase-change solvents are shown in Figure 2. In the current work, we investigated two types of phase-change solvents: a single solvent where phase separation occurs at 90 \({}^{\circ}\)C, hence the decanter (liquid-liquid phase separator) is placed after the intermediate heat exchanger (Figure 2a), and a phase-change solvent mixture that exhibits phase separation at 40 \({}^{\circ}\)C, hence the decanter is placed directly after the absorber (Figure 2b). For the conventional solvents and mixtures, the decanters are redundant. The main process parameters that need to be calculated include the reboiler duty in the stripper, the mass flow rate that enters the stripper, and the stripper temperatures. For the phase-change solvents, the mass flow rate of the stream entering the stripper is calculated through mass balances that consider the phase compositions at conditions around the decanter, hence fully accounting for the liquid-liquid phase separation. For the energetic calculations, the employed shortcut model ([PERSON] et al., 2018) focuses on two areas: the heat exchanger before the stripper and the reboiler after the stripper. The calculation of the reboiler duty takes place through the determination of the temperature of the rich stream that enters the desorber and of the lean stream that exits the stripper by implementing energy balances around the heat exchanger and the reboiler. All the details are reported in [PERSON] et al. (2018). To illustrate the approach described in Section 2, 10 solvents and mixtures (Tables 2 and 3), including two phase-change solvents, were investigated. The single solvents included MEA, AMP, DEA, 3-(methylamino)propylamine (MAPA), and methyl-cyclohexylamine (MCA). The mixtures included MEA with methyldiethanolamine (MDEA), MPA with MDEA, DEA with MDEA, AMP with piperazine (PZ), and 2-(diethylamino)ethanol (DEEA) with MAPA. The non-phase-change amines were previously investigated as CO\({}_{2}\) capture solvents and were retrieved from the published literature. Phase-change solvents are characterized by the presence of a vapor-liquid-liquid equilibrium, where after the phase split, one liquid phase is rich in CO\({}_{2}\), while the other phase is lean in CO\({}_{2}\) and rich in amine. MCA is selected as a representative of phase-change solvents requiring a liquid-liquid phase separator after the intermediate heat exchanger (HX) in the absorption-desorption flowsheet (Figure 2a), whereas DEEA-MAPA requires the liquid-liquid separator before the intermediate heat exchanger (Figure 2b). Figure 2: CO\({}_{2}\) capture flowsheet for phase-change solvents with phase separation (**a**) after the intermediate heat exchanger and (**b**) before the intermediate heat exchanger. The figures have been adapted from [PERSON] et al. (2018) with permission from Elsevier. HX: Heat exchanger. The employed thermodynamic models include the relations of the equilibrium pressure of CO\({}_{2}\) and enthalpy as functions of the loading and temperature. For MEA, the models were from [PERSON] [40], whereas for AMP and AMP/PZ, they were from Oexman [41]. For DEA, MEA/MDEA, DEA/MDEA, and MPA/MDEA, the models were derived from equilibrium data obtained from gSAFT software [42]. For MPA/MDEA, the software uses an equation of state (EoS) called SART-\(\gamma\) Mie [43; 44]. For the other three solvents, the model uses the SART-VR EoS [45]. For MAPA and DEEA/MAPA, models were derived from equilibrium data obtained from [PERSON] [46]. For MCA, the models were derived from equilibrium data obtained from [PERSON] et al. [47] and [PERSON] et al. [48].