Phase-change solvents (PCSs) is a class of chemicals that promises significant cost reductions in post-combustion CO2 capture. However, their use in the design of efficient absorption/desorption processes is challenged by their non-ideal behavior. A generic and flexible model is proposed for the design of phase-change CO2 capture process systems, that enables the effective identification of highly performing flowsheet configurations and recycle stream redistribution policies. The validation of the model using experimental data for the PCS mixture of MAPA/DEEA (3-(Methylamino)-Propylamine/2-(Diethylamino)-Ethanol) indicates only 4% and 0.5% differences in the reboiler duty and in the absorption and desorption temperatures. The novel PCS mixture of S1N/DMCA (N-Cyclohexyl-1,3-Propanediamine/N,N-Dimethylcyclohexylamine) and the PCS MCA (N-methylcyclohexylamine) are used in the optimum design of CO2 capture process units in two industrial cases; a quicklime production plant and a gas-fired power plant. The reboiler duty of S1N/DMCA reaches 2.1 GJ/ton CO2 and the solvent exhibits up to 47% lower operating costs than the conventional MEA (Monoethanolamine), with only 1.7% higher capital costs. The loading of S1N/DMCA reaches up to 1.35 mol CO2/mol of solvent at the exit stream of the phase-separator, whereas this solvent exhibits up to 181% higher CO2 release efficiency than MEA in the desorber. S1N/DMCA is an excellent option for plants with flue gas CO2 concentration as low as 3.5 mol%.