A more detailed description on PSA process (balance equations, boundary conditions, cyclic steady state) can be referred to our prior work. After our initial trail, one PSA unit cannot guarantee the required purity (90% for carbon capture), due to the low CO2 concentration in the flue gas (~ 4%). Herein, we propose to use two PSA in series to gradually improve the purity of CO2. A trade-off relationship is reported between recovery and purity. To maintain a relatively high recovery, the first PSA aims to increase the CO2 purity to 20%~50% (ranging from 25% to 75% among the CO2 purity distribution), while the second one PSA further improve the CO2 purity over 90%.