Apparatus and method for separating carbon dioxide with self recycle loop

A method of separating carbon dioxide, the method comprising steps of:

• (a) feeding a combustion gas into a first separation membrane to obtain a first permeate gas and a first residue gas, discharging the first residue gas from the first separation membrane, and feeding the first permeate gas into a second separation membrane;
• (b) feeding a second residue gas from the second separation membrane into the first separation membrane, and feeding a portion of a second permeate gas from the second separation membrane directly back into the second separation membrane while the portion of the second permeate gas does not pass through a separation membrane other than the second separation membrane to increase a concentration of carbon dioxide in a feed side of the second separation membrane, thereby recycling the second permeate gas that is discharged by passing through a permeate side of the second separation membrane;
• and
• (c) feeding the first residue gas from the first separation membrane into a third separation membrane to obtain a third permeate gas and a third residue gas, discharging the third residue gas from the third separation membrane, and feeding a portion of the third permeate gas back into the third separation membrane while the portion of the third permeate gas does not pass through a separation membrane other than the third separation membrane.