Disclosed are apparatus and method to treat large amounts of flue gas from a pulverized coal combustion power plant. The flue gas is contacted with solid sorbents to selectively absorb CO2, which is then released as a nearly pure CO2 gas stream upon regeneration at higher temperature. The method is capable of handling the necessary sorbent circulation rates of tens of millions of lbs/hr to separate CO2 from a power plant's flue gas stream. Because pressurizing large amounts of flue gas is cost prohibitive, the method of this invention minimizes the overall pressure drop in the absorption section to less than 25 inches of water column. The internal circulation of sorbent within the absorber assembly in the proposed method not only minimizes temperature increases in the absorber to less than 25° F., but also increases the CO2 concentration in the sorbent to near saturation levels. Saturating the sorbent with CO2 in the absorber section minimizes the heat energy needed for sorbent regeneration. The commercial embodiments of the proposed method can be optimized for sorbents with slower or faster absorption kinetics, low or high heat release rates, low or high saturation capacities and slower or faster regeneration kinetics.