Described herein are membrane processes for separating CO2 from flue gas. An exemplary process involves passing a fluid stream including the flue gas across a membrane permeable to CO2 and H2O, removing treated gas from a feed side of the membrane that has less CO2 than the flue gas, and removing permeate from a permeate side of the membrane comprising CO2 and H2O. Suitably, the permeate is removed at a sub-atmospheric vacuum pressure. The permeate is then cooled to remove at least some of the H2O from the permeate and form a smaller volume of H2O-depleted, CO2 enriched permeate.