An apparatus (10, 110, 210, 310) for the separation and recovery of CO2, from air, by a cyclic adsorption/desorption process using a loose particulate sorbent for gas adsorption. The apparatus has a plurality of adjacent, parallel, spaced-apart layers (24, 124, 224, 324), each having a stiff frame supporting a flexible, gas-permeable fabric enclosure for the sorbent. The gas inlet (14, 114, 214, 314) and outlet (18, 118, 216, 316) of the apparatus are on its axially opposite sides, and each layer (24, 124, 224, 324) extending axially within the apparatus. The recovered CO2 can be either supplied to an enclosed space, recycled to an enclosed space, from which the CO2 had been separated, or vented to the exterior of the latter enclosed space.