Disclosed embodiments of the apparatus address the challenges of rotary PSA systems, both axial and radial flow, with M>1 by providing interpenetrating, layered manifolds to accommodate all of the steps of a complex PSA cycle, suitable with equal compactness for any value of “M”. This approach extends readily to accommodate a plurality of rotary PSA modules and their cooperating compression machinery within a single layered manifold assembly for a single PSA plant train. Described embodiments of the rotary PSA apparatus include stators that define fluid ports. In particular embodiments of the described apparatus, a second stator defines pressure swing adsorption cycle sectors, each sector being defined by a light product delivery port, light product withdrawal ports, and light reflux return ports. The adsorber elements may directly contact one or more of the stators in a fluidly sealing manner (i.e., have a clearance gap of from about 0 to about 50 microns) using described reinforced adsorbers. The method comprises providing an embodiment of the described apparatus and then supplying at least one feed fluid to pressurize an adsorber element of the adsorber sets to substantially a higher pressure to initiate a pressure swing adsorption cycle.