Disclosed is a method of sequentially separating and recovering one or more NGLs (129, 229) from a natural gas feedstream (3). Specifically, a raw natural gas feedstream (3) is passed through two or more NGLs separation unit (100, 200) wherein each separation unit removes one or more NGLs from the natural gas feedstream to provide a methane-rich natural gas supply (205). Each separation unit employs an adsorption media and has an adsorption step and a media regeneration step wherein the regeneration step may be operated as a batch process, a semi-continuous process, or a continuous process. One embodiment of this method provides for the use of a different regenerable adsorbent media in each separation unit.

Pressure shift adsorption (PSA) process for producing a gas stream enriched with compound X from a feed gas stream, using N adsorbers with N5, each adsorber being subjected to a pressure cycle having a phase time corresponding to the duration of the pressure cycle divided by the number of adsorbers, and a series of active steps, characterized in that each adsorber n follows the pressure cycle with an offset of one phase time with respect to the pressure cycle of the adsorber n1 with nN, and during each phase time, only one active step or a part of active step takes place.