The disclosed invention relates to a process and apparatus for separating a first fluid from a fluid mixture comprising the first fluid. The process comprises: (A) flowing the fluid mixture into a microchannel separator in contact with a sorption medium, the fluid mixture being maintained in the microchannel separator until at least part of the first fluid is sorbed by the sorption medium, removing non-sorbed parts of the fluid mixture from the microchannel separator; and (B) desorbing first fluid from the sorption medium and removing desorbed first fluid from the microchannel separator. The process and apparatus are suitable for separating nitrogen or methane from a fluid mixture comprising nitrogen and methane. The process and apparatus may be used for rejecting nitrogen in the upgrading of sub-quality methane.