The disclosed invention relates to a process for separating methane or nitrogen from a fluid mixture comprising methane and nitrogen, the process comprising: (A) flowing the fluid mixture into a microchannel separator, the microchannel separator comprising a plurality of process microchannels containing a sorption medium, the fluid mixture being maintained in the microchannel separator until at least part of the methane or nitrogen is sorbed by the sorption medium, and removing non-sorbed parts of the fluid mixture from the microchannel separator; and (B) desorbing the methane or nitrogen from the sorption medium and removing the desorbed methane or nitrogen from the microchannel separator. The process is suitable for upgrading methane from coal mines, landfills, and other sub-quality sources.