Abstract: This invention relates to a process for separating a fluid component from a fluid mixture comprising the fluid component, 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, a header and a footer, the combined internal volume of the header and the footer being up to about 40% of the internal volume of the process microchannels; the fluid mixture being maintained in the microchannel separator until at least part of the fluid component is sorbed by the sorption medium; purging the microchannel separator to displace non-sorbed parts of the fluid mixture from the microchannel separator; and (B) desorbing the fluid component from the sorption medium and flowing a flush fluid through the microchannel separator to displace the desorbed fluid component from the microchannel separator. The process is suitable for purifying oxygen as well as effecting other fluid separations.