A gas-separation membrane module assembly and a gas-separation process using the assembly. The assembly includes a set of tubes, each containing gas-separation membranes, arranged within a housing. The housing contains tube sheets that divide the space within the housing into three separate, gas-tight spaces, with the tubes mounted in the central space. Within this space, each tube has an aperture or hole in its wall that enables gas that has been retained on the feed side of the membranes to flow out of the tubes and into the space. The assembly can be used in various ways to carry out gas separation processes.