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 membrane elements, 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. Feed gas enters the tubes through apertures positioned to feed multiple membrane elements within a tube in parallel, and one or more manifolds are used to collect residue gas from the membrane elements and direct the gas to the residue port or to a second group of membrane elements within the tube. The assembly can be used in various ways to carry out gas separation processes.