A cartridge for processing a fluid, said cartridge comprising: a housing that is generally tubular, having a housing wall, a first end, a second end, and having a midplane located between the first end and the second end; and a plurality of fibers (41, 46), at least some of said fibers being hollow and having porous walls or a semipermeable membrane, at least portions of said plurality of fibers being contained within said housing, said plurality of fibers being potted near their ends in a potting material (84, 132, 180, 230), wherein said plurality of fibers (41, 46) are arranged as a bundle of fibers (68, 198) that are generally parallel to each other at least at said midplane of said housing, and wherein at said midplane of said housing, said fibers (41, 46) are distributed substantially uniformly across a cross-section of said housing taken perpendicular to a longitudinal direction of said housing, and said plurality of fibers in said bundle of fibers having an average fiber-centerline-to-fiber-centerline spacing, wherein, adjacent to said potting material (84, 132, 180, 230), said bundle of fibers contains void flow channels (82, 130) that are substantially open and have a transverse dimension that is at least 3 times said average fiber-centerline-to-fiber-centerline spacing, wherein said void flow channels (82, 130) adjoin an outer circumference of said fiber bundle (68, 198) and extend inwardly to a radially more inward location, further comprising a distributor that is in fluid communication with said void flow channels (82, 130), and wherein said housing comprises a passageway through said housing wall, said passageway being in fluid communication with said void flow channels (82, 130). a housing that is generally tubular, having a housing wall, a first end, a second end, and having a midplane located between the first end and the second end; and a plurality of fibers (41, 46), at least some of said fibers being hollow and having porous walls or a semipermeable membrane, at least portions of said plurality of fibers being contained within said housing, said plurality of fibers being potted near their ends in a potting material (84, 132, 180, 230), wherein said plurality of fibers (41, 46) are arranged as a bundle of fibers (68, 198) that are generally parallel to each other at least at said midplane of said housing, and wherein at said midplane of said housing, said fibers (41, 46) are distributed substantially uniformly across a cross-section of said housing taken perpendicular to a longitudinal direction of said housing, and said plurality of fibers in said bundle of fibers having an average fiber-centerline-to-fiber-centerline spacing, wherein, adjacent to said potting material (84, 132, 180, 230), said bundle of fibers contains void flow channels (82, 130) that are substantially open and have a transverse dimension that is at least 3 times said average fiber-centerline-to-fiber-centerline spacing, wherein said void flow channels (82, 130) adjoin an outer circumference of said fiber bundle (68, 198) and extend inwardly to a radially more inward location, further comprising a distributor that is in fluid communication with said void flow channels (82, 130), and wherein said housing comprises a passageway through said housing wall, said passageway being in fluid communication with said void flow channels (82, 130).