Hollow-fiber membrane processes with a constant external resistance having a constant or variable shell concentration resulting from an operational mode of cocurrent or countercurrent are studied. By solving numerically the continuity mass-conservation equation with the corresponding boundary conditions the lumen laminar mass-transfer coefficients for both cases are correlated The correlations greatly improve the calculating accuracy of the overall mass-transfer coefficient and can be used to obtain the lumen mixed-cup concentration by an algebraic equation substituting the partial differential equation. A separation factor m’ is introduced to characterize the effect of the operational mode. Calculation results demonstrate that the lumen mass-transfer coefficient is independent of the real lumen and shell concentrations but if is greatly influenced by m’. The countercurrent mode, compared to the cocurrent mode, provides not only a higher mean driving force, but a higher lumen mass-transfer coefficient. This conclusion is novel and valid for the tube-shell heat or mass-transfer processes and is supported by the experimental data in the literature and our gas membrane separation experiments.