The transport of dilute species through a hollow fiber membrane has occurred in several separation processes referred to in the literature as membrane extraction, supported liquid membrane, supported gas membranes, pervaporation, gas (vapor) permeation, pertraction and permabsorption. In these processes, the mass transfer often occurs with a constant external resistance and a constant shell concentration, or with a constant external resistance and a varied shell concentration resulting from an operational mode of co-current or counter-current. A set of algebraic expressions are derived to design a single module or modules-in-series and predict the operating performance, using the correlations of lumen mass transfer coefficient as described in our previous study [1]. The theoretical analysis demonstrates that modules-in-series are superior to a long single module or modules-in-parallel for a given separation, since it allows an improved lumen mass transfer rate. The simulations show that the equations suggested in this paper can provide a more accurate design than those reported in the literature.