Computational fluid dynamics simulations are conducted for binary fluid flows over banks of hollow fiber membranes. Separation of carbon dioxide (CO2) from methane (CH4) is studied using hollow fiber membranes structured in different arrangements. The membrane is considered as a functional surface where the mass flux and concentration of each species are coupled and determined as a function of the local partial pressures, the permeability, and the selectivity of the membrane. k-omega Shear Stress Transport (k-omega SST) turbulent model is employed to study steady flow over banks of hollow fiber membrane for values of the Reynolds number up to 1000. Lattice Boltzmann method is used to study transient flow pass an array of diamond shaped hollow fiber membranes. The flow structure around the hollow fiber membranes has strong influence on the separation performance. This study demonstrates that good mixing in the bank of hollow fiber membranes enhances separation. The results show that hollow fiber membrane module with staggered arrangements performs much better than that with inline arrangements. It is also demonstrated here that the transient nature of flows has significant influence on the membrane performance. (C) 2016 Elsevier Ltd. All rights reserved.