Water desalination by reverse osmosis hollow fiber membrane has been widely used to produce fresh water. This work numerically characterizes flux performance of the membrane, concentration polarization and potential fouling sites in the reverse osmosis desalination module containing hollow fiber membranes arranged in an inline and staggered configuration. Steady k-omega SST turbulence model is utilized to study membrane performance. An accurate membrane flux model, the solution-diffusion model, is employed. Hollow fiber membrane surface is treated as a functional boundary where the rate of water permeation is coupled with local concentration along the membrane surface. The rate of water permeation increases and concentration polarization decreases as the feed flow rate is increased. Hollow fiber membranes in the staggered geometry perform better than those in the inline geometry. It is proven by the present study that desalination modules containing hollow fiber membranes should be designed and optimized by careful consideration of their configurations. It is demonstrated here that flows in the hollow fiber bank becomes strongly time dependent at high flow rates and that transient effects could profoundly influence hollow fiber membrane flux performance and characterization of concentration polarization. (C) 2016 Elsevier B.V. All rights reserved.