Time-dependent velocity profile and concentration distributions formed in a single reverse electrodialysis (RED) unit have been successfully pursued using simulation framework for evaluating performance of the unit, i.e., open circuit voltage and short circuit current. The single RED unit consists of two adjunct fluid channels, separated by the semi-permeable membrane. Through one of the channels, sea water flows, and the other is occupied by fresh water, flowing in the opposite direction (countercurrent operation). The diffusion-convection transport of the rate-limiting ion, Na+ in this study, for both channels is treated. The diffusive transport of cation across the membrane is expressed as boundary conditions for the bi-mechanism model. Our simulations conducted using an orthogonal collocation on finite element scheme show that the concentration difference of 35 g/L between sea water and fresh water results in the open circuit voltage of 63 mV and the short circuit current density of 11.5 A/m2. These values are close to ones that were obtained from the experiments.