Reverse electrodialysis (RED) is an electrochemical membrane process that directly converts the energy associated with the concentration difference between two salt solutions into electrical energy by means of a selective controlled mixing. The physics of RED involves the interaction of several phenomena of different nature and space-time scales. Therefore, mathematical modelling and numerical simulation tools are crucial for performance prediction. In this work, a multi-physical modelling approach for the simulation of RED units was developed. A periodic portion of a single cell pair was simulated in two dimensions. Fluid dynamics was simulated by the Navier-Stokes and continuity equations, and ion transfer by the Nernst Planck approach along with the local electroneutrality condition. The Donnan exclusion theory was implemented in order to simulate interfacial phenomena. A sensitivity analysis of the process performance was carried out. Different membrane/channel geometrical configurations were investigated, including flat membranes, either with or without non-conductive spacers, and profiled membranes. The influence of feeds concentration/velocity was also evaluated. Results confirmed that, with respect to the ideal case of plane (empty) channels and planar membranes, non-conductive spacers always reduce the power produced, while profiled membranes may or may not perform better, depending on stack features and operating conditions.