Electrodiffusion of ions in both cation (CEM) and anion exchange membranes (AEM) has been studied with theoretical calculations and experimental studies. Calculations are based on the Finite Element Method (FEM) using COMSOL Multiphysics® software. Nernst-Planck equations are solved in multi-ionic systems where no closed form solutions are available. Simulations are compared with laboratory-scale experiments in terms of current efficiency and membrane selectivity. Simulations revealed unexpected features in transport, due to coupling of ionic fluxes when the local electroneutrality condition is assumed. Transport of weak electrolytes showed the importance of involving ionic equilibria along the concentration profiles in both solutions and membranes, compelling to consider ionic constituents. The advantage of the COMSOL simulations is the ease to find concentration and potential profiles across the entire system, and to split fluxes to diffusion and migration contributions, showing their coupling even in the absence of electric current.