The problem of ion transport in porous media is fundamental to many practical applications such as capacitive deionization, where ions are electrostatically attracted to a porous electrode and stored in the electric double layer, leaving a partially desalinated solution. These electrodes are functionalized to achieve maximum efficiency: it is intended that for each depleted electron one ion is removed. For this purpose, the surface is coated with a polyelectrolyte layer of the same sign as the electronic charge. In this work, the movement of ions from the solution to the soft or polyelectrolyte-coated electrodes is studied. For this purpose, a one-dimensional model is used to study the electric and diffusive fluxes produced by the application of an electric field and the storage of these ions in the micropores. The partial differential equations governing the process are numerically solved using the explicit Euler method. The results of the model indicate that the number of ions removed using soft electrodes is approximately 15% greater than that achieved with bare electrodes. Ion adsorption kinetics show that coated electrodes provide slightly slower adsorption compared to bare electrodes. Regarding the charging time of the micropores, it can be seen that it is a faster process (characteristic time of 100 s) compared to the time in which the ion concentration reaches equilibrium: electromigration is faster than diffusion. Comparing the situations with and without polyelectrolyte coating, it is observed that saturation in the micropores is reached earlier when the electrodes are coated. Concerning the cell geometry, it has been found that the characteristic time is proportional to the length of the spacer and inversely proportional to the length of the electrodes. With regard to microporosity, the rate of the process is approximately constant, irrespective of the number of micropores. Moreover, the number of adsorbed ions strongly depends on their initial concentration. Finally, the analysis of the ionic diffusion coefficient is determinant in the kinetics of the process: Taking into account the tortuosity of the porous electrode, which directly affects the diffusion in the channel, is fundamental to obtain model predictions close to reality.