bed electrodes and a porous separator filled with electrolyte. The electrodes are filled with conducting petroleum coke particles covered respectively with LiMn2O4 selective to lithium ions and polypyrrole selective to anions. It operates in two steps: First, the porous electrodes and the separator are filled with natural brine to extract Li+ and Cl- by intercalation and adsorption. Then, after rinsing with water the reactor is filled with a dilute LiCl recovery solution and LiCl is recovered by reversing the electrical current. A mathematical model for the reactor comprising the Nernst-Planck equation and the battery intercalation model has been developed. The model was solved using the finite element method under the COMSOL Multiphysics environment in order to obtain the electrostatic potential and the ion currents and concentrations across the system. Unlike the asymmetric LiMn2O4/activated carbon super-capacitor, in the lithium extracting reactor the total LiCl concentration decreases in the extraction step and increases in the recovery step. A good agreement between the experimental and simulated potential difference vs. time at constant current validates the model of the reactor. (C) The Author(s) 2018. Published by ECS.