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A mathematical model for reactive-transport processes in porous media is presented. The modeled system includes diffusion, electromigration and electroosmosis as the most relevant transport mechanism and water electrolysis at the electrodes, aqueous species complexation, precipitation and dissolution as the chemical reactions taken place during the treatment time. The model is based on the local chemical equilibrium for most of the reversible chemical reactions occurring in the process. As a novel enhancement of previous models, the local chemical equilibrium reactive-transport model is combined with the solution of the transient equations for the kinetics of those chemical reactions that have representative rates in the same order than the transport mechanisms. The model is validated by comparison of simulation and experimental results for an acid- enhanced electrokinetic treatment of a real Pb-contaminated calcareous soil. The kinetics of the main pH buffering process, the calcite dissolution, was defined by a simplified empirical kinetic law. Results show that the evaluation of kinetic rate entails a significant improvement of the model prediction capability. This work has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 778045. Part of this work was supported financially by the European Commission within the project LIFE12 ENV/IT/442 SEKRET “Sediment electrokinetic remediation technology for heavy metal pollution removal”. Paz-Garcia acknowledges the financial support from the “Proyecto Puente - Plan Propio de Investigación y Transferencia de la Universidad de Málaga”, code: PPIT.UMA.B5.2018/17. Villen-Guzman acknowledges the financial support from the University of Malaga through a postdoctoral contract.