<p>Separation and recovery systems using polymeric membranes have been widely studied for the removal and extraction of metallic species, mainly because they are environmentally friendly and have significant advantages. Mathematical models have been developed to describe the mass transfer mechanism in the extraction process. However, most models are limited to the study of a single-component and do not consider selectivity and the effects of a second metal on the reaction kinetics. Therefore, the aim of this work was to propose a multi-component mathematical model capable of simulating the extraction of metals simultaneously, performing a mass transfer analysis while considering the physical–chemical effects (membrane thickness, reaction kinetics, concentration, etc.) which under real conditions can interfere in the process. The model was solved using the Coupled Integral Equations Approach and validated using experimental and simulated measurements obtained by some researchers. The results demonstrated strong agreement with literature-reported data and highlighted the high reliability of the proposed model, indicating its capability to accurately describe the extraction process through polymeric membranes under different operational conditions. Additionally, the findings confirm its potential as a robust tool for multicomponent extraction simulation and optimization, providing a comprehensive and technically advanced approach for future research in multicomponent extraction processes.</p> Graphical Abstract <p></p>