Mathematical modeling of rare earth element separation in electrodialysis with adjacent anion exchange membranes and ethylenediaminetetraacetic acid as chelating agent

This research delves into the effective use of electrodialysis for the separation of rare earth elements (REEs), specifically separating dysprosium (Dy) from praseodymium (Pr) and neodymium (Nd). A robust mathematical model based on the extended Nernst-Planck equation is introduced, simulating the process within a configuration that includes two adjacent anion exchange membranes. The model integrates aspects such as feed equilibrium, ion exchange within the membrane, and overall ion flux. Validation of the model's predictability was conducted through Chi-squared tests and root mean square error (RMSE) calculations, affirming its capability to accurately predict ion concentrations across different compartments. The study examines essential parameters such as applied voltage, rinse solution concentration, and feed concentration, assessing their impacts on separation performance and energy efficiency. Results indicate that higher voltages above 8 V, while speeding up separation, detrimentally impact energy use. It also highlights a critical balance in rinse solution concentration; lower concentrations below 0.05 mol/L enhance energy efficiency but may undercut separation efficacy due to early depletion. A linear correlation between the necessary rinse concentration and feed concentration was established, with higher feed concentrations demonstrating reduced specific energy consumption, thus enhancing overall efficiency. However, challenges remain in current efficiency due to the independent migration of SO4 2- ions in this specific setup. The findings advocate exploring alternative configurations, like alternating cation and anion exchange membranes, to optimize both environmental and economic aspects of REE separation. This study provides valuable insights and recommendations for refining electrodialysis systems in REE processing, contributing to sustainable and cost-effective electrodialysis systems.