Mathematical Modelling of Rare Earth Elements Recovery by Ion Exchange Leaching from Ion Adsorption Clays

The establishment of a mathematical model for the ion exchange leaching process is key to creating a theoretical basis for the recovery of rare earth elements (REEs) from ion adsorption clay. Given the complexity of the process and limitations of experimental methods, modelling and simulation provide a promising, cost-effective approach to understanding ion exchange leaching mechanisms for REE extraction. Therefore, this study aims to develop a such a model, employing the Shrinking Core Model and utilizing MgSO4 as the leaching solution. A kinetic model was successfully developed based on the rate-determining step equation which belonged to the internal diffusion control. The calculated k value was 0.005, and the initial n value of 1.53 was later modified to 1.33 due to a deviation exceeding 10% in the Normalized Root Mean Square Error (NRMSE) value. The statistical model validation demonstrated a high level of agreement with the index values of d = 0.978, indicating an excellent agreement with experimental data, and a low value of NRMSE = 7.9 %, indicating an excellent performance model. The model consistently exhibits exponential growth in REE leaching efficiency, eventually reaching a maximum of 100% as leaching time progresses, demonstrating the leaching behaviour of REE extraction observed in this model follow the patterns observed in the leaching experiment. In conclusion, the developed kinetic model has the potential to provide reliable data on REE leaching efficiency at different leaching times across various concentrations of MgSO4solution.