Gibbs Energy Minimization Model for Solvent Extraction with Application to Rare-Earths Recovery

The emergence of technologies in which rare-earth elements provide critical functionality has increased the demand for these materials, with important implications for supply security. Recycling provides an option for mitigating supply risk and for creating economic value from the resale of recovered materials. While solvent extraction is a proven technology for rare-earth recovery and separation, its application often requires extensive trial-and-error experimentation to estimate parameter values and determine experimental design configurations. We describe a modeling strategy based on Gibbs energy minimization that incorporates parameter estimation for required thermodynamic properties as well as process design for solvent extraction and illustrate its applicability to rare earths separation. Visualization analysis during parameter estimation revealed a linear relationship between the standard enthalpies of the extractant and respective organo-metal complexes, analogous to the additivity principle for predicting molar volumes of organic compounds. Establishing this relationship reduced the size of the parameter estimation problem and yielded good agreement between model predictions and reported equilibrium extraction data, validating the property estimates for the organic phase species. Design exploration and optimization results map the space of feasible solvent extraction column configurations and identify the set of optimal design parameter values that meet recovery and purity targets.