Constant-pattern design method for the separation of ternary mixtures of rare earth elements using ligand-assisted...

A constant-pattern design method for separating ternary mixtures using ligand-assisted displacement chromatography was developed for non-ideal systems. The general correlation for the minimum column length required to achieve the constant-pattern state for binary separations from our previous study was extended to ternary separations. Additionally, an equation for the yield of a target component as a function of key dimensionless groups was derived based on the constant-pattern mass transfer zone lengths. The column length and operating velocity solved from the two equations ensured the yields and the constant-pattern state for the target components. A selectivity weighted composition factor was developed to allow the design method to specify a minimum target yield for one or multiple components. The design method was verified using simulations and experiments for different targeted yields (70-95%), ligand concentrations (0.03-0.06 M), and feed compositions (1/12-5/6). The targeted yields were achieved or exceeded in all cases tested. The minimum column length required to achieve a constant pattern-state and the productivity of LAD are limited by the lowest selectivity or by a minority component with a low concentration in the feed, even when it does not have the lowest selectivity. Sacrificing the yields of minor components can increase the total productivity significantly. The productivities achieved using this design method are 839 times higher than literature results for ternary separations with the same purity and similar yields.