A generalized parallel pore and surface diffusion model and associated dynamic simulation program have been developed for multicomponent fixed-bed ion-exchange processes. Both equilibrium and nonequilibrium mass action laws are used to describe stoichiometric ion exchange. Model equations are solved numerically for frontal, pulse, or sequential loading processes. Analytical solutions obtained from a local equilibrium theory for binary systems and experimental data of two multicomponent systems served as benchmarks for the numerical solutions. The results indicate that the parallel pore and surface diffusion model should be considered for nonlinear large-particle systems. A parametric study shows that a major difference in fixed-bed dynamics between mass action and Langmuir systems lies in the propagation of diffuse waves of multivalent ions. Generally, the higher the valence or mass action equilibrium constant, the more pronounced the tailing of diffuse waves, which results in apparent adsorption hysteresis in a loading and washing cycle. The apparently irreversibly adsorbed multivalent ions can be eluted by concentrated solutions of lower valence ions, as a result of the relative selectivities of the higher valence against lower valence ions decreasing with increasing total solution phase concentration. This can lead to changes from favorable to unfavorable isotherms and self-sharpening waves to diffuse waves, or vice versa. Other results show that elution order can be reversed for heterovalent ions in elution and displacement chromatography.

A systematic model-based approach is used for development of an efficient carousel ion-exchange process for the selective removal of radioactive 137Cs+ from alkaline nuclear waste solutions. Equilibrium data for two resorcinol−formaldehyde (R−F) cation-exchange resins are correlated by an empirical equation of the Freundlich−Langmuir type over cesium/sodium concentration ratios of 10-9 to 10-2 and sodium concentrations of 1 to 6 N. The standard deviations are 3.5 and 6.6%, respectively. The data cannot be accurately described by mass action equations. A detailed rate model, developed in this study for the periodic countercurrent multicolumn operation of carousel systems, is used with the equilibrium correlations to simulate cesium breakthrough curves from R−F resin columns. Results show that accuracy of the predicted breakthrough curves are directly related to the accuracy of the isotherm data and correlations. Cesium breakthrough position is generally predicted to within 5% or less for 10 of 13 runs over linear superficial velocities of 0.16 to 8.8 cm/min, column lengths of 3.14 to 118.5 cm, and particle radii of 145 to 200 μm. One run shows later breakthrough than predicted as a result of a low potassium concentration in the feed. Two other runs show early breakthroughs as a result of channeling in poorly packed columns of a carousel system. Despite the channeling, strong thermodynamic self-sharpening effects helped establish constant pattern waves in the downstream columns. A case study for a pilot-scale carousel unit shows that 100% utilization of cesium capacity and maximum throughput can be achieved while containing the mass transfer zone within the downstream columns. Since intraparticle diffusion controls spreading of the breakthrough curves, reducing the particle radius from 200 to 145 μm increases throughput by 40%.

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