Prediciton [sic] of breakthrough curve for multicomponent ion exchange systems

A simple method/procedure to predict the shape of the breakthrough curve for multi-component ion exchange systems with favorable isotherms was developed. The procedure was based on an earlier procedure developed by Watson for binary ion exchange and adsorption processes. The procedure uses a calculational method to determine the NTU (ratio of the change in concentration to the driving force) from a plot of the equilibrium curve and operating line for a favorable isotherm. The procedure is applicable only to favorable isotherms because it only addresses constant pattern breakthrough fronts. If a constant pattern front does not exist, the calculations will not be valid. The effective equilibrium curve was developed using binary equilibrium data, mass balance equations for the ions in solution and the ions on the resin, and some simplifying assumptions applicable to constant pattern fronts. Development of the equilibrium curve for an n-component system was generalized and the methodology illustrated with 3 and 4 components ion exchange systems. The shape of the breakthrough curve was predicted for both binary and ternary ion exchange systems and compared to experimental data. Systems evaluated experimentally included 1) Na⁺-H⁺, 2) Cu⁺⁺-Na⁺, 3)Cu⁺⁺-Co⁺⁺, 4) Ca⁺⁺-Co⁺⁺, 5)Ca⁺⁺-H⁺-Na⁺, 6) Ca⁺⁺-Co⁺⁺-Na⁺ and 7) Cu⁺⁺-H⁺ in dilute chloride solutions using a strong cation ion exchange resin (DOWEX).The calculated breakthrough curves agreed favorably to the experimental breakthrough curve. Some deviation at the low concentration range was observed and is probably due to a "constant" pattern front not being developed. A constant pattern front had probably not developed due to the short length of the column (15 4") or the high flow rates (8 5 and 16 5 ml/min) employed with the systems evaluated. For the ternary systems, the calculated NTUs were a little higher than the experimental NTUs at the high concentration range due to the approximation employed-concentration of the least preferred ion(s) is equal to its feed concentration In real cases, the concentration of this ion(s) would be higher but approaching the feed concentration. The HTUs, defined as Vₛ/kբa, were calculated from the experimental data. The effects of flow rate and feed concentration on the NTUs, therefore the length of the front, were also evaluated. The feed concentration had little affect on the NTUs. The HTU increased with flow rate as expected for the Na-H system, however, no noticeable differences were seen in the HTU for the Cu-H-Na system when the flow rate was increased. Molar selectivity was also calculated for Cu-Na and Co-Cu systems and agreed somewhat with the literature values. The resin capacity was determined experimentally from the breakthrough curve.