Modification of breakthrough models in a continuous-flow fixed-bed column: Mathematical characteristics of breakthrough curves and rate profiles

Abstract

In order to more completely describe mathematical characteristics of the breakthrough curve, this work defines the four parameters: Maximum specific breakthrough rate μmax, lag time λ, inflection point ti and half-operating time t50. The breakthrough models include the Bohart–Adams, Thomas, Yoon–Nelson, Clark, Wolborska and dose-response models. Attempts are made to address mathematical relationships between the breakthrough models, propose modified breakthrough models, investigate effects of model parameters on the breakthrough curve and rate profile and reveal their physical meanings. The fitting performance of the breakthrough models is verified by the adsorption of nitrate on the chitosan-Fe(III) composite. The results indicate that the model terms q0m/vc0 and a0x/uc0 are the operating time required to reach 50% breakthrough. The Clark model has the best fitting performance with high adjusted determination factor (Adj. R2 = 0.9976) and low reduced chi-squared value (χ2 = 2.70 × 10−4). In addition, an inconsistency concerning application of the Wolborska model is proposed to avoid this situation where it is repeated in subsequent publications. This work is expected to help readers better understand the breakthrough models and select the appropriate model to analyze the dynamic behaviors in a continuous-flow fixed-bed column.