Development of fractal-like Clark model in a fixed-bed column

Abstract

The Clark model was used to describe a fixed-bed adsorption system based on the combination of the mass-transfer concept and the Freundlich isotherm. The previous study revealed a time-dependent mass-transfer coefficient for the heterogeneous diffusion-limited process. Herein, this work proposed the fractal-like Clark model and its reliability was validated by the adsorption of norfloxacin on granular activated carbon. Moreover, the effects of the model parameters on the breakthrough curves and rate profiles were also investigated. The results indicated that the fractal-like Clark model had a high adjusted coefficient of determination (Adj. R2 > 0.977) and a small Akaike information criterion (AIC < −107.2) in all cases, providing more accurate estimation of the model parameters than the Clark model. As a three-parameter model, the Clark model could provide higher fitting accuracy (Adj. R2 = 0.997) for the adsorption of Cu(II) on Cystoseira crinitophylla biomass. The breakthrough curve became more asymmetric when the parameters n and h deviated from 2 and 0, respectively. The fractal-like Clark model may help readers to better understand the mass-transfer process in a fixed-bed column.