A new strategy for the modeling of asymmetric breakthrough curves from Cr(vi) removal in a fixed-bed column

Fixed-bed adsorption is an effective method for removing Cr(vi) from aqueous solutions, but traditional breakthrough models usually provide a poor fit when modeling asymmetric breakthrough curves. In this study, a magnetic ferric oxalate-loaded hydrothermal carbon (MFO/HC) composite was prepared, and the effects of influent concentration, flow rate, bed height, and pH on Cr(vi) removal in a fixed-bed column were explored. All measured breakthrough curves presented an asymmetric S-shaped profile, accompanied by distinct tailing behavior, which was closely related to the energy heterogeneity of reactive sites. Based on the conceptual classification of early- and late-stage kinetic contributions, two new breakthrough models were developed through the superposition of two independent logistic functions and two independent Gompertz functions, respectively. In all cases, the modified Yoon-Nelson and modified Gompertz models exhibited higher fitting accuracy, and their residuals were randomly distributed. The Bayesian information criterion (BIC) supported the preference for the modified models after accounting for model complexity. Finally, key design parameters were successfully calculated by the fzero, integral, and fminbnd commands of MATLAB software. The significance of this work is to provide a practical modeling approach that shows promising potential for asymmetric breakthrough curves with a long tail.