A critical review of breakthrough models with analytical solutions in a fixed-bed column

The modeling and simulation of the breakthrough curves in a fixed-bed column play a vital role in evaluation of the adsorption capability and prediction of the dynamic adsorption behaviors. With the popular use of the breakthrough models, the relevant mistakes and inconsistencies also rise and are repeated in subsequent publications. This work conducts a profound review of the fundamental principles of continuous adsorption and the underlying assumptions, curve characteristics, intrinsic relationships and application scope of the widely used breakthrough models with analytical solutions. Besides, the physical meanings of the model parameters are clarified, the relevant mistakes and controversies in the fixed-bed studies are addressed and the reasons for the asymmetric breakthrough curves are discussed. Error statistics and residual plot are a good measure of the goodness of fit. The F-test and Akaike's information criterion (AIC) can be used to compare the fitting results from two models for the same dataset. The fractal-like kinetics provides new insights into the diffusion-limited adsorption process in a heterogeneous system. Some empirical breakthrough models are also considered to be an alternative method to description of the dynamic adsorption behaviors. This review aims to help beginners better understand and use the breakthrough models.