Prediction of breakthrough curves for multicomponent adsorption in a fixed-bed column using logistic and Gompertz functions

Abstract

In order to facilely predict the multicomponent breakthrough curves and avoid the complicated numerical solution, this work proposes two empirical models based on the logistic and Gompertz functions. The S-shaped and bell-like curves correspond to the adsorption and displacement processes respectively. The equilibrium loading of each component can be calculated by integration of the measured breakthrough curves. The effects of the model parameters on the breakthrough curves are investigated. The applicability of the two empirical models is validated by three binary and four ternary adsorption systems, including the gas–solid and liquid–solid adsorption. The residual plot and coefficient of determination ( R 2 ) are used to evaluate their fitting quality. The results indicate that the fitting curves agree well with the experimental data and all of the residuals are distributed randomly. The five model parameters ( k , τ , k *, τ * and c ) are easily obtained by the nonlinear regression. For example, the fitting results are k = 1.37 × 10 −2 min −1 , τ = 292 min, k * = 1.25 × 10 −2 min −1 , τ * = 453 min and c = 85.3 for adsorption of n -butyl acetate and p -xylene on granular activated carbon. On the whole, the Gompertz model is superior to the logistic model in terms of the fitting accuracy. The significance of this work is to provide a simple and practical method for prediction of the multicomponent breakthrough curves.