Fitting the Gompertz equation to asymmetric breakthrough curves

Abstract

Fixed bed adsorption studies often report asymmetric breakthrough curves which exhibit a tailing phenomenon as the effluent approaches the influent concentration. Evaluations of models capable of describing such curves are lacking in the literature. This paper examines the ability of the Gompertz equation to correlate asymmetric breakthrough data collated from reports published in the environmental adsorption literature. It is shown that the Gompertz equation, which has received little attention in this field of research, is able to track asymmetric breakthrough curves displaying a moderate degree of tailing. The logistic equation, which is mathematically analogous to the Bohart-Adams, Thomas, and Yoon-Nelson models, cannot effectively describe such asymmetric data. The Gompertz equation provides only an approximate representation of breakthrough data exhibiting a pronounced degree of tailing. To fit such data, this paper presents two modified forms of the Gompertz equation, which are shown to be highly accurate (R2 > 0.996). The Gompertz equation and the two modified versions are useful additions to the toolbox of breakthrough curve modeling which has long been filled with the Bohart-Adams, Thomas, and Yoon-Nelson models. These popular logistic-based equations are confined to fitting symmetric breakthrough curves.