Mathematical modeling of breakthrough curves in dynamic column adsorption: analytical solutions and validation

Water pollution is a critical global problem. The fixed- bed continuous adsorption column provides the most practical application in the industry for wastewater treatment. The mass transfer process in the column can be described using a mass balance differential equation, and a sorbate–adsorbent interaction rate equation. The objective of this work was to describe the mass transfer in an adsorption column, analyzing the differential equations of the process and their analytical solutions. A general rate equation with four parameters was proposed, adding a zero-order parameter. The general model was solved using Laplace Transform method. The model proposed was applied to describe the adsorption of hexavalent chromium on chitosan biopolymer. The theoretical solution found was satisfactory to estimate the experimental breakthrough curves, and the estimated parameters allowed to predict other curves with different operational conditions. The zero-order parameter added relates to the baseline height of the breakthrough curve. The general model proposed generalizes already known plug flow models based on a single rate equation. The present model uses the information obtained from the column and from the equilibrium batch isotherm, which constitutes a useful tool for describing the dynamic adsorption process and to make decisions on column design.