Exponential Model for Adsorption Kinetics

Adsorption is one of the most widely applied techniques for the removal of contaminants from the environment. The effectiveness of an adsorbent is dependent on its kinetics. There are lots of studies on adsorption kinetics, and several mathematical models have been developed to describe this process based on certain perceived underlying mechanism. However, most models which have been used to fit the kinetic data have shown a moderate level of correlation or no fit at all. This is mainly because of error in assuming the governing equation and erroneous assumptions when finding solutions to the governing equations. In this research an exponential model is proposed. It is believed that adsorption of an adsorbate onto an adsorbent follows essentially two stages. There is a rapid stage that tends towards a first phase pseudo-equilibrium (Qr(0)) at a rate of kr and transits at a time ‘tr’ and rate ktr to a slow stage which tends towards a second phase pseudo-equilibrium (Qs(0)) at a rate of ka which marks the climax of the process. Mathematical equations were used to describe this process and solved analytically to obtain the new exponential model. The model was used to estimate kinetic data and compared with the first and second order equations with an R2 of 0.994, 0.999 and 0.998 respectively. The new adsorption parameters Qr(0) , Qs(0), kr, ks, ktr and tr were also extracted from the calibrated model.