Batch Kinetics of Metal Biosorption: Application of the Bohart-Adams Rate Law

Abstract

The most common rate model formulations for metal biosorption in batch systems assume that the uptake process is limited by surface reaction, with the so-called pseudo first order and second order rate equations being the most popular. However, from a modeling perspective the rate coefficients of these equations are of limited use as it is not clear how they can be utilized in the modeling of other process configurations such as fixed bed columns. As an alternative, we advocate a modeling approach predicated on the Bohart-Adams surface reaction rate law because it is of a form that can be readily integrated with the governing equations for batch and fixed bed systems, allowing explicit analytical solutions to be obtained. In this work we fit the batch solution of the Bohart-Adams rate law to kinetic data taken from the literature using a genetic algorithm. The resultant parameter estimates can be used in the fixed bed solution of the Bohart-Adams rate law to generate breakthrough predictions. Moreover, the batch Bohart-Adams rate law is compared with a general nth order surface reaction rate law using the Akaike information criterion approach.