Guideline for modeling solid-liquid adsorption: Kinetics, isotherm, fixed bed, and thermodynamics

During the years, adsorption has garnered considerable attention being one of the most cost-effective and efficient methods for separating contaminants out of liquid phase. A comprehensive understanding of adsorption mechanisms entails several crucial steps, including adsorbent characterization, batch and column adsorption tests, fitting of predefined kinetic and isotherm models, and meticulous thermodynamic analysis. These combined efforts serve to provide clarity and insights into the intricate workings of adsorption phenomena. However, the vast amount of literature published in the field each year is riddled with ill-considered model selections and incorrect parameter analyses. Therefore, the aim of this paper is to establish guidelines for the proper employment of these numerous kinetic, isotherm, and fixed-bed models in various applications. A thorough review has been undertaken, encompassing more than 45 kinetic models, 70 isotherm models, and 45 fixed bed models available hitherto, with their classification determined based on the adsorption mechanisms expounded within each of them. Moreover, five general approaches for modifying fixed-bed models were provided. The physical meanings, assumptions, and interconversion relationships of the models were discussed in detail, along with the information criterion used to evaluate their validity. In addition to commonly used activation energy and Gibbs energy analysis, the methods for calculating site energy distribution were also summarized.