ABSTRACT

The kinetic models were widely used to analyze the dynamic adsorption behaviors in a batch system and reveal the mass-transfer mechanisms. The previous review papers were mainly confined to the description of the kinetic models, assessment of the fitting quality, determination of the model parameters and practical application in the field of water and wastewater treatment. However, the curve characteristics of the kinetic models and their mathematical relations were rarely mentioned in the literature. How to select and determine the optimum model remained to be further discussed. Thus, in addition to improving previous work, the main objectives of this review were: (i) to identify the curve characteristics of the kinetic models by control variates; (ii) to reveal their mathematical relations by variable substitution; (iii) to determine the optimum model by error functions and residual plot; and (iv) to correct some common mistakes in the literature. The pseudo-first-order (PFO) and pseudo-second-order (PSO) equations were two special cases of mixed 1,2-order equation (MOE). The PFO and Furusawa–Smith equations were mathematically equivalent. This review is expected to help readers better understand and use the adsorption kinetic models and provide potential ideas for the development of new kinetic models.

摘要

动力学模型被广泛用于分析批处理系统中的动态吸附行为并揭示传质机制。以往的综述文章主要局限于动力学模型的描述、拟合质量的评估、模型参数的确定以及在水和废水处理领域的实际应用。然而，动力学模型的曲线特征及其数学关系在文献中很少提及。如何选择和确定最优模型还有待进一步讨论。因此，除了改进以前的工作外，本次审查的主要目标是：（i）通过控制变量识别动力学模型的曲线特征；(ii) 通过变量替换揭示它们的数学关系；(iii) 通过误差函数和残差图确定最佳模型；(iv) 纠正文献中的一些常见错误。伪一阶 (PFO) 和伪二阶 (PSO) 方程是混合 1,2 阶方程 (MOE) 的两个特例。PFO 和 Furusawa-Smith 方程在数学上是等效的。这篇综述有望帮助读者更好地理解和使用吸附动力学模型，并为开发新的动力学模型提供潜在的思路。