Predictability of the homogeneous surface diffusion model for activated carbon adsorption kinetics; Formulation of a new mathematical model

The predictive capability of the Homogeneous Surface Diffusion Model (HSDM) for activated carbon adsorption kinetics under different environmental conditions is investigated in this study. Experimental studies conducted at room temperature, neutral pH, with DO concentrations of 0, 4, 9, and 30 mg/l indicate that the HSDM model describes the anoxic adsorption much more accurately than the oxic uptake. This pattern is rationalized as due to the simultaneous adsorption and surface reaction in the oxic batches which is unaccounted for in the HSDM model. Furthermore, the data reveals that divergence from the model fit increased with DO concentration with the HSDM model overpredicting the initial data and underpredicting the latter part of the curve. Kinetic experiments performed for phenol and o-cresol at pH values of 3, 7, and 11 show that HSDM model describes the anoxic data very well, while underpredicting the latter part of the curve. Kinetic experiments performed for phenol and o-cresol at pH values of the largest divergence of the oxic data from the HSDM model was at neutral pH. On the other hand, when the aforementioned kinetic experiments were conducted at temperature values of 8 degrees C, 21 degrees C, and 35 degrees C, the HSDM model was found to describe the anoxic data very well with the fit improving with temperature. The fit of the surface reaction-controlled part of the kinetic curve improved substantially with temperature. A simultaneous adsorption reaction model is formulated to account for the relatively slow telomerization reactions that impact sorbate uptake kinetics and equilibria.