3D mathematical modeling of external mass transfer effect in high-rate adsorption process

Abstract

The effect of external mass transfer on the high-rate adsorption system was evaluated in the present study. In the experimental section, the removal of methyl orange (MO) was carried out by using surfactant modified chitosan-clinoptilolite at specific conditions such as the optimum adsorbent dosage of 11 g L−1, solution pH of 3.5, contact time of about 3 min and constant temperature of 30 °C. The characterization of adsorbent showed the porosity value of 0.064 and the BET surface area of 10.5 m2 g−1. These features of adsorbent established the high-rate adsorption process in which the shape of decay curves is not smooth and the concentration of adsorbate falls quickly. In high-rate adsorption processes, the external mass transfer mechanism has a significant effect on total mass transfer at early time of adsorption. The pore volume and surface diffusion model (PVSDM) were applied for predicting MO concentration decay curves. This model and its parameters could not estimate properly the concentration of MO at the early time of the adsorption process. To overcome this problem, in addition to optimization of surface diffusion coefficient (Ds), the external mass transfer coefficient (ke) was optimized and the effect of those parameters was studied in three dimensions. The optimization provided a better agreement between the model and experimental data in such a way to reduce the error rate. To show better the effect of external mass transfer, Biot number (between (2.15 and 24.05) × 10−3) was applied and it revealed that the adsorption mechanism was controlled by external mass transport. The high external surface area illustrated that in all values of ke and initial concentration of MO, surface diffusion is the dominant mechanism in intraparticle diffusion and the low porosity of adsorbent limited the penetration of adsorbate species into the adsorbent cavities, whereby the pore volume diffusion could be considered negligible.