Mathematical modeling and numerical simulation of sulfamethoxazole adsorption onto sugarcane bagasse in a fixed-bed column.

Having rigorous mathematical models is essential for the design and scaling of adsorption columns. In this study, the dynamic behavior of the sulfamethoxazole adsorption on sugarcane bagasse was studied and compared using analytical models and a theoretical mechanistic model. Initially, fixed-bed column tests were carried out at different flow rates and bed heights. Then, the experimental data were fitted with the most widely used analytical kinetic models, and their fit and fixed-bed parameters were compared with the mechanistic model. Of all analytical models analyzed, the Log-Gompertz model was the one that had the best agreed with experimental data. Although some analytical models fitted the experimental data accurately, their usefulness was questionable. Their parameters did not show a clear relationship with the change in operating conditions, and in certain cases had different behavior from that observed in experimentation. Conversely, the mechanistic model not only predicted the breakthrough curves with great accuracy in the initial and transition stage (R > 0.92; SSE < 0.06), but it also estimated relevant parameters. Additionally, the effects of the global mass transfer coefficient (K) and the axial dispersion coefficient (D) on breakthrough curves were studied using the mechanistic model. Increasing K increased the slope of the breakthrough curves with a faster adsorption rate. Similarly, high values of D produced lower adsorption capacities of the adsorbent; and it was established that the axial dispersion is relevant in SMX adsorption on SB. The theoretical model presented can be used for the design, scaling, and optimization of adsorption columns.