## 3 Results and Discussion
### Fixed-Bed Column Adsorption Evaluation
These results reinforce the conclusion that the methodology employed in this study, alongside with practical models for multicomponent adsorption systems, is advantageous for scaling up the implementation of the processes. The use of asymmetric models derived from Gompertz [72] can further enhance the prediction of experimental data, supporting their application in various adsorption processes for practical implementation. In addition, [PERSON] et al. [40] also concluded that the Gompertz model is superior to the logistic model in terms of the fitting accuracy. Figure 6: Breakthrough curve modeling of (**a**) paracetamol and (**b**) metronidazoleæ adsorption in fixed bed column for Experiment 1 for multicomponent models (conditions: C\({}_{0}\) = 30 mg/L, Q = 5 mL/min and W = 0.5 g). Figure 7: Markov chains of the parameters of the Gompertz model, for the adsorption of paracetamol for Experiment 1: (**a**) c; (**b**) k; (**c**) k*; (**d**) \(\gamma\); and (**e**) \(\tau^{*}\) (conditions: C\({}_{0}\) = 30 mg/L, Q = 5 mL/min and W = 0.5 g). [PERSON] et al. [40] observed that, in multicomponent adsorption systems, the concentration of a compound in the treated effluent may exceed its initial concentration in the feed effluent. The authors attributed this phenomenon to the removal of strongly binding ions in the upper sections of the column, which consequently leads to the release of an equivalent amount of weaker ions. However, in the present study, the typical behavior of multicomponent adsorption was not observed. This discrepancy could be attributed to the fact that the concentration of the compound is not affected by the presence of a compound in the treated effluent. Figure 8: Markov chains of the parameters of the Gompertz model, for the adsorption of metronidazole-zole for Experiment 1: (**a**) \(c\); (**b**) k; (**c**) k*; (**d**) \(\tau_{i}\) and (**e**) \(\tau^{*}\) (conditions: C\({}_{0}\) = 30 mg/L, Q = 5 mL/min and W = 0.5 g). differences in the adsorption dynamics resulting from the specific experimental conditions used. Longer process times may be required to observe this effect fully. Additionally, variations in the feed composition and/or the adsorption properties of the adsorbent could prevent the displacement of weaker ions by those with a higher affinity for the adsorbent. These findings emphasize that each multicomponent system requires a careful evaluation of its unique process dynamics. It is important to note that the parameters of Gompertz models do not provide specific insights into the dominant mechanisms of the adsorption process, as the model was originally developed for different applications. However, [PERSON] et al. [65] observed that the parameters vary with changes in the operational conditions of the fixed-bed column, making the model particularly useful for scale-up studies. [PERSON] et al. [40] concluded that the parameters \(c\), k, \(\tau\), k*, and \(\tau^{\star}\) are essential for tailoring the logistic and Gompertz models to accurately describe adsorption processes. They allow for the adjustment of curve steepness, position, and interaction effects, making the models applicable to multicomponent systems. The observed asymmetry in breakthrough curves arises from differences in adsorption mechanisms, reactant reactivity, and intraparticle diffusion, highlighting the complexity of real-world adsorption systems. By comparing the results by [PERSON] et al. [40] with the ones found in this work is possible to conclude that the parameter's values are in the same order of magnitude for binary fixed-bed adsorption, in which a higher k value implies a steeper curve, indicating more favorable adsorption and \(\tau\) shifts the position of the breakthrough curve along the time axis, aligning with the experimental data. However, it is important to note that the model adjustments to the experimental data yielded R2 \(\approx\) 0.70 for both compounds and models.