## 3 Results and Discussion
### Fixed-Bed Column Adsorption Evaluation
In addition, through the batch experiments, also applied in this work, in item 3.2, the removal efficiencies were between 71% and 98%, showing that the operational conditions applied in the process significantly impact on the feasibility of the technique by simultaneously treating the adsorption of these compounds. Thus, it can be concluded from the results that the best adsorption capacities were obtained at the lowest concentration of the pharmaceuticals, suggesting a faster saturation of the solid when the concentration is higher, also observed by other works reported in the literature [55; 58; 60]. Therefore, the best conditions obtained in the present work refer to Experiment 1, at lower concentration of pollutants, flow rate, and bed height, in which, under these conditions, the process control is facilitated, and there is a smaller amount of adsorbent required, resulting in the minimization of waste generation and lower process costs. The analysis of the breakthrough curves (Figure S2, Supplementary Material) revealed that all curves deviate from the ideal sigmoid (S) shape characteristic of breakthrough curves. The S-shape indicates a vertical alignment of the adsorbed species and is associated with cooperative adsorption. When the breakthrough curve deviates from this format, traditional models commonly used in the literature (such as [PERSON], [PERSON], and Yoon-Nelson) often fail to accurately predict the outcomes due to their inability to account for the curve's asymmetry. This limitation can be addressed by using the Gompertz models [61; 62], which were used in this study, proposed by [PERSON] et al. [40] for multicomponent adsorption systems. It is noteworthy that, as observed in Figure S2, some curves do not reach the saturation point, defined as when 95% of the initial compound concentration is achieved. This is particularly true for the lower concentration mixtures (C\({}_{0}\) = 30 mg/L and 40 mg/L), including the optimal point. Additionally, better column performance is indicated by more favorable parameters, resulting in longer saturation times [50]. This suggests that, for industrial applications, the adsorbent can be utilized for extended periods before requiring replacement or regeneration. It is significant to note that the optimal point corresponds to the lowest adsorbent mass used in this study (W = 0.5 g). It is worth mentioning that [PERSON] et al. [61] also investigated the removal of paracetamol in a fixed-bed column system, finding that the best operating condition was achieved with 0.5 g of GAC, resulting in extended saturation times for the column. They pointed out that increasing the bed mass indefinitely would eventually limit operation due to dispersion effects caused by the increased interstitial spaces within the adsorbent [63]. In Figure 5, the surface area and contour plots for simultaneous pharmaceutical removal by fixed-bed column adsorption are presented, depicting the response factors studied in this work (qmaxPAR (mg/g) and qmaxMTZ (mg/g)). According to Figure 5, the bed height significantly influences the response factors evaluated, particularly in relation to the process flow rate. While some authors in the literature have indicated that a greater bed height increases the total surface area of the adsorbent [50], the adsorption capacity for pharmaceuticals tends to decrease with higher mass. For the conditions assessed, it appears that smaller masses combined with lower flow rates are adequate to achieve optimal adsorption capacity (Figure 5b,e). This behavior can be attributed to three primary factors: (1) not all binding sites may be accessible to adsorbate molecules at greater bed heights, potentially due to overlapping active sites, which leads to the underutilization of certain particles [64]; (2) the channeling effect, where the solution flows preferentially near the column wall where there is more void space [65]; (3) the axial dispersion phenomenon, which can dominate during mass transfer and hinder solute diffusion into the adsorbent pores [66].