## 5 Conclusions  
In this study, the influence of parameters on the adsorption process was investigated through batch-scale experiments, where the optimal conditions for the multicomponent removal of the compounds PAR and MTZ were determined to be pH 7, a mass of 2.0 g, and 60 min of contact time, achieving a removal efficiency of 98.1% for both compounds. Fixed-bed column experiments were also conducted to explore the behavior of pharmaceutical removal processes. It was observed that the initial pharmaceuticals concentration applied to the column significantly affected the response factor of maximum adsorption capacity for paracetamol, followed by the interaction between bed height and flow rate. Although the interaction was not statistically significant for MTZ, a similar trend was observed for this compound. The optimal operating conditions for this stage were determined as C\({}_{0}\) = 50 mg/L, Q = 5 mL/min, and W = 0.5 g. These conditions resulted in maximum adsorption capacities of 49.49 mg/g and 43.64 mg/g for PAR and MTZ, respectively, and the resulted breakthrough curves were asymmetric. Within the application of the Bayesian technique, the multicomponent Gompertz model was selected as the most suitable for representing experimental measurements and can be used to scale-up the process. Thus, the mathematical modeling of the breakthrough curve, applied using Bayesian techniques, has proven to be a capable method for dealing with the complexity of multicomponent systems, which present complex interactions between parameters, reinforcing the reliability of the estimated adsorption parameters. In addition, these findings underscore the complexity of multicomponent adsorption phenomena and emphasize the necessity for experimental and modeling approaches to accurately characterize and predict these interactions. The following supporting information can be downloaded at [[https://www.mdpi.com/article/10.3390/app15137316/s1](https://www.mdpi.com/article/10.3390/app15137316/s1)]([https://www.mdpi.com/article/10.3390/app15137316/s1](https://www.mdpi.com/article/10.3390/app15137316/s1)): NANOVA Table for the Variables: (i) Removal and (ii) Adsorption Capacity; Figure S1. Paretto diagrams for simultaneous pharmaceuticals batch adsorption (A, removal is the response variable; B; Qe is the response variable); Figure S2. Breakthrough Curves Obtained by Simultaneous Adsorption of Pharmaceuticals in a Fixed-Bed Column; Table S2. ANOVA Table for the Response Variables: (i) qmaxPAR and (ii) qmaxMTZof Adsorption in Fixed-Bed Column*; Figure S3. Pareto diagrams for simultaneous pharmaceuticals removal by fixed-bed column adsorption (A, \(\text{q}_{\text{max}\text{PAR}}\) is the response variable; B; \(\text{q}_{\text{maxMTZ}}\) is the response variable)*. L.R.d.C.C. : Conceptualization, Methodology, Software, Validation, Investigation, Writing--Original Draft, Data Curation; J.T.d.O. : Conceptualization, Methodology, Software, Data Curation, Writing--Original Draft, Writing--Review and Editing; F.S.S. : Methodology, Formal Analysis; L.A.F. : Writing--Review and Editing, Supervision. All authors have read and agreed to the published version of the manuscript. The authors gratefully acknowledge the Brazilian financial of the Research Support Foundation of the State of Rio Grande do Sul (FAPERGS). Not applicable. Data Availability Statement: Data will be made available on request. The authors gratefully acknowledge the Graduate Program in Chemical Engineering (PPGEQ/UFRGS) and the Laboratory of Separation and Unit Operations (LASOP) for providing the infrastructure necessary for the development of this research. The authors declare that they have no known competing interests or personal relationships that could have appeared to influence the work reported in this paper. The following abbreviations are used in this manuscript: