## 3 Results and Discussion
### Fixed-Bed Column Adsorption Evaluation
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**Model**} \\ \hline \multicolumn{2}{c}{**Logistic**} & \multicolumn{2}{c}{**Gompertz**} \\ \hline
**Parameters and Units** & **Values Estimated by MCMC** & **Parameters and Units** & **Values Estimated by MCMC** \\ \hline \multicolumn{4}{c}{Paracetamol} \\ \hline c & 65.19 (60.33–68.86) & c & 56.19 (53.62–59.05) \\ k (1/min) & 0.0075 (0.0071–0.0078) & k (1/min) & 0.0045 (0.0044–0.0046) \\ \(\tau\) (min) & 292.44 (288.27–296.10) & \(\tau\) (min) & 205.43 (201.32–209.89) \\ k\({}^{\star}\) (1/min) & 0.019 (0.018–0.020) & k\({}^{\star}\) (1/min) & 0.0165 (0.016–0.017) \\ \(\tau^{\star}\) (min) & 90.52 (89.01–91.91) & \(\tau^{\star}\) (min) & 67.36 (66.30–68.39) \\ R\({}^{2}\) & 0.708 & R\({}^{2}\) & 0.754 \\ R\({}^{2}\)\({}_{\mathrm{ajstd}}\) & 0.686 & R\({}^{2}\)\({}_{\mathrm{ajstd}}\) & 0.736 \\ AIC & 1653.10 & AIC & 1301.10 \\ AIC\({}_{\mathrm{C}}\) & 1653.20 & AIC\({}_{\mathrm{C}}\) & 1301.20 \\ BIC & 1654.20 & BIC & 1302.20 \\ \hline \multicolumn{4}{c}{Metronidazoleze} \\ \hline c & 69.09 (65.75–73.27) & c & 59.27 (56.98–61.63) \\ k (1/min) & 0.0083 (0.0080–0.0086) & k (1/min) & 0.0053 (0.0051–0.0054) \\ \(\tau\) (min) & 249.79 (246.08–253.87) & \(\tau\) (min) & 168.82 (165.14–172.68) \\ k\({}^{\star}\) (1/min) & 0.020 (0.019–0.021) & k\({}^{\star}\) (1/min) & 0.018 (0.017–0.019) \\ \(\tau^{\star}\) (min) & 85.99 (84.51–87.42) & \(\tau^{\star}\) (min) & 63.37 (62.39–64.37) \\ R\({}^{2}\)\({}_{\mathrm{ajstd}}\) & 0.714 & R\({}^{2}\) & 0.760 \\ R\({}^{2}\)\({}_{\mathrm{ajstd}}\) & 0.692 & R\({}^{2}\)\({}_{\mathrm{ajstd}}\) & 0.742 \\ AIC & 1537.60 & AIC & 1207.10 \\ AIC\({}_{\mathrm{C}}\) & 1537.70 & AIC\({}_{\mathrm{C}}\) & 1207.20 \\ BIC & 1538.80 & BIC & 1208.30 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Values for the model parameters and the statistical metrics by the MCMC method for the multicomponent adsorption of Experiment 1 (C\({}_{0}\) = 30 mg/L, Q = 5 mL/min and W = 0.5 g). From Table 7 it is observed that the Gompertz model for multicomponent adsorption provided the best fit for both compounds, with the following statistical metrics: PAR: R\({}^{2}\) = 0.754, adjusted R\({}^{2}\) = 0.736, AIC = 1301.10, AIC\({}_{\text{C}}\) = 1301.20, and BIC = 1302.20; MTZ: R\({}^{2}\) = 0.760, adjusted R\({}^{2}\) = 0.742, AIC = 1207.10, AIC\({}_{\text{C}}\) = 1207.20, and BIC 1208.30. The logistic model represents a more symmetric and idealized breakthrough curve, making it suitable for systems with an even progression from low to high concentration. In contrast, the Gompertz model is more flexible and better suited for systems with delayed breakthroughs, where the transition from low to high concentration is asymmetric. In this study, the Gompertz model was found to better represent the experimental data due to the pronounced asymmetry observed in the breakthrough curves. Furthermore, as shown in Figure 5, the rapid transition from low to high concentrations in the experimental data aligns more closely with the estimates produced by the MCMC technique for the Gompertz model. To verify the convergence of the posterior distributions and confirm the viability of the Gompertz model, the MCMC chains for both paracetamol and metronidazole are presented in Figures 7 and 8, respectively. From Figures 7 and 8 it is possible to observe the convergence of the Markov chains for all parameters estimated from both models through Bayesian inference. This result indicate that the technique is applicable to multicomponent adsorption systems, since the method was able to adequately explore the parameter space. Thus, the MCMC technique is capable of dealing with the complexity of the modeled system, which presents complex interactions between parameters, reinforcing the reliability of the estimated values and allowing the assessment of uncertainties associated with the parameters, being essential to validate the model in complex experimental conditions.