## 4 Results and Discussion
Moreover, it was observed that, in general, the kinetic constant (k\({}_{\text{th}}\)) decreased with increasing C\({}_{0}\), suggesting that the adsorption rate tends to decrease at higher concentrations due to adsorbent saturation, a dynamic also reported by [38]. On the other hand, in the Yoon-Nelson model, the constant k\({}_{\text{yn}}\) increased with the rise of C\({}_{0}\). Thus, it was possible to observe a decrease in the parameter \(\tau\), indicating a shorter contact time required for adsorption to reach half of its capacity, relating to a more dynamic behavior of the adsorbent at higher concentrations. In the Adams-Bohart model, when estimating N\({}_{0}\), it was noted that the constant k\({}_{\text{ba}}\) exhibited non-linear behavior in relation to C\({}_{0}\). This behavior may occur due to the adsorption dynamics at different concentrations and the possible interference of interactions between CO\({}_{2}\) molecules at high concentrations. Furthermore, the Yan model provided similar maximum adsorption capacity estimates to those of the Thomas model, also indicating higher q\({}_{\text{s}}\) at higher concentrations. It was observed that the constant \(\lambda\) decreased with increasing concentration, both when estimating q\({}_{\text{s}}\) and using deterministic q\({}_{\text{s}}\). Figure 4a-c show the breakthrough curves simulated using the estimated maximum adsorption capacity for the Thomas (q\({}_{\text{s}}\)), Adams-Bohart (N\({}_{0}\)) and Yan (q\({}_{\text{s}}\)) models. Figure 5a-c present the breakthrough curves estimated with the deterministic values of q\({}_{\text{s}}\) and N\({}_{0}\) obtained from the study by [30], covering the [PERSON], Yoon-Nelson, Adams-Bohart, and Yan models, including the curve corresponding to the experimental data for proper comparison. As in the analysis for H\({}_{2}\)S gas, the breakthrough curves for CO\({}_{2}\) gas adsorption also showed superior fitting when estimating the maximum adsorption capacity. Among the models examined, the Adams-Bohart model stood out for providing the best fit with the estimate of maximum adsorption capacity at the highest concentration (35 mg/L). However, this model performed the worst in describing the adsorption process without this estimate. The Adams-Bohart model assumes that the adsorption rate is directly related to the residual capacity of the adsorbent and the concentrations of the adsorbed species, recognizing that adsorption equilibrium does not occur instantly and that there is no axial dispersion in the adsorption bed. Additionally, the model suggests that the adsorbate is irreversibly adsorbed, with a local removal rate proportional to the residual capacity of the adsorbent and the concentration of the adsorbate in the gas phase. Thus, the adsorption rate varies according to the availability of adsorption sites on the adsorbent and the concentration of the adsorbate in the gas phase [26; 27]. Although the Adams-Bohart model stood out, the Thomas model also showed good fit for the concentration of 35 mg/g. This model assumes that adsorption kinetics follow a first-order reaction with respect to the adsorbate concentration and that the adsorption isotherm follows the Langmuir model, implying a homogeneous adsorption surface with energetically equivalent adsorption sites. Furthermore, the Thomas model neglects internal and external mass transfer resistances, assuming that the adsorption rate is limited by the adsorption reaction at the active site [21; 23]. When comparing the adsorption process of the two gasses, H\({}_{2}\)S and CO\({}_{2}\), models that considered the estimation of maximum adsorption capacity provided a good description of adsorption processes in fixed-bed columns, better reflecting column dynamics. Conversely, treating this parameter as deterministic tends to result in larger differences between estimated and experimental values.