## 4 Results and Discussion
the Adams-Bohart model was the worst fit without the estimation of N\({}_{0}\), with an R\({}^{2}\) e R\({}^{2}\) Adjusted of 0.9331 and 0.9284, respectively, and a BIC of 3.6145\(\times\)10\({}^{3}\). The Thomas model, commonly used to describe adsorption in fixed-bed systems, showed a higher estimated q\({}_{\text{s}}\) for the lowest concentration (1.327 mg/L), suggesting that the model is more effective in describing the H\({}_{2}\)S adsorption process at lower concentrations. The kinetic constant of the model (k\({}_{\text{th}}\)) decreased with increasing concentration, indicating that the adsorption rate decreases as the initial concentration increases. With the q\({}_{\text{s}}\), estimation, the model exhibited high R\({}^{2}\) and R\({}^{2}\) Adjusted values, suggesting a good fit to the experimental data. The BIC values were relatively low, and the coefficients of determination remained high even without q\({}_{\text{s}}\) estimation, but they were lower compared to when q\({}_{\text{s}}\) was estimated. The Yoon-Nelson model also showed a good fit with high R\({}^{2}\) values for both concentrations, although the model does not include the parameter q\({}_{\text{s}}\). It demonstrated a good representation of the adsorption data. The kinetic constant k\({}_{\text{yn}}\) was higher for the higher concentration (2.577 mg/L), indicating a higher probability of adsorption per unit time, while \(\tau\) was lower at higher concentrations, suggesting faster saturation of the adsorbent bed. For the Adams-Bohart model, it was observed that the constant k\({}_{\text{ba}}\) decreased with increasing C\({}_{0}\) (whether estimating N\({}_{0}\) or not). This behavior suggests that the adsorption rate tends to be higher at lower concentrations, which can be explained by the saturation of adsorption sites. At lower initial concentrations, available adsorption sites fill up more quickly, thereby increasing the adsorption rate represented by k\({}_{\text{ba}}\)[21; 22; 35]. Furthermore, when estimating N\({}_{0}\), the k\({}_{\text{ba}}\) constant adjusted to reflect the change in C\({}_{0}\), reinforcing the inverse relationship between the kinetic constant and the initial concentration of the adsorbate. In the Yan model, it was observed that a\({}_{\text{y}}\) decreased with increasing initial adsorbate concentration. This behavior is associated with the possibility that, for H\({}_{2}\)S adsorption, the maximum adsorption capacity decreases as the initial concentration increases. Additionally, a decrease in (qs) with increasing (C\({}_{0}\)) was observed, which may occur due to competition among adsorbate molecules for adsorption sites [36]. Figure 2a,b presents breakthrough curves simulated using the estimation of maximum adsorption capacity for the Thomas (q\({}_{\text{s}}\)), Adams-Bohart (N\({}_{0}\)) and Yan (q\({}_{\text{s}}\)). Figure 3a,b displays the simulated breakthrough curves with deterministic q\({}_{\text{s}}\) and N\({}_{0}\) obtained from the study by [29], both including the corresponding experimental data curve for the [PERSON], Yoon-Nelson, Adams-Bohart, and Yan models. Figure 2: (**a**) Breakthrough curves for concentration of 1.327 mg/L and (**b**) concentration of 2.577 mg/L with estimated q\({}_{\text{s}}\) and N\({}_{0}\). In general, the models showed better fit when estimating the maximum adsorption capacity, reflecting a more accurate description of the adsorption behavior. Among the models analyzed, the Yan model stood out for providing the best fit. This model was developed to reduce the uncertainty associated with the [PERSON] model, particularly effective in situations involving extremely long or short operating periods. The Yan model considers the absence of axial dispersion, extremely low internal and external diffusion resistances, reversible second-order reaction kinetics (pseudo-second-order), and Langmuir isotherm [28].