## 3 Results and Discussion
### Adsorption Kinetics
However, other researchers have reported that decreasing the grain size increases the adsorption capacity of zeolite. [PERSON] et al. [59] reported that a zeolite particle size of 0.5 mm had the highest ammonium adsorption capacity, which was 64% and 31% higher than that of zeolite with 1.0 and 2.0 mm grain sizes, respectively. [PERSON] et al. [60], in their study, used clinoptiolite-rich zeolite with a similar chemical composition to that used in the present study. Using techniques applicable to the physicochemical and structural characterization of zeolites, they confirmed their porous morphology and substantial specific surface area, which favor both ammonium retention through ion exchange mechanisms and biofilm development due to enhanced surface roughness and porosity. On the other hand, ammonium uptake was significantly reduced in coarse gravel, with q\({}_{e,m}\) equal to only 29.34 mg/kg, six times lower than the uptake in zeolite. In this case, the pseudo-first-order model shows a better fit for the coarse-grained gravel data (Figure 2c, Table 1). It was confirmed that gravel has limited affinity for ammonium, as the adsorption stabilized more slowly and reached much lower maximum levels. The results for the kinetic adsorption of ammonium and orthophosphate are of great importance for the design of treatment systems such as CWs. Kinetic models help to clarify adsorption mechanisms, which depend on the physical and/or chemical characteristics of the adsorbent. The pseudo-second-order fit shows that the dominant process of ammonium adsorption on zeolite is chemisorption, in which ammonium ions are first adsorbed onto the zeolite surface and then into the adsorption sites located in the pores and channels of the zeolite [61]. According to the results, phosphate adsorption in the three porous media tested was much slower and less efficient than ammonium adsorption. The measured adsorption capacity at equilibrium (q\({}_{e,m}\)) for CG-Z, FG-Z, and CG-G was 11.76, 12.35, and 6.44 mg/kg, respectively. As in the case of ammonium, the pseudo-second-order model showed a better fit compared to the pseudo-first-order model, as it achieved higher R\({}^{2}\) values and lower values of both the NOF and MAE compared to the corresponding values of the pseudo-first-order model. Moreover, the measured q\({}_{e,m}\) values were very close to the q\({}_{e,c}\) values calculated from the pseudo-second-order model (Table 1). Zeolite is an aluminosilicate mineral and therefore has a negative surface charge and very low anion exchange capacity, showing low phosphorus adsorption. Phosphate removal occurs mainly through substituent exchange and surface complexation with calcium and aluminum in zeolites, in contrast to the exchange of ammonium cations [62]. The description of phosphate binding to numerous surface groups by [PERSON] et al. [63] is supported by the heterogeneous adsorption sites. The low phosphate adsorption capacity of gravel without chemical alterations is confirmed by the difference in efficiency between zeolites and gravel, which is consistent with the findings of [PERSON] et al. [64]. Figures 4 and 5 for ammonium and phosphate, respectively, show that the [PERSON] and [PERSON] model (Equation (9)) fits the experimental data quite well if they are divided into two or more linear regions. The ammonium adsorption process on the three substrates (i.e., CG-Z, FG-Z and CG-G) is divided into two linear regions (Figure 4). The first region with the steepest slope (blue dots) represents adsorption controlled by external film diffusion, and the second region (orange triangles) corresponds to intra-particle diffusion into the porous structure of zeolite and gravel.