## 5 Discussion
Figure 3a shows the comparison of the uranium concentration estimates, in terms of the mean and 99% credible interval, with the experimental measurements, of case 1 of model 1. It was observed that there was a reduction in the uranium concentration during the bioleaching process and, after approximately 60 h, it showed stability. Due to bacterial oxidation of the mineral, there was an increase in the rate of bacterial growth and, consequently, the concentration of the mineral increased, which resulted in greater recovery by the bacteria until equilibrium was reached. This dynamic may be related to the generation of ferric ions in the process through bacterial oxidation of Fe\({}^{2+}\), which increased bacterial growth and, consequently, the concentration of Fe\({}^{3+}\), resulting in increased recovery of the metal by the bacteria until reaching stability [60]. Figure 3b shows the comparison of the Fe\({}^{2+}\) concentration estimates, in terms of the mean and 99% credible interval, with the experimental measurements, referring to case 2 of model 2. A good agreement between the results is observed, meaning a well-adjusted result, since the Fe\({}^{2+}\) concentration estimates agree with the experimental measurements. In this sense, the kinetic parameters that were adjusted for model 2 were also sufficient for reproducing the experimental concentration profiles. After 60 h of the experiment, the Fe\({}^{2+}\) concentration tended to zero, indicating that the oxidation process of ferrous ions was practically complete. According to [PERSON] et al. [60], this decline in Fe\({}^{2+}\) concentration may be related to the increase of ferric ions in the presence of microorganisms; that is, a precipitation process occurs when Fe\({}^{2+}\) oxidizes to Fe\({}^{3+}\). This implies that bacteria play a key role in the oxidation of ferrous ions in the solution, facilitating the uranium bioleaching process. According to [PERSON] et al. [61], the consumption of Fe\({}^{2+}\) is directly related to the growth of _A. ferrooxidans_, even though it is inversely proportional to it. Figure 3c shows the comparison of the Fe\({}^{3+}\) concentration estimates, in terms of the mean and 99% credible interval, with the experimental measurements, of case 3 of model 3. It was verified that the results presented a good agreement between the estimates and experimental measurements. Thus, model 3 is also capable of reproducing the experimental concentration profiles used in the present work. Initially, in the first 40 h, an increase in the concentration of Fe\({}^{3+}\) is observed, resulting in a greater recovery of the metal, followed by a decrease in the concentration. According to [PERSON] et al. [60], for optimized bioleaching, low initial values of Fe\({}^{3+}\) are required. This behavior may be associated with the presence of ferric ions in the process or may be attributed to the mechanism used for metal recovery. Figure 3d shows the comparison of the cell concentration estimates, in terms of the mean and 99% credible interval, with the experimental measurements, of case 4 of model 3, showing a good fit between estimated variables and experimental measurements. It was observed that the cells reached stability after approximately 50 h of the experiment. This stabilization could be associated with the reduced formation of ferric ions. Thus, as the reaction progressed, there was an increase in the bacterial population, as also reported by [PERSON] et al. (2018). For the case presented in Table 5, it was observed that for the three studied models, there was a good fit of the estimates with the experimental measures. Model 1, which does not present inhibitory effects, proved to be more efficient for estimating uranium and Fe\({}^{3+}\), concentrations, while models 2 and 3, which considered inhibition by product and substrate, respectively, proved to be more adequate for the estimation of cell and Fe\({}^{2+}\), respectively.