## 1 Introduction  
The increase in world demand for mineral goods, combined with the progressive depletion of reserves containing high levels of metals of economic interest and the need to guarantee nuclear fuel for the continuous operation of nuclear power plants in energy production, makes it important to develop alternatives for the treatment of ores containing low levels of these metals, such as uranium [1]. Bideaching is a green technology for extracting, concentrating, or recovering metals from ores or waste, being an environmentally sustainable alternative to conventional hydrometallurgical processes [2; 3; 4]. The recovery of low-grade minerals has become one of the major concerns in mineral exploration. In this context, bacterial leaching, or bioleaching, arises, a technique based on the metabolic activity of microorganisms, which catalyze the process involving the oxidation of iron and the reduction of inorganic sulfur compounds, producing sulfuric acid and ferric ion [5]. Biohydrometallurgy has experienced significant advancement, with the utilization of microorganisms in ore treatment emerging as the most rapidly evolving domain in this field [6]. Several bacteria have already been cataloged and studied in the bioleaching process. Among the most common genera of prokaryotes found in acid-draining heap leach sites is the bacterial species _Acidithiobacillus ferrooxidans_[7]. _Acidithiobacillus ferrooxidans_ is classified as a chemolithotrophic bacterium, meaning it derives its energy from the oxidation of inorganic substrates, basically ferrous ion, and reduced sulfur compounds, including metallic sulfides. Furthermore, it operates as an autotrophic organism, necessitating a supply of nitrogen, phosphorus, and magnesium, in addition to an inorganic source of energy [8]. With the discovery of this bacterium, studies on new extraction techniques and other bacterial species that could play important direct or indirect roles in this metal extraction and recovery process have been intensified [9]. The process of uranium bioleaching and the development of _Acidithiobacillus ferrooxidans_ are influenced by various factors. One crucial parameter is the pH of the nutrient medium, playing a pivotal role in shaping the bioleaching process. As pH increases, proton availability decreases, leading to a slowdown in the oxidation reaction. At elevated pH levels, an excessive product layer forms on ore particle surfaces, creating a barrier between ore particles and metabolites. Research indicates that the optimal pH range for the growth of _Acidithiobacillus ferrooxidans_ falls between 1.5 and 2.5. Temperature is also a significant factor in bioleaching; higher temperatures enhance the leaching rate, although excessively high temperatures can impede microbial growth and activity. Optimal temperatures for this process typically hover around 30 \({}^{\circ}\)C [10; 11]. Increasing the pulp density can enhance ore loading and leach plant utilization rates. However, once the concentration limit is exceeded, it leads to the accumulation of specific metal ions in the solution, exceeding the tolerance limit of microorganisms and thereby inhibiting microbial growth and activity. Hence, slurry concentration ranges between 5% and 10% are considered acceptable [10; 11; 12]. Considering results presented by [PERSON] et al. [13] regarding the ex situ bioremediation of mine water contaminated with U(VI) using _Acidithiobacillus ferrooxidans_ strains, it was observed that elevated uranium concentrations can be detrimental to _Acidithiobacillus ferrooxidans_. This toxicity has the potential to result in a reduction in the efficiency of the bioleaching process. Studying the kinetics of bioleaching kinetics holds importance in assessing the rate at which metals are solubilized by bacteria. An important approach to evaluating reaction kinetics is to use mathematical modeling to understand the mechanisms of the bioleaching process [14].