Water pollution, particularly from elevated fluoride ion (F⁻) concentrations, is a significant challenge in many developing countries, particularly those relying on groundwater. The stable form of fluoride, F⁻, poses health risks, leading to concerns about various diseases and harmful effects. Despite global efforts, high F⁻ concentrations (>1.5 mg L⁻¹) persist in numerous countries, requiring effective and sustainable removal methods. Adsorption, known for its simplicity, cost-effectiveness, and efficiency, stands out as a promising technique for F⁻ removal from drinking water. Successful commercial implementation necessitates the optimization of separation conditions. This systematic literature review focuses on the adsorption process for F⁻ removal, exploring parameters such as temperature, adsorbent particle size, pH, adsorbent mass, and co-existing ions for efficient removal. Observations indicate that, despite the utilization of a diverse range of adsorbents, several limitations persist. These include low adsorption capacity, a sluggish adsorption rate, a restricted pH range, and high associated costs. The mechanistic understanding of adsorption and the ongoing development of novel adsorbents remain focal points for future research. Additionally, there is a need to explore alternative kinetic models grounded in statistical factors and give due consideration to thermodynamic studies.

This work aims to study the efficiency of zinc adsorption onto granular-activated carbon, predicting the mathematical models that best describe the adsorption behavior in a fixed bed column. First, batch scale experiments were performed to evaluate the influence of pH (3 to 6), contact time (5 to 60 min), and absorbent concentration (5 to 25 g L⁻¹) using synthetic effluent. Fixed bed column experiments were performed by varying the adsorbent concentration (10, 13, 20, and 40 g L⁻¹) and the effluent flow rate (15 and 20 mL min⁻¹). Markov Chain Monte Carlo and Bayesian criteria information were applied to describe the phenomena using Langmuir, Freundlich, Temkin, Redlich-Peterson, Sips, Toth, Khan, Radke-Prausnitz, for isotherm models, and Thomas; Yoon-Nelson; Yan; Clark models for breakthrough curve. Adsorption operating best conditions were pH 5, 20 g L⁻¹ of solid, and 50 min of contact time. These parameters allowed 80% of Zn removal, being better described by the Tempki model. In tests on a pilot plant, the Yan model was able to predict the second-order kinetic model, with an increase in the effluent flow and a 50% increase in the bed saturation time with a greater amount of adsorbent solid.

This research is focused on investigating the utilization of Bayesian methodologies, specifically the Markov Chain Monte Carlo method, as well as filter sampling by importance and sequential resampling. The objective is to estimate kinetic parameters and state variables associated with the uranium bioleaching process by Acidithiobacillus ferrooxidans. Experimental data of cell concentration, uranium concentration, and concentrations of ferrous and ferric ions, obtained from literature, were employed. These measurements were evaluated using a mathematical model expressed by a system of ordinary differential equations. Three different mathematical models were evaluated, considering different uncertainties in experimental measurements and mathematical models (1% and 5%). The estimation results presented a good fit to the experimental data, with coefficients of determination in the range of 0.95 to 0.99. The validation of the mathematical models was obtained by reproducing the experimental measurements and the Bayesian techniques proved to be suitable for application in the bioleaching process.

The increase in emissions of toxic gasses such as hydrogen sulfide (H₂S) and carbon dioxide (CO₂), resulting from growing urbanization and industrialization, has caused environmental and public health problems, making the implementation of air purification techniques through adsorption important. Thus, modeling the gas adsorption process is fundamental for good agreement with experimental data, employing mathematical models that enable the prediction of adsorption capacity. In this way, the present work aimed to compare different analytical breakthrough curve models (Thomas, Yoon–Nelson, Adams–Bohart, and Yan) for the adsorption of H₂S and CO₂ in fixed-bed columns, using experimental data from the literature, estimating the curve parameters through the Markov Chain Monte Carlo (MCMC) method with the Metropolis–Hastings algorithm, and ranking using the determination coefficients (R² and R²_Adjusted) and the Bayesian Information Criterion (BIC). The models showed better agreement using the estimation of maximum adsorption capacity (q_s, N₀) and the constants of each model (k_th, k_yn, and k_ba). In the adsorption of H₂S, the Yan model stood out for its precision in estimating q_s. For the adsorption of CO₂, the Adams–Bohart model achieved better results with the estimation of N₀, along with the Yoon–Nelson model. Furthermore, the use of this method allows for a reduction in computational effort compared to models based on complex differential equations.