Mathematical Analysis of CaO Content Variation in Acidic Wastewater and Mineralized Mass Mixture from Central Kyzylkum Phosphorite Based on Exponential Decay Model

This article investigates the reduction behavior of calcium oxide (CaO) content in mixtures of mineralized mass (MM) from Central Kyzylkum phosphorite and acidic wastewater (AWW) from the oil and fat industry, using experimental data and a mathematical approach. The study was conducted at 60°C, with the AWW: MM ratio varying from 100:10 to 100:40. The CaO content in each mixture was determined and analysed in terms of its mass ratio. Results demonstrated a systematic decrease in CaO content with an increasing proportion of MM. The initial rate of decline was rapid and then gradually slowed. An exponential decay model was employed and characterized by parameters. A first-order differential equation was applied and refined using experimental data. The initial value and decay constant were found to be C₀ = 67.39 and k = 0.0401, respectively. The resulting exponential equation showed a high degree of correlation with experimental points (R² ≈ 0.98). This study offers a structured evaluation of CaO behavior in complex systems through mathematical modeling, which can be used to control processes in real technological conditions. The modeling outcomes may serve as a methodological basis for developing kinetic models involving other ions and components in future research.