Quadratic modeling of Al₂O₃ content during hydrochloric acid activation of Navbahor bentonite

The present paper is concerned with mathematical modeling of the change in the Al₂O₃ content in the process of the acid activation of bentonite clay using hydrochloric acid (HCl). The objective of the research was to investigate the effect of the HCl concentration on the Al₂O₃ content in the bentonite and create a mathematical model that describes the relationship between these variables. To do this, bentonite samples were activated with HCl solutions of concentrations 5, 10, 15, and 20%. The acquired data were subjected to analysis by using the quadratic polynomial regression model based on the method of least squares in OriginPro 2026. The adequacy of the model was estimated using the coefficient of determination (R²), the root means square error (RMSE), and the mean absolute error (MAE). The constructed model showed a very good fit to the experimental data (R² = 0.9646, RMSE = 0.2001, and MAE = 0.1790), but the relative error between calculated and experimental values varied from 0.73% to 2.60%. Thus, the results have shown that the suggested model could be successfully applied for the preliminary assessment of Al₂O₃ content at an intermediate concentration of HCl in the range of 5-20% and for the technological calculations. The suggested quadratic polynomial regression model is a valuable mathematical tool for the optimization of the acid activation process of bentonite, for the quantitative evaluation of the changes in Al₂O₃ content, and for the indirect assessment of the sorption properties of the clay.