Statistical Modeling and Experimental Validation of Carbonate Thermochemical Activation of Nepheline–Red Mud Mixtures Using Response Surface Methodology

Carbonate thermochemical activation is a promising approach for modifying the mineralogical structure of nepheline–red mud mixtures prior to subsequent alkaline processing. However, quantitative statistical relationships between activation parameters and phase transformation remain insufficiently explored. In this study, Response Surface Methodology (RSM) combined with a Central Composite Design (CCD) was employed to develop and experimentally validate a quadratic regression model describing the influence of activation temperature, activation time, and NaHCO3 concentration on cancrinite formation. Quantitatively determined cancrinite content obtained by X-ray diffraction (XRD) phase analysis was selected as the mineralogical response variable, enabling direct statistical evaluation of cancrinite-forming transformation. The developed quadratic model was statistically significant (F = 21.24, p < 0.0001) and explained 95.5% of the variability in the measured response (R2 = 0.9550). Activation time exerted the strongest statistical influence on cancrinite formation, while activation temperature and NaHCO3 concentration also showed statistically significant effects; the investigated interaction terms were not statistically significant. Numerical optimization identified a favorable region for cancrinite formation, with a predicted maximum response of 22.75 wt.%. Three independent validation experiments performed at practically selected operating conditions of 260 °C, 4 h, and 110 g/L NaHCO3 yielded an average cancrinite content of 20.0 ± 1.0 wt.%. The principal novelty of the study lies in the use of quantitatively determined cancrinite content as the response variable in RSM, providing a direct statistical description of mineralogical transformation rather than optimization based solely on conventional technological responses. The developed model provides a quantitative framework for evaluating factor effects and identifying favorable activation conditions within the investigated experimental domain.