Sigmoid Neutralization Response of Acidic Soapstock Waste by Mineralized Phosphorite Residues: A 4-Parameter Logistic Approach

This study investigates the neutralization behavior of an acidic wastewater (AWW)–mineralized mass (MM) system at mass ratios ranging from 100:10 to 100:40, processed at 333 K for 30 min. The evolution of pH as a function of MM dosage and the corresponding CaO content (%) in the solid phase were quantitatively evaluated. The solution pH increased sigmoidally from 4.10 to 7.30, while the CaO content rose from 23.92% to 36.96%, approaching a saturation plateau at higher MM dosages. The pH–dose relationship was described using four-parameter logistic (4PL), Gompertz, and Weibull models, all showing a high goodness of fit (R² ≥ 0.97). Model comparison based on AICc and BIC criteria indicated that the Gompertz model provided the best statistical performance, whereas the 4PL model ensured clearer physicochemical interpretability. A strong positive correlation between pH and CaO content was established (Pearson r = 0.9649, n = 7, p < 0.001), enabling estimation of CaO content from pH values. Numerical inversion of the 4PL model combined with a multi-model ensemble approach was used to determine optimal MM dosages for target pH levels. The recommended operating conditions were identified as 100:32 for pH 6.5, 100:36 for pH 6.8, and 100:38 for pH 7.0, with a stabilization zone observed at 100:37–100:40.

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