Optimization and Kinetic Analysis of Direct Alkali Leaching of Silica from Vanadium-Bearing Shale Leaching Residue

The Response Surface Methodology was employed to optimize the leaching parameters for SiO₂ during NaOH alkaline leaching from vanadium acid leaching residues. The kinetic aspect of the process was also investigated. The results illustrate that each factor positively influences the SiO₂ leaching rate, with the significance of these factors ranking as follows: leaching temperature > alkali residue mass ratio > leaching duration. Under these optimal circumstances, the SiO₂ leaching rate can attain a value as high as 95.55%. A kinetic examination of the alkaline leaching process implies that the reaction process is predominantly governed by internal diffusion. The apparent activation energy of the reaction is 11.92 kJ·mol^–1. The kinetic equation is:  \(1+2(1-{\mathrm{x}})-3{\left(1-{\mathrm{x}}\right)}^\frac{2}{3}=\mathrm{10.82}{\mathrm{exp}}(-\frac{1192}{RT})t\) $1+2(1-\mathrm{x})-3{\left(1,-,\mathrm{x}\right)}^{\frac{2}{3}}=10.82\exp (-\frac{1192}{\mathit{RT}})t$ , and the reaction order of NaOH is 0.7284.