456379 Crystallization of Calcium Sulfate Dihydrate during Phosphoric Acid Production in the Presence of Magnesium Ions
Richard D. Braatz
Allan S. Myerson
The production of phosphoric acid from phosphate mineral rock involves the addition of phosphate rock to a concentrated sulfuric acid solution. The induced reactive crystallization process produces a side product of calcium sulfate hydrates which become the filter media in the subsequent acid separation process. For most industrial processes, the dihydrate form of calcium sulfate crystals (gypsum) precipitates and its shape and size distribution are key factors in determining the downstream filtration efficiency . Particularly, the metal ion impurities coming from raw phosphate rock plays an important role as shape modifiers. The presence of impurities in the acid mixture has an impact both thermodynamically and kinetically, although most of the available literature focuses on their role as growth inhibitors and has neglected their potential impact on solution speciation .
Past studies on gypsum crystallization in phosphoric acid solutions usually involve the study of crystal growth and nucleation kinetics [3, 4]. However, past works did not use the correct definition of supersaturation when fitting kinetic parameters. The high concentrations in this multicomponent electrolyte system implies that supersaturation which be written in terms of the solubility product ratio, as governing by nonideal thermodynamics, which requires the com- putation of activity coefficients as well as free ion concentrations. For this purpose, the mixed solvent electrolyte (MSE) model is utilized to capture the solution speciation in order to properly quantify supersaturation at any given condition. The MSE model is a first-principles model that determines solid-liquid equilibrium by calculating excess Gibbs energy from additive pairwise interactions . When impurities are present, additional binary interactions need to be included in the databank, which is carried out by regression analysis using solubility measurements.
Continuous reactive crystallization experiments are carried out with and without additives using a mixed-suspension, mixed-product removal (MSMPR) crystallizer. Crystal size dis- tribution and supersaturation are measured once the process reaches steady state. Different conditions are imposed to acquire both the temperature and supersaturation dependency of the crystallization kinetics . A two-dimensional growth model is developed in order to capture the needle-like crystal morphology and the varying crystal aspect ratio with temperature, which is made possible by performing multi-scale image segmentation  and edge detection using the Canny method . Growth inhibition models such as developed by Kubota and Mullin  are used for numerical quantification of step advancement retardation in the presence of impurities.
Experimental and numerical results are obtained for the base system and in the presence of Mg2+ ions. The results indicate that, while retarding crystal growth, Mg2+ ions tend to increase the crystal aspect ratio and lead to elongated needle-like crystals. The experimental results are consistent with experimental observation reported in the literature . This study goes beyond past studies by providing a full two-dimensional population balance model for a highly concentrated ionic system that includes crystallization kinetics and thermodynamically correct driving force accounting non-ideality as well as the effects of an impurity.
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