Gypsum Crystallization during Phosphoric Acid Production: Modeling and Experiments Using the Mixed-Solvent-Electrolyte Thermodynamic Model

Abstract

The size distributions of calcium sulfate dihydrate crystals formed during the industrial phosphoric acid production process are critical to the acid filtration efficiency. In this work, a thermodynamically consistent definition of supersaturation is derived and modeled using the mixed-solvent-electrolyte framework in OLI software for gypsum in an acid mixture. Continuous reactive crystallization experiments are carried out to estimate the gypsum growth and nucleation kinetics at different temperatures. A population balance model is implemented using the method of characteristics and integrated with the thermodynamic model platform to accurately simulate the dynamic propagation of the solution concentration and particle size distribution. The experimentally fitted kinetic parameters are verified through a comparison with the predicted crystal size distribution (CSD) and supersaturation. The comparison shows a good agreement between the predicted and measured CSD and supersaturation at a temperature range from 25 to 60°C.

Organic electrolyte solutions: Modeling of deviations from ideality within the binding mean spherical approximation

“…It is observed in Table 6 that these two conditions, σ (1) S < 0 and α > 0, are fulfilled, which is a satisfactory outcome, and that the fits are generally of good accuracy. Overall, most values for σ (1) S are of the same order of magnitude (of the order of -0.2 or -0.3).…”

“…Moreover, besides a low value of the deviation (AARD in Table 6), a good fit should be characterized by values of σ (1) S and α that are respectively negative and positive, and do not have unrealistic values. These latter two conditions express the fact that the cation diameter and the relative permittivity are expected to decrease with concentration if the model indeed has some physical meaning.…”

“…Mixed solvent (aqueous-organic) electrolytes have been used for some time now in many industrial processes, for example in order to optimize crystallization [1] and other separation processes in the chemical and pharmaceutical industries, such as water-alcohol distillation [2]. In probably more recent times, solutions of salts in pure organic solvents have been used increasingly in industrial processes and devices as, e.g., in the fabrication of lithium-ion batteries involving different types of carbonates as the solvent [3], of wet double-layer capacitors and supercapacitors, and in electrodeposition, electroplating, etc.…”

“…+ the cation diameter at infinite dilution (the 'intrinsic' diameter of cation), C S the molar concentration of the salt and ε org the relative permittivity of pure solvent. Eqs 23 and 24 introduce two adjustable parameters σ (1) S and α that are characteristic of the electrolyte while σ…”

Determination of kinetics in batch cooling crystallization processes—A sequential parameter estimation approach

“…A judicious algebraic manipulation allows the growth and nucleation rates to be determined independently of other crystallization phenomena, even if those phenomena occur in the same experiment . This approach has been broadly applied in academia and industry to sequentially estimate growth and nucleation kinetics, growth, nucleation and agglomeration kinetics, growth and agglomeration kinetics, growth and breakage kinetics, or growth, nucleation, agglomeration and breakage, and to obtain initial estimates of the kinetic parameters before applying optimal model‐based experimental design to simultaneously fit the whole model …”