Size-dependent growth kinetics model for potassium chloride from seeded chloride solution

It was widely known that crystallization kinetics are the basis for crystallization behavior and crystallizer scale-up design. Cooling crystallization of potassium chloride was an essential unit operation in recycling industry. Some researchers have proposed the strategy of adding seed crystals for the intermittent cooling crystallization process to control the particle size and distribution of the target product. This paper studied the complex function relation between particle size and growth rate of KCI in the crystallization process in a continuous mixed-suspension mixed-product-removal (MSMPR) crystallizer at a steady state. Using the crystallization kinetics data, the mathematical models of coupling crystallization were established based on the population balance equations and mass balance equations. Since population density distributions of products behave multiform under different conditions, based on diffusion theory. The growth rate was obtained by a least square method for the multivariate linear regression, and the reliability of the kinetics model was validated experimentally. Fitting results indicated that some classical models, including several size-independent growth models and size-dependent growth models, such as Bransom, C-R, MJ2, ASL, and MJ3, could not model the size-dependent growth accurately. Based on this situation, an exponential growth model was proposed and confirmed to describe the size-dependent growth behavior. It was found that the model parameters have definite meanings and were strongly related to particle size. Compared with the classical models, this model showed good pertinency and adaptability to experimental results when used to describe the population density distribution and the size-dependent growth rate of KCI. This research could provide a theoretical guide for optimizing the crystallization process and designing industrial crystallizers.