Comparison of the Dynamic and Thermal Behavior of Different Ideal Flow Crystallizers

Abstract

In this simulation study, we compare the dynamics and thermal behavior of different ideal flow crystallizers. The first step in creating mathematical models for the crystallizers was the implementation of the population balance equation. The population balance equation was completed with mass balance equations for the solute and the solvent as well as in the case of non-isothermal crystallizers with an energy balance equation. The solution to the population balance equation, which is a partial differential equation, can only be performed numerically. Using the method of moments, which calculates the moments of the population density function, gives a mathematically simpler model for simulating and analyzing the crystallizers. All crystallizers studied are considered mixed suspension and mixed product crystallizers. In this simulation study, the investigated crystallizers are the batch mixed suspension and mixed product isothermal crystallizer, the batch mixed suspension and mixed product non-isothermal crystallizer, and the continuous mixed suspension and mixed product removal (CMSMPR) non-isothermal crystallizer equipped with a cooling jacket. We consider citric acid as the solid material to be crystallized, and a water–glycol system is used as a cooling medium. Considering the nucleation kinetics, we applied both primary and secondary nucleation. In the case of a crystal growth kinetic, we assumed a size-independent growth rate. The highest expected value and the variance of the crystal product occur in the isotherm batch case, which can be explained by the high crystallization rate caused by the high supersaturation. Contrary to this, in the non-isothermal batch case, the final mean particle size and variance are the lowest. In continuous mode, the variance and mean values are between the values obtained in the two other cases. In this case, the supersaturation is maintained at a constant level in the steady state, and the average residence time of the crystal particles also has an important influence on the crystal size distribution. In the case of non-isothermal crystallization, the simulation studies show that the application of the energy balance provides different dynamics for the crystallizers. The implementation of an energy balances into the mathematical model enables the calculation of the thermal behavior of the crystallizers, enabling the model to be used more widely.

Keywords

• population balance equation
• moments method
• crystallization
• enthalpy balance