Estimation of Nucleation and Growth Kinetics of Benzoic Acid by Population Balance Modeling of a Continuous Cooling Mixed Suspension, Mixed Product Removal Crystallizer

Nucleation and growth kinetics of benzoic acid crystallized by cooling from 1.5:1 (w/w) water/ethanol solutions were determined using a 500 mL continuous mixed suspension, mixed product removal (MSMPR) crystallizer and a mathematical model of the MSMPR process. The developed model solves the population, moment, and mass balance relationships with the kinetic expressions for the system and is coupled with a nonlinear optimization routine for kinetic parameter estimation. Comprehensive experimental data for model fitting and parameter estimation was obtained by varying crystallizer operating conditions to induce changes in the rate-affecting variables for growth and nucleation (temperature, supersaturation, and suspension density). The size distribution was monitored in real-time using focused beam reflectance measurement (FBRM) to identify steady-state and hence to enable on-demand adjustment of the operating conditions to transition multiple steady-states for rapid acquisition of kinetic data. A Malvern Mastersizer was used to quantify the crystal size distribution (CSD) at steady-state, whereas concentration was determined gravimetrically. Six kinetic parameters for crystal growth and nucleation were estimated from the model fitting procedure, which enabled accurate prediction of CSD and concentration results at steady-state.