Modelling of Growth Rate for MSMPR Crystallizer Data

Abstract

One of the most important applications of the population balance approach to MSMPR crystallizer modelling is the recovery of crystal nucleation and growth rates data from steady-state crystal size distributions (RANDOLPH, LARSON). A large number of studies have confirmed that both size-dependent (growth rate is a function of crystal size) and growth rate dispersion (crystals of the same size do not have the same growth rate), causes nonlinearities which limit the usefulness of the RANDOLPH and LARSON approach.A discussion of modelling of crystal growth kinetics for simulated and real MSMPR crystallizer data is presented. In the former case, both linear and non-linear log population density distributions are used. The modelling of growth kinetics is done twiceonce assuming that growth rate dispersion is a source of curvature in the log population density vs size data plot and, again when this curvature is caused by size-dependent growth. Calculations clearly indicate that even for crystallizing systems which follow the McCabe's AL law, both growth rate dispersion and size-dependent growth models lead to proper estimation of growth kinetics. When log population density vs size data plots exhibit curvature, however, use of the size-dependent growth rate approach gives more reliable growth kinetics across a broad crystal size range than those obtained from modelling of growth kinetics by growth rate dispersion.

The Application of Two-Dimensional Population Balance Model To Study the Effect of Temperature Profile on the Crystal Size Distribution and Aspect Ratio

“…where α and β 0 are parameters that represent the dependency of the growth rates on width 13 and temperature, 10 respectively.…”

“…The following equations were chosen for the description of the growth rate of width ( G S ) and length ( G L ), respectively, with the help of previous research. − σ is the relative supersaturation.…”

“…Width: Birth and Spread model with size dependence G normalS = A S 0 ( 1 − e − α L S ) σ 5 / 6 .25em exp ( − β / σ ) β = β 0 / false( R T false) 2 where α and β 0 are parameters that represent the dependency of the growth rates on width and temperature, respectively.…”