Mathematical modelling and analysis of an industrial scale evaporative crystallizer producing lactose monohydrate

Abstract Lactose is industrially produced by a series of concentration steps to supersaturate the solution allowing crystallization to take place. This papers deals with the operation and analysis of a forced circulation evaporative crystallizer producing pharmaceutical lactose. A mathematical model of the operation of the crystallizer was developed. The model comprises of the mass balance, population balance, nucleation kinetics, growth kinetics and lactose solubility and mutarotation rate expressions. The steady state operation of the crystallizer was analysed from the classical mixed suspension mixed product removal (MSMPR) model perspective. It was found that the crystallizer behaviour deviated from ideal MSMPR behaviour with a steep upward curvature in the population density curve for crystal sizes below 40 μm. A size dependent growth (SDG) rate model was used to model the deviation from ideal behaviour. The parameters of the SDG model were estimated by fitting it to the measured population density curve from the crystallizer. The crystallization kinetic parameters like growth and nucleation rate constants were then estimated by fitting the simulated trends to the measured date. The model showed that the average crystal size follows a transient decaying dynamics before settling down to a constant value. This was reflected in the actual data collected from the crystallizer. The transient dynamics disappeared from the model results when a simple size independent growth model was used.