A method of characteristics for solving population balance equations (PBE) describing the adsorption of impurities during crystallization processes

Abstract

International audiencePossible hindering effects of impurities on the crystal growth were shown to take place because of the adsorption of impurity species on the crystal surface. Transient features of this adsorption were observed, such that the growth of a given crystal does not depend on supersaturation only, but also on the time a given particle spent in contact with impurities present in the mother liquor. Meanwhile, few kinetic models describe the effect of impurities on the growth of crystals in solution, and published models are usually derived from data obtained, thanks to specific experiments based on the evaluation of the growth rate of single crystals. Such models are obviously questionable because, in the industrial practice, distributed properties of crystals are actually involved. Considering the “time of contamination” of particles as a new internal variable is thus made necessary. This is the reason why a specific PBE resolution algorithm is presented in this paper. The numerical scheme for the resolution of PBEs is based on the method of characteristics and shown to allow fast and accurate simulation of transient features of the crystal size distribution in the particular case when the growth or nucleation rates are assumed to exhibit unsteady-state dynamics. The algorithm is finally used to simulate the isothermal desupersaturation crystallization of citric acid in water

The Effect of Ultrasound on the Crystallisation of Paracetamol in the Presence of Structurally Similar Impurities

“…Also, an impurity has been reported to affect the solution-mediated phase transformation of the metastable A form to the stable B form of an active pharmaceutical ingredient [11]. The presence of impurities is widely reported to influence crystal growth and crystal morphology [9,[12][13][14][15]. This is the case for amino acids on the habit of glycine crystals [16], or urea crystallisation in the presence of biuret [15].…”

Problems, potentials and future of industrial crystallization

“…Due to the advanced acquisition of knowledge in the field of crystal growth coupled with increasing computational capacities, new dynamic simulation approaches are developing [10,11]. Among them, molecular modeling concepts are applied to predict morphology in the presence of impurities and additives or in the presence of solvents [11].…”

Application of the Method of Characteristics to Population Balance Models Considering Growth and Nucleation Phenomena

“…The numerical test is carried out on 200 grid points. It is evident that MOC resolves all the profiles of the solution in a better way than second order finite volume scheme [13]. …”