Model Based Estimation of 2D Crystallization Kinetics From Concentration and CLD Measurements

Due to the fact that crystal size and shape influence relevant macroscopic properties of solid particles, the understanding and control of these quantities have increasing importance in particulate science. Crystallization, the primary crystal formation and purification process, is usually tracked real-time, in situ, by spectroscopic techniques and Focused Beam Reflectance Measurement (FBRM). This sensor can measure the chord length distribution (CLD) of a population of particles suspended in a solution. The CLD is related to both the size and shape of the particles and it is measured using a rotating infrared laser beam that emanates through the probe window inserted in the suspension. During its rotation, the beam hits the particles within the sample and is reflected back to the probe. The calculated length of laser-crystal intersection is the so-called chord length. FBRM can provide a large amount of useful information during crystallization processes, however, since the CLD is significantly different compared to the actual crystal size and shape distribution (CSD), it is normally not used for the quantification of the kinetics of crystal growth and nucleation. Usually off-line techniques (laser diffraction, microscopy, ultrasound) are exploited. In this study we develop and present a new, projection based forward 2D CSD➔CLD transformation technique. In addition, a 2D population balance model is employed to simulate the evolution of 2D CSD and solute concentration. The model equations are solved by a high resolution finite volume method, involving GPU acceleration for improved simulation time. Such model allows the use of FBRM data for the estimation of the kinetics of crystallization, without relying on off-line measurements of CSD. As model system succinic acid is used. This forms prism-like crystals in the presence of growth rate modifiers. Crystal breakage is minimized through reduced mixing rate and the kinetics of primary and secondary nucleation as well as the growth and dissolution of individual crystal facets were estimated by developing and solving a process optimization problem. The result of the parameter regression was a calibrated model, which simulates fairly the concentration and CLD variations too.