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Estimating Supersaturation and Nucleation and Growth Kinetics from Chord-Length Measurements

Stephanie Barthe, Martha Grover Gallivan, and Ronald W. Rousseau. School of Chemical & Biomolecular Engineering, Georgia Institute of Technology, 311 Ferst Drive, Atlanta, GA 30332-0100

Batch crystallization is widely used in the production of high-value added species. Product properties and downstream processes such as filtration, washing and drying are influenced by crystal morphology and size distribution. Real-time and in-line observation of the evolution of population density, coupled to an ability to compute the kinetics of the system, would constitute major assets in the analysis and control of crystallizer operations and in understanding the phenomena that influence product quality.

Focused-beam reflectance measurement (FBRM) enables monitoring a representation of the crystal population in either batch or continuous crystallization systems. Properly installed, the FBRM records the chord-length density, which is a function of crystal geometry and is related to the population density. A model based on the geometry of the crystal was established to relate both distributions and thus enable computation of the population density from a measured chord-length density. These capabilities have been extended in the present study to include using the FBRM data to determine the prevailing supersaturation and crystallization kinetics in a system of interest. Such capabilities should lead to improved control procedures that, in turn, ensure that downstream processing and product quality meet expectations.

Batch cooling crystallization of paracetamol from ethanol solutions was used to test and illustrate the proposed methodology. Computation of the evolution of the population density and the corresponding solution concentration lead to an estimation of supersaturation, which in turn is used to determine the nucleation and growth kinetics in the system.