Kinetics identification and control of crystallization processes

Nonlinearities in batch crystallization arise due to the complex dependence of particle nucleation and growth rates on supersaturation. Since batch processes are often driven to low supersaturation levels to maximize yields, the maintenance of a desired crystal size distribution (CSD) trajectory throughout the batch by manipulating solubility is highly nonlinear and preferably handled using a model based control law. The first part of this work addresses difficulties encountered when identifying kinetic parameters from batch data. The second part of this work is concerned with the development and experimental demonstration of the model based CSD control.;Kinetic parameter estimation from batch crystallization experiments is investigated using simulated data sets. The data set is generated for a series of input parameters by a dynamic model for batch crystallization developed specifically for this purpose. Measurements consist of initial and final CSD as well as the dynamic solute desupersaturation curve. Starting with initial parameter guesses the dynamic model is then coupled with a nonlinear optimization routine and the parameters are regressed until an objective function derived from the measurement set is optimized. Success in identifying the parameters is shown to be process dependent and accuracy deteriorates when process characteristics result in a relatively higher percentage of product crystals below the measurable range (4 microns). Because of the resulting lower information contents of the product CSD measurements, higher nucleating processes are more difficult to accurately identify. Nonlinear parameter transformations are shown to improve results, however choosing a transformation becomes more difficult as unmeasured crystals increased.;A nonlinear model based control algorithm which utilizes feedback from a scanning laser microscope (LASENTEC) sensor is developed and implemented for mean particle size control in a batch crystallizer. For a bench scale system involving the seeded-drowning out precipitation of potassium sulfate, the control algorithm is demonstrated to work well in response to seed disturbances. The Batch Generic Model Control algorithm developed here utilizes a nonlinear time dependent reduced order model directly in the control law. In this study, the model is identified from historical data of successful batches, however on-line identification may be used if batches change significantly. In contrast to optimization type model based control (such as nonlinear dynamic matrix control) the BGMC algorithm does not require identification of kinetic parameters with respect to the laser measurements. Since the identification problem is mathematically ill-conditioned as well as affected by particle shape and the hydrodynamic distribution of the suspended particle, the BGMC approach is preferred model based algorithm.