Multidimensional Process Models for Seeded Batch Crystallization

Abstract

This contribution focuses on the modeling and numerical approxima- tion of population balance models describing batch and polymorphic crystallization processes. Such processes have wide range applica- tions in ne chemicals, pharmaceutical, minerals, and food indus- tries. Di erent numerical techniques are employed for solving these models in one and two property coordinates. The space-time CE/SE method and the semi-discrete upwind nite volume schemes are de- rived and implemented to solve the batch crystallization models with nes dissolution. The ne dissolution reduces undesirable small crys- tals and improves the quality of a product. A delay in the recycle pipe is also included in the model. Apart from the above mentioned methods, a new numerical technique is introduced to solve a model describing polymorphic crystallization of L-glutamic acid. The sug- gested technique employs together the method of characteristics and Duhamel's principle to approximate the considered model e ciently and accurately. This technique has capability to produce accurate results on coarse meshes and no mesh re nement technique is needed for further improvement in the results. Furthermore, an alternative bivariate quadrature method of moments (QMOM) is developed for solving two-dimensional batch crystallization model involving crys- tals growth, nucleation, aggregation, and small nuclei dissolution in an external loop. The quadrature points and weights are obtained by using the orthogonal polynomials of lower order moments. Several case studies are carried out. The numerical computations demonstrate the eficiency, accuracy, and robustness of the proposed schemes. The results agree with the experimental predictions and could be used for process design and optimization.