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.
