(164d) A Generic Multi-Dimensional Model-Based Framework for Batch Cooling Crystallization Process

Crystallization processes form an important class of separation methods that are frequently used in the chemical, the pharmaceutical and the food industry. The specifications of the crystal product are usually given in terms of crystal size, shape and purity. In order to predict the desired crystal morphology by means of model-based approaches, appropriate models covering the effects of the various operational parameters on the behavior of the crystals are necessary. Crystallization models generally involve three types of dynamic balance equations (population, mass and energy) together with a set of constitutive equations describing the reaction rates, and mass and heat transfer phenomena. In one-dimensional models the population balance equations only consider one inner variable which employs the characteristic length as a measure for crystal size. This approach undoubtedly can be used to obtain a required crystal size distribution (CSD) but is limited only to the description of spherical or cubic crystals. To fully characterize the crystal particles more complex models are necessary, that is, a multi-dimensional population balance modeling approach is needed, where two ? or even three ? characteristic lengths of a crystal can be considered. Recently, the growing interest in crystallization has resulted in the development of constitutive models for nucleation, crystal growth rate and supersaturation. For example, the kinetics considered in the models describes the primary nucleation and independent (size) growth rate and need to be extended if the effect of agitation on crystallization needs to be accounted for. Consequently, there are many types of models available with different levels of complexity such that their selection and use become rather challenging.

In order to cope with the above-mentioned complexity, the aim of this work is to develop a generic multi-dimensional model-based framework for batch cooling crystallization processes that can provide a better understanding of crystallization operations, and from which a large number of specific models for different batch cooling crystallization operational scenarios can be generated. This framework offers the possibility to study single or multi-dimensional crystallization processes for a wide range of chemical systems, and also taking into account the primary and secondary nucleation, crystal growth, agglomeration and breakage phenomena. Moreover, crystallization operations with seeding or without seeding can be handled. The generic framework consists of four main steps: (1) problem definition, where the objective of the specific modeling project is defined; (2) model (process) specifications where the details of chemical systems involved in the crystallization process are provided; (3) model generation and solution; and finally (4) process (operation) analysis. The generality of the approach allows the further development of the crystallization model. It also implies adaptability of the model to reflect changing product demands, and process conditions and even changing of the product to be crystallized or the solvent used. These specific crystallization models generated from the generic crystallization model can subsequently be used in many applications such as process understanding, process control, process-product monitoring and optimization. In this presentation, the application of the multi-dimensional model-based framework will be highlighted through a batch cooling crystallization using adipic acid case study where the objective is to obtain a desired CSD and two-dimensional crystal shape of adipic acid crystals.