Regions of attainable particle sizes in continuous and batch crystallization processes

Author-Highlights
• Continuous and batch crystallization processes are modeled using PBEs.
• Attainable regions (AR) in a diagram of process time vs. particle size are obtained.
• The influence of additional processing constraints on the ARs is investigated.
• The ARs show if fulfilling a set of specifications is possible in given process equipment.

Process alternatives for continuous crystallization, i.e., cascades of mixed suspension, mixed product removal crystallizers (MSMPRCs) and plug flow crystallizers (PFCs), as well as batch crystallizers are discussed and modeled using population balance equations. The attainable region approach that has previously been used in the design of chemical reactor networks and separation systems is applied to the above-mentioned alternatives for crystallization processes in order to identify attainable regions in a diagram of mean product particle size vs. total process residence time. It is demonstrated that the boundaries of these attainable regions can be found numerically by solving appropriate optimization problems and that the region enclosed by these boundaries is fully accessible. Knowing the attainable region of particle sizes, it is possible to generate feasible process alternatives that allow specific particle sizes to be obtained in a given process configuration. The attainable regions presented in this paper are useful to determine whether a desired mean particle size can be achieved in a specific crystallizer type. The concept of the attainable region is illustrated on three case studies: the cooling crystallization of paracetamol grown from ethanol, the anti-solvent crystallization of l-asparagine monohydrate from water using isopropanol as the anti-solvent and the combined cooling/anti-solvent crystallization of aspirin from ethanol using water as the anti-solvent.