A Novel Stochastic Formulation for Predicting and Shaping the Particle Size Distribution in Crystallization Processes

Louisiana State University, Baton Rouge LA

Investigators

Abstract

PI: Romagnoli, Jose Institution: Louisiana State University & Agricultural and Mechanical College Proposal Number: 1132324 Title: A Novel Stochastic Formulation for Predicting and Shaping the Particle Size Distribution in Crystallization Processes Crystallization is a widely used technology for solid-liquid separation in the process industry. It is extensively used in the pharmaceuticals industry to separate the drug from the solvent mixture as well as to ensure the drug crystal product conforms to size and morphology regulations. The crystal size in crystallization processes is one of the most important variables since it influences factors such as filtration rate, de-watering rate, dissolution rate and bioavailability amongst others. The development of mathematical models describing the crystal growth dynamics is a bottleneck towards finding the optimal process performance and to control the crystal size and distribution. Previous studies exploited this by developing population balance models, which implied first principle assumptions and required a detailed knowledge of the physics and thermodynamics of the process. In this project, in place of trying to understand the complex interactions at the microscopic level along the crystallization process, the PI will seek to explain the observed macroscopic behavior towards the development of models to describe the crystal growth dynamics and control of crystal size distribution (CSD). Thus, in an effort to explain the observed macroscopic behavior of crystal growth in an anti-solvent aided crystallization, the PI will incorporate the Fokker?Planck equation (FPE) as the centerpiece of his approach. This is a change in the way crystallization modeling has been done so far and this study is expected to provide new and previously unavailable insight into this fundamental problem. Within this context, the use of FPE represents a new direction in developing a population balance model, taking into account the natural fluctuations present in the crystallization process, and allowing a novel description, in a compact form, of the PSD in time. The research directions will create a new and generic platform for addressing the control of particle size distribution in crystallization operations. The PI plans to formulate and asses the performance of alternative stochastic models. He will investigate analytical solutions for the temporal behavior of the PSD. A multi-model formulation will be used to merge multiple sets of parameters to a single model for the whole operating envelope. Model-based dynamic optimization studies will be performed towards developing optimal operational policies and will be validated using experimental investigations. Broader Impact of the Proposed Activity: Crystallization is a particulate technology that is becoming more and more important industrially. It is estimated that 60% of all products sold by chemical companies are crystalline, polymeric or amorphous solids. Many processes that utilize crystallization apply established ?rule-of-thumb? techniques and know-how in their operations. This work could bring a more scientific foundation into this field. From a practical operation and control point of view the availability of analytical solutions will be valuable for designing practical online model based control strategies. The pilot scale crystallization facilities at LSU, operated using industrial control systems will provide the environment to showcase the results. Although the focus in this project will be on cooling/antisolvent crystallization, the results are generic and could be used for other applications involving particle processes and particle size distribution characterization. Integration of Research and Education: The mathematical/experimental approach, which forms the core of this research, will contribute to training chemical engineering undergraduate and graduate students in the area of mathematical modeling and optimization, thus broadening their knowledge base and better preparing them to tackle real life problems in areas other than traditional process design and operation. The simulations to be developed for the crystallization process operations will be used in class settings. The LSU curriculum already incorporates as part of the Unit Operation Laboratory a section on crystallization. The PI plans to couple the simulations with the experimental work by involving these topics in existing undergraduate courses as class exercises or small projects and then perform validations in the Unit Operations Laboratory through a vertical integration of the topics through a continuing project throughout the semester. It is expected that the results of this project will have immediate effect on undergraduate education and will be used to improve the proficiency of undergraduate students in areas that are not traditionally included in chemical engineering curricula.