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.
Crystallization and specifically antisolvent crystallization, is a widely used chemical engineering separation unit operation process. Since this technique can produce high purity products it is used for the industrial production of many chemical compounds, such as pharmaceuticals, agrochemicals, and fine chemicals. The production of these products is a multi-million dollar industry. Any methods to improve the production of these products would be highly valued and clearly will have an important impact on technology and society in general. Thus, the main objective of this work was to target model-based optimal strategies for crystallization operations specifically targeting crystal size and crystal size distribution (CSD). In particular, take the knowledge gained and translate it into an economically and practically feasible implementation that is utilizable by the industry. Antisolvent crystallization has been modeled for many systems using the traditional population balance modeling approach (PBA). From a modeling perspective and as a novel alternative to the population balance approach, we have shown that it is possible to describe a crystallization process by means of a stochastic approach, which allows description of the Crystal Size Distribution (CSD) evolution with respect to time using the Fokker-Planck equation (FPE). In this approach, rather than understanding the complex interactions at the microscopic level along the crystallization process, one seeks to explain the observed macroscopic behavior. Thus, in an effort to explain the observed macroscopic behavior of crystal growth in an anti-solved aided crystallization, we have incorporated the Fokker–Planck equation (FPE) as the centerpiece of our approach in our research. Overall, the results from our NSF supported research corroborated that the FPE represents a powerful new direction in developing population balance models, taking into account the natural fluctuations present in the crystallization process and allowing a novel description in a compact form of the CSD in time. One key contribution of the FPE approach is the availability of analytical solutions to represent the CSD characteristics evolution through time. Using these capabilities we were able to generate for the first time an operational map of the antisolvent crystallization process and detected input multiplicities within the operating range of the system. These results have been represented as isomean/isovariance maps with respect to antisolvent flow rate and temperature. The presence of input multiplicities should be properly taken into account when designing the process controller. Using controllability analysis tools we were able to uncover the ill-conditioned nature of the control problems arising during the non-isothermal operation of the antisolvent crystallization problem due to input multiplicity. These studies will eventually lead to the definition of proper feedback control strategies required for this type of ill-conditioned problems which is part of our current research. From the particle characterization point of view, a novel image-based multi-resolution sensor for online prediction of crystal size distribution (CSD) was formulated and tested. In the proposed approach, texture analysis (fractal dimension (FD) and energy signatures) as characteristic parameters to follow the crystal growth is utilized. Following the texture information extraction, an artificial neural network nonlinear mapping is incorporated using as inputs the texture information in conjunction with the available on-line process conditions (flowrate and temperature) to predict the CSD. A fully automated laboratory scale software/hardware framework was developed for image sampling, acquisition and processing. This line of research is very promising since will ultimately provide a way to characterize the PSD on-line for implementing a model-based controller using the FPE modelling approach which was the main focus of this research. We envisage that the results of this project will contribute to commercial technology for particle characterization. Currently, there is no clear technology to characterize on line particles, especially as in the case under investigation when particles are touching and overlapping where individual particle characterization is impossible. The strategies we are pursuing in our research will lead to novel strategies to solve those problems and to realize a completely automated system that to be used for on-line mode-based control.
