Multi-impurity adsorption model for modeling crystal purity and shape evolution during crystallization processes in impure media

© 2015 American Chemical Society. The impurity effect on the crystal properties, such as particle size and shape distribution, is significant, having significant impact on the downstream processes as well as on the product effectiveness. Currently very few studies exist that provide a quantitative model to describe crystal purity resulting from crystallization processes in impure media, and none to take into account the simultaneous effect of multiple impurities. Hence, the understanding of the effect of multiple impurities on crystallization process is important in order to obtain the desired product properties. Batch crystallization of potassium dihydrogen phosphate from aqueous solution in the presence of impurities was investigated experimentally by using an online particle vision and measurement tool with real-time image analysis. A mathematical model to describe the crystal purity and aspect ratio is proposed based on a morphological population balance equation including primary nucleation, growth of characteristic faces and multisite, competitive adsorption of impurities. The model parameters were identified and validated using crystallization experiments in mixtures of two impurities with variable composition. The developed and validated model can be an efficient tool for the investigation of crystallization processes in impure media with multiple impurities. The model can also serve as an effective tool for process and product design or optimization

Experimental implementation of a Quality-by-Control (QbC) framework using a mechanistic PBM-based nonlinear model predictive control involving chord length distribution measurement for the batch cooling crystallization of L-ascorbic acid

L-ascorbic acid is synthetized in large industrial scale from glucose and marketed as an immune system strengthening agent and anti-oxidant ingredient. The overall yield of conversion of the precursor glucose to L-ascorbic acid is limited, therefore the crystallization is a critically important step of the L-ascorbic acid production from economic point of view. It is widely accepted that the crystal size distribution (CSD) influences numerous relevant macroscopic properties of the final crystalline product and it also significantly affects the downstream operations. The present paper discusses the chord length distribution (CLD, which is directly related to the CSD) control, during the crystallization of L-ascorbic acid from aqueous solution. Batch crystallization process is employed, which is the classical, and still dominant, operation in fine chemical and pharmaceutical industries. A comparative experimental study of two state-of-the-art Quality-by-Control (QbC) based crystallization design approaches are presented: (1) a model-free QbC based on direct nucleation control (DNC) and (2) a model-based QbC using a novel nonlinear model predicative control (NMPC) framework. In the first investigation, the DNC, a process analytical technology based state-of-the-art model free control strategy, is applied. Although, DNC requires minimal preliminary system information and often provides robust process control, due to the unusual crystallization behavior of L-ascorbic acid, it leads to long batch times and oscillatory operation. In a second study the benefits of model-based QbC approach are demonstrated, based on using a NMPC approach. A population balance based crystallization process model is built and calibrated by estimating the nucleation and growth kinetics from concentration and CLD measurements. A projection based CSD to CLD forward transformation is used in the estimation of nucleation and growth kinetics. For robustness and adaptive behavior, the NMPC is coupled with a growing horizon state estimator, which is aimed to continuously improve the model by re-adjusting the kinetic constants. The study demonstrates that the model-based QbC framework can lead to rapid and robust crystallization process development with the NMPC system presenting good control behavior under significant plant model mismatch (PMM) conditions

Real time image processing based on-line feedback control system for cooling batch crystallization

The direct nucleation control (DNC) is a process analytical technique (PAT) based model free feedback control strategy for batch and continuous crystallization processes, which has been successfully applied in numerous cases. The basic principle of DNC is the use of controlled dissolution cycles to control a measurement directly related to the particle number in the system. During the DNC, in the case of cooling crystallization fines are dissolved by repeated heating-cooling loops. In this context, the controlled variable is the (relative) particle number, which is manipulated using a feedback control approach through the temperature. The particle number is traditionally measured with focused beam reflectance measurement (FBRM), however other PAT tools can also be employed in a similar feedback control setup. Often crystallization processes are also monitored by real-time imaging systems. In the current work a novel DNC setup is proposed in which microscopy images are captured and processed by the means of image analysis in real time. The images are used to extract the relative particle number, which is controlled using the DNC framework. The robustness of the new image analysis based direct nucleation control (IA-DNC) is presented via three case studies with materials having different crystallization properties. The IA-DNC approach uses a Particle Vision probe although other in situ or in line imaging systems can also be used in the framework. The systems are monitored with FBRM for comparison purposes. The setup achieved stable, converged control in most cases and is demonstrated that the IA-DNC has several advantages over the classical FBRM based DNC. The IA-DNC can also be used for real time feedback control of crystal shape

Model reliability of multi-dimensional population balance models for crystallization [abstract]

Model reliability of multi-dimensional population balance models for crystallization [abstract

A framework for model reliability and estimability analysis of crystallization processes with multi-impurity multi-dimensional population balance models

The development of reliable mathematical models for crystallization processes may be very challenging due the complexity of the underlying phenomena, the inherent Population Balance Models (PBMs) and the large number of parameters that need to be identified from experimental data. Due to the poor information content of the experiments, the structure of the model itself and correlation between model parameters, the mathematical model may contain more parameters than can be accurately and reliably identified from the available experimental data. A novel framework for parameter estimability for guaranteed optimal model reliability is proposed then validated by a complex crystallization process. The latter is described by a differential algebraic system which involves a multi-dimensional population balance model that accounts for the combined effects of different crystal growth modifiers/impurities on the crystal size and shape distribution of needle-like crystals. Two estimability methods were combined: the first is based on a sequential orthogonalization of the local sensitivity matrix and the second is Sobol, a variance-based global sensitivities technic. The framework provides a systematic way to assess the quality of two nominal sets of parameters: one obtained from prior knowledge and the second obtained by simultaneous identification using global optimization. A cut-off value was identified from an incremental least square optimization procedure for both estimability methods, providing the required optimal subset of model parameters. The implemented methodology showed that, although noisy aspect ratio data were used, the 8 most influential and least correlated parameters could be reliably identified out of twenty-three, leading to a crystallization model with enhanced prediction capability

Parameter identification, reliability and model discrimination of population balance models for crystallization [Poster]

Parameter identification, reliability and model discrimination of population balance models for crystallization [Poster