Morphology evolution of crystal populations: Modeling and observation analysis

Borchert, Christian; Sundmacher, Kai

doi:10.1016/j.ces.2011.05.057

Cited by 39 publications

(43 citation statements)

References 40 publications

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“…The solubility of L-GA depends on the solute temperature and is given by the following empirical formula (4) Dynamics of the solute concentration can be derived from the mass balance of the liquid in the crystallizer and are given by (5) where is the crystal density. Obviously, the overall dynamical system consists of an ordinary differential equation (ODE) and partial differential equations (PDE), which are coupled.…”

Section: Process Modelingmentioning

confidence: 99%

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Online Parameter Identification of Facet Growth Kinetics in Crystal Morphology Population Balance Models

Dürr¹,

Palis²,

Kienle³

2015

Procedia Engineering

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Particle shape plays an important role in many industrial applications since it can have significant impact on both, processability of particles as well as the properties of the final product. For this reason modeling of the corresponding production process is crucial for developing efficient process optimization and control strategies. The shape evolution of crystals on the process scale can be described conveniently within the framework of morphological population balance modeling. In order of being a reliable tool for the prediction of the crystal shape distribution during the production process as well as for the design of suitable control and optimal production strategies, the models require the estimation of several parameters characterizing the growth rates of the different crystal facets. This is particularly challenging due to the infinite dimensional state space of the models. In this contribution online parameter estimation for the growth rates of L-glutamic acid cooling crystallization is presented. Using a Lyapunov-based approach the parameter adaption laws are computed directly from the infinite dimensional problem formulation. It will be shown that a reasonably fast convergence of the parameter estimates can be achieved even in the presence of measurement noise using appropriate filters.

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Section: Process Modelingmentioning

confidence: 99%

“…Here, morphological population balances being a special form of multivariate PBMs can be used to describe the dynamic shape evolution (e.g. [3], [4]). For the development of process control and optimization schemes the individual facets growth kinetics in the population balance have to be determined.…”

Section: Introductionmentioning

confidence: 99%

Online Parameter Identification of Facet Growth Kinetics in Crystal Morphology Population Balance Models

Dürr¹,

Palis²,

Kienle³

2015

Procedia Engineering

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“…The disperse properties can be modeled by population balance equations (PBEs), as can be seen in [10][11][12][13][14][15][16]. PBEs represent a unifying concept for several different growth mechanisms, including fluidized-bed spray granulation (FBSG), crystallization and aggregation [17][18][19]. However, as dispersity needs to be adjusted in a range of dimensions (size, shape, surface, composition, and structure) [20], precisely modeling the synthesis of QDs using PBEs is a particularly complex task [21].…”

Section: Introductionmentioning

confidence: 99%

Model‐Based Optimization of Ripening Processes with Feedback Modules

et al. 2020

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In order to obtain high-quality particulate products with tailored properties, process conditions and their evolution in time must be chosen appropriately. Although the efficiency of these products depends on their dispersity in several dimensions, in established processes the particle size is usually the decisive variable to adjust. As part of the synthesis of these products, feedback modules are often incorporated so that a time-dependent ratio of the obtained product can flow back into the system. Moreover, the synthesis should be an energy-and resource-efficient process. To provide a means of ensuring this requirement, a model-and gradient-based, numerically efficient optimization tool for particle synthesis is presented which was developed to describe population balance equations incorporating feedback terms.

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“…However, the morphology of a crystal evolves during its growth before a "steady state growth morphology" is obtained (Zhang et al, 2006), which requires more flexible approaches to extract size information. Such approaches, in which crystals are described as parametric polytopes, have been presented by Borchert and Sundmacher (2012) and Hours et al (2014) for monoscopic and stereoscopic setups, respectively.…”

Section: Introductionmentioning

confidence: 99%

An optimization-based approach to extract faceted crystal shapes from stereoscopic images

Schorsch

Hours

Vetter

et al. 2015

Computers & Chemical Engineering

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a b s t r a c tThe size and shape of particles crucially influences the characteristics of solid products. Until recently these quantities were evaluated using light microscopy. However, extracting the three-dimensional shape of a faceted crystal from a single image is a formidable computer vision challenge. In this work we combine stereoscopic imaging devices (e.g., commercial stereoscopic microscopes or the stereoscopic flow through cell that continuously draws samples from a crystallizer ) with a model-based approach in which parametric polytopes are used to describe faceted crystals (Hours et al., 2014). In the shape reconstruction algorithm these parametric polytopes are scaled and rotated until their projections closely match the measured stereoscopic images, which is formulated as a nonlinear optimization problem. The proposed approach is assessed using simulated images and experimental data. We also assess in which cases the proposed approach does or does not provide advantages over concepts using generic particle shapes (Schorsch et al., 2012).

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Morphology evolution of crystal populations: Modeling and observation analysis

Cited by 39 publications

References 40 publications

Online Parameter Identification of Facet Growth Kinetics in Crystal Morphology Population Balance Models

Online Parameter Identification of Facet Growth Kinetics in Crystal Morphology Population Balance Models

Model‐Based Optimization of Ripening Processes with Feedback Modules

An optimization-based approach to extract faceted crystal shapes from stereoscopic images

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