Development, analysis and validation of population models for continuous and batch crystallizers

Gerstlauer, Andreas; Motz, S.; Mitrović, Aleksandra; Gilles, Ernst Dieter

doi:10.1016/s0009-2509(02)00348-2

Cited by 33 publications

(30 citation statements)

References 17 publications

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“…This works considers the physical model derived by Mersmann (2001) and implemented by Gerstlauer et al, (2002):…”

Section: Mechanistic Kinetic Modelling Approachmentioning

confidence: 99%

“…These constants are related to attrition phenomena and crystal growth and have a clear physical meaning: surface related energy increase Γ S and the integration rate constant for crystal growth k r . Gerstlauer et al, (2002) included a constant related to primary nucleation rate C het , which represents the heterogeneity degree of primary nucleation. The present study formulates a leastsquares optimization problem to determine those constants, i.e.…”

Section: Parameter Estimationmentioning

confidence: 99%

“…narrow CSD and specific shape (Gerstlauer et al, 2002. Largely, the quality of the model depends on the assumptions made during its development, the accuracy of the experimental data used for estimation of unknown kinetic parameters, and the numerical algorithm employed to solve the model equations Mesbah et al, 2009).…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, such modelling approach has less unknown parameters compared with the empirical models and can be obtained by a simple formulation of an optimization problem. Gerstlauer et al, (2002) presented the development of the mathematical model proposed by Gahn, C. & Mersmann, A., (1999a) for batch and continuous crystallization. In that model, a constant parameter related to the degree of primary nucleation heterogeneity is considered.…”

Section: Introductionmentioning

confidence: 99%

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A Study on Empirical and Mechanistic Approaches for Modelling Cane Sugar Crystallization

Bolaños¹

2018

Rev. Mex. Ing. Quim.

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This study presents the kinetic modelling for cane sugar batch crystallization. The study is based on two approaches to describe the nucleation (homogeneous primary and secondary) and growth kinetics, and the birth and death rates of crystals: a) empirical models with equations of type power law (TPL) and b) mechanistic approach with thermodynamic equations. Both approaches, describing the phenomena of crystallization at the microscopic level (by solving population balance equation by method of lines), were validated using experimental data from a pilot-scale plant. From the results of both approaches and experimental validation, we conclude that the mechanistic approach best represents the dynamic behavior of cane sugar batch crystallization under different operational conditions than the empirical approach (TPL). Keywords: crystallization, modelling, kinetics, mechanistic and empirical approaches. ResumenEste estudio presenta el modelado cinético para la cristalización por lotes de azúcar de caña. El estudio se basa en dos enfoques para describir las cinéticas de nucleación (primaria homogénea y secundaria), de crecimiento y las tasas de nacimiento y muerte de cristales: a) modelos empíricos con ecuaciones de tipo ley de potencias (TLP) y b) enfoque mecanístico con ecuaciones termodinámicas. Ambos enfoques describen los fenómenos de cristalización a nivel microscópico (con la solución del balance de población por método de líneas) y fueron validados usando datos experimentales provenientes de una planta escala piloto. De los resultados de ambos enfoques y la validación experimental, se concluye que el enfoque mecanístico representa mejor los comportamientos dinámicos de la cristalización por lotes de azúcar de caña bajo diferentes condiciones operativas con respecto al enfoque empírico (TLP). Palabras clave: cristalización, modelado, enfoque mecanístico y empírico.

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“…This works considers the physical model derived by Mersmann (2001) and implemented by Gerstlauer et al, (2002):…”

Section: Mechanistic Kinetic Modelling Approachmentioning

confidence: 99%

Section: Parameter Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Study on Empirical and Mechanistic Approaches for Modelling Cane Sugar Crystallization

Bolaños¹

2018

Rev. Mex. Ing. Quim.

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“…Experimental data are required to develop and validate these expressions in some restricted operating regions. PBM are used in various areas, such as crystallization [113], powder mixing [114], powder milling [115] and wet granulation [116,117]. In extrusion processes, this method can be employed to compute different material properties, such as the active pharmaceutical ingredient (API) or excipient component concentration [118], the RTD [119], the particle size distribution, the liquid content and the porosity [120,121].…”

Section: Population Balance Modeling and Discrete Element Modelingmentioning

confidence: 99%

A Review of Dynamic Models of Hot-Melt Extrusion

2016

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Hot-melt extrusion is commonly applied for forming products, ranging from metals to plastics, rubber and clay composites. It is also increasingly used for the production of pharmaceuticals, such as granules, pellets and tablets. In this context, mathematical modeling plays an important role to determine the best process operating conditions, but also to possibly develop software sensors or controllers. The early models were essentially black-box and relied on the measurement of the residence time distribution. Current models involve mass, energy and momentum balances and consists of (partial) differential equations. This paper presents a literature review of a range of existing models. A common case study is considered to illustrate the predictive capability of the main candidate models, programmed in a simulation environment (e.g., MATLAB). Finally, a comprehensive distributed parameter model capturing the main phenomena is proposed.

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Morphological population balance for modeling crystal growth in face directions

2007

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in Wiley InterScience (www.interscience.wiley.com).A morphological (or polyhedral) population balance (PB) model is presented for modeling the dynamic size evolution of crystals grown from solution in all crystal growth directions. The morphological PB approach uses the crystal shape information for a single crystal obtained from morphology prediction, or experiment as the initial face locations, as well as face growth rates to predict the shape evolution of the crystal population. For each time instant during the crystallization process, the prediction uses its shape at the previous time moment, and the growth rate for the specific crystal habit plane. The methodology is demonstrated through a study of potash alum (KAl (SO 4 ) 2 Á12H 2 O), for which literature data is available for comparison and validation. The discretization method, method of classes, was used to convert the equations to ordinary differential form with the computational domain being discretized into small meshes. The ordinary differential equations ([1.5 million) were then solved simultaneously using the Runge-Kutta-Fehlbergh 4th/5th-order solver with automatic time-step control. The results obtained clearly demonstrate that the morphological PB model developed can predict crystal growth and surface area of individual habit faces in detail, together with crystal shape and size evolution.

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Development, analysis and validation of population models for continuous and batch crystallizers

Cited by 33 publications

References 17 publications

A Study on Empirical and Mechanistic Approaches for Modelling Cane Sugar Crystallization

A Study on Empirical and Mechanistic Approaches for Modelling Cane Sugar Crystallization

A Review of Dynamic Models of Hot-Melt Extrusion

Morphological population balance for modeling crystal growth in face directions

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