On the prediction of crystal shape distributions in a steady-state continuous crystallizer

Borchert, Christian; Nere, Nandkishor K.; Ramkrishna, Doraiswami; Voigt, Andreas; Sundmacher, Kai

doi:10.1016/j.ces.2008.05.009

Cited by 48 publications

(47 citation statements)

References 11 publications

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“…In this paper the authors considered a system in the steady state and checked the influence of the mean residence time on crystal dimensions. In the present work a dynamic model has been developed and solved using GC to check if it converges to the steady state results presented in the paper by Borchert et al (2009). Similarly as in the previous test case the model equations were solved directly to have the dynamic results for comparison.…”

Section: D Casementioning

confidence: 99%

“…The process kinetics has been taken from Borchert et al (2009). In this paper the authors considered a system in the steady state and checked the influence of the mean residence time on crystal dimensions.…”

Section: D Casementioning

confidence: 99%

“…Kinetic constants k g,i and g i are taken directly from the paper by Borchert et al (2009) and the supersaturation is defined as follows:…”

Section: D Casementioning

confidence: 99%

“…It should be noted that the system parameters in the paper by Borchert et al (2009) do not refer to a specific physical system.…”

mentioning

confidence: 99%

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Application of Gaussian cubature to model two-dimensional population balances

Bałdyga

Tyl

Bouaifi

2017

Chemical and Process Engineering

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In many systems of engineering interest the moment transformation of population balance is applied. One of the methods to solve the transformed population balance equations is the quadrature method of moments. It is based on the approximation of the density function in the source term by the Gaussian quadrature so that it preserves the moments of the original distribution. In this work we propose another method to be applied to the multivariate population problem in chemical engineering, namely a Gaussian cubature (GC) technique that applies linear programming for the approximation of the multivariate distribution. Examples of the application of the Gaussian cubature (GC) are presented for four processes typical for chemical engineering applications. The first and second ones are devoted to crystallization modeling with direction-dependent two-dimensional and three-dimensional growth rates, the third one represents drop dispersion accompanied by mass transfer in liquid-liquid dispersions and finally the fourth case regards the aggregation and sintering of particle populations.

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Section: D Casementioning

confidence: 99%

Section: D Casementioning

confidence: 99%

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Application of Gaussian cubature to model two-dimensional population balances

Bałdyga

Tyl

Bouaifi

2017

Chemical and Process Engineering

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“…Borchert et al [99] proposed a multi-dimensional PB to extract shape distributions in a steady state continuous crystalliser for seeded and spontaneous crystallisations. Optimal control algorithms and strategies for crystal shape manipulation were explored to obtain minimum time trajectories with the temperature as the control input [100].…”

Section: Multi-dimensional and Morphological Population Balance Modelsmentioning

confidence: 99%

Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

2016

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Crystal morphology is known to be of great importance to the end-use properties of the crystal product and affect the down-stream processing such as in filtration and drying, but was previously regarded as too challenging to achieve automatic closed-loop control. As a consequence, previous work has focused on control the crystal size distribution (CSD) where the size of a crystal is often defined as the diameter of a sphere that has the same volume of the crystal. This paper reviews very promising new advances made in recent years in morphological population balance models for modelling and simulation of crystal shape distribution (CShD), measurement and estimation of crystal facet growth kinetics, as well as in 2D and 3D imaging for on-line characterisation of crystal morphology and CShD. A framework is presented integrating various components in order to achieve the ultimate objective of model-based closed-loop control of CShD. The knowledge gaps and challenges that require further research are also identified.

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Reformulating multidimensional population balances for predicting crystal size and shape

Kuvadia

Doherty

2013

AIChE Journal

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There is a growing interest in predicting and controlling the size and shape of crystalline particles. Multidimensional population balances have been developed to accomplish this task but they suffer from the drawback of needing rate laws for the absolute growth rate for every family of faces that may appear on the crystal surface. Such growth rates are known for only a handful of crystalline materials and prospects are bleak for extending the library of growth rate data. This raises the question of where the surface growth rates for all the families of faces will come from to drive multidimensional population balance engineering technology. One answer is “from first principles.” We reformulate multidimensional population balances in terms of relative growth rates and show how to create first principles mechanistic models to calculate these quantities for real molecular crystals as a function of supersaturation. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3468–3474, 2013

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On the prediction of crystal shape distributions in a steady-state continuous crystallizer

Cited by 48 publications

References 11 publications

Application of Gaussian cubature to model two-dimensional population balances

Application of Gaussian cubature to model two-dimensional population balances

Measurement, modelling, and closed-loop control of crystal shape distribution: Literature review and future perspectives

Reformulating multidimensional population balances for predicting crystal size and shape

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