Optimal control and simulation of multidimensional crystallization processes

David, L.; Tafti, Danesh K.; Braatz, Richard D.

doi:10.1016/s0098-1354(02)00033-9

Cited by 144 publications

(80 citation statements)

References 25 publications

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“…However, there have been very promising advances recently in both on-line characterization and modelling of crystal shape evolution for crystallisation processes, which could ultimately lead to practical solutions to closed-loop shape control. Ma et al [188] presented a methodology for crystal shape control and optimization in cooling crystallisation of potassium dihydrogen phosphate, which is based on optimizing the temperature profile and other influencing factors such as the seeding mass or the dissolution amount. A multidimensional PB model was developed in their work, which used two characteristic size dimensions to represent the shape of a twelve-faceted crystal.…”

Section: Crystal Shape Optimisation and Control Using Mpbmsmentioning

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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Section: Crystal Shape Optimisation and Control Using Mpbmsmentioning

confidence: 99%

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

2016

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“…The crystallization of KDP (potassium dihydrogen phosphate) from solution was taken as the model system, for which multidimensional kinetic parameters are available in the literature 11,47,49,50,72,73 . As it is shown on Fig.…”

Section: Model Identification and Validation And Sensitivity Studymentioning

confidence: 99%

Multi-Impurity Adsorption Model for Modeling Crystal Purity and Shape Evolution during Crystallization Processes in Impure Media

Borsos

Majumder

Nagy

2015

Crystal Growth & Design

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“…For example, in [4] the PBE in R 2 has been split into two 1D equations and a mixed Euler-Lagrange method has been applied. In the high-resolution finite volume computations [10,[19][20][21] of PBEs, the dimensional splitting has been applied to the PBE to obtain a system of 1D equations. Handling of the coupling conditions between the high-dimensional PBE and the 3D flow and species concentration equations will be more challenging when the PBE is split into a system of 1D equations.…”

Section: Introductionmentioning

confidence: 99%

An operator-splitting Galerkin/SUPG finite element method for population balance equations : stability and convergence

Ganesan

2012

ESAIM: M2AN

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Abstract. We present a heterogeneous finite element method for the solution of a high-dimensional population balance equation, which depends both the physical and the internal property coordinates. The proposed scheme tackles the two main difficulties in the finite element solution of population balance equation: (i) spatial discretization with the standard finite elements, when the dimension of the equation is more than three, (ii) spurious oscillations in the solution induced by standard Galerkin approximation due to pure advection in the internal property coordinates. The key idea is to split the high-dimensional population balance equation into two low-dimensional equations, and discretize the low-dimensional equations separately. In the proposed splitting scheme, the shape of the physical domain can be arbitrary, and different discretizations can be applied to the low-dimensional equations. In particular, we discretize the physical and internal spaces with the standard Galerkin and Streamline Upwind Petrov Galerkin (SUPG) finite elements, respectively. The stability and error estimates of the Galerkin/SUPG finite element discretization of the population balance equation are derived. It is shown that a slightly more regularity, i.e. the mixed partial derivatives of the solution has to be bounded, is necessary for the optimal order of convergence. Numerical results are presented to support the analysis.Mathematics Subject Classification. 35K20, 65M60, 65M12.

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Optimal control and simulation of multidimensional crystallization processes

Cited by 144 publications

References 25 publications

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

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

Multi-Impurity Adsorption Model for Modeling Crystal Purity and Shape Evolution during Crystallization Processes in Impure Media

An operator-splitting Galerkin/SUPG finite element method for population balance equations : stability and convergence

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