Comparison of numerical methods for the simulation of dispersed phase systems

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

doi:10.1016/s0009-2509(02)00349-4

Cited by 70 publications

(46 citation statements)

References 32 publications

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“…Equation (4) was adapted from the equation reported by Motz et al (2002) for batch crystallization. This equation assumes that solvent molecules are not adhered to each other (i.e.…”

Section: General Mathematical Frameworkmentioning

confidence: 99%

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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“…Equation (4) was adapted from the equation reported by Motz et al (2002) for batch crystallization. This equation assumes that solvent molecules are not adhered to each other (i.e.…”

Section: General Mathematical Frameworkmentioning

confidence: 99%

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

Bolaños¹

2018

Rev. Mex. Ing. Quim.

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“…Such methods can be applied both to FD and FV formulations and are fairly simple to implement. This approach has been in use for some time in other research fields, but only recently was it applied to PBEs [122,133,134]. As demonstrated by these recent works, the combination of the FV method with a semi-discrete high resolution scheme is particularly suited for the solution of…”

Section: Finite Differences/volumesmentioning

confidence: 99%

Modeling particle size distribution in emulsion polymerization reactors

Vale

McKenna

2005

Progress in Polymer Science

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A review of the use and limitations of Population Balance Equations (PBE) in the modeling of emulsion polymerisation (EP), and in particular of the particle size distribution of the dispersed system is presented. After looking at the construction of the general form of PBEs for EP, a discussion of the different approaches used to model polymerization kinetics is presented. Following this, specific applications are presented in terms of developing a two-dimensional PBE for the modeling of more complex situations (for example the particle size distribution, PSD, and the composition of polymerizing particles). This review demonstrates that while the PBE approach to modeling EP is potentially very useful, certain problems remain to be solved, notably: the need to make simplifying assumptions about the distribution of free radicals in the particles in order to limit the computation complexity of the models; and the reliance of full models on approximate coagulation models. The review finishes by considering the different numerical techniques used to solve PBEs.

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“…Within this framework it appears that Hulburt and Katz [3] and Valentas and Amundson [4] were among the first who introduced the population balance equation (PBE) into the modelling of chemical engineering processes involving dispersed phase operations. Such processes include unit operations carried out in batch and continuous stirred tanks as well as in differential contacting equipment such as crystallization [5,6], bubble [7] and liquid-liquid extraction columns (LLEC) [8][9][10]. In such unit *Address correspondence to this author at the University of Kaiserslautern, Faculty of Mechanical & Process Engineering, Thermische Verfahrenstechnik , P.O.B.…”

Section: Introductionmentioning

confidence: 99%

LLECMOD: A Bivariate Population Balance Simulation Tool for Liquid- Liquid Extraction Columns

Attarakih¹,

Bart²,

Steinmetz³

et al. 2008

TOCENGJ

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Abstract:The population balance equation finds many applications in modelling poly-dispersed systems arising in many engineering applications such as aerosols dynamics, crystallization, precipitation, granulation, liquid-liquid, gas-liquid, combustion processes and microbial systems. The population balance lays down a modern approach for modelling the complex discrete behaviour of such systems. Due to the industrial importance of liquid-liquid extraction columns for the separation of many chemicals that are not amenable for separation by distillation, a Windows based program called LLECMOD is developed. Due to the multivariate nature of the population of droplets in liquid -liquid extraction columns (with respect to size and solute concentration), a spatially distributed population balance equation is developed. The basis of LLECMOD depends on modern numerical algorithms that couples the computational fluid dynamics and population balances. To avoid the solution of the momentum balance equations (for the continuous and discrete phases), experimental correlations are used for the estimation of the turbulent energy dissipation and the slip velocities of the moving droplets along with interaction frequencies of breakage and coalescence. The design of LLECMOD is flexible in such a way that allows the user to define droplet terminal velocity, energy dissipation, axial dispersion, breakage and coalescence frequencies and the other internal geometrical details of the column. The user input dialog makes the LLECMOD a user-friendly program that enables the user to select the simulation parameters and functions easily. The program is reinforced by a parameter estimation package for the droplet coalescence models. The scale-up and simulation of agitated extraction columns based on the populations balanced model leads to the main application of the simulation tool.

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Comparison of numerical methods for the simulation of dispersed phase systems

Cited by 70 publications

References 32 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

Modeling particle size distribution in emulsion polymerization reactors

LLECMOD: A Bivariate Population Balance Simulation Tool for Liquid- Liquid Extraction Columns

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