Numerical solution of the spatially distributed population balance equation describing the hydrodynamics of interacting liquid–liquid dispersions

Attarakih, Menwer; Bart, Hans‐Jörg; Faqir, Naim M.

doi:10.1016/j.ces.2004.03.005

Cited by 86 publications

(66 citation statements)

References 74 publications

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“…A good review of which is presented by Gourdon et al, [21]. Recently, much work has been done using the population balance modeling in extraction columns [4][5][6][21][22][23][24][25].…”

Section: The Mathematical Modelmentioning

confidence: 99%

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

Jaradat¹,

Attarakih²,

Steinmetz³

et al. 2012

TOCENGJ

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A rigours mathematical model based on the bivariate population balance frame work (the base of LLECMOD ''Liquid-Liquid Extraction Column Module'') for the steady state and dynamic simulation of pulsed liquid-liquid extraction columns is developed. The model simulates the coupled hydrodynamic and mass transfer for pulsed (packed and sieve plate) extraction columns. It is implemented using visual digital FORTRAN and then integrated into the LLECMOD program. Experimental validated correlations are used for the estimation of the droplet terminal velocity in extraction columns based on single and swarm droplet experiments in laboratory scale devices. Additionally, recently published correlations for turbulent energy dissipation, droplet breakage and coalescence frequencies are discussed as being used in this version of LLECMOD. In a case study, LLECMOD is used here to simulate the steady state performance of pulsed extraction columns with two chemical test systems recommended by the European Federation of Chemical Engineering (water-acetone-n-butyl acetate and water-acetone-toluene) and an industrial test system. Model predictions are successfully validated against steady state and transient experimental data, where good agreements are achieved. The simulated results (holdup, mean droplet diameter and mass transfer profiles) compared to the experimental data show that LLECMOD is a powerful simulation tool, which can efficiently predict the dynamic and steady state performance of pulsed extraction columns.

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“…A good review of which is presented by Gourdon et al, [21]. Recently, much work has been done using the population balance modeling in extraction columns [4][5][6][21][22][23][24][25].…”

Section: The Mathematical Modelmentioning

confidence: 99%

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

Jaradat¹,

Attarakih²,

Steinmetz³

et al. 2012

TOCENGJ

View full text Add to dashboard Cite

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“…Note that three types of the continuous phase velocity x u can be distinguished: the steady state, oscillatory and nonoscillatory models [19] and are given in the appendix.…”

Section: Internal Coordinate Discretization: Reduced Modelmentioning

confidence: 99%

“…For more details and implementation aspects, the interested reader could refer to Attarakih et al [19,20] To complete the mathematical model described above, boundary and initial conditions are required. Concerning the boundary conditions, we adopted those of Wilburn [43], while the inlet bivariate number density is taken as:…”

Section: Internal Coordinate Discrete Discretization: Detailed Modelmentioning

confidence: 99%

“…The general spatially distributed population balance EQUATION (SDPBE) describing the coupled hydrodynamics and mass transfer in LLECs in a one spatial domain could be written as [19,20,[28][29][30][31]:…”

Section: The Sdpbementioning

confidence: 99%

“…Consequently, it is expected to find a droplet size distribution along the spatial coordinate of the liquid-liquid contacting equipment. The strong simplification when assuming uniform droplet size distribution based on a mean droplet diameter ( 32 facial area required for the calculation of mass and heat fluxes [16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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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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Process Intensification, 4. Plant Level

Freund

Sundmacher

2011

Ullmann's Encyclopedia of Industrial Chemistry

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The article contains sections titled: 1. Introduction 2. Heat‐Integrated Chemical Reactors 2.1. Autothermal Fixed‐Bed Reactor Concepts 2.1.1. Weakly Exothermic Reactions 2.1.2. Combination of Exo‐ and Endothermic Reactions 2.2. Desorptive Cooling of Reactors 3. Reactive Separations 3.1. Reactive Distillation 3.2. Reactive Stripping 3.3. Reactive Absorption 3.4. Reactive Extraction 3.5. Reactive Crystallization 3.6. Reactive Adsorption 3.6.1. Discontinuous Chromatographic Reactors 3.6.2. Continuous Chromatographic Reactors 3.6.3. Sorption‐Enhanced Reactors 3.7. Membrane Reactors 4. Other Intensification Concepts on the Plant Level 4.1. Hybrid Separations 4.2. Reactive Mechanical Unit Operations

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Numerical solution of the spatially distributed population balance equation describing the hydrodynamics of interacting liquid–liquid dispersions

Cited by 86 publications

References 74 publications

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

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

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

Process Intensification, 4. Plant Level

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