Numerical solution of the bivariate population balance equation for the interacting hydrodynamics and mass transfer in liquid–liquid extraction columns

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

doi:10.1016/j.ces.2004.12.055

Cited by 82 publications

(58 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…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%

“…This allows two of the major populations which mean properties (droplet volume and solute concentrations) to be tracked directly using a fixed particle sizes. A detailed description of the solution algorithms is presented in Attarakih et al, [4,6]. The underlying idea begins by dividing the continuous droplet size into M x finite number of particles for which the ith-division is the local droplet holdup:…”

Section: Solution Of the Population Balance Equation Using Llecmod Prmentioning

confidence: 99%

“…In this way, the bivariate PBE with respect to droplet size and concentration is decoupled into two population balances: One takes into account the droplet hydrodynamics and the other one takes into account solute transfer. This decoupling idea is based on using the Quadrature Method of Moments (QMOM) (see Attarakih et al, [4] for the details). The resulting system of PBEs is an integropartial differential system for which no general analytical solution is known.…”

Section: Solution Of the Population Balance Equation Using Llecmod Prmentioning

confidence: 99%

“…In the population balance model, the droplets can be distinguished by their sizes, which are parameterized over the diameter or volume, under the assumption that all the droplets are spherical. Accordingly, population balance modeling gives the possibilities to improve the simulation quality to optimize the operation of extraction equipment [4,24,[26][27][28][29]. The following integropartial differential equation represents the population balance equation (PBE): …”

Section: Population Balance Modelmentioning

confidence: 99%

“…Accordingly, detailed modeling on a discrete level is needed using the population balance equation as a mathematical framework. The multivariate non-equilibrium population balance models have emerged as an effective tool for the study of the complex coupled hydrodynamics and mass transfer in liquid-liquid extraction columns [4]. Unfortunately, the population balance modeling of extraction columns results in a set of integro-partial differential equations with no general analytical solution.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

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.

show abstract

“…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%

Section: Solution Of the Population Balance Equation Using Llecmod Prmentioning

confidence: 99%

Section: Solution Of the Population Balance Equation Using Llecmod Prmentioning

confidence: 99%

Section: Population Balance Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

show abstract

Interfacial relaxation of droplets caused by mass transfer in a pulsed column

Wang,

Zhou,

Zheng

et al. 2024

AIChE Journal

View full text Add to dashboard Cite

The method developed in our previous work (Wang et al., AIChE J. 2020; 66(8): e16257), was used to study the influence of the mass‐transfer direction and flux on the dynamic interfacial tension (DIFT) in a pulsed column. The breakup frequency was the highest near the entrance of the dispersed droplet, corresponding to the lowest interfacial tension and highest mass transfer flux. The decrease in the interfacial tension was proportional to the square root of mass‐transfer flux, and this difference is defined as a new parameter, named interfacial relaxation. When the mass‐transfer direction was changed from the dispersed phase to continuous phase to the opposite direction, the proportion of binary breakage was decreased from ~80% to ~40% and the interfacial relaxation was more sensitive to the mass‐transfer flux. A DIFT model was finally established based on the interfacial relaxation parameter, which predicted the experimental results with an error of ±10%.

show abstract

Application and parameterization of a one‐dimensional multifluid population balance model to bubble columns

Breit,

Weibel,

von Harbou

2024

AIChE Journal

View full text Add to dashboard Cite

A one‐dimensional (1D) multifluid population balance model approach is presented as a compromise between computational effort and accuracy. The approach is used to test process scenarios, perform sensitivity analysis, and provide a reliable reactor scale‐up and optimization tool. The article focuses on a mini‐plant batch bubble column, where the scale‐up behavior in terms of bubble column height, gas flux, and composition of the liquid phase is investigated. Although simplifications were made, the model requires calibration to experimental data using different calibration methods. An optimal calibration procedure is found that minimizes experimental effort while maximizing scalability. The model was tested on various liquid‐phase compositions, and it was found to reproduce experimental data accurately. However, the model cannot reproduce flow regime changes and does not perform well across substance systems. The study shows that the applied 1D multifluid population balance approach is a valuable and reliable tool in multiphase reactor scale‐up and optimization.

show abstract

Numerical solution of the bivariate population balance equation for the interacting hydrodynamics and mass transfer in liquid–liquid extraction columns

Cited by 82 publications

References 31 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

Interfacial relaxation of droplets caused by mass transfer in a pulsed column

Application and parameterization of a one‐dimensional multifluid population balance model to bubble columns

Contact Info

Product

Resources

About