Solution of the population balance equation using the sectional quadrature method of moments (SQMOM)

A local fixed pivot quadrature method of moments (LFPQMOM) is proposed for the solution of the population balance equation (PBE) for the aggregation and breakage process. First, the sectional representation for aggregation and breakage is presented. The continuous summation of the Dirac Delta function is adopted as the discrete form of the continuous particle size distribution in the local section as performed in short time Fourier transformation (STFT) and the moments in local sections are tracked successfully. Numerical simulation of benchmark test cases including aggregation, breakage, and aggregation breakage combined processes demonstrate that the new method could make good predictions for the moments along with particle size distribution without further assumption. The accuracy in the numerical results of the moments is comparable to or higher than the quadrature method of moment (QMOM) in most of the test cases. In theory, any number of moments can be tracked with the new method, but the computational expense can be relatively large due to many scalar equations that may be included.

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Solution of the population balance equation by the direct dual quadrature method of generalized moments

Chemical Engineering Science ◽

10.1016/j.ces.2013.07.025 ◽

2013 ◽

Vol 101 ◽

pp. 663-673 ◽

Cited By ~ 10

Author(s):

F.P. Santos ◽

J.L. Favero ◽

P.L.C. Lage

Keyword(s):

Balance Equation ◽

Population Balance ◽

Population Balance Equation ◽

Quadrature Method ◽

Generalized Moments

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Extended log-normal method of moments for solving the population balance equation for Brownian coagulation

Aerosol Science and Technology ◽

10.1080/02786826.2018.1562152 ◽

2019 ◽

Vol 53 (3) ◽

pp. 332-343 ◽

Cited By ~ 7

Author(s):

Kaiyuan Wang ◽

Suyuan Yu ◽

Wei Peng

Keyword(s):

Method Of Moments ◽

Balance Equation ◽

Population Balance ◽

Population Balance Equation ◽

Brownian Coagulation ◽

Normal Method ◽

Log Normal

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CFD-PBM Coupled Simulation of Liquid-Liquid Dispersions in Spray Fluidized Bed Extractor: Comparison of Three Numerical Methods

International Journal of Chemical Engineering ◽

10.1155/2019/4836213 ◽

2019 ◽

Vol 2019 ◽

pp. 1-13 ◽

Cited By ~ 1

Author(s):

Dan Zheng ◽

Wei Zou ◽

Chuanfeng Peng ◽

Yuhang Fu ◽

Jie Yan ◽

...

Keyword(s):

Fluidized Bed ◽

Method Of Moments ◽

Chemical Engineering ◽

High Reliability ◽

Scale Up ◽

Population Balance ◽

Numerical Code ◽

Balance Model ◽

Quadrature Method ◽

Quadrature Method Of Moments

A coupled numerical code of the Euler-Euler model and the population balance model (PBM) of the liquid-liquid dispersions in a spray fluidized bed extractor (SFBE) has been performed to investigate the hydrodynamic behavior. A classes method (CM) and two representatively numerical moment-based methods, namely, a quadrature method of moments (QMOM) and a direct quadrature method of moments (DQMOM), are used to solve the PBE for evaluating the effect of the numerical method. The purpose of this article is to compare the results achieved by three methods for solving population balance during liquid-liquid two-phase mixing in a SFBE. The predicted results reveal that the CM has the advantage of computing the droplet size distribution (DSD) directly, but it is computationally expensive if a large number of intervals are needed. The MOMs (QMOM and DQMOM) are preferable to coupling the PBE solution with CFD codes for liquid-liquid dispersions simulations due to their easy application, reasonable accuracy, and high reliability. Comparative results demonstrated the suitability of the DQMOM for modeling the spray fluidized bed extractor with simultaneous droplet breakage and aggregation. This work increases the understanding of the chemical engineering characteristics of multiphase systems and provides a theoretical basis for the quantitative design, scale-up, and optimization of multiphase devices.

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