Solution of population balance equation using quadrature method of moments with an adjustable factor

2007 ◽  
Vol 62 (21) ◽  
pp. 5897-5911 ◽  
Author(s):  
Junwei Su ◽  
Zhaolin Gu ◽  
Yun Li ◽  
Shiyu Feng ◽  
X. Yun Xu
Keyword(s):  
Method Of Moments ◽  
Balance Equation ◽  
Population Balance ◽  
Population Balance Equation ◽  
Quadrature Method ◽  
Quadrature Method Of Moments

scholarly journals Local Fixed Pivot Quadrature Method of Moments for Solution of Population Balance Equation

Processes ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 209 ◽  
Author(s):  
Junwei Su ◽  
Wang Le ◽  
Zhaolin Gu ◽  
Chungang Chen
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Method Of Moments ◽  
Balance Equation ◽  
Population Balance ◽  
New Method ◽  
Population Balance Equation ◽  
Test Cases ◽  
Quadrature Method

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.

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

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
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.

scholarly journals New developments of the Extended Quadrature Method of Moments to solve Population Balance Equations

2018 ◽  
Vol 365 ◽  
pp. 243-268 ◽  
Author(s):  
Maxime Pigou ◽  
Jérôme Morchain ◽  
Pascal Fede ◽  
Marie-Isabelle Penet ◽  
Geoffrey Laronze
Keyword(s):  
Method Of Moments ◽  
Population Balance ◽  
Quadrature Method ◽  
Balance Equations ◽  
New Developments ◽  
Population Balance Equations ◽  
Quadrature Method Of Moments
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