Combined Quadrature Method of Moments and Method of Characteristics Approach for Efficient Solution of Population Balance Models for Dynamic Modeling and Crystal Size Distribution Control of Crystallization Processes

2009 ◽  
Vol 48 (18) ◽  
pp. 8575-8584 ◽  
Author(s):  
E. Aamir ◽  
Z. K. Nagy ◽  
C. D. Rielly ◽  
T. Kleinert ◽  
B. Judat
Keyword(s):  
Size Distribution ◽  
Dynamic Modeling ◽  
Method Of Moments ◽  
Efficient Solution ◽  
Method Of Characteristics ◽  
Crystal Size ◽  
Population Balance ◽  
Crystal Size Distribution ◽  
Quadrature Method ◽  
Quadrature Method Of Moments

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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