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

2013 ◽  
Vol 101 ◽  
pp. 663-673 ◽  
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

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 Analytical time-stepping solution of the discretized population balance equation

2020 ◽  
Vol 135 ◽  
pp. 106741
Author(s):  
Mohamed Ali Jama ◽  
Wenli Zhao ◽  
Waqar Ahmad ◽  
Antonio Buffo ◽  
Ville Alopaeus
Keyword(s):  
Balance Equation ◽  
Population Balance ◽  
Population Balance Equation ◽  
Time Stepping ◽  
Analytical Time

An analytical solution for the population balance equation using a moment method

Particuology ◽  
2015 ◽  
Vol 18 ◽  
pp. 194-200 ◽  
Author(s):  
Mingzhou Yu ◽  
Jianzhong Lin ◽  
Junji Cao ◽  
Martin Seipenbusch
Keyword(s):  
Analytical Solution ◽  
Balance Equation ◽  
Moment Method ◽  
Population Balance ◽  
Population Balance Equation

Bubble-size Experiments and Predictions for Polyurethane Foam using a Population Balance Equation.

2020 ◽  
Author(s):  
Rekha Rao ◽  
Lisa Mondy ◽  
Weston Ortiz ◽  
Christine Roberts ◽  
Melissa Soehnel
Keyword(s):  
Polyurethane Foam ◽  
Bubble Size ◽  
Balance Equation ◽  
Population Balance ◽  
Population Balance Equation
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