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International Journal of Chemical Engineering
Volume 2016, Article ID 8743105, 6 pages
Research Article

Comparison of the Accuracy and Performance of Different Numbers of Classes in Discretised Solution Method for Population Balance Model

1College of Urban Construction and Environmental Engineering, Chongqing University, Chongqing 400044, China
2Chongqing Research Academy of Environmental Sciences, Chongqing 401147, China
3State Environmental Protection Key Laboratory of Environmental Planning and Policy Simulation, Beijing 100011, China

Received 7 June 2016; Revised 5 September 2016; Accepted 15 September 2016

Academic Editor: Doraiswami Ramkrishna

Copyright © 2016 Zhenliang Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


One way of solving population balance model (PBM) in a time efficient way is by means of discretisation of the population property of interest. A computational grid, for example, ( is the volume of particle in class ), could be used to classify the particles in discretisation techniques. However, there are still disagreements in the appropriate number of classes divided by the grids. In this study, the different numbers of classes for solving PBM were compared in terms of accuracy and performance to describe the particle size distribution (PSD) from the flocculation of activated sludge. It is found that the simulated PSDs are similar to the experimental data for all the geometric grids , and there is no obvious difference among the values of calibrated parameter, ratio of breakage rate coefficient and collision efficiency, for each velocity gradient. However, the simulation results with less error could be obtained with larger number of classes, and more computational times, which show exponential relationship with the number of classes, are needed. Considering numerical accuracy and efficiency, the classes 35 or a geometric grid with factor 1.6, aligning with the Fibonacci sequence , is recommended for the particles in the size range of 5.5~1086 μm.