Comparison of the Accuracy and Performance of Different Numbers of Classes in Discretised Solution Method for Population Balance Model
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, vi+1=kvi (vi is the volume of particle in class i), could be used to classify the particles in discretisation techniques....
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | International Journal of Chemical Engineering |
| Online Access: | http://dx.doi.org/10.1155/2016/8743105 |
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| author | Zhenliang Li Zhien Zhou Sheng Zhang Hongqiang Jiang |
| author_facet | Zhenliang Li Zhien Zhou Sheng Zhang Hongqiang Jiang |
| author_sort | Zhenliang Li |
| collection | DOAJ |
| description | 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, vi+1=kvi (vi is the volume of particle in class i), 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 (vi+1:vi≤2), 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 (vi+vi-1≈vi+1), is recommended for the particles in the size range of 5.5~1086 μm. |
| format | Article |
| id | doaj-art-5f3763d723a7459eae73cbcb14d1b8dd |
| institution | Kabale University |
| issn | 1687-806X 1687-8078 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Chemical Engineering |
| spelling | doaj-art-5f3763d723a7459eae73cbcb14d1b8dd2025-08-20T03:34:22ZengWileyInternational Journal of Chemical Engineering1687-806X1687-80782016-01-01201610.1155/2016/87431058743105Comparison of the Accuracy and Performance of Different Numbers of Classes in Discretised Solution Method for Population Balance ModelZhenliang Li0Zhien Zhou1Sheng Zhang2Hongqiang Jiang3College of Urban Construction and Environmental Engineering, Chongqing University, Chongqing 400044, ChinaChongqing Research Academy of Environmental Sciences, Chongqing 401147, ChinaChongqing Research Academy of Environmental Sciences, Chongqing 401147, ChinaState Environmental Protection Key Laboratory of Environmental Planning and Policy Simulation, Beijing 100011, ChinaOne 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, vi+1=kvi (vi is the volume of particle in class i), 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 (vi+1:vi≤2), 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 (vi+vi-1≈vi+1), is recommended for the particles in the size range of 5.5~1086 μm.http://dx.doi.org/10.1155/2016/8743105 |
| spellingShingle | Zhenliang Li Zhien Zhou Sheng Zhang Hongqiang Jiang Comparison of the Accuracy and Performance of Different Numbers of Classes in Discretised Solution Method for Population Balance Model International Journal of Chemical Engineering |
| title | Comparison of the Accuracy and Performance of Different Numbers of Classes in Discretised Solution Method for Population Balance Model |
| title_full | Comparison of the Accuracy and Performance of Different Numbers of Classes in Discretised Solution Method for Population Balance Model |
| title_fullStr | Comparison of the Accuracy and Performance of Different Numbers of Classes in Discretised Solution Method for Population Balance Model |
| title_full_unstemmed | Comparison of the Accuracy and Performance of Different Numbers of Classes in Discretised Solution Method for Population Balance Model |
| title_short | Comparison of the Accuracy and Performance of Different Numbers of Classes in Discretised Solution Method for Population Balance Model |
| title_sort | comparison of the accuracy and performance of different numbers of classes in discretised solution method for population balance model |
| url | http://dx.doi.org/10.1155/2016/8743105 |
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