A new highly efficient and stable population array (PA) algorithm to solve multi-dimension population balance equation
•Fast and accurate numerical solver of a crystallization population balance model.•Efficient computation for multi-dimensional crystal growth problems.•Modelling complex mechanisms including breakage and agglomeration of crystals. Solving the population balance equation (PBE) requires a robust and e...
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| Published in | Chemical engineering science Vol. 246; p. 116994 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
31.12.2021
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0009-2509 1873-4405 |
| DOI | 10.1016/j.ces.2021.116994 |
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| Abstract | •Fast and accurate numerical solver of a crystallization population balance model.•Efficient computation for multi-dimensional crystal growth problems.•Modelling complex mechanisms including breakage and agglomeration of crystals.
Solving the population balance equation (PBE) requires a robust and efficient numerical method. The widely used discretization techniques are prone to numerical diffusion caused by over-prediction of the crystal size. The multi-dimensional solution is highly inefficient due to the computations performed on the unused grids. We present an efficient numerical solver using the population array (PA) method, which employs an array to store the size and counts information as a sparse grid. The two-dimensional pure-growth case using the proposed technique could achieve ten times speedup compared to the high-resolution discretization method. A row compression algorithm is proposed to reduce the computational cost by grouping the crystals with similar internal coordinates. Various numerical cases including crystal growth, continuous crystallization, polymorphic transformation, agglomeration, and breakage were simulated and compared with the analytical solutions and the established high-resolution discretization schemes to confirm the accuracy and computational efficiency of the proposed PA algorithm. |
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| AbstractList | •Fast and accurate numerical solver of a crystallization population balance model.•Efficient computation for multi-dimensional crystal growth problems.•Modelling complex mechanisms including breakage and agglomeration of crystals.
Solving the population balance equation (PBE) requires a robust and efficient numerical method. The widely used discretization techniques are prone to numerical diffusion caused by over-prediction of the crystal size. The multi-dimensional solution is highly inefficient due to the computations performed on the unused grids. We present an efficient numerical solver using the population array (PA) method, which employs an array to store the size and counts information as a sparse grid. The two-dimensional pure-growth case using the proposed technique could achieve ten times speedup compared to the high-resolution discretization method. A row compression algorithm is proposed to reduce the computational cost by grouping the crystals with similar internal coordinates. Various numerical cases including crystal growth, continuous crystallization, polymorphic transformation, agglomeration, and breakage were simulated and compared with the analytical solutions and the established high-resolution discretization schemes to confirm the accuracy and computational efficiency of the proposed PA algorithm. |
| ArticleNumber | 116994 |
| Author | Wu, Yuanyi Rohani, Sohrab |
| Author_xml | – sequence: 1 givenname: Yuanyi surname: Wu fullname: Wu, Yuanyi – sequence: 2 givenname: Sohrab orcidid: 0000-0002-1667-1736 surname: Rohani fullname: Rohani, Sohrab email: srohani@uwo.ca |
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| Cites_doi | 10.1021/ie401287w 10.1145/2833157.2833162 10.1016/j.jaerosci.2003.11.012 10.1021/ie020627l 10.1021/acs.cgd.7b00645 10.1016/j.powtec.2020.08.022 10.1016/S0009-2509(97)00307-2 10.1016/j.compchemeng.2016.03.023 10.1016/S0021-9797(78)80008-3 10.1016/0009-2509(96)88489-2 10.1021/acs.cgd.9b01482 10.1016/0009-2509(95)00355-X 10.1016/j.compchemeng.2004.09.011 10.1016/j.jcrysgro.2005.11.001 10.1002/aic.10228 10.1002/aic.690220505 10.1002/aic.14837 10.1080/02786826.2013.823642 10.1016/B978-0-444-63965-3.50030-1 10.1016/j.compchemeng.2020.106781 10.1002/ceat.201400769 10.1002/aic.690360504 10.1016/j.powtec.2015.05.029 10.1021/acs.cgd.0c00986 10.1016/j.advwatres.2013.05.006 10.1002/aic.690420708 10.1016/j.ces.2015.02.014 10.1016/0021-9991(78)90058-X 10.1021/acs.cgd.8b00883 10.1016/j.advwatres.2019.103382 10.1016/j.jaerosci.2012.04.003 10.1016/j.jcrysgro.2018.10.061 |
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| Keywords | Multi-dimensional population balance equation Agglomeration and breakage modeling Numerical solution Crystallization modeling |
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| SubjectTerms | Agglomeration and breakage modeling Crystallization modeling Multi-dimensional population balance equation Numerical solution |
| Title | A new highly efficient and stable population array (PA) algorithm to solve multi-dimension population balance equation |
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