A hybrid particle-number and particle model for efficient solution of population balance equations
This work presents a hybrid particle-number and particle model to improve efficiency in solving population balance equations for type spaces spanning spherical and aggregate particles. The particle-number model tracks simpler, spherical particles cheaply by storing only the number of particles with...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2020
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| Online Access: | https://hdl.handle.net/10356/143382 |
| _version_ | 1811681290860101632 |
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| author | Boje, Astrid Akroyd, Jethro Kraft, Markus |
| author2 | School of Chemical and Biomedical Engineering |
| author_facet | School of Chemical and Biomedical Engineering Boje, Astrid Akroyd, Jethro Kraft, Markus |
| author_sort | Boje, Astrid |
| collection | NTU |
| description | This work presents a hybrid particle-number and particle model to improve efficiency in solving population balance equations for type spaces spanning spherical and aggregate particles. The particle-number model tracks simpler, spherical particles cheaply by storing only the number of particles with a given one-dimensional internal coordinate, while the particle model allows resolution of the detailed aggregate structure that occurs due to collision and coagulation between particles by storing distinct computational entries for each particle. This approach is exact if primary particles are defined by their monomer count and the particle-number model increments in single monomers. A stochastic method is used to solve the population balance equations for the combined type space. The hybrid method works well for large ensembles ( particles) with a detailed particle model, where performing a finite number of particle-number updates is demonstrated to be 40–50% cheaper than updating an equivalent ensemble of discrete particles. These savings can be traded for a larger sample volume to increase the resolution in the particle size distribution or more repeat runs to reduce the total error. Run time improvements are curtailed at very high surface growth and coagulation rates due to the fixed cost of growth updates on the large aggregates formed; however, the hybrid method is still attractive in this case as its primary purpose is to reduce error by preventing saturation of the ensemble with simple particles at high inception rates. |
| first_indexed | 2024-10-01T03:38:36Z |
| format | Journal Article |
| id | ntu-10356/143382 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T03:38:36Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | ntu-10356/1433822023-12-29T06:46:47Z A hybrid particle-number and particle model for efficient solution of population balance equations Boje, Astrid Akroyd, Jethro Kraft, Markus School of Chemical and Biomedical Engineering Cambridge Centre for Advanced Research and Education in Singapore, CREATE Engineering::Chemical engineering Hybrid Method Particle Model This work presents a hybrid particle-number and particle model to improve efficiency in solving population balance equations for type spaces spanning spherical and aggregate particles. The particle-number model tracks simpler, spherical particles cheaply by storing only the number of particles with a given one-dimensional internal coordinate, while the particle model allows resolution of the detailed aggregate structure that occurs due to collision and coagulation between particles by storing distinct computational entries for each particle. This approach is exact if primary particles are defined by their monomer count and the particle-number model increments in single monomers. A stochastic method is used to solve the population balance equations for the combined type space. The hybrid method works well for large ensembles ( particles) with a detailed particle model, where performing a finite number of particle-number updates is demonstrated to be 40–50% cheaper than updating an equivalent ensemble of discrete particles. These savings can be traded for a larger sample volume to increase the resolution in the particle size distribution or more repeat runs to reduce the total error. Run time improvements are curtailed at very high surface growth and coagulation rates due to the fixed cost of growth updates on the large aggregates formed; however, the hybrid method is still attractive in this case as its primary purpose is to reduce error by preventing saturation of the ensemble with simple particles at high inception rates. National Research Foundation (NRF) Accepted version This project is partly funded by the National Research Foundation (NRF), Prime Minister’s Office, Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) programme. The authors would also like to thank Venator for financial support. 2020-08-28T07:14:04Z 2020-08-28T07:14:04Z 2019 Journal Article Boje, A., Akroyd, J., & Kraft, M. (2019). A hybrid particle-number and particle model for efficient solution of population balance equations. Journal of Computational Physics, 389, 189-218. doi:10.1016/j.jcp.2019.03.033 0021-9991 https://hdl.handle.net/10356/143382 10.1016/j.jcp.2019.03.033 2-s2.0-85064956296 389 189 218 en Journal of Computational Physics © 2019 Elsevier Inc. All rights reserved. This paper was published in Journal of Computational Physics and is made available with permission of Elsevier Inc. application/pdf |
| spellingShingle | Engineering::Chemical engineering Hybrid Method Particle Model Boje, Astrid Akroyd, Jethro Kraft, Markus A hybrid particle-number and particle model for efficient solution of population balance equations |
| title | A hybrid particle-number and particle model for efficient solution of population balance equations |
| title_full | A hybrid particle-number and particle model for efficient solution of population balance equations |
| title_fullStr | A hybrid particle-number and particle model for efficient solution of population balance equations |
| title_full_unstemmed | A hybrid particle-number and particle model for efficient solution of population balance equations |
| title_short | A hybrid particle-number and particle model for efficient solution of population balance equations |
| title_sort | hybrid particle number and particle model for efficient solution of population balance equations |
| topic | Engineering::Chemical engineering Hybrid Method Particle Model |
| url | https://hdl.handle.net/10356/143382 |
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