Application of binomial distribution for daughter particles in simulation of particle size distribution by population balance model

LI Zhenliang; LU Peili; ZHANG Daijun; ZHOU Zhi'en; ZHANG Sheng; HE Qiang

doi:10.11949/j.issn.0438-1157.20170675

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Application of binomial distribution for daughter particles in simulation of particle size distribution by population balance model

更新时间：2025-12-10

- Application of binomial distribution for daughter particles in simulation of particle size distribution by population balance model
- CIESC Journal Issue 9, Pages: 3397-3403(2017)
- 作者机构：
  
  1. 重庆大学城市建筑与环境工程学院,重庆,400044
  2. 重庆市环境科学研究院,重庆,401147
  3. 重庆大学煤矿灾害动力学与控制国家重点实验室,重庆,400044
  4. 重庆大学环境科学系,重庆,400044
  5. 重庆大学三峡库区生态环境教育部重点实验室,重庆,400044
- 作者简介：
- 基金信息：
- DOI：10.11949/j.issn.0438-1157.20170675
  CLC： Q028.5
- Online First：05 September 2017，
  
  Published：05 September 2017
- 稿件说明：
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LI Zhenliang, LU Peili, ZHANG Daijun, et al. Application of binomial distribution for daughter particles in simulation of particle size distribution by population balance model[J]. CIESC Journal, 2017, (9): 3397-3403.
DOI：

LI Zhenliang, LU Peili, ZHANG Daijun, et al. Application of binomial distribution for daughter particles in simulation of particle size distribution by population balance model[J]. CIESC Journal, 2017, (9): 3397-3403. DOI： 10.11949/j.issn.0438-1157.20170675.

摘要

提出了一种适用于几何网格的子粒子二项式分布函数，并应用于种群平衡模型模拟活性污泥絮凝后的粒度分布。结果表明：与二元分布相比，该二项式分布可以得到更准确的粒度分布和平均粒度模拟值；通过校核二项式分布参数Cp的取值，可以提高粒度分布和平均粒度的模拟精度。相比于二元分布或正态分布只能描述一种类型的子粒子分布，该二项式分布具有较强的适应性，调整参数Cp的取值，可以得到更多可能的子粒子分布；参数Cp还可以表征粒子的破碎方式——较小的Cp值表征粒子具有较强的稳定性，易破碎生成较大的子粒子；较大的Cp值表征粒子具有较弱的稳定性，易破碎生成较小的子粒子。

Abstract

A binomial distribution function suitable for geometric grid was proposed and applied in population balance model (PBM) to simulate the particle size distribution (PSD) of activated sludge after flocculation. The results showed that the PSD and mean size simulated by using binomial distribution give better agreement with the experimental data than those simulated by using binary distribution. The accuracy of simulation of PSD and mean size can be improved by calibrating the value of parameter Cp of binomial distribution function. Different from other daughter particle distribution which can only describe one-type daughter particle distribution

the binomial distribution function shows a strong adaptability and can present more probable daughter particle distributions through adjusting the parameter Cp. Moreover

the value of parameter Cp might also characterize breakage behavior of particle:a smaller Cp value might imply that the particle display strong stability leading to large numbers of large daughter particle

whereas a larger Cp value might imply that the particle display weak stability and the large-scale fragmentation resulting in large numbers of small daughter particle.

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