二项式分布在种群平衡模型模拟粒度分布中的应用

doi:10.11949/j.issn.0438-1157.20170675

化工学报 ›› 2017, Vol. 68 ›› Issue (9): 3397-3403.DOI: 10.11949/j.issn.0438-1157.20170675

二项式分布在种群平衡模型模拟粒度分布中的应用

李振亮^1,2, 卢培利^3,4, 张代钧^3,4, 周志恩², 张晟², 何强^1,5

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

收稿日期:2017-05-25 修回日期:2017-06-29 出版日期:2017-09-05 发布日期:2017-09-05
通讯作者: 卢培利
基金资助:
国家自然科学基金项目（5160091049）；重庆市科委专项基金项目（2015CSTC-JBKY-01605）；重庆市基础科学与前沿技术研究专项项目（CSTC2016jcyjA0506）。

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

LI Zhenliang^1,2, LU Peili^3,4, ZHANG Daijun^3,4, ZHOU Zhi'en², ZHANG Sheng², HE Qiang^1,5

1 College of Urban Construction and Environmental Engineering, Chongqing University, Chongqing 400044, China;
2 Chongqing Research Academy of Environmental Sciences, Chongqing 401147, China;
3 State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, China;
4 Department of Environmental Science, Chongqing University, Chongqing 400044, China;
5 Key Laboratory of the Three Gorges Reservoir Region's Eco-environment, Ministry of Education, Chongqing University, Chongqing 400045, China

Received:2017-05-25 Revised:2017-06-29 Online:2017-09-05 Published:2017-09-05
Contact: 10.11949/j.issn.0438-1157.20170675
Supported by:
supported by the National Natural Science Foundation of China (5160091049),the Natural Science Foundation of Chongqing (2015CSTC-JBKY-01605) and the Chongqing Research Program of Basic Research and Frontier Technology (CSTC2016jcyjA0506).

摘要/Abstract

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C_p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C_p的取值，可以得到更多可能的子粒子分布；参数C_p还可以表征粒子的破碎方式——较小的C_p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C_p值表征粒子具有较弱的稳定性，易破碎生成较小的子粒子。

关键词: 种群平衡, 二项式分布, 粒度分布, 数值模拟, 破碎, 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 C_p 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 C_p. Moreover, the value of parameter C_p might also characterize breakage behavior of particle:a smaller C_p value might imply that the particle display strong stability leading to large numbers of large daughter particle, whereas a larger C_p value might imply that the particle display weak stability and the large-scale fragmentation resulting in large numbers of small daughter particle.

Key words: population balance, binomial distribution, particle size distribution, numerical simulation, breakage, daughter particle

中图分类号:

TQ028.5

李振亮, 卢培利, 张代钧, 周志恩, 张晟, 何强. 二项式分布在种群平衡模型模拟粒度分布中的应用[J]. 化工学报, 2017, 68(9): 3397-3403.

LI Zhenliang, LU Peili, ZHANG Daijun, ZHOU Zhi'en, ZHANG Sheng, HE Qiang. Application of binomial distribution for daughter particles in simulation of particle size distribution by population balance model[J]. CIESC Journal, 2017, 68(9): 3397-3403.

参考文献 32

[1]	郑建祥, 许帅, 王京阳,等. 基于微分代数积分矩量法的聚并器超细粒子聚团研究[J]. 化工学报, 2017, 68(1):119-128. ZHENG J X, XU S,WANG J Y, et al. Simulation of ultrafine particle aggregation in aggregation device by differential-algebraic quadrature method of moments[J]. CIESC Journal, 2017, 68(1):119-128.
[2]	王铁峰. 气液-浆-反应器流体力学行为的实验研究和数值模拟[D]. 北京:清华大学, 2004. WANG T F. Experimental study and numerical simulation on the hydrodynamics in gas-liquid (slurry) reactors[D]. Beijing:Tsinghua University, 2004.
[3]	BRIESEN H. Simulation of crystal size and shape by means of a reduced two-dimensional population balance model[J]. Chemical Engineering Science, 2006, 61(1):104-112.
[4]	LEE K F, DOSTA M, MCGUIRE A D, et al. Development of a multi-compartment population balance model for high-shear wet granulation with discrete element method[J]. Computers & Chemical Engineering, 2017, 99:171-184.
[5]	WANG B, MOSBACH S, SCHMUTZHARD S, et al. Modelling soot formation from wall films in a gasoline direct injection engine using a detailed population balance model[J]. Applied Energy, 2016, 163:154-166.
[6]	DUCOSTE J. A two-scale PBM for modeling turbulent flocculation in water treatment processes[J]. Chemical Engineering Science, 2002, 57(12):2157-2168.
[7]	NOPENS I, KOEGST T, MAHIEU K, et al. PBM and activated sludge flocculation:from experimental data to calibrated model[J]. AIChE Journal, 2005, 51(5):1548-1557.
[8]	DING A, HOUNSLOW M J, BIGGS C A. Population balance modelling of activated sludge flocculation:investigating the size dependence of aggregation, breakage and collision efficiency[J]. Chemical Engineering Science, 2006, 61(1):63-74.
[9]	YEOW Y L, LIOW J, LEONG Y. A general procedure for obtaining the evolving particle-size distribution of flocculating suspensions[J]. AIChE Journal, 2012, 58(10):3043-3053.
[10]	JELDRES R I, CONCHA F, TOLEDO P G. Population balance modelling of particle flocculation with attention to aggregate restructuring and permeability[J]. Advances in Colloid & Interface Science, 2015, 224:62.
[11]	LI Z L, LU P L, ZHANG D J, et al. Population balance modeling of activated sludge flocculation:investigating the influence of extracellular polymeric substances (EPS) content and zeta potential on flocculation dynamics[J]. Separation & Purification Technology, 2016, 162:91-100.
[12]	JARVIS P, JEFFERSON B, GREGORY J, et al. A review of floc strength and breakage[J]. Water Research, 2005, 39(14):3121-3137.
[13]	YUAN Y, FARNOOD R R. Strength and breakage of activated sludge flocs[J]. Powder Technology, 2010, 199(2):111-119.
[14]	SCHUETZ S, PIESCHE M. A model of the coagulation process with solid particles and flocs in a turbulent flow[J]. Chemical Engineering Science, 2002, 57(20):4357-4368.
[15]	SPICER P T, PRATSINIS S E. Coagulation and fragmentation:universal steady-state particle-size distribution[J]. AIChE Journal, 1996, 42(6):1612-1620.
[16]	ZHANG J J, LI X Y. Modeling particle-size distribution dynamics in a flocculation system[J]. AIChE Journal, 2003, 49(7):1870-1882.
[17]	SERRA T, CASAMITJANA X. Modelling the aggregation and break-up of fractal aggregates in a shear flow[J]. Flow, Turbulence and Combustion, 1997, 59(2):255-268.
[18]	MAGGI F, MIETTA F, WINTERWERP J C. Effect of variable fractal dimension on the floc size distribution of suspended cohesive sediment[J]. Journal of Hydrology, 2007, 343(1):43-55.
[19]	苏军伟, 顾兆林, XU X Y. 离散相系统种群平衡模型的求解算法[J]. 中国科学:化学, 2010, 40(2):144-160. SU J W, GU Z L, XU X Y. Advances of solution methods of population balance equation for disperse phase system[J]. Scientia Sinica Chimica, 2010, 40(2):144-160.
[20]	LI Z L, ZHOU Z E, ZHANG S, et al. Comparison of the accuracy and performance of different numbers of classes in discretised solution method for population balance model[J]. International Journal of Chemical Engineering, 2016, 2:1-6.
[21]	RAMKRISHNA D. Population Balances:Theory and Applications to Particulate Systems in Engineering[M]. London:Academic Press, 2000.
[22]	KUMAR S, RAMKRISHNA D. On the solution of population balance equations by discretization(Ⅱ):A fixed pivot technique[J]. Chemical Engineering Science, 1996, 51(8):1311-1332.
[23]	THOMAS D N, JUDD S J, FAWCETT N. Flocculation modelling:a review[J]. Water Research, 1999, 33(7):1579-1592.
[24]	LI X Y, LOGAN B. Collision frequencies between fractal aggregates and small particles in a turbulently sheared fluid[J]. Environmental Science & Technology, 1997, 31(4):1237-1242.
[25]	BIGGS C A, LANT P A. Modelling activated sludge flocculation using population balances[J]. Powder Technology, 2002, 124(3):201-211.
[26]	MIETTA F, CHASSAGNE C, VERNEY R, et al. On the behavior of mud floc size distribution:model calibration and model behavior[J]. Ocean Dynamics, 2011, 61(2):257-271.
[27]	FLESCH J C, SPICER P T, PRATSINIS S E. Laminar and turbulent shear-induced flocculation of fractal aggregates[J]. AIChE Journal, 1999, 45(5):1114-1124.
[28]	LI Z L, ZHANG D J, LU P L, et al. Population balance model and calibration method for simulating the time evolution of floc size distribution of activated sludge flocculation[J]. Desalination and Water Treatment, 2017, 67:41-50.
[29]	MAGGI F. Flocculation dynamics of cohesive sediment[D]. Delft:Delft University of Technology, 2005.
[30]	李振亮, 张代钧, 卢培利,等. 活性污泥粒度分布与分形维数的影响因素[J]. 环境科学, 2013, 34(10):3975-3980. LI Z L, ZHANG D J, LU P L, et al. Influencing factors of floc size distribution and fractal dimension of activated sludge[J]. Environmental Science, 2013, 34(10):3975-3980.
[31]	WILEN B M, JIN B, LANT P. The influence of key chemical constituents in activated sludge on surface and flocculating properties[J]. Water Research, 2003, 37(9):2127-39.
[32]	SHENG G P, YU H Q, LI X Y. Extracellular polymeric substances (EPS) of microbial aggregates in biological wastewater treatment systems:a review[J]. Biotechnology Advances, 2010, 28(6):882-894.

二项式分布在种群平衡模型模拟粒度分布中的应用

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

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献 32

相关文章 15

编辑推荐

Metrics

本文评价

[1]	宋嘉豪, 王文. 斯特林发动机与高温热管耦合运行特性研究[J]. 化工学报, 2023, 74(S1): 287-294.
[2]	张思雨, 殷勇高, 贾鹏琦, 叶威. 双U型地埋管群跨季节蓄热特性研究[J]. 化工学报, 2023, 74(S1): 295-301.
[3]	叶展羽, 山訸, 徐震原. 用于太阳能蒸发的折纸式蒸发器性能仿真[J]. 化工学报, 2023, 74(S1): 132-140.
[4]	张义飞, 刘舫辰, 张双星, 杜文静. 超临界二氧化碳用印刷电路板式换热器性能分析[J]. 化工学报, 2023, 74(S1): 183-190.
[5]	王志国, 薛孟, 董芋双, 张田震, 秦晓凯, 韩强. 基于裂隙粗糙性表征方法的地热岩体热流耦合数值模拟与分析[J]. 化工学报, 2023, 74(S1): 223-234.
[6]	何松, 刘乔迈, 谢广烁, 王斯民, 肖娟. 高浓度水煤浆管道气膜减阻两相流模拟及代理辅助优化[J]. 化工学报, 2023, 74(9): 3766-3774.
[7]	袁佳琦, 刘政, 黄锐, 张乐福, 贺登辉. 泡状入流条件下旋流泵能量转换特性研究[J]. 化工学报, 2023, 74(9): 3807-3820.
[8]	韩晨, 司徒友珉, 朱斌, 许建良, 郭晓镭, 刘海峰. 协同处理废液的多喷嘴粉煤气化炉内反应流动研究[J]. 化工学报, 2023, 74(8): 3266-3278.
[9]	邢雷, 苗春雨, 蒋明虎, 赵立新, 李新亚. 井下微型气液旋流分离器优化设计与性能分析[J]. 化工学报, 2023, 74(8): 3394-3406.
[10]	程小松, 殷勇高, 车春文. 不同工质在溶液除湿真空再生系统中的性能对比[J]. 化工学报, 2023, 74(8): 3494-3501.
[11]	刘文竹, 云和明, 王宝雪, 胡明哲, 仲崇龙. 基于场协同和耗散的微通道拓扑优化研究[J]. 化工学报, 2023, 74(8): 3329-3341.
[12]	洪瑞, 袁宝强, 杜文静. 垂直上升管内超临界二氧化碳传热恶化机理分析[J]. 化工学报, 2023, 74(8): 3309-3319.
[13]	黄可欣, 李彤, 李桉琦, 林梅. 加装旋转叶轮T型通道流场的模态分解[J]. 化工学报, 2023, 74(7): 2848-2857.
[14]	史方哲, 甘云华. 超薄热管启动特性和传热性能数值模拟[J]. 化工学报, 2023, 74(7): 2814-2823.
[15]	朱兴驰, 郭志远, 纪志永, 汪婧, 张盼盼, 刘杰, 赵颖颖, 袁俊生. 选择性电渗析镁锂分离过程模拟优化[J]. 化工学报, 2023, 74(6): 2477-2485.