Simulation of rare earth extraction process based on separation coefficient correction

doi:10.11949/.0438-1157.20191481

Abstract

Abstract:

Because the process simulation model based on rare earth extraction mechanism does not consider the extraction efficiency of the extraction tank, it is difficult for the content of the components output by the model to meet the actual industrial conditions. Therefore, this paper combines the mechanism model with a data-driven method to establish the rare earth extraction process simulation which based on the correction of separation coefficient. Firstly, on the basis of the rare earth extraction process mechanism model with relative separation coefficient, the correction value of separation coefficient is introduced to expand the mechanism model of rare earth extraction. Secondly, the data-driven method and Fibonacci tree optimization algorithm(FTO) are used to optimize the correction value at all levels, and MATLAB GUI is used to develop the rare earth extraction process simulation system. Finally, according to the actual data of industrial field, the process of rare earth extraction is simulated and verified when the working condition is changed. The results show that the simulation of the process constructed in this paper conforms to the actual working conditions of the rare earth extraction process.

Key words: rare earth extraction, component content, separation coefficient correction, FTO, process simulation

摘要：

由于基于稀土萃取机理的流程仿真模型没有考虑萃取槽的萃取效率，导致模型输出的各级组分含量难以符合工业实际工况，为此，本文将机理模型与数据驱动的方法相结合，建立基于分离系数校正的稀土萃取流程模拟。首先，在相对分离系数的稀土萃取流程机理模型的基础上，引入分离系数校正值，实现对稀土萃取机理模型的扩充；其次，运用数据驱动方法，利用斐波那契树优化算法对各级校正值进行优化求解，并使用MATLAB GUI，开发稀土萃取流程模拟系统；最后，结合工业现场实际数据，验证本文流程模拟在工况改变时的动态性能，结果表明本文所建流程模拟符合稀土萃取流程实际工况。

关键词: 稀土萃取, 组分含量, 分离系数校正, 斐波那契树优化算法, 流程模拟

CLC Number:

TP 391.9

Hui YANG, Wenhao DAI, Rongxiu LU, Jianyong ZHU. Simulation of rare earth extraction process based on separation coefficient correction[J]. CIESC Journal, 2020, 71(7): 3180-3190.

杨辉, 代文豪, 陆荣秀, 朱建勇. 基于分离系数校正的稀土萃取流程模拟[J]. 化工学报, 2020, 71(7): 3180-3190.

Figures/Tables 13

Fig.1 Process flow of rare earth countercurrent extraction

Table 1 Actual separation coefficient in different stages of rare earth extraction and separation

级数	相邻分离系数	相对分离系数
萃取段	$β i = 1, β 2, ?, β L, β L + 1, 1 L + 2, ?, 1 N - 1, 1 N$	$β C / 1 = ∏ i = 1 C β i$
进料级	$β i = 1, β 2, ?, β L, β L + 1, β L + 2, ?, β N - 1, β N$	$β C / 1 = ∏ i = 1 C β i$
洗涤段	$β i = 1, 12, ?, 1 L - 1, β L, β L + 1, ?, β N - 1, β N$	$β C / N = ∏ i = 1 C β i$

Table 1 Actual separation coefficient in different stages of rare earth extraction and separation

级数	相邻分离系数	相对分离系数
萃取段	$β i = 1, β 2, ?, β L, β L + 1, 1 L + 2, ?, 1 N - 1, 1 N$	$β C / 1 = ∏ i = 1 C β i$
进料级	$β i = 1, β 2, ?, β L, β L + 1, β L + 2, ?, β N - 1, β N$	$β C / 1 = ∏ i = 1 C β i$
洗涤段	$β i = 1, 12, ?, 1 L - 1, β L, β L + 1, ?, β N - 1, β N$	$β C / N = ∏ i = 1 C β i$

Table 2 Component distribution of organic phase feed system

级序	$G ˉ$	G
1	$S ˉ$	$f B'$
…i…	… $S ˉ$ …	…W…
n-1	$S ˉ$	W
n	$S ˉ$ +1	W
n+1	$S ˉ$ +1	W
…j…	… $S ˉ$ +1…	…W…
n+m-1	$S ˉ$ +1	W
n+m	$f A'$	W

Table 2 Component distribution of organic phase feed system

级序	$G ˉ$	G
1	$S ˉ$	$f B'$
…i…	… $S ˉ$ …	…W…
n-1	$S ˉ$	W
n	$S ˉ$ +1	W
n+1	$S ˉ$ +1	W
…j…	… $S ˉ$ +1…	…W…
n+m-1	$S ˉ$ +1	W
n+m	$f A'$	W

Fig.2 Flow chart of FTO solving K

Table 3 Main process indexes of CePr/Nd extraction process

参数	数值
料液中Ce组分含量(质量分数)	0.4445
料液中Pr组分含量(质量分数)	0.1842
料液中Nd组分含量(质量分数)	0.3713
Ce/Pr的分离系数	2.03
Pr/Nd的分离系数	1.55
萃取段级数n	26
洗涤段级数m	34
萃取量 $S ˉ$	0.99
出口指标P_A,P_B	0.9995,0.9995

Table 3 Main process indexes of CePr/Nd extraction process

参数	数值
料液中Ce组分含量(质量分数)	0.4445
料液中Pr组分含量(质量分数)	0.1842
料液中Nd组分含量(质量分数)	0.3713
Ce/Pr的分离系数	2.03
Pr/Nd的分离系数	1.55
萃取段级数n	26
洗涤段级数m	34
萃取量 $S ˉ$	0.99
出口指标P_A,P_B	0.9995,0.9995

Table 4 Performance indexs of FTO with different parameters

P-Q	MIN	MAX	MEAN	STD
4-5	6.05×10^-11	2.21×10^-8	7.34×10^-9	7.64×10^-9
4-6	2.51×10^-12	8.94×10^-9	1.76×10^-9	2.94×10^-9
4-7	6.13×10^-13	6.87×10^-9	2.35×10^-9	2.12×10^-9
4-8	1.33×10^-16	2.38×10^-9	3.50×10^-10	7.38×10^-10
4-9	9.83×10^-15	4.65×10^-9	7.76×10^-10	1.44×10^-9
4-10	1.11×10^-13	1.15×10^-9	1.90×10^-10	3.54×10^-10
5-6	7.10×10^-18	1.36×10^-8	2.49×10^-9	4.39×10^-9
5-7	6.13×10^-13	2.89×10^-9	1.19×10^-9	1.02×10^-9
5-8	3.51×10^-19	2.88×10^-10	3.73×10^-11	8.97×10^-11
5-9	4.19×10^-17	1.00×10^-9	1.65×10^-10	3.07×10^-10
5-10	2.58×10^-16	2.32×10^-10	4.52×10^-11	8.53×10^-11
6-7	7.41×10^-19	6.01×10^-10	7.35×10^-11	1.86×10^-10
6-8	3.33×10^-¹⁹	2.34×10^-¹²	3.94×10^-¹³	7.37×10^-¹³
6-9	3.33×10^-¹⁹	2.46×10^-9	2.68×10^-10	7.72×10^-10
6-10	3.33×10^-¹⁹	1.21×10^-10	2.70×10^-11	4.55×10^-11
7-8	7.62×10^-17	1.09×10^-9	1.65×10^-10	3.50×10^-10
7-9	3.33×10^-¹⁹	4.95×10^-10	9.44×10^-11	1.95×10^-10
7-10	3.33×10^-¹⁹	6.71×10^-10	6.72×10^-11	2.12×10^-10
8-9	3.33×10^-¹⁹	1.00×10^-9	2.00×10^-10	3.58×10^-10
8-10	3.33×10^-¹⁹	1.33×10^-10	2.48×10^-11	5.15×10^-11
9-10	3.90×10^-18	6.12×10^-11	7.47×10^-12	1.90×10^-11

Fig.3 Calculated values of coefficients at all stages

Fig.4 Structure diagram of rare earth extraction process simulation system

Fig.5 Main interface of rare earth extraction process simulation system

Table 5 Component of feed in CePr/Nd extraction process

组分	含量（质量分数）
Ce	0.5124
Pr	0.1468
Nd	0.3408

Fig.6 Comparison between content calculated by process simulation system and actual values

Table 6 Performance standard value calculated by process simulation system

组分	MEANRE/%	MAXRE/%	RMSE
Ce	0.3894	4.4792	6.706×10^-5
Pr	0.3513	3.9512	4.228×10^-5
Nd	0.1791	3.7665	3.9071×10^-5

Fig.7 Absolute value of relative error of each component content after calculation of process simulation system

References 30

1	徐光宪. 稀土[M]. 北京: 冶金工业出版社, 2012.
	Xu G X. Rare Earths[M]. Beijing: Metallurgical Industry Press, 2012.
2	吴声, 廖春生, 贾江涛, 等. 多组分多出口稀土串级萃取静态优化设计研究(I)：静态设计算法[J]. 中国稀土学报, 2004, 22(1): 17-21.
	Wu S, Liao C S, Jia J T, et al. Static optimization design of multi-component and multi-export rare earth cascade extraction (Ⅰ): Static design algorithm[J]. Journal of the Chinese Rare Earth Society, 2004, 22(1): 17-21.
3	吴声, 廖春生, 贾江涛, 等. 多组分多出口稀土串级萃取静态优化设计研究(Ⅱ)：静态程序设计及动态仿真验证[J]. 中国稀土学报, 2004, 22(2): 171-176.
	Wu S, Liao C S, Jia J T, et al. Static optimization design of multi-component and multi-export rare earth cascade extraction (Ⅱ)： Static programming and dynamic simulation verification[J]. Journal of the Chinese Rare Earth Society, 2004, 22(2): 171-176.
4	王振华. 多组分稀土萃取分离工艺的理论设计[J]. 稀土, 1995, 16(6): 10-14.
	Wang Z H. Theoretical design of multi-component rare earth extraction and separation process[J]. Chinese Rare Earths, 1995, 16(6): 10-14.
5	钟学明. 多组分稀土串级萃取有效分离系数的研究[J]. 稀土, 2009, 30(2): 57-60.
	Zhong X M. Study on effective separation factor for multi-component rare earths in counter-current extraction[J]. Chinese Rare Earths, 2009, 30(2): 57-60.
6	丁永权, 衷路生, 杨辉. 任意组分两出口体系串级萃取静态优化设计研究[J]. 中国稀土学报, 2010, 28(1): 53-59.
	Ding Y Q, Zhong L S, Yang H. Study on static optimization design of two outlets cascade extraction for any component[J]. Journal of the Chinese Rare Earth Society, 2010, 28(1): 53-59.
7	丁永权, 喻民, 刘正平, 等. 多组分稀土体系串级萃取分离理论级数计算公式[J]. 稀土, 2003, 24(3): 8-10+30.
	Ding Y Q, Yu M, Liu Z P, et al. Formulate for calculating the number of stages in multi-component rare earth elements cascade extraction[J]. Chinese Rare Earths, 2003, 24(3): 8-10+30.
8	Ryu K H, Lee C, Lee G G, et al. Modeling and simulation of solvent extraction processes for purifying rare earth metals with PC88A[J]. Korean Journal of Chemical Engineering, 2013, 30(10): 1946-1953.
9	Yun C Y, Lee C, Lee G G, et al. Modeling and simulation of multicomponent solvent extraction processes to purify rare earth metals[J]. Hydrometallurgy, 2016, 159: 40-45.
10	Anitha M, Singh H. Artificial neural network simulation of rare earths solvent extraction equilibrium data[J]. Desalination, 2008, 232(1/2/3): 59-70.
11	王振华. 稀土串级萃取分离过程的数学模型和计算机仿真[J]. 中国稀土学报, 2002, 20(s3): 132-135.
	Wang Z H. Mathematical model and computer simulation of separation process of rare earth cascade extraction[J]. Journal of the Chinese Rare Earth Society, 2002, 20(s3): 132-135.
12	Serralunga F J, Mussati M C, Aguirre P A. Model adaptation for real-time optimization in energy systems[J]. Industrial & Engineering Chemistry Research, 2013, 52(47): 16795-16810.
13	Zhang J, Mao Z Z, Jia R D, et al. Real time optimization based on a serial hybrid model for gold cyanidation leaching process[J]. Minerals Engineering, 2015, 134(70): 467-476.
14	董易, 施心陵, 王霞, 等. 斐波那契树优化算法求解多峰函数全局最优解的可达性分析[J]. 自动化学报, 2018, 44(9): 145-155.
	Dong Y, Shi X L, Wang X, et al. On accessibility of Fibonacci tree optimization algorithm for global optima of multi-modal functions[J]. Acta Automatica Sinica, 2018, 44(9): 145-155.
15	王霞, 吕丹桔, 董易, 等. 基于斐波那契树优化算法的切削参数多方案优化方法[J]. 控制与决策, 2018, 33(8): 1373-1381.
	Wang X, Lyu D J, Dong Y, et al. Cutting parameters multi-scheme optimization based on Fibonacci tree optimization algorithm[J]. Control and Decision, 2018, 33(8): 1373-1381.
16	贾文君, 张福景, 柴天佑. 稀土串级萃取分离过程智能优化控制仿真系统[J]. 系统仿真学报, 2007, 19(2): 304-307.
	Jia W J, Zhang F J, Chai T Y. Simulation system for intelligent optimal control of rare earth cascade extraction separation process[J]. Journal of System Simulation, 2007, 19(2): 304-307.
17	Yang H, Xu F P, Lu R X, et al. Component content distribution profile control in rare earth countercurrent extraction process[J]. Chinese Journal of Chemical Engineering， 2015, 23(1): 192-198.
18	丁永权, 刘正平, 陈立红. 多组分稀土体系串级萃取分离理论(Ⅰ)：多组分稀土体系串级萃取分离的静态平衡出口级组成的计算[J]. 中国稀土学报, 2002， (S2): 159-161.
	Ding Y Q, Liu Z P, Chen L H. Theory of multistage rare earth system cascade extraction separation (I)： Calculation of static equilibrium export stage composition of multicomponent rare earth system by cascade extraction separation[J]. Journal of the Chinese Rare Earth Society, 2002， (S2): 159-161.
19	朱建勇, 杨辉, 陆荣秀, 等. 基于静态设定和动态补偿的铈镨钕萃取过程药剂量优化控制[J]. 自动化学报, 2019, 45(6): 1186-1197.
	Zhu J Y, Yang H, Lu R X, et al. Static setting and dynamic compensation based optimal control for the flow rate of the reagent in CePr/Nd extraction process[J]. Acta Automatica Sinica, 2019, 45(6): 1186-1197.
20	杨辉, 朱凡, 陆荣秀, 等. 基于ANFIS模型的Pr/Nd萃取过程预测控制[J]. 化工学报, 2016, 67(3): 982-990.
	Yang H, Zhu F, Lu R X, et al. ANFIS model-based predictive control for Pr/Nd cascade extraction process[J]. CIESC Journal, 2016, 67(3): 982-990.
21	Boussaïd I, Lepagnot J, Siarry P. A survey on optimization metaheuristics[J]. Information Sciences, 2013, 237: 82-117.
22	宁爱平, 张雪英. 人工蜂群算法的收敛性分析[J]. 控制与决策, 2013, 28(10): 1554-1558.
	Ning A P, Zhang X Y. Convergence analysis of artificial bee colony algorithm[J]. Control and Decision, 2013, 28(10): 1554-1558.
23	Wang J, Fan X, Zhang C, et al. A graph-based ant colony optimization approach for integrated process planning and scheduling[J]. Chinese Journal of Chemical Engineering, 2014, 22: 748-753.
24	Xu Y, Wang Z Y, Zhu Q X. An improved hybrid genetic algorithm for chemical plant layout optimization with novel non-overlapping and toxic gas dispersion constraints [J]. Chinese Journal of Chemical Engineering, 2013, 21(4): 412-419.
25	de Castro L N, von Zuben F J. Learning and optimization using the clonal selection principle[J]. IEEE Transactions on Evolutionary Computation, 2002, 6(3): 239-251.
26	Castro L N D, Timmis J. An artificial immune network for multimodal function optimization[C]// Conference on Genetic & Evolutionary Computation, 2005.
27	Li B L, Shi X L, Gou C X, et al. Multivariant optimization algorithm for multimodal optimization[J]. Applied Mechanics and Materials, 2014, 483: 453-457.
28	Gou C X, Shi X L, Li B L, et al. Multivariant optimization algorithm with absorption for multimodal optimization[J]. Applied Mechanics & Materials, 2014, 483: 458-464.
29	Zhang S H, Shi X L, Li P, et al. Golden section Fibonacci tree optimization algorithm for multimodal function optimization[J]. Acta Electronica Sinica, 2017, 45(4): 791-798.
30	Subasi M, Yildirim N, Bünyamin Y. An improvement on Fibonacci search method in optimization theory[J]. Applied Mathematics and Computation, 2004, 147(3): 893-901.

[1]	Ruihang ZHANG, Pan CAO, Feng YANG, Kun LI, Peng XIAO, Chun DENG, Bei LIU, Changyu SUN, Guangjin CHEN. Analysis of key parameters affecting product purity of natural gas ethane recovery process via ZIF-8 nanofluid [J]. CIESC Journal, 2023, 74(8): 3386-3393.
[2]	Xuerong GU, Shuoshi LIU, Siyu YANG. Research on multi-parameter optimization method based on parallel EGO and surrogate-assisted model [J]. CIESC Journal, 2023, 74(3): 1205-1215.
[3]	Senshan CAO, Feng XU, Xionglin LUO. Process simulation of stream circulation system based on stability: [J]. CIESC Journal, 2022, 73(3): 1256-1269.
[4]	Li LIU, Peng JIANG, Wei WANG, Tonghuan ZHANG, Liwen MU, Xiaohua LU, Jiahua ZHU. Coupling process simulation and random forest model for analyzing and predicting biomass-to-hydrogen conversion [J]. CIESC Journal, 2022, 73(11): 5230-5239.
[5]	Qian LIU, Xianglan ZHANG, Zhiping LI, Zhuoqi LI, Hong YU. Multiscale screening of ionic liquids as extractive solvents for oil-hydroxybenzene separation [J]. CIESC Journal, 2022, 73(11): 5011-5024.
[6]	Zixuan HUANG, Huan CHEN, Hai LI, Minglong WANG, Guangjin CHEN, Bei LIU. Process simulation and energy consumption analysis of CO₂/N₂ pilot-scale separation using ZIF-8 slurry [J]. CIESC Journal, 2022, 73(1): 322-331.
[7]	Jianyuan XU, Yanyang WU, Jumei XU, Yangfeng PENG. Study on vapor-liquid equilibria and distillation simulation of 1,3,5-trimethylbenzene-1,2,4-trimethylbenzene and 1,3,5-trimethylbenzene-2-ethyltoluene at 2 kPa [J]. CIESC Journal, 2021, 72(9): 4504-4510.
[8]	Yuanxin FANG, Wu XIAO, Xiaobin JIANG, Xiangcun LI, Gaohong HE, Xuemei WU. Process design and simulation of membrane separation coupled with CO₂ electrocatalytic hydrogenation to formic acid [J]. CIESC Journal, 2021, 72(9): 4740-4749.
[9]	Zhenxing SONG, Xianbao CUI, Ying ZHANG, Xuemei ZHANG, Jie HE, Tianyang FENG, Jixiao WANG. Synthesis of n-hexyl acetate via reactive distillation catalyzed by mixed ionic liquids [J]. CIESC Journal, 2021, 72(8): 4155-4165.
[10]	CAO Jian, FENG Xin, JI Xiaoyan, LU Xiaohua. Study on the theoretical limit performance of multi-pressure evaporation ORC based on zeotropic mixture [J]. CIESC Journal, 2021, 72(7): 3780-3787.
[11]	Yonghou XIAO, Hongyan XIAO, Benyuan LI, Jianliang QIN, Shuang QIU, Gaohong HE. Optimization of helium/methane adsorption separation process based on Aspen Adsorption simulation [J]. CIESC Journal, 2019, 70(7): 2556-2563.
[12]	Jianyong ZHU, Xuqian ZHANG, Hui YANG, Rongxiu LU. Soft-sensing of Pr/Nd component content under different single illumination conditions [J]. CIESC Journal, 2019, 70(2): 780-788.
[13]	SHI Ce, YU Ji, GAO Dong, WANG Haibin, YAO Shanjing, LIN Dongqiang. Process simulation and economic evaluation of monoclonal antibody production [J]. CIESC Journal, 2018, 69(7): 3198-3207.
[14]	LU Rongxiu, HE Lijuan, YANG Hui, ZHANG Guoqing. Component content control with zone control for rare earth extraction process [J]. CIESC Journal, 2017, 68(3): 1058-1064.
[15]	LU Rongxiu, YE Zhaobin, YANG Hui, HE Feng. Multi-RBF models based prediction of component content for Pr/Nd extraction process [J]. CIESC Journal, 2016, 67(3): 974-981.