棋盘模型同步优化质量交换网络

doi:10.19596/j.cnki.1001-246x.8566

摘要/Abstract

摘要：

提出一个质量交换网络的棋盘模型, 该模型具有结构紧凑、表达简洁、流股排列顺序可以灵活改变等特点。我们在强制进化随机游走算法中加入随机消去传质单元阶段, 将算法与棋盘模型相结合, 并以传质量作为优化变量。最后, 使用蚀刻厂回收铜与废水脱酚算例进行验证, 所获结构的年综合费用比文献的最优值下降5.8‰和1.6‰, 该同步优化方法具有良好的搜索区域和搜索能力。

关键词: 质量交换网络, 棋盘模型, 强制进化随机游走算法, 全局最优化

Abstract:

A chessboard model of mass exchange networks (CBM-MEN) is proposed. The CBM-MEN has characteristics of compact structure, simple expression, and flexible stream arrangement. A phase of eliminating mass exchanger is added to a random walk algorithm with compulsive evolution. The algorithm is combined with the chessboard model. During optimization process, the mass exchange load is used as an optimization variable. Finally, the simultaneous optimization method is applied to two cases, recovery of copper from liquid effluents of an etching plant and dephenolization of aqueous wastes. The total annual cost of optimized structures is decreased by 5.8‰ and 1.6‰, respectively. It shows that the method has good search domain and search capability.

Key words: mass exchange network, chessboard model, random walk algorithm with compulsive evolution, global optimization

易智康, 崔国民, 周志强, 肖媛, 熊思恒, 马秀宝. 棋盘模型同步优化质量交换网络[J]. 计算物理, 2023, 40(4): 500-510.

Zhikang YI, Guomin CUI, Zhiqiang ZHOU, Yuan XIAO, Siheng XIONG, Xiubao MA. A Chessboard Model for Simultaneous Optimization of Mass Exchange Networks[J]. Chinese Journal of Computational Physics, 2023, 40(4): 500-510.

图/表 14

图1 质量交换网络示意图

Fig.1 A schematic of a MEN

图2 每个传质单元内部的传质过程

Fig.2 Mass transfer process in a mass transfer unit

图3 棋盘模型(每个圆圈代表一个质量交换单元。)

Fig.3 A chessboard model (A sphere represents a mass exchange unit.)

图4 改变贫、富流股的排列排序

Fig.4 Changing the stream arrangement

图5 适用于棋盘模型的RWCE算法流程图

Fig.5 A flowchart of RWCE algorithm applied to the chessboard model

图6 随机消去传质单元与生成阶段的流程图

Fig.6 A flowchart of random elimination of mass transfer unit and generation stage

图7 从蚀刻厂的废液中回收铜

Fig.7 Recovery of copper from liquid effluents of an etching plant

表1 算例1的流股数据

Table 1 Stream data in Case 1

rich stream	G/(kg·s^-1)	yⁱⁿ/(kg·kg^-1)	y^out/(kg·kg^-1)	lean stream	L/(kg·s^-1)	xⁱⁿ/(kg·kg^-1)	x^out/(kg·kg^-1)	Cost/(＄·s·kg^-1·a^-1)
R₁	0.25	0.13	0.1	S₁	∞	0.03	0.07	58 680
R₂	0.1	0.06	0.02	S₂	∞	0.001	0.002	704 160

图8 算例1优化后的结构TAC = 48 479 ＄·a-1

Fig.8 The optimized structure in Case 1, TAC = 48 479 ＄·a-1

表2 算例1的优化结果

Table 2 Summary of final result in published works for Case 1

Method	L₁/(kg·s^-1)	L₂/(kg·s^-1)	Number of trays	Packed height/m	Number of units	Splits rich/lean	TAC/(＄·a^-1)	difference/%
Ref.[9]	0.276	0.023	4	0.457	3	0/1	52 300^*	7.88
Ref.[24]	0.3	0.021	4	0.309	3	0/1	52 068^*	7.40
Ref.[13]	0.276 9	0.022 1	4	0.319	3	0/1	50 855^*	4.90
Ref.[23]	0.279	0.018 6	4	0.33	3	0/0	49 000	1.07
Ref.[4]	0.281	0.018 4	4	0.33	3	0/0	49 000	1.07
Ref.[15]	0.278 6	0.018 4	4	0.295	3	0/0	48 763	0.58
This work	0.27797	0.018 08	4	0.288 77	3	0/0	48 479	0.00

表3 算例2的流股数据

Table 3 Stream data in Case 2

rich stream		G/(kg·s^-1)		yⁱⁿ/(kg·kg^-1)		y^out/(kg·kg^-1)
R1		2		0.05		0.010
R2		1		0.03		0.006

lean stream	L/(kg·s^-1)		xⁱⁿ/(kg·kg^-1)		x^out/(kg·kg^-1)	Cost/(＄·s·kg^-1)
S1	≤5		0.005		0.015	free
S2	≤3		0.01		0.030	free
S3	∞		0.001 3		0.015	309 600

图9 算例2优化后的结构，TAC = 336 892 ＄·a-1

Fig.9 The optimized structure in Case 2, TAC = 336 892 ＄·a-1

表4 算例2的优化结果

Table 4 Summary of final result in published works for Case 2

Method	L₁/(kg·s^-1)	L₂/(kg·s^-1)	L₃/(kg·s^-1)	Number of trays	Number of units	Splits rich/lean	TAC/(＄·a^-1)	difference/%
Ref.[12]					5	0/2	358 292^*	6.35
Ref.[3]	5	2.22	0.704	28	7	0/1	345 416^*	2.53
Ref.[25]	5	2.205	0.723		6	0/0	339 168	0.68
Ref.[12]	5	2.214	0.71	26	6	0/0	338 168	0.38
Ref.[17]	4.729	2.32	0.751 7	23	6	0/0	337 422	0.16
This work	5	2.196	0.735 3	24	6	0/0	336 892	0.00

图10 基础RWCE和改进RWCE对算例2的寻优过程

Fig.10 Optimization process of base RWCE and improved RWCE in Case 2

参考文献 25

1	El-HALWAGI M M , MANOUSIOUTHAKIS V . Synthesis of mass exchange networks[J]. AIChE Journal, 1989, 35 (8): 1233- 1244. DOI
2	HALLALE N , FRASER D M . Capital and total cost targets for mass exchange networks Part 2:Detailed capital cost models[J]. Computers and Chemical Engineering, 2000, 23 (11/12): 1681- 1699.
3	HALLALE N , FRASER D M . Capital and total cost targets for mass exchange networks Part 1:Simple capital cost models[J]. Computers and Chemical Engineering, 2000, 23 (11/12): 1661- 1679.
4	HALLALE N , FRASER D M . Supertargeting for mass exchange networks Part Ⅱ: Applications[J]. Chemical Engineering Research and Design, 2000, 78 (2): 208- 216. DOI
5	HALLALE N , FRASER D M . Supertargeting for mass exchange networks Part Ⅰ: Targeting and design techniques[J]. Chemical Engineering Research and Design, 2000, 78 (2): 202- 207. DOI
6	FARRAG N M , KAMEL D A , GHALLAB A O , et al. Graphical design and analysis of mass exchange networks using composition driving forces[J]. South African Journal of Chemical Engineering, 2021, 36, 94- 104. DOI
7	PAPALEXANDRI K P , PISTIKOPOULOS E N , FLOUDAS A . Mass-exchange networks for waste minimization-A simultaneous approach[J]. Chemical Engineering Research & Design, 1994, 72 (3): 279- 294.
8	李绍军, 阳永荣. 利用改进的遗传算法进行质量交换网络的最优综合[J]. 化工学报, 2002, 53 (1): 60- 65.
9	CHEN C L , HUNG P S . Simultaneous synthesis of mass exchange networks for waste minimization[J]. Computers & Chemical Engineering, 2005, 29 (7): 1561- 1576.
10	YEE T F , GROSSMANN I E . Simultaneous optimization models for heat integration-Ⅱ: Heat exchanger network synthesis[J]. Computers & Chemical Engineering, 1990, 14 (10): 1165- 1184.
11	陈理. 基于传质浓度差同步优化多组分质量交换网络[D]. 大连: 大连理工大学, 2008.
12	ISAFIADE A J , FRASER D M . Interval based MINLP superstructure synthesis of mass exchange networks[J]. Chemical Engineering Research and Design, 2008, 86 (8): 909- 924. DOI
13	VELÁZQUEZ-GUEVARA M Á, URIBE-RAMÍREZ A R, GÓMEZ-CASTRO F I, et al. Optimal synthesis of mass exchange networks through a state-task representation superstructure[M]//Computer Aided Chemical Engineering. Elsevier, 2018, 43: 331-336.
14	侯创, 罗明生, 徐文星. 取整函数优化基于超结构模型的质量交换网络[J]. 化学反应工程与工艺, 2020, 36 (2): 108- 116.
15	MA X B , GAI Z L , CUI G M , et al. Mass exchanger network synthesis based on random walk algorithm with compulsive evolution[J]. Chinese Journal of Computational Physics, 2022, 39 (4): 479- 490.
16	ZHANG H , CUI G , XIAO Y , et al. A novel simultaneous optimization model with efficient stream arrangement for heat exchanger network synthesis[J]. Applied Thermal Engineering, 2017, 110, 1659- 1673. DOI
17	谢会, 史彬, 鄢烈祥, 等. 列队竞争算法综合质量交换网络[J]. 计算机与应用化学, 2010, 27 (12): 1617- 1620.
18	TREYBAL R E . Mass transfer operations (3rd editioin)[M]. Singapore: McGraw-Hill, 1981.
19	SHENOY U V , FRASER D M . A new formulation of the Kremser equation for sizing mass exchangers[J]. Chemical Engineering Science, 2003, 58 (22): 5121- 5124. DOI
20	LI J , CUI G M , CHEN J X , et al. Simultaneous synthesis of heat exchanger network by random walk algorithm with compulsive evolution based on trilevel protection strategy[J]. Chinese Journal of Computational Physics, 2019, 36 (1): 69- 79.
21	XU Y , CUI G M . Heat exchanger network optimization using structural perturbation strategy[J]. Chinese Journal of Computational Physics, 2020, 37 (6): 734- 744.
22	EI-HALWAGI M M , MANOUSIOUTHAKIS V . Automatic synthesis of mass-exchange networks with single-component targets[J]. Chemical Engineering Science, 1990, 45 (9): 2813- 2831. DOI
23	HALLALE N. Capital cost targets for the optimum synthesis of mass exchange networks[D]. Cape Town: University of Cape Town, 1998.
24	VELÁZQUEZ-GUEVARA M Á , URIBE-RAMÍREZ A R , GÓMEZ-CASTRO F I , et al. Synthesis of mass exchange networks: A novel mathematical programming approach[J]. Computers & Chemical Engineering, 2018, 115, 226- 232.
25	AZEEZ O S , ISAFIADE A J , FRASER D M . Supply-based superstructure synthesis of heat and mass exchange networks[J]. Computers & Chemical Engineering, 2013, 56 (1): 184- 201.

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