Reserve empty node strategy applied to optimization of heat exchanger networks

doi:10.11949/0438-1157.20241468

Abstract

Abstract:

When optimizing heat exchanger networks using the RWCE algorithm, the randomness of the algorithm may result in heat exchangers being placed consecutively on adjacent nodes, which can affect the generation of new units. In order to solve this problem, this study proposes a reserved node strategy to improve the algorithm. To promote the competition of heat exchange units on the split nodes, the node unstructured model is improved to the split continuous node unstructured model. The existence of multiple nodes on diverging nodes can also effectively prevent the situation where heat exchangers are placed consecutively on adjacent nodes, thereby promoting mutual competition among nodes. Finally, the effectiveness of the strategy was verified using two examples, H4C5 and H10C5, and the annual comprehensive costs were 2890453 USD/a and 5091842 USD/a, respectively, which proved the effectiveness of the improved RWCE algorithm in heat exchange network optimization.

Key words: algorithm, system engineering, optimal design, heat exchanger network, structural evolution

摘要：

使用RWCE算法优化换热网络时，算法的随机性可能导致连续节点上存在换热单元，从而影响后续新单元的生成。为了解决这一问题，提出一种预留节点策略改良该算法。为了促进分流节点上换热单元的竞争，将节点非结构模型改良成分流连续节点非结构模型。分流上存在多个节点，也会有效避免出现连续节点上存在换热单元的状况发生，有效促进节点之间的相互竞争。最终使用H4C5和H10C5两个算例验证该策略的有效性，得到的年综合费用分别是2890453 USD/a和5091842 USD/a，由此证明了将该策略改良RWCE算法在换热网络优化上的有效性。

关键词: 算法, 系统工程, 优化设计, 换热网络, 结构进化

CLC Number:

TQ 028.8

Xiaolong WU, Xiaohuang HUANG, Yuan XIAO, Linghai SHAN, Jiahui YE, Guomin CUI. Reserve empty node strategy applied to optimization of heat exchanger networks[J]. CIESC Journal, 2025, 76(7): 3388-3402.

吴小龙, 黄晓璜, 肖媛, 单灵海, 叶家慧, 崔国民. 一种预留节点策略应用于换热网络优化[J]. 化工学报, 2025, 76(7): 3388-3402.

Figures/Tables 19

Fig.1 Structural diagram of H3C2 split heat exchanger network

Fig.2 Schematic diagram of continuous heat exchange unit

Fig.3 Node on flow stock is occupied

Fig.4 Effect of node location on heat exchanger units

Fig.5 Variation curve of unit heat transfer quantity

Fig.6 Continuous node unstructured model

Fig.7 Continuous node unstructured model with three nodes on shunt

Fig.8 Competition diagram of heat exchange units on the same branch flow

Fig.9 Structure before rearrangement of heat exchange unit

Fig.10 Structure of rearrangement of heat flow strands

Fig.11 Structure of rearrangement of thermal unit

Fig.12 Optimization curves of different methods

Fig.13 Structure when policy is not in effect

Fig.14 Structure without new units generated after strategy takes effect

Fig.15 Structure after new unit is generated

Fig.16 Optimization results of case 1

Table 1 Comparison of optimization results in case 1

来源	换热单元数	Q_HU/MW	Q_CU/MW	TAC/(USD/a)
文献^[22]	14	23.90	31.62	2920933
文献^[23]	15	24.40	32.15	2883847
文献^[24]	12	23.85	31.57	2919675
文献^[25]	15	24.14	31.86	2918341
文献^[26]	15	24.94	30.12	2917682
本研究	12	23.76	31.48	2890453

Fig.17 Optimization results of case 2

Table 2 Comparison of optimization results in case 2

来源	换热单元个数	Q_HU/MW	Q_CU/MW	TAC/(USD/a)
文献^[27]	24	41.35	59.20	6019310
文献^[28]	29	43.28	61.15	5613283
文献^[29]	22	27.38	45.25	5233287
文献^[30]	26	27.16	44.97	5177785
本文	24	26.50	44.37	5091842

References 30

[1]	李倩. 夹点技术在某纺织工程换热网络优化设计中的应用[J]. 纺织科学研究, 2023, 34(7): 58-61.
	Li Q. Application of pinch technology in optimal design of heat exchange network in a textile project[J]. Textile Science Research, 2023, 34(7): 58-61.
[2]	张春伟, 崔国民, 陈上, 等. 采用结构进化策略的Lagrange乘子法优化换热网络[J]. 化工进展, 2016, 35(4): 1047-1055.
	Zhang C W, Cui G M, Chen S, et al. Lagrange multiplier method combined with structure evolution strategy for heat exchanger network synthesis[J]. Chemical Industry and Engineering Progress, 2016, 35(4): 1047-1055.
[3]	Trivedi K K, O'Neill B K, Roach J R. Synthesis of heat exchanger networks featuring multiple pinch points[J]. Computers & Chemical Engineering, 1989, 13(3): 291-294.
[4]	Ciric A R, Floudas C A. Application of the simultaneous match-network optimization approach to the pseudo-pinch problem[J]. Computers & Chemical Engineering, 1990, 14(3): 241-250.
[5]	Wood R M, Suaysompol K, O'Neill B K, et al. A new option for heat exchanger network design[J]. Chemical Engineering Progress, 1991, 87(9): 38-44.
[6]	Rév E, Fonyó Z. Hidden and pseudo pinch phenomena and relaxation in the synthesis of heat-exchange networks[J]. Computers & Chemical Engineering, 1986, 10(6): 601-607.
[7]	Suaysompol K, Wood R. The flexible pinch design method for heat exchanger networks(Ⅰ): Heuristic guidelines for free hand designs[J]. Chemical Engineering Research & Design, 2000, 69: 458-464.
[8]	胡向柏, 崔国民, 涂惟民, 等. 换热网络的函数逼近割平面全局最优化方法[J]. 工程热物理学报, 2010, 31(6): 995-997.
	Hu X B, Cui G M, Tu W M, et al. Cutting-plane method with function approximation for global optimization of heat exchanger networks[J]. Journal of Engineering Thermophysics, 2010, 31(6): 995-997.
[9]	吕岩岩. 场协同下的换热器网络整体强化技术研究[D]. 上海: 上海理工大学, 2009.
	Lv Y Y. Study on integral strengthening technology of heat exchanger network under field synergy[D]. Shanghai: University of Shanghai for Science & Technology, 2009.
[10]	赖向京. 原子团簇结构预测的现实途径—高性能启发式算法[D]. 武汉: 华中科技大学, 2012.
	Lai X J. A realistic way to predict the structure of atomic clusters - a high-performance heuristic algorithm[D]. Wuhan: Huazhong University of Science and Technology, 2012.
[11]	Pavão L V, Costa C B B, Ravagnani M A S S. Heat Exchanger Network Synthesis without stream splits using parallelized and simplified simulated Annealing and Particle Swarm Optimization[J]. Chemical Engineering Science, 2017, 158: 96-107.
[12]	段欢欢, 崔国民, 陈家星, 等. 一种多种群混合搜索微分进化算法优化换热网络[J]. 热能动力工程, 2016, 31(12): 1-6, 120.
	Duan H H, Cui G M, Chen J X, et al. A differential evolution algorithm with hybrid search strategy based on multi-population for heat exchanger network synthesis[J]. Journal of Engineering for Thermal Energy and Power, 2016, 31(12): 1-6, 120.
[13]	Zhang H L, Huang X H, Peng F Y, et al. A novel two-step synthesis method with weakening strategy for solving large-scale heat exchanger networks[J]. Journal of Cleaner Production, 2020, 275: 123103.
[14]	周静, 崔国民, 彭富裕, 等. 基于改进参数的粒子群算法的换热网络优化[J]. 能源研究与信息, 2019, 35(2): 106-109, 116.
	Zhou J, Cui G M, Peng F Y, et al. Optimization of heat exchange network based on particle swarm with improved parameters[J]. Energy Research and Information, 2019, 35(2): 106-109, 116.
[15]	Xiao Y, Cui G M. A novel random walk algorithm with compulsive evolution for heat exchanger network synthesis[J]. Applied Thermal Engineering, 2017, 115: 1118-1127.
[16]	杨智华, 崔国民, 刘薇薇, 等. 换热网络中换热单元竞争分析及策略改进[J]. 系统工程, 2022, 40(6): 33-42.
	Yang Z H, Cui G M, Liu W W, et al. Competition analysis and strategy improvement of heat exchange unit in heat exchange network[J]. Systems Engineering, 2022, 40(6): 33-42.
[17]	杨岭, 崔国民, 徐玥, 等. 换热网络中大步长与接受差解的关联分析及改进策略[J]. 热能动力工程, 2021, 36(6): 9-15, 38.
	Yang L, Cui G M, Xu Y, et al. Correlation analysis and improvement strategy of large step length and accepting imperfect solution in heat exchanger network[J]. Journal of Engineering for Thermal Energy and Power, 2021, 36(6): 9-15, 38.
[18]	刘薇薇, 崔国民, 张璐, 等. 一种应用于换热网络综合的阻尼优化方法[J]. 化工学报, 2022, 73(5): 2060-2072.
	Liu W W, Cui G M, Zhang L, et al. Damping optimization method for heat exchange network synthesis[J]. CIESC Journal, 2022, 73(5): 2060-2072.
[19]	Björk K M, Pettersson F. Optimization of large-scale heat exchanger network synthesis problems[C]// Proceedings of the IASTED International Conference on Modelling and Simulation. 2003: 313-318.
[20]	Khorasany R M, Fesanghary M. A novel approach for synthesis of cost-optimal heat exchanger networks[J]. Computers & Chemical Engineering, 2009, 33(8): 1363-1370.
[21]	韩新宇, 崔国民, 肖媛, 等. 动态区域禁忌匹配策略提高新生换热单元竞争力[J]. 计算物理, 2022, 39(1): 71-82.
	Han X Y, Cui G M, Xiao Y, et al. Dynamic region taboo matching strategy for improving competitiveness of new heat exchange units[J]. Chinese Journal of Computational Physics, 2022, 39(1): 71-82.
[22]	Brandt C, Fieg G, Luo X. Efficient synthesis of heat exchanger networks combining heuristic approaches with a genetic algorithm[J]. Heat and Mass Transfer, 2011, 47(8): 1019-1026.
[23]	Yang Z K, Zhang N, Smith R. Enhanced superstructure optimization for heat exchanger network synthesis using deterministic approach[J]. Frontiers in Sustainability, 2022, 3: 976717.
[24]	Feyli B, Soltani H, Hajimohammadi R, et al. A reliable approach for heat exchanger networks synthesis with stream splitting by coupling genetic algorithm with modified quasi-linear programming method[J]. Chemical Engineering Science, 2022, 248: 117140.
[25]	张红亮, 崔国民, 朱玉双, 等. 特殊换热网络算例优化与分析[J]. 化工进展, 2018, 37(5): 1692-1701.
	Zhang H L, Cui G M, Zhu Y S, et al. Optimization and analysis of specific heat exchanger network cases[J]. Chemical Industry and Engineering Progress, 2018, 37(5): 1692-1701.
[26]	Xu Y, Cui G M, Deng W D, et al. Relaxation strategy for heat exchanger network synthesis with fixed capital cost[J]. Applied Thermal Engineering, 2019, 152: 184-195.
[27]	Trivedi K K, O'Neill B K, Roach J R, et al. A new dual-temperature design method for the synthesis of heat exchanger networks[J]. Computers & Chemical Engineering, 1989, 13(6): 667-685
[28]	Rev E, Fonyo Z. Diverse pinch concept for heat exchange network synthesis: the case of different heat transfer conditions[J]. Chemical Engineering Science, 1991, 46(7): 1623-1634.
[29]	曹美, 崔国民, 陈家星, 等. 换热网络非结构模型中交叉结构的分析[J]. 高校化学工程学报, 2019, 33(4): 911-921.
	Cao M, Cui G M, Chen J X, et al. Analysis of cross structures in non-structural model for heat exchanger network[J]. Journal of Chemical Engineering of Chinese Universities, 2019, 33(4): 911-921.
[30]	赵倩倩, 崔国民, 苏戈曼, 等. 采用新单元换热量生成与分布概率协调策略优化换热网络[J]. 热能动力工程, 2020, 35(5): 17-23, 63.
	Zhao Q Q, Cui G M, Su G M, et al. Heat exchange network optimization by coordination strategy of heat transfer and distribution probability of new unit[J]. Journal of Engineering for Thermal Energy and Power, 2020, 35(5): 17-23, 63.

Related Articles 15

[1]	Xiaoguang MI, Guogang SUN, Hao CHENG, Xiaohui ZHANG. Performance simulation model and validation of printed circuit natural gas cooler [J]. CIESC Journal, 2025, 76(S1): 426-434.
[2]	Siyuan WANG, Guoqiang LIU, Tong XIONG, Gang YAN. Characteristics of non-uniform wind velocity distribution in window air conditioner axial fans and their impact on optimizing condenser circuit optimization [J]. CIESC Journal, 2025, 76(S1): 205-216.
[3]	Jichao GUO, Xiaoxiao XU, Yunlong SUN. Airflow simulation and optimization based on $C O 2$ concentration in plant factory [J]. CIESC Journal, 2025, 76(S1): 237-245.
[4]	Ziteng YAN, Feilong ZHAN, Guoliang DING. Structural design and effect verification of casing-type distributor used in air-conditioners [J]. CIESC Journal, 2025, 76(S1): 152-159.
[5]	Tao WANG, Guangming LI, Qiuxia HU, Jing XU. Optimization of warpage process for two-color injection products based on temporal evolution particle swarm optimization algorithm [J]. CIESC Journal, 2025, 76(7): 3403-3415.
[6]	Hanchuan ZHANG, Chao SHANG, Wenxiang LYU, Dexiang HUANG, Yaning ZHANG. Operating conditions pattern recognition and yield prediction for FCCU based on unsupervised time series clustering [J]. CIESC Journal, 2025, 76(6): 2781-2790.
[7]	Haohao ZHANG, Li GUO, Xinyi LI, Jinyi CHEN, Chao HUA, Ping LU. Research progress on optimal design and dynamic control of dividing wall column [J]. CIESC Journal, 2025, 76(6): 2434-2450.
[8]	Lin LI, Mingmei WANG, Erwei SONG, Wenwen WANG, Yaochang ZHANG, Erqiang WANG. Thermodynamic analysis and optimization of isoprene/n-pentane separation process [J]. CIESC Journal, 2025, 76(6): 2549-2558.
[9]	Jingxin ZHANG, Jiaojie HE, Qingwang CAI, Ziyi KANG, Yusi YANG, Tong WANG, Xiantao CAO, Liwei YANG. Prediction of COD concentration in wastewater treatment plant effluent based on secondary decomposition and BiLSTM [J]. CIESC Journal, 2025, 76(6): 2859-2871.
[10]	Yi CHEN, Yuan XIAO, Guomin CUI. Parallel evolutionary and mass-heat analogy optimization method of mass exchange network [J]. CIESC Journal, 2025, 76(6): 2755-2769.
[11]	Fuyu WANG, Xuanyi ZHOU. Leakage estimation in a chemical tank farm with unsteady adjoint equation and genetic algorithm [J]. CIESC Journal, 2025, 76(6): 3104-3114.
[12]	Yifei WANG, Jingjie REN, Mingshu BI, Haotian YE. Multi-objective optimization of cyclohexane oxidation process parameters based on inherent safety and economic performance [J]. CIESC Journal, 2025, 76(6): 2722-2732.
[13]	Xiaotong XIANG, Xudong DUAN, Simin WANG. Research on performance of PEM electrolyzer driven by multi-objective optimization [J]. CIESC Journal, 2025, 76(6): 2626-2637.
[14]	Yulun WU, Zhenlei WANG, Xin WANG. Contrastive learning based on method for identifying operating conditions of ethylene cracking furnace [J]. CIESC Journal, 2025, 76(6): 2733-2742.
[15]	Minggang GUO, Xiaohang YANG, Yan DAI, Panpan MI, Shixin MA, Gaohong HE, Wu XIAO, Fujun CUI. Optimal design of integration process for helium extraction from helium-poor pipeline natural gas with diversified products [J]. CIESC Journal, 2025, 76(5): 2251-2261.