Multi-objective constrained optimization method for heat exchanger network considering comprehensive economy and entransy

doi:10.11949/0438-1157.20190975

Abstract

Abstract:

For the optimization of the heat exchange network, not only the“quantity”of energy recovery, but also the“quality”dissipation problem in the energy recovery process must be considered. On the premise of the maximum energy recovery(MER) of the heat exchanger network, based on the entransy dissipation theory in the process of irreversible heat transfer, aiming at the highest entransy efficiency which represents the energy recovery quality, we establish a multi-objective mixed integer nonlinear programming (MOMINLP) model, which comprehensively consider the quantity and quality of energy recovery and the economics of the heat exchanger network. According to the characteristics of the model targets, the heat exchanger network is optimized step-by-step based on the ε-constraint algorithm, the maximum energy recovery and minimum total annual cost (TAC) of the heat exchanger network are accurately solved in turn with the BARON software. Then, with the solved results multiplied by the relaxation coefficient ε_i as the constraint condition for narrowing the search area, the Pareto frontier of the entransy efficiency under the constraints of energy and economy is obtained. Through calculating the classic 10SP1 case, the optimal solution as the minimum ratio of economy to efficiency is obtained when the relaxation coefficient is 1.05, and compared with the results of other literature optimization methods, the multi-objective constrained optimization method in this paper can find the comprehensive optimal solution faster. Finally, the entransy efficiency of different optimization schemes is compared through the heat exchanger networks composite curve in T-Q diagram, which indicates that divide the heat exchanger network into internal part and surplus part firstly, and then optimize the scheme according to the economy and entransy efficiency, this method can reduce the irreversible loss of internal part and increase the temperature of the surplus part.

Key words: heat exchanger network, ε-constrained method, multi-objective, optimal design, integration, process control

摘要：

换热网络优化中不仅要考虑能量回收的“量”，还要考虑能量回收过程中“质”的耗散问题。在换热网络最大能量回收的前提下，基于不可逆传热过程中的耗散理论，以代表能量回收品质的效率最高为目标，建立综合能量回收数量、品质并同时考虑换热网络经济性的多目标混合整数非线性规划（MOMINLP）模型。根据模型目标有主次之分的特点，基于ε约束法对模型进行分步优化并结合BARON软件进行精确求解，依次求解换热网络的最大能量回收量(MER)与最低年均总成本(TAC)，再将所得结果乘以松弛系数ε_i作为缩小搜索区域的约束条件,获得能量与成本约束下效率的Pareto前沿。通过对经典10SP1案例进行计算求解，最终得到最大能量回收量下，费用松弛系数为1.05时费效比最小的优化方案，而且本文的多目标约束优化方法能够更快求得综合的最优解。最后通过T-Q图中的换热网络组合曲线对比不同优化方案的效率，将换热网络划分为内部换热部分与剩余流股部分，多目标约束优化方法能够降低内部换热不可逆损失，提高剩余流股的温度。

关键词: 换热网络, ε-约束法, 多目标, 优化设计, 集成, 过程控制

CLC Number:

TQ 021.8

Lei WANG, Yuting CHEN, Yanyan XU, Shuang YE, Weiguang HUANG. Multi-objective constrained optimization method for heat exchanger network considering comprehensive economy and entransy[J]. CIESC Journal, 2020, 71(3): 1189-1201.

王磊, 陈玉婷, 徐燕燕, 叶爽, 黄伟光. 综合考虑经济性与效率的换热网络多目标约束优化方法[J]. 化工学报, 2020, 71(3): 1189-1201.

Figures/Tables 13

Fig.1 Schematic diagram of HEN problem

Fig.2 HEN composite curves

Fig.3 HEN retrofit composite curves

Fig.4 HEN superstructure model

Fig.5 Multi-objective constrained algorithm in HEN

Fig.6 ε-Constrained algorithm narrowing search area

Table 1 10SP1 problem data

流体	入口温度/K	出口温度/K	热容流率/（kW?K^-1）
H1	433	366	8.79
H2	522	411	10.55
H3	500	339	14.77
H4	544	422	12.56
H5	472	339	17.73
C1	333	433	7.62
C2	389	495	6.08
C3	311	494	8.44
C4	355	450	17.28
C5	366	478	13.90
HU	509	509	—
CU	311	355	—

Fig.7 Pareto frontier between TAC and SE

Fig.8 Comparison of increase in different ε2 values

Fig.9 Result based on MEE target constrained in MER and TAC

Fig.10 Result based on TAC target constrained in MER

Fig.11 Retrofit composite curves from different results

Table 2 Comparison of results among several methods

文献	搜索方法	TAC_AMTD/USD	TAC^*_AMTD /USD	SE/(kW?K)	η	计算时间^④(CPU time)/s
Floudas	弯曲分解方法	41406	41469.1	701813	0.732	—
Lewin	遗传算法	40977.7	41028.1	712364	0.743	—
方法1^①	BARON	41007.2	41265.3	701624	0.731	1312.61
方法2^②	ε约束法	40870	41001.9	699959	0.730	242.70
本文方法^③	ε约束法	42157.9	43289.2	740800	0.772	23.61

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