数学规划与图形方法相结合设计热集成用水网络

doi:10.11949/0438-1157.20200559

摘要/Abstract

摘要：

将数学规划法与图形方法相结合探究单杂质用水网络与换热网络的集成问题。首先构建混合整数非线性规划模型（MINLP），在最小公用工程消耗下优化流股参数未知情况下的分离系统组合曲线面积，得到了最为节能、换热面积最小的用水网络结构。在此基础上，提出了新的分离系统组合曲线演化步骤和规则，可以得到换热单元数目较小的换热网络结构。算例表明，与现有的基于分离系统的热集成用水网络设计方法相比，在最小化公用工程用量的同时可以进一步降低换热器数目与总换热面积。

关键词: 用水网络, 能量集成, 混合整数非线性规划, 组合曲线, 换热网络设计

Abstract:

The mathematical programming method and the graphic method are combined to explore the heat integrated water allocation networks. First, a mixed integer non-linear programming model (MINLP) was constructed to optimize the combined curve area of the separation system in the case of unknown stream parameters under minimum utility consumption, and the most energy-efficient water network structure with the minimum heat exchange area was obtained. Then, design heuristics are proposed for the composite curve of the new separation system. The heat exchanger network structure with a small number of heat exchange units can be obtained. The calculation example shows that compared with the existing design method of heat integrated water network based on separation system, it can further reduce the number of heat exchangers and the total heat exchange area while minimizing the amount of public works.

Key words: water network, energy integration, mixed-integer nonlinear programming model, composite curve, heat exchanger network design

中图分类号:

TQ 021.8

彭肖祎, 董轩, 廖祖维, 杨遥, 孙婧元, 蒋斌波, 王靖岱, 阳永荣. 数学规划与图形方法相结合设计热集成用水网络[J]. 化工学报, 2021, 72(2): 1047-1058.

PENG Xiaoyi, DONG Xuan, LIAO Zuwei, YANG Yao, SUN Jingyuan, JIANG Binbo, WANG Jingdai, YANG Yongrong. Optimal design of heat integrated water allocation networks combining mathematical programming with graphical tools[J]. CIESC Journal, 2021, 72(2): 1047-1058.

图/表 12

图1 热集成用水网络问题示意图

Fig.1 Illustration of heat integrated water allocation networks

图2 冷热组合曲线面积示意图

Fig.2 Schematic diagram of combined curve area

表1 四用水单元的数据

Table 1 Water-using operation data

用水单元	最大入口浓度/ppm	最大出口浓度/ppm	操作温度/℃	极限流率/ (kg/s)	移除杂质负荷/(g/s)
1	0	100	40	20	2
2	50	100	100	100	5
3	50	800	75	40	30
4	400	800	50	10	4

图3 用水网络结构与组合曲线对照图

Fig.3 Match of the water network and the energy composite curves

图4 换热匹配数为1的组合曲线演化过程

Fig.4 Modification of combination curve with 1 heat exchange matching

图5 换热匹配数为2的组合曲线演化过程

Fig.5 Modification of combination curve with 2 heat exchange matching

图6 换热匹配数为3的组合曲线演化过程

Fig.6 Modification of combination curve with 3 heat exchange matching

表2 图6(e)和图6(f)的结果对比

Table 2 Design comparison of Fig.6(e) and Fig.6(f)

图	换热量/kW					换热面积/m²
图	Q₁	Q₂	Q₃	H	换热量总和	S₁	S₂	S₃	S_H	换热面积总和
图6(e)	3569.9	7097.8	7560	3780	22007.7	524.6	1419.6	1512	269.6	3725.8
图6(f)	3570	630.4	14027.4	3780	22007.7	524.6	120.7	3221.1	269.6	4136

表3 本文与文献的设计结果对比

Table 3 Overall design comparison

文献	新鲜水用量/( kg/s)	换热器个数	公用工程用量/ kW	换热量/kW	总换热面积/ m²
[43]	90	4	3780	22008.0	3915.2
[35]	90	4	3780	22260.0	3775.4
本文[图6(e)]	90	4	3780	22007.7	3725.8

图7 换热匹配数为4的组合曲线演化过程

Fig.7 Modification of combination curve with 4 heat exchange matching

图8 四种换热网络结构图

Fig.8 Heat exchanger networks with heat exchange matching of 1—4

表4 四种换热匹配的设计结果对比

Table 4 Comparison of four design results

换热匹配个数	换热单元个数	总换热面积/m²	总换热量/kW
1	2	6024.6	22007.7
2	3	4420.0	22007.7
3	4	3725.8	22007.7
4	5	3596.3	22007.7

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