化工学报 ›› 2025, Vol. 76 ›› Issue (1): 241-255.DOI: 10.11949/0438-1157.20240761
李海东1(), 张奇琪1, 杨路1, AKRAM Naeem2, 常承林1(
), 莫文龙3,4, 申威峰1
收稿日期:
2024-07-05
修回日期:
2024-08-02
出版日期:
2025-01-25
发布日期:
2025-02-08
通讯作者:
常承林
作者简介:
李海东(2000—),男,硕士研究生,202218021091@stu.cqu.edu.cn
基金资助:
Haidong LI1(), Qiqi ZHANG1, Lu YANG1, Naeem AKRAM2, Chenglin CHANG1(
), Wenlong MO3,4, Weifeng SHEN1
Received:
2024-07-05
Revised:
2024-08-02
Online:
2025-01-25
Published:
2025-02-08
Contact:
Chenglin CHANG
摘要:
管壳式换热器是石油、化工等过程工业中应用最广泛的热量回收设备,其数学模型通常是十分复杂的非线性优化问题,现有的商业求解器和优化算法存在运算时间长、收敛困难、易陷入局部最优等难题。针对这些难题,参考管壳式换热器制造标准,将换热器内构件尺寸定义成离散变量,分别以最小化换热面积、年度总费用、环境影响因子及最大化传热效率为目标函数,建立管壳式换热器详细设计的混合整数非线性规划模型。同时,对传统智能进化算法包括遗传算法、粒子群算法及模拟退火算法进行改进,使得换热器设计变量能够在一系列离散值中自由选择,不需要对优化结果进行人工圆整处理。案例测试结果表明,改进的智能进化算法能在1.0 s内得到最优设计方案,相对于全局求解器,优化时间节约99%以上,提高了优化求解效率;相对于局部求解器,改进的智能进化算法能够获取全局最优解,换热面积节约15.4%~56.6%,年度总费用节约 15.8%~77.8%,保证设计质量。通过多目标优化在不同目标函数之间进行权衡,通过灵敏度分析展示了不同设计变量对目标函数的影响趋势。
中图分类号:
李海东, 张奇琪, 杨路, AKRAM Naeem, 常承林, 莫文龙, 申威峰. 采用智能进化算法的管壳式换热器详细设计[J]. 化工学报, 2025, 76(1): 241-255.
Haidong LI, Qiqi ZHANG, Lu YANG, Naeem AKRAM, Chenglin CHANG, Wenlong MO, Weifeng SHEN. Detailed design of shell-and-tube heat exchanger using intelligent evolutionary algorithms[J]. CIESC Journal, 2025, 76(1): 241-255.
变量 | 取值 |
---|---|
管外径/m | 0.019, 0.025, 0.031, 0.038, 0.051 |
总管长/m | 1.219, 1.829, 2.439, 3.049, 3.658, 4.877, 6.098 |
换热管间径比 | 1.25,1.33,1.50 |
换热管排布方式 | 正方形布局,三角形布局 |
管程数 | 1,2,4,6 |
挡板数 | 1,2,3,…,20 |
壳程直径 / m | 0.787, 0.838, 0.889, 0.940, 0.991, 1.067, 1.143, 1.219, 1.372, 1.524 |
表1 设计变量离散值
Table 1 Design variable discrete values
变量 | 取值 |
---|---|
管外径/m | 0.019, 0.025, 0.031, 0.038, 0.051 |
总管长/m | 1.219, 1.829, 2.439, 3.049, 3.658, 4.877, 6.098 |
换热管间径比 | 1.25,1.33,1.50 |
换热管排布方式 | 正方形布局,三角形布局 |
管程数 | 1,2,4,6 |
挡板数 | 1,2,3,…,20 |
壳程直径 / m | 0.787, 0.838, 0.889, 0.940, 0.991, 1.067, 1.143, 1.219, 1.372, 1.524 |
案例 | 最小化换热面积Area/m2 | 最小化年度总费用TAC/(104 USD/a) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
DICOPT | BARON | GA | SA | PSO | DICOPT | BARON | GA | SA | PSO | |
案例1 | NC | 624.6 | 624.6 | 624.6 | 624.6 | 1.836 | 1.349 | 1.349 | 1.349 | 1.349 |
案例2 | 369.0 | 319.7 | 319.7 | 319.7 | 319.7 | 0.987 | 0.817 | 0.817 | 0.817 | 0.817 |
案例3 | NC | 199.3 | 199.3 | 199.3 | 199.3 | 0.862 | 0.529 | 0.529 | 0.529 | 0.529 |
案例4 | NC | 143.8 | 143.8 | 143.8 | 143.8 | NC | 0.558 | 0.558 | 0.558 | 0.558 |
案例5 | 385.0 | 332.1 | 332.1 | 332.1 | 332.1 | 0.905 | 0.781 | 0.781 | 0.781 | 0.781 |
案例6 | 325.0 | 207.6 | 207.6 | 207.6 | 207.6 | 0.843 | 0.592 | 0.592 | 0.592 | 0.592 |
案例7 | 995.0 | 915.2 | 915.2 | 915.2 | 915.2 | 2.558 | 1.889 | 1.889 | 1.889 | 1.889 |
案例8 | 367.0 | 287.5 | 287.5 | 287.5 | 287.5 | 0.999 | 0.799 | 0.799 | 0.799 | 0.799 |
案例9 | NC | 327.8 | 327.8 | 327.8 | 327.8 | 1.664 | 0.936 | 0.936 | 0.936 | 0.936 |
表2 换热面积和年度总费用优化结果
Table 2 Heat transfer area and total annual cost optimization results
案例 | 最小化换热面积Area/m2 | 最小化年度总费用TAC/(104 USD/a) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
DICOPT | BARON | GA | SA | PSO | DICOPT | BARON | GA | SA | PSO | |
案例1 | NC | 624.6 | 624.6 | 624.6 | 624.6 | 1.836 | 1.349 | 1.349 | 1.349 | 1.349 |
案例2 | 369.0 | 319.7 | 319.7 | 319.7 | 319.7 | 0.987 | 0.817 | 0.817 | 0.817 | 0.817 |
案例3 | NC | 199.3 | 199.3 | 199.3 | 199.3 | 0.862 | 0.529 | 0.529 | 0.529 | 0.529 |
案例4 | NC | 143.8 | 143.8 | 143.8 | 143.8 | NC | 0.558 | 0.558 | 0.558 | 0.558 |
案例5 | 385.0 | 332.1 | 332.1 | 332.1 | 332.1 | 0.905 | 0.781 | 0.781 | 0.781 | 0.781 |
案例6 | 325.0 | 207.6 | 207.6 | 207.6 | 207.6 | 0.843 | 0.592 | 0.592 | 0.592 | 0.592 |
案例7 | 995.0 | 915.2 | 915.2 | 915.2 | 915.2 | 2.558 | 1.889 | 1.889 | 1.889 | 1.889 |
案例8 | 367.0 | 287.5 | 287.5 | 287.5 | 287.5 | 0.999 | 0.799 | 0.799 | 0.799 | 0.799 |
案例9 | NC | 327.8 | 327.8 | 327.8 | 327.8 | 1.664 | 0.936 | 0.936 | 0.936 | 0.936 |
案例 | 最小环境影响因子EI/(103 points/a) | 最大传热效率ɛ | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
DICOPT | BARON | GA | SA | PSO | DICOPT | BARON | GA | SA | PSO | |
案例1 | NC | 5.770 | 5.770 | 5.770 | 5.770 | 0.800 | 0.831 | 0.831 | 0.831 | 0.831 |
案例2 | 3.351 | 3.020 | 3.020 | 3.020 | 3.020 | 0.887 | 0.894 | 0.894 | 0.894 | 0.894 |
案例3 | 1.761 | 1.722 | 1.722 | 1.722 | 1.722 | 0.829 | 0.829 | 0.829 | 0.829 | 0.829 |
案例4 | 1.897 | 1.844 | 1.844 | 1.844 | 1.844 | 0.765 | 0.772 | 0.772 | 0.772 | 0.772 |
案例5 | 2.943 | 2.878 | 2.878 | 2.878 | 2.878 | 0.936 | 0.936 | 0.936 | 0.936 | 0.936 |
案例6 | 2.002 | 2.002 | 2.002 | 2.002 | 2.002 | 0.815 | 0.822 | 0.822 | 0.822 | 0.822 |
案例7 | NC | 8.340 | 8.340 | 8.340 | 8.340 | NC | 0.883 | 0.883 | 0.883 | 0.883 |
案例8 | 2.950 | 2.950 | 2.950 | 2.950 | 2.950 | 0.672 | 0.672 | 0.672 | 0.672 | 0.672 |
案例9 | 3.889 | 3.622 | 3.622 | 3.622 | 3.622 | 0.659 | 0.659 | 0.659 | 0.659 | 0.659 |
表3 环境影响因子和传热效率优化结果
Table 3 Environmental impact factor and heat transfer efficiency optimization results
案例 | 最小环境影响因子EI/(103 points/a) | 最大传热效率ɛ | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
DICOPT | BARON | GA | SA | PSO | DICOPT | BARON | GA | SA | PSO | |
案例1 | NC | 5.770 | 5.770 | 5.770 | 5.770 | 0.800 | 0.831 | 0.831 | 0.831 | 0.831 |
案例2 | 3.351 | 3.020 | 3.020 | 3.020 | 3.020 | 0.887 | 0.894 | 0.894 | 0.894 | 0.894 |
案例3 | 1.761 | 1.722 | 1.722 | 1.722 | 1.722 | 0.829 | 0.829 | 0.829 | 0.829 | 0.829 |
案例4 | 1.897 | 1.844 | 1.844 | 1.844 | 1.844 | 0.765 | 0.772 | 0.772 | 0.772 | 0.772 |
案例5 | 2.943 | 2.878 | 2.878 | 2.878 | 2.878 | 0.936 | 0.936 | 0.936 | 0.936 | 0.936 |
案例6 | 2.002 | 2.002 | 2.002 | 2.002 | 2.002 | 0.815 | 0.822 | 0.822 | 0.822 | 0.822 |
案例7 | NC | 8.340 | 8.340 | 8.340 | 8.340 | NC | 0.883 | 0.883 | 0.883 | 0.883 |
案例8 | 2.950 | 2.950 | 2.950 | 2.950 | 2.950 | 0.672 | 0.672 | 0.672 | 0.672 | 0.672 |
案例9 | 3.889 | 3.622 | 3.622 | 3.622 | 3.622 | 0.659 | 0.659 | 0.659 | 0.659 | 0.659 |
参数 | 案例8 | 案例9 |
---|---|---|
管外径/m | 0.025 | 0.019 |
总管长/m | 4.877 | 6.098 |
换热管间径比 | 1.25 | 1.33 |
换热管排布方式 | 正三角形排布 | 正方形排布 |
管程数 | 2 | 4 |
挡板数 | 5 | 6 |
壳程直径 / m | 1.143 | 1.067 |
换热器传热效率 | 0.476(0.474~0.648) | 0.515(0.474~0.627) |
表 4 管壳式换热器详细设计参数
Table 4 Detailed design parameters of shell-and-tube heat exchanger
参数 | 案例8 | 案例9 |
---|---|---|
管外径/m | 0.025 | 0.019 |
总管长/m | 4.877 | 6.098 |
换热管间径比 | 1.25 | 1.33 |
换热管排布方式 | 正三角形排布 | 正方形排布 |
管程数 | 2 | 4 |
挡板数 | 5 | 6 |
壳程直径 / m | 1.143 | 1.067 |
换热器传热效率 | 0.476(0.474~0.648) | 0.515(0.474~0.627) |
输入参数 | 案例1 | 案例2 | 案例3 | 案例4 | ||||
---|---|---|---|---|---|---|---|---|
原油 | 冷水 | 原油 | 冷水 | 甲醇 | 冷水 | 热水 | 甲醇 | |
质量流量/(kg/s) | 110.0 | 228.8 | 50.0 | 56.6 | 27.8 | 56.6 | 40.0 | 133.3 |
进口温度/℃ | 90 | 30 | 100 | 30 | 70 | 30 | 220.0 | 30.0 |
出口温度/℃ | 50 | 40 | 50 | 40 | 40 | 40 | 110.2 | 80.0 |
压降上限/kPa | 100 | 100 | 60 | 50 | 70 | 100 | 70 | 70 |
质量密度/(kg/m3) | 786 | 995 | 786 | 995 | 750 | 995 | 888 | 750 |
黏度/(mPa·s) | 1.89 | 0.72 | 1.89 | 0.8 | 0.34 | 0.8 | 0.15 | 0.34 |
比定压热容/(J/(kg·K)) | 2177 | 4187 | 2177 | 4187 | 2840 | 4187 | 4312 | 284 |
热导率/(W/(m·K)) | 0.12 | 0.59 | 0.12 | 0.59 | 0.19 | 0.59 | 0.17 | 0.19 |
污垢系数/(m2·K/W) | 0.0002 | 0.0004 | 0.0002 | 0.0003 | 0.0002 | 0.0002 | 0.0001 | 0.0001 |
表A1 案例1~4的物流数据
Table A1 Stream data of Cases 1—4
输入参数 | 案例1 | 案例2 | 案例3 | 案例4 | ||||
---|---|---|---|---|---|---|---|---|
原油 | 冷水 | 原油 | 冷水 | 甲醇 | 冷水 | 热水 | 甲醇 | |
质量流量/(kg/s) | 110.0 | 228.8 | 50.0 | 56.6 | 27.8 | 56.6 | 40.0 | 133.3 |
进口温度/℃ | 90 | 30 | 100 | 30 | 70 | 30 | 220.0 | 30.0 |
出口温度/℃ | 50 | 40 | 50 | 40 | 40 | 40 | 110.2 | 80.0 |
压降上限/kPa | 100 | 100 | 60 | 50 | 70 | 100 | 70 | 70 |
质量密度/(kg/m3) | 786 | 995 | 786 | 995 | 750 | 995 | 888 | 750 |
黏度/(mPa·s) | 1.89 | 0.72 | 1.89 | 0.8 | 0.34 | 0.8 | 0.15 | 0.34 |
比定压热容/(J/(kg·K)) | 2177 | 4187 | 2177 | 4187 | 2840 | 4187 | 4312 | 284 |
热导率/(W/(m·K)) | 0.12 | 0.59 | 0.12 | 0.59 | 0.19 | 0.59 | 0.17 | 0.19 |
污垢系数/(m2·K/W) | 0.0002 | 0.0004 | 0.0002 | 0.0003 | 0.0002 | 0.0002 | 0.0001 | 0.0001 |
输入参数 | 案例5 | 案例6 | 案例7 | 案例8 | 案例9 | |||||
---|---|---|---|---|---|---|---|---|---|---|
乙醇 | 冷水 | 热水 | 蔗糖水 | 蔗糖水 | 冷水 | 乙醇 | 丙酮 | 乙醇 | 丙酮 | |
质量流量/(kg/s) | 55.6 | 295.0 | 40.0 | 133.3 | 83.3 | 358.3 | 111.1 | 166.7 | 111.1 | 166.7 |
进口温度/℃ | 150 | 30 | 220.0 | 30 | 90.0 | 30 | 190 | 30 | 190 | 30 |
出口温度/℃ | 60 | 40 | 80.8 | 80.0 | 40.0 | 40.0 | 120.0 | 79.7 | 120.0 | 79.7 |
压降上限/kPa | 70 | 70 | 70 | 70 | 100 | 100 | 100 | 100 | 100 | 100 |
质量密度/(kg/m3) | 789 | 995 | 888 | 1080 | 1080 | 995 | 789 | 736 | 789 | 736 |
黏度/(mPa·s) | 0.67 | 0.80 | 0.15 | 1.30 | 1.30 | 0.80 | 0.67 | 0.21 | 0.67 | 0.21 |
比定压热容/(J/(kg·K)) | 2470 | 4187 | 4312 | 3601 | 3601 | 4187 | 2470 | 2320 | 2470 | 2320 |
热导率/(W/(m·K)) | 0.17 | 0.59 | 0.70 | 0.58 | 0.58 | 0.59 | 0.17 | 0.14 | 0.17 | 0.14 |
污垢系数/(m2·K/W) | 0.0002 | 0.0004 | 0.0001 | 0.0001 | 0.0001 | 0.0004 | 0.0002 | 0.0002 | 0.0002 | 0.0002 |
表A2 案例5~9的物流数据
Table A2 Stream data of Cases 5—9
输入参数 | 案例5 | 案例6 | 案例7 | 案例8 | 案例9 | |||||
---|---|---|---|---|---|---|---|---|---|---|
乙醇 | 冷水 | 热水 | 蔗糖水 | 蔗糖水 | 冷水 | 乙醇 | 丙酮 | 乙醇 | 丙酮 | |
质量流量/(kg/s) | 55.6 | 295.0 | 40.0 | 133.3 | 83.3 | 358.3 | 111.1 | 166.7 | 111.1 | 166.7 |
进口温度/℃ | 150 | 30 | 220.0 | 30 | 90.0 | 30 | 190 | 30 | 190 | 30 |
出口温度/℃ | 60 | 40 | 80.8 | 80.0 | 40.0 | 40.0 | 120.0 | 79.7 | 120.0 | 79.7 |
压降上限/kPa | 70 | 70 | 70 | 70 | 100 | 100 | 100 | 100 | 100 | 100 |
质量密度/(kg/m3) | 789 | 995 | 888 | 1080 | 1080 | 995 | 789 | 736 | 789 | 736 |
黏度/(mPa·s) | 0.67 | 0.80 | 0.15 | 1.30 | 1.30 | 0.80 | 0.67 | 0.21 | 0.67 | 0.21 |
比定压热容/(J/(kg·K)) | 2470 | 4187 | 4312 | 3601 | 3601 | 4187 | 2470 | 2320 | 2470 | 2320 |
热导率/(W/(m·K)) | 0.17 | 0.59 | 0.70 | 0.58 | 0.58 | 0.59 | 0.17 | 0.14 | 0.17 | 0.14 |
污垢系数/(m2·K/W) | 0.0002 | 0.0004 | 0.0001 | 0.0001 | 0.0001 | 0.0004 | 0.0002 | 0.0002 | 0.0002 | 0.0002 |
Available scheme | Area/m2 | TAC/(USD/a) | EI/(points/a) | ε |
---|---|---|---|---|
Ⅰ | 309.38 | 19312.98 | 8041.44 | 0.473 |
Ⅱ | 321.34 | 16799.88 | 6907.75 | 0.491 |
Ⅲ | 405.50 | 10503.09 | 4082.60 | 0.487 |
Ⅳ | 411.72 | 8716.09 | 3278.36 | 0.476 |
表A3 案例8的Pareto最优解
Table A3 Pareto optimal solution of Case 8
Available scheme | Area/m2 | TAC/(USD/a) | EI/(points/a) | ε |
---|---|---|---|---|
Ⅰ | 309.38 | 19312.98 | 8041.44 | 0.473 |
Ⅱ | 321.34 | 16799.88 | 6907.75 | 0.491 |
Ⅲ | 405.50 | 10503.09 | 4082.60 | 0.487 |
Ⅳ | 411.72 | 8716.09 | 3278.36 | 0.476 |
Available scheme | Area/m2 | TAC/(USD/a) | EI/(points/a) | ε |
---|---|---|---|---|
Ⅰ | 356.46 | 26660.45 | 11360.57 | 0.477 |
Ⅱ | 388.28 | 18749.83 | 7798.38 | 0.486 |
Ⅲ | 405.50 | 16814.57 | 6930.30 | 0.483 |
Ⅳ | 448.13 | 13836.30 | 5602.66 | 0.490 |
Ⅴ | 457.25 | 11526.50 | 4564.55 | 0.515 |
表A4 案例9的Pareto最优解
Table A4 Pareto optimal solution of Case 9
Available scheme | Area/m2 | TAC/(USD/a) | EI/(points/a) | ε |
---|---|---|---|---|
Ⅰ | 356.46 | 26660.45 | 11360.57 | 0.477 |
Ⅱ | 388.28 | 18749.83 | 7798.38 | 0.486 |
Ⅲ | 405.50 | 16814.57 | 6930.30 | 0.483 |
Ⅳ | 448.13 | 13836.30 | 5602.66 | 0.490 |
Ⅴ | 457.25 | 11526.50 | 4564.55 | 0.515 |
Available scheme | Case 8(Ranking) | Case 9(Ranking) |
---|---|---|
Ⅰ | 0.3083(4) | 0.3614(5) |
Ⅱ | 0.4434(3) | 0.5610(4) |
Ⅲ | 0.6558(2) | 0.6157(3) |
Ⅳ | 0.6908(1) | 0.6124(2) |
Ⅴ | — | 0.6386(1) |
表A5 TOPSIS决策结果
Table A5 TOPSIS decision result
Available scheme | Case 8(Ranking) | Case 9(Ranking) |
---|---|---|
Ⅰ | 0.3083(4) | 0.3614(5) |
Ⅱ | 0.4434(3) | 0.5610(4) |
Ⅲ | 0.6558(2) | 0.6157(3) |
Ⅳ | 0.6908(1) | 0.6124(2) |
Ⅴ | — | 0.6386(1) |
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