换热网络结构性能相关性分析及优化

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摘要

在换热网络的优化问题中，传统的优化技术都基于分级超结构模型，其中存

在着大量的换热网络结构。这些结构的变化容易引起综合费用的突变，导致目标

函数在整型变量上的不可微，严重影响优化进程的可行性和连续性。迄今为止，

整型变量的优化问题仍然是换热网络优化的瓶颈。鉴于此，本文分析了换热网络

结构与性能的相关性，提出了新的优化方法来处理换热网络整型变量的优化问题。

主要工作如下：

首先，基于单体换热器的稳态数学模型，通过正交试验和方差分析，评估综

合费用在不同流体参数变化时的波动程度。采用回归分析法，拟合换热网络结构

与性能相关性因子，旨在表征换热网络结构与性能之间的定量关联。

然后，基于换热网络超结构模型，采用排列组合的方式生成一系列连续变化

的结构，计算与之对应的换热网络综合费用，验证了换热网络中潜在的结构与性

能连续性的关系。基于数学排列法和换热网络结构与性能相关性因子，探讨连续

性结构的生成策略以满足换热网络性能的连续性变化。

继之，结合最速下降法的思想，初步探讨处理换热网络整型变量的方法。根

据换热网络结构与性能的连续性，在传统优化技术的基础上，引入连续性搜索的

概念。改进传统的牛顿优化算法和模拟退火算法，将连续性结构序列作为优化变

量，建立新的换热网络整型变量的优化方法。

最后，在传统数学模型的基础上，加入限制投资费用的等式约束和公用工程

用量的惩罚项。对现有的换热网络结构进行重新优化，以保证优化后的换热网络

在满足投资费用限制的前提下，公用工程用量最小。借助换热器的动态数学模型

和索引矩阵，建立换热网络的动态数学模型。评估投资费用的约束条件对换热网

络动态特性及柔性的影响程度。

关键词：换热网络整型变量连续性原理

ABSTRACT

In the heat exchanger network optimization problems, the traditional optimization

techniques are based on the model of hierarchical superstructure, of which there is a

large number of heat exchanger network structure. These changes in the structure easily

lead to mutations of annual costs that cause the objective function to be

non-differentiable by the integer variable, having serious impact on the optimization of

process feasibility and continuity. So far, the integer variable optimization problem is

still the bottleneck of the heat exchanger network optimization. In view of this, the

paper analyzes the correlation between structure and performance in heat exchanger

network, then finding a new optimization method to deal with the heat exchanger

network optimization problem of integer variables. The main tasks are as follows:

First, based on the steady-state mathematical model for the monomer heat

exchanger, this paper assess the degree of fluctuation of annual costs with the change of

fluid parameters through orthogonal test and variance analysis. Then, by Correlation

Analysis, this paper presents the relativity factor of structures and performances in the

heat exchanger network, intending to characterize the quantitative correlation between

structure and performance in the heat exchanger network.

Then, based on the heat exchanger network superstructure model, the permutations

and combinations is used to generate a series of structure changing continuously and the

corresponding annual costs is calculate. This paper verify the potential characteristics of

the continuity between structure and performance in the heat exchanger network. Based

on the mathematical permutations and the relativity factor of structures and

performances in the heat exchanger network, this paper explored the strategy for the

generation of continuity structure to meet the continuity of change of the heat exchanger

network performance.

Followed, by the combination of the idea of the steepest descent method, it is

studied preliminary to dealing with the integer variable in heat exchanger network.

According to the continuity between structure and performance in heat exchanger

network, this paper introduced the concept of continuity search on the basis of

traditional optimization techniques. By improving the traditional Newton optimization

algorithm and simulated annealing algorithm, this paper use the sequence of continuity

structure as optimization variables to create a new optimization method for integer

variables in heat exchanger network.

Finally, in the traditional mathematical model, adding the equality constraints to

limiting the investment costs and the penalty term of public works. Re-optimize the

existing structure of heat exchanger network to meet the investment costs constraints

with the minimum amount of public works. With dynamic mathematical model of the

heat exchanger and the index matrix, it’s established a dynamic mathematical model of

the heat exchanger network. Evaluate the degree of impact on the dynamic

characteristics and the flexible of heat exchanger network, caused to the investment cost

constraints.

Key Word：heat exchanger network, integer variable, continuity

中文摘要

ABSTRACT

第一章绪论················································································································ 1

1.1 课题研究的背景······························································································ 1

1.2 国内外研究现状······························································································ 2

1.2.1 换热网络优化算法的研究现状 ····························································· 4

1.2.2 整型变量优化方法的研究现状 ····························································· 5

1.2.3 换热网络动态特性及柔性的研究现状 ················································· 6

1.3 本文主要研究内容·························································································· 6

第二章换热网络结构与性能的关联··········································································· 8

2.1 单一换热器的正交试验·················································································· 8

2.1.1 实验因素及指标的确定········································································· 9

2.1.2 正交试验的方差分析··········································································· 10

2.2 各因素数学形式的确定················································································ 11

2.3 换热网络正交试验设计················································································ 13

2.4 建立换热网络结构与性能相关因子 ···························································· 15

2.4.1 考虑交互作用的非线性拟合 ······························································· 15

2.4.2 忽略交互作用的线性拟合 ··································································· 16

2.5 算例检验 ······································································································· 17

2.6 本章小结 ······································································································· 19

第三章换热网络结构的连续性················································································· 21

3.1 换热网络的连续性原理················································································ 21

3.1.1 连续性结构的排列方式······································································· 21

3.1.2 换热网络连续性原理的验证 ······························································· 24

3.2 排列组合法生成的连续性结构 ···································································· 26

3.2.1 连续性结构的生成策略······································································· 26

3.2.2 算例检验 ······························································································ 28

3.3 相关因子生成的连续性结构········································································ 30

3.3.1 连续性结构的生成策略······································································· 30

3.3.2 算例验证 ······························································································ 31

3.4 本章小结 ······································································································· 32

第四章基于连续性的换热网络优化········································································· 34

4.1 最速下降法优化整型变量············································································ 34

4.1.1 最速下降算法的优化策略 ································································· 35

4.1.2 算例验证····························································································· 36

4.2 排列组合法优化整型变量············································································ 37

4.2.1 基于数学排列的优化策略 ································································· 37

4.2.2 算例验证····························································································· 39

4.3 基于相关因子优化整型变量········································································ 41

4.3.1 基于相关因子的退火模拟优化策略 ················································· 41

4.3.2 算例验证····························································································· 43

4.4 本章小结 ······································································································· 44

第五章限制投资费用的换热网络优化与运行 ························································· 45

5.1 投资费用与运行费用的权衡关系 ································································ 45

5.2 限制投资费用的换热网络数学模型 ···························································· 46

5.3 限制投资费用的换热网络优化问题 ···························································· 47

5.3.1 基于蒙特卡洛法的优化策略 ······························································· 47

5.3.2 算例验证 ······························································································ 49

5.4 限制投资费用的换热网络动态特性 ···························································· 50

5.4.1 换热网络的动态模型··········································································· 51

5.4.2 动态特性分析······················································································· 52

5.5 本章小结 ······································································································· 56

第六章结论与展望 ···································································································· 58

6.1 主要结论 ······································································································· 58

6.2 研究展望 ······································································································· 59

符号说明表 ·················································································································· 60

参考文献 ······················································································································ 61

在读期间公开发表的论文、专利及承担科研项目 ··················································· 67

致谢·························································································································· 68

第一章绪论

1.1 课题研究的背景

从长远的历史发展来看，每一次变革都和能源紧密相关，人类社会的每一次

进步也都离不开能源的需求，能源是全球发展所依赖的根本资源。自工业革命以

来，随着人类对物质需求的不断膨胀，科学技术的应用也随之飞快发展。这虽然

推进了工业规模的急速扩大，但也导致了全球传统能源的过度开采。同时，工业

生产和人民日常生活的能源消耗仍然极度地依赖于传统的一次性能源。2012 年，

国际能源署发布一份能源调查报告[1]。在该报告中提供了的各种能源在全球消耗的

比例：煤炭占 20.0%、石油占 36.3%、天然气占 24.9%、核电占 10.2%、水电占 2.3%、

可燃可再生能源占 4.9%、地热能、太阳能、风能及热能等占 1.4%。从中可见，一

次性的传统能源仍然是全球能源消耗的主要资源。虽然拥有高新技术的国家都在

着重挖掘新能源的利用潜力，如：风能和生物质能等，但在长期的一段时间里人

类社会还是无力摆脱对传统能源的依赖[2]。以当今对石化能源的开采进度来看，在

全球范围内原油剩余探明储量仅剩 42 年，天然气和煤炭分别也分别是 60 年和 122

年[3]。人类发展到今天，能源的贮存量与社会的需求已经形成了巨大的反差，如何

高效利用能源必然成为全球人类发展的首要问题。

自改革开放以来，我国的科学技术与工业经济高速发展，对能源的需求空前

巨大。此外，由于能源开采与利用技术的极大落后，我国的能源消耗量仍然处于

传统能源消费大国的行列，而且二氧化碳的排放量居世界首位。我国的人均能源

拥有量不仅落后于大多数国家，能源的利用率也处于世界末端。据统计，我国的

单位GDP能耗约为世界平均值的 4.3 倍[4]。这是因为我国在能源的利用水平、贮量

分配和巨大需求这三者之间存在突出矛盾。其中最主要的有两个方面：一方面是

生产过程中的单位能耗比较高。国内工业生产的单位能耗比发达国家高 90％，加

权平均高 40%左右[5]。在国内，大型火电厂的煤耗为每千瓦时 404 克标准煤，而在

发达国家，平均煤耗为每千瓦时 317 克标准煤；此外，国内钢铁厂生产一吨钢铁

的能耗平均为 966 公斤标准煤，而国际先进水平是 656 公斤标准煤。我国的工业

生产的单位能耗落后于国际先进水平 3～4倍。另一方面是单位能耗所产生的附加

值比较低，国内的每公斤标准煤的生产总值为 0.36 美元，而发达国家的水平为 1.86

美元，是我国的 5.2 倍。所以努力提高我国的能源利用率是保障国民生活和国家稳

定发展的重要问题[6]。

在工业生产过程中，过程系统被广泛应用于工业领域，无疑对能源的有效利

用起了至关重要的作用。随着我国工业生产的飞速发展，过程系统的规模也在不

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摘要：

摘要在换热网络的优化问题中，传统的优化技术都基于分级超结构模型，其中存在着大量的换热网络结构。这些结构的变化容易引起综合费用的突变，导致目标函数在整型变量上的不可微，严重影响优化进程的可行性和连续性。迄今为止，整型变量的优化问题仍然是换热网络优化的瓶颈。鉴于此，本文分析了换热网络结构与性能的相关性，提出了新的优化方法来处理换热网络整型变量的优化问题。主要工作如下：首先，基于单体换热器的稳态数学模型，通过正交试验和方差分析，评估综合费用在不同流体参数变化时的波动程度。采用回归分析法，拟合换热网络结构与性能相关性因子，旨在表征换热网络结构与性能之间的定量关联。然后，基于换热网络超结构模型，采用排列...

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