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

换热网络结构性能相关性分析及优化

断的扩大。特别在石油、化工、冶金等能源消耗密集型行业，生产工艺的复杂性

导致有大量的工艺流体需要加热或冷却到目标温度以达到一定的工艺要求。这意

味着过程系统内部存在巨大的能量可以被有效合理地利用。这就需要设计一个热

系统，即换热网络，将这些流体合理地进行匹配，充分利用各工艺流体潜在的冷、

热量，提高系统内部的整体热量回收能力，降低生产过程的能量消耗并减少系统

对外部能量的依赖。换热网络主要是由若干个换热器，辅助加热器和冷却器组成，

按照特定的拓扑结构，通过换热器将多股冷热流体进行集成与换热，使工艺流体

能达到生产工艺的温度标准[7]。换热网络作为过程系统的主要换热环节，其性能自

然成为评价过程系统是否有效利用能量的重要指标。

换热网络优化问题不仅在工业应用的领域中得到了极大的关注，成为研究的

热点，而且在数学应用的领域中也有长期的研究，得到了成熟的发展。虽然众多

的研究者都长期致力于对换热网络优化问题的处理，但仍然没有能在离散整型变

量（换热网络结构）的优化工作上有巨大的突破。迄今为止，还没有任何一种优

化算法或是优化技术能有效地处理离散整型变量的优化问题。从数学模型的角度

来看，换热网络的优化问题是在有约束条件下的混合整数非线性问题，其优化目

标是获得综合费用的最优解[8]。对于大型的换热网络，为了得到目标函数的最优解，

设计者就必须处理好整型变量的优化问题，但在实际优化工作中，存在诸多难点：

1）换热网络内部传热机理决定了问题的非线性。这一特性造成在换热网络的结构

变化时，换热网络性能的变化极其复杂；2）冷热物流间不同的匹配关系及换热器

不同的分布位置，导致换热网络优化中产生大量的离散整型变量（换热网络的结

构）；3）换热网络结构直接地决定了换热网络回收热量的能力[9]，离散整型变量

的处理也根本上影响了优化的质量。这些因素之间相互影响和耦合，使得换热网

络优化的局部最优解星罗棋布，严重阻碍了优化工作的连续性。

复杂换热网络所需的换热器数目众多，整型变量的多维性也使得优化的走向

错综复杂，极大地限制了传统方法的优化质量[10]。现有的优化技术方法在处理换

热网络问题时，仍然会陷入局部最小解，甚至可能会得到一个不可行解，所以在

换热网络优化技术的研究中，如何解决整型变量的优化是一个不容忽视的问题，

讨论换热网络的性能与结构之间的相关性也变得尤为重要。

1.2 国内外研究现状

随着社会的不断发展，换热网络作为工业生产中的关键要素，在降低生产能

耗方面起到的作用受到了越来也多的关注。在热力系统中，不仅单体换热设备的

设计与改造技术不断地完善，而且换热网络的集成技术也得以长足稳定的发展。

第一章绪论

无论是换热网络的前期稳态设计还是后期操作运行，国内外研究者都对其进行了

大量的研究，并开发了一系列的优化技术用于工业生产的系统优化。早在 1968 年，

Masso[11]就率先提出：换热网络优化不能仅从数学的角度去考虑，在优化过程中更

要注重换热网络本身的传热机理和适当的物流匹配。1978 年，Umeda[12]根据热力

学原理，首先制定热系统的温焓图，然后根据温焓曲线对冷热流体进行综合匹配

并提出：热系统集成优化的关键是物流的匹配方式，即找到适合的换热网络结构。

当今，主流的换热网络优化技术包括：基于热力学的夹点分析技术、基于数

学规划法的确定性优化技术和基于启发式方法的随机性优化技术。在实际工业生

产中，应用最广泛的是夹点分析技术。设计者大多认为优化或改造过程系统时，

夹点分析技术能帮助设计者清晰规范地找出系统在能量利用方面的潜在瓶颈，迅

速地得到理想的设计结果。Linnhoff[13]在1978 年引入了热集成的概念并建立发展

了夹点分析技术，提出了需要遵循的步骤：首先利用温焓图确定热系统的总能量

复合曲线并建立最佳的最小传热温差，然后修正总能量复合曲线，以热流通量为

零的温位点作为夹点的位置，计算可能实现的最大热回收量及所需的最少公用工

程，最后寻找最优的流体匹配使换热网络实现热量回收的最大化，建立适当的换

热网络热集成系统。这项研究成果能清晰地指导设计者如何确定最佳的换热网络

的结构，对提高热系统的总体能效起到了开创性的指导意义。之后，一些研究者

在该基础上加以改进使得夹点技术更加符合实际运用。1989 年，Trividi[14]提出了

双夹点的概念，保证了换热器的内部温差也大于夹点温差，提高了夹点技术的精

确性。同年，Fraser[15]以流量代替温差作为夹点位置的判断标准，对特殊的水网络

进行了集成优化并取得了较好的结果。

之后，随着我国工业规模的不断扩大，夹点分析技术越来越受到国内研究者

的关注。1991 年，李有润[16]在国内的学术领域系统地阐述了夹点分析技术。姚平

经[17]教授对窄点法也进行了发展，建立了三温差法设计优化换热网络。2005 年，

陆贞[18]基于夹点分析技术，研究了换热网络中运行费用和投资费用之间的权衡关

系，提出了从理论上确定最佳夹点温位的指导性方法。

此外与夹点技术相比，同一时期被提出并得到发展的还有基于数学规划法的

确定性优化技术。数学规划法从应用数学的角度将换热网络的优化问题概括为混

合整数非线性的优化问题。该优化方法引入了整型变量的概念来表达传统意义上

的换热网络结构，借助成熟的数学优化算法对换热网络问题进行更深入、精确的

研究。1983 年，Grossmann[19-21]对换热网络建立线性规划的数学模型，通过LP转

换算法确定了换热网络的最小换热单元数目以及所需消耗的最少公用工程用量。

1986 年，Floudas[22]提出了一种换热网络超结构模型，能表达所有可能的流体匹配

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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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