用水网络优化设计的研究
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摘要
水资源短缺是人类面临的重大问题。节约用水，提高水资源的利用效率，是解决水资源短缺问题的重要一环。一个企业或社区所有用水过程的集合构成一个用水网络，它也是一个质量交换网络。对于这样的网络，如何合理安排用水过程，即如何优化用水网络的设计以节约新鲜水用量，是非常有意义的课题。近十几年来有许多学者对此开展了认真的研究，提出了许多有价值的观点和方法，如夹点分析法和超结构法等。然而，由于问题本身的复杂性，加上对于用水网络优化本身认识尚存差异，所提的方法要么仅适用于比较简单的问题(如夹点分析法)，要么对复杂问题求解困难(如超结构法)。作者在夹点分析法和已有超结构法有关理论成果的基础上，从分析各类用水网络的特性入手，以数学规划为工具，对用水网络的最小新鲜水量问题，最优设计问题进行了系统而深入的研究，发展了一套比较完善的方法。主要内容有以下几点：
1、依次研究了单组分再利用、再生循环以及再生再利用过程的最小用水量问题。提出了确定用水过程最小用水量的数学规划法。对单组分再利用和再生循环过程，采用线性规划求解；对再生再利用过程，通过引入二元变量λ_j来表达新鲜水和再生水提供的质量交换量，从而建立混合整数非线性规划模型，提出了求解最小用水量的两步规划法：第一步优化最小新鲜水用量，第二步在最小新鲜水用量的条件下优化相应的最小再生水用量。
2、研究了再生再利用过程的最小新鲜水用量和再生浓度之间的关系，得出了与文献中关于“夹点再生能获得最小新鲜水用量”不同的观点：最小新鲜水用量和再生浓度有关；存在最低再生浓度C_b，它有三种可能：夹点之下，夹点处以及夹点之上，因此夹点再生不一定能获得最小新鲜水用量。通过三个例子验证了这一观点。
3、对于再利用和单组分再生循环过程，提出了逐步规划的优化设计方法：首先按限定浓度对各操作进行排序，然后对序列中的单元操作通过求解数学规划问题进行逐级匹配。对单组分问题只需对一个操作序列进行逐级优化匹配，而对多组分问题则需对多个操作序列分别逐级优化匹配，并从中选出一个用水量最小的设计。分别对单组分再利用、多组分再利用以及单组分再生循环问题，提出了逐步线性规划的优化设计方法。并针对逐步线性规划法求解多组分再利用过程存在的不足，提出了逐步非线性规划的优化设计方法。
4、针对较复杂的多组分用水过程，作者提出了基于序贯操作模型的整体优化设
计策略:对于一个给定的操作序列，假定排在操作i之前的所有操作的出口水流都是
操作i的水源，在此前提下作者建立了多组分用水过程的序贯操作模型。这样，多组
分用水网络的设计问题可表达为一个双层优化的非线性规划:内层用来寻找给定操
作序列情况下的最优解，外层则是在所有可能的操作序列中搜索最优序列。用两个
例子说明了所提出的新方法。与己经提出的超结构方法相比，新方法求解更容易。
5、对含再生再利用的用水网络设计，作者提出了基于再生再利用序贯操作模型
的整体优化设计策略。该策略的核心在于建立优化模型，作者通过引入再生前过程
操作的质量交换分配系数必，将各操作视为以不同的质量交换分配系数ai分别分配在
再生前过程和再生后过程，在此前提下建立了含再生再利用过程的序贯操作模型。
这样，单组分和多组分含再生再利用的用水网络设计问题可表达为一个混合整数非
线性规划(MINLP)，其中对于多组分问题为一个双层优化的混合整数非线性规划。
因为再生再利用过程的设计问题是一个多目标规划问题，作者采用分层排序法求解
上述模型，即首先优化整个过程的最小新鲜水用量，然后依次优化再生水用量和整
个过程的操作单元数目。
6、对于含有热集成的用水网络提出了两阶段法的分解设计策略。这种设计策略
的特点是:考虑了用水网络和换热网络之间的藕合作用，在设计的第一阶段—用
水网络设计阶段，以同时的用水量最小和朋损最小为目标来进行设计，从而实现整
个过程的用水最小化并为第二阶段的换热网络设计提供最合理的冷流和热流股以确
保能量的合理利用。对于单组分系统，第一阶段以同时的用水量最小和炳损最小为
目标采用逐步双线性规划法来设计用水网络。对于多组分系统，第一阶段按基于序
贯操作模型的多组分用水网络的整体设计策略，以同时的用水量最小和朋损最小为
目标采用两步非线性规划法进行求解。对于设计的第二阶段—换热网络设计，可
直接采用文献中的方法。
7、以经济性为目标研究了多组分用水网络的设计问题。作者采用基于序贯操作
模型的整体优化方法来进行设计。给出了用水网络的经济模型，其中当新鲜水价格
为分段函数时，通过引入两元变量几来表达新鲜水费用。分三种不同情况探讨了以
年投资费用和操作费用之和，即年度总费用为目标多组分用水网络设计。对实例进
行求解并与文献结果相比较，证明了本文方法的优越性。\
Scarcity of water is a life-and-death problem that human being is facing. Economically using water and improving the utilization efficiency of water resource is a important aspect of solving the problem of scarcity of water. The aggregation of the whole water-using processes in a business or community forms a water-using network, which is also a mass exchange network. For this sort of network, it is worthy of investigation arranging the water-using processes properly, i.e. optimizing water-using processes to reduce both fresh water consumption and wastewater production. In recent years, many scholars devoted themselves to the research of water-using network design, and presented many valuable ideas and methods, such as water pinch analysis and superstructure methods. However because of the complexity of the problem itself and the cognitive diversity towards the optimization problem of water-using network, the methods proposed either are only applied to the simple problem or are difficult to search the optima
l solution for a large-scale problem. Basing on the existing achievements (such as water pinch analysis and superstructure methods), approaching from the characteristics of the variable water-using networks and taking the mathematical programming as a tool, the author makes a systematic and deep research on the problem of determining the minimum fresh water consumption and the problem of optimization design, and developed a set of sound methods. The main contents are extracted and listed below:
1) This paper approaches reuse, regeneration recycling and regeneration reuse process for single contaminant, and addressed a mathematical programming method for determining minimum flowrate of fresh and regenerated water in water-using processes. The mathematical formulation of the synthesis problem leads to a linear programming for reuse and reuse recycling process of single contaminant. For the regeneration reuse process, the binary variable j is introduced to express the mass load supplied by the fresh water and regenerated water. Accordingly the design problem can be formulated as a mixed integer nonlinear programming (MINLP), and a two-step programming method is presented: In step 1, a programming with the objective of minfwx is used to determine the minimum flowrate of fresh water, then under the same constraints with step 1, a programming with the objective of minfreg in step 2 is used to determine the minimum flowrate of regenerated water corresponding to the minimum flowrate of fresh wa
ter.
2) The relationship between the minimum fresh water flowrate required, fws, and inlet concentration to regeneration process, Cr, is investigated and a new conclusion is drawn,
which differs from thaf'regeneration of water at pinch minimizes fresh water flowrate" derived from the literature: the minimum fresh water flowrate fws is a function of Cr, and there exist three relationships between fws, and Cr, which indicate three possibilities for Cb : below the pinch, above the pinch or at the pinch. Therefore, in some cases, regeneration at pinch concentration can't always ensure the minimum fresh water consumption. Three examples are solved to demonstrate the new conclusion.
3) For the reuse process and the regeneration recycling process of single contaminant, the step-by-step programming method is presented: From the beginning, the processes are collated according to the limiting operating data, and then the matching between the rich streams and lean steams (water sources) is optimized step by step in accordance to the collated process sequence by solving the mathematical programming problem. For single contaminant, only one sequence needs to be solved, while for multiple contaminants, several sequence need to be solved and the design of minimum fresh water consumption is chosen among them by comparing the results of different operation sequence. For reuse process of single contaminant and multiple contaminants along with regeneration recycling process of single contaminant respectively, the step-by-step linea
1、依次研究了单组分再利用、再生循环以及再生再利用过程的最小用水量问题。提出了确定用水过程最小用水量的数学规划法。对单组分再利用和再生循环过程，采用线性规划求解；对再生再利用过程，通过引入二元变量λ_j来表达新鲜水和再生水提供的质量交换量，从而建立混合整数非线性规划模型，提出了求解最小用水量的两步规划法：第一步优化最小新鲜水用量，第二步在最小新鲜水用量的条件下优化相应的最小再生水用量。
2、研究了再生再利用过程的最小新鲜水用量和再生浓度之间的关系，得出了与文献中关于“夹点再生能获得最小新鲜水用量”不同的观点：最小新鲜水用量和再生浓度有关；存在最低再生浓度C_b，它有三种可能：夹点之下，夹点处以及夹点之上，因此夹点再生不一定能获得最小新鲜水用量。通过三个例子验证了这一观点。
3、对于再利用和单组分再生循环过程，提出了逐步规划的优化设计方法：首先按限定浓度对各操作进行排序，然后对序列中的单元操作通过求解数学规划问题进行逐级匹配。对单组分问题只需对一个操作序列进行逐级优化匹配，而对多组分问题则需对多个操作序列分别逐级优化匹配，并从中选出一个用水量最小的设计。分别对单组分再利用、多组分再利用以及单组分再生循环问题，提出了逐步线性规划的优化设计方法。并针对逐步线性规划法求解多组分再利用过程存在的不足，提出了逐步非线性规划的优化设计方法。
4、针对较复杂的多组分用水过程，作者提出了基于序贯操作模型的整体优化设
计策略:对于一个给定的操作序列，假定排在操作i之前的所有操作的出口水流都是
操作i的水源，在此前提下作者建立了多组分用水过程的序贯操作模型。这样，多组
分用水网络的设计问题可表达为一个双层优化的非线性规划:内层用来寻找给定操
作序列情况下的最优解，外层则是在所有可能的操作序列中搜索最优序列。用两个
例子说明了所提出的新方法。与己经提出的超结构方法相比，新方法求解更容易。
5、对含再生再利用的用水网络设计，作者提出了基于再生再利用序贯操作模型
的整体优化设计策略。该策略的核心在于建立优化模型，作者通过引入再生前过程
操作的质量交换分配系数必，将各操作视为以不同的质量交换分配系数ai分别分配在
再生前过程和再生后过程，在此前提下建立了含再生再利用过程的序贯操作模型。
这样，单组分和多组分含再生再利用的用水网络设计问题可表达为一个混合整数非
线性规划(MINLP)，其中对于多组分问题为一个双层优化的混合整数非线性规划。
因为再生再利用过程的设计问题是一个多目标规划问题，作者采用分层排序法求解
上述模型，即首先优化整个过程的最小新鲜水用量，然后依次优化再生水用量和整
个过程的操作单元数目。
6、对于含有热集成的用水网络提出了两阶段法的分解设计策略。这种设计策略
的特点是:考虑了用水网络和换热网络之间的藕合作用，在设计的第一阶段—用
水网络设计阶段，以同时的用水量最小和朋损最小为目标来进行设计，从而实现整
个过程的用水最小化并为第二阶段的换热网络设计提供最合理的冷流和热流股以确
保能量的合理利用。对于单组分系统，第一阶段以同时的用水量最小和炳损最小为
目标采用逐步双线性规划法来设计用水网络。对于多组分系统，第一阶段按基于序
贯操作模型的多组分用水网络的整体设计策略，以同时的用水量最小和朋损最小为
目标采用两步非线性规划法进行求解。对于设计的第二阶段—换热网络设计，可
直接采用文献中的方法。
7、以经济性为目标研究了多组分用水网络的设计问题。作者采用基于序贯操作
模型的整体优化方法来进行设计。给出了用水网络的经济模型，其中当新鲜水价格
为分段函数时，通过引入两元变量几来表达新鲜水费用。分三种不同情况探讨了以
年投资费用和操作费用之和，即年度总费用为目标多组分用水网络设计。对实例进
行求解并与文献结果相比较，证明了本文方法的优越性。\
Scarcity of water is a life-and-death problem that human being is facing. Economically using water and improving the utilization efficiency of water resource is a important aspect of solving the problem of scarcity of water. The aggregation of the whole water-using processes in a business or community forms a water-using network, which is also a mass exchange network. For this sort of network, it is worthy of investigation arranging the water-using processes properly, i.e. optimizing water-using processes to reduce both fresh water consumption and wastewater production. In recent years, many scholars devoted themselves to the research of water-using network design, and presented many valuable ideas and methods, such as water pinch analysis and superstructure methods. However because of the complexity of the problem itself and the cognitive diversity towards the optimization problem of water-using network, the methods proposed either are only applied to the simple problem or are difficult to search the optima
l solution for a large-scale problem. Basing on the existing achievements (such as water pinch analysis and superstructure methods), approaching from the characteristics of the variable water-using networks and taking the mathematical programming as a tool, the author makes a systematic and deep research on the problem of determining the minimum fresh water consumption and the problem of optimization design, and developed a set of sound methods. The main contents are extracted and listed below:
1) This paper approaches reuse, regeneration recycling and regeneration reuse process for single contaminant, and addressed a mathematical programming method for determining minimum flowrate of fresh and regenerated water in water-using processes. The mathematical formulation of the synthesis problem leads to a linear programming for reuse and reuse recycling process of single contaminant. For the regeneration reuse process, the binary variable j is introduced to express the mass load supplied by the fresh water and regenerated water. Accordingly the design problem can be formulated as a mixed integer nonlinear programming (MINLP), and a two-step programming method is presented: In step 1, a programming with the objective of minfwx is used to determine the minimum flowrate of fresh water, then under the same constraints with step 1, a programming with the objective of minfreg in step 2 is used to determine the minimum flowrate of regenerated water corresponding to the minimum flowrate of fresh wa
ter.
2) The relationship between the minimum fresh water flowrate required, fws, and inlet concentration to regeneration process, Cr, is investigated and a new conclusion is drawn,
which differs from thaf'regeneration of water at pinch minimizes fresh water flowrate" derived from the literature: the minimum fresh water flowrate fws is a function of Cr, and there exist three relationships between fws, and Cr, which indicate three possibilities for Cb : below the pinch, above the pinch or at the pinch. Therefore, in some cases, regeneration at pinch concentration can't always ensure the minimum fresh water consumption. Three examples are solved to demonstrate the new conclusion.
3) For the reuse process and the regeneration recycling process of single contaminant, the step-by-step programming method is presented: From the beginning, the processes are collated according to the limiting operating data, and then the matching between the rich streams and lean steams (water sources) is optimized step by step in accordance to the collated process sequence by solving the mathematical programming problem. For single contaminant, only one sequence needs to be solved, while for multiple contaminants, several sequence need to be solved and the design of minimum fresh water consumption is chosen among them by comparing the results of different operation sequence. For reuse process of single contaminant and multiple contaminants along with regeneration recycling process of single contaminant respectively, the step-by-step linea
引文
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[72]. Doyle, S. J. & Smith, R., Targeting water reuse with multiple contaminants, Transactions of International Chemical Engineering, Part B, 1997, 75(3), 181-189
[73]. Bin Wang, Xiao Feng, Zaoxiao Zhang, A design methodology for
multiple-contaminant water networks with single internal water main, Computers and Chemical Engineering, 27(2003): 903-911
[74]. N. Hallale. A new graphical targeting method for water Minimization, Advances in Environmental Research, 6(2002): 377-390
[75]．姚平经，华贲，项曙光，杨友麒．《工业用水节约与废减量》．中国石化出版社．2001．9
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