城市供水管网氯的优化配置
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摘要
针对城市供水管网末端余氯不达标的问题，本课题在水质检测分析
的基础上，采用一级反应动力学方程对余氯衰减变化规律进行模拟，
并利用余氯衰减模型，建立管网加氯点、加氯量的优化配置模型，以
保证管网中各点余氯均符合水质标准。
首先，对管网中余氯的衰减变化规律及影响因素进行研究。通过对
天津市某区管网连续的水质检测，研究管网水质变化规律，分析了 pH、
温度、浊度、细菌总数、AOC（可同化有机碳）、消毒副产物等因素对
余氯的影响，其中重点对余氯、细菌总数、AOC 三者关系进行定量分
析，并建立了细菌滋生的数学模型。
其次，建立余氯衰减模型并对模型进行校核。余氯衰减模型采用
一级动力学方程，其中氯的衰减速率系数包括主体水衰减系数和管壁
衰减系数两部分。前者通过实验室静态实验求得，后者在现场实测数
据的基础上通过高斯—牛顿法求得。监测点之间的传输时间通过水力
模拟确定。对建立的模型通过实测数据进行校验，结果表明实测值与
模拟值吻合得较好，模型的精确度较高，能够反应管网中余氯的衰减
变化规律。
再次，氯的优化配置模型的研究。加氯点的优化配置采用 0－1 规
划，以年投资费用最低为目标函数，各点余氯达标为约束条件。在确
定最优加氯点的基础上，加氯量优化模型以耗氯量最小为目标函数，
管网各点余氯达标为约束条件。模型的求解通过 Lingo 软件实现。同
样使管网余氯达标，经过优化配置与仅在水厂增加投氯量相比，所需
费用大大降低，水质情况显著提高，充分说明了中途补氯的经济合理
性和技术可行性。
最后，提出管网水质控制措施。通过余氯衰减模型和氯的优化配
置模型，对管网中余氯不达标点进行中途补氯。并且针对管网水质的
其它问题，提出一系列合理有效的控制措施，从而保证向用户提供安
全可靠的饮用水。
Residual chlorine is often short at the end of urban water distribution network.
So the thesis introduces the conventional first-order model to describe chlorine decay
in water distribution system based on water quality monitoring and analysis.
According to the decay model, an optimizing model on chlorine allocation is
established to decide the optimal chlorination point and chlorine dosage. These
models can ensure that residual chlorine satisfies the water quality standard.
Firstly, by continual water quality monitoring, the change rule of water quality
in distribution network is studied, the effect on residual chlorine of pH, temperature,
turbidity, bacteria, AOC(assimilable organic carbon), disinfection by product etc. is
analyzed. The relation of residual chlorine, bacteria and AOC is quantificationally
discussed and the mathematical model of bacteria growing is established.
Secondly, residual chlorine decay model is developed and verified. The model
adopts the first-order dynamic equation. In the equation, chlorine decay rate
coefficient includes bulk decay rate coefficient which is determined by deriving the
best fit with a lot of experimental data and wall decay rate coefficient which is
gained by Gauss-Newton method with spot monitoring data. Water transmission time
between two monitoring points is available by water power model. After determining
the chlorine decay rate coefficient, the model accuracy is verified by using
experimental data. The result shows that simulation value has good agreement with
experimental data. Therefore the decay model can be used to simulate chlorine decay
of water distribution system.
Thirdly, optimizing model of chlorine allocation is established. The optimal
allocation of chlorination point adopts 0-1 programming. Model is founded with the
lowest cost per year as objective function and residual chlorine standard as
constraints. After finding out the optimal points, the optimizing model of chlorine
dosage is established with the lowest dosage as objective function and residual
chlorine standard as constraints. The models are solved by Lingo software. In case
that residual chlorine meets the water quality standard, compared with chlorine
dosing only in water supply plant, adding chlorine in water distribution network by
optimizing model proves to be more economical and effective.
Lastly, control measures for water quality in distribution system are put forward.
Chlorine is added where residual chlorine doesn't reach the standard by decay model
and optimizing model. With regard to other questions of water quality in distribution
system, a series of reasonable and effective measures are brought forward to supply
safe and reliable drinking water for consumers.
的基础上，采用一级反应动力学方程对余氯衰减变化规律进行模拟，
并利用余氯衰减模型，建立管网加氯点、加氯量的优化配置模型，以
保证管网中各点余氯均符合水质标准。
首先，对管网中余氯的衰减变化规律及影响因素进行研究。通过对
天津市某区管网连续的水质检测，研究管网水质变化规律，分析了 pH、
温度、浊度、细菌总数、AOC（可同化有机碳）、消毒副产物等因素对
余氯的影响，其中重点对余氯、细菌总数、AOC 三者关系进行定量分
析，并建立了细菌滋生的数学模型。
其次，建立余氯衰减模型并对模型进行校核。余氯衰减模型采用
一级动力学方程，其中氯的衰减速率系数包括主体水衰减系数和管壁
衰减系数两部分。前者通过实验室静态实验求得，后者在现场实测数
据的基础上通过高斯—牛顿法求得。监测点之间的传输时间通过水力
模拟确定。对建立的模型通过实测数据进行校验，结果表明实测值与
模拟值吻合得较好，模型的精确度较高，能够反应管网中余氯的衰减
变化规律。
再次，氯的优化配置模型的研究。加氯点的优化配置采用 0－1 规
划，以年投资费用最低为目标函数，各点余氯达标为约束条件。在确
定最优加氯点的基础上，加氯量优化模型以耗氯量最小为目标函数，
管网各点余氯达标为约束条件。模型的求解通过 Lingo 软件实现。同
样使管网余氯达标，经过优化配置与仅在水厂增加投氯量相比，所需
费用大大降低，水质情况显著提高，充分说明了中途补氯的经济合理
性和技术可行性。
最后，提出管网水质控制措施。通过余氯衰减模型和氯的优化配
置模型，对管网中余氯不达标点进行中途补氯。并且针对管网水质的
其它问题，提出一系列合理有效的控制措施，从而保证向用户提供安
全可靠的饮用水。
Residual chlorine is often short at the end of urban water distribution network.
So the thesis introduces the conventional first-order model to describe chlorine decay
in water distribution system based on water quality monitoring and analysis.
According to the decay model, an optimizing model on chlorine allocation is
established to decide the optimal chlorination point and chlorine dosage. These
models can ensure that residual chlorine satisfies the water quality standard.
Firstly, by continual water quality monitoring, the change rule of water quality
in distribution network is studied, the effect on residual chlorine of pH, temperature,
turbidity, bacteria, AOC(assimilable organic carbon), disinfection by product etc. is
analyzed. The relation of residual chlorine, bacteria and AOC is quantificationally
discussed and the mathematical model of bacteria growing is established.
Secondly, residual chlorine decay model is developed and verified. The model
adopts the first-order dynamic equation. In the equation, chlorine decay rate
coefficient includes bulk decay rate coefficient which is determined by deriving the
best fit with a lot of experimental data and wall decay rate coefficient which is
gained by Gauss-Newton method with spot monitoring data. Water transmission time
between two monitoring points is available by water power model. After determining
the chlorine decay rate coefficient, the model accuracy is verified by using
experimental data. The result shows that simulation value has good agreement with
experimental data. Therefore the decay model can be used to simulate chlorine decay
of water distribution system.
Thirdly, optimizing model of chlorine allocation is established. The optimal
allocation of chlorination point adopts 0-1 programming. Model is founded with the
lowest cost per year as objective function and residual chlorine standard as
constraints. After finding out the optimal points, the optimizing model of chlorine
dosage is established with the lowest dosage as objective function and residual
chlorine standard as constraints. The models are solved by Lingo software. In case
that residual chlorine meets the water quality standard, compared with chlorine
dosing only in water supply plant, adding chlorine in water distribution network by
optimizing model proves to be more economical and effective.
Lastly, control measures for water quality in distribution system are put forward.
Chlorine is added where residual chlorine doesn't reach the standard by decay model
and optimizing model. With regard to other questions of water quality in distribution
system, a series of reasonable and effective measures are brought forward to supply
safe and reliable drinking water for consumers.
引文
[1] 汪光焘，城市供水行业 2000 年技术进步发展规划，北京：建筑工
业出版社，1993
[2] 姚志麟等，环境卫生学，1994，人民卫生出版社，109－110
[3] Grayman W M, Clark R M, Males R M, Modeling distribution system
water quality: dynamic approach[J], J water resource planning and
management,1998,114(3):295-312
[4] Clark R M, Developing and applying the water supply simulation
model[J], J AWWA, 1986, 78(8): 929-943
[5] Males R M, Clark R M, Wehrman P J, et al. Algorithm for mixing
problems in water systems[J], J Hydraulic engineering, 1985,111(2):
206-219
[6] Lious C P, Kroon J R, Modeling the propagation of waterborne
substances in distribution networks[J], AWWA, 1987,79(11): 54-58
[7] Rossman L A, Paul F Boulo, Tom Altman, Discrete volume-element
method for network water-quality models[J], Journal of water
resource planning and management, 1993, 119(5): 32-40
[8] Chaudhry M H, Islam M R, Water quality modeling in pipe
networks[M], 1995, Netherlard: Improving Efficiency and Reliability
in Water Distribution Systems, Kluwer Academic publishers
[9] Levis A Rossman, Robert M Clark, Walter M Grayman, Modeling
chlorine residual in drinking water distribution systems[J], Journal of
Environment Engineering, 1994, 120(4): 86-95
[10]Rodriguez M J, West J R, Powell J, et al, Application of two
approaches to model chlorine residuals in Severn Trent Ltd(STD)
distribution systems[J], Water Science and Technology, 1997, 36(5):
317-324
[11]B Coulbeck, Computer applications in water supply, 1988, New York
N Y: Research Studies Press, John and Sons
[12]Elaine C, Sodowski, Computer-generated optimal pumping schedules,
J AWWA, 1995(7)
[13]王占生、刘文君，微污染水源饮用水处理，北京：中国建筑工业出
版社，1999，244－247
66
参考文献
[14]徐洪福，城市供水管网水质变化规律与控制措施研究：[博士学位
论文]，哈尔滨，哈尔滨工业大学，2003
[15]同济大学主编，给水工程，中国建筑工业出版社，1980
[16]王权，郑传林，给水处理中加氯量的影响因素，山东建筑工程学院
学报，2000，15（1）：34－36
[17]张明浩，高松，生活饮用水加氯消毒工艺中几项主要影响因素的讨
论和综合控制，西南给排水，2000，第 4 期：7－10
[18]丁英锋，王启山，自来水加氯消毒副产物及其前体物（THMFP）
的研究与发展，天津城市建设学院学报，2001，7（2）：128－131
[19]J J ROOK, Haloforms in drinking water, J AWWA, 1976(3): 168
[20]U S National Cancer Institute, Report on Carcinogenicity Bioassary
of Chloroform, 1976, (5)
[21]Slnger P C, Humic Substances as precursors for potentially harmful
disinfection by－products[J], Water Science and Technology, 1999,
40(9): 25-30
[22]Steven C Allgier et al, Evaluating NF for DBP Control with the BSMT,
J AWWA, 1995
[23]张晓健，李爽，消毒副产物总致癌风险的首要指标参数——卤乙酸，
给水排水，2000，26（8）：l－6
[24]李爽、张晓健，两个中心城市饮用水中消毒副产物的调查，中国给
水排水，2000，26（8）：l－5
[25]张绍园，姜兆春，王菊思，饮用水消毒副产物控制技术研究现状与
发展，水处理技术，1998，24（1）：7－13
[26]陶建科，火正红，给水管网建模中建立计算机供水系统管网图形和
在地形图上划定节点流量区域的方法，给水排水，23（6）：5－8
[27]杜晓明，刘遂庆，利用营业抄表用水量，计算给水管网节点流量的
方法，城市公用事业，2003，17（2）：14－17
[28]陈涛、张国亮，化工传递过程基础，北京：化学工业出版社，2002，
205－267
[29]王运东、骆广生、刘谦，传递过程原理，北京：清华大学出版社，
2002，60－98
[30]周建华、赵洪宾、薛罡，配水管网中与有机物反应的余氯衰减动力
学模型，环境科学，2003，24（3）：45－49
[31]徐成贤，陈志平，李乃成，近代优化方法，北京：科学出版社，2002，
211－222
67
参考文献
[32]李冲，王兴华，求解一类非光滑优化问题的 Gauss－Newton 法，
自然科学进展，2000，10（4）：372－374
[33]Womersley R S, Local properties of algorithms minimizing
nonsmooth composite functions, Mathematical Programming, 1985,
32: 69
[34]Jittomtrum K, Osbome M R, Strong uniqueness and second order
convergence in nonlinear discrete approximation, Numerische
Mathematik, 1980, 34: 439
[35]Burke J V, Ferris M C, A Gauss-Newton method for convex composite
optimization, Mathematical Programming, 1995, 71: 179
[36]齐晶瑶，李欣，关于供水管道内余氯消耗机理的探讨，给水排水，
2000，26（8）：66－69
[37]李欣，宋学峰，配水管网水质变化的研究（Ⅱ）——余氯消耗动力
学机制的研究，哈尔滨建筑大学学报，1999，32（3），52－56
[38]国家环境保护总局编，水和废水监测分析方法，北京：中国环境科
学出版社，2002，170
[39]吴育华，杜纲，管理科学基础，天津：天津大学出版社，2001，49
－54
[40]《运筹学》教材编写组编，运筹学，北京：清华大学出版社，1996，
124－128
[41]Rhodes Trussell R, Safeguarding distribution system integrity, J
AWWA, 1999, 91(1): 52
[42]黄晓东，王占生，饮用水消毒的若干技术问题探讨，上海环境科学，
2002，21（2）：116－117
[43]张艳琴，崔晓波，饮用水中微生物的稳定性，山西化工，2001，21
（4）
[44]Singley J. E. and Tingye Lee, Pipe loop system augments corrosion
studies, J AWWA, 1984, (8): 76-88
[45]Mackenthun K. M. and L. E. Keup, Biological problems encounted in
water supplies, AWWA, 1970, (8): 520-525
[46]罗岳平，邱振华，李宁，合理规划管网冲洗工作，给水排水，1998，
24（4）：27－31
[47]徐兰京，给排水管材现状及管道内壁水质分析，给水排水，1999，
25（10）：66－68
[48]姚东，防治二次污染，改善管网水质，城镇供水，2002，（3）：34
－35
68
参考文献
[49]O H Tuovinen, et al, Bacterial, chemical and mineralogical
characteristics of tubercles in distribution pipelines, J AWWA,
1980(11): 626-635
[50]Chen X, Stewart P S, Chlorine penetration into artifical biofilm is
limited by a reaction-diffusion interaction, Environmental Science
and Technology, 1996(6): 2078-2083
业出版社，1993
[2] 姚志麟等，环境卫生学，1994，人民卫生出版社，109－110
[3] Grayman W M, Clark R M, Males R M, Modeling distribution system
water quality: dynamic approach[J], J water resource planning and
management,1998,114(3):295-312
[4] Clark R M, Developing and applying the water supply simulation
model[J], J AWWA, 1986, 78(8): 929-943
[5] Males R M, Clark R M, Wehrman P J, et al. Algorithm for mixing
problems in water systems[J], J Hydraulic engineering, 1985,111(2):
206-219
[6] Lious C P, Kroon J R, Modeling the propagation of waterborne
substances in distribution networks[J], AWWA, 1987,79(11): 54-58
[7] Rossman L A, Paul F Boulo, Tom Altman, Discrete volume-element
method for network water-quality models[J], Journal of water
resource planning and management, 1993, 119(5): 32-40
[8] Chaudhry M H, Islam M R, Water quality modeling in pipe
networks[M], 1995, Netherlard: Improving Efficiency and Reliability
in Water Distribution Systems, Kluwer Academic publishers
[9] Levis A Rossman, Robert M Clark, Walter M Grayman, Modeling
chlorine residual in drinking water distribution systems[J], Journal of
Environment Engineering, 1994, 120(4): 86-95
[10]Rodriguez M J, West J R, Powell J, et al, Application of two
approaches to model chlorine residuals in Severn Trent Ltd(STD)
distribution systems[J], Water Science and Technology, 1997, 36(5):
317-324
[11]B Coulbeck, Computer applications in water supply, 1988, New York
N Y: Research Studies Press, John and Sons
[12]Elaine C, Sodowski, Computer-generated optimal pumping schedules,
J AWWA, 1995(7)
[13]王占生、刘文君，微污染水源饮用水处理，北京：中国建筑工业出
版社，1999，244－247
66
参考文献
[14]徐洪福，城市供水管网水质变化规律与控制措施研究：[博士学位
论文]，哈尔滨，哈尔滨工业大学，2003
[15]同济大学主编，给水工程，中国建筑工业出版社，1980
[16]王权，郑传林，给水处理中加氯量的影响因素，山东建筑工程学院
学报，2000，15（1）：34－36
[17]张明浩，高松，生活饮用水加氯消毒工艺中几项主要影响因素的讨
论和综合控制，西南给排水，2000，第 4 期：7－10
[18]丁英锋，王启山，自来水加氯消毒副产物及其前体物（THMFP）
的研究与发展，天津城市建设学院学报，2001，7（2）：128－131
[19]J J ROOK, Haloforms in drinking water, J AWWA, 1976(3): 168
[20]U S National Cancer Institute, Report on Carcinogenicity Bioassary
of Chloroform, 1976, (5)
[21]Slnger P C, Humic Substances as precursors for potentially harmful
disinfection by－products[J], Water Science and Technology, 1999,
40(9): 25-30
[22]Steven C Allgier et al, Evaluating NF for DBP Control with the BSMT,
J AWWA, 1995
[23]张晓健，李爽，消毒副产物总致癌风险的首要指标参数——卤乙酸，
给水排水，2000，26（8）：l－6
[24]李爽、张晓健，两个中心城市饮用水中消毒副产物的调查，中国给
水排水，2000，26（8）：l－5
[25]张绍园，姜兆春，王菊思，饮用水消毒副产物控制技术研究现状与
发展，水处理技术，1998，24（1）：7－13
[26]陶建科，火正红，给水管网建模中建立计算机供水系统管网图形和
在地形图上划定节点流量区域的方法，给水排水，23（6）：5－8
[27]杜晓明，刘遂庆，利用营业抄表用水量，计算给水管网节点流量的
方法，城市公用事业，2003，17（2）：14－17
[28]陈涛、张国亮，化工传递过程基础，北京：化学工业出版社，2002，
205－267
[29]王运东、骆广生、刘谦，传递过程原理，北京：清华大学出版社，
2002，60－98
[30]周建华、赵洪宾、薛罡，配水管网中与有机物反应的余氯衰减动力
学模型，环境科学，2003，24（3）：45－49
[31]徐成贤，陈志平，李乃成，近代优化方法，北京：科学出版社，2002，
211－222
67
参考文献
[32]李冲，王兴华，求解一类非光滑优化问题的 Gauss－Newton 法，
自然科学进展，2000，10（4）：372－374
[33]Womersley R S, Local properties of algorithms minimizing
nonsmooth composite functions, Mathematical Programming, 1985,
32: 69
[34]Jittomtrum K, Osbome M R, Strong uniqueness and second order
convergence in nonlinear discrete approximation, Numerische
Mathematik, 1980, 34: 439
[35]Burke J V, Ferris M C, A Gauss-Newton method for convex composite
optimization, Mathematical Programming, 1995, 71: 179
[36]齐晶瑶，李欣，关于供水管道内余氯消耗机理的探讨，给水排水，
2000，26（8）：66－69
[37]李欣，宋学峰，配水管网水质变化的研究（Ⅱ）——余氯消耗动力
学机制的研究，哈尔滨建筑大学学报，1999，32（3），52－56
[38]国家环境保护总局编，水和废水监测分析方法，北京：中国环境科
学出版社，2002，170
[39]吴育华，杜纲，管理科学基础，天津：天津大学出版社，2001，49
－54
[40]《运筹学》教材编写组编，运筹学，北京：清华大学出版社，1996，
124－128
[41]Rhodes Trussell R, Safeguarding distribution system integrity, J
AWWA, 1999, 91(1): 52
[42]黄晓东，王占生，饮用水消毒的若干技术问题探讨，上海环境科学，
2002，21（2）：116－117
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