Optimal Scheduling of Booster Disinfection in Water Distribution Systems
Publication: Journal of Water Resources Planning and Management
Volume 124, Issue 2
Abstract
Booster disinfection is the addition of disinfectant at locations distributed throughout a water distribution system. Such a strategy can reduce the mass of disinfectant required to maintain a detectable residual at points of consumption in the distribution system, which may lead to reduced formation of disinfectant by-products in particular trihalomethanes. Here an optimization model is formulated for the dynamic schedule of disinfectant injections; this schedule minimizes the total dose required to satisfy residual constraints over an infinite-time horizon. This infinite-time problem is reduced to a solvable finite-time optimal scheduling model by assuming periodicity of mass injections and network hydraulics. Furthermore, this model is linear since the principle of linear superposition is shown to apply to disinfectant concentrations resulting from multiple disinfectant injections over time. A matrix generator code was developed to interface with the EPANET network water quality model. This code automatically generates the linear programming formulation of the optimal scheduling model, which is then solved using the simplex algorithm. Results from application of the model suggest that booster disinfection can reduce the amount of disinfectant required to satisfy concentration constraints, when compared to conventional disinfection only at the source. The optimal booster schedule reduced the average disinfectant concentration within the distribution system and, in some cases, the variability of these concentrations. The number of booster stations, booster location, and distribution system hydraulics were shown to affect the optimal schedule.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ahlfeld, D. P., and Heidari, M.(1994). “Applications of optimal hydraulic control to groundwater systems.”J. Water Resour. Plng. and Mgmt., ASCE, 120(3), 350–365.
2.
Biswas, P., Lu, C., and Clark, R. M.(1993). “Chlorine concentration decay in pipes.”Water Res., 27(12), 1715–1724.
3.
Boccelli, D. L., Tryby, M. E., Koechling, M. T., Uber, J. G., and Summers, R. S. (1997). “Bulk decay kinetics of rechlorinated water.”Proc., 1997 Annu. Conf.mdashVol. C, American Water Works Association, Denver, Colo., 357–374.
4.
Boulos, P. F., Altman, T., Jarrige, P., and Collevati, F.(1995). “Discrete simulation approach for network–water-quality models.”J. Water Resour. Plng. and Mgmt., ASCE, 121(1), 49–60.
5.
Bull, R. J., and Kopfler, R. C. (1991). Health effects of disinfectants and disinfection by-products. American Water Works Association Research Foundation, Denver, Colo.
6.
Charnes, A., and Cooper, W. W.(1959). “Chance-constrained programming.”Mgmt. Sci., 6(1), 73–79.
7.
Chow, V. T., Maidment, D. R., and Mays, L. W. (1988). Applied hydrology. McGraw-Hill Book Co. Inc., New York, N.Y., 204–213.
8.
Clark, R. M., Grayman, W. M., Males, R. M., and Hess, A. F.(1993). “Modeling contaminant propagation in drinking water distribution systems.”J. Envir. Engrg., ASCE, 119(2), 349–364.
9.
Ellis, H., and Bowman, M. L.(1994). “Critical loads and development of acid rain control options.”J. Envir. Engrg., ASCE, 120(2), 273–290.
10.
Gorelick, S. M.(1983). “Review of distributed parameter groundwater management modeling methods.”Water Resour. Res., 19(2), 305–319.
11.
Grayman, W. M., and Clark, R. M.(1993). “Using computer models to determine the effect of storage on water quality.”J. AWWA, 85(7), 67–77.
12.
Grayman, W. M., Clark, R. M., and Males, R. M.(1988). “Modeling distribution-system water quality: dynamic approach.”J. Water Resour. Plng. and Mgmt., ASCE, 114(3), 295–312.
13.
Grayman, W. M., Deininger, R. A., Green, A., Boulos, P. F., Bowcock, R. W., and Godwin, C. C.(1996). “Water quality and mixing models for tanks and reservoirs.”J. AWWA, 88(7), 60–73.
14.
Hillier, F. S., and Lieberman, G. J. (1980). Introduction to operations research. Holden-Day, Inc., Oakland, Calif., 68–91.
15.
Liou, C. P., and Kroon, J. R.(1987). “Modeling the propagation of waterborne substances in distribution networks.”J. AWWA, 79(11), 54–58.
16.
Luenberger, D. G. (1979). Introduction to dynamic systems: theory, models, and applications. John Wiley & Sons, Inc., New York, N.Y., 108–121.
17.
Matalas, N. C., and Fiering, M. B. (1977). “Water-resource systems planning.”Climate, climatic change, and water supply, National Academy of Sciences, New York, N.Y., 99–110.
18.
Murtagh, B. (1981). Advanced linear programming: computation and practice. McGraw-Hill International, New York, N.Y.
19.
Murtagh, B. A., and Saunders, M. A. (1987). Minos 5.1 user's guide. Stanford Optimization Lab., Stanford University, Stanford, Calif.
20.
Oppenheim, A. V., and Willsky, A. S. (1997). Signals and systems, 2nd Ed., Prentice-Hall, Inc., Englewood Cliffs, N.J., 77–90.
21.
Rao, H. S., and Bree, D. Jr.(1977). “Extended period simulation of water systems—part A.”J. Hydr. Div., ASCE, 103(2), 97–108.
22.
Revelle, C. S., Loucks, D. P., and Lynn, W. R. (1967). “A management model for water quality control.”J. Water Pollution Control Fedn., 39(6).
23.
Revelle, C. S., Loucks, D. P., and Lynn, W. R.(1968). “Linear programming applied to water quality management.”Water Resour. Res., 4(1), 1–9.
24.
Rossman, L. A. (1993). EPANET users manual. Risk Reduction Engrg. Lab., U.S. Environmental Protection Agency, Cincinnati, Ohio.
25.
Rossman, L. A., and Boulos, P. F.(1996). “Numerical methods for modeling water quality in distribution systems: a comparison.”J. Water Resour. Plng. and Mgmt., ASCE, 122(2), 137–146.
26.
Rossman, L. A., Boulos, P. F., and Altman, T.(1993). “Discrete volume-element method for network water-quality models.”J. Water Resour. Plng. and Mgmt., ASCE, 119(5), 505–517.
27.
Rossman, L. A., Clark, R. M., and Grayman, W. M.(1994). “Modeling chlorine residuals in drinking-water distribution systems.”J. Envir. Engrg., ASCE, 120(4), 803–820.
28.
Seborg, D. E., Edgar, T. F., and Mellichamp, D. A. (1989). Process dynamics and control. John Wiley & Sons, Inc., New York, N.Y., 224–245.
29.
Uber, J. G., Brill, E. D. Jr., and Pfeffer, J. T.(1992). “Use of mathematical programming methods for complex systems.”J. Water Resour. Plng. and Mgmt., ASCE, 118(3), 281–294.
30.
Wagner, H. M. (1969). Principles of operations research with applications to managerial decisions. Prentice-Hall, Inc., Englewood Cliffs, N.J., 361–365.
31.
Watkins, D. W. Jr., and McKinney, D. C. (1977). `'Finding robust solutions to water resources problems.”J. Water Resour. Plng. and Mgmt., ASCE, 123(1), 49–58.
32.
Zierolf, M. L., Polycarpou, M. M., and Uber, J. G. (1998). “Development and auto-calibration of an input-output model of chlorine transport in drinking water distribution systems.”IEEE Trans. on Control Sys. Technol., 6(2).
Information & Authors
Information
Published In
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Mar 1, 1998
Published in print: Mar 1998
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.