Optimizing Water Quality Treatment Levels for Water Distribution Systems under Mixing Uncertainty at Junctions
Publication: Journal of Water Resources Planning and Management
Volume 148, Issue 5
Abstract
A real-life water distribution system (WDS) contains uncertainty in numerous stages. This makes the optimal management and design of a WDS a complex problem. Water quality has also become a significant factor in the design and management of a WDS. Our objective was to incorporate water quality uncertainty in the WDS design problem. The mixing level was assumed to be uncertain and used to design the WDS such that the design was immune to the level of mixing. This method aimed to yield designs that satisfied the nodal concentration constraints irrespective of the mixing level in the junctions. Two optimization methodologies, robust optimization and info-gap decision theory combined with a cuckoo search optimization algorithm, were proposed to solve this problem. An illustrative example grid network was used to understand nonuniform mixing and explain the design methodology using both methodologies. Then these methodologies were applied to solve a similar treatment plant problem on a modified Fossolo network. The results also exhibited a significant variation in cost between complete mixing and nonuniform mixing. The WDS designs obtained from both methods were evaluated through Monte Carlo simulations.
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Data Availability Statement
All data, models, or codes that support this study’s findings are available from the corresponding author upon reasonable request.
Acknowledgments
This research was funded by the Israel Science Foundation (Grant No. 555/18).
References
Babayan, A., Z. Kapelan, D. Savic, and G. Walters. 2005. “Least-cost design of water distribution networks under demand uncertainty.” J. Water Resour. Plann. Manage. 131 (5): 375–382. https://doi.org/10.1061/(ASCE)0733-9496(2005)131:5(375).
Babayan, A. V., D. A. Savic, G. A. Walters, and Z. S. Kapelan. 2007. “Robust least-cost design of water distribution networks using redundancy and integration-based methodologies.” J. Water Resour. Plann. Manage. 133 (1): 67–77. https://doi.org/10.1061/(ASCE)0733-9496(2007)133:1(67).
Basupi, I., and Z. Kapelan. 2015. “Flexible water distribution system design under future demand uncertainty.” J. Water Resour. Plann. Manage. 141 (4): 04014067. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000416.
Ben-Haim, Y. 2006. Info-gap decision theory: Decisions under severe uncertainty. Amsterdam, Netherlands: Elsevier.
Ben-Tal, A., and A. Nemirovski. 1998. “Robust convex optimization.” Math. Oper. Res. 23 (4): 769–805. https://doi.org/10.1287/moor.23.4.769.
Bragalli, C., C. D’ambrosio, J. Lee, A. Lodi, and P. Toth. 2006. “An MINLP solution method for a water network problem.” In Proc., European Symposium on Algorithms, 696–707. Berlin: Springer.
Chung, G., K. Lansey, and G. Bayraksan. 2009. “Reliable water supply system design under uncertainty.” Environ. Modell. Software 24 (4): 449–462. https://doi.org/10.1016/j.envsoft.2008.08.007.
Ghelichi, Z., J. Tajik, and M. S. Pishvaee. 2018. “A novel robust optimization approach for an integrated municipal water distribution system design under uncertainty: A case study of Mashhad.” Comput. Chem. Eng. 110 (Feb): 13–34. https://doi.org/10.1016/j.compchemeng.2017.11.017.
Giustolisi, O., D. Laucelli, and A. F. Colombo. 2009. “Deterministic versus stochastic design of water distribution networks.” J. Water Resour. Plann. Manage. 135 (2): 117–127. https://doi.org/10.1061/(ASCE)0733-9496(2009)135:2(117).
Gupta, R., and P. R. Bhave. 2007. “Fuzzy parameters in pipe network analysis.” Civ. Eng. Environ. Syst. 24 (1): 33–54. https://doi.org/10.1080/10286600601024822.
Hart, D., J. S. Rodriguez, J. Burkhardt, B. Borchers, C. Laird, R. Murray, K. Klise, and T. Haxton. 2019. “Quantifying hydraulic and water quality uncertainty to inform sampling of drinking water distribution systems.” J. Water Resour. Plann. Manage. 145 (1): 4018084. https://doi.org/10.1061/(ASCE)WR.1943-5452.0001005.
Hipel, K. W., and Y. Ben-Haim. 1999. “Decision making in an uncertain world: Information-gap modeling in water resources management.” IEEE Trans. Syst. Man Cybern. Part C Appl. Rev. 29 (4): 506–517. https://doi.org/10.1109/5326.798765.
Ho, C. K., and S. S. Khalsa. 2008. “EPANET-BAM: Water quality modeling with incomplete mixing in pipe junctions.” In Proc., Water Distribution Systems Analysis, 1–11. Reston, VA: ASCE.
Ho, C. K., L. Orear Jr., J. L. Wright, and S. A. McKenna. 2008. “Contaminant mixing at pipe joints: Comparison between laboratory flow experiments and computational fluid dynamics models.” In Proc., 8th Annual Water Distribution Systems Analysis Symp. 2006, 1–18. Reston, VA: ASCE.
Housh, M. 2017. “Non-probabilistic robust optimization approach for flood control system design.” Environ. Modell. Software 95 (Sep): 48–60. https://doi.org/10.1016/j.envsoft.2017.05.003.
Housh, M., A. Ostfeld, and U. Shamir. 2011. “Optimal multiyear management of a water supply system under uncertainty: Robust counterpart approach.” Water Resour. Res. 47 (10): 1–15. https://doi.org/10.1029/2011WR010596.
Jung, D., G. Chung, and J. H. Kim. 2012. “Optimal design of water distribution systems considering uncertainties in demands and roughness coefficients.” In Proc., 12th Annual Conf. on Water Distribution Systems Analysis 2010, 1390–1399. Reston, VA: ASCE.
Kang, D. S., M. F. K. Pasha, and K. Lansey. 2009. “Approximate methods for uncertainty analysis of water distribution systems.” Urban Water J. 6 (3): 233–249. https://doi.org/10.1080/15730620802566844.
Kapelan, Z., A. V. Babayan, D. A. Savic, G. A. Walters, and S. T. Khu. 2004. “Two new approaches for the stochastic least cost design of water distribution systems.” Water Sci. Technol. Water Supply 4 (5–6): 355–363.
Kapelan, Z. S., D. A. Savic, and G. A. Walters. 2005. “Multiobjective design of water distribution systems under uncertainty.” Water Resour. Res. 41 (11): 1–15. https://doi.org/10.1029/2004WR003787.
Lansey, K. E., N. Duan, L. W. Mays, and Y. Tung. 1989. “Water distribution system design under uncertainties.” J. Water Resour. Plann. Manage. 115 (5): 630–645. https://doi.org/10.1061/(ASCE)0733-9496(1989)115:5(630).
Marquez Calvo, O. O., C. Quintiliani, L. Alfonso, C. Di Cristo, A. Leopardi, D. Solomatine, and G. de Marinis. 2019. “Robust optimization of valve management to improve water quality in WDNs under demand uncertainty.” Urban Water J. 15 (10): 943–952. https://doi.org/10.1080/1573062X.2019.1595673.
Naderi, M. J., and M. S. Pishvaee. 2017. “Robust bi-objective macroscopic municipal water supply network redesign and rehabilitation.” Water Resour. Manage. 31 (9): 2689–2711. https://doi.org/10.1007/s11269-017-1655-0.
Naveen Naidu, M., P. S. Boindala, A. Vasan, and M. R. R. Varma. 2020. “Optimization of water distribution networks using cuckoo search algorithm.” In Advances in intelligent systems and computing. Singapore: Springer.
Paez, N., J. Saldarriaga, and J. Bohorquez. 2017. “Water quality modeling considering incomplete mixing in extended periods.” Procedia Eng. 186 (571): 54–60. https://doi.org/10.1016/j.proeng.2017.03.207.
Pankaj, B. S., M. N. Naidu, A. Vasan, and M. R. Varma. 2020. “Self-adaptive cuckoo search algorithm for optimal design of water distribution systems.” Water Resour. Manage. 34 (10): 3129–3146. https://doi.org/10.1007/s11269-020-02597-2.
Pasha, M. F. K., and K. Lansey. 2005. “Analysis of uncertainty on water distribution hydraulics and water quality.” In Proc., 2005 World Water and Environmental Resources Congress: Impacts of Global Climate Change, 10. Reston, VA: ASCE.
Pasha, M. F. K., and K. Lansey. 2010. “Effect of parameter uncertainty on water quality predictions in distribution systems—Case study.” J. Hydroinf. 12 (1): 1–21. https://doi.org/10.2166/hydro.2010.053.
Perelman, L., M. Housh, and A. Ostfeld. 2013a. “Least-cost design of water distribution systems under demand uncertainty: The robust counterpart approach.” J. Hydroinf. 15 (3): 737–750. https://doi.org/10.2166/hydro.2013.138.
Perelman, L., M. Housh, and A. Ostfeld. 2013b. “Robust optimization for water distribution systems least cost design.” Water Resour. Res. 49 (10): 6795–6809. https://doi.org/10.1002/wrcr.20539.
Roach, T., Z. Kapelan, and R. Ledbetter. 2015. “Comparison of info-gap and robust optimization methods for integrated water resource management under severe uncertainty.” Procedia Eng. 119 (1): 874–883. https://doi.org/10.1016/j.proeng.2015.08.955.
Song, I., P. Romero-Gomez, and C. Y. Choi. 2009. “Experimental verification of incomplete solute mixing in a pressurized pipe network with multiple cross junctions.” J. Hydraul. Eng. 135 (11): 1005–1011. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000095.
Tolson, B. A., H. R. Maier, A. R. Simpson, and B. J. Lence. 2004. “Genetic algorithms for reliability-based optimization of water distribution systems.” J. Water Resour. Plann. Manage. 130 (1): 63–72. https://doi.org/10.1061/(ASCE)0733-9496(2004)130:1(63).
Wang, Q., S. Liu, H. Wang, and D. A. Savić. 2012. “Multi-objective cuckoo search for the optimal design of water distribution systems.” In Proc., 2012 Int. Conf. on Civil Engineering and Urban Planning, 402–405. Reston, VA: ASCE.
Webb, S. W., and B. G. Van Bloemen Waanders. 2007. “High fidelity computational fluid dynamics for mixing in water distribution systems.” In Proc., 8th Annual Water Distribution Systems Analysis Symp. 2006, 154. Reston, VA: ASCE.
Yang, X. S., and S. Deb. 2009. “Cuckoo search via Lévy flights.” In Proc., 2009 World Congress on Nature and Biologically Inspired Computing, NABIC 2009, 210–214. New York: IEEE.
Yu, T., L. Tao, Y. Shao, and T. Zhang. 2015. “Experimental study of solute mixing at double-tee junctions in water distribution systems.” Water Sci. Technol. Water Supply 15 (3): 474–482. https://doi.org/10.2166/ws.2014.128.
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© 2022 American Society of Civil Engineers.
History
Received: Mar 19, 2021
Accepted: Dec 29, 2021
Published online: Feb 28, 2022
Published in print: May 1, 2022
Discussion open until: Jul 28, 2022
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