Convex Heuristics for Optimal Placement and Operation of Valves and Chlorine Boosters in Water Networks
Publication: Journal of Water Resources Planning and Management
Volume 148, Issue 2
Abstract
This paper investigates the problem of optimal placement and operation of valves and chlorine boosters in water networks. The objective is to minimize average zone pressure while penalizing deviations from target chlorine concentrations. The problem formulation includes nonconvex quadratic terms within constraints representing the energy conservation law for each pipe, and discretized differential equations modeling advective transport of chlorine concentrations. Moreover, binary variables model the placement of valves and chlorine boosters. The resulting optimization problem is a nonconvex mixed integer nonlinear program, which is difficult to solve, especially when large water networks are considered. We develop a new convex heuristic to optimally place and operate valves and chlorine boosters in water networks, while estimating the optimality gaps for the computed solutions. We evaluate the proposed heuristic using case studies with varying sizes and levels of connectivity and complexity, including two large operational water networks. The convex heuristic is shown to generate good-quality feasible solutions in all problem instances with bounds on the optimality gap comparable to the level of uncertainty inherent in hydraulic and water quality models.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Data sets including the hydraulic models of the considered case studies are available in a repository in accordance with funder data retention policies: https://doi.org/10.17632/ws9pwxkbb2.
Acknowledgments
Filippo Pecci and Ivan Stoianov are supported by Engineering and Physical Sciences Research Council (EPSRC) (EP/P004229/1, Dynamically Adaptive and Resilient Water Supply Networks for a Sustainable Future). Avi Ostfeld is supported by the Israel Science Foundation (Grant No. 555/18).
References
Abokifa, A. A., A. Maheshwari, R. D. Gudi, and P. Biswas. 2019. “Influence of dead-end sections of drinking water distribution networks on optimization of booster chlorination systems.” J. Water Resour. Plann. Manage. 145 (12): 04019053. https://doi.org/10.1061/(ASCE)WR.1943-5452.0001125.
Abokifa, A. A., Y. J. Yang, C. S. Lo, and P. Biswas. 2016. “Water quality modeling in the dead end sections of drinking water distribution networks.” Water Res. 89 (Feb): 107–117. https://doi.org/10.1016/j.watres.2015.11.025.
Avvedimento, S., S. Todeschini, C. Giudicianni, A. Di Nardo, T. Walski, and E. Creaco. 2020. “Modulating nodal outflows to guarantee sufficient disinfectant residuals in water distribution networks.” J. Water Resour. Plann. Manage. 146 (8): 04020066. https://doi.org/10.1061/(ASCE)WR.1943-5452.0001254.
Belotti, P., J. Lee, L. Liberti, F. Margot, and A. Wächter. 2009. “Branching and bounds tightening techniques for non-convex MINLP.” Optim. Methods Software 24 (4–5): 597–634. https://doi.org/10.1080/10556780903087124.
Boccelli, D. L., M. E. Tryby, J. G. Uber, L. A. Rossman, M. L. Zierolf, and M. M. Polycarpou. 1998. “Optimal scheduling of booster disinfection in water distribution networks.” J. Water Resour. Plann. Manage. 124 (2): 99–111. https://doi.org/10.1061/(ASCE)0733-9496(1998)124:2(99).
Boyd, S., and L. Vandenberghe. 2004. Convex optimization. Cambridge, UK: Cambridge University Press.
Bragalli, C., C. D’Ambrosio, J. Lee, A. Lodi, and P. Toth. 2012. “On the optimal design of water distribution networks: A practical MINLP approach.” Optim. Eng. 13 (2): 219–246. https://doi.org/10.1007/s11081-011-9141-7.
Broad, D. R., G. C. Dandy, and H. R. Maier. 2015. “A systematic approach to determining metamodel scope for risk-based optimization and its application to water distribution system design.” Environ. Modell. Software 69 (Jul): 382–395. https://doi.org/10.1016/j.envsoft.2014.11.015.
Carrico, B. T., and P. C. Singer. 2009. “Impact of booster chlorination on THM production: A simulated analysis.” J. Environ. Eng. 135 (10): 928–935. https://doi.org/10.1061/(ASCE)0733-9372(2009)135:10(928).
Deuerlein, J. W. 2008. “Decomposition model of a general water supply network graph.” J. Hydraul. Eng. 134 (6): 822–832. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:6(822).
Eck, B. J., and M. Mevissen. 2012. Non-linear optimization with quadratic pipe friction. IBM Research Division.
Eck, B. J., and M. Mevissen. 2015. “Quadratic approximations for pipe friction.” J. Hydroinf. 17 (3): 462–472. https://doi.org/10.2166/hydro.2014.170.
Gurobi Optimization. 2020. “Gurobi optimizer 9.0 reference manual.” Accessed July 5, 2021. https://www.gurobi.com/documentation/9.0/refman/.
Hallam, N. B., J. R. West, C. F. Forster, J. C. Powell, and I. Spencer. 2002. “The decay of chlorine associated with the pipe wall in water distribution systems.” Water Res. 36 (14): 3479–3488. https://doi.org/10.1016/S0043-1354(02)00056-8.
Islam, M. R., M. H. Chaudhry, and R. M. Clark. 1999. “Inverse modeling of chlorine concentration in pipe networks under dynamic condition.” J. Environ. Eng. 125 (3): 296–298. https://doi.org/10.1061/(ASCE)0733-9372(1999)125:3(296).
Kang, D., and K. Lansey. 2010. “Real-time optimal valve operation and booster disinfection for water quality in water distribution systems.” J. Water Resour. Plann. Manage. 136 (4): 463–473. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000056.
Lambert, A., and J. Thornton. 2011. “The relationships between pressure and bursts: A state-of-the-art update.” Water 21 (Apr): 37–38.
Lansey, K., F. Pasha, S. Pool, W. Elshorbagy, and J. Uber. 2007. “Locating satellite booster disinfectant stations.” J. Water Resour. Plann. Manage. 133 (4): 372–376. https://doi.org/10.1061/(ASCE)0733-9496(2007)133:4(372).
Maier, S. H., R. S. Powell, and C. A. Woodward. 2000. “Calibration and comparison of chlorine decay models for a test water distribution system.” Water Res. 34 (8): 2301–2309. https://doi.org/10.1016/S0043-1354(99)00413-3.
Ohar, Z., and A. Ostfeld. 2014. “Optimal design and operation of booster chlorination stations layout in water distribution systems.” Water Res. 58 (Jul): 209–220. https://doi.org/10.1016/j.watres.2014.03.070.
Ostfeld, A., and E. Salomons. 2006. “Conjunctive optimal scheduling of pumping and booster chlorine injections in water distribution systems.” Eng. Optim. 38 (3): 337–352. https://doi.org/10.1080/03052150500478007.
Pecci, F., E. Abraham, and I. Stoianov. 2017. “Quadratic head loss approximations for optimisation of problems in water supply networks.” J. Hydroinf. 19 (4): 493–506. https://doi.org/10.2166/hydro.2017.080.
Pecci, F., I. Stoianov, and A. Ostfeld. 2021. “Relax-tighten-round algorithm for optimal placement and control of valves and chlorine boosters in water networks.” Eur. J. Oper. Res. 295 (2): 690–698. https://doi.org/10.1016/j.ejor.2021.03.004.
Polycarpou, M. M., J. G. Uber, Z. Wang, F. Shang, and M. Brdys. 2002. “Feedback control of water quality.” IEEE Control Syst. Mag. 22 (3): 68–87. https://doi.org/10.1109/MCS.2002.1004013.
Propato, M., and J. G. Uber. 2004a. “Booster system design using mixed-integer quadratic programming.” J. Water Resour. Plann. Manage. 130 (4): 348–352. https://doi.org/10.1061/(ASCE)0733-9496(2004)130:4(348).
Propato, M., and J. G. Uber. 2004b. “Linear least-squares formulation for operation of booster disinfection systems.” J. Water Resour. Plann. Manage. 130 (1): 53–62. https://doi.org/10.1061/(ASCE)0733-9496(2004)130:1(53).
Quilliam, R. S., M. Weidmann, V. Moresco, H. Purshouse, Z. O’Hara, and D. M. Oliver. 2020. “COVID-19: The environmental implications of shedding SARS-CoV-2 in human faeces.” Environ. Int. 140 (Apr): 105790. https://doi.org/10.1016/j.envint.2020.105790.
Rossman, L. A. 2000. EPANET 2. Washington, DC: USEPA.
Rossman, L. A., and P. F. Boulos. 1996. “Numerical methods for modeling water quality in distribution systems: A comparison.” J. Water Resour. Plann. Manage. 122 (2): 137–146. https://doi.org/10.1061/(ASCE)0733-9496(1996)122:2(137).
Sakomoto, T., M. Lutaaya, and E. Abraham. 2020. “Managing water quality in intermittent supply systems: The Case of Mukono Town, Uganda.” Water (Switzerland) 12 (3): 1–16. https://doi.org/10.3390/w12030806.
Tryby, M. E., D. L. Boccelli, J. G. Uber, and L. A. Rossman. 2002. “Facility location model for booster disinfection of water supply networks.” J. Water Resour. Plann. Manage. 128 (5): 322–333. https://doi.org/10.1061/(ASCE)0733-9496(2002)128:5(322).
Ulanicki, B., P. Bounds, J. Rance, and L. Reynolds. 2000. “Open and closed loop pressure control for leakage reduction.” Urban Water 2 (2): 105–114. https://doi.org/10.1016/S1462-0758(00)00048-0.
Waechter, A., and L. T. Biegler. 2006. “On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming.” Math. Program. 106 (1): 25–57. https://doi.org/10.1007/s10107-004-0559-y.
Waldron, A., F. Pecci, and I. Stoianov. 2019. “BWFLnet + data.” Mendeley Data. Accessed November 8, 2021. https://data.mendeley.com/datasets/srt4vr5k38/3.
Waldron, A., F. Pecci, and I. Stoianov. 2020. “Regularisation of an inverse problem for parameter estimation in water distribution networks.” J. Water Resour. Plann. Manage. 146 (9): 04020076. https://doi.org/10.1061/(ASCE)WR.1943-5452.0001273.
Walski, T. 2019. “Raising the bar on disinfectant residuals.” World Water Mag. Water Environ. Fed. 42 (4): 34–35.
Wright, R., E. Abraham, P. Parpas, and I. Stoianov. 2015. “Control of water distribution networks with dynamic DMA topology using strictly feasible sequential convex programming.” Water Resour. Res. 51 (12): 9925–9941. https://doi.org/10.1002/2015WR017466.
Yang, J. Y., J. A. Goodrich, R. M. Clark, and S. Y. Li. 2008. “Modeling and testing of reactive contaminant transport in drinking water pipes: Chlorine response and implications for online contaminant detection.” Water Res. 42 (6–7): 1397–1412. https://doi.org/10.1016/j.watres.2007.10.009.
Information & Authors
Information
Published In
Journal of Water Resources Planning and Management
Volume 148 • Issue 2 • February 2022
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Jul 9, 2021
Accepted: Oct 13, 2021
Published online: Nov 24, 2021
Published in print: Feb 1, 2022
Discussion open until: Apr 24, 2022
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.
Cited by
- Bradley Jenks, Filippo Pecci, Ivan Stoianov, Optimal design-for-control of self-cleaning water distribution networks using a convex multi-start algorithm, Water Research, 10.1016/j.watres.2023.119602, 231, (119602), (2023).
- Tomer Shmaya, Avi Ostfeld, A Graph-Theory-Based PRV Placement Algorithm for Reducing Water Age in Water Distribution Systems, Water, 10.3390/w14233796, 14, 23, (3796), (2022).
- Filippo Pecci, Ivan Stoianov, Avi Ostfeld, Optimal Design-for-Control of Chlorine Booster Systems in Water Networks via Convex Optimization, 2022 European Control Conference (ECC), 10.23919/ECC55457.2022.9838063, (1988-1993), (2022).