(346f) Solution of Large Scale Stochastic Programming Problems for Optimal Placement of Booster Stations in Water Networks
Public water distribution networks are large complex systems with many access points, leading to the potential for accidental or deliberate contamination. A fixed grid of sensors can serve as an early-warning detection system to flag a contamination in the network. The problem of optimal sensor placement within these drinking water distribution systems has been extensively studied (Berry et al. (2005b); Ostfeld and Salomons (2004a); Murray et al. (2010). After a contamination has been detected by the early-warning detection system, one probable response is to collect manual water sample for laboratory analysis. Once a contamination has been confirmed by this analysis, a no-drink order could be given. However, the laboratory analysis can take several hours or more, while the contaminant continues to spread through the network. Disinfectant booster stations can help mitigate the effect of potential contamination by injecting additional (yet safe) amounts of disinfectant immediately following the initial warning (Parks and VanBriesen, 2009). Moreover, optimal placement of these booster stations can help in efficiently reducing the impact of a contamination incident.
In this work, we present a stochastic programming formulation for optimal placement of disinfectant booster stations. The formulation considers uncertainty in both location and time of a contamination scenario. For realistic large-scale water distribution networks, with hundreds of thousands of possible contamination scenarios, the formulation results in an intractably large Mixed Integer Linear Programming (MILP) problem. Fortunately, there is tremendous symmetry in the problem structure, which can be exploited to reduce the problem size by almost 5 orders of magnitude (for a 3,000 node network). The results highlight the effectiveness of booster stations in reducing the overall impact on the population, which is measured using two different metrics – mass of contaminant consumed, and population dosed above a cumulative mass threshold. Additionally, we also study the importance of various factors that influence the performance of disinfectant booster stations. These include the number and locations of sensors, the injected contaminant and its potential to react with chlorine, the location where the contaminant is introduced, the time it takes to detect the contamination, and the time delay between detection and initiation of booster disinfection.
Berry, J. W., Fleischer, L., Hart, W. E., Phillips, C. A., and Watson, J. P. (2005b). Sensor Placement in Municipal Water Networks. Journal of Water Resources Planning and Management, 131:237.
Ostfeld, A. and Salomons, E. (2004a). Optimal Layout of Early Warning Detection Stations for Water Distribution Systems Security. Journal of Water Resources Planning and Management, 130(5):377–385
Murray, R., Haxton, T. M., Janke, R. J., Hart, W. E., Berry, J., and Phillips, C. A. (2010). Sensor Network Design for Drinking Water Contamination Warning Systems: A Compendium of Re- search Results and Case Studies using the TEVA-SPOT-Report.US Environmental Protection Agency, Washington, DC. Technical report, EPA/600/R-09/141.
Parks, S. and VanBriesen, J. (2009). Booster Disinfection for Response to Contamination in a Drinking Water Distribution System. Journal of Water Resources Planning and Management, 135:502–511.