Accidental or intentional contamination of water distribution systems by chemical and biological agents can pose significant health risks to consumers, as well as have social and economic impacts. Several researchers have proposed the development of early-warning detection systems based on an installed sensor network within the distribution system. However, detecting the presence of a contaminant is only a part of the overall contamination problem. Adequate emergency response mechanisms must also be developed in conjunction with these early-warning systems, which include detailed cleanup and control strategies to return the water distribution system to an operational state. We have been working actively with researchers at Sandia National Laboratories and engineers at PUB Singapore to develop an integrated optimal response management package for protection of water distribution systems based on a series of mixed-integer programming formulations.
Here, we present large-scale mixed-integer linear program (MILP) formulations for performing optimal emergency response techniques. Various techniques are studied such as performing source inversion, obtaining optimal locations for additional manual sampling, choosing optimal placement of booster stations for rapid distribution of useful chemical agents, and evaluating network flushing techniques for removing unwanted agents.
In previous work, we focused on the development of effective source inversion techniques, including mixed-integer formulations for optimal manual sampling. In this present research, we have developed a mixed integer linear programming formulation for optimal placement of chlorine booster stations considering uncertainty. This produces a large-scale stochastic programming formulation with discrete decisions for booster station placement, and hundreds of thousands of scenarios for different potential realizations of contamination locations and times. This formulation presents two significant challenges. First, calculating all of the contamination scenarios can be time consuming, and we have developed a novel water quality model that scales exceptionally well to large networks, allowing for efficient solution of large sets of scenarios. The accuracy and computational complexity of this model is compared against existing water quality simulation tools. Second, the solution of such a large-scale mixed-integer linear programming problem can be very difficult. In this particular problem formulation, and based on certain scenario parameters, we show that a large number of the scenarios can be collapsed into several blocks, yielding an exact mathematical formulation with a tractable number of explicit scenarios. These two techniques allow for efficient formulation and solution of this challenging problem.
These tools have been integrated within a software framework for optimal response management of contamination events. The effectiveness of this package is demonstrated on two real-world water distribution networks, including a large-scale network model with approximately 13,000 nodes.
Sandia National Laboratories is a multi-program laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.