Climate Change and its effects in water scarcity has become an important challenge for cities with water management problems. These problems require an integral planning of the city, which can be supported by optimization. The main goal of the research is to provide a regional optimization model for water networks, including new treatment options. The model is formulated as a multi objective mixed integer programming problem, focused on environmental and economic impact of the network, minimizing water extracted from natural sources and total cost. The formulation is developed with the goal programming methodology. The model covers a complete existing city scale water network, including 4 different options of water reuse within the city: drinking water, fresh water, irrigation, and discharge in natural courses. The case study is Santiago, capital of Chile, which is the political, economic, and insti tutional center of Chile. If both objective functions have equal importance to configure the solution, the following ideas characterize the optimal water network: (i) it is more environmentally and economically convenient to reuse water within the network rather than recycling water to the natural source; (ii) the reuse of water is preferred in the form of irrigation and drinking qualities rather than industrial qualities to reduce transport costs, and (iii) the modification of the current treatment plants is preferred, because of the high cost of installation of new plants. An environmental and cost effective solution for Santiago, Chile, can reduce the source water extraction in 35.7%. The model can be implemented in other contexts, providing orientations to decision makers so as to plan city scale water networks with simultaneous environmental and economic considerations.
Water resource management is a crucial issue today when global warming is advancing, generating water shortages in several world countries. Mathematical and optimization tools have addressed these problems, including new alternative water sources. Water networks are designed to cover consumption. In this context, pumping is critical in modeling water networks through optimization techniques because of the nonlinear terms from the extended Bernoulli equation with the Darcy−Weisbach friction term. This paper compares four strategies to simplify these terms, focusing on the nonlinear constraints generated by the extended Bernoulli equation with the Darcy−Weisbach friction term. This equation has a significant impact on operation costs because of pumping power. The four simplification strategies were compared with a focus on (i) solution, (ii) error, and (iii) execution time. The best results were obtained with a two-stage strategy to address large MINLP multiobjective problems. This strategy is applied to a model with three objective functions (freshwater inlet, global warming potential, and total cost) to illustrate the simplification performance in a city-scale water network. The problem is focused on a case study in Santiago, Chile, and is based on a previous formulation. By solving the multiobjective problem, some results and changes in the network are obtained. When the three objective functions have all the same importance, the results show the following: (i) The current location of water treatment plants is suboptimal. (ii) Water recycling in the city is the best option, with drinking and irrigation qualities. (iii) With the optimal configuration, Santiago can reduce their water consumption by 30%, increasing the economic cost by 108% and the global warming potential by 49%. Finally, this model can be implemented in other contexts to approach nonlinearities by the extended Bernoulli equation with the Darcy−Weisbach friction term in large-scale water networks.
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