Reclaimed water distribution network design under temporal and spatial growth and demand uncertainties

A significant-but underutilized-water resource is reclaimed water, i.e., treated wastewater that is reintroduced for various purposes. Especially in water scarce regions, reclaimed water is often the only remaining source of water to meet increasing population and water demands. In this paper, we develop a new model formulation for the cost-effective branched reclaimed water network design and solve it with an exact optimization method. We consider both construction and energy costs expended over a twenty-year period. Unlike other formulations, uncertain reclaimed water demands, temporal and spatial population changes are explicitly considered in our two-staged construction and expansion model. In order for the system to meet higher demands during the peak times and to evaluate energy use, we consider two pumping conditions: one with average demands, which is used to compute the average energy consumption, and the other with peak demands, which dominates pipe size and pump station capacity selection. By introducing binary variables that indicate discrete pipe and pump sizes, we linearize the nonlinear hydraulic equations and objective function terms. We develop methods to significantly reduce the problem dimension by exploiting the problem characteristics and network structure. Our computational results indicate that these methods are very effective. Finally, we apply our model to design a reclaimed water network for a realistic municipal system under estimated demand and population scenarios, and analyze the sensitivity of the system to model parameters.