An optimization model for the allocation of water resources

Abstract

Critical water shortages, triggered by increasing demands and decreasing supplies, are growing in frequency and spatial extent pausing major challenges for water resources managers around the world. This paper presents an integer linear programming decision support model for the optimal treatment and allocation of water resources. The model seeks to minimize the total water cost which includes the economic cost of treatment and distribution, as well as the associated environmental costs. The model is unique in its ability to account for spatially distributed water supply and demand nodes, as well as multiple water supply (seawater, surface, ground and wastewater) and demand (irrigation, potable, and industrial) types and qualities. It accommodates various treatment technologies, different energy recovery levels, and resource availabilities or capacities. The optimal solution yields volumes of water transported from each supply source to each treatment plant and treated by an appropriate technology in order to satisfy multiple water demands at different required water qualities with the lowest overall economic and environmental costs. The model is applied to a case study. Results showed that the distance of brackish water sources and the environmental cost, observed in terms of carbon savings only, had limited impact on the optimal solution with the demand for the base case being met through a combination of conventional water and wastewater treatment and brackish water reverse osmosis. Sensitivity analysis is performed to determine the effects of variations in demand/supply volumes as well as variable distances and environmental cost. Sensitivity analysis showed that increased demand under limited resources can be met through the introduction of seawater desalination plants, initially through multi effect distillation combined with residual thermal energy then augmented with seawater reverse osmosis plants with further increase in demand.