Optimal and Fair Distribution of Water Under Water Scarcity Scenarios at a Macroscopic Level
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RESEARCH PAPER
Optimal and Fair Distribution of Water Under Water Scarcity Scenarios at a Macroscopic Level Rogelio Ochoa‑Barragán1 · Fabricio Nápoles‑Rivera1 · José María Ponce‑Ortega1 Received: 12 June 2020 / Revised: 14 October 2020 / Accepted: 19 October 2020 © University of Tehran 2020
Abstract This paper presents an optimization approach for designing water allocation systems at macroscopic level under water scarcity conditions. The proposed approach accounts for the proper water distribution of the available sources (dams, deep wells, lakes, rivers, etc.) and the incorporation of artificial sources (rainwater harvesting systems, and recycled water) to satisfy domestic and agricultural demands in a specific region at the maximum revenue. The proposed mathematical model incorporates fair distribution schemes (Social Welfare, Rawls and Nash Schemes), which allow determining fair water distribution options under water scarcity conditions. A case study for the city of Morelia in Mexico is presented to show the applicability of the proposed optimization approach. Results show that it is possible to obtain fair solutions for the water allocation for all the users under different water scarcity conditions. Article Highlights • • • •
A mathematical model is developed for optimal water management at macroscopic level. Fair distribution schemes are proposed under water scarcity scenarios. Harvested rainwater and reclaimed water give flexibility to the water network. Results show balanced distribution under water scarcity conditions.
Keywords Distribution schemes · Optimization · Fair water allocation · Rainwater harvesting · Water reclamation List of Symbols Parameters AMax n Maximum capacity of artificial pond n Aan Available area of collection for artificial ponds in location n Asl Available area of collection for storage tanks in location l Area of collection for source i for direct ADPW i precipitation Electronic supplementary material The online version of this article (https://doi.org/10.1007/s41742-020-00297-8) contains supplementary material, which is available to authorized users. * José María Ponce‑Ortega [email protected] 1
Chemical Engineering Department, Universidad Michoacana de San Nicolás de Hidalgo, Av. Francisco J. Mújica, S/N, Ciudad Universitaria, Edificio V1, 58060 Morelia, Michoacán, México
Area of collection for source i for runoff water AROW i ASC Water sale cost for agricultural use Ces Runoff coefficient for storage tanks catchment areas Cea Runoff coefficient for artificial ponds catchment areas CTAA Treatment cost of rainwater for agricultural use CTAD Treatment cost of rainwater for domestic use CTNA Treatment cost of natural sources for agricultural use CTND Treatment cost of natural sources for domestic use CTPA Treatment cost of regenerating wastewater for agricultural use CTPE Treatment cost of wastewater before final disposal Water demand in domestic sink j at time t Dds j,t as Dh,t Water demand in agricultural sink h at time t
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