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Minimization of Total Pumping Cost from an Aquifer to a Water Tank, Via a Pipe Network

Author

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  • N. Nagkoulis

    (Aristotle University of Thessaloniki)

  • K.L. Katsifarakis

    (Aristotle University of Thessaloniki)

Abstract

In this paper, we have investigated minimization of total cost to pump a given flow rate from any number (n) of wells up to a water tank, under steady-state flow conditions. Regarding groundwater flow, we have considered infinite or semi-infinite aquifers, to which the method of images applies. Additional regional groundwater flow can be taken into account, too. The pipe network connecting the wells to the tank can include junctions at the locations of the wells only. Moreover, all pumps have equal efficiency. We have derived a new analytical formula, which holds at the critical points of the total cost function. Based on this formula, we derived a system of n equations and n unknowns, to calculate the well flow rate combinations which correspond to the critical points of the total cost function. The n-1 equations are 2nd degree polynomials, while the remaining one is linear, expressing the constraint that the sum of well flow rates must be equal the required total flow rate. The solution of the system can be achieved using commercial solvers. Moreover, we have concluded that there is one feasible solution that minimizes the total cost. Finally, we present a tabulation process to facilitate the use of solvers and we provide and discuss two illustrative examples.

Suggested Citation

  • N. Nagkoulis & K.L. Katsifarakis, 2020. "Minimization of Total Pumping Cost from an Aquifer to a Water Tank, Via a Pipe Network," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(13), pages 4147-4162, October.
    • Handle: RePEc:spr:waterr:v:34:y:2020:i:13:d:10.1007_s11269-020-02661-x
    DOI: 10.1007/s11269-020-02661-x
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    References listed on IDEAS

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    Cited by:

    1. Nikolaos Nagkoulis & Konstantinos L. Katsifarakis, 2022. "Using Game Theory to Assign Groundwater Pumping Schedules," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(5), pages 1571-1586, March.
    2. Jimmy H. Gutiérrez-Bahamondes & Daniel Mora-Melia & Bastián Valdivia-Muñoz & Fabián Silva-Aravena & Pedro L. Iglesias-Rey, 2023. "Infeasibility Maps: Application to the Optimization of the Design of Pumping Stations in Water Distribution Networks," Mathematics, MDPI, vol. 11(7), pages 1-16, March.
    3. Bohong Wang & Yongtu Liang & Wei Zhao & Yun Shen & Meng Yuan & Zhimin Li & Jian Guo, 2021. "A Continuous Pump Location Optimization Method for Water Pipe Network Design," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(2), pages 447-464, January.

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