Determination of the optimal location of wells in aquifers with an accurate simulation-optimization model based on the meshless local Petrov-Galerkin

  • Ali Mohtashami
  • Seyed Arman Hashemi MonfaredEmail author
  • Gholamreza Azizyan
  • Abolfazl Akbarpour
Original Paper


In this research, a simulation-optimization model is utilized to determine the optimum location of wells on two unconfined aquifers (steady condition and transient state) with different boundary conditions. Meshless local Petrov-Galerkin (MLPG) and particle swarm optimization (PSO) are employed for the simulation model and optimization algorithm, respectively. MLPG model is first verified by comparing results with analytical and finite difference solutions. The obtained results from MLPG show more accuracy than FDM. In PSO, the objective function is defined as the summation of the absolute difference between water table before and after extraction in each node. In the first aquifer, results show that the content of objective function before using simulation-optimization model is 61 m; however, it reaches 17 m when the optimal location is selected. The value of objective function after using simulation-optimization model has 27% reduction in value. The second aquifer has ten extraction wells and investigated in two cases with different boundary conditions. In both cases, the value of objective function is decreased significantly after applying SO model.


Optimal location of wells Meshless local Petrov-Galerkin Particle swarm optimization Unconfined aquifers 


  1. Akbari A, Bagri RA, Bordas SPA, Rabczuk T (2010) Analysis of ThermoelasticWaves in a two-dimensional functionally graded materials domain by the Meshless local Petrov-Galerkin (MLPG) method. Comput Model Eng Sci 65(1):27–74Google Scholar
  2. Al-Naeem A (2014) Effect of excess pumping on groundwater salinity and water level in hail region of Saudi Arabia. Res J Environ Toxicol 8(3):124–135CrossRefGoogle Scholar
  3. Atluri SN, Zhu TA (1998) A new MEshless method (MLPG) approach in computational mechanics. Comput Mech 22(2):117–127CrossRefGoogle Scholar
  4. Atluri SN, Zhu TL (2000) The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics. Comput Mech 25:169–179CrossRefGoogle Scholar
  5. Ayvaz MT (2009) Application of harmony search algorithm to the solution of groundwater. Adv Water Resour 32:916–924CrossRefGoogle Scholar
  6. Ayvaz MT, Karahan H (2008) Simulation/optimization model for the identification of unknown groundwater well locations and pumping rates. J Hydrol 257:76–92CrossRefGoogle Scholar
  7. Bartolino J, Cunningham WL (2003) Ground-water depletion across the nation, USGSGoogle Scholar
  8. Bear J (1979) Hydraulics of groundwater, the University of Michigan. McGraw-Hill International Book CoGoogle Scholar
  9. Belytschko T, Lu YY, Gu L (1994) Elements free Galerkin methods. Int J Numer Methods Eng 30(2):229–256CrossRefGoogle Scholar
  10. Blaszyk T, Gorski J (1981) Ground-water quality changes during exploitation. Groundwater 19:28–33CrossRefGoogle Scholar
  11. Boddula Swathi, T.I. Eldho, (2014) Groundwater flow simulation in unconfined aquifers using meshless local Petrov–Galerkin method. Engineering Analysis with Boundary Elements 48:43-52CrossRefGoogle Scholar
  12. Cyriac R, Rastogi AK (2016) Optimization of pumping policy using coupled finite element-particle swarm optimization modelling. ISH J Hydraul Eng 22(1):88–99CrossRefGoogle Scholar
  13. Duouit J (1863) Estudes Theoriques et Pratiques sur le Mouvement desEaux. Dunod, ParisGoogle Scholar
  14. El-Ghandour HA, Elsaid A (2013) Groundwater management using a new coupled model of flow analytical solution and particle swarm optimization. Int J Water Resour Environ Eng 5(1):1–11CrossRefGoogle Scholar
  15. Elsheikh WHY, Shigidi AMT (2018) OPTIMIZATION OF PUMPING FROM AL-SIDIR WELLFIELD, BARA AQUIFER, 2nd conference of civil engineering, SudanGoogle Scholar
  16. Ganji Khorramdel N, Mohammadi K, Monem MJ (2008) Optimization of observation well network for the estimation of groundwater balance using double water table fluctuation method. J Water Soil 22(2):359–370Google Scholar
  17. Gaur S, Chahar BR, Graillot D (2011) Analytic elements method and particle swarm optimization based simulation–optimization model for groundwater management. J Hydrol 402:217–227CrossRefGoogle Scholar
  18. Ghaseminijad A, Shourian M (2019) A simulation–optimization approach for optimal design of groundwater withdrawal wells’ location and pumping rateconsidering desalination constraints. Environ Earth Sci 78:270–281CrossRefGoogle Scholar
  19. Gill MK, Kaheil YH, Khalil A, McKee M, Bastidas L (2006) Multiobjective particle swarm optimization for parameter estimation in hydrology. Water Resour Res 42(7)Google Scholar
  20. Gou X, Hu T, Wu C, Zhang T, Lv Y (2013) Multi-objective optimization of the proposed multi-reservoir operating policy using improved NSPSO. Water Resour Manag 27:2137–2153CrossRefGoogle Scholar
  21. Hamraz BS, Akbarpour A, Pourreza Bilondi M, Sadeghi Tabas S (2015) On the assessment of ground water parameter uncertainty over an arid aquifer. Arab J Geosci 8(12):10759–10773CrossRefGoogle Scholar
  22. Izady A, Abdalla O, Joodavi A, Chen M (2017) Groundwater Modeling and Sustainability of a Transboundary Hardrock–Alluvium Aquifer in North Oman Mountains. Water 9(3):161CrossRefGoogle Scholar
  23. Izquierdo J, Montalvo I, Pérez R, Tavera M (2008) Optimization in water systems: a PSO approach, in Proceedings of the 2008 Spring simulation multiconferenceGoogle Scholar
  24. Joodavi A, Zare M, Mahootchi M (2015) Development and application of a stochastic optimization model for groundwater management: crop pattern and conjuctive use consideration. Stoch Environ Res Risk Assesss 29(6):1637–1648CrossRefGoogle Scholar
  25. Kennedy J, Eberhart R (1995) Particle swarm optimization, in Proceeding of IEEE Intenational Conference on neural networksGoogle Scholar
  26. Ketabchi H, Ataie-Ashtiani B (2015) Assessment of a parallel evolutionary optimization approach for efficient management of coastal aquifers. Environ Model Softw 74:21–38CrossRefGoogle Scholar
  27. Kulkarni NH (2015) Numerical simulation of groundwater recharge from an injection well. Int J Water Resour Environ Eng 7(5):75–83CrossRefGoogle Scholar
  28. Kumar N, Reddy J (2007) Multipurpose reservoir operation using particle swarm optimization. J Water Resour Plan Manag 133:192–201CrossRefGoogle Scholar
  29. Liu G (2002) Mesh free methods: moving beyond the finite element method. CRC press, Boca RatonCrossRefGoogle Scholar
  30. Liu GR, Gu YT (2005) An introduction to Meshfree methods and their programming. Springer, SingaporeGoogle Scholar
  31. Mategaonkar Meenal, T. I. Eldho, (2011a) MESHLESS POINT COLLOCATION METHOD FOR 1D AND 2D GROUNDWATER FLOW SIMULATION. ISH Journal of Hydraulic Engineering 17 (1):71-87CrossRefGoogle Scholar
  32. Mategaonkar Meenal, T.I. Eldho, (2011b) Simulation of groundwater flow in unconfined aquifer using meshfree point collocation method. Engineering Analysis with Boundary Elements 35 (4):700-707CrossRefGoogle Scholar
  33. McKinney D, Lin M (1994) Genetic algorithm solution of groundwater management models. Water Resour Manag 30:1897–1906CrossRefGoogle Scholar
  34. Mohtashami A, Akbarpour A, Mollazadeh M (2017a) Development of two dimensional groundwater flow simulation model using meshless method based on MLS approximation function in unconfined aquifer in transient state. J Hydroinf 19(5):640–652CrossRefGoogle Scholar
  35. Mohtashami A, Akbarpour A, Mollazadeh M (2017b) Modeling of groundwater flow in unconfined aquifer in steady state with meshless local Petrov-Galerkin. Modares Mech Eng 17(2):393–403Google Scholar
  36. Mohtashami A, Hashemi Monfared SA, Azizyan G, Akbarpour A (2019) Determination the capture zone of wells by using meshless local Petrov-Galerkin numerical model in confined aquifer in unsteady state( case study: Birjand aquifer). Iranian J Ecohydrol 6(1):239–255Google Scholar
  37. Mollazadeh M, Barani G A, Rasouli A (2008) Optimiztion the shape of gravity dams using particle swarm optimization, in 6th of Iranian hydraulic conference, ShahrekordGoogle Scholar
  38. Saadatpour M, Afshar A (2013) Multi objective simulation-optimization approach in pollution spill response management model in reservoirs. Water Resour Manag 27:1851–1865CrossRefGoogle Scholar
  39. Sadeghi Tabas S, Akbarpour A, Pourreza Bilondi M, Samadi SZ (2015) Application of cuckoo optimization algorithm in automatic calibration of aquifer hydrodynamic parameters using mathematical model. Iranian J Irrig Drain 9(2):345–356Google Scholar
  40. Sadeghi Tabas S, Samadi SZ, Akbarpour A, Pourreza Bilondi M (2016) Sustainable groundwater modeling using single-and multi-objective optimization algorithm. J Hydroinf 18(5):1–18Google Scholar
  41. Saeedpanah I, Samsami-Khodadad H (2015) Numerical simulation of groundwaters flow by using analytical particle, in 8th National Congress of civil engineering, BabolGoogle Scholar
  42. Stacey A, Jancic M, Grundy I (2003) Particle swarm optimization with mutation, in Congress on Evolutionary ComputationGoogle Scholar
  43. Tissa HI, Doll P (1989) A discrete kernel method of Charactristic model of solute transport in water table Aqufers. Water Resour Manag 25(5):857–867Google Scholar
  44. Vrugt JA, Robinson BA (2007) Improved evolutionary optimization from genetically adaptive multimethod search. PNAS Proc Natl Acad Sci U S A 104(3):708–711CrossRefGoogle Scholar
  45. Zambrano-Bigiarini M, Rojas R (2006) A model-independent particle swarm optimisation software for model calibration. Environ Model Softw 43:5–25CrossRefGoogle Scholar
  46. Zhang Z, Jiang Y, Zhang S, Geng S, Wang H, Sang G (2014) An adaptive particle swarm optimization algorithm for reservoir operation optimization. Appl Soft Comput 18:167–177CrossRefGoogle Scholar

Copyright information

© Saudi Society for Geosciences 2020

Authors and Affiliations

  • Ali Mohtashami
    • 1
  • Seyed Arman Hashemi Monfared
    • 2
    Email author
  • Gholamreza Azizyan
    • 3
  • Abolfazl Akbarpour
    • 4
  1. 1.Faculty of EngineeringUniversity of Sistan and BaluchestanZahedanIran
  2. 2.Civil Engineering DepartmentUniversity of Sistan and BaluchestanZahedanIran
  3. 3.Civil Engineering DepartmentUniversity of Sistan and BaluchestanZahedanIran
  4. 4.Civil Engineering DepartmentUniversity of BirjandBirjandIran

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