Vol.:(0123456789) 1 3 Environmental Earth Sciences (2019) 78:270 https://doi.org/10.1007/s12665-019-8273-5 ORIGINAL ARTICLE A simulation–optimization approach for optimal design of groundwater withdrawal wells’ location and pumping rate considering desalination constraints Ali Ghaseminejad 1  · Mojtaba Shourian 1 Received: 6 March 2018 / Accepted: 15 April 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract In this study, a simulation–optimization approach for optimal determination of groundwater withdrawal wells location and pumping rate is developed while incorporating quantitative and water-quality objectives into the objective function simultane- ously. The proposed model integrates the groundwater fow simulation model MODFLOW and particle-swarm optimization (PSO) algorithm and is applied to Sarakhs aquifer in Iran as the case study to minimize the total cost of drilling, transfer, and water treatment. Discharges and the location of pumping wells are taken as the decision variables. In addition, the maximum pumping rate and maximum allowable water-table drawdown while meeting the required quality for domestic water are incorporated as the constraints. Results show that the proposed approach not only satisfes the constraints, but also reduces the cost of water withdrawal comparing the existing plan. Sensitivity analysis indicates that results are not signifcantly sensitive to variation in aquifer’s hydraulic conductivity, while the maximum pumping rate directly afects the number of required wells and can, therefore, make a considerable change in the fnal cost. Keywords Groundwater wells · Optimal placement and discharge · Simulation–optimization · MODFLOW · PSO Introduction Improper well location and excessive groundwater pumping can cause serious damage to the aquifer and lead to numer- ous economic consequences. One of the major problems in the management of groundwater resources is how to deter- mine the suitable number, location, and pumping rate of designing wells. These wells should be able to satisfy the agricultural, industrial, and domestic water demands. In addition, the plan also must meet the requirements of sus- tainable development and environmental standards (Elçi and Ayvaz 2014). Excessive withdrawal from wells can cause long-term drawdown of groundwater and lead to undesir- able consequences such as seepage of low-quality water into wells, reduced level of surface water resources such as rivers and lakes and ground subsidence (Conkling 1946). Drilling new wells and expansion of piping and water treatment facilities require extensive energy and fnancial resources, so determining the optimal location and pumping rate of new wells not only will satisfy water demands and environmental requirements, but will also lead to signifcant costs savings. Many examples of the use of a simulation–optimiza- tion approach in the solution of groundwater-management problems can be found in the literature. These studies difer in the numerical model used to simulate the groundwater fow system, types of algorithms used to solve optimization problems, and the kind of groundwater-management issues (Ahlfeld et al. 2005). Initial groundwater-management stud- ies based on coupled simulation–optimization models were usually performed using gradient-based optimization tech- niques. Since groundwater-management problems usually have non-convex solution spaces, application of gradient- based optimization techniques does not guarantee to fnd the optimal solutions (McKinney and Lin 1994). Therefore, evolutionary algorithms are generally more efcient for the solution of these problems. Mantoglou et al. (2004) solved a groundwater-management problem in the coastal aquifers with two non-linear and evolutionary algorithms and then compared the solutions. Their results showed that although * Mojtaba Shourian m_shourian@sbu.ac.ir 1 Department of Civil, Water and Environmental Engineering, Technical and Engineering College, Shahid Beheshti University, Tehran, Iran