Multi-objective optimization of pumping rates and well placement in coastal aquifers

Abstract

Saltwater intrusion, commonly associated with extensive groundwater extraction, is an important problem for coastal regions. In this study, we present a multi-objective optimization approach to determine pumping rates and well locations to prevent saltwater intrusion, while satisfying desired extraction rates in coastal aquifers. The proposed method is an iterative sub-domain method, in which the proposed algorithm searches for the optimal solution by perturbing the well locations and pumping rates simultaneously. The decision variables of the optimization problem are modeled as continuous independent variables. Sharp interface solution for homogenous steady state problem is used along with the Dupuit and Ghyben-Herzberg assumptions. Using this approach, the direct method of searching for saltwater intrusion points is formulated by comparing the location of the stagnation points of the flow field, and the saltwater intrusion profiles obtained from the single-potential theory solution. The search for the optimal solution, within each sub-domain, is conducted using genetic algorithm. The multi-objective problem is formulated to maximize pumping rates while minimizing the distance between critical stagnation point and the reference coastline location, such that the wells are placed as closely to the coast as possible. Several numerical experiments are conducted to evaluate the effectiveness of the proposed method. As a case study, the numerical results obtained from the proposed method are compared with the work of Cheng et al. [Water Resour. Res. 36 (2000) 2155]. This comparison yielded higher pumping rates than what was reported in their study. The sequential use of multi-objective criteria, with pre-selected weights, successfully demonstrated the capability of the model to achieve two objectives simultaneously. The proposed approach provides a cost effective solution to an important management problem in coastal aquifers.