Multi-Objective Optimization of Pumping Rates and Well Placement in Coastal Aquifers

Abstract

Saltwater intrusion, which is commonly associated with extensive groundwater extraction, is an important problem for coastal regions. To avoid saltwater intrusion and maintain the integrity of coastal aquifers, proper management of groundwater supplies is necessary. In this study, which includes the research results of phase one of our two phase research program, 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 interative sub-domain method, in which the 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. In the proposed approach, sharp interface solution for homogenous steady state problem is used along with the Dupuit and Ghyben-Herzberg assumptions. The analytical solution developed follows the single-potential theory concept introduced by Strack [1976]. Using this approach, the direct method of searching for saltwater intrusion points is formulated by comparing the location of the stagnation points of flow fields, and the saltwater intrusion profiles obtained from the single-potential theory solution. These critical conditions are incorporated into the formulation as the constraints of the problem. The search for the optimal solution, within each sub-domain, is conducted using Genetic Algorithm (GA). 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. The efficiency of the optimization process is improved by solving the problem through a sub-domain perturbation approach. 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., [2000], with the proposed approach yielding higher pumping rates than was reported in their study. The sequential use of multi-objective criteria, with pre-selected weights, successfully demonstrates the capability of the model to achieve two objectives simultaneously. This approach provides cost effective solutions to an important management problem in coastal aquifers. In phase two of the proposed research program, 3-D density dependent models will be solved to evaluate saltwater intrusion problem. The optimization algorithm developed in this study will be coupled to the 3-D models to determine the optimal solutions in a similar manner.