Abstract

In this research, a steady state analytical solution is suggested and derived for the groundwater flow equation in a homogeneous unconfined aquifer. The solution can be used for calculating the hydraulic heads in a complex flow field caused by multi injection-pumping wells having different rates in a domain subjected to a uniform recharge. The analytical method, used for flow simulation, is coupled with the Particle Swarm Optimization (PSO) method, used for optimization, to solve the groundwater management problem. A new model called Analytic-PSO, which consists of the two methods, is originally developed. The performance of the proposed model was tested on a popular hypothetical example to maximize the total pumping rate from located well system at steady state condition. The results show the superiority of the proposed model to obtain the maximum pumping rate compared with other methods of previous work. The application was extended to use the Analytic-PSO model for determination of both the optimal location and maximum pumping rate for each well for the pre-specified number of wells in the same hypothetical example. Obtained results of the hypothetical example illustrate the ability of the Analytic-PSO model to solve efficiently the groundwater management problem in the real field aquifers.

Key words: Groundwater management, analytical solution, particle swarm optimization, optimization methods, Fourier series.