Optimal ground-water remediation with well location as a decision variable: Model development

A new formulation for the optimal design of aquifer remediation strategies is presented in which the well location problem is solved by explicitly incorporating the spatial coordinates and pumping rates of wells as decision variables. The Hermite interpolation function is used to represent the well location as a continuous function of space and to facilitate the incorporation of a barrier function for containing the well location within the model domain. The management model combines the numerical simulation of ground-water flow and contaminant transport with optimization methods to select the optimal location and pump rate by moving each well within the problem domain unrestricted by nodal location. The details of the numerical implementation required to incorporate well locations as decision variables in a two-dimensional Galerkin finite element discretization of the ground-water flow and contaminant transport equations are presented. The approach is contrasted with an optimization model for ground-water quality management in which optimal well locations are chosen from a number of preselected candidate locations. A simple hypothetical problem is solved to compare these two approaches and examine the numerical behaviour of the new formulation. The results indicate that a formulation in which well location is a decision variable can be implemented and that improved solutions are possible. The results are also used to demonstrate how this approach can be used to solve problems in which the initial costs of well installation are included.