Optimal management of a regional aquifer under salinization conditions

Salinization of an aquifer results from the movement and dispersion of saline water bodies within it and/or from inflow of saline waters across boundaries, including through recharge. Salinity does not exceed a few thousand parts per million, so the effects of density on the flow can be neglected. The objective of management is to maximize the net benefit from the water extracted subject to constraints on the amount of salt taken out with the water. The management model presented in this paper contains simulation of flow and transport of salinity, developed for a two-dimensional essentially horizontal confined aquifer, linked to a nonsmooth optimization algorithm. The simulator is based on a finite element formulation, in which the convective term is treated by the streamline-upwind Petrov-Galerkin (SUPG) method. SUPG is shown to reduce substantially the oscillations present in conventional finite element solutions of the transport equation, especially when the advective term dominates. The derivatives of the dependent variables, heads and concentrations at points in the field, with respect to the decision variables, the pumping rates, are computed in the simulator, using analytical expressions based on sensitivity theory. These derivatives are transmitted to the optimization algorithm, which uses the bundle-trust method for nonsmooth optimization. Application to a synthetic aquifer is demonstrated and analyzed.