Optimal management of a regional aquifer under salinization conditions

Salinization of an aquifer results from the movement and dispersion of sali ne water bodies within it and/or from inflow of saline waters across bounda ries, including through recharge. Salinity does not exceed a few thousand p arts per million, so the effects of density on the flow can be neglected. T he objective of management is to maximize the net benefit from the water ex tracted subject to constraints on the amount of salt taken out with the wat er. The management model presented in this paper contains simulation of flo w and transport of salinity, developed for a two-dimensional essentially ho rizontal confined aquifer, linked to a nonsmooth optimization algorithm. Th e simulator is based on a finite element formulation, in which the convecti ve term is treated by the streamline-upwind Petrov-Galerkin (SUPG) method. SUPG is shown to reduce substantially the oscillations present in conventio nal finite element solutions of the transport equation, especially when the advective term dominates. The derivatives of the dependent variables, head s and concentrations at points in the field, with respect to the decision v ariables, the pumping rates, are computed in the simulator, using analytica l expressions based on sensitivity theory. These derivatives are transmitte d to the optimization algorithm, which uses the bundle-trust method for non smooth optimization. Application to a synthetic aquifer is demonstrated and analyzed.