In this paper, we consider the flow of fresh and saltwater in a saturated porous medium in order to describe the seawater intrusion. Starting from a formulation with constant densities respectively of fresh and of saltwater, whose velocity is proportional to the gradient of pressure (Darcy's law), we consider the formal asymptotic shallow water limit as the ratio between the thickness and the horizontal length of the porous medium tends to zero. In this limit, we derive the Dupuit-Forchheimer condition and as a consequence reduced models of Boussinesq type both in the cases of unconfined and confined aquifers.
