Vertical average for modeling seawater intrusion

Abstract

Seawater intrusion in coastal aquifers is a 3‐D phenomenon. However, 3‐D regional aquifer models are often limited by insufficient geological and hydrological data, the large horizontal to vertical scales ratio, and by numerical constraints. We present an effective formulation for modeling seawater intrusion that relies on a dimensional reduction of the original density‐dependent flow and transport problem. We carry out a vertical integration of the 3‐D problem and arrive at a coupled set of 2‐D equations for the mean flux and salt concentration, which are essentially identical to those of 2‐D groundwater flow. However, two new terms emerge from the integration: (1) Darcy's law needs not only the buoyancy term reflecting aquifer bottom slope, but also another one reflecting variability of aquifer thickness; and (2) transport requires a new term reflecting vertical variations of groundwater flux, which are essential for density‐dependent flow and we approximate by means of a Fickian dispersion term. The proposed equations are verified by direct steady state numerical simulations of confined aquifers. The results show that the effective formulation correctly reflects the effective dynamics in the 3‐D system.