Simplifications in modeling seawater intrusion: validity and scope

Abstract

Modeling seawater intrusion has evolved from a tool for understanding to a water management need, but it remains a challenge. Inherent difficulties of solute transport modeling (e.g., assessment of dispersion coefficients; three-dimensional complexity of aquifer geometries and heterogeneity in hydraulic parameters) are combined with the concentration dependence of density. This dependence causes flow and transport to become coupled and the resulting problem non-linear. Irregular patterns of salinity may be caused by many factor such as variable thickness formations, heterogeneity and variations in the depth of the aquifer boundaries, among others. In homogeneous aquifers where the horizontal extend is large compared to the constant thickness, aquifer topography may become critical. The effective gravity is controlled by the boundaries slope and shape. When the lateral slope is large, vertical flow can become of lesser order compared to the lateral flow. The lateral slope leads to a dramatic increase in seawater penetration, caused by the development of sub-horizontal seawater convection cells. These effects can be quantified by means of a lateral buoyancy dimensionless number. Since the main component of flow is horizontal, one would expect vertical flux to be of subleading order and thus negligible. Unfortunately, vertical fluxes produce mixing mechanisms that are lost in the simplified 2D areal model. This causes discrepancies between the results of 3D and 2D areal models. These mechanisms can be approximated by an additional term in the dispersion tensor that arises from vertical integration of the original 3D governing equations. The resulting 2D model approximates the 3D dynamics with satisfactory results.