A correction factor to account for mixing in Ghyben-Herzberg and critical pumping rate approximations of seawater intrusion in coastal aquifers

Abstract

The classic Ghyben-Herzberg estimate of the depth of the freshwater-saltwater interface together with the Dupuit approximation is a useful tool for developing analytical solutions to many seawater intrusion problems. On the basis of these assumptions, Strack (1976) developed a single-potential theory to calculate critical pumping rates in a coastal pumping scenario. The sharp interface assumption and, in particular, this analytical solution are widely used to study seawater intrusion and the sustainable management of groundwater resources in coastal aquifers. The sharp interface assumption neglects mixing and implicitly assumes that salt water remains static. Consequently, this approximation overestimates the penetration of the saltwater front and underestimates the critical pumping rates that ensure a freshwater supply. We investigate the error introduced by adopting the sharp interface approximation, and we include the effects of dispersion on the formulation of Strack (1976). To this end, we perform numerical three-dimensional variable density flow simulations. We find that Strack's equations can be extended to the case of mixing zone if the density factor is multiplied by an empirically derived dispersion factor [1 - (α T/b′)1/6], where αT is transverse dispersivity and b' is aquifer thickness. We find that this factor can be used not only to estimate the critical pumping rate but also to correct the Ghyben-Herzberg estimate of the interface depth. Its simplicity facilitates the generalization of sharp interface analytical solutions and good predictions of seawater penetration for a broad range of conditions. Copyright 2011 by the American Geophysical Union.