The Henry problem has played a key role in our understanding of seawater intrusion into coastal aquifers and in benchmarking density dependent flow codes. This paper seeks to modify Henry’s problem to ensure sensitivity to density variations and vertical salinity profiles that resemble field observations. In the proposed problem, the “dispersive Henry problem”, mixing is represented by means of the traditional Scheidegger dispersion tensor (dispersivity times water flux). Anisotropy in the hydraulic conductivity is acknowledged and Henry’s seaside boundary condition of prescribed salt concentration is replaced by a flux dependent boundary condition, which represents more realistically salt transport across the seaside boundary. This problem turns out to be very sensitive to density variations and its solution gets closer to reality. However, an improvement in the traditional Henry problem (gain in sensitivity and realism) can be also achieved if the value of the Peclet number is significantly reduced.
Although the dispersive problem lacks an analytical solution, it can shed light on flow in coastal aquifers. It provides significant information about the factors controlling seawater penetration, width of the mixing zone and influx of seawater. The width of the mixing zone depends basically on dispersion with longitudinal and transverse dispersion controlling different parts of the mixing zone but displaying similar overall effects. Toe penetration is mainly controlled by the horizontal permeability and by the geometric mean of the dispersivities. Finally, transverse dispersivity and the geometric mean of the hydraulic conductivity are the leading parameters controlling the amount of saltwater that enters the aquifer
Abstract
The Henry problem has played a key role in our understanding of [...]
The seawater intrusion process is characterized by the difference in freshwater and seawater density that causes freshwater to float on seawater. Many confined aquifers have a large horizontal extension with respect to thickness. In these cases, while buoyancy acts in the vertical direction, flow is confined between the upper and bottom boundaries and the effect of gravity is controlled by variations of aquifer elevation. Therefore, the effective gravity is controlled by the slope and the shape of the aquifer boundaries. Variability in the topography of the aquifer boundaries is one case where 3D analysis is necessary. In this work, density-dependent flow processes caused by 3D aquifer geometry are studied numerically and specifically, considering a lateral slope of the aquifer boundaries. Sub-horizontal circulation cells are formed in the saltwater entering the aquifer. The penetration of the saltwater can be quantified by a dimensionless buoyancy number that measures the lateral slope of the aquifer relative to freshwater flux. The penetration of the seawater intrusion wedge is controlled more by this slope than by the aquifer thickness and dispersivity. Thus, the slope must be taken into account in order to accurately evaluate seawater intrusion.