Analytical solutions of seawater intrusion in sloping confined and unconfined coastal aquifers

Abstract

Sloping coastal aquifers in reality are ubiquitous and well documented. Steady state sharp‐interface analytical solutions for describing seawater intrusion in sloping confined and unconfined coastal aquifers are developed based on the Dupuit‐Forchheimer approximation. Specifically, analytical solutions based on the constant‐flux inland boundary condition are derived by solving the discharge equation for the interface zone with the continuity conditions of the head and flux applied at the interface between the freshwater zone and the interface zone. Analytical solutions for the constant‐head inland boundary are then obtained by developing the relationship between the inland freshwater flux and hydraulic head and combining this relationship with the solutions of the constant‐flux inland boundary. It is found that for the constant‐flux inland boundary, the shape of the saltwater interface is independent of the geometry of the bottom confining layer for both aquifer types, despite that the geometry of the bottom confining layer determines the location of the interface tip. This is attributed to that the hydraulic head at the interface is identical to that of the coastal boundary, so the shape of the bed below the interface is irrelevant to the interface position. Moreover, developed analytical solutions with an empirical factor on the density factor are in good agreement with the results of variable‐density flow numerical modeling. Analytical solutions developed in this study provide a powerful tool for assessment of seawater intrusion in sloping coastal aquifers as well as in coastal aquifers with a known freshwater flux but an arbitrary geometry of the bottom confining layer.

Integrative management of saltwater intrusion in poorly-constrained semi-arid coastal aquifer at Ras El-Hekma, Northwestern Coast, Egypt

“…Lu et al, 2016 andZhou (2011), used analytical solutions for seawater-freshwater interface characterizations, to determine the lateral seawater intrusion zone, and to estimate the volume of seawater in coastal aquifers.…”

A Study on the Cause of Layered Seawater Intrusion in the Daqing River Estuary of Liaodong Bay, China

“…Seawater intrusion is a density-dependent flow problem [4,28,29]. Several methods have been developed to address it, including analytical solution, experimental and simulation methods [18,21,23,24,[28][29][30][31][32]. Analytical solution is always used to locate a steady fresh-saltwater interface location under many assumed conditions [19,[33][34][35].…”

Experiment and Numerical Simulation of Seawater Intrusion under the Influences of Tidal Fluctuation and Groundwater Exploitation in Coastal Multilayered Aquifers

“…Two types of flow models were developed for seawater intrusion simulation, including the sharp interface models and mixing interface models [14,[19][20][21][22][23][24]. There are many analytical solutions for variable density flow models to solve the coupled seawater intrusion equations under special conditions [6,19,20,25]. Most of the analytical solutions are predominantly based on the Ghyben-Herzberg relation in the sharp interface models, in which the freshwater and saltwater are treated as separated fluids by an interface.…”