Abstract
The Henry problem (HP) continues to play a useful role in theoretical and practical studies related to seawater intrusion (SWI) into coastal aquifers. The popularity of this problem is attributed to its simplicity and precision to the existence of semi-analytical (SA) solutions. The first SA solution has been developed for a high uniform diffusion coefficient. Several further studies have contributed more realistic solutions with lower diffusion coefficients or velocity-dependent dispersion. All the existing SA solutions are limited to homogenous and isotropic domains. This work attempts to improve the realism of the SA solution of the dispersive HP by extending it to heterogeneous and anisotropic coastal aquifers. The solution is obtained using the Fourier series method. A special hydraulic conductivity–depth model describing stratified heterogeneity is used for mathematical convenience. An efficient technique is developed to solve the flow and transport equations in the spectral space. With this technique, we show that the HP can be solved in the spectral space with the salt concentration as primary unknown. Several examples are generated, and the SA solutions are compared against an in-house finite element code. The results provide high-quality data assessed by quantitative indicators that can be effectively used for code verification in realistic configurations of heterogeneity and anisotropy. The SA solution is used to explain contradictory results stated in the previous works about the effect of anisotropy on the saltwater wedge. It is also used to investigate the combined influence of stratification and anisotropy on relevant metrics characterizing SWI. At a constant gravity number, anisotropy leads to landward migration of the saltwater wedge, more intense saltwater flux, a wider mixing zone and shallower groundwater discharge zone to the sea. The influence of stratified heterogeneity is more pronounced in highly anisotropic aquifers. The stratification rate and anisotropy have complementary effects on all SWI metrics, except for the depth of the discharge zone.
Highlights
The HenryHenry problem problem (HP) (HP) [1][1] is is widely widely used used as as aa surrogate surrogate for for the the understanding understanding of of seawater seawaterThe intrusion (SWI)processes in coastal aquifers [2].It is an abstraction of seawater intrusion (SWI) in a vertical cross-section intrusion (SWI) processes in coastal aquifers [2]
We show that the HP can be solved in the spectral space with only the concentration as the primary unknown
We evaluated the SA solutions for two cases dealing with increased rates of heterogeneity (Υ = 1.5 and 3) and a constant large-scale gravity number (NG = 3.11)
Summary
Processes in coastal aquifers [2]. It is an abstraction of SWI in a vertical cross-section intrusion (SWI) processes in coastal aquifers [2]. It is an abstraction of SWI in a vertical cross-section of a confined coastal aquifer perpendicular to the shoreline. This aquifer, inland freshwater flow aofconfined coastal aquifer perpendicular to the shoreline. In In this aquifer, anan inland freshwater flow is is in equilibrium with the seawater intruded from the seaside, due to its higher density (Figure 1)
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