Analytical Study on the Tidal Wave Propagation Coupled with Vertical Leakage from a Vertically Heterogeneous Aquitard in a Coastal Leaky Aquifer System

Abstract

Abstract Analytical studies on the tidal wave propagation in a coastal leaky aquifer commonly assume that the low-permeability aquitard is homogeneous. The aquitard is, however, vertically heterogeneous in nature due to varying soil types along the burial depth as can be frequently seen from borehole logs. In this study, an innovative analytical model is developed to explore the vertical heterogeneity in aquitard hydraulic conductivity (K) and specific storage (Ss) on the tidal wave propagation coupling with vertical leakage from the aquitard. The novelty behind the newly derived analytical solution is attributed to the fact that the aquitard along the burial depth can be divided into any number of homogeneous zones, each of which is associated with distinct K and Ss values, so that arbitrary vertical heterogeneity pattern of aquitard K and Ss can be captured. Theoretical analysis results reveal that an interlayer within the aquitard with a smaller K can significantly enhance the amplitude and phase shift of periodic groundwater head fluctuations in the leaky aquifer, while a larger Ss of the interlayer will weaken the amplitude and phase shift provided a relatively small aquitard K. Buried locations of the interlayer also implement nonnegligible effects on the tidal wave propagation. For the scenario of exponentially decaying aquitard K and Ss, which is commonly encountered for a thick aquitard, a larger decay exponent results in smaller amplitude and phase shift. This analytical study highlights the importance of vertical aquitard heterogeneity on tidal wave propagation in a coastal leaky aquifer system.