Experimental and numerical investigation of saltwater intrusion dynamics on sloping sandy beach under static seaside boundary condition

Highlights

• Study of stability of density dependent flow in porous media.

• Revels circulation pattern around interface zone.

• Low stratified layer changes the interface flow pattern.

• Pore pressure response to density driven flow was measured in sandbox model.

Abstract

Two-dimensional sandbox experiments were conducted to investigate the variable-density circulation and flow patterns in sloping beach configurations. The experiments provide new benchmark results for validating the sandbox models based on quantitative and qualitative measurements. Previous studies have considered density dependent flow in porous media, vertical beach face saltwater boundary, and multilayered hydrogeology ignoring a sloping beach face, which is a much more common phenomenon in real world. The present study considers sloping beach face under both homogeneous and low-permeability strata configurations. The geohydraulic processes encountered were quantified through pore-water pressure measurements and image analysis techniques. Moreover, validations were performed with numerical simulations (FEFLOW). A simple image analysis procedure is proposed with respect to two-dimensional laboratory scale benchmark experiments. Experimental results provided a detailed circulation flow path within and outside the saltwater wedge with sloping beach face. Fingering effect in porous media was also observed for both the experiments during initial time periods. Stability analysis shows the existence of a stationary convective flow pattern followed by gravitational instabilities under the quasi-steady state condition.

Introduction

Variable-density flow in porous media is related to the dynamics of groundwater flow in coastal aquifers. Density driven flow in porous media remains one of the challenging problems owing to its inherent non-linearity, and limited availability of analytical solutions and availability of standard/field data set [1]. In recent years, different in-situ observation based methods were proposed to identify the fluid dynamics of density dependent flows [2], [3], [4]. However, experimental quantification is necessary to evaluate the performance of mathematical/numerical models. The laboratory experiments (or benchmark tests) give advantages of known boundary and initial conditions, known porous material properties over the field experiments. Thus laboratory sand box model can be used as a useful instrument for flow visualization and for in-situ measurements. Generally, one-dimensional experiments are performed to study the behavior of flow in porous media under the influence of high density fluid [5], [6], [7], [8]. Few studies [9], [10], [11] were carried out using laboratory scale two-dimensional ($2D$) sandbox experiments for identifying interface between two varying density fluids and their flow through stratified porous medium. Laboratory-scale experiments are widely used to investigate the behavior of saltwater interface (SWI) [9], [10], [11], [12], [13], [14], [15], [16], [17]. These studies mostly focused on the dispersive mixing zone while solving the variants of the Henry problem [18]. Recent studies are also available on numerical simulation of density dependent flows [19], [20], [21], [22]. Most of the works have either used a vertical saltwater boundary or homogeneous configuration to understand the density dependent flow process.

The density gradient at sloping (non-vertical) boundary plays a vital role in changing the hydraulic gradient and contaminant transport across the SWI. The previous works focused on the position, shape and thickness of the saltwater–freshwater transition zone for density dependent flow in porous media. However, these studies have rarely observed convective saltwater circulation phenomenon [23]. It is well known that variable density flows in porous media can become unstable [24]. The occurrence of fingering is caused by flow instabilities due to differences in viscosity and density values between two miscible fluids. Instabilities and fingering develop when a denser fluid lies above the lighter fluid [25], [26], [27], [28]. Viscous fingers develop and can be visualized in the form of the corrugated interface [29]. The fingers propagate rapidly, until they reach a stable convective flow regime.

The results of density-coupled groundwater flow simulations are typically represented as isolines [30], [31], [32] or vector plots of the groundwater velocity [33], [34]. Experimentally saltwater circulation pattern cannot be determined from these types of information. Circulation patterns in steady state mixed convection problems can be identified from the streamline plots. The density-driven circulation can be conceptually divided into two consecutive processes: (i) flow of high density fluid (in counter clockwise direction) towards low density fluid due to density gradient , and (ii) upward flow of low density fluid towards free surface of the interface. Moreover, limited numbers of studies are available on growth of circulation pattern due to density driven forces [23].

The steady state interface of freshwater/saltwater was studied by many researchers in the context of multiple permeable layers. Limited number of studies are available on the effects of low permeability layer on SWI [35], [36], [37]. However, none of these studies have reported understanding of the density dependent flow process associated with thin stratified low permeability layer. The relative position and thickness of the stratified porous layer has significant effect on the density dependent flows. As per our knowledge, no study has presented laboratory experiments to study quantitative and qualitative saltwater dynamics in porous media. The present study provides the pore water pressure variation under sloping beach face condition for the experimental time periods. This quantitative analysis captures the dynamics of flow and transport processes. Variable density flow experiment is an essential tool to test the reliability of numerical simulations under realistic geometric conditions.  [10] has performed laboratory scale experiment to get benchmark data for density dependent Henry problem.

The present study extends the experimental analysis to both confined and unconfined strata configurations. The aim of this study is to provide reliable data for validation of numerical simulation. The present work also focuses on effect of low permeability layer on SWI through laboratory experiments and numerical studies. Evolution of time dependent interface was captured through experiments. Moreover, flow circulation patterns were investigated in different zones (saltwater/freshwater). Experimental data were acquired in the forms of images and pore water pressure measurements (through pressure transducers). Interface movement and flow circulation patterns were determined based on processed images. These results were validated by using a numerical simulation model FEFLOW [38].