A simple method for locating the fresh water-salt water interface using pressure data

Salt water intrusion is a key issue in dealing with exploitation, restoration, and management of fresh ground water in coastal aquifers. Constant monitoring of the fresh water-salt water interface is necessary for proper management of ground water resources. This study presents a simple method to estimate the depth of the fresh water-salt water interface in coastal aquifers using two sets of pressure data obtained from the fresh and saline zones within a single borehole. This method uses the density difference between fresh water and saline water and can practically be used at coastal aquifers that have a relatively sharp fresh water-salt water interface with a thin transition zone. The proposed method was applied to data collected from a coastal aquifer on Jeju Island, Korea, to estimate the variations in the depth of the interface. The interface varied with daily tidal fluctuations and heavy rainfall in the rainy season. The estimated depth of the interface showed a good agreement with the measured electrical conductivity profile.     

Estimation of the inland extending length of the freshwater–saltwater interface in coastal unconfined aquifers

ABSTRACT

The inland extending length of the freshwater–saltwater interface toe is useful in studies of seawater intrusion in coastal areas. The submarine fresh groundwater discharge in coastal zones is affected not only by hydraulic conductivity and hydraulic gradient of the aquifer, but also by the position of the interface. Two observation wells at different distances from the coast are required to calculate the fresh groundwater flow rate in coastal unconfined aquifers. By considering that the submarine groundwater discharge is equal to the groundwater flow rate, the length of the interface toe extending inland can be estimated when the groundwater flow is at a steady-flow state. Aquifers with horizontal and sloping confined beds and without/with unique surface vertical infiltration are considered. Examples used to illustrate the application of these methods indicate that the inland extending lengths of the interface toe in aquifers with vertical surface infiltration are much shorter than those in aquifers without vertical surface infiltration, and the length of the interface in aquifers with a horizontal confining lower bed are smaller than those in aquifers with a confining lower bed sloping towards the sea. The extent of the interface on the northwestern coast near the city of Beihai in southern Guangxi, China, on 18 January 2013 was estimated as 471–478 m.

Editor M.C. Acreman Associate editor not assigned     

Analytic Element Modeling of Steady Interface Flow in Multilayer Aquifers Using AnAqSim

This paper presents the analytic element modeling approach implemented in the software AnAqSim for simulating steady groundwater flow with a sharp fresh‐salt interface in multilayer (three‐dimensional) aquifer systems. Compared with numerical methods for variable‐density interface modeling, this approach allows quick model construction and can yield useful guidance about the three‐dimensional configuration of an interface even at a large scale. The approach employs subdomains and multiple layers as outlined by Fitts (2010) with the addition of discharge potentials for shallow interface flow (Strack 1989). The following simplifying assumptions are made: steady flow, a sharp interface between fresh‐ and salt water, static salt water, and no resistance to vertical flow and hydrostatic heads within each fresh water layer. A key component of this approach is a transition to a thin fixed minimum fresh water thickness mode when the fresh water thickness approaches zero. This allows the solution to converge and determine the steady interface position without a long transient simulation. The approach is checked against the widely used numerical codes SEAWAT and SWI/MODFLOW and a hypothetical application of the method to a coastal wellfield is presented.     

Analytical Solutions for Determination of Non-Steady- State and Steady-State Capture Zones

This paper presents analytical solutions for determining non-steady-state capture zones produced by a single recovery well and steady-state capture zones produced by multiple recovery wells. Analysis of non-steady-slate capture zones is based on the lime-dependent location of caplure zone stagnation points and the geometric similarity between steady-slate and non-steady-state capture zones. The analytical solution of steady-state capture zones is obtained from spatial variations of discharge potential across the capture zone boundary. Both capture zone analyses are based on the assumptions of uniform flow field with a constant hydraulic conductivity, the Dupuit assumption of insignificant vertical flow, a negligible delayed yield, and a fully penetrating well with a constant pumping rate. For a ground water pump-and-trcat remediation program, the pumping rate and well location design variables can be adjusted to ensure containment of the ground water contaminant plume.     

Impact of coastal land reclamation on ground water level and the sea water interface

Land reclamation in coastal areas may have a significant effect on local ground water systems. Steady-state analytic solutions based on Dupuit and Ghyben-Herzberg assumptions are derived to evaluate this effect. Two situations are considered, both with ground water flow resulting from precipitation recharge: the coastal aquifer of an extensive landmass and an island. The results show that after reclamation, the water table rises and the salt water-fresh water interface moves seaward. The degree of these changes depends on the extent of reclamation and the hydraulic conductivity of the fill material. For the island situation, the reclamation displaces the ground water divide and changes the ground water conditions in the entire island. An unintended advantage of the reclamation is an increase of fresh ground water resource because the reclaimed land can be an additional aquifer and rain recharge takes place over a larger area.     

Biased monitoring of fresh water-salt water mixing zone in coastal aquifers

In coastal aquifers, significant vertical hydraulic gradients are formed where fresh water and underlying salt water discharge together upward to the seafloor. Monitoring boreholes may act as "short circuits" along these vertical gradients, connecting between the higher and the lower hydraulic head zones. When a sea tide is introduced, the fluctuations of both the water table and the depth of the mixing zone are also biased due to this effect. This problem is intensified in places of long-screen monitoring boreholes, which are common in many places in the world. For example, all approximately 500 boreholes of the fresh water-salt water mixing zone in the coastal aquifer of Israel are installed with 10 to 50 m long screens. We present field measurements of these fluctuations, along with a three-dimensional numerical model. We find that the in-well fluctuation magnitude of the mixing zone is an order of magnitude larger than that in the porous media of the actual aquifer. The primary parameters that affect the magnitude of this bias are the anisotropy of the aquifer conductivity and the borehole hydraulic parameters. With no sea tide, borehole interference is higher for the anisotropic case because the vertical hydraulic gradients are high. When tides are introduced, the amplitude of the mixing zone fluctuation is higher for the isotropic case because the overall effective hydraulic conductivity is greater than the conductivity in the anisotropic case. In the aquifer, the fresh water-salt water mixing zone fluctuations are dampened, and tens of meters inland from the shoreline, the fluctuations are on the order of few centimeters.     

The impact of highly permeable layer on hydraulic system in a coastal aquifer

This study is aimed to understand the hydraulic mechanism of coastal aquifer systems that include highly permeable layers (HPLs). These hydrologic conditions can be found in many volcanic islands that are composed of a series of lava flows discharged into sea or other standing body of water. In the first part, we developed a numerical model based on the geologic and hydrologic data obtained from the eastern Jeju Island, Korea, of which the aquifer contains clinker and hyaloclastite layers. The simulation results reproduced spatial location of fresh‐saline water interface, especially the abrupt decline of interface at the inland part and the thickness variation of transition zone along the cross‐section observed at the eastern Jeju coastal aquifer. We were able to find out that these phenomena are strongly related to the presence of the HPL. In the second part, quantitative analyses were conducted with the use of hypothetical models in order to understand the dynamic characteristics of coastal system that includes HPLs. A series of sensitivity studies were conducted to assess the effect of the horizontal length and vertical depth of HPL on the spatial location of the interface toe and the configuration of transition zone. Various case studies have shown that the seawater intruded into the inland more as the horizontal length of HPL was increased and its vertical depth was decreased. In other simulations including two HPLs, the vertical distance between these two HPLs primarily controlled the flow regime, flux variations, and the configuration of the transition zone. Finally, we performed simulations to evaluate the effect of a rising sea‐level. This study provides more understanding of how the presence of HPL controls the seawater intrusion processes, and the spatial configurations of fresh‐saline water interface at coastal aquifers. Copyright © 2012 John Wiley & Sons, Ltd.     

Geophysical monitoring and evaluation of coastal plain aquifers

We use time domain electromagnetic (TDEM) soundings to monitor ground water conditions beneath the coastal plain in eastern North Carolina. The TDEM method measures the earth's response to an induced electromagnetic field. The resulting signal is converted, through a complex inversion process, to apparent resistivity values, which can be directly correlated to borehole resistivity logs. TDEM soundings are used to map the interface between fresh and salt water within coastal aquifers, and estimate depth to basement when siting new monitoring wells. Focused TDEM surveys have identified areas of salt water encroachment caused by high volumes of discharge from local supply wells. Electromagnetic sounding, when used in tandem with the state's network of monitoring wells, is an accurate and inexpensive tool for evaluating fresh water/salt water relationships on both local and regional scales within coastal plain aquifers.     

The Interface Configuration of the Fresh‐/Dead Sea Water – Theory and Measurements

The high‐density Dead Sea water (1.235 g/cm³) forms a special interface configuration with the fresh groundwater resources of its surrounding aquifers. The fresh groundwater column beneath its surroundings is around one tenth of its length compared to oceanic water. This fact alone indicates the vulnerability of the fresh groundwater resources to the impacts of changes in the Dead Sea level and to saltwater migration. Ghyben‐Herzberg and Glover equations were used to calculate the volumes of water in coastal aquifers which were replaced by freshwater due to the interface seaward migration as a result of the drop in the level of the Dead Sea. For that purpose, the dynamic equation of Glover approach has been integrated to accommodate that type of interface readjustment. The calculated amounts of freshwater which substituted salt Dead Sea water due to the migration of interface are 3.21 · 10¹¹ m³, from a Dead Sea level of –392 m to τ411 m below sea level. The average porosity of coastal aquifers was calculated to range from 2.8 to 2.94%. Geoelectric sounding measurements showed that areas underlying the coastal aquifers formerly occupied by the Dead Sea water are gradually becoming flushed and occupied by freshwater. The latter is becoming salinized due to the residuals of Dead Sea water in the aquifer matrix, the present salinity of which is lower than that of the Dead Sea water. At the same time salt dissolution from the Lisan Marl formation is causing collapses along the shorelines in the form of sinkholes, tens of meters in diameter and depth.     

Effects of sea-level rise on ground water flow in a coastal aquifer system

The effects of sea-level rise on the depth to the fresh water/salt water interface were simulated by using a density-dependent, three-dimensional numerical ground water flow model for a simplified hypothetical fresh water lens that is similar to shallow, coastal aquifers found along the Atlantic coast of the United States. Simulations of sea-level rise of 2.65 mm/year from 1929 to 2050 resulted in an increase in water levels relative to a fixed datum, yet a net decrease in water levels relative to the increased sea-level position. The net decrease in water levels was much greater near a gaining stream than farther from the stream. The difference in the change in water levels is attributed to the dampening effect of the stream on water level changes in response to sea-level rise. In response to the decreased water level altitudes relative to local sea level, the depth to the fresh water/salt water interface decreased. This reduction in the thickness of the fresh water lens varied throughout the aquifer and was greatly affected by proximity to a ground water fed stream and whether the stream was tidally influenced. Away from the stream, the thickness of the fresh water lens decreased by about 2% from 1929 to 2050, whereas the fresh water lens thickness decreased by about 22% to 31% for the same period near the stream, depending on whether the stream was tidally influenced. The difference in the change in the fresh water/salt water interface position is controlled by the difference in the net decline in water levels relative to local sea level.     

Discussion about the validity of sharp‐interface models to deal with seawater intrusion in coastal aquifers

Analytical models have been exhaustively used to study simple seawater intrusion problems and the sustainable management of groundwater resources in coastal aquifers because of its simplicity, easy implementation, and low computational cost. Most of these models are based on the sharp‐interface approximation and the Ghyben–Herzberg relation, and their governing equations are expressed in terms of a single potential theory to calculate critical pumping rates in a coastal pumping scenario. The Ghyben–Herzberg approach neglects mixing of fresh water and seawater and implicitly assumes that salt water remains static. Therefore, the results of the analytical solutions may be inaccurate and unacceptable for some real‐complex case studies. This paper provides insight into the validity of sharp‐interface models to deal with seawater intrusion in coastal aquifers, i.e. when they can be applied to obtain accurate enough results. For that purpose, this work compares sharp‐interface solutions, based on the Ghyben–Herzberg approach, with numerical three‐dimensional variable‐density flow simulations for a set of heterogeneous groundwater flow and mass transport parameters, and different scenarios of spatially distributed recharge values and spatial wells placement. The numerical experiment has been carried out in a 3D unconfined synthetic aquifer using the finite difference numerical code SEAWAT for solving the coupled partial differential equations of flow and density‐dependent transport. This paper finds under which situations the sharp‐interface solution gives good predictions in terms of seawater penetration, transition zone width and critical pumping rates. Additionally, the simulation runs indicate to which parameters and scenarios the results are more sensitive. Copyright © 2013 John Wiley & Sons, Ltd.     

A Correction on Coastal Heads for Groundwater Flow Models

We introduce a simple correction to coastal heads for constant‐density groundwater flow models that contain a coastal boundary, based on previous analytical solutions for interface flow. The results demonstrate that accurate discharge to the sea in confined aquifers can be obtained by direct application of Darcy's law (for constant‐density flow) if the coastal heads are corrected to ((α + 1)/α)h_s ? B/2α, in which h_s is the mean sea level above the aquifer base, B is the aquifer thickness, and α is the density factor. For unconfined aquifers, the coastal head should be assigned the value . The accuracy of using these corrections is demonstrated by consistency between constant‐density Darcy's solution and variable‐density flow numerical simulations. The errors introduced by adopting two previous approaches (i.e., no correction and using the equivalent fresh water head at the middle position of the aquifer to represent the hydraulic head at the coastal boundary) are evaluated. Sensitivity analysis shows that errors in discharge to the sea could be larger than 100% for typical coastal aquifer parameter ranges. The location of observation wells relative to the toe is a key factor controlling the estimation error, as it determines the relative aquifer length of constant‐density flow relative to variable‐density flow. The coastal head correction method introduced in this study facilitates the rapid and accurate estimation of the fresh water flux from a given hydraulic head measurement and allows for an improved representation of the coastal boundary condition in regional constant‐density groundwater flow models.     

Approximate analysis of upconing

The change of the salinity distribution in coastal aquifers due to pumpage is often described as an upconing of the interface between saline and fresh water. Sea and fresh water are miscible fluids, however. Therefore, dispersion of salinity in the aquifer affects the upconing process. An estimate of the effect of salinity dispersion on the dynamics of the flow as well as on the salinity distribution in the aquifer is presented in this study. The phenomenon is described as a migration of a sharp interface perturbed by small disturbances due to salinity dispersion. The creation of the mixing zone between fresh and saline water is described as a formation of a boundary layer in the vicinity of the sharp interface. This method is primarily recommended for flow fields in which simple representation of the sharp interface migration is obtainable.     

Maximizing Net Extraction Using an Injection‐Extraction Well Pair in a Coastal Aquifer

In this study, we examine the maximum net extraction rate from the novel arrangement of an injection‐extraction well pair in a coastal aquifer, where fresh groundwater is reinjected through the injection well located between the interface toe and extraction well. Complex potential theory is employed to derive a new analytical solution for the maximum net extraction rate and corresponding stagnation‐point locations and recirculation ratio, assuming steady‐state, sharp‐interface conditions. The injection‐extraction well‐pair system outperforms a traditional single extraction well in terms of net extraction rate for a broad range of well placement and pumping rates, which is up to 50% higher for an aquifer with a thickness of 20 m, hydraulic conductivity of 10 m/d, and fresh water influx of 0.24 m²/d. Sensitivity analyses show that for a given fresh water discharge from an inland aquifer, a larger maximum net extraction is expected in cases with a smaller hydraulic conductivity or a smaller aquifer thickness, notwithstanding physical limits to drawdown at the pumping well that are not considered here. For an extraction well with a fixed location, the optimal net extraction rate linearly increases with the distance between the injection well and the sea, and the corresponding injection rate and recirculation ratio also increase. The analytical analysis in this study provides initial guidance for the design of well‐pair systems in coastal aquifers, and is therefore an extension beyond previous applications of analytical solutions of coastal pumping that apply only to extraction or injection wells.     

On the shape of the non-steady interface intersecting discontinuities in permeability

The simplifying assumption is often made, that when two fluids (whether miscible or immiscible) occupy the void space of a porous medium, they are separated by a sharp interface. Examples are the phreatic surface (between air and water) and the interface between fresh and salt water in a coastal aquifer. The orientation of such a sharp interface as it crosses a surface of discontinuity between media of different permeabilities, and as it intersects an impervious boundary, is shown to depend not only on the fluid and porous media properties, but also on the direction and rate of motion of the interface. Thus, advancing and retreating interfaces intersect boundaries of discontinuity in permeability at different angles.     

A New Operational Paradigm for Small‐Scale ASR in Saline Aquifers

A new operational paradigm is presented for small‐scale aquifer storage and recovery systems (ASR) in saline aquifers. Regular ASR is often not feasible for small‐scale storage in saline aquifers because fresh water floats to the top of the aquifer where it is unrecoverable. In the new paradigm, fresh water storage is combined with salt water extraction from below the fresh water cone. The salt water extraction counteracts the buoyancy due to the density difference between fresh water and salt water, thus preventing the fresh water from floating up. The proposed approach is applied to assess the feasibility of ASR for the seasonal storage of fresh water produced by desalination plants in tourist resorts along the Egyptian Red Sea coast. In these situations, the continuous extraction of salt water can be used for desalination purposes. An analytical Dupuit solution is presented for the steady flow of salt water toward a well with a volume of fresh water floating on top of the cone of depression. The required salt water discharge for the storage of a given volume of fresh water can be computed with the analytical solution. Numerical modeling is applied to determine how the stored fresh water can be recovered. Three recovery approaches are examined. Fresh water recovery rates on the order of 70% are achievable when salt water is extracted in high volumes, subsurface impermeable barriers are constructed at a distance from the well, or several fresh water recovery drains are used. The effect of ambient flow and interruptions of salt water pumping on the recovery efficiency are reported.     

Application of an Analytical Solution as a Screening Tool for Sea Water Intrusion

Sea water intrusion into aquifers is problematic in many coastal areas. The physics and chemistry of this issue are complex, and sea water intrusion remains challenging to quantify. Simple assessment tools like analytical models offer advantages of rapid application, but their applicability to field situations is unclear. This study examines the reliability of a popular sharp‐interface analytical approach for estimating the extent of sea water in a homogeneous coastal aquifer subjected to pumping and regional flow effects and under steady‐state conditions. The analytical model is tested against observations from Canada, the United States, and Australia to assess its utility as an initial approximation of sea water extent for the purposes of rapid groundwater management decision making. The occurrence of sea water intrusion resulting in increased salinity at pumping wells was correctly predicted in approximately 60% of cases. Application of a correction to account for dispersion did not markedly improve the results. Failure of the analytical model to provide correct predictions can be attributed to mismatches between its simplifying assumptions and more complex field settings. The best results occurred where the toe of the salt water wedge is expected to be the closest to the coast under predevelopment conditions. Predictions were the poorest for aquifers where the salt water wedge was expected to extend further inland under predevelopment conditions and was therefore more dispersive prior to pumping. Sharp‐interface solutions remain useful tools to screen for the vulnerability of coastal aquifers to sea water intrusion, although the significant sources of uncertainty identified in this study require careful consideration to avoid misinterpreting sharp‐interface results.     

Impact of Sea-Level Rise on Sea Water Intrusion in Coastal Aquifers

Despite its purported importance, previous studies of the influence of sea-level rise on coastal aquifers have focused on specific sites, and a generalized systematic analysis of the general case of the sea water intrusion response to sea-level rise has not been reported. In this study, a simple conceptual framework is used to provide a first-order assessment of sea water intrusion changes in coastal unconfined aquifers in response to sea-level rise. Two conceptual models are tested: (1) flux-controlled systems, in which ground water discharge to the sea is persistent despite changes in sea level, and (2) head-controlled systems, whereby ground water abstractions or surface features maintain the head condition in the aquifer despite sea-level changes. The conceptualization assumes steady-state conditions, a sharp interface sea water-fresh water transition zone, homogeneous and isotropic aquifer properties, and constant recharge. In the case of constant flux conditions, the upper limit for sea water intrusion due to sea-level rise (up to 1.5 m is tested) is no greater than 50 m for typical values of recharge, hydraulic conductivity, and aquifer depth. This is in striking contrast to the constant head cases, in which the magnitude of salt water toe migration is on the order of hundreds of meters to several kilometers for the same sea-level rise. This study has highlighted the importance of inland boundary conditions on the sea-level rise impact. It identifies combinations of hydrogeologic parameters that control whether large or small salt water toe migration will occur for any given change in a hydrogeologic variable.     

Hydraulic head applications of flow logs in the study of heterogeneous aquifers

Permeability profiles derived from high-resolution flow logs in heterogeneous aquifers provide a limited sample of the most permeable beds or fractures determining the hydraulic properties of those aquifers. This paper demonstrates that flow logs can also be used to infer the large-scale properties of aquifers surrounding boreholes. The analysis is based on the interpretation of the hydraulic head values estimated from the flow log analysis. Pairs of quasi-steady flow profiles obtained under ambient conditions and while either pumping or injecting are used to estimate the hydraulic head in each water-producing zone. Although the analysis yields localized estimates of transmissivity for a few water-producing zones, the hydraulic head estimates apply to the far-field aquifers to which these zones are connected. The hydraulic head data are combined with information from other sources to identify the large-scale structure of heterogeneous aquifers. More complicated cross-borehole flow experiments are used to characterize the pattern of connection between large-scale aquifer units inferred from the hydraulic head estimates. The interpretation of hydraulic heads in situ under steady and transient conditions is illustrated by several case studies, including an example with heterogeneous permeable beds in an unconsolidated aquifer, and four examples with heterogeneous distributions of bedding planes and/or fractures in bedrock aquifers.     

Vulnerability indicators of sea water intrusion

In this paper, simple indicators of the propensity for sea water intrusion (SWI) to occur (referred to as "SWI vulnerability indicators") are devised. The analysis is based on an existing analytical solution for the steady-state position of a sharp fresh water-salt water interface. Interface characteristics, that is, the wedge toe location and sea water volume, are used in quantifying SWI in both confined and unconfined aquifers. Rates-of-change (partial derivatives of the analytical solution) in the wedge toe or sea water volume are used to quantify the aquifer vulnerability to various stress situations, including (1) sea-level rise; (2) change in recharge (e.g., due to climate change); and (3) change in seaward discharge. A selection of coastal aquifer cases is used to apply the SWI vulnerability indicators, and the proposed methodology produces interpretations of SWI vulnerability that are broadly consistent with more comprehensive investigations. Several inferences regarding SWI vulnerability arise from the analysis, including: (1) sea-level rise impacts are more extensive in aquifers with head-controlled rather than flux-controlled inland boundaries, whereas the opposite is true for recharge change impacts; (2) sea-level rise does not induce SWI in constant-discharge confined aquifers; (3) SWI vulnerability varies depending on the causal factor, and therefore vulnerability composites are needed that differentiate vulnerability to such threats as sea-level rise, climate change, and changes in seaward groundwater discharge. We contend that the approach is an improvement over existing methods for characterizing SWI vulnerability, because the method has theoretical underpinnings and yet calculations are simple, although the coastal aquifer conceptualization is highly idealized.