A general solution for groundwater flow in an estuarine's leaky aquifer system after considering aquifer anisotropy

This paper presents an analytical model for describing the tidal effects in a two‐dimensional leaky confined aquifer system in an estuarine delta where ocean and river meet. This system has an unconfined aquifer on top and a confined aquifer on the bottom with an aquitard in between the two. The unconfined and confined aquifers interact with each other through leakage. It was assumed that the aquitard storage was negligible and that the leakage was linearly proportional to the head difference between the unconfined and confined aquifers. This model's solution was based on the separation of variables method. Two existing solutions that deal with the head fluctuation in one‐dimensional or two‐dimensional leaky confined aquifers are shown as special cases in the present solution. Based on this new solution, the dynamic effect of the water table's fluctuations can be clearly explored, as well as the influence of leakage on the behaviour of fluctuations in groundwater levels in the leaky aquifer system. Copyright © 2015 John Wiley & Sons, Ltd.     

A semi‐analytical solution for groundwater responses to stream‐stage variations and tidal fluctuations in a coastal aquifer

A two‐dimensional semi‐analytical solution to analyse stream–aquifer interactions in a coastal aquifer where groundwater level responds to tidal effects is presented. The conceptual model considered is a two‐dimensional subsurface system with stream and coastline boundaries at right angles. The dimensional and non‐dimensional boundary value problems were solved for water level in the aquifer by successive application of Laplace and Fourier transform techniques, and the results were obtained by numerical inversion of the transformed solution. The solution was then verified by reducing the solutions to one‐dimensional known problems and comparing the results with those from previous studies. Hypothetical examples were used to examine the characteristics of water‐level variations due to the variations in stream stage and the fluctuations in tide level. Sensitivity analysis indicated that streambed leakance has no influence over the amplitude of groundwater fluctuations, but that the effect of stream stage increases with increasing leakance. Little difference was observed in the water level for different aquifer penetration ratios with narrow stream width. Increases in streambed leakance caused increases in the effect of aquifer penetration by the stream on the water level. An increased specific yield value resulted in decreased amplitude of water fluctuations and mean water level, and showed that water‐level variations due to stream and tidal boundaries are sensitive to specific yield. Copyright © 2006 John Wiley & Sons, Ltd.     

Groundwater response to tidal fluctuations in a leaky confined coastal aquifer with a finite length

The study on the hydraulic properties of coastal aquifers has significant implications both in hydrological sciences and environmental engineering. Although many analytical solutions are available, most of them are based on the same basic assumption that assumes aquifers extend landward semi‐infinitely, which does not necessarily reflect the reality. In this study, the general solutions for a leaky confined coastal aquifer have been developed that consider both finitely landward constant‐head and no‐flow boundaries. The newly developed solutions were then used to examine theoretically the joint effects of leakage and aquifer length on hydraulic head fluctuations within the leaky confined aquifer, and the validity of using the simplified solution, which assumes the aquifer is semi‐infinite. The results illustrated that the use of the simplified solution may cause significant errors, depending on joint effects of leakage and aquifer length. A dimensionless characteristic parameter was then proposed as an index for judging the applicability of the simplified solution. In addition, practical application of the general solution for the constant‐head inland boundary was used to characterize the hydraulic properties of a leaky confined aquifer using the data collected from a field site at the Seine River estuary, France, and the versatility of the general solution was further justified.     

A general solution for tide‐induced groundwater fluctuation in an estuarine‐coastal confined and unconfined aquifer system

This paper presents an analytical solution to tide‐induced head fluctuations in a two‐dimensional estuarine‐coastal aquifer system that consists of an unconfined aquifer and a heterogeneous confined aquifer extending under a tidal river with a semipermeable layer between them. This study considers the joint effects of tidal‐river leakage, inland leakage, dimensionless transmissivity between the tidal‐river and inland confined aquifer, and transmissivity anisotropic ratios. The analytical solution for this model is obtained via the separation of variables method. Three existing solutions related to head fluctuation in one‐ or two‐dimensional leaky confined aquifers are considered as special cases in the present solution. This study shows that there is a threshold of tidal‐river confined aquifer length. When the tidal‐river length is greater than the threshold length, the inland head fluctuations remain sensitive to the leakage effect but become insensitive to the tidal‐river width and dimensionless transmissivity. Considering leakage and transmissivity anisotropy, this study also demonstrates that at a location farther from the river–inland boundary, head fluctuations increase with increasing leakage and transmissivity anisotropy; the maximum head fluctuation occurs when leakage and transmissivity anisotropy are both at their maximum values. The combined action of the 3 effects of loading, tidal‐river aquifer leakage, and inland aquifer leakage differs significantly according to various aquifer parameters. The analytical solution in this paper can be applied to demonstrate the behaviours of the head fluctuations of an estuarine‐coastal aquifer system, and the head fluctuations can be clearly described when the tidal and hydrogeological parameters are derived from field measurement data or hypothetical cases.     

Two‐dimensional flow response to tidal fluctuation in a heterogeneous aquifer‐aquitard system

In alluvial coastal aquifers, finer sediments are preferentially deposited along the downstream direction, so the hydraulic conductivity is generally heterogeneous and changes with distance from the coastline. To investigate the influence of aquifer heterogeneity on seawater‐groundwater interaction, a new two‐dimensional model characterising groundwater flow in an aquifer‐aquitard system was developed assuming that the hydraulic conductivity of the aquifer linearly increases with the distance from the coastline along the inland direction. A closed‐form analytical solution was derived using the separation‐of‐variables method. Comparing the new solution with the numerical solution by comsol Multiphysics (Sweden) based on the finite‐element method, one can see that the new solution agreed with the numerical solution very well except at the early time. We found that both aquitard leakance and the heterogeneity factor (b) could result in the propagation bias. The propagation bias represents the inconsistency between the theoretical calculation and the observed strong attenuation and small time lag between the head and tide fluctuations. The attenuation decreased with perpendicular distance from the coastline (x‐axis), whereas the time lag increased with distance along the x‐axis. The relationship between the time lag and the distance along the x‐axis seemed to be linear when b was 0.001 m^?1, whereas it obeyed a power function when b was greater than 0.01 m^?1. Copyright © 2014 John Wiley & Sons, Ltd.     

Radial groundwater flow to a finite diameter well in a leaky confined aquifer with a finite‐thickness skin

A mathematical model that describes the drawdown due to constant pumpage from a finite radius well in a two‐zone leaky confined aquifer system is presented. The aquifer system is overlain by an aquitard and underlain by an impermeable formation. A skin zone of constant thickness exists around the wellbore. A general solution to a two‐zone leaky confined aquifer system in Laplace domain is developed and inverted numerically to the time‐domain solution using the modified Crump (1976) algorithm. The results show that the drawdown distribution is significantly influenced by the properties and thickness of the skin zone and aquitard. The sensitivity analyses of parameters of the aquifer and aquitard are performed to illustrate their effects on drawdowns in a two‐zone leaky confined aquifer system. For the negative‐skin case, the drawdown is very sensitive to the relative change in the formation transmissivity. For the positive‐skin case, the drawdown is also sensitive to the relative changes in the skin thickness, and both the skin and formation transmissivities over the entire pumping period and the well radius and formation storage coefficient at early pumping time. Copyright © 2009 John Wiley & Sons, Ltd.     

An analytical solution for the head distribution in a tidal leaky confined aquifer extending an infinite distance under the sea

A mathematical model is developed to investigate the effects of tidal fluctuations and leakage on the groundwater head of leaky confined aquifer extending an infinite distance under the sea. The leakages of the offshore and inland aquitards are two dominant factors controlling the groundwater fluctuation. The tidal influence distance from the coast decreases significantly with the dimensionless leakage of the inland aquitard (u_i). The fluctuation of groundwater level in the inland part of the leaky confined aquifer increases significantly with the dimensionless leakage of the offshore aquitard (u_o). The influence of the tidal propagation parameter of an unconfined aquifer on the head fluctuation of the leaky confined aquifer is comparatively conspicuous when u_i is large and u_o is small. In other words, ignoring water table fluctuation of the unconfined aquifer will give large errors in predicting the fluctuation, time lag, and tidal influence distance of the leaky confined aquifer for large u_i and small u_o. On the contrary, the influence of the tidal propagation parameter of a leaky confined aquifer on the head fluctuation of the leaky confined aquifer is large for large u_o and small u_i.     

Determination of aquifer parameters based on measurements of tidal effects on a coastal aquifer near Beihai,China

Measurements of the tide and groundwater levels in coastal zones are of importance in determining the properties of coastal aquifers. The solution to a one‐dimensional unsteady groundwater flow model in a coastal confined aquifer with sinusoidal fluctuation of the tide shows that the tidal efficiency decreases exponentially with distance and the time lag increases linearly with distance from the coast. The aquifer property described by the ratio of storage coefficient to transmissivity is determined if the damping constant of the tidal efficiency or the slope of the time lag with distance are obtained on the basis of tidal measurements. Hourly observations of the tide and groundwater levels at 10 wells on the northern coast near Beihai, China show that with distance from the coast, tidal efficiency decreases roughly exponentially and the time lag increases roughly linearly. The estimated ratio of storage coefficient to transmissivity of the confined aquifer ranges from 1·169 × 10^?6 d m^?2 to 1·83 × 10^?7 d m^?2. For a given transmissivity of 750 m² d^?1, the storage coefficient of the aquifer is 8·7675 × 10^?4 with the tidal efficiency method and 1·3725 × 10^?4 with the time lag method. The damping constant of the tidal efficiency with distance can be defined as the tidal propagation coefficient. The value of the confined aquifer is determined as 0·0018892 m^?1. Copyright © 2007 John Wiley & Sons, Ltd.     

A new analytical solution of tidal water table fluctuations in a coastal unconfined aquifer

This paper presents a new perturbation solution of the non-linear Boussinesq equation for one-dimensional tidal groundwater flow in a coastal unconfined aquifer. Built upon the work of Parlange et al. [Parlange, J.-Y., Stagnitti, F., Starr, J.L., Braddock, R.D., 1984. Free-surface flow in porous media and periodic solution of the shallow-flow approximation, J. Hydrol., 70, 251–263], the solution adopts a new perturbation parameter that is by definition less than unit, and thus is applicable to a wider range of physical conditions within the constraint of the Boussinesq approximation. This approach avoids a secular term in the third-order perturbation equation of Parlange et al. (1984), enabling the derivation of the third- and higher-order solutions. In comparison with a numerical (“exact”) solution, the new perturbation solution is shown to be slightly more accurate than that of Parlange et al. (1984) with the second-order approximation. The obtained third-order solution exhibits considerable improvement in accuracy. In relatively simple analytical forms, the present perturbation solution will help to understand better the non-linear characteristics of tidal water table fluctuations in as modeled by the non-linear Boussinesq equation coastal unconfined aquifers.     

The enhancing effect on tidal signals of a submarine spring connected to a semi-infinite confined aquifer

Abstract

Submarine springs play an important role in submarine groundwater discharge (SGD). To investigate the effects of these springs on the propagation of tidal signals in coastal confined aquifers, this paper considers a general coastal aquifer system with a submarine spring on the seabed where the length of the aquifer's offshore extent is finite and its submarine outlet is covered by an impermeable outlet-capping. An approximate analytical solution is obtained for describing the tidal head fluctuations in the aquifer. Solution analyses indicate that the error of the approximate analytical solution is negligible when both distances from the spring hole to the coastline and to the submarine outlet-capping are much greater than the radius of the spring hole. Sensitivity tests are conducted to investigate the effects of hydraulic properties, tidal and spring geometric configuration parameters on the tidal signal propagation in the inland aquifer. For aquifers with infinite offshore length, or without submarine springs, existing solutions in the literature are obtained. The comparison of groundwater head fluctuations for the cases with and without a submarine spring demonstrate the enhancing effect of the submarine spring on tidal signal propagation in the inland aquifer. Three situations that fit our model assumptions are given for future potential applications. A hypothetical example is used to show the possibility of identifying a spring's location using the present analytical solution together with tidal signals observed from inland wells.

Editor D. Koutsoyiannis; Associate editor Y. Guttmann

Citation Xia, Y.Q., Li, H.L., Yang, Y., and Huang, W., 2012. Enhancing effect on tidal signals of a submarine spring related to a semi-infinite confined aquifer. Hydrological Sciences Journal, 57 (6), 1231–1248.     

Analysis of benzene transport in a two‐dimensional aquifer model

In this study, the fate and transport of aqueous benzene was investigated in a laboratory‐scale homogeneous aquifer by conducting a two‐dimensional plume test. Benzene solution was introduced as a pulse type along the width of the aquifer model through a recharge zone situated at the upper‐left part of the model and followed by a steady state flow. Solution samples were collected at various locations on the front side of the model to capture two‐dimensional plumes at discrete time intervals. The benzene plumes showed a moderate retardation relative to chloride plumes observed from the previous study conducted for the same aquifer model. The retardation factor was obtained from the ratio of travel distances of benzene peaks to chloride peaks from the injection point, computed using a line integral method. Mass recovery of aqueous benzene revealed that there was a significant reduction of benzene mass, indicating the occurrence of volatilization and/or irreversible sorption during transport. Thus, retardation along with volatilization and/or irreversible sorption may be important processes affecting the fate and transport of aqueous benzene in the aquifer model. Copyright © 2005 John Wiley & Sons, Ltd.     

A two-dimensional analytical solution of groundwater responses to tidal loading in an estuary and ocean

Previous studies on tidal dynamics of coastal aquifers have focussed on the inland propagation of oceanic tides in the cross-shore direction, a configuration that is essentially one-dimensional. Aquifers at natural coasts can also be influenced by tidal waves in nearby estuaries, resulting in a more complex behaviour of head fluctuations in the aquifers. We present an analytical solution to the two-dimensional depth-averaged groundwater flow equation for a semi-infinite aquifer subject to oscillating head conditions at the boundaries. The solution describes the tidal dynamics of a coastal aquifer that is adjacent to a cross-shore estuary. Both the effects of oceanic and estuarine tides on the aquifer are included in the solution. The analytical prediction of the head fluctuations is verified by comparison with numerical solutions computed using a standard finite-difference method. An essential feature of the present analytical solution is the interaction between the cross- and along-shore tidal waves in the aquifer area near the estuary’s entry. As the distance from the estuary or coastline increases, the wave interaction is weakened and the aquifer response is reduced, respectively, to the one-dimensional solution for oceanic tides or the solution of Sun (Sun H. A two-dimensional analytical solution of groundwater response to tidal loading in an estuary, Water Resour Res 1997;33:1429–35) for two-dimensional non-interacting tidal waves.     

Forest fire effects on groundwater in a coastal aquifer (Ravenna,Italy)

We examined the fire‐induced changes in groundwater recharge rate. This aspect is particularly important in the case of large forested areas growing over a coastal aquifer affected by saltwater intrusion. In the Ravenna coastal area (Italy), pine forests grow on coastal dune belts, overlying a sandy unconfined aquifer, which is strongly affected by marine ingression. Three groundwater profiles across the forest and perpendicular to the coastline were monitored for groundwater level, physical, and chemical parameters. The aims were to define groundwater quality, recharge rate, freshwater volume, and highlight change, which occurred after a forest fire with reference to pre‐fire conditions. Analytical solutions based on Darcy Law and the Dupuit Equation were applied to calculate unconfined flow and compare recharge rates among the profiles. The estimated recharge rates increased in the partially and completely burnt areas (219 and 511 mm year^?1, respectively) compared with the pristine pine forest area (73 mm year^?1). Although pre‐fire conditions were similar in all monitored profiles, a post‐fire decrease in salinity was observed across the burnt forest, along with an increase in infiltration and freshwater lens thickness. This was attributed to decrease canopy interception and evapotranspiration caused by vegetation absence after the fire. This research provided an example of positive forest fire feedback on the quantity and quality of fresh groundwater resources in a lowland coastal aquifer affected by saltwater intrusion, with limited availability of freshwater resources. The fire provided an opportunity to evaluate a new forest management approach and consider the restoration and promotion of native dune herbaceous vegetation.     

Groundwater evolution and mean water age inferred from hydrochemical and isotopic tracers in a tropical confined aquifer

The coastal confined aquifer in the Gulf of Urabá (Colombia) is an important water source for the banana agro‐industry as well as for urban and rural communities. However, the main processes controlling recharge and mixing in the aquifer are still poorly understood. Hydrochemical analyses and stable isotope monitoring were conducted to (a) determine groundwater recharge origin, mean groundwater age, and the main processes governing groundwater chemistry and the potential mixing of marine water and the influence of diffusive processes from the two surrounding aquitard layers. Hydrochemical data indicate that the main processes affecting the dissolved chemical composition include cation exchange, dissolution of carbonated and CO₂, and silicate weathering. δ¹⁸O and δ²H compositions combined with ¹⁴C data highlight the differences in climatic conditions between the recharge zone and the confined section of the aquifer, which is close to the Atlantic Ocean. Groundwater samples with ¹⁴C ages from recent to 28,300 years BP show a depleted isotopic trend ranging from ?6.43‰ to ?9.14‰ in δ¹⁸O and from ?43.2‰ to ?65.7‰ in δ²H. The most depleted δ¹⁸O and δ²H compositions suggest a cooler recharge climate than the current conditions (corresponding to the last glacial period of the late Pleistocene). Depleted δ¹³C values in the total dissolved inorganic carbon indicate the existence of organic material oxidation processes within the geologic formation. These results can be used or transferred to enhance groundwater modelling efforts in other confined coastal aquifers of South America where scarcity of long‐term monitoring data limits water resources planification under a changing climate.     

Rainfall infiltration‐derived submarine groundwater discharge from multi‐layered aquifer system terminating at the coastline

This article investigates the quantity of submarine groundwater discharge (SGD) from a coastal multi‐layered aquifer system in response to constant rainfall infiltration. The system comprises an unconfined aquifer, a leaky confined aquifer and an aquitard between them and terminates at the coastline. An approximate analytical solution is derived based on the following assumptions: (i) flow is horizontal in the aquifers and vertical in the aquitard, and (ii) flow in the unconfined aquifer is described by nonlinear Boussinesq equation. The analytical solution is compared with numerical solutions of the strictly two‐dimensional nonlinear model to validate the model assumptions used for the analytical solution. The SGD from the leaky confined aquifer increases with the inland rainfall infiltration recharge and the specific leakage of aquitard. The maximum SGD ranges from 1·87 to 10·37 m³ per day per meter of shoreline when rainfall infiltration ranges from 18·2 to 182 mm/year and the specific leakage of aquitard varies from 10^?9 to 10^?1 l/day. Copyright © 2011 John Wiley & Sons, Ltd.     

Wellbore flow‐rate solution for a constant‐head test in two‐zone finite confined aquifers

The solution describing the wellbore flow rate in a constant‐head test integrated with an optimization approach is commonly used to analyze observed wellbore flow‐rate data for estimating the hydrogeological parameters of low‐permeability aquifers. To our knowledge, the wellbore flow‐rate solution for the constant‐head test in a two‐zone finite‐extent confined aquifer has never been reported so far in the literature. This article is first to develop a mathematical model for describing the head distribution in the two‐zone aquifer. The Laplace domain solutions for the head distributions and wellbore flow rate in a two‐zone finite confined aquifer are derived using the Laplace transform, and their corresponding time domain solutions are then obtained using the Bromwich integral method and residue theorem. These new solutions are expressed in terms of an infinite series with Bessel functions and not straightforward to calculate numerically. A large‐time solution for the wellbore flow rate is therefore developed by employing the relationship of small Laplace variable versus large time variable and L'Hospital's rule. The result shows that the large‐time solution is identical to the steady‐state solution obtained after applying the Tauberian theorem into the Laplace domain solution. This large‐time solution can reduce to the Thiem equation in the case of no skin. Finally, the newly developed solution is used to investigate the effects of outer boundary distance and conductivity ratio on the wellbore flow rate. Copyright © 2011 John Wiley & Sons, Ltd.     

Tidal effects on groundwater dynamics in unconfined aquifers

The variation of seawater level resulting from tidal fluctuations is usually neglected in regional groundwater flow studies. Although the tidal oscillation is damped near the shoreline, there is a quasi‐steady‐state rise in the mean water‐table position, which may have an influence on regional groundwater flow. In this paper the effects of tidal fluctuations on groundwater hydraulics are investigated using a variably saturated numerical model that includes the effects of a realistic mild beach slope, seepage face and the unsaturated zone. In particular the impact of these factors on the velocity field in the aquifer is assessed. Simulations show that the tidal fluctuation has substantial consequences for the local velocity field in the vicinity of the exit face, which affects the nearshore migration of contaminant in coastal aquifers. An overheight in the water table as a result of the tidal fluctuation is observed and this has a significant effect on groundwater discharge to the sea when the landward boundary condition is a constant water level. The effect of beach slope is very significant and simplifying the problem by considering a vertical beach face causes serious errors in predicting the water‐table position and the groundwater flux. For media with a high effective capillary fringe, the moisture retained above the water table is important in determining the effects of the tidal fluctuations. Copyright © 2001 John Wiley & Sons, Ltd.     

Surface water–groundwater exchange dynamics in a tidal freshwater zone

In coastal rivers, tides can propagate for tens to hundreds of kilometres inland beyond the saltwater line. Yet the influence of tides on river–aquifer connectivity and solute transport in tidal freshwater zones (TFZs) is largely unknown. We estimate that along the TFZ of White Clay Creek (Delaware, USA), 11% of river water exchanges through tidal bank storage zones. Additional hyporheic processes such as flow through bedforms likely contribute even more exchange. The turnover length associated with tidal bank storage is 150 km, on the order of turnover lengths for all hyporheic exchange processes in non‐tidal rivers of similar size. Based on measurements at a transect of piezometers located 17 km from the coast, tides exchange 0.36 m³ of water across the banks and 0.86 m³ across the bed per unit river length. Exchange fluxes range from ?1.66 to 2.26 m day^?1 across the bank and ?0.84 to 1.88 m day^?1 across the bed. During rising tide, river water infiltrates into the riparian aquifer, and the downstream transport rate in the channel is low. During falling tide, stored groundwater is released to the river, and the downstream transport rate in the channel increases. Tidal bank storage zones may remove nutrients or other contaminants from river water and attenuate nutrient loads to coasts. Alternating expansion and contraction of aerobic zones in the riparian aquifer likely influence contaminant removal along flow paths. A clear need exists to understand contaminant removal and other ecosystem services in TFZs and adopt best management practices to promote these ecosystem services. Copyright © 2015 John Wiley & Sons, Ltd.     

Two‐dimensional solute transport for periodic flow in isotropic porous media: an analytical solution

In this article, a mathematical model is presented for the dispersion problem in finite porous media in which the flow is two‐dimensional, the seepage flow velocity is periodic, and dispersion parameter is proportional to the flow velocity. In addition to these, first‐order decay and zero‐order production parameters have also been considered directly proportional to the velocity. Retardation factor is taken into account in the present problem. First‐type boundary condition of periodic nature is considered at the extreme end of the boundary. Mixed‐type boundary condition is assumed at the origin of the domain. A classical mathematical substitution transforms the original advection–dispersion equation into diffusion equation in terms of other dependent and independent variables, with constant coefficients. Laplace transform technique is used to obtain the analytical solution. Copyright © 2011 John Wiley & Sons, Ltd.