Recharge characteristics of an unconfined aquifer from the rainfall-water table relationship

The determination of recharge levels of unconfined aquifers, recharged entirely by rainfall, is done by developing a model for the aquifer that estimates the water-table levels from the history of rainfall observations and past water-table levels. In the present analysis, the model parameters that influence the recharge were not only assumed to be time dependent but also to have varying dependence rates for various parameters. Such a model is solved by the use of a recursive least-squares method. The variable-rate parameter variation is incorporated using a random walk model. From the field tests conducted at Tomago Sandbeds, Newcastle, Australia, it was observed that the assumption of variable rates of time dependency of recharge parameters produced better estimates of water-table levels compared to that with constant-recharge parameters. It was observed that considerable recharge due to rainfall occurred on the very same day of rainfall. The increase in water-table level was insignificant for subsequent days of rainfall. The level of recharge very much depends upon the intensity and history of rainfall. Isolated rainfalls, even of the order of 25 mm day⁻¹, had no significant effect on the water-table levels.     

Determination of longitudinal dispersivity in an unconfined sandy aquifer

Study of the mobility of contaminants in an aquifer is an important issue for the proper remediation of contaminated groundwater. Determination of associated solute transport parameters therefore is essential for investigation of the extent to which groundwater can be contaminated. This study aimed at determining solute transport parameters for an unconfined sandy aquifer at a laboratory scale through various tracer tests using a conservative solute as a tracer. Tracer tests consisted of both well‐tracer tests (single and double wells) and an aquifer tracer test using a plume‐capturing device such as time domain reflectometry (TDR). The results showed that longitudinal dispersivities estimated from the single and double well‐tracer tests were 2·2 cm and 13·5 cm for a travel distance of 9·3 cm and 13·5 cm from the injection point respectively. These results agreed reasonably well with the results of the aquifer tracer test. The solute transport parameters obtained at multiple points in the aquifer through the aquifer tracer test revealed that the dispersivity length was proportional to the travel distance by a factor of 0·3, which was moderately higher than the value of 0·1 given in the literature. Copyright © 2002 John Wiley & Sons, Ltd.     

Optimizing remediation of an unconfined aquifer using a hybrid algorithm

We present a novel hybrid algorithm, integrating a genetic algorithm (GA) and constrained differential dynamic programming (CDDP), to achieve remediation planning for an unconfined aquifer. The objective function includes both fixed and dynamic operation costs. GA determines the primary structure of the proposed algorithm, and a chromosome therein implemented by a series of binary digits represents a potential network design. The time-varying optimal operation cost associated with the network design is computed by the CDDP, in which is embedded a numerical transport model. Several computational approaches, including a chromosome bookkeeping procedure, are implemented to alleviate computational loading. Additionally, case studies that involve fixed and time-varying operating costs for confined and unconfined aquifers, respectively, are discussed to elucidate the effectiveness of the proposed algorithm. Simulation results indicate that the fixed costs markedly affect the optimal design, including the number and locations of the wells. Furthermore, the solution obtained using the confined approximation for an unconfined aquifer may be infeasible, as determined by an unconfined simulation.     

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.     

Analysis of an unconfined aquifer subject to asynchronous dual-tide propagation

Most published solutions for aquifer responses to ocean tides focus on the one-sided attenuation of the signal as it propagates inland. However, island aquifers experience periodic forcing from the entire coast, which can lead to integrated effects of different tidal signals, especially on narrow high-permeability islands. In general, studies disregard a potential time lag as the tidal wave sweeps around the island. We present a one-dimensional analytical solution to the ground water flow equation subject to asynchronous and asymmetric oscillating head conditions on opposite boundaries and test it on data from an unconfined volcanic aquifer in Maui. The solution considers sediment-damping effects at the coastline. The response of Maui Aquifers indicate that water table elevations near the center of the aquifer are influenced by a combination of tides from opposite coasts. A better match between the observed ground water head and the theoretical response can be obtained with the proposed dual-tide solution than with single-sided solutions. Hydraulic diffusivity was estimated to be 2.3 × 10⁷ m²/d. This translates into a hydraulic conductivity of 500 m/d, assuming a specific yield of 0.04 and an aquifer thickness of 1.8 km. A numerical experiment confirmed the hydraulic diffusivity value and showed that the y -intercepts of the modal attenuation and phase differences estimated by regression can approximate damping factors caused by low-permeability units at the boundary.     

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.     

Travel time to a well pumping an unconfined aquifer without recharge

A solution is given for the travel time to a well pumping an ideal, horizontal unconfined aquifer, under steady-state conditions, when recharge from infiltration is negligible. Three forms of the solution are provided: a closed-form solution, an integral to be calculated in a worksheet, and a simple equation. The three forms of the solution give travel times nearly identical to those obtained using a finite-element code for saturated and unsaturated flow and particle tracking.     

Monitoring of drawdown pattern during pumping in an unconfined physical aquifer model

In this study, we attempted to analyse a drawdown pattern around a pumping well in an unconfined sandy gravelly aquifer constructed in a laboratory tank by means of both experimental and numerical modelling of groundwater flow. The physical model consisted of recharge, aquifer and discharge zones. Permeability and specific yield of the aquifer material were determined by Dupuit approximation under steady‐state flow and stepwise gravitational drainage of groundwater, respectively. The drawdown of water table in pumping and neighbouring observation wells was monitored to investigate the effect of no‐flow boundary on the drawdown pattern during pumping for three different boundary conditions: (i) no recharge and no discharge with four no‐flow boundaries (Case 1); (ii) no recharge and reservoir with three no‐flow boundaries (Case 2); (iii) recharge and discharge with two no‐flow boundaries (Case 3). Based on the aquifer parameters, numerical modelling was also performed to compare the simulated drawdown with that observed. Results showed that a large difference existed between the simulated drawdown and that observed in wells for all cases. The reason for the difference could be explained by the formation of a curvilinear type water table between wells rather than a linear one due to a delayed response of water table in the capillary fringe. This phenomenon was also investigated from a mass balance study on the pumping volume. The curvilinear type of water table was further evidenced by measurement of water contents at several positions in the aquifer between wells using time domain reflectometry (TDR). This indicates that the existing groundwater flow model applicable to an unconfined aquifer lacks the capacity to describe a slow response of water table in the aquifer and care should be taken in the interpretation of water table formation in the aquifer during pumping. Copyright © 2001 John Wiley & Sons, Ltd.     

Conduit properties and karstification in the unconfined Floridan aquifer

Exchange of water between conduits and matrix is an important control on regional chemical compositions, karstification, and quality of ground water resources in karst aquifers. A sinking stream (Santa Fe River Sink) and its resurgence (River Rise) in the unconfined portion of the Floridan Aquifer provide the opportunity to monitor conduit inflow and outflow. The use of temperature as a tracer allows determination of residence times and velocities through the conduit system. Based on temperature records from two high water events, flow is reasonably represented as pipe flow with a cross-sectional area of 380 m2, although this model may be complicated by losses of water from the conduit system at higher discharge rates. Over the course of the study year, the River Rise discharged a total of 1.9 x 10(7) m3 more water than entered the River Sink, reflecting net contribution of ground water from the matrix into the conduit system. However, as River Sink discharge rates peaked following three rainfall events during the study period, the conduit system lost water, presumably into the matrix. Surface water in high flow events is typically undersaturated with respect to calcite and thus may lead to dissolution, depending on its residence time in the matrix. A calculation of local denudation is larger than other regional estimates, perhaps reflecting return of water to conduits before calcite equilibrium is reached. The exchange of matrix and conduit water is an important variable in karst hydrology that should be considered in management of these water resources.     

Unconfined aquifer and slow drainage

One of the particular features of unsteady free surface flow is the phenomenon of the slow draining of water-bearing materials. This phenomenon is usually identified and referred to as delayed yield from storage, introduced to scientific literature by Boulton.     

Estimation of the effective precipitation recharge coefficient in an unconfined aquifer using stochastic analysis

Effectively managing groundwater relies heavily on estimating the amount of precipitation that may infiltrate the subsurface and supply groundwater. In this study, we present a novel estimation method based on a stochastic approach to evaluate the quantity of precipitation that may recharge groundwater. The precipitation recharge coefficient is also investigated based on an unconfined aquifer with an unbound, infinitely extended boundary condition. Moreover, a spectrum's relationship to the precipitation and groundwater level variation is also derived. The precipitation recharge coefficient can be obtained from the solution of the spectrum equation. Furthermore, sensitivity analysis is performed in order to determine the key variable on the precipitation recharge coefficient. Analysis results indicate that the location of an observation well affects the estimated precipitation recharge coefficient. If the precipitation recharge area is large enough, the precipitation recharge coefficient becomes insensitive to the location of the observation well. The spectrum's relationship between the precipitation recharge and groundwater level variation is also applied when estimating the precipitation recharge coefficient upstream of the Cho‐Shui River alluvial fan. According to those results, the precipitation recharge coefficient is 0·03 and the amount of groundwater recharge from precipitation is 35 million tons of water annually upstream of the Cho‐Shui River alluvial fan. Copyright © 2000 John Wiley & Sons, Ltd.     

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.     

Analysis of the water content in an unconfined aquifer with a partially penetrated pumping well

Most methods developed to represent water flow phenomena in an unconfined aquifer with a fully penetrated pumping well are either numerical, such as the well‐known FEMWTER model, or experimental; analytical models of a partially penetrated pumping well are rare. This study employs the linearized Richards equation as the governing equation, with the aid of Fourier Integral Transformation, to obtain an analytical solution of the water content distribution in an unconfined aquifer with a partially penetrated pumping well. The results from this study could serve to substantiate in some sense results from numerical models. In addition, the theory developed herein can be modified to simulate a vacuum‐pressured pumping well since it is derived by considering, among others, the location and length of a well screen with fluxes. Copyright © 2008 John Wiley & Sons, Ltd.     

The influence of delayed drainage on data from pumping tests in unconfined aquifers

Equations are derived for the flow to a pumped well in an aquifer having uniform anisotropy and overlain by a low-permeability aquitard. The water-table is assumed to be located in the aquitard. Drainage from the capillary zone above the water-table is taken into account.The differential equation for the flow in the aquifer is identical with that derived in a previous paper. The formation constants may therefore be evaluated by using type curves as described in that paper.A well-known pumping test is reanalysed, using the equations in the present paper. It is shown that the time-drawdown curves can be explained only by the existence of a low-permeability stratum in the vicinity of the water-table. In this example the slow draining of the unsaturated zone above the water-table seems to be a significant factor in determining the shape of the time-drawdown curves.     

Analytical model for aquifer response incorporating distributed stream leakage

An analytical model of stream/aquifer interaction is proposed that predicts drawdown in an aquifer with leakage from a finite-width stream induced by pumping from a well. The model is formulated based on the assumptions of stream partial penetration, a semipervious streambed, and distributed recharge across a finite-width stream. Advantages of the analytical solution include its simple structure, consisting of the Theis well function with integral modifications. The solution is derived for the semi-infinite domain between the stream and pumping well, which is of primary interest to hydrogeologists. Previous stream/aquifer analytical models are compared to the analytical solution based on dimensionless drawdown profiles. Drawdown in the aquifer near a wide stream was found to be less than that predicted by a solution that ignored stream width. Deviations between the proposed analytical solutions and previous solutions increase as stream width increases. For a hypothetical stream/aquifer system, the proposed analytical solution was equivalent to prior solutions when the ratio of the distance between the stream and aquifer to the stream width was greater than 25. This analytical solution may provide improved estimates of aquifer and streambed leakage parameters by curve fitting experimental field drawdown data.     

Steady, annual, and monthly recharge implied by deep unconfined aquifer flow

We consider the response of a deep unconfined horizontal aquifer to steady, annual, and monthly recharge. A groundwater divide and a zero head reservoir constrain the aquifer, so that sinusoidal monthly and aperiodic annual recharge fluctuations create transient specific discharge near the reservoir and an unsteady water table elevation inland. One existing and two new long-term data sets from the Plymouth-Carver Aquifer in southeastern Massachusetts calibrate and confirm hydraulic properties in a set of analytical models. [Geohydrology and simulated groundwater flow, 1992] data and a new power law for tritiugenic helium to tritium ratios calibrate the steady recharge that drives the classical parabolic model of steady hydraulics [Applied Hydrogeology, 2001]. Observed water table and gradient fluctuations calibrate the transient recharge models. In the latter regard, monitoring wells within 1 km of Buttermilk Bay exhibit appreciable specific discharge and reduced water table fluctuations. We apply [Trans Am Geophys Union 32(1951)238] periodic model to the monthly hydraulics and a recharge convolution integral [J Hydrol 126(1991)315] to annual flow. An infiltration fraction of 0.79 and a consumptive use coefficient of 1.08×10⁻⁸ m/s °C relate recharge to precipitation and daylight weighted temperature across all three time scales. Errors associated with this recharge relation decrease with increasing time scale.     

An analytical solution for ground water transit time through unconfined aquifers

An exact, closed-form analytical solution is developed for calculating ground water transit times within Dupuit-type flow systems. The solution applies to steady-state, saturated flow through an unconfined, horizontal aquifer recharged by surface infiltration and discharging to a downgradient fixed-head boundary. The upgradient boundary can represent, using the same equation, a no-flow boundary or a fixed head. The approach is unique for calculating travel times because it makes no a priori assumptions regarding the limit of the water table rise with respect to the minimum saturated aquifer thickness. The computed travel times are verified against a numerical model, and examples are provided, which show that the predicted travel times can be on the order of nine times longer relative to existing analytical solutions.     

Spatio‐temporal analysis of groundwater recharge and mound dynamics in an unconfined aquifer: a GIS‐based approach

Groundwater recharge and mounding of water‐table is a complex phenomenon involving time‐ and space‐dependent hydrologic processes. The effect of long‐term groundwater mounding in the aquifer depends on soil, aquifer geometry and the area contributing to recharge. In this paper, a GIS‐based spatio‐temporal algorithm has been developed for the groundwater mound dynamics to estimate the potential rise in the water‐table and groundwater volume balance residual in an unconfined aquifer. The recharge and mound dynamics as predicted using the methodology recommended here were compared with those using the Hantush equation, and the differences were quite significant. The significance of the study is to assess the effectiveness of the basin in terms of its hydrologic and hydraulic properties for sustainable management of groundwater recharge. Copyright © 2007 John Wiley & Sons, Ltd.     

An analytical solution for describing the transient temperature distribution in an aquifer thermal energy storage system

A mathematical model is developed for predicting the temperature distribution in an aquifer thermal energy storage (ATES) system, which consists of a confined aquifer bounded from above and below by the rocks of different geological properties. The main transfer processes of heat include the conduction and advection in the aquifer and the conduction in the rocks. The semi‐analytical solution in dimensionless form for the model is developed by Laplace transforms and its corresponding time‐domain solution is evaluated by the modified Crump method. Field geothermal property data are used to simulate the temperature distribution in an ATES system. The results show that the heat transfer in the aquifer is fast and has a vast effect on the vicinity of the wellbore. However, the aquifer temperature decreases with increasing radial and vertical distances. The temperature in the aquifer may be overestimated when ignoring the effect of thermal conductivity. The temperature distribution in an ATES system depends on the vertical thermal conduction in the rocks and the horizontal advection and thermal conduction in the aquifer. The present solution is useful in designing and simulating the heat injection facility in the ATES systems. Copyright © 2010 John Wiley & Sons, Ltd.     

Analytical methods for transient flow to a well in a confined-unconfined aquifer

Concurrent existence of confined and unconfined zones of an aquifer can arise owing to ground water withdrawal by pumping. Using Girinskii's potential function, Chen (1974, 1983) developed an approximate analytical solution to analyze transient ground water flow to a pumping well in an aquifer that changes from an initially confined system to a system with both unconfined and confined regimes. This article presents the details of the Chen model and then compares it with the analytical model developed by Moench and Prickett (1972) for the same problem. Hypothetical pumping test examples in which the aquifer undergoes conversion from confined to water table conditions are solved by the two analytical models and also a numerical model based on MODFLOW. Comparison of the results suggests that the solutions of the Chen model give better results than the Moench and Prickett model except when the radial distance is very large or aquifer thickness is large compared with drawdown.