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A new mathematical model is developed to describe the flow in response to a constant-head pumping (or constant-head test, CHT) in a leaky unconfined aquifer system of infinite lateral extent with considering unsaturated flow. The model consists of an unsaturated zone on the top, an unconfined aquifer in the middle, and a second aquifer (aquitard) at the bottom. The unsaturated flow is described by Richard's equation, and the flows in unconfined aquifer and second layer are governed by the groundwater flow equation. The well partially penetrates the unconfined aquifer with a constant head in the well due to CHT. The governing equations of the model are linearized by the perturbation method and Gardner's exponential model is adopted to describe the soil retention curves. The solution of the model for drawdown distribution is obtained by applying the methods of Laplace transform and Weber transform. Then the solution for the wellbore flowrate is derived from the drawdown solution with Darcy's law. The issue of the equivalence of normalized drawdown predicted by the present solution for constant-head pumping and Tartakovsky and Neuman's (2007) solution for constant-rate pumping is discussed. On the basis of the wellbore flowrate solution, the results of the sensitivity analysis indicate that the wellbore flowrate is very sensitive to the changes in the radial hydraulic conductivity and the thickness of the saturated zone. Moreover, the results predicted from the present wellbore flowrate solution indicate that this new solution can reduce to Chang’s et al. (2010a) solution for homogenous aquifers when the dimensionless unsaturated exponent approaches 100. The unsaturated zone can be considered as infinite extent in the vertical direction if the thickness ratio of the unsaturated zone to the unconfined aquifer is equal to or greater than one. As for the leakage effect, it can be ignored when the vertical hydraulic conductivity ratio (i.e., the vertical hydraulic conductivity of the lower layer over that of the unconfined aquifer) is smaller than 0.1. The present solution is compared with the numerical solution from FEMWATER for validation and the results indicate good match between these two solutions. Finally, the present solution is applied to a set of field drawdown data obtained from a CHT for the estimation of hydrogeologic parameters. [ABSTRACT FROM AUTHOR]

Highlights: [•] We model stream filtration (SDR) induced by pumping in three-kinds of aquifers. [•] The time-domain solutions are in terms of a simple series with fast convergence. [•] Neglecting vertical flow in a leaky aquifer underestimates the SDR. [•] Uncertainty in the SDR prediction is evaluated by the Monte Carlo simulation. [•] The model’s SDR prediction agrees well with a field SDR experiment. [ABSTRACT FROM AUTHOR]

Summary: The bending of aquitard like a plate due to aquifer pumping and compression is often encountered in many practical problems of subsurface flow. This reaction will have large influence on the release of the volume of water from the aquifer, which is essential for the planning and management of groundwater resources in aquifers. However, the groundwater flow induced by pumping in a leaky aquifer system is often assumed that the total stress of aquifer maintains constant all the time and the mechanical behavior of the aquitard formation is negligible. Therefore, this paper devotes to the investigation of the effect of aquitard bending on the drawdown distribution in a leaky aquifer system, which is obviously of interest in groundwater hydrology. Based on the work of Wang et al. (2004) this study develops a mathematical model for investigating the impacts of aquitard bending and leakage rate on the drawdown of the confined aquifer due to a constant-rate pumping in the leaky aquifer system. This model contains three equations; two flow equations delineate the transient drawdown distributions in the aquitard and the confined aquifer, while the other describes the vertical displacement in response to the aquitard bending. For the case of no aquitard bending, this new solution can reduce to the Hantush Laplace-domain solution (Hantush, 1960). On the other hand, this solution without the leakage effect can reduce to the time domain solution of Wang et al. (2004). The results show that the aquifer drawdown is influenced by the bending effect at early time and by the leakage effect at late time. The results of sensitivity analysis indicate that the aquifer compaction is sensitive only at early time, causing less amount of water released from the pumped aquifer than that predicted by the traditional groundwater theory. The dimensionless drawdown is rather sensitive to aquitard’s hydraulic conductivity at late time. Additionally, both the hydraulic conductivity and thickness of the aquifer are the most sensitive parameters in influencing the predicted dimensionless drawdown. [Copyright &y& Elsevier]

Abstract: The effect of tidal fluctuation on groundwater flow is an important issue from many aspects in coastal areas. This paper develops a new analytical solution to describe the groundwater fluctuation in a sloping coastal aquifer system which comprises an upper unconfined aquifer, a lower confined aquifer, and an aquitard in between. The solution is allowed to investigate the effects of bottom slope and leakage as well as aquifer parameters on head fluctuations in both unconfined and confined aquifers. The research result indicates that the effect of the bottom angle on the groundwater fluctuation and time lag is significant in the unconfined aquifer and not negligible if the leakage in the confined aquifer is large. In addition, the joint effects of aquifer parameters and bottom angle on groundwater fluctuation and time lag are also discussed. [Copyright &y& Elsevier]

Summary: Radial collector wells are often constructed near a stream to obtain more water and produce smaller drawdown in comparison with traditional vertical wells. This paper aims at developing a mathematical model for describing head distributions induced by pumping in a radial collector well near a stream in an unconfined aquifer. A low permeable streambed between the stream and the aquifer is considered. The first-order free surface equation is used to describe the movement of water table. A point-sink solution of the model is developed first by a general transform combining Fourier sine and cosine transforms and then by Fourier transform and Laplace transform. The transient solution of head distributions for different well types such as the horizontal well or radial collector well can be obtained by integrating the point-sink solution along the well. Based on Darcy’s law and the developed solution, an equation for temporal stream depletion rate describing filtration from the stream is then obtained. The steady-state solutions for filtration can be obtained from the transient solution when neglecting the exponential term associated with time. It is found that steady-state filtration depends only on the ratio of streambed permeability over aquifer permeability. Steady-state filtration equals water extraction from a well when the ratio is larger than 10−2. The streambed is regarded as completely impermeable when the ratio is less than 10−7. Additionally, the lowest water table happens near the well before occurrence of filtration. The lowest water table moves landward and away from the well after filtration occurs. [ABSTRACT FROM AUTHOR]

Abstract: A dome-shaped layer can be selected as a storage site for fluid injection. In this study, we develop a mathematical model for simulating transient head distribution in a heterogeneous and anisotropic dome-shaped layer due to a constant-head injection in a fully penetrating well. In the model, a form of step change is adopted to approximate the upper and lower boundaries of the dome and then the layer is split into two regions. The Laplace-domain solution of the model is developed using the Laplace transform and method of separation of variables. The transient injection rate at wellbore can then be obtained based on Darcy’s law and Bromwich integral method. The predicted head contours from the head solution show significant vertical flow components near the location of step change in the dome reservoir. The results of sensitivity analysis indicate that the hydraulic conductivity is the most sensitive parameter and the specific storage is the least sensitive one to the injection rate after a short period of injection time. In addition, the injection rate for a dome reservoir is also very sensitive to the change of the height for the reservoir near the injection well (first region) at a very early injection time. In contrast, the injection rate is more sensitive to the change of the height of the second region than that of the first region at late time. This analytical solution may be used as a primary tool to assess the capacity of fluid injection to various dome reservoirs. [Copyright &y& Elsevier]

Abstract: The objective of this paper is to present an analytical solution for describing the head distribution in an unconfined aquifer with a single pumping horizontal well parallel to a fully penetrating stream. The Laplace-domain solution is developed by applying Fourier sine, Fourier and Laplace transforms to the governing equation as well as the associated initial and boundary conditions. The time-domain solution is obtained after taking the inverse Laplace transform along with the Bromwich integral method and inverse Fourier and Fourier sine transforms. The upper boundary condition of the aquifer is represented by the free surface equation in which the second-order slope terms are neglected. Based on the solution and Darcy’s law, the equation representing the stream depletion rate is then derived. The solution can simulate head distributions in an aquifer infinitely extending in horizontal direction if the well is located far away from the stream. In addition, the solution can also simulate head distributions in confined aquifers if specific yield is set zero. It is shown that the solution can be applied practically to evaluate flow to a horizontal well. [Copyright &y& Elsevier]

• An analytical model for radially convergent tracer test in a two-zone aquifer is built. • The validity of using the model to actual asymmetrical tracer transport is assessed. • The effects of vertical dispersion and skin zone on breakthrough curve are examined. Radially convergent tracer test (RCT) with an extraction well and a tracer injection well is commonly conducted for determining aquifer dispersivity associated with the spreading of contamination plume. A variety of analytical models for RCT have been proposed, but the effects of skin zone and vertical dispersion are rarely explored. In addition, little attention is paid to the validity of those analytical models assuming asymmetrical tracer transport (ATT) as radially symmetrical transport (RST) toward the pumping well. This study develops a new analytical model for RCT subject to the above-mentioned effects in a confined aquifer with a skin zone around the wellbore. The Laplace-domain solution of the model for a continuous or instantaneous input is developed. A finite element solution (FES) for ATT is also developed to verify the Laplace-domain solution based on RST. Results suggest ATT can be regarded as RST in predicting the breakthrough curve (BTC) at the pumping well when four quantitative conditions are met. A lumped dimensionless parameter dominates those two effects on the BTC. Both the FES and Laplace-domain solution agree with monitored concentration data from a field RCT. [ABSTRACT FROM AUTHOR]

Magnetic nanoparticles modified by third-generation dendrimers (MNP-G3) and MNP-G3 further modified by ethylenediaminetetraacetic acid (EDTA) (MNP-G3-EDTA) were conducted to investigate their ability for recovery of precious metals (Pd(IV), Au(III), Pd(II) and Ag(I)) in water. Experiments were carried out using batch reactors for the studies of adsorption kinetics, adsorption isotherms, competitive adsorption and regeneration. The pseudo second-order model is the best-fit model among others suggesting that the adsorption of precious metals by MNP-G3 in water is a chemisorption process. Three adsorption isotherms namely Langmuir, Freundlich and Dubinin-Radushkevich isotherm were examined and the results showed the similarities and consistency of both linear and nonlinear analyses. Pd(IV) and Au(III) with higher valence exhibited relatively better adsorption efficiency than Pd(II) and Ag(I) with lower valence suggesting that the adsorption of precious metals by MNP-G3 is a function of valence. In the presence of the competing ion Zn(II), the adsorption efficiency of MNP-G3 for all four precious metals was declined significantly. The use of MNP-G3-EDTA revealed an increase in the adsorption efficiency for all four precious metals. However, the low selectivity of MNP-G3 towards precious metals was not enhanced by the modification of EDTA onto the MNP-G3. The regeneration of metal-laden MNP-G3 can be readily performed by using 1.0% HCl solution as a desorbent solution. [ABSTRACT FROM AUTHOR]

This study proposes an analytical and meshless model for three-dimensional transient flow induced by multiple wells in a stream-confined aquifer system with arbitrary nonuniform aquifer thickness. The model involves allocating external image wells near the aquifer boundary. The aquifer drawdown is defined as Theis' solution plus a simple series expanded by complementary error functions reflecting the boundary effects of the stream and impervious stratum. The solution for stream depletion rate (SDR) can be derived based on the drawdown solution. Results suggest the Dupuit assumption of no vertical flow is valid to estimate SDRs affected by the landward exponentially decreasing thickness. The SDR induced by multiple wells is the same as that by a single well if the total well discharge rate and stream-well distances in the multiple well case are identical to those in the single well case. The present solution outperforms a finite difference solution in computational efficiency. • A meshless model for 3D flow in a pumped confined aquifer with a stream is built. • The analytical solutions of aquifer drawdown and stream depletion rate are derived. • The solution is applicable to aquifer thickness varying spatially and arbitrarily. • The solution can easily handle the problem of multiple well pumping. • The solution is a simple and efficient alternative to a finite difference solution. [ABSTRACT FROM AUTHOR]

This study develops a general analytical model for describing transient drawdown distribution induced by pumping at a finite-radius well in a radial two-zone confined aquifer of finite areal extent with Robin-type condition at both inner and outer boundaries. This model is also applicable to heat conduction problems for a composite hollow cylinder on the basis of the analogy between heat flow and groundwater flow. The time-domain solution of the model is derived by the methods of Laplace transform, Bromwich integral, and residue theorem. This new solution can reduce to the solution for constant-head test (CHT) or constant-rate test (CRT) problem by specifying appropriate coefficients at the Robin inner boundary condition. The solution describing the flow rate across the wellbore due to CHT is further developed by applying Darcy’s law to the new solution. In addition, steady-state solutions for both CHT and CRT are also developed based on the approximation for Bessel functions with very small argument values. Many existing solutions for transient flow in homogeneous or two-zone finite aquifers with Dirichlet or no-flow condition at the outer boundary are shown to be special cases of the present solution. Furthermore, the sensitivity analysis is also performed to investigate the behaviors of the wellbore flow due to CHT and the aquifer drawdown induced by CRT in response to the change in each of aquifer parameters. [ABSTRACT FROM AUTHOR]

Summary The prediction of groundwater level fluctuation due to tidal waves propagation in coastal aquifers is important for the planning and management of water resources in coastal areas. A two-dimensional (2-D) analytical solution is derived to describe the tidal groundwater fluctuation in an aquifer bounded by three water–land boundaries that form a U-shaped coastline. Two opposite sides represent estuary–land boundaries on which the amplitude attenuation and phase shift of the tidal movement in the estuary are considered while the third side is an ocean–land boundary. The effects of wave interaction due to the propagation of oscillating oceanic tides in the cross-shore direction inland and the transmission of the two opposite estuarine tides in the along-shore direction are investigated. Three existing head-fluctuation solutions can be considered as special cases of the present solution; one is for one-dimensional flow and the other two are for 2-D flow. A transition distance ranging from 10 to 15 times of tidal propagation length along the shoreline can be estimated based on the solution. This distance can be used to judge whether the interaction among tides is significant. The influences of hydraulic properties on the tidal fluctuations within the aquifer can therefore be assessed quantitatively. Based on sensitivity analyses, one can conclude that the tidal head is most sensitive to the transmissivity and storativity of the aquifer, and least to the damping coefficient of tidal amplitude and wave number along the estuary. The sensitivities of head fluctuation to the changes of transmissivity and storativity depend on the shoreline length and whether the interaction among waves is significant. On the other hand, the sensitivities of head fluctuation to the changes of damping coefficient and wave number increase with diagonal distance from the entry of estuary and reach the largest magnitude near the estuary far away seashore. [ABSTRACT FROM AUTHOR]

Abstract: It is of practical interest to investigate the natural evaporation of volatile organic compounds (VOCs) after the removal of a leaking tank situated on the top of the soil. This study aims to develop a mathematical model to predict mole fraction distributions and migration of evaporation front for two VOCs emanating from residual non-aqueous phase liquid (NAPL) due to the leak from the tank in a homogeneous soil. Considering the location of the front and the regions above and below the front, a numerical model for the diffusive transport of VOCs in unsaturated soils was developed using the finite difference method with a moving grid approach. The model was further simplified to the case of single VOC and solved analytically by Boltzmann''s transformation with a moving boundary. Analytical expressions for the depth and moving speed of the front for a single VOC were then obtained for practical use. Finally, the developed model was used to predict the concentration distributions of VOCs below the land surface and examine the factors affecting the location and moving speed of the evaporation front. [Copyright &y& Elsevier]

An aquifer with a wellbore surrounded by a finite-thickness skin, such as a gravel pack, can be regarded as a radial two-zone system. In this study, a mathematical model is developed to describe contaminant transport in a radial two-zone confined aquifer system. The solution of the model equations can be used to delineate contaminant transport in such a two-zone aquifer system and to investigate the skin effect on the temporal and spatial concentration distribution. The present solution is shown to reduce to an existing solution for transport in a homogeneous aquifer in the case when there is no wellbore skin. The results predicted from the solution indicate that the skin effect has a significant impact on the concentration distribution at early time. But an abrupt change in the spatial concentration distribution may occur at the interface of the skin zone and aquifer formation zone. The results from a sensitivity analysis reveal that dispersivity in the formation zone has a more significant effect on the concentration distribution than do the effects of skin thickness and dispersivity in the skin zone., (Copyright © 2012 Elsevier B.V. All rights reserved.)

The heat of high-level nuclear waste may be generated and released from a canister at final disposal sites. The waste heat may affect the engineering properties of waste canisters, buffers, and backfill material in the emplacement tunnel and the host rock. This study addresses the problem of the heat generated from the waste canister and analyzes the heat distribution between the buffer and the host rock, which is considered as a radial two-layer heat flux problem. A conceptual model is first constructed for the heat conduction in a nuclear waste repository and then mathematical equations are formulated for modeling heat flow distribution at repository sites. The Laplace transforms are employed to develop a solution for the temperature distributions in the buffer and the host rock in the Laplace domain, which is numerically inverted to the time-domain solution using the modified Crump method. The transient temperature distributions for both the single- and multi-borehole cases are simulated in the hypothetical geological repositories of nuclear waste. The results show that the temperature distributions in the thermal field are significantly affected by the decay heat of the waste canister, the thermal properties of the buffer and the host rock, the disposal spacing, and the thickness of the host rock at a nuclear waste repository.

Biswas et al. (1993. A model for chlorine concentration decay in pipes. Water Res. 27(12), 1715-1724) presented an analytical solution of a two-dimensional (2-D) steady-state chlorine transport equation in a pipe under the turbulent condition and employed fractional error function and regression technique to develop an approximate solution. However, their approximate solution may not give a good result if the wall decay parameter is large. This paper provides a more accurate approximate solution of the 2-D steady-state chlorine transport equation under the turbulent condition. This new approximate solution has advantages of easy evaluation and good accuracy when compared with the approximate solution given by Biswas et al. (1993). In addition, this paper also develops a methodology that combines simulated annealing (SA) with this new approximate solution to determine the wall decay parameter. Two cases are chosen to demonstrate the application of the present approximate solution and methodology. The first case is to use this new approximate solution in simulating chlorine decay in pipes with the experiment-observed data given by Rossman (2006. The effect of advanced treatment on chlorine decay in metallic pipes. Water Res. 40(13), 2493-2502), while the second case presents the determination of the wall consumption at the end of the pipe network.

Slug test data obtained from tests performed in an unconfined aquifer are commonly analyzed by graphical or numerical approaches to determine the aquifer parameters. This paper derives three fourth-degree polynomials to represent the relationship between Bouwer and Rice's coefficients and the ratio of the screen length to the radius of the gravel envelope. A numerical approach using the nonlinear least squares and Newton's method is used to determine hydraulic conductivity from the best fit of the slug test data. The method of nonlinear least squares minimizes the sum of the squares of the differences between the predicted and observed water levels inside the well. With the polynomials, the hydraulic conductivity can be obtained by simply solving the nonlinear least squares equation by Newton's method. A computer code, SLUGBR, was developed from the derived polynomials using the proposed numerical approach. The results of analyzing two slug test datasets show that SLUGBR can determine hydraulic conductivity with very good accuracy.