Unsteady flow to wells in layered and fissured aquifer systems

A solution has been developed for the calculation of drawdowns in leaky and confined multiaquifer systems, pumped by a well of constant discharge penetrating one or more of the aquifers. In contrast to earlier solutions the effects of elastic storage in separating and bounding aquitards have now completely been accounted for.

The computing technique is based on the numerical inversion of the Laplace transform. Two different methods are used and results are compared with an analytical solution. Both Stehfest's¹ algorithm and Schapery's² least squares method yield accurate results in a fraction of the computation time required for the analytical evaluation.

Selected sets of time-drawdown and distance-drawdown curves are plotted to illustrate multiple-aquifer well flow and to compare new solutions with results which were previously published. The analogy with flow is unconfined and fissured aquifers is demonstrated by multilayer models, representing multiple-porosity formations with linear and diffusive crossflow.     

Three-dimensional flow in the storative semiconfining layers of a leaky aquifer

An analytical solution for three-dimensional (3D) flow in the storative semiconfining layers of a leaky aquifer fully penetrated by a production well is developed in this article to provide a method from which accurate hydraulic parameters in the semiconfining layers can be derived from aquifer test data. The analysis of synthetic aquifer test data with the 3D analytical solution in the semiconfining layers provided more accurate optimal hydraulic parameters than those derived using the available quasi-two-dimensional (2D) solution. Differences between the 3D and 2D flow solutions in the semiconfining layers become larger when a no flow boundary condition is imposed at either at the top of the upper semiconfining layer or at the bottom of the lower semiconfining layer or when the hydraulic conductivity ratio of the semiconfining layer to the aquifer is larger than 0.001. In addition, differences between the 3D and 2D flow solutions in the semiconfining layers are illustrated when the thickness ratio of the semiconfining layer to the aquifer is changed. Analysis of water level data from two hypothetical and one real aquifer test showed that the 3D solution in the semiconfining layers provides lower correlation coefficients among hydraulic parameters than the 2D solution.     

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.     

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.     

A discrete space continuous time modeling approach to nonsteady flow in a leaky aquifer system of finite configuration

Existing analytical procedures for nonsteady flow in a leaky confined aquifer assume that the aquifer system is areally infinite. A technique is presented that treats a leaky confined aquifer system of finite configuration. By means of a discrete space continuous time (DSCT) modeling approach, the partial differential equation governing the flow system is transformed into a set of ordinary differential equations that can be easily integrated numerically on a high speed digital computer using available scientific subroutines. The finite difference formulation is in effect an explicit scheme. A criterion is developed for which the scheme is computationally stable. A numerical example is presented.     

Pumping-induced drawdown and stream depletion in a leaky aquifer system

The impact of ground water pumping on nearby streams is often estimated using analytic models of the interconnected stream-aquifer system. A common assumption of these models is that the pumped aquifer is underlain by an impermeable formation. A new semianalytic solution for drawdown and stream depletion has been developed that does not require this assumption. This solution shows that pumping-induced flow (leakage) through an underlying aquitard can be an important recharge mechanism in many stream-aquifer systems. The relative importance of this source of recharge increases with the distance between the pumping well and the stream. The distance at which leakage becomes the primary component of the pumping-induced recharge depends on the specific properties of the aquifer, aquitard, and streambed. Even when the aquitard is orders of magnitude less transmissive than the aquifer, leakage can be an important recharge mechanism because of the large surface area over which it occurs. Failure to consider aquitard leakage can lead to large overestimations of both the drawdown produced by pumping and the contribution of stream depletion to the pumping-induced recharge. The ramifications for water resources management and water rights adjudication can be significant. A hypothetical example helps illustrate these points and demonstrates that more attention should be given to estimating the properties of aquitards underlying stream-aquifer systems. The solution presented here should serve as a relatively simple but versatile tool for practical assessments of pumping-induced stream-aquifer interactions. However, this solution should not be used for such assessments without site-specific data that indicate pumping has induced leakage through the aquitard.     

Evaluation of confidence intervals for a steady-state leaky aquifer model

The fact that dependent variables of groundwater models are generally nonlinear functions of model parameters is shown to be a potentially significant factor in calculating accurate confidence intervals for both model parameters and functions of the parameters, such as the values of dependent variables calculated by the model. The Lagrangian method of Vecchia and Cooley [Vecchia, A.V. & Cooley, R.L., Water Resources Research, 1987, 23(7), 1237–1250] was used to calculate nonlinear Scheffé-type confidence intervals for the parameters and the simulated heads of a steady-state groundwater flow model covering 450 km² of a leaky aquifer. The nonlinear confidence intervals are compared to corresponding linear intervals. As suggested by the significant nonlinearity of the regression model, linear confidence intervals are often not accurate. The commonly made assumption that widths of linear confidence intervals always underestimate the actual (nonlinear) widths was not correct. Results show that nonlinear effects can cause the nonlinear intervals to be asymmetric and either larger or smaller than the linear approximations. Prior information on transmissivities helps reduce the size of the confidence intervals, with the most notable effects occurring for the parameters on which there is prior information and for head values in parameter zones for which there is prior information on the parameters.     

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.     

Flow to an eccentric well in a leaky circular aquifer with varied lateral replenishment

Summary An analytical solution is obtained for the flow to an eccentric well in a leaky circular aquifer with lateral replenishment, both for steady and unsteady cases. The flows for external boundary conditions of constant head and zero flux, which were treated previously, follow in the limit from a more general boundary condition. Graphs are developed to show the influence of vertical leakage and lateral replenishment on the relationship between drawdown at the well and eccentricity.Other symbols are defined in the text as they occur.     

Field investigation of the groundwater contribution to baseflow in an urban stream from a Quaternary aquifer with a leaky base

Groundwater contributions to baseflow in Minnehaha Creek, a creek located in a highly developed watershed in the Minneapolis-St. Paul metropolitan area, from the watershed's Quaternary aquifer were quantified as part of an effort to manage low flow conditions in the creek. Considerable uncertainty exists with any single method used to quantify groundwater contributions to baseflow; therefore, a “weight of evidence” approach in which methods spanning multiple spatial scales was utilized. Analyses conducted at the watershed-scale (streamflow separation and stable isotope analyses) were corroborated with site-scale measurements (piezometer, seepage meter, and streambed temperature profiles) over a multi-year period to understand processes and conditions controlling connectivity between the stream, its shallow aquifer system and other flow sources. In the case of Minnehaha Creek, groundwater discharge was found to range from 6.2 to 23 mm year⁻¹, which represented only 5 to 11% of annual streamflow during the study period. From the weight of evidence, it is conjectured that regional-scale hydrogeological conditions control groundwater discharge in Minnehaha Creek. Implications of these results with regard to possible augmentation of baseflow by increasing groundwater recharge with infiltration of stormwater are discussed.     

Steady flow to a well near a stream with a leaky bed

We present an explicit analytic solution for steady, two-dimensional ground water flow to a well near a leaky streambed that penetrates the aquifer partially. Leakage from the stream is approximated as occurring along the centerline of the stream. The problem domain is infinite and pumping on one side of the stream induces flow on the other side. The solution includes the effects of uniform flow in the far field and a sloping hydraulic head in the stream. We use the solution to investigate the interaction between ground water and surface water in the stream, the effects of pumping on the opposite side of the stream, and the effects of the leaky streambed on the capture zone envelope of the well. We develop a relationship between parameters such that the pumping well will not capture water from the stream, or from the opposite side of the stream. When the discharge of the well is large enough to capture water from the stream, the shape of the capture zone envelope depends on flow conditions on the side of the stream opposite the well.     

A two‐dimensional analytical solution for groundwater flow in a leaky confined aquifer system near open tidal water

Groundwater in coastal areas is commonly disturbed by tidal fluctuations. A two‐dimensional analytical solution is derived to describe the groundwater fluctuation in a leaky confined aquifer system near open tidal water under the assumption that the groundwater head in the confined aquifer fluctuates in response to sea tide whereas that of the overlying unconfined aquifer remains constant. The analytical solution presented here is an extension of the solution by Sun for two‐dimensional groundwater flow in a confined aquifer and the solution by Jiao and Tang for one‐dimensional groundwater flow in a leaky confined aquifer. The analytical solution is compared with a two‐dimensional finite difference solution. On the basis of the analytical solution, the groundwater head distribution in a leaky confined aquifer in response to tidal boundaries is examined and the influence of leakage on groundwater fluctuation is discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

Analytical solution of water table fluctuations above an inclined leaky layer due to ditch recharge

Ditch recharge is a method used for raising a water table. However, if the aquifer lies above a leaky layer, then the leaky bed will have an effect on the height of the water table. This paper attempts to provide an analytical solution of the transient state to the linearized Boussinesq equation. The solution proposed in this paper is intended for a generalized form of the leaky layer, with the boundary condition of the water level moving according to an exponential form. The results of theoretical analysis and experimental studies can provide a much better explanation of ditch recharge on an inclined leaky layer. Copyright © 2006 John Wiley & Sons, Ltd.     

Using nitrate to quantify quick flow in a karst aquifer

In karst aquifers, contaminated recharge can degrade spring water quality, but quantifying the rapid recharge (quick flow) component of spring flow is challenging because of its temporal variability. Here, we investigate the use of nitrate in a two-endmember mixing model to quantify quick flow in Barton Springs, Austin, Texas. Historical nitrate data from recharging creeks and Barton Springs were evaluated to determine a representative nitrate concentration for the aquifer water endmember (1.5 mg/L) and the quick flow endmember (0.17 mg/L for nonstormflow conditions and 0.25 mg/L for stormflow conditions). Under nonstormflow conditions for 1990 to 2005, model results indicated that quick flow contributed from 0% to 55% of spring flow. The nitrate-based two-endmember model was applied to the response of Barton Springs to a storm and results compared to those produced using the same model with δ¹⁸O and specific conductance (SC) as tracers. Additionally, the mixing model was modified to allow endmember quick flow values to vary over time. Of the three tracers, nitrate appears to be the most advantageous because it is conservative and because the difference between the concentrations in the two endmembers is large relative to their variance. The δ¹⁸O-based model was very sensitive to variability within the quick flow endmember, and SC was not conservative over the timescale of the storm response. We conclude that a nitrate-based two-endmember mixing model might provide a useful approach for quantifying the temporally variable quick flow component of spring flow in some karst systems.     

Groundwater flow through a Miliolite limestone aquifer

Abstract

This paper describes a study of groundwater flow in a coastal Miliolite limestone aquifer in western India. An examination of field information suggested that the transmissivity of the aquifer varies significantly between high and low groundwater heads. Pumping tests indicate that this is due to the development of major fissures in the upper part of the aquifer. A regional groundwater model with varying transmissivities is used to represent the field behaviour. The model is also used to examine the effect of artificial recharge on the alleviation of saline intrusion problems in the coastal area.     

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.     

Analytic solutions for interface flow in combined confined and semi-confined,coastal aquifers

Analytic solutions are presented for steady interface flow in aquifers consisting of a confined and a semi-confined section. The total discharge is constant in the confined section and is directed towards the semi-confined section, which is bounded on top by a leaky layer that separates the aquifer from the sea. All solutions are based on the Dupuit approximation. The interface position is fully determined by two dimensionless parameters. The first parameter is the product of the uniform gradient towards the sea and the dimensionless leakage factor divided by the dimensionless density difference. The second dimensionless parameter is the length of the semi-confined section divided by the leakage factor. Four types of flow are distinguished. For cases I and II the interface does not reach the end of the semi-confined section, while it does for cases III and IV. For cases I and III the interface extends into the confined section, while for cases II and IV it remains entirely in the semi-confined section. Analytic solutions are presented for the position of the interface for all four cases. Diagrams are presented to determine the type of flow and the position of the interface toe based on the two dimensionless parameters. The pre-development position of the interface along the Georgia coast is computed as an illustration of the practical application of the presented formulas. Another practical application is the estimation of how far a numerical model of seawater intrusion should be extended into the sea for accurate simulations.     

Two-region non-Darcian flow toward a well in a confined aquifer

We have derived an analytical solution for two-region flow toward a well in a confined aquifer based on a linearization method. The two-region flow includes Izbash non-Darcian flow near the well and Darcian flow in the rest of the aquifer. The wellbore storage is also considered. The type curves in the non-Darcian and Darcian flow domains are obtained by a numerical Laplace inversion method incorporated in MATLAB programs. We have compared our results with the one-region Darcian flow model (Theis). Our solutions agree with those of Sen [Sen Z. Type curves for two-region well flow. J Hydr Eng 1988;114(12):1461–84] which were obtained using the Boltzmann transform at late times for fully turbulent flow, while some difference has been found at early and moderate times. We have defined a dimensionless non-Darcian hydraulic conductivity term which is shown to be a key parameter for analyzing the two-region flow. A smaller dimensionless non-Darcian hydraulic conductivity results in a larger drawdown in the non-Darcian flow region at late times. However, the dimensionless non-Darcian hydraulic conductivity does not affect the slope of the dimensionless drawdown versus the logarithmic dimensionless time in the non-Darcian flow region at late times. The dimensionless non-Darcian hydraulic conductivity does not affect the late time drawdown in the Darcian flow region.     

Unsteady inter-porosity flow modeling for a multiple media reservoir

The paper deals with unsteady inter-porosity flow modeling of underground fluid in a multiple media reservoir. Assuming spherical vugs, symmetrically distributed pressure, negligible inter-porosity flow between matrix and vug systems and centrifugal flow of the fluid from matrix blocks or vugs to fractures, and treating media directly connected with wellbore as the fracture system, we establish and solve a model of unsteady inter-porosity flow for dual and triple porosity media reservoirs. We provide simulated graphs of pressure and pressure derivative log-log type curves, and analyze the transient flow process and characteristics of type curves affected by different parameters. The new type curves of unsteady inter-porosity flow modeling are evidently different in shape and characteristics from those of pseudo-steady inter-porosity flow modeling. The location of dimensionless pressure of unsteady inter-porosity is lower than that of pseudo-steady inter-porosity, which indicates that unsteady inter-porosity flow accelerates an energy supplement during production. Qualitatively, the unsteady inter-porosity flow modeling reduces the classical V-shaped response. We also estimated parameters from well test data in real applications using this model.