Dissolution of nonaqueous phase liquid pools in anisotropic aquifers

A two-dimensional numerical transport model is developed to determine the effect of aquifer anisotropy and heterogeneity on mass transfer from a dense nonaqueous phase liquid (DNAPL) pool. The appropriate steady state groundwater flow equation is solved implicitly whereas the equation describing the transport of a sorbing contaminant in a confined aquifer is solved by the alternating direction implicit method. Statistical anisotropy in the aquifer is introduced by two-dimensional, random log-normal hydraulic conductivity field realizations with different directional correlation lengths. Model simulations indicate that DNAPL pool dissolution is enhanced by increasing the mean log-transformed hydraulic conductivity, groundwater flow velocity, and/or anisotropy ratio. The variance of the log-transformed hydraulic conductivity distribution is shown to be inversely proportional to the average mass transfer coefficient.     

General well function for soil vapor extraction

This paper develops a well function applicable to extraction of groundwater or soil vapor from a well under the most common field test conditions. The general well function (Perina and Lee, 2006) [12] is adapted to soil vapor extraction and constant head boundary at the top. For groundwater flow, the general well function now applies to an extraction well of finite diameter with uniform drawdown along the screen, finite-thickness skin, and partially penetrating an unconfined, confined, and leaky aquifer, or an aquifer underneath a reservoir. With a change of arguments, the model applies to soil vapor extraction from a vadose zone with no cover or with leaky cover at the ground surface. The extraction well can operate in specified drawdown (pressure for soil vapor) or specified flowrate mode. Frictional well loss is computed as flow-only dependent component of the drawdown inside the extraction well. In general case, the calculated flow distribution is not proportional to screen length for a multiscreen well.     

Influence of piezometer construction on groundwater sampling in fractured rock

A numerical model for groundwater flow and solute transport was employed to examine the influence of the screen and sandpack on the collection of a representative geochemical sample from a piezometer monitoring well installation in a discretely fractured bedrock aquifer. The optimization of screen and sandpack combinations was explored for the potential to reduce purging times and volumes in practice. Simulations accounted for the location of the fractures along the well screen, fracture aperture, screen length, and the pumping rate. The variability in the required purging times (t(99)-the time required to achieve 99% fractional contribution from the formation to pump discharge) can be explained by: (1) the relative hydraulic conductivities of the components of the system (fracture, sandpack, and screen), (2) the truncation of the flow field from the fracture to the screen by the upper and/or lower boundary of the sandpack of the flow field from another fracture, and (3) time-dependent drawdown. During pumping, only a portion of the sandpack may actually become hydraulically active. The optimal configuration (shortest purging time) is achieved when the ratios of the screen, sandpack, and fracture hydraulic conductivities are close to 1:1:1. More importantly, the role of the fracture hydraulic conductivity in the ratios is not as crucial to reducing t(99) as having the hydraulic conductivities of the screen and sandpack as similar as possible. This study provides a better understanding of well dynamics during pumping for the purpose of obtaining representative groundwater samples.     

Application Procedures for the Electromagnetic Borehole Flowmeter in Shallow Unconfined Aquifers

It is increasingly common for the electromagnetic borehole flowmeter (EBF) to he used to measure hydraulic conductivity (K) distributions in subsurface flow systems. Past applications involving the EBF have been made mostly in confined aquifers (Kabala 1994; Boman et al. 1997; Podgorney and Ritzi 1997; Ruud and Kabala 1997a, 1997b; Flach et al. 2000), and it has been common to set up a flow field around a test well using a small pump that is located near the top of the well screen (Mob, and Young 1993). In thin, unconfined aquifers that exhibit ground water tables near the ground surface and that undergo drawdown during pumping, such a configuration can be problematical because pumping and associated drawdown may effectively isolate the upper portion of the aquifer from the flowmeter. In these instances, a steady-state flow field in the vicinity of the test well may be created using injection rather than pumping, allowing for testing in the otherwise isolated upper portion of the aquifer located near the initial water table position. Using procedures developed by Molz and Young (1993), which were modified for an injection mode application, testing was conducted to determine whether or not the injection mode would provide useful information in a shallow, unconfined aquifer that required the collection of data near the initial water table position. Results indicated that the injection mode for the EBF was well suited for this objective.     

Three-dimensional semi-analytical solution to groundwater flow in confined and unconfined wedge-shaped aquifers

The Laplace domain solutions have been obtained for three-dimensional groundwater flow to a well in confined and unconfined wedge-shaped aquifers. The solutions take into account partial penetration effects, instantaneous drainage or delayed yield, vertical anisotropy and the water table boundary condition. As a basis, the Laplace domain solutions for drawdown created by a point source in uniform, anisotropic confined and unconfined wedge-shaped aquifers are first derived. Then, by the principle of superposition the point source solutions are extended to the cases of partially and fully penetrating wells. Unlike the previous solution for the confined aquifer that contains improper integrals arising from the Hankel transform [Yeh HD, Chang YC. New analytical solutions for groundwater flow in wedge-shaped aquifers with various topographic boundary conditions. Adv Water Resour 2006;26:471–80], numerical evaluation of our solution is relatively easy using well known numerical Laplace inversion methods. The effects of wedge angle, pumping well location and observation point location on drawdown and the effects of partial penetration, screen location and delay index on the wedge boundary hydraulic gradient in unconfined aquifers have also been investigated. The results are presented in the form of dimensionless drawdown-time and boundary gradient-time type curves. The curves are useful for parameter identification, calculation of stream depletion rates and the assessment of water budgets in river basins.     

Simulation of groundwater flow in a crystalline rock aquifer system in Southern Ghana – An evaluation of the effects of increased groundwater abstraction on the aquifers using a transient groundwater flow model

Monitored groundwater level data, well logs, and aquifer data as well as the relevant surface hydrological data were used to conceptualise the hydrogeological system of the Densu Basin in Southern Ghana. The objective was to numerically derive the hydraulic conductivity field for better characterization of the aquifer system and for simulating the effects of increasing groundwater abstraction on the aquifer system in the basin. The hydraulic conductivity field has been generated in this study through model calibration. This study finds that hydraulic conductivity ranges between a low of 2 m/d in the middle sections of the basin and about 40 m/d in the south. Clear differences in the underlying geology have been indicated in the distribution of aquifer hydraulic conductivities. This is in consonance with the general assertion that the hydrogeological properties of the aquifers in the crystalline basement terrains are controlled by the degree of fracturing and/or weathering of the country rock. The transient model suggest aquifer specific storage values to range between 6.0 × 10^?5 m^?1 and 2.1 × 10^?4 m^?1 which are within acceptable range of values normally quoted for similar lithologies in the literature. There is an apparent subtle decrease in groundwater recharge from about 13% of the annual precipitation in 2005 to about 10.3% of the precipitation in 2008. The transient model was used to simulate responses of the system to annual increment of groundwater abstraction by 20% at the 2008 recharge rates for the period 2009 – 2024. The results suggest that the system will not be able to sustain this level of abstraction as it would lead to a basin wide drawdown in the hydraulic head by 4 m by the end of the prediction period. It further suggests a safe annual increment in groundwater abstraction by 5% under business as usual recharge conditions. Identification and protection of groundwater recharge areas in the basin are recommended in order to safeguard the integrity of the resource under the scenario of increased abstraction for commercial activities in the basin. Copyright © 2012 John Wiley & Sons, Ltd.     

Response to pumping of a weathered-fractured granite aquifer

A pumping test in a granite aquifer provides information about the interaction between the upper weathered zone and lower fractured zone. A radial flow numerical model is used to interpret the test and estimate aquifer parameters. This model successfully reproduces both the fractured zone response and the shallow weathered zone response which is characterised by increasing drawdown even after abstraction ceases. When the deep fractured aquifer was exploited, a serious decline in groundwater heads and yields occurred; this behaviour can be reproduced by the model. The model is then used to investigate the effective long-term exploitation of the aquifer and the results indicate that dug-cum-bore wells can be used for the safe and efficient exploitation of the aquifer resources.     

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.     

Assessing radial transmissivity variation in heterogeneous aquifers using analytical techniques

Pumping tests are one of the most commonly used in situ testing techniques for assessing aquifer hydraulic properties. Numerous researches have been conducted to predict the effects of aquifer heterogeneity on the groundwater levels during pumping tests. The objectives of the present work were as follows: (1) to predict drawdown conditions and to estimate aquifer properties during pumping tests undertaken in radially symmetric heterogeneous aquifers, and (2) to identify a method for assessing the transmissivity field along the radial coordinate in radially symmetric and fully heterogeneous transmissivity fields. The first objective was achieved by expanding an existing analytical drawdown formulation that was valid for a radially symmetric confined aquifer with two concentric zones around the pumping well to an N concentric zone confined aquifer having a constant transmissivity value within each zone. The formulation was evaluated for aquifers with three and four concentric zones to assess the effects of the transmissivity field on the drawdown conditions. The specific conditions under which aquifer properties could be identified using traditional methods of analysis were also evaluated. The second objective was achieved by implementing the inverse solution algorithm (ISA), which was developed for petroleum reservoirs to groundwater aquifer settings. The results showed that the drawdown values are influenced by a volumetric integral of a weighting function and the transmissivity field within the cone of depression. The weighting function migrates in tandem with the expanding cone of depression. The ability of the ISA to predict radially symmetric and log‐normally distributed transmissivity fields was assessed against analytical and numerical benchmarks. The results of this investigation indicated that the ISA method is a viable technique for evaluating the radial transmissivity variations of heterogeneous aquifer settings. Copyright © 2013 John Wiley & Sons, Ltd.     

An Analysis of Low-Flow Ground Water Sampling Methodology

Low-flow ground water sampling methodology can minimize well disturbance and aggravated colloid transport into samples obtained from monitoring wells. However, in low hydraulic conductivity formations, low-flow sampling methodology can cause excessive drawdown that can result in screen desaturation and high ground water velocities in the vicinity of the well, causing unwanted colloid and soil transport into ground water samples taken from the well. Ground water velocities may increase several fold above that of the natural setting. To examine the drawdown behavior of a monitoring well, mathematical relationships can be developed that allow prediction of the steady-state drawdown for constant low-flow pumping rates based on well geometry and aquifer properties. The equations also estimate the time necessary to reach drawdown equilibrium. These same equations can be used to estimate the relative contribution of water entering a sampling device from either the well standpipe or the aquifer. Such equations can be useful in planning a low-flow sampling program and may suggest when to collect a water sample. In low hydraulic conductivity formations, the equations suggest that drawdown may not stabilize for well depths, violating the minimal drawdown requirement of the low-flow technique. In such cases, it may be more appropriate to collect a slug or passive sample from the well screen, under the assumption that the water in the well screen is in equilibrium with the surrounding aquifer.     

Predicting Collector Well Yields with MODFLOW

Groundwater flow models are commonly used to design new wells and wellfields. As the spatial scale of the problem is large and much local‐scale detail is not needed, modelers often utilize two‐dimensional (2D) or quasi three‐dimensional models based on the Dupuit‐Forchheimer assumption. Dupuit models offer a robust set of tools for simulating regional groundwater flow including interactions with surface waters, the potential for well interference, and varying aquifer properties and recharge rates. However, given an assumed operating water level or drawdown at a well screen, Dupuit models systematically overpredict well yields. For design purposes, this discrepancy is unacceptable, and a method for predicting accurate well yields is needed. While published methods exist for vertical wells, little guidance is available for predicting yields in horizontal screens or collector wells. In plan view, a horizontal screen has a linear geometry, and will likely extend over several neighboring cells that may not align with rows or columns in a numerical model. Furthermore, the model must account for the effects of converging three‐dimensional (3D) flow to the well screens and hydraulic interference among the well screens; these all depend on the design of a specific well. This paper presents a new method for simulating the yield of angled or horizontal well screens in numerical groundwater flow models, specifically using the USGS code MODFLOW. The new method is compared to a detailed, 3D analytic element model of a collector well in a field of uniform flow.     

River–aquifer interactions in a semi‐arid environment stressed by groundwater abstraction

Rivers and aquifers are, in many cases, a connected resource and as such the interactions between them need to be understood and quantified for the resource to be managed appropriately. The objective of this paper is to advance the understanding of river–aquifer interactions processes in semi‐arid environments stressed by groundwater abstraction. This is performed using data from a specific catchment where records of precipitation, evapotranspiration, river flow, groundwater levels and groundwater abstraction are analysed using basic statistics, hydrograph analysis and a simple mathematical model to determine the processes causing the spatial and temporal changes in river–aquifer interactions. This combined approach provides a novel but simple methodology to analyse river–aquifer interactions, which can be applied to catchments worldwide. The analysis revealed that the groundwater levels have declined (~ 3 m) since the onset of groundwater abstraction. The decline is predominantly due to the abstraction rather than climatic changes (r = 0.84 for the relationship between groundwater abstraction and groundwater levels; r = 0.92 for the relationship between decline in groundwater levels and magnitude of seasonal drawdown). It is then demonstrated that, since the onset of abstraction, the river has changed from being gaining to losing during low‐flow periods, defined as periods with flow less than 0.5, 1.0 or 1.5 GL/day (1 GL/day = 1 × 10⁶ m³/day). If defined as < 1.0 GL/day, low‐flow periods constitute approximately 65% of the river flows; the periods where the river is losing at low‐flow conditions are thus significant. Importantly, there was a significant delay (> 10 years) between the onset of groundwater abstraction and the changeover from gaining to losing conditions. Finally, a relationship between the groundwater gradient towards the river and the river flow at low‐flow is demonstrated. The results have important implications for water management as well as water ecology and quality. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Groundwater Flow Field Distortion by Monitoring Wells and Passive Flux Meters

Due to differences in hydraulic conductivity and effects of well construction geometry, groundwater lateral flow through a monitoring well typically differs from groundwater flow in the surrounding aquifer. These differences must be well understood in order to apply passive measuring techniques, such as passive flux meters (PFMs) used for the measurement of groundwater and contaminant mass fluxes. To understand these differences, lab flow tank experiments were performed to evaluate the influences of the well screen, the surrounding filter pack and the presence of a PFM on the natural groundwater flux through a monitoring well. The results were compared with analytical calculations of flow field distortion based on the potential theory of Drost et al. (1968). Measured well flow field distortion factors were found to be lower than calculated flow field distortion factors, while measured PFM flow field distortion factors were comparable to the calculated ones. However, this latter is not the case for all conditions. The slotted geometry of the well screen seems to make a correct analytical calculation challenging for conditions where flow field deviation occurs, because the potential theory assumes a uniform flow field. Finally, plots of the functional relationships of the distortion of the flow field with the hydraulic conductivities of the filter screen, surrounding filter pack and corresponding radii make it possible to design well construction to optimally function during PFM applications.     

Solutions for Non‐Darcian Flow to an Extended Well in Fractured Rock

We have investigated non‐Darcian flow to a vertical fracture represented as an extended well using a linearization procedure and a finite difference method in this study. Approximate analytical solutions have been obtained with and without the consideration of fracture storage based on the linearization procedure. A numerical solution for such a non‐Darcian flow case has also been obtained with a finite difference method. We have compared the numerical solution with the approximate analytical solutions obtained by the linearization method and the Boltzmann transform. The results indicate that the linearized solution agrees generally well with the numerical solution at late times, and underestimates the dimensionless drawdown at early times, no matter if the fracture storage is considered or not. When the fracture storage is excluded, the Boltzmann transform solution overestimates the dimensionless drawdown during the entire pumping period. The dimensionless drawdowns in the fracture with fracture storage for different values of dimensionless non‐Darcian hydraulic conductivity β approach the same asymptotic value at early times. A larger β value results in a smaller dimensionless drawdown in both the fracture and the aquifer when the fracture storage is included. The dimensionless drawdown is approximately proportional to the square root of the dimensionless time at late times.     

Modified Theis equation by considering the bending effect of the confining unit

The Theis equation has been widely used to study the transient movement of groundwater as a result of pumping in a confined aquifer. It is well known that the observed drawdown at early times has an obvious departure from the theoretical drawdown based on the Theis equation. The Theis equation was derived under the assumption that total stress in the aquifer was constant and the mechanical behavior of the confining unit was neglected. However, most geological formations, especially those which are well consolidated, have rigidity and therefore may bend like a plate to a certain extent. The increase in the effective stress in the aquifer due to pumping may not contribute entirely to the compression of the aquifer, but may be partially cancelled out by bending of the overlying aquitard. This means only a part of the total stress is used to compact the aquifer, or the aquifer cannot produce as much water as estimated from the Theis equation. This paper investigated the impact of the bending effect of the confining unit on drawdown. An analytical model which couples flow in the aquifer and bending of the confining unit was presented. The theory is based on elastic plates and solutions were given to the drawdown of groundwater level and deflection of the overlying formation. The drawdown estimated from the new equation was compared with that from the Theis equation. It can be concluded that drawdown from the Theis equation is less than the drawdown predicted by including the bending effect of the confining unit. Both a hypothetical example and a field pumping test in Shandong Province, China, were used to demonstrate the bending effect of the confining unit in the analysis of pumping test data. This paper demonstrated that the initial disagreement between observed drawdown and the Theis solution could be caused by the bending effect of the confining unit, a phenomenon not well addressed in traditional pumping test analysis. A quantitative understanding of this phenomenon can provide improved guidelines for analyzing drawdown data in a confined aquifer.     

Semi-analytical solutions of groundwater flow in multi-zone (patchy) wedge-shaped aquifers

Alluvial fans are potential sites of potable groundwater in many parts of the world. Characteristics of alluvial fans sediments are changed radially from high energy coarse-grained deposition near the apex to low energy fine-grained deposition downstream so that patchy wedge-shaped aquifers with radial heterogeneity are formed. The hydraulic parameters of the aquifers (e.g. hydraulic conductivity and specific storage) change in the same fashion. Analytical or semi-analytical solutions of the flow in wedge-shaped aquifers are available for homogeneous cases. In this paper we derive semi-analytical solutions of groundwater flow to a well in multi-zone wedge-shaped aquifers. Solutions are provided for three wedge boundary configurations namely: constant head–constant head wedge, constant head–barrier wedge and barrier–barrier wedge. Derivation involves the use of integral transforms methods. The effect of heterogeneity ratios of zones on the response of the aquifer is examined. The results are presented in form of drawdown and drawdown derivative type curves. Heterogeneity has a significant effect on over all response of the pumped aquifer. Solutions help understanding the behavior of heterogeneous multi-zone aquifers for sustainable development of the groundwater resources in alluvial fans.     

The impact of well drawdowns on the mixing process of river water and groundwater and water quality in a riverside well field,Northeast China

Riverbank filtration (RBF) has been widely used throughout the world as an effective means to regulate surface water and groundwater resources and pretreat raw water for municipal water supply. The quality of the water from a riverside well field and the mixing ratios of surface water and groundwater is primarily impacted by the hydrodynamic processes in the RBF system. The RBF system is largely controlled by the water exploiting system in addition to the natural hydrologic condition of the river–aquifer system. As one of the most important design parameters of the riverside well field, the drawdown of groundwater level greatly determines the water head differences between the river water and groundwater as well as the field flow net, which subsequently impacts the mixing of river water and groundwater and water quality significantly. This study aimed to improve the understanding of the mixing process between the surface water and groundwater and estimate the impact of the RBF on the mixing ratio of surface water–groundwater and water quality quantitatively. A set of field pumping tests with various groundwater level drawdowns were carried out independently and successively at a riverside field with a single pumping well near the Songhua River in Northeast China in August 2017. During these tests, the water levels and hydrochemical parameters of the Songhua River, the adjacent aquifer, and the pumping well were monitored. The dynamic mixing process of the river water and groundwater and water quality under various drawdown conditions were analysed systematically using analytical methods. The results obtained from Dupuit method and the Mirror Image method in conjunction with the Hydrochemical Tracing method showed that the pumping water directly from the river water reached 60% ± 10% after a steady flow net was established. The larger the proportion of the pumping water captured from the river, the better quality of the pumping water was, because the quality of the river water (only limited to some water quality parameters monitored which were minority) was better than that of the groundwater. The results also showed that total Fe, TDS, total hardness, COD_Mn, and K⁺ were relatively sensitive to the changes of groundwater drawdown, and their concentrations decreased with an increase in the groundwater drawdown. It can be concluded that both the mixing ratio of the surface water and the groundwater and the water quality of the riverside well field can be regulated through adjusting the designed drawdown of the groundwater level, which is helpful for the design and the optimization of the riverside well water intake engineering.     

Flowing Well—Time-Domain Solution and Inverse Problem Revisited

Time-domain analytical solution for groundwater flow to a fully penetrating flowing well is derived using the same substitution technique used to re-derive (Perina 2010) the Theis (1935) equation and the approximate solution by Mishra and Guyonnet (1992) is confirmed. The exponential integral-based flowing well function is a computationally effective alternative to the original Jacob and Lohman (1952) solution in integral form. For a constant drawdown test, the ratio of drawdown at an observation well to the flowrate is equivalent to drawdown response to pumping at unit constant rate; the transformed observations can be analyzed using the Theis (1935) function. Analysis of field test shows that simultaneous fitting to measurements of flow from the test well and drawdown at an observation well results in more accurate and better resolved estimates of aquifer properties than fitting to flow observations only.