Time-series modeling of reservoir effects on river nitrate concentrations

Saylorville Reservoir is a 24.1 km² impoundment of the Des Moines River located approximately 10 km north of the City of Des Moines, Iowa, USA. Surface water from the Des Moines River used for drinking water supply is impaired for nitrate–nitrogen. Monthly mean nitrate concentration data collected upstream and downstream of the reservoir for a 30-year period (1977–2006) were selected for time-series analysis. Our objectives were to (1) develop a model describing nitrate concentrations downstream of the reservoir as a function of the concentrations entering the reservoir and (2) use the model to provide a 1-month ahead forecast for downstream water quality. Results indicated that downstream nitrate can be effectively modeled using a transfer function approach that utilized inflow concentrations during the current and previous month as input variables. Inflow concentrations were modeled using an AR(20) model, with the higher order model consistent with temporal correlation noted by others. The transfer function model suggested that the reservoir is reducing nitrate concentrations by 22 ± 6%, a reduction that greatly exceeds previous estimates. Monthly nitrate forecasted with the model were nearly all within a 95% prediction interval of their actual measured values and did not appear greatly affected by flow variations.     

Travel-time based model of bioremediation using circulation wells

Vertical circulation wells can efficiently provide microorganisms with substrates needed for enhanced bioremediation. We present a travel-time based approach for modeling bioreactive transport in a flow field caused by a series of circulation wells. Mixing within the aquifer is due to the differences in sorption behavior of the reactants. Neglecting local dispersion, transport simplifies to a single one-dimensional problem with constant coefficients for each well. Recirculation is characterized by the discharge densities over travel time. We apply the model to the stimulation of cometabolic dechlorination of trichloroethene (TCE) by alternate injection of oxygen and toluene into the circulation wells. Mixing within the wells can be minimized by interposing sufficiently long breaks between the oxygen and toluene pulses. In our simulation, the proposed injection scheme stimulates biomass growth without risking biofouling of the aquifer.     

A new analytical solution solved by triple series equations method for constant-head tests in confined aquifers

The constant-head pumping tests are usually employed to determine the aquifer parameters and they can be performed in fully or partially penetrating wells. Generally, the Dirichlet condition is prescribed along the well screen and the Neumann type no-flow condition is specified over the unscreened part of the test well. The mathematical model describing the aquifer response to a constant-head test performed in a fully penetrating well can be easily solved by the conventional integral transform technique under the uniform Dirichlet-type condition along the rim of wellbore. However, the boundary condition for a test well with partial penetration should be considered as a mixed-type condition. This mixed boundary value problem in a confined aquifer system of infinite radial extent and finite vertical extent is solved by the Laplace and finite Fourier transforms in conjunction with the triple series equations method. This approach provides analytical results for the drawdown in a partially penetrating well for arbitrary location of the well screen in a finite thickness aquifer. The semi-analytical solutions are particularly useful for the practical applications from the computational point of view.     

Multilayer analytic element modeling of radial collector wells

A new multilayer approach is presented for the modeling of ground water flow to radial collector wells. The approach allows for the inclusion of all aspects of the unique boundary condition along the lateral arms of a collector well, including skin effect and internal friction losses due to flow in the arms. The hydraulic conductivity may differ between horizontal layers within the aquifer, and vertical anisotropy can be taken into account. The approach is based on the multilayer analytic element method, such that regional flow and local three-dimensional detail may be simulated simultaneously and accurately within one regional model. Horizontal flow inside a layer is computed analytically, while vertical flow is approximated with a standard finite-difference scheme. Results obtained with the proposed approach compare well to results obtained with three-dimensional analytic element solutions for flow in unconfined aquifers. The presented approach may be applied to predict the yield of a collector well in a regional setting and to compute the origin and residence time, and thus the quality, of water pumped by the collector well. As an example, the addition of three lateral arms to a collector well that already has three laterals is investigated. The new arms are added at an elevation of 2 m above the existing laterals. The yield increase of the collector well is computed as a function of the lengths of the three new arms.     

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.     

On seasonal and semi-annual approach for flood frequency analysis

As a supplementary method to the conventional flood frequency analysis based on annual peak flows, we propose an approach in this paper to infer the flood frequency distribution on quarterly and semi-annual time scale, which are then converted to annual time scale to obtain the floods corresponding to return periods in unit of year. Two criteria for test of data independence, namely, minimum 7 and 15-day interval between two consecutive peak flows, are tested. The proposed approach was applied to Des Moines River at Fort Dodge, Iowa, USA using its 62 years of observation daily flows. The results show that the estimated floods for given return periods from quarter-annual data series are in general higher than the corresponding estimated floods from semi-annual data series, which is further larger than estimated floods from annual peak flows. The floods estimated from semi-annual data series agree well with the results of previous US Geological Survey study.     

Dual‐Screened Vertical Circulation Wells for Groundwater Lowering in Unconfined Aquifers

A new type of vertical circulation well (VCW) is used for groundwater dewatering at construction sites. This type of VCW consists of an abstraction screen in the upper part and an injection screen in the lower part of a borehole, whereby drawdown is achieved without net withdrawal of groundwater from the aquifer. The objective of this study is to evaluate the operation of such wells including the identification of relevant factors and parameters based on field data of a test site and comprehensive numerical simulations. The numerical model is able to delineate the drawdown of groundwater table, defined as free‐surface, by coupling the arbitrary Lagrangian–Eulerian algorithm with the groundwater flow equation. Model validation is achieved by comparing the field observations with the model results. Eventually, the influences of selected well operation and aquifer parameters on drawdown and on the groundwater flow field are investigated by means of parameter sensitivity analysis. The results show that the drawdown is proportional to the flow rate, inversely proportional to the aquifer conductivity, and almost independent of the aquifer anisotropy in the direct vicinity of the well. The position of the abstraction screen has a stronger effect on drawdown than the position of the injection screen. The streamline pattern depends strongly on the separation length of the screens and on the aquifer anisotropy, but not on the flow rate and the horizontal hydraulic conductivity.     

Estimating hydraulic properties using a moving-model approach and multiple aquifer tests

A new method was developed for characterizing geohydrologic columns that extended >600 m deep at sites with as many as six discrete aquifers. This method was applied at 12 sites within the Southwest Florida Water Management District. Sites typically were equipped with multiple production wells, one for each aquifer and one or more observation wells per aquifer. The average hydraulic properties of the aquifers and confining units within radii of 30 to >300 m were characterized at each site. Aquifers were pumped individually and water levels were monitored in stressed and adjacent aquifers during each pumping event. Drawdowns at a site were interpreted using a radial numerical model that extended from land surface to the base of the geohydrologic column and simulated all pumping events. Conceptually, the radial model moves between stress periods and recenters on the production well during each test. Hydraulic conductivity was assumed homogeneous and isotropic within each aquifer and confining unit. Hydraulic property estimates for all of the aquifers and confining units were consistent and reasonable because results from multiple aquifers and pumping events were analyzed simultaneously.     

Decision Analysis for Pump-and-Treat Design

The use of decision analysis (DA) has been proposed as a technique for selecting from among alternative designs for subsurface remediation. To assess the ability of DA to generate consistent decisions for the widely practiced pump-and-treat (PAT) strategy, 27 candidate PAT designs were compared for a case study site. The sensitivity of the alternative selection to various modeling assumptions was examined, including the complexity of the site-specific numerical models, the assumed degree of aquifer heterogeneity, the manner of defining failure, and the assumed cost of failure. The initial net-present-worth analysis resulted in the selection of one of two designs that included injection wells for effluent disposal and hydraulic control. However, when the injection wells were excluded from consideration, the selection from a diverse set of alternative PAT designs was highly sensitive to the particular modeling assumptions. In general, the practical usefulness of the DA approach is dependent on the ability to characterize the nature and probability of system failure.     

Modeling Flow into Horizontal Wells in a Dupuit-Forchheimer Model

Horizontal wells or radial collector wells are used in shallow aquifers to enhance water withdrawal rates. Groundwater flow patterns near these wells are three-dimensional (3D), but difficult to represent in a 3D numerical model because of the high degree of grid refinement needed. However, for the purpose of designing water withdrawal systems, it is sufficient to obtain the correct production rate of these wells for a given drawdown. We developed a Cauchy boundary condition along a horizontal well in a Dupuit-Forchheimer model. Such a steady-state 2D model is not only useful for predicting groundwater withdrawal rates but also for capture zone delineation in the context of source water protection. A comparison of our Dupuit-Forchheimer model for a radial collector well with a 3D model yields a nearly exact production rate. Particular attention is given to horizontal wells that extend underneath a river. A comparison of our approach with a 3D solution for this case yields satisfactory results, at least for moderate-to-large river bottom resistances.     

Information effect on remediation design of contaminated aquifers using the pump and treat method

We examine the effect of uncertainty due to limited information on the remediation design of a contaminated aquifer using the pump and treat method. The hydraulic conductivity and contaminant concentration distributions for a fictitious contaminated aquifer are generated assuming a limited number of sampling locations. Stochastic optimization with multiple realizations is used to account for aquifer uncertainty. The optimization process involves a genetic algorithm (GA). As the number of realizations increases, a greater extraction rate and more wells are needed. There was a total cost increase, but the optimal remediation designs became more reliable. Stochastic optimization analysis also determines the locations for extraction wells, the variation in extraction rates as a function of the change of well locations, and the reliability of the optimal designs. The number of realizations (stack number) that caused the design factors to converge could be determined. Effective stochastic optimization may be achieved by reducing computational resources. An increase in the variability of the conductivity distribution requires more extraction wells. Information about potential extraction wells can be used to prevent failure of the remediation task.     

Finite layer method for flow in layered radial two-zone aquifer systems

A new finite layer method (FLM) is presented in this paper for transient flow analysis in layered radial two-zone aquifer systems. A radial two-zone system is an aquifer configuration in which a circular aquifer with finite radius is surrounded by a matrix possessing different permeability and storage properties. The aquifers can be pumped from fully or partially penetrating wells of infinitesimal radius. The trial function for drawdown is obtained through the use of piecewise linear correction functions in the present method. The trial function can satisfy the continuity conditions of flow and possess an appropriate continuity of C(0) at the two-zone interface. On the basis of Galerkin's method and the continuity condition of flow, the finite layer formulation is derived. The proposed method can cope with the anisotropy and layered heterogeneity in radial two-zone aquifer systems. Several numerical examples are presented to verify the validity of the present method through comparison with the analytical solution and the numerical results based on the finite difference method, in which a test of three-dimensional (3D) flow to a partially penetrating well in anisotropic two-zone aquifers is included. Furthermore, an additional application in simulating the two-zone flow in aquitard-aquifer systems is presented to demonstrate the applicability of FLM in modeling flow in more complex aquifer systems.     

Modeling of Contaminant Movement Near Pumping Wells: Saturated-Unsaturated Flow with Particle Tracking

A transient axisymmetric saturated-unsaturated numerical flow model was coupled with a particle tracking model to investigate the movement of contaminants when a shallow unconfined aquifer is pumped at a constant rate. The particle tracking model keeps track of locations and masses of solutes in the aquifer, and the time of capture by the well. At the end of each time-step the flow model solves the Richard's equation for the hydraulic head distribution from which elemental velocities are calculated. Solutes are then displaced for a period equivalent to the time-step using both the magnitude and direction of the elemental velocities. Numerical experiments were performed to investigate effluent concentrations in wells with screens of different length and in different positions relative to zones of stratified contamination. At early times of pumping the effluent concentrations were similar to the concentrations adjacent to the well screen, but at late times, the concentrations approached the vertically averaged concentration in the aquifer. Time to attain the vertically averaged concentration was determined by the well geometry, initial location of the contaminant plume in relation to the well screen, and hydraulic properties of the aquifer. The results are consistent with the hydraulics of flow to a pumping well and of particular importance, they demonstrate that short-term pump tests could give erroneous design concentrations for pump-and-treat systems. The model provides a means of quantifying arrival times and mixing ratios. It could therefore provide a useful means of designing production wells in aquifers with stratified contamination and more efficient recovery systems for aquifer remediation.     

Domestic Well Capture Zone and Influence of the Gravel Pack Length

Domestic wells in North America and elsewhere are typically constructed at relatively shallow depths and with the sand or gravel pack extending far above the intake screen of the well (shallow well seal). The source areas of these domestic wells and the effect of an extended gravel pack on the source area are typically unknown, and few resources exist for estimating these. In this article, we use detailed, high-resolution ground water modeling to estimate the capture zone (source area) of a typical domestic well located in an alluvial aquifer. Results for a wide range of aquifer and gravel pack hydraulic conductivities are compared to a simple analytical model. Correction factors for the analytical model are computed based on statistical regression of the numerical results against the analytical model. This tool can be applied to estimate the source area of a domestic well for a wide range of conditions. We show that an extended gravel pack above the well screen may contribute significantly to the overall inflow to a domestic well, especially in less permeable aquifers, where that contribution may range from 20% to 50% and that an extended gravel pack may lead to a significantly elongated capture zone, in some instances, nearly doubling the length of the capture zone. Extending the gravel pack much above the intake screen therefore significantly increases the vulnerability of the water source.     

Arsenic Management Through Well Modification and Simulation

Arsenic concentrations can be managed with a relatively simple strategy of grouting instead of completely destroying a selected interval of well. The strategy of selective grouting was investigated in Antelope Valley, California, where groundwater supplies most of the water demand. Naturally occurring arsenic typically exceeds concentrations of 10 µg/L in the water produced from these long-screened wells. The vertical distributions of arsenic concentrations in intervals of the aquifer contributing water to selected supply wells were characterized with depth-dependent water-quality sampling and flow logs. Arsenic primarily entered the lower half of the wells where lacustrine clay deposits and a deeper aquifer occurred. Five wells were modified by grouting from below the top of the lacustrine clay deposits to the bottom of the well, which reduced produced arsenic concentrations to less than 2 µg/L in four of the five wells. Long-term viability of well modification and reduction of specific capacity was assessed for well 4-54 with AnalyzeHOLE, which creates and uses axisymmetric, radial MODFLOW models. Two radial models were calibrated to observed borehole flows, drawdowns, and transmissivity by estimating hydraulic-conductivity values in the aquifer system and gravel packs of the original and modified wells. Lithology also constrained hydraulic-conductivity estimates as regularization observations. Well encrustations caused as much as 2 µg/L increase in simulated arsenic concentration by reducing the contribution of flow from the aquifer system above the lacustrine clay deposits. Simulated arsenic concentrations in the modified well remained less than 3 µg/L over a 20-year period.     

Temporal changes in the vertical distribution of flow and chloride in deep wells

The combination of flowmeter and depth-dependent water-quality data was used to evaluate the quantity and source of high-chloride water yielded from different depths to eight production wells in the Pleasant Valley area of southern California. The wells were screened from 117 to 437 m below land surface, and in most cases, flow from the aquifer into the wells was not uniformly distributed throughout the well screen. Wells having as little as 6 m of screen in the overlying upper aquifer system yielded as much as 50% of their water from the upper system during drought periods, while the deeper parts of the well screens yielded 15% or less of the total yield of the wells. Mixing of water within wells during pumping degraded higher-quality water with poorer-quality water from deeper depths, and in some cases with poorer-quality water from the overlying upper aquifer system. Changes in the mixture of water within a well, resulting from changes in the distribution of flow into the well, changed the quality of water from the surface discharge of wells over time. The combination of flowmeter and depth-dependent water quality data yielded information about sources of high-chloride water to wells that was not available on the basis of samples collected from nearby observation wells. Changing well design to eliminate small quantities of poor-quality water from deeper parts of the well may improve the quality of water from some wells without greatly reducing well yield.     

Comparison of Hydraulic Conductivity Values Obtained from Aquifer Pumping Tests and Conservative Tracer Tests

Afield site was established in an area of glacial outwash near Des Moines, Iowa. Hydraulic conductivity (K) of the outwash was measured in various ways including six pumping tests and two natural-gradient Cl^- tracer tests. The velocity of the conservative tracer was converted to K using measured gradients and effective porosity determined from two radial-convergent Cl^- tracer tests.
K values measured from the conservative tracer tests are approximately one-tenth to one-twentieth the average pumping-test value. Thus the K relevant to solute transport does not reflect the K measured by pumping tests. This discrepancy may be caused by the different scale and dimensionality of the two test types. Dispersion may prevent solutes from flowing exclusively within smaller high-conductivity paths which strongly affect the K measured by pumping tests.     

Convergence of deterministic and stochastic approaches in optimal remediation design of a contaminated aquifer

The comparison between two series of optimal remediation designs using deterministic and stochastic approaches showed a number of converging features. Limited sampling measurements in a supposed contaminated aquifer formed the hydraulic conductivity field and the initial concentration distribution used in the optimization process. The deterministic and stochastic approaches employed a single simulation–optimization method and a multiple realization approach, respectively. For both approaches, the optimization model made use of a genetic algorithm. In the deterministic approach, the total cost, extraction rate, and the number of wells used increase when the design must satisfy the intensified concentration constraint. Growing the stack size in the stochastic approach also brings about same effects. In particular, the change in the selection frequency of the used extraction wells, with increasing stack size, for the stochastic approach can indicate the locations of required additional wells in the deterministic approach due to the intensified constraints. These converging features between the two approaches reveal that a deterministic optimization approach with controlled constraints is achievable enough to design reliable remediation strategies, and the results of a stochastic optimization approach are readily available to real contaminated sites.     

Analysis of steady ground water flow toward wells in a confined-unconfined aquifer

A confined aquifer may become unconfined near the pumping wells when the water level falls below the confining unit in the case where the pumping rate is great and the excess hydraulic head over the top of the aquifer is small. Girinskii's potential function is applied to analyze the steady ground water flow induced by pumping wells with a constant-head boundary in a mixed confined-unconfined aquifer. The solution of the single-well problem is derived, and the critical radial distance at which the flow changes from confined to unconfined condition is obtained. Using image wells and the superposition method, an analytic solution is presented to study steady ground water flow induced by a group of pumping wells in an aquifer bounded by a river with constant head. A dimensionless function is introduced to determine whether a water table condition exists or not near the pumping wells. An example with three pumping wells is used to demonstrate the patterns of potentiometric surface and development of water table around the wells.     

Improved characterization of small "u" for Jacob pumping test analysis methods

Numerous refinements have been proposed to traditional pumping test analyses, yet many hydrogeologists continue to use the Jacob method due to its simplicity. Recent research favors hydraulic tomography and inverse numerical modeling of pumping test data. However, at sites with few wells, or relatively short screens, the data requirements of these methods may be impractical within physical and fiscal constraints. Alternatively, an improved understanding of the assumptions and limitations of Theis and, due to their widespread usage, Jacob analyses, leads to improved interpretations in data-poor environments. A fundamental requirement of Jacob is a "small" value of u = f(r(2)/t), with radial distance, r, and pumping time, t. However, selection of a too stringent (i.e., too low) maximum permissible u-value, u(max), results in rejection of usable data from wells beyond a maximum radius, r(max). Conversely, data from small radii, less than r(min), where turbulent- and vertical-flow components arise, can result in acceptance of inappropriate data. Usage of drawdown data from wells too close to the pumping well, and exclusion of data from wells deemed too far, can cause unrealistic aquifer transmissivity, permeability, and storativity determinations. Here, data from an extensive well field in a glacial-outwash aquifer in north-central Minnesota, USA, are used to develop a new estimate for u(max). Traditionally quoted values for u(max) range from 0.01 to 0.05. Our proposed value for Jacob distance-drawdown analyses is significantly higher with u(max) up to 0.2, resulting in larger allowable r(max)-values and a higher likelihood of inclusion of additional wells in such pumping test analyses.