ASSESSMENT OF HYDRAULIC PROPERTIES IN AN UNCONFINED ALLUVIAL AQUIFER NEAR GRAND ISLAND,NEBRASKA1

ABSTRACT: A method is presented to analyze time-drawdown data from one or more observation wells for the calculation of four hydraulic parameters for unconfined aquifers: vertical hydraulic conductivity, horizontal hydraulic conductivity, storage coefficient, and specific yield. The hydraulic parameter results are further analyzed for reliability and the possible ranges of the actual parameter values. After verification using a theoretical example, the method was used to analyze pumping test data from 22 observation wells in an unconfined alluvial aquifer near Grand Island, Nebraska. Results indicate that this method can be used to efficiently calculate the four hydraulic parameters in this type of aquifer. The method can also identify the impact of measurement errors on the parameter estimates, and provide ranges of the actual parameter values. The parameter values calculated using this method were compared to those determined using other theories. It is found that this method is very useful for calculating the hydraulic properties from pumping test data and for analyzing the parameter reliability.     

DETERMINATION OF UNCONFINED AQUIFER HYDRAULIC PROPERTIES FROM RECOVERY TEST DATA1

ABSTRACT: This paper analyzes the sensitivity of drawdown to four hydraulic parameters in unconfined aquifers: horizontal and vertical hydraulic conductivity K_r and K_z, storage coefficient S, and specific yield S_y. Sensitivity coefficients indicate that the sensitivity vanes with time for each aquifer parameter, and K_r, K_z, S, and S_y are identifiable from recovery test data. An inverse method was used to calculate the four parameters from residual drawdowns. Results of application examples demonstrate that residual data provide valid information in the determination of unconfined aquifer hydraulic parameters.     

A Semianalytical Solution for Residual Drawdown at a Finite Diameter Well in a Confined Aquifer

After the end of pumping the water level in the observation well starts to recover and the reduced drawdown during the recovery period is named as the residual drawdown. Traditional approaches in analyzing the data of residual drawdown for estimating the aquifer hydraulic parameters are mostly based on the application of superposition principle and Theis equation. In addition, the effect of wellbore storage is commonly ignored in the evaluation even if the test well has a finite diameter. In this article, we develop a mathematical model for describing the residual drawdown with considering the wellbore storage effect and the existing drawdown distribution produced by the pumping part of the test. The Laplace‐domain solution of the model is derived using the Laplace transform technique and the time‐domain result is inverted based on the Stehfest algorithm. This new solution shows that the residual drawdown associated with the boundary and initial conditions are related to the well drawdown and the aquifer drawdown, respectively. The well residual drawdown will be overestimated by the Theis residual drawdown solution in the early recovery part if neglecting the wellbore storage. On the other hand, the Theis residual drawdown solution can be used to approximate the present residual drawdown solution in the late recovery part of the test.     

DETERMINATION OF HYDRAULIC C.ONDUCTWITY TENSOR USING A NONLINEAR LEAST SQUARES ESTIMATOR1

ABSTRACT: Reliable and consistent estimation of the components of the hydraulic conductivity tensor provides information needed to make proper decisions regarding clean up and restoration of contaminated aquifers. In this study, the nonlinear least-squares estimation technique was applied to drawdown versus time data from three or more observation wells to determine a theoretical ellipse of equal drawdown. The angle of rotation of this ellipse with respect to the working coordinate axes was determined by a procedure based on contouring the drawdowns at a given time. This ellipse, in turn, was used to estimate the directions and magnitudes of the horizontal components of the hydraulic conductivity tensor. The technique is applicable to confined, as well as leaky, aquifers. Sources of error in this technique include nonhomogeneity of the aquifer and partial penetration of the pumping and observation wells into the aquifer. The procedure presented may be used as an additional tool to verify computations of hydraulic conductivity anisotropy based on other techniques.     

RESULTS OF ACIDIZING WATER WELLS IN ARIZONA1

Two wellfields have been developed to provide water for a coal fired electric generating station in Arizona. Wellfield No. 1 penetrates the unconfined Coconino Sandstone aquifer, and wellfield No. 2 penetrates the composite Kaibab Limestone-Coconino Sandstone aquifer where ground water occurs under confined conditions. A well in each wellfield was pumped and water level drawdown data were collected before and after acidizing. The drawdown data at the various pumping rates were analyzed to determine the potential benefits of acidizing production water wells in both wellfields. After acidizing, the specific capacity of the well in wellfield No. 1 was improved about 50 percent at water production rates ranging from about 200 to 500 gallons per minute (gpm) (13 to 32 liters per second (lps)). After acidizing, the specific capacity of the well completed in wellfield No. 2 was improved about 100 percent at pumping rates ranging from about 1,250 to 2,200 gpm (79 to 139 lps). An annual saving of approximately 11 percent in pumping costs can be realized in wellfield No. 2, and savings are approximately four percent in wellfield No. 1. Acidization is beneficial for wells that can produce more than 500 gpm (32 lps), and is of marginal value for those that produce less than that amount.     

NUMERICAL ANALYSIS OF PUMPING FROM CONFINED-UNCONFINED AQUIFERS1

ABSTRACT: A numerical method is presented for the analysis of a pumped well in a homogeneous aquifer with allowance made for the decrease in saturated depth, vertical components of flow, the possibility of regions of the aquifer changing between the confined and unconfined states and the effect of different outer boundaries. The method is based on a discrete space, backward difference time, approximation. A particular example considered in detail concerns heavy pumping from one of a regular array of wells in an unconfined aquifer until the drawdown in the well reaches a critical value. Non-dimensional curves are presented relating the time and volume dewatered to the quantity discharged from the well. A further example investigates the effect of an initial confining pressure on the aquifer behaviour.     

ESTIMATING AQUIFER PARAMETERS FROM A HORIZONTAL WELL PUMPING TEST IN AN UNCONFINED AQUIFER1

ABSTRACT: A pumping test on a phreatic glacial till aquifer was performed near Ames, Iowa, in November 1990. The head in a horizontal well was pumped down rapidly and then held constant for the duration of the 30-hour test. Throughout the test, the flow rate at the pumped well and the head at an adjacent vertical observation well were recorded. The pumping test data were used to determine the hydraulic conductivity and specific yield of the aquifer. The results indicate a hydraulic conductivity of 2.23 × 10^?5 cm/s and a representative specific yield of 0.03. Hydraulic conductivity was calculated by a simple integration of Darcy's Law after extrapolating the data to steady state. Specific yield was determined by use of several methods from the literature and a new method proposed by the author. The results show that specific yield increases with time, and that each method is within an order of magnitude of the others.     

OBSERVATION WELL NETWORK DESIGN FOR PUMPING TESTS IN UNCONFINED AQUIFERS1

ABSTRACT: This paper presents a method for determining locations of observation wells to be used in conducting pumping tests in unconfined aquifers. Sensitivity coefficients, the distribution of relative errors, and the correlation coefficients between four aquifer parameters (horizontal and vertical hydraulic conductivities K_r and K_z, storage coefficient S, and specific yield S_y) are used as the criteria for the design of observation well networks and the interpretation of pumping tests. The contours of the relative errors over a vertical profile are very useful in selecting the “best” location of an observation well. Results from theoretical analyses suggest that a wide range of locations is suitable for the determination of K_r and that good locations for the determination of K_z and S may be poorly suited for the determination of S_y. Consideration must be given to the position and lengths of the pumping well screen in the selection of observation well locations. For a given location, the quality of test data can be improved by using high pumping rates and frequent sampling of drawdowns. We found that a minimum of two and preferably three observation locations are needed along a given transect. Results of the four parameters from a single well analysis may contain higher uncertainties. However, composite analyses of multiple observation wells can reduce the correlation between the four aquifer parameters, particularly between K_r and S_y, thus, improving the quality of parameter estimation. Results from two pumping tests conducted at sites located in Nebraska were examined with regard to the proposed methodology.     

INTERPRETATION OF THE DUAL PROGRAM FOR OPTIMAL GROUNDWATER HYDRAULIC CONTROL1

ABSTRACT: Optimization formulations for hydraulic control that take the form of linear programs possess a corresponding dual linear program. The economic and physical interpretations of the dual linear program are examined for formulations in which hydraulic head in groundwater systems is constiained. In each case it is shown that the dual linear program has a physically meaningful interpretation. For a hydraulic gradient control formulation used for remedial analysis it is shown that the dual variable can be interpreted as the remedial benefit due to each gradient control constraint. The dual linear program maximizes the remedial benefit. The value of the dual variable can be used to compute such useful properties as the total remedial benefit of pumping at a specific location. For a formulation that optimizes aquifer yield while constraining drawdown the dual variable can be used to measure the total cost of drawdown capacity consumption per unit of pumping at a specific location. The dual program minimizes the cost of drawdown capacity consumption. By examining the meaning of the dual linear program an alternate statement of the problem under study is revealed. Quantities arising from the dual program add to the value of the optimization approach. Significant new information can be derived from existing linear optimization formulations with minimal additional computational effort.     

Estimating Hydraulic Properties of Volcanic Aquifers Using Constant‐Rate and Variable‐Rate Aquifer Tests1

Abstract: In recent years the ground‐water demand of the population of the island of Maui, Hawaii, has significantly increased. To ensure prudent management of the ground‐water resources, an improved understanding of ground‐water flow systems is needed. At present, large‐scale estimations of aquifer properties are lacking for Maui. Seven analytical methods using constant‐rate and variable‐rate withdrawals for single wells provide an estimate of hydraulic conductivity and transmissivity for 103 wells in central Maui. Methods based on constant‐rate tests, although not widely used on Maui, offer reasonable estimates. Step‐drawdown tests, which are more abundantly used than other tests, provide similar estimates as constant‐rate tests. A numerical model validates the suitability of analytical solutions for step‐drawdown tests and additionally provides an estimate of storage parameters. The results show that hydraulic conductivity is log‐normally distributed and that for dike‐free volcanic rocks it ranges over several orders of magnitude from 1 to 2,500 m/d. The arithmetic mean, geometric mean, and median values of hydraulic conductivity are respectively 520, 280, and 370 m/d for basalt and 80, 50, and 30 m/d for sediment. A geostatistical approach using ordinary kriging yields a prediction of hydraulic conductivity on a larger scale. Overall, the results are in agreement with values published for other Hawaiian islands.     

VARIABLE DISCHARGE TYPE CURVE SOLUTIONS FOR CONFINED AQUIFERS1

ABSTRACT: Almost all of the existing solutions of aquifer test analysis assume constant discharge rate boundary conditions. In many actual pumping tests, constant discharge cannot be maintained. This paper presents a general solution for an aquifer test with variable discharge. The exact solution of drawdown distribution around an infinitesimally small diameter well in a uniform, horizontal, extensive, homogeneous, and isotropic confined aquifer is presented when the discharge changes with time during the aquifer test period. A general equation for the type curves resulting from any discharge variability is given, and its application for the exponential changes is presented in detail. A simple straight line procedure is proposed for field applications by considering late time drawdown data. The consideration of constant discharge leads to overestimation of transmissivity but storativity is underestimated. Practical application of the discharge variability is illustrated by a field example.     

IDENTIFICATION OF AN OPTIMAL GROUNDWATER MANAGEMENT STRATEGY IN A CONTAMINATED AQUIFER1

A groundwater hydraulic management model is used to identify the optimal strategy for allocating limited fresh-water supplies and containing wastes in a hypothetical aquifer affected by brine contamination from surface disposal ponds. The present cost of pumping from a network of potential supply and interception wells is minimized over a five-year planning period, subject to a set of hydraulic, institutional, and legal constraints. Hydraulic constraints are formulated using linear systems theory to describe drawdown and velocity variables as linear functions of supply and interception well discharge decision variables. Successful validation of the optimal management strategy suggests that the model formulation can feasibly be applied to define management options for locally contaminated aquifer systems which are used to fulfill fresh-water demands.     

Modeling the Potential Impact of Seasonal and Inactive Multi‐Aquifer Wells on Contaminant Movement to Public Water‐Supply Wells1

Johnson, R.L., B.R. Clark, M.K. Landon, L.J. Kauffman, and S.M. Eberts, 2011. Modeling the Potential Impact of Seasonal and Inactive Multi‐Aquifer Wells on Contaminant Movement to Public Water‐Supply Wells. Journal of the American Water Resources Association (JAWRA) 47(3):588‐596. DOI: 10.1111/j.1752‐1688.2011.00526.x Abstract: Wells screened across multiple aquifers can provide pathways for the movement of surprisingly large volumes of groundwater to confined aquifers used for public water supply (PWS). Using a simple numerical model, we examine the impact of several pumping scenarios on leakage from an unconfined aquifer to a confined aquifer and conclude that a single inactive multi‐aquifer well can contribute nearly 10% of total PWS well flow over a wide range of pumping rates. This leakage can occur even when the multi‐aquifer well is more than a kilometer from the PWS well. The contribution from multi‐aquifer wells may be greater under conditions where seasonal pumping (e.g., irrigation) creates large, widespread downward hydraulic gradients between aquifers. Under those conditions, water can continue to leak down a multi‐aquifer well from an unconfined aquifer to a confined aquifer even when those multi‐aquifer wells are actively pumped. An important implication is that, if an unconfined aquifer is contaminated, multi‐aquifer wells can increase the vulnerability of a confined‐aquifer PWS well.     

OPTIMIZATION OF INTERMITTENT PUMPING SCHEDULES FOR AQUIFER REMEDIATION USING A GENETIC ALGORITHM1

ABSTRACT: Using a genetic algorithm (GA), optimal intermittent pumping schedules were established to simulate pump‐and‐treat remediation of a contaminated aquifer with known hydraulic limitations and a water miscible contaminant, located within the Duke Forest in Durham, North Carolina. The objectives of the optimization model were to minimize total costs, minimize health risks, and maximize the amount of contaminant removed from the aquifer. Stochastic ground water and contaminant transport models were required to provide estimates of contaminant concentrations at pumping wells. Optimization model simulations defined a tradeoff curve between the pumping cost and the amount of contaminant extracted from the aquifer. For this specific aquifer/miscible contaminant combination, the model simulations indicated that pump‐and‐treat remediation using intermittent pumping schedules for each pumping well produced significant reductions in predicted contaminant concentrations and associated health risks at a reasonable cost, after a remediation time of two years.     

Comparison of Aquifer Sustainability Under Groundwater Administrations in Oklahoma and Texas1

Mittelstet, Aaron R., Michael D. Smolen, Garey A. Fox, and Damian C. Adams, 2011. Comparison of Aquifer Sustainability Under Groundwater Administrations in Oklahoma and Texas. Journal of the American Water Resources Association (JAWRA) 1‐8. DOI: 10.1111/j.1752‐1688.2011.00524.x Abstract: We compared two approaches to administration of groundwater law on a hydrologic model of the North Canadian River, an alluvial aquifer in northwestern Oklahoma. Oklahoma limits pumping rates to retain 50% aquifer saturated thickness after 20 years of groundwater use. The Texas Panhandle Groundwater Conservation District’s (GCD) rules limit pumping to a rate that consumes no more than 50% of saturated thickness in 50 years, with reevaluation and readjustment of permits every 5 years. Using a hydrologic model (MODFLOW), we simulated river‐groundwater interaction and aquifer dynamics under increasing levels of “development” (i.e., increasing groundwater withdrawals). Oklahoma’s approach initially would limit groundwater extraction more than the GCD approach, but the GCD approach would be more protective in the long run. Under Oklahoma rules more than half of aquifer storage would be depleted when development reaches 65%. Reevaluation of permits under the Texas Panhandle GCD approach would severely limit pumping as the 50% level is approached. Both Oklahoma and Texas Panhandle GCD approaches would deplete alluvial base flow at approximately 10% development. Results suggest periodic review of permits could protect aquifer storage and river base flow. Modeling total aquifer storage is more sensitive to recharge rate and aquifer hydraulic conductivity than to specific yield, while river leakage is most sensitive to aquifer hydraulic conductivity followed by specific yield.     

USING SENSITIVITY ANALYSIS TO ASSIST PARAMETER ZONATION IN GROUND WATER FLOW MODEL1

ABSTRACT: For numerical modeling of ground water movement in a real aquifer system, the aquifer is usually divided into hydrogeologically defined zones, each with its own parameter values. The responses of the system, such as head or drawdown, are often available only in some of the zones. The estimated parameters of all the zones are based on the measured response in these limited zones. However, the estimates for some of the zones may be very uncertain, and these zones are therefore not justified by the data. In this paper, an approach is presented to understand which zone may produce uncertain parameter values and should be lumped with its neighbor. This approach is demonstrated using a regional numerical model for pumping test analysis in the Nottinghamshire aquifer, UK. A step-by-step process is used in identifying the aquifer zones and estimating their parameters based on the principle of using the smallest possible numbers of zones and parameters for adequate representation of the drawdown response. After the parameters of each zone are estimated, the sensitivity features of these parameters are examined. The results show that the parameters in one zone can be estimated properly by the drawdown in another zone only when there is significant sensitivity. For transmissivity, sensitivity between zones occurs when there is significant flow between them. For storativity, sufficient sensitivity can occur without large flows between the zones, provided that one zone causes significant drawdown in the other. This idea can be extended to the flow model for a large aquifer system. If the aquifer is divided in such a way that aquifer responses are not sensitive to the parameters in some of the zones, the parameters in those zones cannot be estimated properly and should be lumped into their neighboring zones. In this way, a simple but more reasonable model can be built.     

ESTIMATING TRANSMISSIVITY AND HYDRAULIC CONDUCTIVITY OF CHICOT AQUIFER FROM SPECIFIC CAPACITY DATA1

ABSTRACT: Specific capacity data obtained from Well Construction reports which are available from USGS offices, can provide useful estimates of tranamissivity (T), and hydraulic conductivity (K), of an aquifer. The Chicot Aquifer in Louisiana is one of the largest sources of fresh ground water in North America. Hydrologic data collected for the Chicot Aquifer indicate that specific capacity tests can be used in estimating local and regional values for T and K, if the Cooper-Jacob equation for transient flow is used with proper corrections for well loss and partial penetration. Where full scale pumping test data are scarce, specific capacity test data that are adequately distributed spatially can be used to map changes in T and K values and can be summarized statistically to indicate applicable regional values. A computer program called “TGUESS” which is available from International Ground Water Modeling Center, Holcomb Research Institute, was used in this study. The contour maps for T and K values are prepared for different well depth intervals to avoid wide variation of values.     

MODELING GROUND WATER FLOW USING FLUX BOUNDARY CONDITIONS1

ABSTRACT: Determination of the boundary conditions for modeling ground water flow is a critical point especially in regional models. Normally the regional models require model areas that are greater than the given area of interest. This work focuses on the prediction of hydraulic heads in regional models using flux boundary conditions. The model uses flux boundary conditions that were estimated using a radial flow analog and Darcy's law. The regional model that is presented uses no parameter identification (inverse estimation) procedures. In the present work, the Houston area was used. The simulation of the hydrological conditions of the Chicot and Evangeline Aquifers that underlie the Houston area were made using the available information about the geological profile in the Houston region and the current information about the existing production wells. The regional model works as a forward problem. The system parameters such as hydraulic conductivity, specific storage, and hydrological stresses were specified, and the model predicts the hydraulic head. Actual data from piezometers operated by the U.S. Geological Survey (USGS) in many places throughout Houston were used as initial conditions. Some piezometric head data were generated using the regional variable theory called kriging to supply head estimates in areas where data were unavailable. The Modular Three Dimensional Finite Difference Groundwater Flow Model developed by the USGS was used to predict the hydraulic heads. The predicted ground water heads are compared to the actual data. The results show that the model performs well for locations where data were available.     

AQUIFER PARAMETERS FROM CONSTANT DRAWDOWN NONSTEADY-LEAKY TYPE CURVES1

ABSTRACT: A drain function and set of type curves were defined for the mathematical solution that represents one-dimensional flow under nonsteady conditions in a leaky aquifer for the constant drawdown boundary condition. A match point procedure was developed for determining the aquifer parameters transmissivity, storage coefficient, and leakance based on the drain function and type curves. Use of the procedure is illustrated by an example that utilizes simulated aquifer drawdowns and flowrate data. The drain function and type curves developed in this investigation include the effects of leakage for the constant drawdown boundary condition, which is not included in the existing drain function and type curve found in the literature. Thus, a new set of type curves was developed that can be used to analyze drawdowns for one-dimensional flow in a leaky aquifer with constant drawdown at a line sink. Applications would include flow to a canal or river, drainage of agricultural lands, and dewatering associated with strip mining operations.     

EVALUATION OF A STREAM AQUIFER ANALYSIS TEST USING ANALYTICAL SOLUTIONS AND FIELD DATA1

ABSTRACT: Considerable advancements have been made in the development of analytical solutions for predicting the effects of pumping wells on adjacent streams and rivers. However, these solutions have not been sufficiently evaluated against field data. The objective of this research is to evaluate the predictive performance of recently proposed analytical solutions for unsteady stream depletion using field data collected during a stream/aquifer analysis test at the Tamarack State Wildlife Area in eastern Colorado. Two primary stream/aquifer interactions exist at the Tamarack site: (1) between the South Platte River and the alluvial aquifer and (2) between a backwater stream and the alluvial aquifer. A pumping test is performed next to the backwater stream channel. Drawdown measured in observation wells is matched to predictions by recently proposed analytical solutions to derive estimates of aquifer and streambed parameters. These estimates are compared to documented aquifer properties and field measured streambed conductivity. The analytical solutions are capable of estimating reasonable values of both aquifer and streambed parameters with one solution capable of simultaneously estimating delayed aquifer yield and stream flow recharge. However, for long term water management, it is reasonable to use simplified analytical solutions not concerned with early‐time delayed yield effects. For this site, changes in the water level in the stream during the test and a varying water level profile at the beginning of the pumping test influence the application of the analytical solutions.