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.     

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.     

DRAWDOWN DUE TO PUMPING IN AN ANISOTROPIC AQUIFER1

ABSTRACT: A variable change is used to convert drawdown formulas for isotropic aquifers for use where the aquifer is anisotropic. Contours of the cone of depression assume an oval configuration with the major and minor axes oriented in the directions for which the permeability is greated and least. The case of a well pumped at a constant rate, the case of a well drawing water at a constant rate from an aquifer with a leaky roof and the flowing artesian well case are treated. In all cases the well is considered to completely penetrate the aquifer.     

NONSTEADY FLOW TO A WELL WITH TIME DEPENDENT DRAWDOWN1

Confined flow toward a single well of finite radius in an extensive aquifer of uniform transmissibility is studied under the assumption of time-dependent drawdown. Three particular cases are considered: (a) linear drawdown (including constant drawdown); (b) exponential drawdown; (c) periodic (sinusoidal) drawdown. The differential equation governing unsteady axial symmetric flow toward a single well in a confined aquifer is solved for the three different situations by the use of the Laplace transform method. The resulting expressions are integrated by adapting a modified Gemant scheme. General computer programs have been developed and operated for several combinations of characteristics. The results are plotted to show the effect of time dependent drawdown on the variation of the well discharge and the piezometric head distribution.     

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.     

OPTIMAL MANAGEMENT OF A REGIONAL AQUIFER IN EASTERN SAUDI ARABIA1

ABSTRACT: This paper describes the formulation and application of a ground-water hydraulic management model to determine the optimal development and operating policies of a regional aquifer in the Eastern Province of Saudi Arabia. The hydraulic response of the aquifer system is represented by a simulation model that is linked to an optimization management model using response functions. Yearly optimal ground-water extraction rates over a planning horizon of 15 years are determined for four scenarios, each reflecting alternative ground-water development policies. The results are presented in the form of tradeoff curves, relating drawdowns to optimal pumpage, which may enhance the decisionmaker's ability to select the best development policy from a set of alternatives. The results illustrate how various optimal management schemes can be devised to increase the total withdrawal from the aquifer while preventing excessive de-watering.     

Behavior of beaver in lakes with varying water levels in Northern Minnesota

We studied the effects of winter water drawdowns (2.3 m) on beavers in Voyageurs National Park, Minnesota, USA. Our study was designed to sample areas within the park that differed in water drawdown regime. Lodges were counted and beavers were livetrapped and radio-implanted to study behavior, movements, and mortality. Active beaver lodge density, determined by aerial survey in 1984 and 1986, was greatest along the shoreline of the drawdown reservoir. In winter beavers living on the drawdown reservoir spent less time inside their lodges than did beavers from stable water environments, foraged more above ice, and they were unable to fully use stored food. Only one case of starvation in the drawdown reservoir was documented, but beavers in reservoirs that were drawn down survived winter in poorer condition than did beavers living in areas in which water levels remained high. In spite of an increasing population and lack of widespread mortality, winter water drawdowns did alter beaver behavior. To reduce these impacts, total annual water fluctuation should not exceed 1.5 m, and winter drawdown should not exceed 0.7 m. Possible management alternatives and costs are discussed.     

DETERMINATION OF AQUIFER PARAMETERS USING REGRESSION ANALYSIS1

ABSTRACT: Transmissivity and storativity of an aquifer are usually determined by analysis of steady or nonsteady pumping test data. The classical methods of nonsteady pumping test analysis are mostly graphical in nature and are, therefore, subject to errors of judgment in curve fitting, interpolating, and reading graphs and charts. A method is described here which does not require construction of graphs or use of charts and tables. The transmissivity and the storativity are calculated using regression analysis of the nonsteady time drawdown field data. The calculations can readily be performed on a hand held calculator. The procedure is described using four examples, and the results are compared with those obtained from graphical techniques. It is shown that the method is a viable alternative to the type curve solution of Theis or Straight line solution of Jacob for nonleaky artesian aquifers. However, the regression method poses problem in the cases of leaky artesian and water table aquifers.     

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.     

NON-STEADY SPHERICAL FLOW TO A CAVITY WELL IN AN INFINITE NON-LEAKY AQUIFER1

ABSTRACT: The non-steady drawdown distribution near a cavity well discharging from an infinite non-leaky artesian aquifer is presented. The variation of drawdown with time and distance caused by a cavity well of constant discharge in a confined aquifer of uniform thickness and uniform permeability is obtained. The solution is expressed in a series form which converges rapidly so that only two terms of the series are needed to obtain an accuracy of more than 95 percent. A simplified approach has been suggested to find the aquifer characteristics.     

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.     

ANALYSIS OF PUMPING TESTS: SIGNIFICANCE OF WELL DIAMETER,PARTIAL PENETRATION,AND NOISE1

ABSTRACT: The nonlinear least squares (NLS) method was applied to pumping and recovery aquifer test data in confined and unconfined aquifers with finite diameter and partially penetrating pumping wells, and with partially penetrating piezometers or observation wells. It was demonstrated that noiseless and moderately noisy drawdown data from observation points located less than two saturated thicknesses of the aquifer from the pumping well produced an exact or acceptable set of parameters when the diameter of the pumping well was included in the analysis. The accuracy of the estimated parameters, particularly that of specific storage, decreased with increases in the noise level in the observed drawdown data. With consideration of the well radii, the noiseless drawdown data from the pumping well in an unconfined aquifer produced good estimates of horizontal and vertical hydraulic conductivities and specific yield, but the estimated specific storage was unacceptable. When noisy data from the pumping well were used, an acceptable set of parameters was not obtained. Further experiments with noisy drawdown data in an unconfined aquifer revealed that when the well diameter was included in the analysis, hydraulic conductivity, specific yield and vertical hydraulic conductivity may be estimated rather effectively from piezometers located over a range of distances from the pumping well. Estimation of specific storage became less reliable for piezometers located at distances greater than the initial saturated thickness of the aquifer. Application of the NLS to field pumping and recovery data from a confined aquifer showed that the estimated parameters from the two tests were in good agreement only when the well diameter was included in the analysis. Without consideration of well radii, the estimated values of hydraulic conductivity from the pumping and recovery tests were off by a factor of four.     

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.     

The Transboundary Nature of the Allende–Piedras Negras Aquifer Using a Numerical Model Approach

The Allende–Piedras Negras (APN) aquifer is located between the states of Texas (United States [U.S.]) and Coahuila (Mexico). The Rio Grande crosses the aquifer, acting as a natural and political divide between the countries. However, it remains unclear whether the APN aquifer can be considered a truly transboundary aquifer flow system, which would potentially require joint management by two different administrative jurisdictions. The main purpose of this study was to evaluate the transboundary nature of this aquifer. This was achieved by developing a detailed hydrogeological model to analyze the direction of volumetric fluxes within the APN aquifer using Visual MODFLOW. The model simulated a spatially averaged cumulative drawdown of 0.76 m for the entire aquifer over an 18‐year modeling period (2000–2017). The flow convergence zone, previously located below the Rio Grande, has shifted to the U.S. side in most locations, driven by higher pumping rates of the wells located near the river. This shift of the convergence zone from one country to the other means that groundwater recharge from one side flows underneath the river to the other side. This qualifies the APN aquifer as a “transboundary groundwater flow system.” The procedure followed in this study may be applied to other aquifers that straddle the U.S.–Mexico border and may motivate future modeling studies on other poorly studied transboundary aquifers around the world and thereby enable bi‐national aquifer management.     

ANALYTICAL REGRESSION STAGE ANALYSIS FOR DEVILS HOLE,DEATH VALLEY NATIONAL PARK,NEVADA1

ABSTRACT: Devils Hole is a collapse depression connected to the regional carbonate aquifer of the Death Valley ground water flow system. Devils Hole pool is home to an endangered pupfish that was threatened when irrigation pumping in nearby Ash Meadows lowered the pool stage in the 1960s. Pumping at Ash Meadows ultimately ceased, and the stage recovered until 1988, when it began to decline, a trend that continued until at least 2004. Regional ground water pumping and changes in recharge are considered the principal potential stresses causing long term stage changes. A regression was found between pumpage and Devils Hole water levels. Though precipitation in distant mountain ranges is the source of recharge to the flow system, the stage of Devils Hole shows small change in stage from 1937 to 1963, a period during which ground water withdrawals were small and the major stress on stage would have been recharge. Multiple regression analyses, made by including the cumulative departure from normal precipitation with pumpage as independent variables, did not improve the regression. Drawdown at Devils Hole was calculated by the Theis Equation for nearby pumping centers to incorporate time delay and drawdown attenuation. The Theis drawdowns were used as surrogates for pumpage in multiple regression analyses. The model coefficient for the regression, R²= 0.982, indicated that changes in Devils Hole were largely due to effects of pumping at Ash Meadows, Amargosa Desert, and Army 1.     

RECHARGE TO ALLUVIAL VALLEY AQUIFERS FROM OVERBANK FLOW AND EXCESS INFILTRATION1

ABSTRACT: Recharge is an important parameter for models that simulate water and contaminant transport in unconfined aquifers. Unfortunately, measurements of actual recharge are not usually available causing recharge to be estimated or possibly added to the calibration procedure. In this study, differences between observed water-table elevations and water-table elevations simulated with a model based on the one-dimensional Boussinesq equation were used to identify both the timing and quantity of recharge to an alluvial valley aquifer. Observed water table elevations and river stage data were recorded during a five-year period from 1991 to 1995 at the Ohio Management Systems Evaluation Area located in south-central Ohio. Direct recharge attributed to overbank flow during and shortly after flood conditions accounted for 65 percent of the total recharge computed during the five-year study period. Recharge of excess infiltration to the aquifer was intermittent and occurred soon after large rainfall events and high river stage. Specification of constant recharge with time values in ground-water simulation models seems inappropriate for stream-aquifer systems given the strong influence of the river on water table elevations in these systems.     

OPTIMAL GROUND WATER MANAGEMENT IN TWO-AQUIFER SYSTEMS1

ABSTRACT; This paper presents a numerical model for the prediction of optimal ground water withdrawal from a two-aquifer system by observing a set of constraints determined by the ecological conditions of the ground water basin. The aquifer system consists of an upper unconfined and a lower confined aquifer with a leaky stratum between them. It is assumed that water is withdrawn from the confined aquifer only, but the unconfined aquifer will also be affected due to the leakiness of the layer separating the upper and lower aquifers. Simulation and linear programming are employed for developing a computer model for the optimal management of such systems, with the objectives of determining withdrawal rates for predetermined ground water levels.     

INTEGRATING GEOGRAPHIC INFORMATION SYSTEMS IN GROUND-WATER APPLICATIONS USING NUMERICAL MODELING TECHNIQUES1

ABSTRACT: The Sand and Gravel Aquifer is the sole source of potable water in Escambia County, Florida. In order to better understand the hydraulics of the aquifer, a numerical computer model of the aquifer was developed. The model applied a finite element technique which allowed for density-dependent transport and flow in three dimensions. The modeling technique was integrated with GIS to develop a system for optimal management of the resource. The GIS was the primary tool in the development of the model grid, as well as being the integral component in the modeling procedure. Multiple model grids were developed for simulating regional flow and local flow/transport phenomena. The model grids were generated by the GIS where nodal and element sequencing were recorded. The grid topology was stored in the GIS with the element numbers, node numbers, and the related hydrogeologic attributes. The Triangulated Irregular Network (TIN) module was used for transferring interpolated value between GIS coverages. TIN allowed a fit of the model grid to the physical dimensions of the aquifer and for interpolating boundary values for telescopically refined grids. Calculations between TIN surfaces provided the residuals of the dependent variable from observed TIN surfaces. Model calibration was conducted within the GIS environment through a combination of visual and relational querying. The GIS provided an integrated environment which facilitated model analyses and data storage and retrieval.     

INTEGRATING GEOGRAPHIC INFORMATION SYSTEMS AND MODFLOW FOR GROUND WATER RESOURCE ASSESSMENTS1

ABSTRACT: The Floridan Aquifer is the primary source of water in the coastal area of Santa Rosa County, Florida. In order to optimize well field design and analyze aquifer stress problems, the USGS MODFLOW code (McDonald and Harbaugh, 1988) is applied to develop a numerical computer model of the aquifer. The Geographical Information System (GIS) is the primary tool used in the development of the model grid, performance of the modeling procedure, and model analysis. The GIS is used in generating multiple grids in which to simulate both regional scale and local scale flow. The grid topology is recorded in geographic coordinates which facilitates geo-referencing and orientation of the grid to base maps and data coyerages. The GIS allows data transfer from various coverages to the nodes of the block centered grid where hydrogeologic information is stored as attributes to the grid coverage. From this grid coverage, pertinent information is queried within the GIS environment and used to generate the input files for the MODFLOW simulation. After MODFLOW execution, simulated heads and drawdown are imported into the grid coverage where residual error and recharge rates can be calculated. Contoured surfaces are then created for selected data sets including simulated heads, drawdown, residual error, and recharge rates. Model calibration is conducted utilizing the GIS to generate and process data sets associated with model simulations.     

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.