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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

DRAWDOWN AT TIME-DEPENDENT FLOWRATE1

ABSTRACT: The exact solution for the drawdown in and around a well in a homogeneous, isotropic, and confined aquifer is presented if the well discharge is a function of time. The effect of the storage capacity of the well is also taken into consideration. Two types of flowrate functions are studied, namely linear and exponential functions, and the results are plotted in graphs.     

SENSITIVITY OF GROUNDWATER FLOW MODELS TO VERTICAL VARIABILITY OF AQUIFER CONSTANTS1

ABSTRACT: The Ogallala aquifer in the Oklahoma Panhandle is in need of better management because of increased groundwater demand which has caused declines in static water levels at an alarming rate. A groundwater management computer model was developed for the Ogallala aquifer in the Texas Panhandle and treats the aquifer as a homogeneous system. In this study, the computer model has been modified in order to evaluate the effects of vertical layering on semi-static water level changes which occur during the dewatering of a single unconfined aquifer. The modified model was applied to a study area near Guymon, Oklahoma, using both the homogeneous and the multilayered cases. The aquifer is characterized by a saturated thickness of 400 feet. The accumulated drawdown values of the homogeneous and the multilayered cases demonstrate that an average difference of approximately 22% of the original saturated thickness occurs between the two cases before the base of the aquifer is encountered. Approximately 25% more time is required to dewater the layered aquifer. Thus, vertical variations of lithology in an aquifer such as the Ogallala should be considered when prediction is made relative to groundwater management.     

EDWARDS AQUIFER EVALUATION: KINNEY COUNTY,TEXAS1

ABSTRACT: The Edwards Aquifer is one of the most studied and most prolific aquifers in the United States. The aquifer is a heavily fractured and faulted carbonate aquifer with transmissivities in excess of 100 ft²/s. The City of San Antonio relies upon the Edwards Aquifer as its sole source for water. Much work has been done on quantifying recharge to the aquifer and discharge from wells and acquiring aquifer characteristics from pumping tests, specific capacity tests, and geophysical logs. Although the aquifer has been well studied in Bexar County, much less is known about the Edwards Aquifer in Kinney County. This is partly due to the lower population within the county (approximately 3,500 people) relative to the eastern counties (Uvalde, Medina, Bexar, Comal, and Hays) and the great distance of Kinney County from high profile discharge areas such as the City of San Antonio and Comal and San Marcos Springs. Three key products resulted from this study: (1) exploratory well drilling and the largest aquifer test in the county that were conducted to evaluate the well yields within a 10,000 acre study area in which a drawdown of 2.5 ft approximately 1.2 miles away was observed while pumping at approximately 4,600 gpm; (2) a recharge estimate for the Edwards Aquifer within Kinney County of approximately 71,382 ac‐ft/yr; and (3) locating the Brackettville Groundwater Divide from an evaluation of ground water flow direction and hydrograph analysis. These results help evaluate the complex hydraulics occurring within Kinney County and aid in development of ground water modeling that will be used in managing the Edwards Aquifer.     

DECLINING POTENTIOMETRIC LEVELS IN FORT WALTON BEACH AREA,FLORIDA1

ABSTRACT: The Fort Walton Beach area is presently faced with an excessive drawdown of the potentiometric level in the upper Floridan aquifer. Based on available data, the potentiometric level in the Floridan aquifer has dropped 162 feet since 1936. This declining potentiometric level can lead to problems and possible loss of the natural resource on a long-term basis. However, if corrective measures or programs for proper management of groundwater resources are undertaken at this time, the potential problems may be averted.     

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.     

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.     

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.     

UTILIZING INDUCED RECHARGE FOR REGIONAL AQUIFER MANAGEMENT1

ABSTRACT: The deep aquifers of the Portland Basin are used as a regional water supply by at least six municipalities in Oregon and Washington. Maximum continuous use of the aquifers in 1998 was 13 mgd and peak emergency use was 55 mgd. Continuous use of the deep aquifers at a rate of 55 mgd has been proposed and inchoate water rights have been reserved for expansion of pumping to 121 mgd. A study was completed, using a calibrated ground water flow model, to evaluate the role of induced recharge from the Columbia River in mitigating aquifer drawdown from continuous‐use and expanded pumping scenarios in the center and eastern areas of the basin. The absolute average residual was less than 3.6 feet for steady‐state model calibrations, and less than 8.0 feet for transient calibration to a 42 mgd pumping event in 1987 with 170 feet of drawdown. Continuous use of the aquifers at a rate of 55 mgd is predicted to increase drawdown to 210 feet. Expansion of pumping to 121 mgd in the center basin is predicted to cause 400 feet of drawdown. However, expansion of pumping in the east basin is predicted to result in only 220 feet of drawdown because of induced recharge from the Columbia River.     

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.     

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.     

RECIRCULATING WELLS: GROUND WATER REMEDIATION AND PROTECTION OF SURFACE WATER RESOURCES1

ABSTRACT: Several chlorinated solvent plumes threaten the sole‐source aquifer underlying the Massachusetts Military Reservation at the western end of Cape Cod. Sensitive surface water features including ponds, cranberry bogs, and coastal wetlands are hydraulically connected to the aquifer. For one of the plumes (CS‐10 the original remedy of 120 extraction and reinjection wells has the potential for significant disruption of surface water hydrology, through the localized drawdown and mounding of the water table. Recirculating wells with in‐well air stripping offer a cost‐effective alternative to conventional pump‐and‐treat technology that does not adversely affect the configuration of the water table. Pilot testing of a two well system, pumping 300 gpm, showed a capture radius of > 200 feet per well, in‐well trichloroethylene (TCE) removal efficiencies of 92 to 98 percent per recirculation cycle, an average of three recirculation cycles within the capture zone, and no measurable effect on water table elevations at any point within the recirculation/treatment zone. During 120 days of operation, the mean concentration of TCE in the treatment zone was reduced by 83 percent, from 1,111 μg/l to 184 μg/l. Full‐scale design projections indicate that 60 wells at an average spacing of 160 feet, having an aggregate recirculation 11 MGD, can contain the CS‐b plume without ground water extraction or adverse hydraulic effects on surface water resources. The estimated capital costs for such a system are about $7 million, and annual operations‐and‐maintenance costs should be about $1.4 million, 40 percent of those associated with a pump and treat system over a 20‐year period.