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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Analytical Solutions to the Linearized Boussinesq Equation for Assessing the Effects of Recharge on Aquifer Discharge1

Boggs, Kevin G., Robert W. Van Kirk, Gary S. Johnson, Jerry P. Fairley, and P. Steve Porter, 2010. Analytical Solutions to the Linearized Boussinesq Equation for Assessing the Effects of Recharge on Aquifer Discharge. Journal of the American Water Resources Association (JAWRA) 46(6):1116–1132. DOI: 10.1111/j.1752-1688.2010.00479.x Abstract: There is a need to develop a general understanding of how variations in aquifer recharge are reflected in discharge. Analytical solutions to the linearized Boussinesq equation governing flow in an unconfined aquifer provide a unified mathematical framework to quantify relationships among lag time, attenuation and distance between aquifer recharge and discharge and the effect of an up-gradient no-flow boundary. We applied this framework to three types of recharge: (1) instantaneous, (2) periodic, and (3) constant rate for a finite duration. When the temporal scale of recharge exceeds the diffusive aquifer time scale, recharge will be reflected in discharge quickly and with little attenuation. When aquifer time scale is large, most recharge events are shorter in scale than that of the aquifer, resulting in large attenuation. Attenuation is more sensitive to boundary effects than lag time, and boundary effects increase as recharge time scale increases. Boundary effects can often be ignored when the recharge source is farther than 1/3 of the domain length away from the no-flow boundary. We illustrate analytical results with application to the economically critical Eastern Snake River Plain Aquifer in Idaho. In this aquifer, detectable annual and decadal cycles in discharge can result from recharge no farther than 20 and 60 km away from the discharge point, respectively. The effects of more distant, long-term recharge can be detected only after a time lag of several decades.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

What is a static head measurement? Evaluating structural error and implications for regional groundwater modeling

Most groundwater modelers avoid using static heads measured from active production wells because they can introduce a bias into model calibration. However, in the deep confined Cambrian-Ordovician Sandstone Aquifer System in the Central Midcontinent of North America, dedicated observation wells are sparse and remote from areas of most concentrated pumping. As a result, in areas where drawdown is the greatest and modeling is most needed, only static heads from production wells are available for calibration. This paper evaluates two leading sources of discrepancies in using production well data, spatial and temporal structural error (S.E.). A simple Theis solution is used to evaluate the potential magnitude of spatial S.E. when calibrating a regional MODFLOW model with coarse cell resolution. Despite theoretical analyses indicating that spatial S.E. could be significant, statistical analysis of the model results suggests that temporal S.E. is dominant. Long (ranging over decades) or frequent (monthly) head datasets are key in understanding temporal S.E., to better capture water-level variability. In this study, the range in static head observations impacted estimates of the remaining time a well could extract water from the aquifer by 0.1 to 16.0 years. This uncertainty in future water supply is highly relevant to stakeholders and must be assessed in hydrographs depicting risk.