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.     

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.     

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.     

IDENTIFICATION OF AQUIFER DISPERSIVITIES: METHODS OF ANALYSIS AND PARAMETER UNCERTAINTY1

ABSTRACT: This paper presents a method for estimating aquifer dispersivities in solute transport models. Sensitivity equations are derived for the calculation of sensitivity coefficients. A modified Gauss-Newton algorithm is used to perform the least-squares minimization. A statistical procedure is outlined to assess reliability of the estimated parameters. The solute transport model is solved by the upstream weighted, multiple cell balance method which combines the concepts of local mass balance and finite element approximations. A one-dimensional solute transport problem in a vertical column system is first used to illustrate the inverse technique. A second example considers the parameter identification problem for three-dimensional solute transport with a unidirectional steady and uniform flow field. The third example solves the parameter identification problem in a three-dimensional, stream-aquifer, solute transport system with steady state flow. Numerical experiments are conducted to study data requirements for parameter identification.     

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.     

SEASONAL PUMPING VARIATION EFFECTS ON WELLHEAD PROTECTION AREA DELINEATION1

ABSTRACT: Delineation of a welihead protection area (WHPA) is the key element in welihead protection programs for drinking water supplies. WHPAs are often delineated under idealized conditions using simple steady-state assumptions, which lead to an incorrect estimation of area and geometry. In this paper, we compare the results from a simple steady-state procedure commonly employed in WHPA delineation with a more complex transient approach that allows consideration of seasonal variation in pumping rates. We also introduce a transient procedure to delineate time-related capture zones using a numerical ground water flow and transport model. Welihead delineation is examined for two municipal wells in Tipton, Oklahoma, using a ten-year time-of-travel criterion. In the steady-state procedure, where we assumed constant pumping rates, we used GPTRAC, a semi-analytical model, and MOC, a numerical model. The capture zone delineated by GPTRAC is comparable in shape with the capture zone delineated by MOC but not in size due to the differences in solution schemes. In the transient procedure, we used MOC and considered the seasonal variation in pumping rates. The capture zones delineated in this procedure were larger than the capture zones delineated by the steady-state procedure using the same model. Further analysis showed that a higher drawdown was predicted in the transient procedure than in the steady-state procedure, which is the reason for larger capture zones.     

APPLICATION OF TABU SEARCH TO GROUND WATER PARAMETER ZONATION1

ABSTRACT: The spatial distribution of hydrogeologic parameter is an important issue in ground water simulation. One of the methods is to divide an area into several zones such that parameters are assumed to be constant within zone. The purpose of this study is to apply Tabu Search (TS) to find the best zonation of parameters that can result in the best ground water simulation. The initial zonation can be determined as the Thiessen method, and then zonation is optimized by T.S. The mean square error between simulated and observed hydraulic heads was used as the objective function. A designed confined aquifer with known zonation was used as an example to test the proposed method. Results indicated that Tabu Search can locate the optimal zonation successfully and avoid being trapped by local optimal zonations. Besides this, four other arbitrary initial zonations can be directed to the optimal zonation by TS, which proves the robustness of the proposed method. The method proposed in this study is feasible and expected to work well in the field problems with sufficient sampling of concerned parameters.     

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.     

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.     

A LUMPED APPROACH TO THE INVERSE PROBLEM IN GROUND WATER HYDROLOGY1

ABSTRACT: A solution procedure to solve the inverse problem in ground water, based on lumped approach, has been proposed. The method has the following advantages: 1) exact determination of the boundary conditions and the physical laws of flow through porous media is not required; 2) all errors of approximation in describing the boundary conditions, physical laws, and the aquifer properties are lumped into the surrogate parameters; and 3) the same mathematical model can be employed both in the identification process and in the subsequent management studies. The optimal values of the surrogate parameters are found by using a multidimensional unconstrained optimization code devised by Powell. The solution procedure and the convergence characteristics of the proposed algorithm have been illustrated by two hypothetical problems.     

A Stochastic Modeling Approach to Address Hydrogeologic Uncertainties in Modeling Wellhead Protection Boundaries in Karst Aquifers1

Abstract: Development of any numerical ground‐water model is dependent on hydrogeologic data describing the subsurface. These data are obtained from geologic core analyses, stratigraphic analyses, aquifer performance tests, and geophysical studies. But typically in remote areas, these types of data are very sparse and site‐specific in terms of the aerial extent of the resource to be modeled. Uncertainties exist as to how well the available data from a few locations defines a heterogeneous surficial aquifer such as the Biscayne Aquifer in Miami‐Dade County, Florida. This is particularly the case when an exceptionally conductive horizontal flow zone is detected at one site due to specialized testing that was not historically conducted at the other at sites that provided data for the model. Not adequately accounting for the potential effect of the high flow zone in the aquifer within a ground‐water numerical model, even though the zone may be of very limited thickness, might underpredict the well field protection capture boundaries. Applied Stochastic ground‐water modeling in determining well field protection zones is steadily becoming important in addressing the uncertainty of the hydrogeologic subsurface parameters, specifically in karstic heterogeneous aquifers. This is particularly important in addressing the uncertainty of a 60‐day travel time capture zone in the Northwest Well Field, Miami‐Dade County, where a predominantly high flow zone controls much of the flow in the production wells. A stochastic ground‐water modeling application along with combination of pilot points and regularization technique is presented to further consolidate the uncertainty of the subsurface.     

SHORT-TERM FORECASTING OF SNOWMELT RUNOFF USING ARMAX MODELS1

ABSTRACT: Time series models of the ARMAX class were investigated for use in forecasting daily riverflow resulting from combined snowmelt/rainfall. The Snowmelt Runoff Model (Martinec-Rango Model) is shown to have a form similar to the ARMAX model. The advantage of the ARMAX approach is that analytical model identification and parameter estimation techniques are available. In addition, previous forecast errors can be included to improve forecasts and confidence limits can be estimated for the forecasts. Diagnostic checks are available to determine if the model is performing properly. Finally, Kalman filtering can be used to allow the model parameters to vary continuously to reflect changing basin runoff conditions. The above advantages result in improved flow forecasts with fewer model parameters.     

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.     

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.     

GENERALIZED WATERSHED LOADING FUNCTIONS FOR STREAM FLOW NUTRIENTS1

ABSTRACT: Loading functions are proposed as a general model for estimating monthly nitrogen and phosphorus fluxes in stream flow. The functions have a simple mathematical structure, describe a wide range of rural and urban nonpoint sources, and couple surface runoff and ground water discharge. Rural runoff loads are computed from daily runoff and erosion and monthly sediment yield calculations. Urban runoff loads are based on daily nutrient accumulation rates and exponential wash off functions. Ground water discharge is determined by lumped parameter unsaturated and saturated zone soil moisture balances. Default values for model chemical parameters were estimated from literature values. Validation studies over a three-year period for an 850 km² watershed showed that the loading functions explained at least 90 percent of the observed monthly variation in dissolved and total nitrogen and phosphorus fluxes in stream flow. Errors in model predictions of mean monthly fluxes were: dissolved phosphorus - 4 percent; total phosphorus - 2 percent; dissolved nitrogen - 18 percent; and total nitrogen - 28 percent. These results were obtained without model calibration.     

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.     

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.     

Model Development and Calibration of a Saltwater Intrusion Model in Southern California1

Abstract: A nine‐layered confined‐unconfined flow and transport model is developed for the Alamitos saltwater intrusion barrier in Southern California. The conceptual model is based on the geological structure of the coastal aquifer system. The key parameters in the flow and transport models are calibrated using a two‐phase procedure which matches the types of data available for calibration. Because of the abundance of point measurements of hydraulic conductivity, the heterogeneous and random hydraulic conductivity field for each of the five aquifers is estimated by the geostatiscal method of natural‐neighbor‐kriging in Phase 1. In Phase 2, the longitudinal and transverse dispersivities in the transport model are estimated by a traditional inverse procedure that minimizes the least‐squares error for concentration (LSE‐CON). The minimum LSE‐CON is achieved near 15.2 and 1.52 m for the longitudinal and transverse dispersivities, respectively. Additional simulations with increasing transport parameter complexity did not yield significant improvements in LSE‐CON. Also, tracking least‐squares error for head while parametrically varying the transport parameters revealed there is a negligible interaction between predicted head and transport parameters.     

Testing a Simple Field Method for Assessing Nitrate Removal in Riparian Zones1

Abstract: Being able to identify riparian sites that function better for nitrate removal from groundwater is critical to using efficiently the riparian zones for water quality management. For this purpose, managers need a method that is quick, inexpensive, and accurate enough to enable effective management decisions. This study assesses the precision and accuracy of a simple method using three ground water wells and one measurement date for determining nitrate removal characteristics of riparian buffer zones. The method is a scaled‐down version of a complex field research method that consists of a large network of wells and piezometers monitored monthly for over two years. Results using the simplified method were compared to those from the reference research method on a date‐by‐date basis on eight sites covering a wide range of hydrogeomorphic settings. The accuracy of the three‐well, 1 day measurement method was relatively good for assessing nitrate concentration depletion across riparian zones, but poor for assessing the distance necessary to achieve a 90% nitrate removal and for estimating water and nitrate fluxes compared to the reference method. The simplified three‐well method provides relatively better estimates of water and nitrate fluxes on sites where ground‐water flow is parallel to the water table through homogeneous aquifer material, but such conditions may not be geographically widespread. Despite limited overall accuracy, some parameters that are estimated using the simplified method may be useful to water resource managers. Nitrate depletion information may be used to assess the adequacy of existing buffers to achieve nitrate concentration goals for runoff. Estimates of field nitrate runoff and buffer removal fluxes may be adequate for prioritizing management toward sites where riparian buffers are likely to have greater impact on stream water quality.