aqtesolv for windows user's guide

AQTESOLV for Windows

User's Guide

By HydroSOLVE, Inc.

Software Developed By: Glenn M. Duffield, HydroSOLVE, Inc.Manual Authored By: Glenn M. Duffield, HydroSOLVE, Inc.

Copyright 1996-2000 Glenn M. Duffield, HydroSOLVE, Inc.

All rights reserved. No part of this manual may be reproduced or transmitted in any form or by any means, electronicor mechanical, including photocopy, recording, or any information storage and retrieval system, without permission inwriting from the author.

Microsoft is a registered trademark and Windows is a trademark of Microsoft Corp.AQTESOLV is a registered trademark of ARCADIS Geraghty & Miller, Inc.This manual was produced using Doc-To-Help® by WexTech Systems, Inc.

HydroSOLVE, Inc.2303 Horseferry Court

Reston, VA 20191-2739Tel (703) 264-9024Fax (209) 254-8831

[email protected]

24-Jul-2000

AQTESOLV for Windows User's Guide Contents •• i

Contents

Getting Started 1

AQTESOLV for Windows Features ..................................................................................... 1Data Management .................................................................................................. 1Visual Matching..................................................................................................... 1Automatic Matching............................................................................................... 2Statistical Analysis ................................................................................................. 2Plots and Reports.................................................................................................... 2

Help..................................................................................................................................... 3Contents, Index and Search .................................................................................... 3Using Help ............................................................................................................. 3Tip of the Day ........................................................................................................ 3AQTESOLV on the Web........................................................................................ 3About AQTESOLV ................................................................................................ 3

Interface Features................................................................................................................. 3Opening a New Window......................................................................................... 4Cascading Windows ............................................................................................... 4Tiling Windows...................................................................................................... 4Arrange Icons......................................................................................................... 4Refresh................................................................................................................... 4Toolbar................................................................................................................... 4Status Bar............................................................................................................... 4

Tools.................................................................................................................................... 5

Guided Tours 7

Overview ............................................................................................................................. 7Analyzing a Pumping Test ................................................................................................... 7Analyzing a Slug Test ........................................................................................................ 11Additional Tutorials........................................................................................................... 15

Working With Data Sets 17

What is an AQTESOLV for Windows Data Set? ................................................................ 17Managing Data Set Files .................................................................................................... 17

Creating a New Data Set ...................................................................................... 17Saving a Data Set ................................................................................................. 18Opening a Data Set .............................................................................................. 19Closing a Data Set................................................................................................ 19Sending a Data Set as Mail................................................................................... 19Opening a Recently Used Data Set........................................................................ 19Exiting AQTESOLV for Windows ....................................................................... 19

Import Wizards.................................................................................................................. 19AQTESOLV for DOS Import Wizard................................................................... 19

ii •• Contents AQTESOLV for Windows User's Guide

Observation Data Import Wizard.......................................................................... 20Pumping Rate Data Import Wizard ...................................................................... 21

Editing Data Sets ............................................................................................................... 23Units .................................................................................................................... 23Annotations.......................................................................................................... 23Aquifer Data ........................................................................................................ 24Pumping Well ...................................................................................................... 25Observation Well ................................................................................................. 28Slug Test Well ..................................................................................................... 31Test Type ............................................................................................................. 34

Plots 35

Overview ........................................................................................................................... 35Choosing a Plot.................................................................................................................. 35

Displacement vs. Time Plot .................................................................................. 35Composite Plot..................................................................................................... 36Residual vs. Time Plot.......................................................................................... 36Residual vs. Simulated Plot .................................................................................. 36Normal Probability Plot........................................................................................ 36Discharge vs. Time Plot ....................................................................................... 37Derivative vs. Time Plot ....................................................................................... 37Radial Flow Plot................................................................................................... 37Linear Flow Plot................................................................................................... 38Bilinear Flow Plot ................................................................................................ 38Spherical Flow Plot .............................................................................................. 39

Changing Plot Axes ........................................................................................................... 39Linear Axes.......................................................................................................... 39Semi-Log Axes..................................................................................................... 39Log Axes.............................................................................................................. 39

Choosing Plot Options ....................................................................................................... 39Plots Tab (View>Options) .................................................................................... 39Family Tab (View>Options)................................................................................. 40Derivative Tab (View>Options)............................................................................ 40Valid Time Tab (View>Options).......................................................................... 41Step Test Tab (View>Options) ............................................................................. 41

Formatting Plots ................................................................................................................ 41Graph Tab (View>Format)................................................................................... 41X and Y Axis Tabs (View>Format)...................................................................... 42Legend Tab (View>Format) ................................................................................. 42Solution Tab (View>Format)................................................................................ 43Family Tab (View>Format).................................................................................. 43Theis Curve Tab (View>Format).......................................................................... 43Fitted Tab (View>Format).................................................................................... 44

Zoom ................................................................................................................................. 44Contouring Results ............................................................................................................ 44

Step 1. Grid Output File (Grid Wizard) ............................................................... 44Step 2. Specify Grid Dimensions (Grid Wizard) .................................................. 45Step 3. Display Contour Plot (Grid Wizard) ........................................................ 45

Reports 47

Overview ........................................................................................................................... 47Choosing a Report ............................................................................................................. 47

AQTESOLV for Windows User's Guide Contents •• iii

Diagnostic Report................................................................................................. 47Complete Report................................................................................................... 47Error Log ............................................................................................................. 47

Formatting Reports ............................................................................................................ 47

Choosing a Solution 49

Overview ........................................................................................................................... 49Confined Aquifer Solutions................................................................................................ 49

Theis (1935) Solution for a Pumping Test in a Confined Aquifer.......................... 50Cooper-Jacob (1946) Solution for a Pumping Test in a Confined Aquifer ............. 55Papadopulos-Cooper (1967) Solution for a Pumping Test in a Confined Aquifer .. 58Theis (1935) Solution for a Recovery Test in a Confined Aquifer ......................... 62Theis (1935) Solution for a Step Drawdown Test in a Confined Aquifer ............... 65Hantush (1962) Solution for a Pumping Test in a Wedge-Shaped Confined Aquifer68Murdoch (1994) Solution for Flow to a Trench..................................................... 70Cooper-Bredehoeft-Papadopulos (1967) Solution for a Slug Test in a ConfinedAquifer................................................................................................................. 72Bouwer-Rice (1976) Solution for a Slug Test in a Confined Aquifer ..................... 73Hvorslev (1951) Solution for a Slug Test in a Confined Aquifer ........................... 73Hyder et al. (1994) Solution for a Slug Test in a Confined Aquifer (KGS Model) . 73

Unconfined Aquifer Solutions ............................................................................................ 76Theis (1935) Solution for a Pumping Test in an Unconfined Aquifer.................... 76Cooper-Jacob (1946) Solution for a Pumping Test in an Unconfined Aquifer........ 78Neuman (1974) Solution for a Pumping Test in an Unconfined Aquifer ............... 79Quick Neuman Solution for a Pumping Test in an Unconfined Aquifer ................ 86Streltsova (1974) Solution for a Pumping Test in an Unconfined Aquifer ............. 87Moench (1997) Solution for a Pumping Test in an Unconfined Aquifer ................ 90Bouwer-Rice (1976) Solution for a Slug Test in an Unconfined Aquifer ............... 95Hvorslev (1951) Solution for a Slug Test in an Unconfined Aquifer...................... 96Hyder et al. (1994) Solution for a Slug Test in an Unconfined Aquifer (KGS Model)98

Leaky Aquifer Solutions................................................................................................... 103Hantush-Jacob (1955) Solution for a Pumping Test in a Leaky Aquifer .............. 103Hantush (1960) Solution for a Pumping Test in a Leaky Aquifer ........................ 109Moench (1985) Solution for a Pumping Test in a Leaky Aquifer......................... 113Neuman-Witherspoon (1969) Solution for a Pumping Test in a Leaky Aquifer ... 117

Fractured Aquifer Solutions ............................................................................................. 121Moench (1984) Solution for a Pumping Test in a Fractured Aquifer with Slab-Shaped Blocks.................................................................................................... 121Moench (1984) Solution for a Pumping Test in a Fractured Aquifer with SphericalShaped Blocks.................................................................................................... 127Gringarten-Witherspoon (1972) Solution for a Pumping Test in a Fractured Aquiferwith a Plane Vertical Fracture ............................................................................ 131Gringarten-Ramey (1974) Solution for a Pumping Test in a Fractured Aquifer witha Plane Horizontal Fracture ................................................................................ 135

List of Symbols ................................................................................................................ 141

Estimating Aquifer Coefficients 143

Overview ......................................................................................................................... 143Automatic Curve Matching .............................................................................................. 143

Estimation Tab (Match>Automatic) ................................................................... 144Parameters Tab (Match>Automatic) ................................................................... 145Options Tab (Match>Automatic) ........................................................................ 145

iv •• Contents AQTESOLV for Windows User's Guide

How Automatic Curve Matching Works ..............................................................145Visual Curve Matching.....................................................................................................147

Visual Matching with Aquifer Test Solutions ......................................................147Visual Matching with Diagnostic Plots................................................................147Visual Matching with Derivative Plots ................................................................148Active Type Curves .............................................................................................149Matching Early/Late Data ...................................................................................149Matching Type Curve Families ...........................................................................150

Toolbox for Curve Matching.............................................................................................150Tweak Tab (Match>Toolbox) ..............................................................................150Parameters Tab (Match>Toolbox) .......................................................................150Options Tab (Match>Toolbox) ............................................................................151

Obtaining Output 153

Overview ..........................................................................................................................153Printing Options ...............................................................................................................153

Print....................................................................................................................153Print Preview ......................................................................................................153Print Setup ..........................................................................................................153Page Setup ..........................................................................................................153Troubleshooting ..................................................................................................154

Export Options .................................................................................................................155Export Plot Data..................................................................................................155Export Type Curve ..............................................................................................155Export Windows Metafile....................................................................................155Export Grid File ..................................................................................................155

Clipboard Functions..........................................................................................................155Copy ...................................................................................................................155

References 157

Glossary of Terms 161

AQTESOLV for Windows User's Guide Getting Started •• 1

Getting Started

AQTESOLV for Windows FeaturesAQTESOLV for Windows is a powerful yet easy-to-use tool for hydrogeologists andengineers that features a comprehensive suite of analytical solutions for determiningaquifer properties from pumping tests and slug tests. After first entering orimporting data from an aquifer test, you can access visual and automatic curvematching methods for confined, unconfined, leaky and fractured aquifers. Visualcurve matching is analogous to traditional methods of aquifer test analysis withgraph paper and type curves. The sophisticated automatic curve-matching featureenhances aquifer test analysis by providing greater objectivity and a detailedstatistical evaluation of the results. AQTESOLV for Windows also features manyoptions for obtaining report quality graphics to summarize the results of youranalysis.

Data ManagementAQTESOLV for Windows helps you manage aquifer test data with data manage-ment tools for entering, editing and importing data. Wizards guide you through thecreation of data sets for pumping tests and slug tests. Error checking ensuresconsistent and complete data entry. Flexible specification of measurement units letsyou enter data in English and metric systems. Retrieval of data from a pressuretransducer is easy using the Import Wizard in AQTESOLV for Windows.

Visual MatchingThe visual curve-matching feature in AQTESOLV for Windows lets you analyzeaquifer tests using the traditional method of matching type curves or straight linesto time-displacement data measured during an aquifer test.

AQTESOLV for Windows provides a comprehensive set of tools for visual typecurve analysis. With a plot of the data displayed on the computer screen, you canmatch a type curve to your data in an interactive manner. By simply moving yourmouse, you can move a type curve on the screen and watch AQTESOLV forWindows update the values of aquifer properties. Use the new Active TypeCurve feature to overcome limitations of traditional static type curves and extendvisual curve matching to any solution including derivatives. Adjust hydraulic

2 •• Getting Started AQTESOLV for Windows User's Guide

properties with the Tweak Parameters option to perform sensitivity analysis andfine-tune the match of a solution.

Automatic MatchingThe powerful automatic curve-matching feature provided by AQTESOLV forWindows uses nonlinear weighted least-squares parameter estimation to match typecurves or straight lines to time-displacement data measured during an aquifer test.

The automatic curve matching feature minimizes the errors between the position ofthe type curve and your data and provides statistical measures of the type curve “fit”such as the precision of the estimated aquifer properties and error distributions.

Statistical AnalysisAutomatic curve matching provides statistical criteria measuring the “fit” of a typecurve to your data. The statistics give you an objective basis for comparing thematch of several different solutions to the same set of data.

Automatic curve matching computes standard errors of the estimated parametersthat allow you to evaluate the precision of the parameter estimates and to constructapproximate confidence intervals. Statistics for the model errors provide a basis forchoosing between different aquifer test solutions that produce similar visualmatches.

Plots and ReportsAQTESOLV for Windows helps you visualize the results of your aquifer testanalyses by providing eleven graphical representations.

• displacement vs. time plot

• composite plot

• residuals vs. time plot

• residuals vs. simulated displacement plot

• normality test for residuals

• derivative vs. time plot

• discharge vs. time plot

• radial flow plot

• linear flow plot

• bilinear flow plot

• spherical flow plot

In addition, AQTESOLV for Windows includes report options that document thecontents of data sets and summarize the results of matching analytical solutions todata.

• complete aquifer test analysis report

• diagnostic statistics summary

• error log


The error log feature enables you to quickly identify any deficiencies orinconsistencies detected in your data set.

HelpThe Help menu provides you with options for exploring the AQTESOLV forWindows online User's Guide.

Contents, Index and SearchChoose Contents and Index from the Help menu to view the contents and indexin the AQTESOLV for Windows online User's Guide.

Select Search… from the Help menu and click the Find tab to search the onlinedocumentation for help topics.

Choose What's This? From the Help menu or click on the toolbar to obtainHelp about a specific menu option or button. Move the Context Help cursor over amenu option or button, and click the mouse to obtain context-sensitive help.

Using HelpChoose Using Help from the Help menu to view instructions for navigating theWindows help system.

Tip of the DayChoose Tip of the Day… from the Help menu to display helpful tips.

AQTESOLV on the WebChoose AQTESOLV on the Web from the Help menu to select options forproduct information and technical support available at the AQTESOLV forWindows web site (http://www.aqtesolv.com).

Select the Support option to access the AQTESOLV for Windows KnowledgeBase, a free web-based service providing answers to frequently asked questions(FAQs), tips and examples.

About AQTESOLVChoose About AQTESOLV... from the Help menu or click on the toolbar todisplay program copyright and version information for AQTESOLV for Windows.

Interface FeaturesOptions for various interface features are available in the View and Windowmenus.

4 •• Getting Started AQTESOLV for Windows User's Guide

Opening a New WindowChoose New Window from the Window menu to open a new window for theactive data set.

Cascading WindowsChoose Cascade from the Window menu to cascade windows from the upper leftcorner of the AQTESOLV for Windows client area.

Tiling WindowsChoose Tile Horizontal or Tile Vertical from the Window menu to tile windowshorizontally or vertically, respectively.

Arrange IconsChoose Arrange Icons from the Window menu to arrange window icons at thebottom of the screen.

RefreshClick on the toolbar torefresh the display

Choose Refresh from the View menu to refresh (redraw) the plot or report in theactive window.

ToolbarChoose Toolbar from the View menu to enable/disable the AQTESOLV forWindows toolbar.

Status BarChoose Status Bar from the View menu to enable/disable the status bar shown atthe bottom of the AQTESOLV for Windows display. The status bar contains fourpanes that indicate messages and status information.

Message Pane

The first pane in the status bar supplies descriptive messages for menuoptions.

Check Errors Indicator

The second pane in the status bar displays the message Check Errorsif AQTESOLV for Windows detects errors in active data set. Toview the errors, choose Error Log from the View menu.

Test Type Indicator

The third pane in the status bar displays either Pumping Test orSlug Test to indicate the type of test contained in the active dataset.


Solution Indicator

The fourth pane in the status bar displays the current solution for theactive data set. AQTESOLV for Windows will prompt you tochoose a solution if the data set contains sufficient data to performa forward solution.

ToolsThe Tools menu provides options for running other Windows applications (e.g.,ModelCad for Windows, TWODAN and WinSitu). Use these applications inconjunction with AQTESOLV for Windows to increase your productivity. ChooseConfigure… from the Tools menu to configure the applications.

AQTESOLV for Windows User's Guide Guided Tours •• 7

Guided Tours

OverviewThe Guided Tours provide you with step-by-step instructions illustrating the useof AQTESOLV for Windows in the analysis of pumping tests and slug tests. Thetours show you how to perform visual and automatic curve matching, changebetween plot and report views, open multiple windows for the same data set, obtainprinted output and much more. Regardless of whether you are a novice or an expertin analyzing aquifer test data, it is recommended that you take the time to gothrough the guided tours to become familiar with AQTESOLV for Windows.

Analyzing a Pumping TestThe first stop in the guided tour shows you how to use AQTESOLV for Windows toanalyze a constant-rate pumping test in a confined aquifer. This step-by-stepexample illustrates the use of visual and automatic curve matching to estimate thehydraulic properties of the aquifer.

Open a New Data SetOpen a new data set by choosing New from the File menu. In the New Data Setdialog box, choose Guided Tour from the list box to initialize the new data setwith default values. AQTESOLV for Windows opens a new window with an ErrorLog view that reports any errors identified in the data set.

Enter Data for Pumping TestUnits Choose Units... from the Edit menu to select units of measurement for the data set.

1. Select ft (feet) for Length, min (minutes) for Time, consistent forPumping Rate and consistent for Hyd. Conductivity.

2. Click OK.

Consistent units For this data set, consistent units for pumping rate are cubic feet-per-minute;consistent units for hydraulic conductivity are feet-per-minute.

Title Choose Annotations... from the Edit menu to edit the data set title.

1. In the Title tab, enter Theis Verification for the Title.

2. Click OK.

8 •• Guided Tours AQTESOLV for Windows User's Guide

Aquifer data Choose Aquifer Data... from the Edit menu to edit aquifer data.

1. In the General tab, enter 100.0 for the value of SaturatedThickness.

2. Click OK.

Pumping well data Choose Pumping Well>Edit... from the Edit menu to edit pumping well data.

1. In the Construction tab, enter 0.1 for both Wellbore Radius andCasing Radius.

2. In the Rates tab, enter values of 0.0 and 3.14159 for time and rate,respectively, where time is in minutes and rate is in cubic feet-per-minute.

TIPSEnter rates for a pumping test as a sequence of pumping periods.Define each pumping period by entering the starting time andpumping rate for the period. The first pumping period should have atime = 0.0 indicating the start of the test. In simulate recovery, enteran additional pumping period with the time when the pump was shutoff and a pumping rate = 0.0.

3. Click OK.

Observation well data Choose Obs. Well>Edit... from the Edit menu to edit observation well data.

1. In the General tab, enter a value of 100.0 for the X-Coordinatelocation of the well.

2. In the Observations tab, you can enter observation data from thekeyboard or import data from a file. All of the time values should begreater than the start of the first pumping period entered for thepumping well (i.e., > 0.0). All of the displacement values should begreater than zero.

Enter the following 10 measurements (set all weights equal to 1.0):

Time Displacement0.5 0.04891 0.21945 1.22310 1.82350 3.355100 4.038500 5.6391000 6.3325000 7.9410000 8.633

TIPSTo save time, you can copy the values of time and displacement fromthe table shown above and paste them into AQTESOLV for Windowsusing the Paste button.

2. When you have finished entering the observations, click OK.


After you have completed the previous data entry steps, the Error Log displayed inthe active window should show that the data set contains no errors. Now you areready to display the data, choose a solution and estimate aquifer properties.

Save Data SetChoose Save As... from the File menu to save the data you have entered into thecurrent data set.

1. Enter TOUR1.AQT for the file name.

2. Click OK to save the data set.

Display Plot in WindowChoose Displacement-Time from the View menu to display a plot ofdisplacement vs. time in the active window. The window displays a plot of theobservation well data on semi-logarithmic axes.

Choose Theis SolutionChoose Solution... from the Match menu to choose a solution for analyzing thepumping test.

1. Choose the Confined Theis (1935) solution.

2. Click OK.

After you have selected the Theis solution for a pumping test in a confined aquifer,AQTESOLV for Windows updates the window by plotting the data on doublelogarithmic axes, superimposing the Theis type curve on the plot, and adding thecurrent values of transmissivity (T), storage coefficient (S), hydraulic conductivityanisotropy ratio (Kz/KrKz/Kr) and saturated thickness (b) to the legend.

For details concerning the Theis solution, see "Theis (1935) Solution for a PumpingTest in a Confined Aquifer" on page 50.

Perform Visual Matching with TheisThe Theis type curve solution computes drawdown for fully penetrating wells in aconfined aquifer using the following equations:

sQ

T

e

ydy

y

u

=−∞

∫4π

ur S

Tt=

2

4

where s is drawdown, Q is pumping rate, T is transmissivity, r is radial distance be-tween pumping and observation wells, S is storage coefficient, and t is time.

Hydrogeologists commonly refer to the exponential integral in the drawdownequation as the Theis well function, abbreviated as w(u). Therefore, we can writethe Theis drawdown equation in compact notation as follows:

sQ

Tw u=

4π( )

To analyze a pumping test using the Theis type curve method, one plots drawdownas a function of time on double logarithmic axes. By matching a type curve drawn


by plotting w(u) as a function of 1/u, one can estimate the values of transmissivityand storage coefficient by visual analysis.

Choose Visual from the Match menu to perform visual curve matching with theTheis type curve.

1. To begin interactively moving the type curve, move the mouse cursorover the plot, click the left mouse button, and hold it down.

2. As you move the mouse, the type curve also moves. AQTESOLV forWindows updates the values of the aquifer properties, T and S, in thelegend as the type curve position changes.

3. When you have finished matching the type curve to the observationwell data, release the left mouse button to end visual curve matching.

Perform Automatic Matching with TheisChoose Automatic... from the Match menu to perform automatic curve matchingwith the Theis type curve solution.

AQTESOLV for Windows uses nonlinear least-squares parameter estimation tomatch a solution to observation well data. The estimation procedure performs asequence of iterations to minimize the residual sum of squares (RSS) criterion. Theresiduals are the errors between the computed and observed values of displacement.

1. Click the Estimate button to begin the automatic estimationprocedure.

2. As the automatic estimation procedure completes iterations, a progresswindow displays the changes in the residual sum of squares (RSS)criterion and the values of the aquifer properties. After the automaticestimation procedure finishes, AQTESOLV for Windows displays amessage box containing residual summary statistics. Click OK toclose the message box.

3. Click the Close button to close the progress window and click OK tofinish.

Print ResultsChoose Print... from the File menu to print a copy of the type curve solution. Toselect a printer other than the default, click the Setup... button and choose a newprinter. Click the OK button to print the type curve plot.

Open a New Window for a Diagnostic PlotChoose New Window from the Window menu to open a second window for theactive data set. The initial view in the second window is the same as the previouslyactive window.

1. Select Normal Probability from the View menu to plot values ofresiduals (errors) plotted on normal probability axes in the newwindow. This view option is only available after you have performedautomatic curve matching.

2. After you have inspected the normal probability plot, close thewindow.


Diagnostic test for normaldistribution of residuals

If the residuals are normally distributed, they will fall on a straight line whenplotted on normal probability axes. Deviations from a normal distribution mayindicate that the chosen analytical solution is inadequate for the analysis.

Grid/Contour ResultsChoose Contour… from the View menu to prepare a grid file for contouring andoptionally create and display a contour plot with Surfer for Windows (version 6 orhigher). Enter the following data in the Grid Wizard.

1. In Step 1 of the Grid Wizard, enter TOUR1.GRD for the Grid file.Choose X-Y (Plan) for the Grid Orientation. Click Next > tocontinue.

2. In Step 2 of the Grid Wizard, enter values of -100, 100 and 26 for theMin, Max and No. of Lines, respectively, for each coordinatedirection. Enter values of 0 and 100 for the Min and Max Depths.Enter a value of 10 for the Time since the start of pumping.

3. In Step 3 of the Grid Wizard, check Display grid file with Surfer ifyou wish to display a contour plot with Surfer for Windows (version 6or higher).

4. Click the Finish button to prepare the grid file and optionally createand display the contour plot.

Save Data SetChoose Save from the File menu to save your work in the TOUR1.AQT data set.

Analyzing a Slug TestThe second sample in the guided tour illustrates the analysis of a slug test in aconfined aquifer using a type-curve solution by Cooper, Bredehoeft andPapadopulos and a straight-line solution by Bouwer and Rice. The step-by-stepinstructions in this example lead you through the use of visual and automatic curvematching to estimate aquifer properties from slug test data.

Open a New Data SetOpen a new data set by choosing New from the File menu. In the New Data Setdialog box, choose Guided Tour from the list box to initialize the new data setwith default values. AQTESOLV for Windows opens a new window with an ErrorLog view that reports any errors identified in the data set.

Enter Data for Slug TestUnits Choose Units... from the Edit menu to select units of measurement for the data set.

1. Select m (meters) for Length, min (minutes) for Time, and cm/sec(centimeters-per-second) for Hyd. Conductivity.

2. Click OK.

Title Choose Annotations... from the Edit menu to edit the data set title.

1. In the Title tab, enter Confined Slug Test for the Title.

2. Click OK.


Slug test data Choose Slug Test Well... from the Edit menu to edit slug test data.

1. In the General tab, enter 0.56 for Initial Displacement.

2. In the Aquifer tab, enter 100.0 for Saturated Thickness.

3. In the Screen tab, enter 100.0 for Screen Length and 100.0 forTotal Depth of Penetration.

4. In the Radius tab, enter 0.076 for Casing Radius and 0.076 forWellbore Radius.

5. In the Observations tab, you can enter observation data from thekeyboard or import data from a file. Enter the following 21measurements (set all weights equal to 1.0):

Time Displacement3 0.4576 0.3929 0.34512 0.30815 0.2818 0.25221 0.22424 0.20527 0.18730 0.16833 0.14936 0.1439 0.13142 0.11245 0.10848 0.09351 0.08954 0.08257 0.07560 0.07163 0.065




Save Data SetChoose Save As... from the File menu to save the data you have entered into thecurrent data set.

1. Enter TOUR2.AQT for the file name.


2. Click OK.

Display Report in WindowChoose Report from the View menu to display a complete report of the data set inthe active window.

Complete report The complete report displays in report format all of the data contained in the activedata set. The report also shows parameters estimated by visual or automatic curvematching. The report includes diagnostic statistics if you have performed automaticestimation.

Display Plot in WindowChoose Displacement-Time from the View menu to display a plot ofdisplacement vs. time in the active window. The window displays the data plottedon semi-logarithmic axes.

Choose Cooper Et Al. SolutionChoose Solution... from the Match menu to choose a solution for analyzing theslug test.

1. Choose the Confined Cooper-Bredehoeft-Papadopulos (1967)solution.

2. Click OK.

For details concerning the Cooper-Bredehoeft-Papadopulos slug test solution, see"Cooper-Bredehoeft-Papadopulos (1967) Solution for a Slug Test in a ConfinedAquifer" on page 72.

Perform Automatic Matching with Cooper Et Al.Choose Automatic... from the Match menu to perform automatic curve matchingwith the Cooper-Bredehoeft-Papadopulos type curve solution.

1. Click the Estimate button to begin the automatic estimationprocedure.



Display Diagnostic Report in WindowChoose Diagnostics from the View menu to display a report containingdiagnostic statistics for the estimated aquifer properties in the active window.

Diagnostic report In the diagnostic report, the standard errors indicate the precision of the estimatedparameters. Ideally, the standard errors should be small compared to the estimates.The correlation matrix shows correlations between the estimated parameters andmay indicate estimation difficulties when strong correlations exist. The diagnosticreport also displays summary statistics for the model residuals.


Display Plot in WindowChoose Displacement-Time from the View menu to display a plot ofdisplacement vs. time in the active window.

Choose Bouwer-Rice SolutionChange the solution by choosing Solution... from the Match menu.

1. Choose the Confined Bouwer-Rice (1976) solution.

2. Click OK.

After you have selected the Bouwer-Rice straight-line solution for a slug test in aconfined aquifer, AQTESOLV for Windows updates the window by plotting thedata on semi-logarithmic axes and superimposing a straight line predicted by theBouwer-Rice solution on the plot.

For details on the Bouwer-Rice slug test solution, see "Bouwer-Rice (1976) Solutionfor a Slug Test in an Unconfined Aquifer" on page 95.

Perform Visual Matching with Bouwer-RiceChoose Visual from the Match menu to perform visual curve matching of theBouwer-Rice solution to the slug test data.

1. To begin interactively matching the Bouwer-Rice solution to the data,click the left mouse button and hold it down to anchor a point alongthe new straight line you wish to match to the data.

2. As you move the mouse, AQTESOLV for Windows drags a straightline between the anchor point and the mouse cursor.

3. When you have finished matching the Bouwer-Rice solution to theobservation well data, release the left mouse button. AQTESOLV forWindows computes new estimates of hydraulic conductivity (K) and y-axis intercept (y0) and updates the straight line displayed on the plot.

Estimation tip For most slug tests, one should use visual matching to obtain the most meaningfulestimate of K with the Bouwer-Rice solution because visual matching gives yougreater control over the range of data that you want to match with the straight line.If you choose to attempt automatic matching with the Bouwer-Rice solution, youshould assign weights of zero to the measurements not within the range of data thatyou want to match.

Perform Sensitivity AnalysisChoose Toolbox… from the Match menu and click the Tweak tab to performsensitivity analysis for the Bouwer-Rice solution.

1. From the Parameter list, choose K (i.e., hydraulic conductivity) asthe parameter that you want to tweak.

2. Click the arrow buttons or the scroll bar to tweak the value of theparameter. For the Bouwer-Rice solution, tweaking the value of Kchanges the slope of the line. Check Apply changesautomatically to update the plot while you tweak the parameters.

3. Click Cancel to ignore your changes.


Save Data SetChoose Save from the File menu to save your work in the TOUR2.AQT data set.

Additional TutorialsThe on-line version of this User's Guide contains additional tutorials for pumpingtest and slug test solutions found in AQTESOLV for Windows. To access thesetutorials, choose Index from the Help menu to access the Table of Contents forthe on-line help manual.

Pumping Test TutorialsTheis (1935) solution for a confined aquifer

Cooper-Jacob (1946) solution for a confined aquifer

Papadopulos-Cooper (1967) large-diameter well solution for a confined aquifer

Theis (1935) solution for a recovery test in a confined aquifer

Theis (1935) solution for a step drawdown test in a confined aquifer

Hantush (1962) solution for a wedge-shaped aquifer

Murdoch (1994) solution for a interceptor trench

Theis (1935) solution for an unconfined aquifer

Cooper-Jacob (1946) solution for an unconfined aquifer

Neuman (1974) and Quick Neuman solutions for an unconfined aquifer

Streltsova (1974) solution for an unconfined aquifer

Moench (1997) large-diameter well solution for an unconfined aquifer

Hantush-Jacob (1955) solution for a leaky aquifer

Hantush (1960) solution for a leaky aquifer

Moench (1985) large-diameter well solution for a leaky aquifer

Neuman-Witherspoon (1969) solution for leaky two-aquifer system

Moench (1984) solution for a double-porosity fractured aquifer (slab-shaped blocks)

Moench (1984) solution for a double-porosity fractured aquifer (spherical blocks)

Gringarten-Witherspoon (1972) solution for a fractured aquifer with a plane verticalfracture

Gringarten-Ramey (1974) solution for a fractured aquifer with a plane horizontalfracture

Slug Test TutorialsCooper-Bredehoeft-Papadopulos (1967) solution for a confined aquifer

Bouwer-Rice (1979) solution for an unconfined aquifer

Hvorslev (1951) solution for an unconfined aquifer

Hyder et al. (1995) solution for an unconfined aquifer


Tutorials Illustrating Selected TopicsImporting data logger files (Tutorial, Tutorial, Tutorial, Tutorial, Tutorial)

Variable pumping rates with recovery (Tutorial, Tutorial)

Multiple observation wells (Tutorial, Tutorial)

Active type curves (Tutorial)

Type curve families (Tutorial)

Tweaking parameters (Tutorial)

Sensitivity analysis (Guided Tour, Tutorial)

Linear flow plot (Tutorial)

Contouring results (Guided Tour)

AQTESOLV for Windows User's Guide Working With Data Sets •• 17

Working With Data Sets

What is an AQTESOLV for Windows Data Set?An AQTESOLV for Windows data set is a file that you create usingAQTESOLV for Windows to save work from an aquifer test analysis session. Itcontains data from an aquifer test (e.g., aquifer geometry data, test well data,pumping data and time-displacement data) and information concerning the solutionmethod used to analyze the test data (e.g., solution method and aquifer properties).A data set also contains data that you enter to format plots and reports. In otherwords, an AQTESOLV for Windows data set contains a complete record of youraquifer test analysis at the time you save it.

Managing Data Set Files

Creating a New Data SetClick on the toolbar toopen a new data set

Select New from the File menu to create a new AQTESOLV for Windows data set.

From the New Data Set dialog box, choose a template or wizard from the list boxto create a new data set.

When you create a new data set, AQTESOLV for Windows automatically opens anError Log window that indicates data items that you need to enter for a completedata set. The Error Log view displays deficiencies and inconsistencies in the dataset. After completing data entry, view the data by choosing an option from theView menu.

Default (File>New)

1. Choose New… from the File menu.

2. Select the Default template from the list to create a new data set withdefault values. You can choose options from the Edit menu to modifythe default values in the data set.

Guided Tour (File>New)


18 •• Working With Data Sets AQTESOLV for Windows User's Guide

2. Select the Guided Tour template from the list to create a new dataset containing default values for a "Guided Tour" example containedin this manual.

Import AQTESOLV for DOS Wizard (File>New)


2. Select the Import AQTESOLV for DOS Wizard from the list tohelp you import a data set created with a DOS version of AQTESOLV.

Pumping Test Wizard (File>New)


2. Select the Pumping Test Wizard from the list to help you create anew data set for a typical pumping test. This wizard also allows you toimport time-displacement data from a pressure transducer file.

Slug Test Wizard (File>New)


2. Select the Slug Test Wizard from the list to help you create a newdata set for a typical slug test. This wizard also allows you to importtime-displacement data from a pressure transducer file.

Template Wizard (File>New)


2. Select the Template Wizard from the list to help you create a newdata set using an existing AQTESOLV for Windows data set as acustom template. For example, use the Template Wizard to copydata from a master data set when you have performed duplicate tests(e.g., slug tests) in the same test well.

Tutorial (File>New)


2. The Tutorial template creates a new data set containing default valuesfor a tutorial contained in this manual.

Saving a Data SetYou have two options for saving an AQTESOLV for Windows data set.

To save data set using the current file name

Click on the toolbar tosave the active data set

Choose Save from the File menu to save an AQTESOLV forWindows data set on disk using the current file name.

To save data set with a new file name

1. Select Save As... from the File menu to specify a file namebefore you save the data set.

2. Enter a file name for the data set you want to save.

3. Click OK to save the data set using the file name.


Opening a Data SetClick on the toolbar toopen an existing data set

Choose Open... from the File menu to open an existing data set created withAQTESOLV for Windows.

1. Enter the file name of the data set you want to open.

2. Click the OK button to retrieve the data set.

Closing a Data SetChoose Close from the File menu to close the active data set. If you have changedany data, AQTESOLV for Windows prompts you to save the modified data set.

Sending a Data Set as MailChoose Send Mail… from the File menu to send the active data set as an e-mailattachment.

Opening a Recently Used Data SetSelect a file name from the list at the bottom of the File menu to open a recentlyused data set.

Exiting AQTESOLV for WindowsTo exit AQTESOLV for Windows, choose Exit from the File menu.

Import WizardsAQTESOLV for Windows provides easy-to-use wizards for importing data into thesoftware. These wizards allow you to import AQTESOLV for DOS data sets andfiles (e.g., from data loggers) containing field measurements.

AQTESOLV for DOS Import WizardImport data sets created withDOS versions of AQTESOLV.

Use the Import AQTESOLV for DOS Wizard to import data sets created withany DOS version of AQTESOLV.

1. Choose New from the File menu and select Import AQTESOLV forDOS Wizard from the New Data Set dialog box to import theAQTESOLV for DOS data set.

2. Follow the steps in the Import AQTESOLV for DOS Wizard toimport a file containing an AQTESOLV for DOS data set.

3. Check Convert all data sets with .DAT extension in thisfolder if you want to convert all of your old AQTESOLV for DOSdata sets (with a .DAT extension) in the folder you have selected intoAQTESOLV for Windows data sets (with a .AQT extension).

TIPS


1. You also can select Import… from the File menu and chooseAQTESOLV for DOS Data Set from the Import dialog box toimport an AQTESOLV for DOS data set into the active data set.

2. Before using this procedure for importing an AQTESOLV for DOSdata set, be sure you have created a new data set or opened an existingdata set file.

Observation Data Import WizardCreate a delimited text file toimport measurementsrecorded by a pressuretransducer.

Import time, displacement and measurement weight data for an observation or slugtest well with the Observation Data Import Wizard, a flexible tool forimporting measurements from text files. The Import Wizard supports delimitedtext files created by many different types of loggers.

The import file may contain one or more columns of data separated by comma,blank or tab delimiters. The wizard automatically searches for the row containingthe first observation, or you can specify the starting row in the file. Transformationand filter operations also allow you to modify and reduce the data during the importprocess.

Importing Observation Data for a Pumping Test

Choose Obs. Well>Edit… from the Edit menu. In the Observations tab, clickImport.

Importing Observation Data for a Slug Test

Choose Slug Test Well… from the Edit menu. In the Observations tab, clickImport.

TIPS

1. You also can select Import… from the File menu and chooseObservation Well Measurements from the Import dialog box toimport observation data for either a pumping test or slug test.

2. Before using one of these procedures for importing observation data,be sure you have created a new data set or opened an existing data setfile.

Step 1. Open Import File (Import Observations)

1. Enter a path and filename for a text file containing observation data.Click Browse... to search for a file.

2. To view a specified file, click View Import File....

3. To append data from the import file to observation data in the data set,check the Append observations from import file to data setbox.

4. Click Next > to proceed to Step 2.

Step 2. Identify File Structure (Import Observations)

1. Enter the No. of Columns contained in the file. The total number ofcolumns contained in the file may be greater than the number ofcolumns that you wish to import.


2. Enter a number for the Starting Row containing the first observationthat you wish to import from the file.

TIPSClick Select Starting Row... to view the import file. You canselect the first row in the file that you want to import by double-clicking it.

3. Specify the Data to Import from the file. Check the data items(elapsed time, date/clock time, displacement and measurement weight)that you are importing and their column locations in the file.

TIPSWhen importing date/clock time values, AQTESOLV for Windowscomputes elapsed time assuming the Starting Row contains the dateand time at the start of the test.


Step 3. Specify Transformation and Filter Operations(Import Observations)

1. Select Pre-Filter Operations for transforming time anddisplacement data contained in the file. Enter constants forsubtraction and multiplication operations.

TIPSSubtract the static water level from each value of displacementcontained in the file to transform depth to water values todisplacement values. To transform negative displacements to positivedisplacements, multiply each displacement value by -1.

2. Click Filters... to select options for filtering the data imported fromthe file.

TIPSUse filters to reduce the number of observations contained in theimport file. Retain time values with a uniform logarithmic spacing ordisplacement values that exceed a minimum threshold.

3. Click Finish to import the file.

Pumping Rate Data Import WizardCreate a delimited text file toimport measurementsrecorded by a data logger.

Import pumping rate data for a pumping well with the Pumping Period ImportWizard, a flexible tool for importing measurements from text files. The ImportWizard supports delimited text files created by many different types of dataloggers.

The import file may contain one or more columns of data separated by comma,blank or tab delimiters. The wizard automatically searches for the row containingthe first pumping period, or you can choose the starting row in the file.Transformation and filter operations also allow you to modify and reduce the dataduring the import process.

Importing Pumping Rate Data for a Pumping Test


Choose Pumping Well>Edit… from the Edit menu. In the Rates tab, clickImport.

TIPS

1. You also can select Import… from the File menu and choosePumping Rate Measurements from the Import dialog box toimport pumping rate data for a pumping test.

2. Before using one of these procedures for importing observation data,be sure you have created a new data set or opened an existing data setfile.

Step 1. Open Import File (Import Rates)

1. Enter a path and filename for a text file containing pumping perioddata. Click Browse... to search for a file.

2. To view a specified file, click View Import File....

3. To append data from the import file to pumping period data in thedata set, check the Append pumping periods from import fileto data set box.


Step 2. Identify File Structure (Import Rates)

1. Enter the No. of Columns contained in the file. The total number ofcolumns contained in the file may be greater than the number ofcolumns that you wish to import.

2. Enter a number for the Starting Row containing the first pumpingperiod that you wish to import from the file.

TIPSClick Select Starting Row... to view the import file. You canselect the first row in the file that you want to import by double-clicking it.

3. Specify the Data to Import from the file. Check the data items(starting time of the pumping period expressed as an elapsed time ordate/clock value and pumping rate) that you are importing and theircolumn locations in the file.

TIPSWhen importing date/clock time values, AQTESOLV for Windowscomputes elapsed time assuming the Starting Row contains the dateand time at the start of the test.


Step 3. Specify Transformation and Filter Operations(Import Rates)

1. Select Pre-Filter Operations for transforming time and pumpingrate data contained in the file. Enter constants for subtraction andmultiplication operations.


2. Click Filters... to select options for filtering the data imported fromthe file.

TIPSUse filters to reduce the number of pumping periods. Retain ratevalues exceeding a minimum threshold (AQTESOLV for Windowstime-averages intermediate values not retained).

3. Click Finish to import the file.

Editing Data SetsThe Edit menu provides options for entering or modifying data in the active dataset. Selecting any of the options will open property sheets that prompt you forinformation stored in AQTESOLV data sets.

UnitsChoose Units... from the Edit menu to select units of measurement for time,length, pumping rate and hydraulic conductivity.

Dimensionally consistentunits

Unless otherwise specified, AQTESOLV for Windows assumes that pumping ratesand hydraulic conductivity/transmissivity units are dimensionally consistent withthe units specified for length and time. For example, if the units of length and timewere feet and minutes, respectively, the dimensionally consistent units would beft3/min cubic feet per minute for pumping rate and ft2/day square feet per day fortransmissivity.

Optional units for pumpingrate and hydraulicconductivity

For those not wishing to use dimensionally “consistent” units, AQTESOLV forWindows provides options for pumping rate units including gallons and liters (e.g.,gpm and L/sec). For units of hydraulic conductivity/transmissivity, you also canselect units containing gallons (e.g., gpm/ft2 gal/min/sq. ft).

AnnotationsSelect Annotations… from the Edit menu to enter information used to annotateplots and reports prepared by AQTESOLV for Windows.

Title Tab (Edit>Annotations)

Choose Annotations… from the Edit menu and click the Title tab to enter a titlefor the data set.

Project Info Tab (Edit>Annotations)

Choose Annotations… from the Edit menu and click the Project Info tab toenter information for any of the following items into the active data set (each itemmay contain up to 30 characters):

• client name

• project number

• location of test

• test well name


• observation well name

• date of test

End Notes Tab (Edit>Annotations)

Choose Annotations… from the Edit menu and click the End Notes tab to enterend notes for a report.

Aquifer DataSelect Aquifer Data... from the Edit menu to enter aquifer geometry and specialhydraulic property data into the active data set.

General Tab (Edit>Aquifer Data)

Choose Aquifer Data… from the Edit menu and click the General tab to entergeneral aquifer information.

Saturated thickness

1. Enter the saturated thickness [L] of the aquifer measured fromthe top of the aquifer (or the water table) to the bottom of theaquifer.

2. In an unconfined aquifer, the maximum displacement should notexceed the saturated thickness.

Hydraulic conductivity ratio

1. Enter the vertical to horizontal hydraulic conductivityratio (Kz/KrKz/Kr) [dimensionless] for pumping test solutionsapplying the Hantush (1961a,b) corrections for partiallypenetrating wells.

2. The Neuman (1974) solution for pumping tests in unconfinedaquifers, which estimates the value of Kz/Kr Kz/Kr in the value ofthe β beta parameter, does not use the hydraulic conductivity ratiovalue entered in the aquifer data.

Double-Porosity Tab (Edit>Aquifer Data)

Choose Aquifer Data… from the Edit menu and click the Double Porosity tabto enter data for a double-porosity fractured aquifer.

Thickness of slab-shaped matrix blocks

Enter the thickness [L] of slab-shaped matrix blocks for the Moench(1984) solution for a double-porosity fractured aquifer with slab-shaped blocks.

Diameter of spherical blocks

Enter the diameter [L] of spherical blocks for the Moench (1984)solution for a double-porosity fractured aquifer with sphericalblocks.


Single Fracture Tab (Edit>Aquifer Data)

Choose Aquifer Data… from the Edit menu and click the Single Fracture tabto enter data for a single vertical or horizontal fracture.

Vertical fracture

Enter the total length [L] (equals two times half-length) of a verticalplane fracture for the Gringarten-Witherspoon (1972) solution fora confined aquifer with a single vertical fracture.

Horizontal fracture

1. Enter the radius [L] of a horizontal plane fracture for theGringarten-Ramey (1974) solution for a confined aquifer with asingle horizontal fracture.

2. Enter the depth [L] from the top of the aquifer to the horizontalfracture.

Wedge Tab (Edit>Aquifer Data)

Choose Aquifer Data… from the Edit menu and click the Wedge tab to enterdata for a wedge-shaped aquifer.

Slope orientation angle

1. Enter the orientation of the slope on the base of a wedge-shapedaquifer as the angle measured in a counterclockwisedirection from the positive x-coordinate axis to the vectororiented in the updip direction of the slope.

2. Enter the slope orientation angle in degrees.

Trench Tab (Edit>Aquifer Data)

Choose Aquifer Data… from the Edit menu and click the Trench tab to enterdata for a trench.

Trench length

Enter the total length [L] (equals two times half-length) of a trenchfor the Murdoch (1994) solution for a confined aquifer with a fullypenetrating trench.

Pumping WellChoose the Pumping Well option from the Edit menu. Select Edit..., Add... orDelete... from the popup submenu to edit, add or delete a pumping well. Choosingthe option to edit or add a pumping well allows you to enter or modify well data.

General Tab (Edit>Pumping Well)

Choose Pumping Well>Edit… from the Edit menu and click the General tab toedit general information for a pumping well.

Well name

Enter a name to identify the well.

Well coordinates


1. AQTESOLV for Windows uses an x-y coordinate system [L]to compute distances between pumping wells and observationwells.

2. For a simple pumping test involving only one pumping well andone observation well, locate the pumping well at x=0.0 and y=0.0.Locate the observation well at x=r and y=0.0 where r is the radialdistance between the pumping and observation wells.

Construction Tab (Edit>Pumping Well)

Choose Pumping Well>Edit… from the Edit menu and click the Constructiontab to edit well construction data for a pumping well.

Large-diameter well data

1. To analyze pumping tests using large-diameter well solutions,enter values for the casing radius [L] and wellbore radius[L] of the pumping well.

2. If the value for either of these two variables is 0.0, AQTESOLVfor Windows assumes the pumping well has an infinitesimalradius.

Well penetration data

1. A well is fully penetrating if its screen or perforated intervalextends over the full saturated thickness of the aquifer.

2. The screen of a partially penetrating well only extends over aportion of an aquifer's saturated thickness. For a partiallypenetrating well, enter depths [L] from the top of the aquifer (orwater table) to the top and bottom of the well screen.

3. The bottom of well screen depth must be greater than the top ofwell screen depth. The minimum depth for the top of the wellscreen is 0.0; the maximum depth for the bottom of the wellscreen is the saturated thickness of the aquifer.

Rates Tab (Edit>Pumping Well)

Choose Pumping Well>Edit… from the Edit menu and click the Rates tab toenter pumping rate data for the well. Options allow you to enter rates from thekeyboard, import rates from a file or copy/paste data from another application.

To enter pumping period data from the keyboard

1. Enter pumping history data in the spreadsheet as a sequence ofpumping periods.

2. Click Insert Row to insert a row in the spreadsheet.

3. Click Add Rows… to add rows to the spreadsheet.

TIPSEnter rates for a variable-rate test by entering a sequence ofpumping periods. Define pumping periods by entering thestarting time and pumping rate for the period. The first pumpingperiod should have a time = 0.0. For recovery, enter an additionalperiod with the time when the pump was shut off and a pumpingrate = 0.0.


To delete pumping period data

1. Select one or more rows in the spreadsheet.

2. Click Delete to delete the selected row(s). Before deleting thedata, AQTESOLV for Windows prompts to confirm your action.

To copy pumping period data to the clipboard


2. Click Copy to copy the selected row(s) to the clipboard.

To paste pumping period data from the clipboard

1. Copy time and pumping rate data to the clipboard using anotherWindows application (e.g., a spreadsheet).

2. Click Paste to paste the time and pumping rate data from theclipboard into the spreadsheet.

To import pumping period data from a file

1. Click Import to start the Pumping Period Import Wizard forimporting pumping history data from a file.

2. Follow the steps in the wizard (see "Pumping Rate Data ImportWizard" on page 21) to import delimited text files created bymany different types of data loggers. Transformation and filteroperations also allow you to modify and reduce the data during theimport process.

To search for a specific time or pumping rate

1. Click Search to open a dialog box for the search.

2. Enter the data vector (time or pumping rate) that you wish tosearch and the specific value.

3. Click OK to search for the value.

To transform pumping period data

1. Select the row(s) for the pumping period(s) that you want totransform.

2. Click Math to choose a transformation.

3. Enter the data vector (time or pumping rate) that you wish totransform.

4. Select a transformation operation (add, subtract, multiply, divideor replace).

5. Check the box to perform the transformation and click OK.Before transforming the data, AQTESOLV for Windows promptsto confirm your action.

To filter pumping period data

1. Click Filters to choose filtering operations.

2. Select filter operations for discarding or retaining pumpingperiods.

TIPS


Use filters to reduce the number of pumping periods. Retain ratevalues exceeding a minimum threshold (AQTESOLV forWindows time-averages intermediate values not retained).

3. Click OK to filter the data. Before filtering the data, AQTESOLVfor Windows prompts to confirm your action.

Symbol Tab (Edit>Pumping Well)

Choose Pumping Well>Edit… from the Edit menu and click the Symbol tab tochange the attributes of symbols displayed on data plots.

Symbol

Select a symbol type (circle, square, etc.) from the Symbol box.

Size

Select a symbol size from the Size box.

Thickness

Enter a Thickness for the symbol.

Color

Click Color to choose a color for the symbol.

Observation WellChoose the Obs. Well option from the Edit menu. Select Edit..., Add... orDelete... from the popup menu to edit, add or delete an observation well. If you areediting or adding an observation well, the Observation Well Data dialog boxallows you to enter data for the observation well.

General Tab (Edit>Observation Well)

Choose Obs. Well>Edit… from the Edit menu and click the General tab to editgeneral information for an observation well.

Well name


Well coordinates

1. AQTESOLV for Windows uses an x-y coordinate system [L]to compute distances between pumping wells and observationwells.

2. For a simple pumping test involving only one pumping well andone observation well, locate the pumping well at x=0.0 and y=0.0.Locate the observation well at x=r and y=0.0 where r is the radialdistance between the pumping and observation wells.

Construction Tab (Edit>Observation Well)

Choose Obs. Well>Edit… from the Edit menu and click the Construction tabto edit well construction data for an observation well.

Well penetration data


1. A well is fully penetrating if its screen or perforated intervalextends over the full saturated thickness of the aquifer.

2. The screen of a partially penetrating well only extends over aportion of an aquifer's saturated thickness. For a partiallypenetrating well, enter depths [L] from the top of the aquifer (orwater table) to the top and bottom of the well screen.

3. The bottom of well screen depth must be greater than the top ofwell screen depth. The minimum depth for the top of the wellscreen is 0.0; the maximum depth for the bottom of the wellscreen is the saturated thickness of the aquifer.

4. A piezometer (in contrast to an observation well) is an open-ended pipe installed in an aquifer to measure hydraulic head at aspecific depth. The piezometer depth [L] is distance from thetop of the aquifer (or water table) to the piezometer opening.

Observations Tab (Edit>Observation Well)

Choose Obs. Well>Edit… from the Edit menu and click the Observations tabto enter time-displacement data for the well. Options allow you to enter observationdata from the keyboard, import observations from a file or copy/paste data fromanother application.

To enter observation data from the keyboard

1. Enter values of time, displacement and weight in the spreadsheet.



TIPSAssign weights to indicate the relative weight of eachmeasurement during automatic curve matching. Assign a weightof zero for measurements you wish automatic curve matching toignore.

To delete observation data



To copy observation data to the clipboard



To paste observation data from the clipboard

1. Copy observation data to the clipboard using another Windowsapplication (e.g., a spreadsheet). Each observation should includetime and displacement values (weights are optional).

2. Click Paste to paste the observation data from the clipboard intothe spreadsheet.



1. Click Import to start the Observation Data Import Wizardfor importing observation data from a file.

Follow the steps in the wizard (see "TIPS



2. Observation Data Import Wizard" on page 19) to import delimitedtext files created by many different types of data loggers.Transformation and filter operations also allow you to modify andreduce the data during the import process.

To search for a specific time, displacement or weight


2. Enter the data vector (time, displacement or weight) that you wishto search and the specific value.


To transform observation data

1. Select the row(s) for the observation(s) that you want to transform.

2. Click Math to open a dialog box for the transformation operation.

3. Enter the data vector (time, displacement or weight) that you wishto transform.



To filter observation data

1. Click Filters to open a dialog box for the filtering operations.

2. Select filter operations for discarding or retaining observations.

TIPSUse filters to reduce the number of observations. Retain timevalues having a uniform logarithmic spacing or displacementvalues exceeding a minimum threshold.

3. Click OK to filter the observations. Before filtering the data,AQTESOLV for Windows prompts to confirm your action.

Symbol Tab (Edit>Observation Well)

Choose Obs. Well>Edit… from the Edit menu and click the Symbol tab tochange the attributes of symbols displayed on data plots.

Symbol



Size


Thickness

Enter a Thickness for the symbol.

Color


Slug Test WellChoose Slug Test Well... from the Edit menu to enter data for a slug test.

General Tab (Edit>Slug Test Well)

Choose Slug Test Well… from the Edit menu and click the General tab to entergeneral information for a slug test.

Well name


Initial displacement

Enter the initial displacement [L] measured in the well due theinstantaneous withdrawal or injection of water.

Aquifer Tab (Edit>Slug Test Well)

Choose Slug Test Well… from the Edit menu and click the Aquifer tab to enteraquifer data for a slug test.

Saturated thickness

1. Enter the saturated thickness [L] of the aquifer measured fromthe top of the aquifer (or the water table) to the bottom of theaquifer.

2. In an unconfined aquifer, the maximum displacement should notexceed the saturated thickness.

Hydraulic conductivity ratio

Enter the vertical to horizontal hydraulic conductivity ratio(Kv/KhKv/Kh) [dimensionless].

Screen Tab (Edit>Slug Test Well)

Choose Slug Test Well… from the Edit menu and click the Screen tab to enterwell construction information for a slug test.

Screen length

Enter the length of the well screen [L].

Penetration depth

1. Enter the total depth [L] of penetration by the well screen.


2. For unconfined aquifers, enter the depth from the water tableto the bottom of the well screen (static water column height).

3. For confined aquifers, enter the depth from the top of theaquifer to the bottom of the well screen.

Radius Tab (Edit>Slug Test Well)

Choose Slug Test Well… from the Edit menu and click the Radius tab to enterwell construction information for a slug test.

Casing radius

Enter the inside radius of the well casing [L].

Well radius

Enter the effective radius of the well screen/wellbore [L].

Skin radius

Enter the outer radius of the well skin [L], if applicable.

Filter pack porosity

Enter the effective porosity of the filter or gravel packenvelope [dimensionless].

Apply correction for partially submerged screen

Check this option to correct the casing radius for the porosity of thegravel pack (see "Bouwer-Rice (1976) Solution for a Slug Test inan Unconfined Aquifer" on page 95 and "Hvorslev (1951)Solution for a Slug Test in an Unconfined Aquifer" on page 96).

Observations Tab (Edit>Slug Test Well)

Choose Slug Test Well… from the Edit menu and click the Observations tabto enter time-displacement data for the well. Options allow you to enter observationdata from the keyboard, import observations from a file or copy/paste data fromanother application.

To enter observation data from the keyboard

1. Enter values of time, displacement and weight in the spreadsheet.



TIPSAssign weights to indicate the relative weight of eachmeasurement during automatic curve matching. Assign a weightof zero for measurements you wish automatic curve matching toignore.

To delete observation data



To copy observation data to the clipboard




To paste observation data from the clipboard

1. Copy observation data to the clipboard using another Windowsapplication (e.g., a spreadsheet). Each observation should includetime and displacement values (weights are optional).

2. Click Paste to paste the observation data from the clipboard intothe spreadsheet.


1. Click Import to start the Observation Data Import Wizardfor importing observation data from a file.

Follow the steps in the wizard (see "TIPS



2. Observation Data Import Wizard" on page 19) to import delimitedtext files created by many different types of data loggers.Transformation and filter operations also allow you to modify andreduce the data during the import process.

To search for a specific time, displacement or weight


2. Enter the data vector (time, displacement or weight) that you wishto search and the specific value.


To transform observation data

1. Select the row(s) for the observation(s) that you want to transform.

2. Click Math to open a dialog box for the transformation operation.

3. Enter the data vector (time, displacement or weight) that you wishto transform.



To filter observation data

1. Click Filters to open a dialog box for the filtering operations.

2. Select filter operations for discarding or retaining observations.

TIPS


Use filters to reduce the number of observations. Retain timevalues having a uniform logarithmic spacing or displacementvalues exceeding a minimum threshold.

3. Click OK to filter the observations. Before filtering the data,AQTESOLV for Windows prompts to confirm your action.

Symbol Tab (Edit>Slug Test Well)

Choose Slug Test Well… from the Edit menu and click the Symbol tab tochange the attributes of symbols displayed on data plots.

Symbol


Size


Thickness

Enter a thickness for the symbol.

Color


Test TypeChoose Test Type... from the Edit menu to select the type of test (pumping test orslug test) contained in an AQTESOLV for Windows data set.

Setting the test type in a new data set

1. When you open a new AQTESOLV for Windows data set, the testtype is defined automatically when you enter pumping test or slugtest data.

2. If you enter data for a pumping well or observation well,AQTESOLV for Windows defines the test type as Pumping Test.

3. If you enter data for a slug test well, AQTESOLV for Windowsdefines the test type as Slug Test.

Changing the test type in a data set

1. The Edit menu only enables options for the type of test containedin a data set.

2. Choose Test Type... from the Edit menu to change the test type.

AQTESOLV for Windows User's Guide Plots •• 35

Plots

OverviewThe View menu provides options for viewing data, solutions and estimation results.Two general types of views, plots and reports, are available for viewing data andsolutions, and evaluating estimation results. Other options in the View menu allowyou to customize the appearance of your plot.

Select plot views from theView menu or the toolbar listbox

Graphical formats for viewing aquifer test (displacement) data and matchinganalytical solutions include displacement vs. time, composite and derivativevs. time plots. AQTESOLV for Windows also provides discharge vs. timeplots to view discharge rates from variable rate pumping tests.

Use diagnostic plots toidentify appropriate aquifertest solutions

Radial flow, linear flow, bilinear flow and spherical flow plots help you tochoose appropriate models for your data set. Use these diagnostic plots to identifybehavior produced by wellbore storage, fracture flow and double-porosityphenomena.

Perform automatic estimationto view residual plots

Graphical formats for examining residuals (errors) from the matching of analyticalsolutions to aquifer test data include residual vs. time, residual vs. simulateddisplacement and normal probability plots.

Choosing a PlotChoose a plot view (Displacement-Time, Composite, etc.) from optionscontained in the View menu or from the list box on the toolbar.

Displacement vs. Time PlotChoose the Displacement-Time option from the View menu to plot values ofdisplacement as a function of time in the active window.

• The Displacement-Time plot allows you to analyze displacementdata from one or more observation wells.

36 •• Plots AQTESOLV for Windows User's Guide

• Displacement-Time plots show one type curve for each observationwell.

TIPSChoose Visual from the Match menu to match a solution to the data.

Composite PlotSelect Composite from the View menu to plot values of displacement as afunction of time divided by the square of radial distance (t/r2).

• The Composite plot allows you to analyze displacement data fromone or more observation wells.

• For pumping test solutions containing only two parameters,Composite plots display a single type curve regardless of the numberof observation wells shown on the plot. For solutions involving threeor more parameters, Composite plots show one type curve for eachobservation well.

• Composite plots are only active for pumping tests.

TIPSChoose Visual from the Match menu to match a solution to the data.

Residual vs. Time PlotPerform automatic matchingto view a residual vs. timeplot

Plot residual values as a function of time by choosing Residual-Time from theView menu.

• Ideally, the residual values should not exhibit correlation with time.

• When Residual-Time data are plotted linear axes, AQTESOLV forWindows fits a straight line to the data to indicate the degree to whichthe residuals are biased with respect to time.

Residual vs. Simulated PlotPerform automatic matchingto view a residual vs.simulated plot

Plot residual values as a function of simulated displacement by choosing Residual-Simulated from the View menu.

• Ideally, the residual values should not exhibit correlation with thevalues of simulated displacement.

• When Residual-Simulated data are plotted on linear axes,AQTESOLV for Windows fits a straight line to the data to indicate thedegree to which the residuals are biased with respect to simulateddisplacement.

Normal Probability PlotPerform automatic matchingto view a normal probabilityplot

Choose Normal Probability from the View menu to plot residual values onnormal probability axes.


• A Normal Probability plot displays the standard normal deviates ofthe ranked residuals (residuals sorted from smallest to largest) as afunction of the residual values.

• If the residuals are normally distributed, they will fall on a straightline when plotted on normal probability axes. AQTESOLV forWindows fits a straight line to residuals shown on the NormalProbability plot to measure the degree to which the residuals fit thenormality assumption.

• Deviations from a normal distribution may indicate inadequacy in thefit of the aquifer model to the data.

• After sorting the residual values for all observation wells, AQTESOLVfor Windows plots the standard normal deviates using the plot symbolfor the first observation well.

Discharge vs. Time PlotTo view pumping well discharge rates from a variable-rate pumping test, chooseDischarge-Time from the View menu.

• The Discharge-Time view option allows you to view constant orvariable pumping rates for one or more pumping wells.

• Discharge-Time plots are only active for pumping tests.

Derivative vs. Time PlotChoose Derivative-Time from the View menu to display the derivative ofdisplacement data as a function of logarithmic time. If you have chosen a solution,AQTESOLV for Windows also plots the derivative of the solution.

• The Derivative-Time view option allows you to view the derivativeof displacement measurements from one or more observation wells.

• Derivative-Time plots provide a useful diagnostic tool for detectingdeviations in the rate of displacement change. For example,interpretation of a Derivative-Time plot can help in theidentification of wellbore storage, aquifer boundaries, leakage anddelayed gravity response.

• AQTESOLV for Windows computes derivatives for displacementusing either nearest neighbor or smoothing techniques. ChooseOptions... from the View menu to select the method used tocalculate derivatives from displacement data.

• AQTESOLV for Windows computes the derivative of displacementwith respect to logarithmic time.

Radial Flow PlotChoose Radial Flow from the View menu to plot displacement as a function oftime.

• Radial Flow plots are useful diagnostic tools for identifying radial(infinite-acting aquifer) flow behavior or wellbore storage.


• On semi-logarithmic axes, late-time data exhibiting a straightline on a Radial Flow plot are indicative of radial flowconditions in an infinite-acting aquifer.

• On double logarithmic axes, early-time data exhibiting a unitslope on a Radial Flow plot are indicative of wellbore storage.

TIPSChoose Visual from the Match menu to match a line with unit slopeto data plotted on a Radial Flow plot with log-log axes. To position aline with a fixed unit slope, click a point on the plot where you want todraw the line.

• View one or more observation wells on Radial Flow plots.

Linear Flow PlotChoose Linear Flow from the View menu to plot displacement as a function of thesquare root of time.

• Linear Flow plots are useful diagnostic tools for identifying fractureflow behavior.

• On double logarithmic axes, early-time data exhibiting a unitslope on a Linear Flow plot are indicative of linear flowconditions to a single fracture with infinite conductivity oruniform flux along the fracture.

TIPSChoose Visual from the Match menu to match a line with unit slopeto data plotted on a Linear Flow plot with log-log axes. To position aline with a fixed unit slope, click a point on the plot where you want todraw the line.

• View one or more observation wells on Linear Flow plots.

Bilinear Flow PlotChoose Bilinear Flow from the View menu to plot displacement as a function ofthe fourth root of time.

• Bilinear Flow plots are useful diagnostic tools for identifyingfracture flow behavior.

• On double logarithmic axes, early-time data exhibiting a unitslope on a Bilinear Flow plot are indicative of bilinear flowconditions to a single fracture with finite conductivity.

TIPSChoose Visual from the Match menu to match a line with unit slopeto data plotted on a Bilinear Flow plot with log-log axes. To position aline with a fixed unit slope, click a point on the plot where you want todraw the line.

• View one or more observation wells on Bilinear Flow plots.


Spherical Flow PlotChoose Spherical Flow from the View menu to plot displacement as a function ofthe inverse square root of time.

• Spherical Flow plots are useful diagnostic tools for identifyingspherical flow behavior.

• On double logarithmic axes, early-time data exhibiting a unitslope on a Spherical Flow plot are indicative of spherical flowconditions.

TIPSChoose Visual from the Match menu to match a line with unit slopeto data plotted on a Spherical Flow plot with log-log axes. To positiona line with a fixed unit slope, click a point on the plot where you wantto draw the line.

• View one or more observation wells on Spherical Flow plots.

Changing Plot AxesChoose convenient options from the View menu to change the display axes onplots. Options include linear axes, semi-log axes and logarithmic axes.

Linear AxesChoose Linear Axes from the View menu to display a plot with linear x and yaxes.

Semi-Log AxesChoose Semi-Log Axes from the View menu to display a plot with logarithmic xand linear y axes.

Log AxesChoose Log Axes from the View menu to display a plot with logarithmic x and yaxes.

Choosing Plot OptionsChoose Options... from the View menu to select optional plot items and enterparameters controlling the display of type curve families, derivatives and validtimes.

Plots Tab (View>Options)Choose Options… from the View menu and click the Plots tab to select optionalitems to display on plots.

What to display


1. Check options to display on plots (Data, Legend, Type Curve,Curve Family, Theis Curve and Valid Time).

2. The option to display a Type Curve applies to displacement vs.time and composite plots.

3. The option to display a Curve Family only applies to selectedsolutions having three or more parameters and displacement vs.time or composite plots. Click the Family tab to set more optionsfor displaying type curve families.

4. The option to display bounding Theis Curves applies to selectedsolutions and displacement vs. time and composite plots.

For example, this option displays two bounding Theis curves forthe Neuman (1974) solution for unconfined aquifers. The firstcurve uses the values of T and S and the second curve uses T andSy.

5. The option to display the Valid Time applies to the Cooper-Jacob(1946) solution for confined or unconfined aquifers. Selectingthis option shows the time after which the straight-lineapproximation solution becomes valid on displacement vs. timeand composite plots. Click the Valid Time tab to set the criticalvalue of u used to compute the valid time.

Family Tab (View>Options)Choose Options… from the View menu and click the Family tab to select optionsfor displaying type curve families.

Display options

1. For a type curve family consisting of two curves, select the optionto Show Two Curves Using Multipliers. The Upper curve,displayed above the active type curve, has a multiplier less than 1;the Lower curve, displayed below the active type curve, has amultiplier greater than 1.

2. For a complete set of type curves, choose the option to ShowPreset Family of Curves.

3. Select Show Custom Family of Curves to display type curvesfrom the values shown in the list box. Use the New and Deletebuttons to add or remove curve values. Click the Clear button toremove all curves from the list. The Reset button restores curvevalues.

4. Choose the Show Family option in the Plots tab to enable thedisplay of type curve families.

Derivative Tab (View>Options)Choose Options… from the View menu and click the Derivative tab to selectoptions for derivative plots.

Calculation method


1. Choose a method for calculating derivatives from time-displacement data (nearest neighbor or smoothing).

2. The nearest neighbor option provides the least amount ofsmoothing for "noisy" data and works well for displacement datathat show ideal response.

3. The smoothing option allows you to choose a "smoothingfactor" for the calculation of derivatives from "noisy" data. Enterthe smallest smoothing factor to discern the derivative patternfrom the data.

Valid Time Tab (View>Options)Choose Options… from the View menu and click the Valid Time tab to selectoptions for displaying the valid time for the Cooper-Jacob (1946) and Theis (1935)residual drawdown solutions.

Validity criterion for straight-line methods

1. Set the Critical Value of u used to compute the valid timedisplayed for the Cooper-Jacob (1946) solution when you enablethe Show Valid Time option in the Plots tab. A conservativecritical value of u is 0.01.

2. Enter the Estimated Value of S (storativity) to compute thevalid time displayed with the Theis (1935) residual drawdownmethod for recovery tests.

Step Test Tab (View>Options)Choose Options… from the View menu and click the Step Test tab to selectoptions for the Theis (1935) step drawdown solution.

Step test prediction time

1. Set the Step test prediction time used in the well losspredicion equation.

2. For more information on the well loss prediction equation, see"Theis (1935) Solution for a Step Drawdown Test in a ConfinedAquifer" on page 65.

Formatting PlotsChoose Options… from the View menu to select options for formatting a plot'sgraph and axes, legend and colors.

Graph Tab (View>Format)Choose Format… from the View menu and click the Graph tab to edit parameterscontrolling the appearance of plots.

Axis and tickmark thickness

Enter Thickness values for lines drawn for plot axes and tickmarks.


Font

Click the Font... button to change the font used to display axis labels.

Color

Click the Color... button to change the color used for drawing the axislabels.

Origin

Check the Upper Left Origin box to place the origin of the plot axesin the upper left corner of the plot.

Graph Paper

Check the Show Graph Paper box to display horizontal and verticallines at the major tickmarks of the graph.

Magnification

Enter a value between 0.5 and 1.5 for the Magnification Factor toadjust the length of the plot axes.

X and Y Axis Tabs (View>Format)Choose Format… from the View menu and click the X Axis or Y Axis tab to editparameters plot axes.

Options

1. Edit parameters controlling axis ranges, tickmarks and labels.Choose minimum and maximum values, major and minortickmarks, and tickmark label spacing for each axis.

2. Select the axis Label boxes to choose x- and y-axis labels.Choose one of the predefined axis labels or enter a new label.

3. Select the Units boxes to choose a format for appending units tothe x- and y-axis labels.

Legend Tab (View>Format)Choose Format… from the View menu and click the Legend tab to select optionsfor plot legends.

Text attributes

1. Select the text to edit (Standard, Title, Proj. Info).

2. Click the Font... button to change the font used to display theselected text.

3. Click the Color... button to change the color used for the selectedtext.

Printer options

1. Choose a Style from the list to format the appearance of printedoutput.


2. Click Browse… to select a Windows bitmap (.bmp) filecontaining a company logo (or other graphic) that you would liketo display on printed output (not all Styles include a logo).

3. Check the items that you would like display in the printed legend(e.g., title, project info, aquifer data, well data, etc.).

Solution Tab (View>Format)Choose Format… from the View menu and click the Solution tab to edit theproperties of lines/curves plotted for an aquifer test solution.

Style

Choose a Style for the line/curve plotted for a solution.

Thickness

Enter the Thickness of the line/curve plotted for a solution.

Color

Click the Color… button to change the color of the line/curve plottedfor a solution.

Family Tab (View>Format)Choose Format… from the View menu and click the Family tab to edit theproperties of the optional curves plotted for a type curve family.

Style

Choose a Style for the optional type curve family.

Thickness

Enter the Thickness of the optional type curve family.

Color

Click the Color… button to change the color of the optional typecurve family.

Font

Click the Font… button to change the font used for labeling membersof the optional type curve family.

Theis Curve Tab (View>Format)Choose Format… from the View menu and click the Theis Curve tab to edit theproperties of optional Theis curve superimposed on pumping test solutions.

Style

Choose a Style for the optional Theis curve.

Thickness

Enter the Thickness of the optional Theis curve.


Color

Click the Color… button to change the color of the optional Theiscurve.

Fitted Tab (View>Format)Choose Format… from the View menu and click the Fitted tab to edit theproperties of the optional fitted line plotted on residual plots.

Style

Choose a Style for the optional fitted line.

Thickness

Enter the Thickness of the optional fitted line.

Color

Click the Color… button to change the color of the optional fittedline.

ZoomChoose Zoom... from the View menu to change the size of the plot within theactive window.

1. Enter a Zoom Factor ranging from 0.5 to 5.

2. Use this option to scale the size of a plot within the active window. Toscale the length of axes for all plots attached to the active data set, see"Plots Tab (View>Options)" on page 39.

Contouring ResultsClick on the toolbar togrid and contour data

Choose Contour… from the View menu to prepare a grid file for contouring andoptionally create a contour plot with Surfer for Windows (version 6 or higher).

TIPS

1. Enter values greater than zero for casing radius and wellbore radiusfor each pumping well (see "Construction Tab (Edit>Pumping Well)"on page 26).

Step 1. Grid Output File (Grid Wizard)1. Enter a path and filename for a Grid File that will contain the

gridded data for a contour plot. Click Browse... to search for a file.

2. Choose the Grid Orientation for a contour plot in plan or cross-sectional view.



Step 2. Specify Grid Dimensions (Grid Wizard)1. Enter Grid Dimensions using X-Y coordinates for a plan view or X-

Z/Y-Z coordinates for cross-sectional views. Enter Minimum andMaximum values to define the extent of the grid. Enter the No. ofLines to specify the number of grid lines in each coordinate direction.

2. Enter Constants to define the depth interval for a contour plot inplan view or the constant coordinate in cross-sectional view. Enter theTime (i.e., the elapsed time since the start of pumping) for thecalculations.


Step 3. Display Contour Plot (Grid Wizard)1. Check Display grid file with Surfer to create and display a contour

plot with Surfer for Windows (version 6 or higher). If you do not havethe Surfer application or if you only wish to create a grid file, simplyclick Finish.

2. Choose a plot option (Contour, Surface or Surface w/ fillcontours).

3. If you have created a file containing contour levels for use with Surfer,you can select a Contour Levels file. Click Browse… to search fora Levels file.

4. If you have created a file containing posting data for use with Surfer,you can select a Posting Data file. Click Browse… to search for aposting file. To append pumping well and observation well coordinatedata to the file, check Add well data to posting file.

5. Click Finish to create the grid file and optionally display a contourplot.

AQTESOLV for Windows User's Guide Reports •• 47

Reports

OverviewSelect Report Views from theView menu or the toolbar listbox

The View menu provides you with a Diagnostic report and a Complete reportthat display text summaries of your data set and the results of your aquifer testanalysis. An Error Log report identifies any errors that your active data set maycontain.

Choosing a Report

Diagnostic ReportPerform automatic estimationto view diagnostic report

Choose Diagnostics from the View menu to display a report containingestimation statistics for parameters (hydraulic properties) and residuals. Thediagnostics report contains standard errors for estimated parameters, correlationsbetween estimated parameters and residual summary statistics.

Complete ReportChoose Report from the View menu to display a complete report summarizing thecontents of the AQTESOLV for Windows data set and estimation results in textformat.

Error LogChoose Error Log from the View menu to display a report identifying any errorscontained in the active data set. Select this report option if you are entering datainto a new data set or if the message Check Errors appears on the status bar.

Formatting ReportsChoose Format... from the View menu to open a dialog box for formatting reports.

Header Text

Enter text for the header of a report.

48 •• Reports AQTESOLV for Windows User's Guide

Footer Text

Enter text for the footer of a report.

Printer Options

Choose options for including blocks of text in a report.

Font

Click the Font... button to choose a font for the report.

Color

Click the Color... button to choose a color for the report.

AQTESOLV for Windows User's Guide Choosing a Solution •• 49

Choosing a Solution

OverviewAQTESOLV for Windows provides analytical solutions for confined, unconfined,leaky and fractured aquifers. The solutions allow you to determine the hydraulicproperties of aquifers through automatic or visual curve matching.

Choose Solution… from the Match menu to select a solution for analyzingpumping tests or slug tests.

Confined Aquifer SolutionsChoose Solution… from the Match menu to choose a solution for analyzing apumping test or slug test in a confined aquifer.

Solutions for Pumping Tests in Confined Aquifers

1. Theis (1935) type curve solution

2. Cooper-Jacob (1946) straight line solution

3. Papadopulos-Cooper (1967) type curve solution for a large-diameterpumping well

4. Theis (1935) straight line solution for residual drawdown duringrecovery

5. Theis (1935) type curve solution for drawdown in a pumping wellduring a step drawdown test including linear and nonlinear well losses

6. Hantush (1962) type curve solution for a wedge-shaped aquifer

7. Murdoch (1994) type curve solution for flow to a trench

Solutions for Slug Tests in Confined Aquifers

1. Cooper-Bredehoeft-Papadopulos (1967) type curve solution

2. Bouwer-Rice (1976) straight line solution

3. Hvorslev (1951) straight line solution

4. Hyder et al. (1995) type curve solution (KGS Model)

50 •• Choosing a Solution AQTESOLV for Windows User's Guide

Theis (1935) Solution for a Pumping Test in aConfined AquiferTheis (1935) derived an equation which predicts water-level displacement in aconfined aquifer in response to pumping:

sQ

T

e

ydy

y

u

=−∞

∫4π

ur S

Tt=

2

4

Hydrogeologists commonly refer to the exponential integral in the drawdownequation as the Theis well function, abbreviated as w(u). Therefore, we can writethe Theis drawdown equation in compact notation as follows:

s

QT

w u=4π

( )

Refer to the "List of Symbols" on page 141 for a description of the parameters andvariables contained in the equations for this solution.

Hantush (1961a,b) derived equations for the effects of partial penetration in aconfined aquifer. For a piezometer, the partial penetration correction is as follows:

sQ

Tw u

b

l d n

n l

b

n d

b

n z

b

w u K Kn rb

n

z r

= +−

− ⋅ ⋅

=

∞

∑4

2 1

1π ππ π π

π

( )( )

[sin( ) sin( )] cos( )

( , / )

For an observation, the following partial penetration correction applies:

sQ

Tw u

b

l d l d n

n l

b

n d

bn l

b

n d

bw u K K

n r

b

n

z r

= +− ′ − ′

− ⋅

′−

′⋅

=

∞

∑4

2 12

2 21π π

π π

π π π

( )( )( )

[sin( ) sin( )]

[sin( ) sin( )] ( , / )

where w(u) is the Theis well function confined aquifers, w(u,βbeta) is the Hantushwell function for leaky aquifers (see "Hantush-Jacob (1955) Solution for a PumpingTest in a Leaky Aquifer" on page 103) and

βπ

= K Kn rbz r/

With these equations, it is possible to estimate values of T and S from time-displacement data measured during a constant-rate pumping test. For partiallypenetrating wells, AQTESOLV for Windows also estimates the values ofKz/KrKz/Kr and b.

AQTESOLV for Windows uses a general procedure involving the principle ofsuperposition in the form of the Duhamel integral to analyze variable-rate pumpingtests (Streltsova 1988). A particularly useful application of this method ofintegration is piecewise approximation of the discharge rate by a sequence of stepfunctions. In this form, the discharge rate is considered constant for a sequence of


discrete time intervals. The equations for the Theis solution with variable pumpingrate are as follows:

sT

Q Q w u Qi ii

n

= − =−=

∑1

401 0

1π( ) ( ) ,

ur S

T t tt t

in=

−> =

−−

2

11 04

0( )

, and t

where n is the number of pumping intervals.

aquiclude

aquiclude

aquiferT,S,Kz/Kr

Q

b

s1 s2potentiometric surface

after pumping

potentiometric surfacebefore pumping

r1

r2

Solution Assumptions

• aquifer has infinite areal extent

• aquifer is homogeneous, isotropic and of uniform thickness

• pumping well is fully or partially penetrating

• flow to pumping well is horizontal when pumping well is fullypenetrating

• aquifer is confined

• flow is unsteady

• water is released instantaneously from storage with decline ofhydraulic head

• diameter of pumping well is very small so that storage in the well canbe neglected

Data Requirements

• pumping and observation well locations

• pumping rate(s)

• observation well measurements (time and displacement)

• partial penetration depths (optional)


• saturated thickness (for partially penetrating wells)

• hydraulic conductivity anisotropy ratio (for partially penetrating wells)

Solution Options

• variable pumping rates

• multiple pumping wells

• multiple observation wells

• partially penetrating wells

Reference

Hantush, M.S., 1961a. Drawdown around a partially penetrating well,Jour. of the Hyd. Div., Proc. of the Am. Soc. of Civil Eng., vol. 87, no.HY4, pp. 83-98.

Hantush, M.S., 1961b. Aquifer tests on partially penetrating wells, Jour. ofthe Hyd. Div., Proc. of the Am. Soc. of Civil Eng., vol. 87, no. HY5,pp. 171-194.

Streltsova, T.D., 1988. Well Testing in Heterogeneous Formations, JohnWiley & Sons, New York, 413p.

Theis, C.V., 1935. The relation between the lowering of the piezometricsurface and the rate and duration of discharge of a well usinggroundwater storage, Am. Geophys. Union Trans., vol. 16, pp. 519-524.

Tutorial

In this tutorial, you will use the Theis type curve solution to create and analyze avariable-rate pumping test. This tutorial shows you how to use visual curvematching with active type curves and automatic curve matching to match the Theistype curve to drawdown and recovery data.

Open a New Data Set

Open a new data set by choosing New from the File menu. In the New Data Setdialog box, choose Tutorial in the list box and click OK to initialize the new dataset with default values. AQTESOLV for Windows opens a new window with anError Log view that reports any errors identified in the data set.

Enter Data for Pumping Test

Choose Units... from the Edit menu to select units of measurement for the data set.

1. Select m (meters) for Length, day (days) for Time, consistent forPumping Rate and m/day (meters/day) for Hyd. Conductivity.

2. Consistent units for pumping rate are cubic meters-per-day.

3. Click OK.

Choose Annotations... from the Edit menu to edit the data set title.

1. In the Title tab, enter Variable Rate Pumping Test with Recoveryfor the Title.

2. Click OK.


Choose Aquifer Data... from the Edit menu to edit aquifer data.


2. Click OK.

Choose Pumping Well>Edit... from the Edit menu edit pumping well data.

1. In the Rates tab, enter the following four pumping periods in thespreadsheet:

Time Rate0 5000.020833 7000.055556 6000.10417 0

2. Click OK.

Choose Obs. Well>Edit... from the Edit menu to edit data for the observationwell.


2. In the Observations tab, enter the following 19 measurements in thespreadsheet (set all weights equal to 1.0):

Time Displacement0.0034722 1.380.0069444 1.650.010417 1.810.013889 1.930.017361 2.020.020833 2.090.024306 2.680.027778 2.850.03125 2.960.034722 3.050.038194 3.120.041667 3.180.048611 3.290.055556 3.380.0625 3.130.069444 3.150.076389 3.170.090278 3.230.10417 3.290.10486 2.380.10764 1.650.11111 1.340.12153 0.95

3. Click OK.



Save Data Set

Choose Save As... from the File menu to save the data you have entered into thecurrent data set.

1. Enter THEIS1.AQT for the file name.


Change View in Window

Choose Displacement-Time from the View menu to display a plot ofdisplacement vs. time in the active window. The window displays a plot of theobservation well data on semi-logarithmic axes.

Choose Theis Solution

Choose Solution... from the Match menu to choose a solution for analyzing apumping test in a confined aquifer.

1. Choose the Confined Theis (1935) solution.

2. Click OK.

After you have selected the Theis solution for a pumping test in a confined aquifer,AQTESOLV for Windows updates the window by plotting the data on doublelogarithmic axes, superimposing the Theis type curve on the plot, and adding thecurrent values of transmissivity (T), storage coefficient (S), hydraulic conductivityanisotropy ratio (Kz/KrKz/Kr) and saturated thickness (b) to the legend. The Theissolution only estimates T and S for fully penetrating wells..

For solutions such as the Theis (1935) solution that support AQTESOLV forWindows' variable pumping rate feature, you can plot type curves for data sets thatinclude both drawdown and recovery data. AQTESOLV for Windows uses theprinciple of superposition to compute displacements for the pumping and recoveryphases of the test.

Perform Visual Matching with Theis

Choose Visual from the Match menu to perform visual curve matching with theTheis type curve.

1. To begin interactively moving the type curve, move the mouse cursorover the plot, click the left mouse button and hold it down.



Use Active Type Curves with Theis

Choose Toolbox… from the Match menu to invoke active type curves.

1. In the Options tab, check the option for Active type curves.

2. Click OK.


Choose Visual from the Match menu and repeat the steps for visual curvematching using the active type curve feature. Compared with static type curves,active type curves allow you to match variable-rate pumping tests effectivelywith visual curve matching.

Perform Automatic Matching with Theis

Choose Automatic... from the Match menu to perform automatic matching withthe Theis type curve solution.

1. Click Estimate to begin automatic estimation.



The plot shown in the active window displays the values of transmissivity(T=100.1) and storage coefficient (S=0.0009994) determined by automaticestimation.

Save Data Set

Choose Save from the File menu to save your work in the THEIS1.AQT data set.

Cooper-Jacob (1946) Solution for a Pumping Test ina Confined AquiferFor large values of time, Cooper and Jacob (1946) proposed the following equationfor displacement in a confined aquifer in response to pumping:

sT

Tt

r S=

2 30Q

4

2 252

.log(

.)

π

Refer to the "List of Symbols" on page 141 for a description of the parameters andvariables contained in this equation.

The Cooper-Jacob solution derives from the truncation of an infinite seriesexpression for Theis well function (see "Theis (1935) Solution for a Pumping Testin a Confined Aquifer" on page 50). The following expression computes the valueof the Theis well function, abbreviated as w(u):

w u u uu u u

( ) . ln( )! ! !

= − − + −⋅

+⋅

−⋅

+0 57722 2 3 3 4 4

2 3 4

K

For small values of the variable u (e.g., u ≤ 0.01), the Cooper-Jacob solutionapproximates the Theis well function using only the first two terms of theexpression for w(u):

w u u( ) . ln( )≅ − −0 5772

Therefore, the Cooper-Jacob equation for displacement becomes as follows:


sQ

T

r S= − −

40 5772

4Tt

2

π. ln( )

where r is distance between the pumping and observation wells, S is storagecoefficient, T is transmissivity and t is time. After rearranging and rewriting asdecimal logarithms, the drawdown equation reduces to the following relationship:

sT

Tt

r S=

230Q

4

2 252

.log(

.)

π

By plotting s as a function of log(t) on semi-logarithmic axes, one can determinevalues of T and S by drawing a straight line through the data. When using thismethod, it is important to match the line to data points with values of time largeenough to make the variable u less than a critical value (e.g., u ≤ 0.01).

aquiclude

aquiclude

aquiferT,S

Q

b

s1 s2

potentiometric surfaceafter pumping


r1

r2

Assumptions



• aquifer potentiometric surface is initially horizontal

• pumping well is fully penetrating

• flow to pumping well is horizontal





• values of u are small (i.e., r is small and t is large)


Data Requirements


• pumping rate(s)


Solution Options



Reference

Cooper, H.H. and C.E. Jacob, 1946. A generalized graphical method forevaluating formation constants and summarizing well field history,Am. Geophys. Union Trans., vol. 27, pp. 526-534.

Tutorial

Open Data Set

Choose Open... from the File menu to open a data set stored on disk. You willopen the data set created and saved in the tutorial for the Theis (1935) solution.

1. Enter THEIS1.AQT for the name of the data set.

2. Click OK to open the data set.


If necessary, choose Displacement-Time from the View menu to display a plot ofdisplacement vs. time in the active window.

Choose Cooper-Jacob Solution


1. Choose the Confined Cooper-Jacob (1946) solution.

2. Click OK.

After you have selected the Cooper-Jacob solution, AQTESOLV for Windowsupdates the window by plotting the data on semi-logarithmic axes, superimposingthe Cooper-Jacob straight line on the plot, and adding the current values oftransmissivity (T) and storage coefficient (S) to the legend.

The Cooper-Jacob (1946) solution supports variable pumping rates, but only duringpumping phases of a test. AQTESOLV for Windows will ignore the recovery datacontained in this data set.

Check Validity of Cooper-Jacob

Choose Options… from the View menu.

1. In the Plots tab, check the Valid Time option to display the timeafter which the Cooper-Jacob straight-line approximation of the Theis(1935) solution is valid.

2. Click OK.

Perform Visual Matching with Cooper-Jacob


Choose Visual from the Match menu to perform visual matching using theCooper-Jacob straight-line solution.

1. To begin interactively matching the Cooper-Jacob solution to the data,click the left mouse button and hold it down to anchor a point alongthe new straight line you wish to match to the data.


3. When you have finished matching the Cooper-Jacob solution to theobservation well data, release the left mouse button. AQTESOLV forWindows computes new estimates of transmissivity (T) and storagecoefficient (S) and updates the straight line displayed on the plot.

Perform Automatic Matching with Cooper-Jacob

Choose Automatic... from the Match menu to perform automatic matching usingthe Cooper-Jacob solution.




The plot shown in the active window displays the values of transmissivity(T=100.6) and storage coefficient (S=0.0009745) determined by automaticestimation.

Save Data Set

Choose Save As... from the File menu to save your work.

1. Enter JACOB1.AQT for the file name.


Papadopulos-Cooper (1967) Solution for a PumpingTest in a Confined AquiferPapadopulos and Cooper (1967) derived a solution for a large-diameter pumpingwell in a confined aquifer as follows:

sQ

TF u

r

rw

=4π

α( , , )

Fe J A Y B

A Bd

u

=− −

−

−∞

∫8 1

2 2 40 0

2 2 20

απ

βρ β βρ ββ β β

ββ ρ( )[ ( ) ( ) ( ) ( )]

[ ( )] [ ( )]

/

A Y Y( ) ( ) ( )β β β α β= −0 12

B J J( ) ( ) ( )β β β α β= −0 12


ur S

=2

4Tt

α =r S

rw

c

2

2

ρ =r

rw


AQTESOLV for Windows allows you to analyze both constant- and variable-ratepumping tests using the Papadopulos-Cooper solution. For tests with a variabledischarge rate, the program uses the principle of superposition to computedrawdown in the aquifer. For more information concerning the application of theprinciple of superposition in variable-rate pumping tests, refer to the "Theis (1935)Solution for a Pumping Test in a Confined Aquifer" on page 50.

By matching type curves of the Papadopulos-Cooper well function to data plotted ondouble logarithmic axes, it is possible to determine values of T and S for a confinedaquifer and the value of the pumping well radius (rw). If a data set contains morethan one pumping well, AQTESOLV for Windows estimates the well radius for thefirst pumping well contained in the data set.

aquiclude

aquiclude

aquiferT,S

Q

b


after pumping


r1

r2

2rc

2rw

Note that the well radius (rw) may be larger or smaller than the casing radius (rc).

Assumptions










Data Requirements


• pumping rate(s)


• casing radius and wellbore radius for pumping well(s)

Solution Options

• large-diameter pumping wells




Reference

Papadopulos, I.S. and H.H. Cooper, 1967. Drawdown in a well of largediameter, Water Resources Research, vol. 3, pp. 241-244.

Tutorial

In this tutorial, you will use the Papadopulos-Cooper type curve solution to createand analyze a constant-rate pumping test with a large-diameter pumping well in aconfined aquifer. This tutorial shows you how to use automatic curve matching tomatch the Papadopulos-Cooper type curve to drawdown data measured during thetest.

Open a New Data Set




1. Select ft (feet) for Length, min (minutes) for Time, cu. ft/min (cubicfeet-per-minute) for Pumping Rate and consistent units for Hyd.Conductivity.

2. Click OK.


1. In the Title tab, enter Large-Diameter Well Pumping Test for theTitle.

2. Click OK.




2. Click OK.

Choose Pumping Well>Edit... from the Edit menu edit pumping well data.


2. In the Rates tab, enter values of 0.0 and 0.000314159 for time andrate, respectively, where time is in minutes and rate is in cubic feet-per-minute.

3. Click OK.



2. In the Observations tab, click the Import button to importobservation well measurements from a delimited text file using theObservation Data Import Wizard. In Step 1 of the ImportWizard, enter PC1.DAT for the name of the import file. The filePC1.DAT contains time and displacement data arranged in twocolumns separated by a tab delimiter. Click Next.

3. In Step 2 of the Import Wizard, enter data describing the structure ofthe import file. The Import Wizard automatically determines thatthe import file contains 2 columns of data. Enter 1 for the ElapsedTime column and 2 for the Displacement column. Click Next.

4. In Step 3 of the Import Wizard, choose transformation and filteroptions for the data contained in the import file. Retain the defaultsettings, and click Finish.

5. After AQTESOLV for Windows has finished importing the data, amessage box displays the number of observations imported from thefile. Click OK.

6. Click OK.


Save Data Set


1. Enter PAPADOP1.AQT for the file name.



Choose Displacement-Time from the View menu to display a plot ofdisplacement vs. time in the active window. The window displays a plot of theobservation well data on semi-log axes.


Choose Papadopulos-Cooper Solution

Change the aquifer model and solution by choosing Solution... from the Matchmenu to choose a solution for analyzing a pumping test in a confined aquifer.

1. Choose the Confined Papadopulos-Cooper (1967) solution.

2. Click OK.

After you have selected the Papadopulos-Cooper solution for a large-diameter wellpumping test in a confined aquifer, AQTESOLV for Windows updates the windowby plotting the data on double logarithmic axes, superimposing a Papadopulos-Cooper type curve on the plot, and displaying values of transmissivity (T), storagecoefficient (S) and wellbore radius (Rw) in the legend.

Perform Automatic Matching with Papadopulos-Cooper

Choose Automatic... from the Match menu to perform automatic matching usingthe Papadopulos-Cooper type curve solution.




The plot shown in the active window displays the values of transmissivity(T=2.513E-05), storage coefficient (S=9.442E-05) and wellbore radius(Rw=0.9949) determined by automatic estimation.

Display Theis Type Curve

Choose Options… from the View menu and click the Plots tab. Check theTheis Curve(s) option to superimpose a Theis type curve on the plot using thecurrent values of T and S.

Save Data Set

Choose Save from the File menu to save your work in the PAPADOP1.AQT dataset.

Theis (1935) Solution for a Recovery Test in aConfined AquiferTheis (1935) proposed a straight-line solution for determining transmissivity andstorativity from residual displacement data collected during the recovery phase of apumping test:

′′ = ′′ − ′sQ

Tt t S

4π[ln( / ) ln( )]

where s" is residual displacement, Q is pumping rate, T is transmissivity, t is timesince pumping began, t" is time since pumping stopped and S' is the ratio ofstorativity during pumping to storativity during recovery.


By plotting s" as a function of log(t/t") on semi-logarithmic axes, one can determinevalues of T and S' by drawing a straight line through the data. Without theinfluence of boundary effects, the value of S' determined from the intercept of thestraight line with the log(t/t") axis should be close to unity. A value of S' > 1.0indicates the influence of a recharge boundary during the test. Conversely, a valueof S' < 1.0 suggests the presence of a barrier or no-flow boundary.

When using this method, it is important to match the line to data points with valuesof time large enough to make the variable u less than a critical value (see "Cooper-Jacob (1946) Solution for a Pumping Test in a Confined Aquifer" on page 55).

Assumptions











Data Requirements


• pumping rate(s)


Solution Options


Reference


Tutorial

In this tutorial, you will use the Theis Recovery solution to analyze the variable ratepumping test data set created and saved in the tutorial for the Theis solution. Thistutorial shows you how to use visual and automatic curve matching to fit a straightline to recovery data measured during a variable-rate pumping test.

Open Data Set


Choose Open... from the File menu to open a data set stored on disk. You willopen the data set created and saved in the tutorial for the Theis (1935) solution.

1. Enter THEIS1.AQT for the name of the data set.



If necessary, choose Displacement-Time from the View menu to display a plot ofdisplacement vs. time in the active window.

Choose Theis Recovery Solution


1. Choose the Confined Theis Residual Drawdown (1935) solution.

2. Click OK.

After you have selected the Theis Recovery solution for a pumping test in a confinedaquifer, AQTESOLV for Windows updates the window by plotting the data onsemi-logarithmic axes, superimposing the Theis Recovery straight line on the plot,and adding the current values of transmissivity (T) and ratio of storage coefficientduring pumping to storage coefficient during recovery (S') to the legend.

The Theis Recovery (1935) solution supports AQTESOLV for Windows' variablepumping rate feature, but only during the first recovery phase of a test.AQTESOLV for Windows will ignore any data following the first recovery phase ofa test.

Perform Visual Matching with Theis Recovery

Choose Visual from the Match menu to perform visual matching using the TheisRecovery straight line solution.

1. To begin interactively matching the Theis Recovery solution to thedata, click the left mouse button and hold it down to anchor a pointalong the new straight line you wish to match to the data.


3. When you have finished matching the Theis Recovery solution to theobservation well data, release the left mouse button. AQTESOLV forWindows computes new estimates of transmissivity (T) and storagecoefficient ratio (S') and updates the straight line displayed on the plot.

Perform Automatic Matching with Theis Recovery

Choose Automatic... from the Match menu to perform automatic matching usingthe Theis Recovery solution.





The plot shown in the active window displays the values of transmissivity(T=103.3) and storage coefficient (S'=0.9275) determined by automatic estimation.

Save Data Set


1. Enter THEISR1.AQT for the file name.

2. Click OK button to save the data set.

Theis (1935) Solution for a Step Drawdown Test in aConfined AquiferA step drawdown test is a single-well pumping test designed to investigate theperformance of a pumping well under variable discharge rate conditions. In a steptest, the discharge rate in the pumping well is increased from an initially lowconstant rate through a sequence of pumping intervals of progressively greaterconstant rates. In each step of the test, the drawdown in the pumping well isallowed to stabilize. Each step is typically of equal duration, lasting fromapproximately 30 minutes to 2 hours (Kruseman and de Ridder 1990).

Various researchers have investigated the performance of pumping wells todetermine well losses as a function of discharge rate. Jacob (1947) proposed thefollowing drawdown equation that accounts for linear and nonlinear head losses inthe pumping well:

s B r t Q CQw e= +( , ) 2

where B(re,t) is the linear head-loss coefficient and C is the nonlinear well-losscoefficient. The linear head-loss coefficient B(re,t) is a function of the effective orequivalent radius of the well re and time t. The equivalent well radius (re) is definedas the radial distance from the well at which the theoretical drawdown equals thedrawdown immediately outside the well screen. The linear head-loss coefficientconsists of two components:

B r t B r t Be w( , ) ( , )= +1 2

where B1(rw,t) is the linear aquifer-loss coefficient and B2 is the linear well-losscoefficient. The linear aquifer-loss coefficient B1(rw,t) is a function of the radius ofthe well (rw) and time (t). Ramey (1982) defines the linear well-loss coefficient B2

in terms of a wellbore skin factor (Sw) as follows:

S B Tw = ⋅2 2π

Rorabaugh (1953) modified Jacob's equation to account for variations in thenonlinear well-loss term:

s B r t Q CQw eP= +( , )

where P is the order of nonlinear well losses. According to Rorabaugh (1953), thevalue of P can assume values ranging from 1.5 to 3.5 depending on the value of Q,but many researchers accept the value of P=2 as proposed by Jacob (1947).


The efficiency of a pumping well, which expresses the relationship betweentheoretical and actual drawdown in the well, is computed as follows (Kruseman andde Ridder 1990):

Ew = ⋅theoretical drawdown

actual drawdown100%

EB Q

B B Q CQw p=+ +

⋅1

1 2

100%( )

The Theis (1935) solution ("Theis (1935) Solution for a Pumping Test in aConfined Aquifer" on page 50), modified to include linear and nonlinear welllosses, for a pumping well in a confined aquifer is expressed as follows:

( )sQ

Tw u S CQw w

P= + +4

2π

( )

ur S

Ttw=2

4

In this equation, the Theis well function w(u), the wellbore skin factor and the termCQP account for linear aquifer losses, linear well losses and nonlinear well losses,respectively. Refer to the "List of Symbols" on page 141 for a description of theparameters and variables contained in the equations for this solution.

AQTESOLV for Windows allows you to analyze both constant- and variable-ratepumping tests using the Theis solution. For tests with a variable discharge rate, theprogram uses the principle of superposition to compute drawdown in the aquifer.For more information concerning the application of the principle of superposition invariable-rate pumping tests, refer to the "Theis (1935) Solution for a Pumping Testin a Confined Aquifer" on page 50.

The Theis step-drawdown test solution predicts drawdown in a pumping well forany discharge rate Q and any time t. The solution can be written in the form of theJacob-Rorabaugh equation to predict drawdown in the pumping well at a specifiedvalue of time:

s B r t Q CQw e pP= +( , )

where tp is the specified prediction time. AQTESOLV for Windows allows you toenter the prediction time tp to calculate the coefficient B(re,tp) used in the predictionequation.


aquiclude

aquiclude

aquiferT,S

Q

b

sw potentiometric surfaceafter pumping











Data Requirements


• pumping rate(s)


Solution Options




References

Jacob, C.E., 1947. Drawdown test to determine effective radius of artesianwell, Trans. Amer. Soc. of Civil Engrs., vol. 112, paper 2321, pp.1047-1064.


Ramey, H.J., 1982. Well-loss function and the skin effect: A review. In:Narasimhan, T.N. (ed.) Recent trends in hydrogeology, Geol. Soc.Am., special paper 189, pp. 265-271.

Rorabaugh, M.J., 1953. Graphical and theoretical analysis of step-drawdown test of artesian well, Proc. Amer. Soc. Civil Engrs., vol. 79,separate no. 362, 23 pp.


Tutorial

Perform one of the following tutorials to learn how to use the Theis solution:

1. Guided Tour (see "Analyzing a Pumping Test" on page 7)

2. Theis (1935) solution for a pumping test in a confined aquifer (see"Tutorial" on page 52)

Hantush (1962) Solution for a Pumping Test in aWedge-Shaped Confined AquiferHantush (1962) derived an equation which predicts water-level displacement in awedge-shaped confined aquifer in response to pumping:

sQ

Te

e

ydyr a

y r a y

u

=− −∞

∫4

2 24

πθ/ cos

/

ur S

Tt=

2

4

b b e x x a= − −0

2 0( )/

Ordinarily, the slope on the base of the confined aquifer varies exponentially in thex-coordinate direction and is constant in the y-coordinate direction. The slopeorientation angle θtheta measures the orientation of the slope in relation to the x-coordinate axis and is measured counterclockwise from the positive x-coordinateaxis to the vector oriented in the updip direction of the slope. The parameter a is aconstant defining the variation in thickness of the wedge-shaped aquifer.

The solution assumes that the change in aquifer thickness as a function of distancemeets the following criterion:

dbdx

< 0 20.

and that the duration of pumping does not exceed the following limitation:

tr S

K

a a

bs< =

0

2

0020 2 10

where r ln

Hydrogeologists commonly refer to the exponential integral in the drawdownequation as the Hantush well function (see "Hantush-Jacob (1955) Solution for a


Pumping Test in a Leaky Aquifer" on page 103). Refer to the "List of Symbols" onpage 141 for a description of the parameters and variables contained in theequations for this solution.

AQTESOLV for Windows allows you to analyze both constant- and variable-ratepumping tests using the Hantush wedge-shaped aquifer solution. For tests with avariable discharge rate, the program uses the principle of superposition to computedrawdown in the aquifer. For more information concerning the application of theprinciple of superposition in variable-rate pumping tests, refer to the "Theis (1935)Solution for a Pumping Test in a Confined Aquifer" on page 50.

aquiclude

aquiclude

aquiferT,S,a

Q(x0,y0)

b

s1 s2 potentiometric surfaceafter pumping


r1

r2

b0



• aquifer is homogeneous and isotropic







• the thickness of the aquifer varies exponentially in the direction offlow

• the rate of change in aquifer thickness in the direction of flow does notexceed 0.20

• the influence of pumping has not extended beyond the section of theaquifer at which the tangents of the maximum angles of dip of theconfining beds are greater than 0.20


Data Requirements


• pumping rate(s)


Solution Options



Reference

Hantush, M.S., 1962. Flow of ground water in sands of nonuniformthickness; 3. Flow to wells, Jour. Geophys. Res., vol. 67, no. 4, pp.1527-1534.

Tutorial

Perform the tutorial for the Hantush-Jacob (1955) solution for pumping test in aleaky aquifer (see "Tutorial" on page 106) to learn how to use this solution.

Murdoch (1994) Solution for Flow to a TrenchMurdoch (1994) presented a method for analyzing transient flow to an interceptortrench based on the analytical solutions by Gringarten and Witherspoon (1972) andGringarten, Ramey and Raghavan (1974) for flow to a well in a confined infiniteradial system intersecting a single uniform-flux plane vertical fracture (see"Gringarten-Witherspoon (1972) Solution for a Pumping Test in a FracturedAquifer with a Plane Vertical Fracture" on page 131).

In this solution, the trench parallels the x axis of the coordinate system and has alength of L (=2xt). Refer to the "List of Symbols" on page 141 for a description ofthe parameters and variables contained in the equations.

aquiclude

aquiclude

aquiferKx,Ss,Ky/Kx

Q

b

s1



r1

xttrench


Assumptions


• aquifer has uniform thickness


• interceptor trench and observation wells are fully penetrating

• confined aquifer represented by anisotropic system with a singleinterceptor trench



Data Requirements

• interceptor trench and observation well locations

• pumping rate(s)


• saturated thickness of aquifer

• length of trench

Solution Options

• variable pumping rate



Reference

Murdoch, L.C., 1994. Transient analyses of an interceptor trench, WaterResources Research, vol. 30, no. 11, pp. 3023-3031.

Tutorial

Perform the tutorial for the Gringarten-Witherspoon (1972) solution for pumpingtest in a fractured aquifer with a single vertical fracture (see "Tutorial" on page 133)to learn how to use this solution.

Instead of entering fracture data for this solution, enter data for the trench asfollows:

1. Choose Aquifer Data… from the Edit menu. In the Trench tab,enter the length of the trench.

2. Choose Pumping Well>Edit… from the Edit menu. In theGeneral tab, enter well coordinates at the center of the trench. In theRates tab, enter the pumping rate(s) for the trench.


Cooper-Bredehoeft-Papadopulos (1967) Solutionfor a Slug Test in a Confined AquiferCooper et al. (1967) derived an analytical solution describing the water-levelresponse due to the instantaneous injection or withdrawal of water from a well in aconfined aquifer. The equation for the Laplace transform solution is as follows:

hr Ss K rq

Tq r qK r q K r qw

w w w

=+

0 0

0 12

( )

[ ( ) ( )]α

q pS T= ( / ) /1 2

α =r S

rw

c

2

2


By matching type curves of the Cooper-Bredehoeft-Papadopulos slug test solution todata plotted on semi-logarithmic axes, it is possible to determine values of T and Sfor a confined aquifer and the value of the well radius (rw).

aquiclude

aquiclude

aquiferT,S

Q

b

H0 potentiometric surfaceafter slug withdrawal

potentiometric surfacebefore slug withdrawal

2rc

2rw

Note that the well radius (rw) may be larger or smaller than the casing radius (rc).

Assumptions




• a volume of water, V, is injected into or discharged from the wellinstantaneously

• test well is fully penetrating

• flow to test well is horizontal





Data Requirements

• test well measurements (time and displacement)

• initial displacement

• casing radius and wellbore radius for test well


• screen length

• total depth of well penetration

• porosity of gravel pack (optional)

• hydraulic conductivity anisotropy ratio (optional)

Reference

Cooper, H.H., J.D. Bredehoeft and S.S. Papadopulos, 1967. Response of afinite-diameter well to an instantaneous charge of water, WaterResources Research, vol. 3, no. 1, pp. 263-269.

Tutorial

The Guided Tour (see "Analyzing a Slug Test" on page 11) contains a tutorial forthe Cooper-Bredehoeft-Papadopulos slug test solution.

Bouwer-Rice (1976) Solution for a Slug Test in aConfined AquiferFor information concerning this solution, refer to "Bouwer-Rice (1976) Solution fora Slug Test in an Unconfined Aquifer" on page 95.

Hvorslev (1951) Solution for a Slug Test in aConfined AquiferFor information concerning this solution, refer to "Hvorslev (1951) Solution for aSlug Test in an Unconfined Aquifer" on page 96.

Hyder et al. (1994) Solution for a Slug Test in aConfined Aquifer (KGS Model)Hyder et al. (1994) derived an analytical solution, also known as the KGS Model,describing the water-level response due to the instantaneous injection or withdrawalof water from a partially penetrating well in a confined aquifer. The equation forthe Laplace transform solution is as follows:


]p)2/(1[

)2/(h

Ωγ+Ωγ

=

2c

2s2w

rLSr2

=α

1r2r K/K=γ

ηω=Ω ∫+ζ

ζ

− d]f)(F[F1

1c1

c

)](I)(K[

)](I)(K[f

1111121

1011021 υ∆+υ∆υ

υ∆−υ∆=

L/z=η

L/d=ζ

2/1i

22ii )pR( +ωψ=υ

2/12ii )a/A(=ψ

rizii K/KA =

wr/La =

λγα= 2/R1

2/R 2 α=

1s2s S/S=λ

)(K)(KN

)(K)(K sk11sk20sk21sk101 ξυξυγ

−ξυξυ=∆

)(I)(KN

)(K)(I sk11sk20sk21sk102 ξυξυγ

+ξυξυ=∆

21 /N υυ=

wsksk r/r=ξ

otherwise 1,

dLz d, z 0,B(z)

transformcosine Fourier finite inverseF

B(z)of transformcosine Fourier finite)(F1-

c

c

+><

=

=

=ω



By matching type curves of the KGS Model slug test solution to data plotted onsemi-logarithmic axes, it is possible to determine values of K, SsSs and Kz/KrKz/Krfor the confined aquifer and K, SsSs and Kz/KrKz/Kr for the filter pack.

d

aquiclude

b

potentiometric surfaceafter slug injection

potentiometric surfacebefore slug injection

2rsk

2rc,2rw

H0

L

aquiferK,Ss,Kz/Kr

filter packK,Ss,Kz/Kr

wellbore skin

Assumptions


• aquifer is homogeneous and of uniform thickness






Data Requirements



• casing radius, wellbore radius and well skin radius for test well


• screen length


Reference

Hyder, Z, J.J. Butler, Jr., C.D. McElwee and W. Liu, 1994. Slug tests inpartially penetrating wells, Water Resources Research, vol. 30, no. 11,pp. 2945-2957.


Tutorial

Perform the tutorial for the Hyder et al. (1995) solution for a slug test in anunconfined aquifer (see "Tutorial" on page 101) to learn how to use this solution.

Unconfined Aquifer SolutionsChoose Solution... from the Match menu to choose a solution for analyzing apumping test or slug test in an unconfined aquifer.

Solutions for Pumping Tests in Unconfined Aquifers

1. Theis (1935) type curve solution

2. Cooper-Jacob (1946) straight line solution

3. Neuman (1974) type curve solution

4. Quick Neuman type curve solution

5. Streltsova (1974) type curve solution for piezometers

6. Moench (1997) type solution for a large-diameter pumping well

Solutions for Slug Tests in Unconfined Aquifers

1. Bouwer-Rice (1976) straight-line solution

2. Hvorslev (1951) straight-line solution

3. Hyder et al. (1995) type curve solution (KGS Model)

Theis (1935) Solution for a Pumping Test in anUnconfined AquiferThe Theis (1935) solution (see “Theis (1935) Solution” on page 50) is applicable tounconfined aquifers through the correction of drawdown data as follows:

′ = −s s s b( / )2 2

where s' is corrected displacement, s is observed displacement and b is saturatedthickness of the aquifer. This correction only applies to pumping tests in whichwater is withdrawn from an unconfined aquifer; it is not appropriate for injectiontests.

The corrected displacement (s') predicted by this equation reaches a maximum ofone-half the aquifer saturated thickness (0.5b) when the observed displacement isequal to the aquifer saturated thickness (s = b). Of course, complete dewatering ofthe aquifer (s = b) is not a realistic condition; however, in some cases, thedisplacement predicted with this correction equation along a type curve may exceedthe saturated thickness of the aquifer.

Assumptions






• aquifer is unconfined




• no delayed gravity response in aquifer

• flow velocity is proportional to tangent of the hydraulic gradientinstead of the sine (which is actually the case)

• flow is horizontal and uniform in a vertical section through the axis ofthe well

• displacement is small relative to saturated thickness of aquifer

Data Requirements


• pumping rate(s)


• aquifer saturated thickness

Solution Options




References


Kruseman, G.P. and N.A. DeRidder, 1990. Analysis and Evaluation ofPumping Test Data (2nd ed.), Publication 47, Intern. Inst. for LandReclamation and Improvement, Wageningen, The Netherlands, 370p.

Tutorial

Perform one of the following tutorials to learn how to use the Theis solution:

1. Guided Tour (see "Analyzing a Pumping Test" on page 7)

2. Theis (1935) solution for a pumping test in a confined aquifer (see"Tutorial" on page 52)


Cooper-Jacob (1946) Solution for a Pumping Test inan Unconfined AquiferThe Cooper-Jacob (1946) solution (see “Cooper-Jacob (1946) Solution” on page 55)is applicable to unconfined aquifers through the correction of drawdown data asfollows:

′ = −s s s b( / )2 2

where s' is corrected displacement, s is observed displacement and b is saturatedthickness of the aquifer. This correction only applies to pumping tests in whichwater is withdrawn from an unconfined aquifer; it is not appropriate for injectiontests.

The corrected displacement (s') predicted by this equation reaches a maximum ofone-half the aquifer saturated thickness (0.5b) when the observed displacement isequal to the aquifer saturated thickness (s = b). Of course, complete dewatering ofthe aquifer (s = b) is not a realistic condition; however, in some cases, thedisplacement predicted with this correction equation along a type curve may exceedthe saturated thickness of the aquifer.

Assumptions










• no delayed gravity response in aquifer

• flow velocity is proportional to tangent of the hydraulic gradientinstead of the sine (which is actually the case)

• flow is horizontal and uniform in a vertical section through the axis ofthe well

• displacement is small relative to saturated thickness of aquifer

Data Requirements


• pumping rate(s)




Solution Options



References

Cooper, H.H. and C.E. Jacob, 1946. A generalized graphical method forevaluating formation constants and summarizing well field history,Am. Geophys. Union Trans., vol. 27, pp. 526-534.

Kruseman, G.P. and N.A. DeRidder, 1990. Analysis and Evaluation ofPumping Test Data (2nd ed.), Publication 47, Intern. Inst. for LandReclamation and Improvement, Wageningen, The Netherlands, 370p.

Tutorial

Perform the tutorial for the Cooper-Jacob (1946) solution for a pumping test in aconfined aquifer (see "Tutorial" on page 57) to learn how to use this solution.

Neuman (1974) Solution for a Pumping Test in anUnconfined AquiferNeuman (1974) derived an analytical solution for unsteady flow to a partiallypenetrating well in an unconfined aquifer with delayed gravity response:

sQ

TyJ y u y u y dyn

n

= +

=

∞∞

∑∫44 0 0

10πβ( ) ( ) ( )

β =r K

b Kz

r

2

2

σ =S

Sy

For a partially penetrating pumping well, the drawdown in a piezometer is foundusing the following equations:

u yt y z

y yd l

l d

os D

D D

D D

( ) exp[ ( )]cosh( )

( ) ( ) / cosh( )sinh[ ( )] sinh[ ( )]

( )sin( )

=− − −

+ + − −⋅

− − −−

1

11 1

202

02

02 2

02 2

0

0 0

0

β γ γσ γ γ σ γ

γ γγ

u yt y z

y yd l

l d

ns n n D

n n n

n D n D

D D n

( ) exp[ ( )]cos( )

( ) ( ) / cos( )sin[ ( )] sin[ ( )]

( )sin( )

=− − +

− + − +⋅

− − −−

1

11 1

2 2

2 2 2 2 2

β γ γσ γ γ σ γ

γ γγ

For a partially penetrating pumping well, the drawdown in a partially penetratingobservation well is found using the following equations:


u yt y z z

y yd l

z z l d

os D D

D D

D D D D

( ) exp[ ( )]sinh( ) sinh( )

( ) ( ) / cosh( )sinh[ ( ) sinh[ ( )]

( ) ( )sin( )

=− − − −

+ + − −⋅

− − −− −

1

11 1

202

0 2 0 12

02 2

02 2

0

0 0

2 1 0 0

β γ γ γσ γ γ σ γ

γ γγ γ

u yt y z z

y yd l

z z l d

ns n n D n D

n n n

n D n D

D D n D D n

( ) exp[ ( )]sin( ) sin( )

( ) ( ) / cos( )sin[ ( )] sin[ ( )]

( ) ( )sin( )

=− − + −

− + − +⋅

− − −− −

1

11 1

2 22 1

2 2 2 2 2

2 1

β γ γ γσ γ γ σ γ

γ γγ γ

The gamma terms are the roots of the following equations:

σγ γ γ γ γ

σγ γ γ γ π γ π

0 02

02

0 02 2

2 2

0

0 2 1 2 1

sinh( ) ( ) cosh( ) ,

sin( ) ( ) cos( ) , ( ) / ( / ) ,

− − = <

+ + = − < < ≥

y yand

y n n nn n n n n

Refer to the "List of Symbols" on page 141 for a description of the parameters andvariables contained in the equations.

AQTESOLV for Windows allows you to analyze both constant- and variable-ratepumping tests using the Neuman solution. For tests with a variable discharge rate,the program uses the principle of superposition to compute drawdown in theaquifer. For more information concerning the application of the principle ofsuperposition in variable-rate pumping tests, refer to the "Theis (1935) Solution fora Pumping Test in a Confined Aquifer" on page 50.

The Neuman solution supports observation wells and piezometers. Use this solutionto estimate values of transmissivity, elastic storage coefficient, specific yield andβbeta (or Kz/KrKz/Kr for a data set containing more than one pair of pumping andobservation wells) in an unconfined aquifer.

aquiclude

aquiferT,S,Sy,Kz/Kr

Q

b

s1 s2



r1

r2

zDz1D

z2D

dD

lD


Entering partial penetrationdata for observation wells orpiezometers

The equations of Neuman (1974) for a partially penetrating observation well or apiezometer use elevations measured from the base of the unconfined aquifer (z1D,z2D, zD); however, when entering partial penetration data for observation wells andpiezometers into AQTESOLV for Windows, input depths measured from thepotentiometric surface before pumping (static water table).

Assumptions


• aquifer is homogeneous and has uniform thickness





Data Requirements


• pumping rate(s)




Solution Options





Visual Curve Matching

In practice, one uses two sets of type curves to analyze a pumping test in anunconfined aquifer with the Neuman solution. Type A curves match early timedata and Type B curves match late time data:

sQ

Tw uA A=

4πβ( , )

sQ

Tw uB B=

4πβ( , )

To analyze a pumping test using the Neuman type curve method, one plotsdrawdown as a function of time on double logarithmic axes. By matching twofamilies of type curves drawn by plotting w(uA,β) as a function of 1/uA and w(uB,β)as a function of 1/uB, one can estimate the values of transmissivity, storagecoefficient, specific yield and βbeta by visual analysis.


Procedure for Visual Curve Matching

1. Match Type A curves to early drawdown data to estimate T, Sand βbeta.

2. Match Type B curves to late drawdown data to estimate T, SYyand βbeta.

3. Choose Toolbox… from the Match menu and click theOptions tab. Select the Match early data (Type A) or Matchlate data (Type B) option. Click OK.

4. Choose Visual from the Match menu to invoke visual curvematching.

5. Select values of the βbeta parameter from Curve list on thetoolbar.

6. Click and hold the left mouse button down to drag the Neumantype curves to a new position on the screen. Release the leftmouse button when you have finished moving the curves.

Partial Penetration Type Curves

AQTESOLV for Windows stores Type A and Type B curves for fully penetratingwells. If your data set contains partially penetrating wells, however, you mustcompute new Type A and Type B curves for the partial penetration depths of thepumping and observation wells. AQTESOLV for Windows automatically promptsyou when new partial penetration type curves are required for your data set.

Computing Curves

Choose Calculate in the Partial Penetration Curves dialog box tocompute partial penetration curves using partial penetration datafor the pumping and observation wells. AQTESOLV forWindows will save the partial penetration curves with the data set.

Retrieving Curves From Disk

Choose Retrieve from disk from the Partial Penetration Curvesdialog box to open a disk file containing partial penetration typecurves. The format of the file is compatible with DOS versions ofAQTESOLV.

Saving Curves on Disk

After computing partial penetration type curves, AQTESOLV forWindows prompts you to save the type curve data on disk. Theformat of the file created by AQTESOLV for Windows iscompatible with DOS versions of AQTESOLV.

References

Neuman, S.P., 1974. Effect of partial penetration on flow in unconfinedaquifers considering delayed gravity response, Water ResourcesResearch, vol. 10, no. 2, pp. 303-312.

Moench, A.F., 1993. Computation of type curves for flow to partiallypenetrating wells in water-table aquifers, Ground Water, vol. 31, no.6, pp. 966-971.


Moench, A.F., 1996. Flow to a well in a water-table aquifer: an improvedLaplace transform solution, Ground Water, vol. 34, no. 4, pp. 593-596.

Tutorial

In this tutorial, you will use the Neuman and Quick Neuman type curve solutions toanalyze a constant rate pumping test in an unconfined aquifer. This tutorial showsyou how to use visual and automatic curve matching to match Neuman type curvesto drawdown data measured during the test.

Open a New Data Set




1. Select ft (feet) for Length, min (minutes) for Time, gal/min(gallons-per-minute) for Pumping Rate and ft/min (feet/minute) forHyd. Conductivity.

2. Click OK.


1. In the Title tab, enter Fairborn, Ohio for the Title.

2. Click OK.



2. Click OK.

Choose Pumping Well>Edit... from the Edit menu to edit pumping well data.

1. In the Rate tab, enter values of 0.0 and 1080.0 for time and rate,respectively, where time is in minutes and rate is in gallons-per-minute.

2. Click OK.



2. In the Observations tab, click the Import button to importobservation well measurements from a delimited text file using theObservation Data Import Wizard. In Step 1 of the ImportWizard, enter FAIRBORN.DAT for the name of the import file. Thefile FAIRBORN.DAT contains time and displacement data arrangedin two columns separated by a tab delimiter. Click Next.

3. In Step 2 of the Import Wizard, enter data describing the structure ofthe import file. The Import Wizard automatically determines that


the import file contains 2 columns of data. Enter 1 for the ElapsedTime column and 2 for the Displacement column. Click Next.



6. Click OK.


Save Data Set


1. Enter NEUMAN1.AQT for the file name.




Choose Quick Neuman Solution

Change the aquifer model and solution by choosing Solution... from the Matchmenu to choose a solution for analyzing a pumping test in an unconfined aquifer.

1. Choose the Unconfined Quick Neuman solution.

2. Click OK.

After you have selected the Quick Neuman solution for a pumping test in anunconfined aquifer, AQTESOLV for Windows updates the window by plotting thedata on double logarithmic axes, superimposing a Neuman type curve on the plot,and displaying values of transmissivity (T), storage coefficient (S), specific yield(Sy) and beta in the legend.

The Quick Neuman implementation of the Neuman solution, rather than the fullNeuman solution, is ideal for most situations. Computations with Quick Neumanare much faster than Neuman with virtually no loss in accuracy. Therefore, youshould use Quick Neuman for initial estimation followed by Neuman to refine theestimates obtained with Quick Neuman.

Perform Visual Matching with Quick Neuman

Visually match the Quick Neuman solution to the data as follows:

1. Click Match Early Data on the toolbar to toggle the match early data(Type A) option and simultaneously invoke visual curve matching.

2. Select the value of the βbeta parameter from Curve list on the toolbar.Choose a curve with a shape that matches the early data.


3. To begin interactively moving the Type A curve, move the mousecursor over the plot, click the left mouse button and hold it down.

4. As you move the mouse, the type curve also moves. AQTESOLV forWindows updates the values of T and S in the legend as you move theType A curve.

5. When you have finished matching the Type A curve to the early data,release the left mouse button to end visual curve matching and redrawthe complete type curve.

6. Click Match Late Data on the toolbar to toggle the match late data(Type B) option and simultaneously invoke visual curve matching.

7. Follow the procedure for Type A curve matching to fit a Type B curveto the late data. As you move the Type B curve, AQTESOLV forWindows updates the values of T and Sy in the legend.

You should obtain a match using a value of 0.06 for beta. If necessary, repeat thepreceding steps to finish matching the Type A and B curves.

Perform Automatic Matching with Quick Neuman

Choose Automatic... from the Match menu to perform automatic matching usingthe Neuman type curve solution.




The plot shown in the active window displays the values of transmissivity(T=24.04), storage coefficient (S=0.0.002111), specific yield (Sy=0.1061) and beta(=0.04458) determined by automatic estimation.

Choose Neuman Solution


1. Choose the Unconfined Neuman (1974) solution.

2. Click OK.

Compared to the Quick Neuman implementation of the Neuman solution, the fullNeuman implementation is computationally more intensive and therefore requiresgreater time to plot the type curve. In all other respects, working with the Neumansolution for visual and automatic curve matching is identical to Quick Neuman.

Save Data Set

Choose Save from the File menu to save your work in the NEUMAN1.AQT dataset.


Quick Neuman Solution for a Pumping Test in anUnconfined AquiferThe Quick Neuman solution option provided by AQTESOLV for Windowscomputes Neuman type curves using a two-stage interpolation technique.QuickNeuman yields essentially the same results as the Neuman solution option,only much more quickly. Therefore, Quick Neuman is a viable alternative forperforming automatic curve matching prior to using Neuman (see "Neuman (1974)Solution for a Pumping Test in an Unconfined Aquifer" on page 79).

Assumptions







Data Requirements


• pumping rate(s)




Solution Options





Reference

Neuman, S.P., 1974. Effect of partial penetration on flow in unconfinedaquifers considering delayed gravity response, Water ResourcesResearch, vol. 10, no. 2, pp. 303-312.

Tutorial

To learn how to use the Quick Neuman solution, perform the tutorial for theNeuman (1974) Solution for a Pumping Test in an Unconfined Aquifer.


Streltsova (1974) Solution for a Pumping Test in anUnconfined AquiferStreltsova (1974) derived an analytical solution for the water-level response in apiezometer due to unsteady flow to a pumping well in an unconfined aquifer withdelayed gravity response:

sQ

T l d R nerfc

R n

R nerfc

R ndy

R n zn

l dy

R n zn

l dy

D D

n

n d

l

DD D

DD D

D

D

=−

− −

= + − −−

−

= + − −−

+

=−∞

∞

∑ ∫41

1

2

1

2

12

12

1

1

2

2

1

2

2

2

π τ τ

β

β

( )( )

( )

( )

( )

( )

( )( )

( )( )

β =r K

b Kz

r

2

2

τ =tK

Sbz


AQTESOLV for Windows allows you to analyze both constant- and variable-ratepumping tests using the Streltsova solution. For tests with a variable discharge rate,the program uses the principle of superposition to compute drawdown in theaquifer. For more information concerning the application of the principle ofsuperposition in variable-rate pumping tests, refer to the "Theis (1935) Solution fora Pumping Test in a Confined Aquifer" on page 50.

The Streltsova solution only supports piezometers, not observation wells. Use thissolution to estimate values of transmissivity, elastic storage coefficient and βbeta (orKz/KrKz/Kr for a data set containing more than one pumping well/piezometer pair)in an unconfined aquifer.

aquiclude

aquiferT,S,Kz/Kr

Q

b

s1potentiometric surface

after pumping


r1

zD

dD

lD


Entering piezometer data The equations of Streltsova (1974) for a piezometer use elevations measured fromthe base of the unconfined aquifer (zD); however, when entering partial penetrationdata for into AQTESOLV for Windows, input depth measured from thepotentiometric surface before pumping (static water table).

Assumptions







Data Requirements


• pumping rate(s)

• piezometer measurements (time and displacement)


• piezometer depth (solution only supports piezometers)

Solution Options



• multiple piezometers

• partial penetration (in a piezometer only)

Reference

Streltsova, T.D., 1974. Drawdown in compressible unconfined aquifer,Jour. of the Hyd. Div., Proc. of the Am. Soc. of Civil Eng., vol. 100,no. HY11, pp. 1601-1616.

Tutorial

In this tutorial, you will use the Streltsova solution to analyze the constant ratepumping test data set created and saved in the tutorial for the Neuman unconfinedaquifer solution. You will change the observation well to a piezometer and usevisual curve matching to match a Streltsova type curve to the drawdown data.

Open Data Set

Choose Open... from the File menu to open a dialog box for opening a data setstored on disk. You will open the data set created and saved in the tutorial for theNeuman (1974) solution.

1. Enter NEUMAN1.AQT for the name of the data set.




If necessary, choose Error Log from the View menu to display an Error Log reportin the active window.

Edit Observation Well Data in Data Set


1. In the Construction tab, click Piezometer to change theobservation well to a piezometer.

2. Enter 39.0 for the Piezometer Depth.

3. Click OK.


Save Data Set

Choose Save As... from the File menu to save the modified data you have enteredinto the data set.

1. Enter STRELT1.AQT for the name of the file.



Choose Displacement-Time from the View menu to display a plot ofdisplacement vs. time in the active window.

Choose Streltsova Solution


1. Choose the Unconfined Streltsova (1974) solution.

2. Click OK.

After you have selected the Streltsova solution for a pumping test in an unconfinedaquifer, AQTESOLV for Windows updates the window by plotting the data ondouble logarithmic axes, superimposing a Streltsova type curve on the plot, anddisplaying values of transmissivity (T), storage coefficient (S) and beta in thelegend.

Display Type Curve Family

Choose Options… from the View menu and click the Plots tab. Check theCurve Family option to superimpose a family of type curves for the Streltsovasolution on the plot. The legend shows the values of the beta parameter for the twoadditional curves displayed with this option.

Click the Family tab to customize the curve family.

Perform Visual Matching with Streltsova

Choose Visual from the Match menu to perform visual curve matching with theStreltsova type curve solution.



2. As you move the mouse, the type curve also moves. AQTESOLV forWindows updates the values of the aquifer properties, T and S, in thelegend as you move the type curve.

3. When you have finished matching the type curve to the piezometerdata, release the left mouse button to end visual curve matching.

Choose Toolbox... from the Match menu and click the Parameters tab tochange the value of beta used to compute the Streltsova type curve.

1. Enter 0.12 for the value of beta.

2. Click OK.

Repeat the steps for moving the type curve to match the Streltsova solution to thedata.

When you finish matching the type curve, you will discover that the Streltsovasolution for a piezometer does not reproduce the results obtained in the tutorial forthe Neuman solution for fully penetrating wells.

Save Data Set

Choose Save from the File menu to save your work in the STRELT1.AQT dataset.

Moench (1997) Solution for a Pumping Test in anUnconfined AquiferMoench (1997) derived an analytical solution for unsteady flow to a partiallypenetrating large-diameter well in an unconfined aquifer with delayed gravityresponse. The Laplace transform solution for dimensionless drawdown in thepumped well is as follows:

hA S

p(l d pW A SwD

w

D D D w

=+

− + +2

1

( )

)[ ( )]

The following equations are the Laplace transform solutions for dimensionlessdrawdown in a piezometer:

hE

p(l d pW A SD

D D D w

=− + +

2

1)[ ( )]

or an observation well:

hE

p(l d pW A SD

D D D w

'

)[ ( )]=

′− + +

2

1

where

Al d

K q d l

q K qD D

n n D n D

n n n n nn

=−

− − −+=

∞

∑2 1 1

05 20

2

10( )

( )sin[ ( ) sin[ ( )]

( )[ . sin( )]

ε εε ε ε


EK q r z d l

q K qn D n D n D n D

n n n nn

=− − −

+=

∞

∑21 1

05 20

10

( )cos( )sin[ ( ) sin[ ( )]

( )[ . sin( )]

ε ε εε ε

′ =−

− +

⋅

− − −

=

∞

∑EK q r z z

z z q K q

d l

n D n D n D

D D n n n n nn

n D n D

20 5 2

1 1

0 2 1

2 1 10

( )[sin( ) sin( )]

( ) ( )[ . sin( )]

sin[ ( ) sin[ ( )]

ε εε ε ε

ε ε

Wr

r S l dDc

w s

=−

ππ

2

22 ( )

q p

q r pr

n n w

n D n D

= +

= +

( )

( )

ε β

ε β

2

2 2

βww z

r

r K

b K=

2

2

β =r K

b Kz

r

2

2

rr

rDw

=

σ =S

Sy

γ α= 1bS Ky z/

and are the roots ofnε

ε εσβ γn n

w

p

ptan( )

( / )=

+

The parameter α1alpha is a fitting parameter for drainage from the unsaturated zoneand has units of inverse time (T-11/T). A large value of α1alpha effectivelyeliminates this parameter from the solution. Refer to the "List of Symbols" on page141 for a description of the parameters and variables contained in the equations.

AQTESOLV for Windows allows you to analyze both constant- and variable-ratepumping tests using the Moench solution. For tests with a variable discharge rate,the program uses the principle of superposition to compute drawdown in theaquifer. For more information concerning the application of the principle ofsuperposition in variable-rate pumping tests, refer to the "Theis (1935) Solution fora Pumping Test in a Confined Aquifer" on page 50.

The Moench solution supports observation wells and piezometers. Use this solutionto estimate values of transmissivity, elastic storage coefficient, specific yield andβbeta (or Kz/KrKz/Kr for a data set containing more than one pair of pumping andobservation wells), well radius, wellbore skin factor, and α1alpha in an unconfinedaquifer.


aquiclude

aquiferT,S,Sy,Kz/Kr,α1

Q

b

s1 s2



r1

r2

zDz1D

z2D

dD

lD

Entering partial penetrationdata for observation wells orpiezometers

The equations of Moench (1997) for a partially penetrating observation well orpiezometer use elevations measured from the base of the unconfined aquifer (z1D,z2D, zD); however, when entering partial penetration data for observation wells andpiezometers into AQTESOLV for Windows, input depths measured from thepotentiometric surface before pumping (static water table).

Assumptions






Data Requirements


• pumping rate(s)





Solution Options







Reference

Moench, A.F., 1997. Flow to a well of finite diameter in a homogeneous,anisotropic water table aquifer, Water Resources Research, vol. 33, no.6, pp. 1397-1407.

Tutorial

In this tutorial, you will use the Moench solution to analyze the constant ratepumping test data set created and saved in the tutorial for the Neuman unconfinedaquifer solution. In this tutorial you will add large-diameter well data and useautomatic curve matching to match a Moench type curve to the drawdown data.

Open Data Set

Choose Open... from the File menu to open a data set stored on disk. You willopen the data set created and saved in the tutorial for the Neuman (1974) solution.

1. Enter NEUMAN1.AQT for the name of the data set.



If necessary, choose Error Log from the View menu to display an Error Log reportin the active window.

Add Large-Diameter Well Data to Data Set

Choose Pumping Well>Edit... from the Edit menu to edit data for the pumpingwell.


2. Click OK.

To analyze pumping tests using large-diameter well solutions, you must enter valuesfor the wellbore radius and casing radius of the pumping well(s). If the values ofeither of these two variables is 0.0, AQTESOLV for Windows assumes the pumpingwell radius is infinitesimal; if you enter 0.0 for either value, AQTESOLV forWindows will not allow you to select any of the large-diameter well solutionscontained in the program.


Save Data Set

Choose Save As... from the File menu to save the modified data you have enteredinto the data set.

1. Enter MOENCHU1.AQT for the name of the file.

2. Click OK.




Choose Moench Solution


1. Choose the Unconfined Moench (1997) solution.

2. Click OK.

After you have selected the Moench solution for a pumping test in an unconfinedaquifer, AQTESOLV for Windows updates the window by plotting the data ondouble logarithmic axes, superimposing a Moench type curve on the plot, anddisplaying values of transmissivity (T), storage coefficient (S), specific yield (Sy),beta, wellbore skin factor (Sw), well radius (Rw) and alpha in the legend.

Due to the large number of parameters in the Moench unconfined aquifer solution,it is not practical to develop type curves for traditional visual analysis. Therefore,AQTESOLV for Windows provides you with the ability to match the Moenchsolution to your data by manually changing values of the seven parameters in thesolution until you achieve a satisfactory match or by using automatic estimation.

Edit Parameters Prior to Estimation

Choose Automatic... from the Match menu and click the Parameters tab to editparameter values and constraints and to enable/disable estimation of parametersduring automatic estimation.

1. Enter a value of 0.0 for Sw and set Estimation to Inactive.

2. Enter a value of 1.0 for Rw and set Estimation to Inactive.

3. Set Estimation of alpha to Inactive. A large value of alpha (e.g.,1.0E+30) effectively removes this fitting parameter from thecomputation of the type curve.

4. Click OK.

Perform Automatic Matching with Moench

Choose Automatic... from the Match menu to open a dialog box for performingautomatic matching of the Moench type curve solution to the observation well data.




The plot shown in the active window displays the values of transmissivity(T=24.33), storage coefficient (S=0.001758), specific yield (Sy=0.1019) and beta(=0.04463) determined by automatic estimation. The changes in the parametersfrom those estimated using the Neuman solution indicate only a small wellborestorage effect in this example. To view the effect of wellbore storage on the typecurve, choose Unconfined... from the Solution menu and select the Neuman(1974) solution.

Save Data Set


Choose Save from the File menu to save your work in the MOENCHU1.AQTdata set.

Bouwer-Rice (1976) Solution for a Slug Test in anUnconfined AquiferBouwer and Rice (1976) developed an empirical relationship describing the water-level response in an unconfined aquifer due to the instantaneous injection orwithdrawal of water from a well:

ln( ) ln( )ln( / )

s sKLt

r r rtce e we

0 2

2− =

r r n r rce c w c= + −2 2 2( )

r rK

Kwe wz

r

=

Bouwer and Rice (1976) recommend computing an equivalent casing radius (rce) tocorrect for the porosity of the gravel pack when the height of the static watercolumn in the well is less than the screen length (i.e., the screen is partiallysubmerged). AQTESOLV for Windows computes the equivalent casing radiususing the value of porosity (n) specified in the data set; a porosity equal to zero (0.0)results in no correction to the casing radius.

Zlotnik (1994) advises the use of an equivalent wellbore radius (rwe) if the aquifer isanisotropic in a vertical plane and the well is partially penetrating. AQTESOLVfor Windows automatically computes the equivalent wellbore radius using the valueof anisotropy ratio (Kz/Kr) specified in the data set; an anisotropy ratio equal tounity (1.0) results in no correction to the well radius.


aquiclude

aquiferK,Kz/Kr

b



L

2rw

2rc

s0

H


Assumptions





• aquifer is confined or unconfined

• flow is steady

Data Requirements





• screen length




References

Bouwer, H., 1989. The Bouwer and Rice slug test--an update, GroundWater, vol. 27, no. 3, pp. 304-309.

Bouwer, H. and R.C. Rice, 1976. A slug test method for determininghydraulic conductivity of unconfined aquifers with completely orpartially penetrating wells, Water Resources Research, vol. 12, no. 3,pp. 423-428.

Zlotnik, V., 1994. Interpretation of slug and packer tests in anisotropicaquifers, Ground Water, vol. 32, no. 5, pp. 761-766.

Tutorial

The Guided Tour (see "Analyzing a Slug Test" on page 11) contains a tutorial forthe Bouwer-Rice slug test solution.

Hvorslev (1951) Solution for a Slug Test in anUnconfined AquiferHvorslev (1951) developed an empirical relationship describing the water-levelresponse in an unconfined aquifer due to the instantaneous injection or withdrawalof water from a well:

ln( ) ln( )ln( / ( / ) )

s sKLt

r L r L rt

ce we we

0 2 2

2

2 1 2− =

+ +


r r n r rce c w c= + −2 2 2( )

r rK

Kwe wz

r

=

The Hvorslev (1951) solution assumes that the unconfined aquifer has infiniteextent, both horizontally and vertically. For this reason, the solution by Bouwer andRice (see "Bouwer-Rice (1976) Solution for a Slug Test in an Unconfined Aquifer"on page 95) may be more appropriate when the thickness of the aquifer is known.

Bouwer and Rice (1976) recommend computing an equivalent casing radius (rce) tocorrect for the porosity of the gravel pack when the height of the static watercolumn in the well is less than the screen length (i.e., the screen is partiallysubmerged). AQTESOLV for Windows computes the equivalent casing radiususing the value of porosity (n) specified in the data set; a porosity equal to zero (0.0)results in no correction to the casing radius.


aquiclude

aquiferK,Kz/Kr

b



L

2rw

2rc

s0

H

Assumptions

• aquifer has infinite areal and vertical extent

• aquifer is homogeneous




• flow is steady

Data Requirements






• screen length




References

Bouwer, H. and R.C. Rice, 1976. A slug test method for determininghydraulic conductivity of unconfined aquifers with completely orpartially penetrating wells, Water Resources Research, vol. 12, no. 3,pp. 423-428.

Hvorslev, M.J., 1951. Time Lag and Soil Permeability in Ground-WaterObservations, Bull. No. 36, Waterways Exper. Sta. Corps of Engrs,U.S. Army, Vicksburg, Mississippi, pp. 1-50.

Tutorial

Use of the Hvorslev solution is essentially identical to the Bouwer-Rice slug testsolution. Refer to the Guided Tour (see "Analyzing a Slug Test" on page 11) whichcontains a tutorial for the Bouwer-Rice solution.

Hyder et al. (1994) Solution for a Slug Test in anUnconfined Aquifer (KGS Model)Hyder et al. (1994) derived an analytical solution, also known as the KGS Model,describing the water-level response due to the instantaneous injection or withdrawalof water from a partially penetrating well in an unconfined aquifer. The equationfor the Laplace transform solution is as follows:

*]p)2/(1[

*)2/(h

Ωγ+Ωγ

=

2c

2s2w

r

LSr2=α

1r2r K/K=γ

ηω=Ω ∫+ζ

ζ

− d]f*)(F[F*1

1s1

s

)](I)(K[

)](I)(K[f

1111121

1011021 υ∆+υ∆υ

υ∆−υ∆=

L/z=η

L/d=ζ


2/1i

22ii )pR( +ωψ=υ

2/12ii )a/A(=ψ

rizii K/KA =

wr/La =

λγα= 2/R1

2/R 2 α=

1s2s S/S=λ

)(K)(KN

)(K)(K sk11sk20sk21sk101 ξυξυγ

−ξυξυ=∆

)(I)(KN

)(K)(I sk11sk20sk21sk102 ξυξυγ

+ξυξυ=∆

21 /N υυ=

wsksk r/r=ξ

otherwise 1,

dLz d, z 0,B(z)

transformsine Fourier finite modified inverseF

B(z)of transformsine Fourier finite ifiedmod*)(F1-

s

s

+><

=

=

=ω


By matching type curves of the KGS Model slug test solution to data plotted onsemi-logarithmic axes, it is possible to determine values of K, SsSs and Kz/KrKz/Krfor the unconfined aquifer and K, SsSs and Kz/KrKz/Kr for the filter pack.


d

aquiclude

b



2rsk

2rc,2rw

H0

L

aquiferK,Ss,Kz/Kr

filter packK,Ss,Kz/Kr

wellbore skin

Assumptions








Data Requirements



• casing radius, wellbore radius and well skin radius for test well


• screen length


Reference

Hyder, Z, J.J. Butler, Jr., C.D. McElwee and W. Liu, 1994. Slug tests inpartially penetrating wells, Water Resources Research, vol. 30, no. 11,pp. 2945-2957.


Tutorial

In this tutorial, you will use the KGS Model to create and analyze a slug test. Thistutorial shows you how to use visual and automatic curve matching to match theKGS Model to displacement data measured during the slug test.

Open a New Data Set


Enter Data for Slug Test


1. Select m (meters) for Length, sec (seconds) for Time, and m/day(meters-per-day) for Hyd. Conductivity.

2. Click OK.


1. In the Title tab, enter Unconfined Slug Test for the Title.

2. Click OK.

Choose Slug Test Well... from the Edit menu to edit slug test data.

1. In the General tab, enter 0.671 for Initial Displacement.

2. In the Aquifer tab, enter 47.87 for Saturated Thickness.

3. In the Screen tab, enter 1.52 for Screen Length and 18.29 forTotal Depth of Penetration.

4. In the Radius tab, enter 0.064 for Casing Radius and 0.125 forWellbore Radius and Well Skin Radius.

5. In the Observations tab, click the Import button to importobservation well measurements from a delimited text file using theObservation Data Import Wizard. In Step 1 of the ImportWizard, enter PRATT4-2.DAT for the name of the import file. Thefile contains time and displacement data arranged in two columnsseparated by a tab delimiter. Click Next.




9. Click OK.



Save Data Set


1. Enter KGS1.AQT for the file name.




Choose KGS Model Solution

Change the aquifer model and solution by choosing Solution... from the Matchmenu to choose a solution for analyzing a slug test in an unconfined aquifer.

1. Choose the Unconfined KGS Model (1995) solution.

2. Click OK.

After you have selected the KGS Model solution for a slug test in an unconfinedaquifer, AQTESOLV for Windows updates the window by plotting the data onsemi-log axes, superimposing a KGS Model type curve on the plot, and displayingvalues of radial hydraulic conductivity (KrKr), specific storage (SsSs) and hydraulicconductivity anisotropy ratio (Kz/KrKz/Kr) in the legend.

To analyze a slug test using the KGS Model type curve method, one plots relativedisplacement as a function of time on semi-log axes. By matching a family of typecurves, one can estimate the values of hydraulic conductivity, specific storage andhydraulic conductivity anisotropy ratio of the aquifer by visual analysis.

Perform Visual Matching with KGS Model

Choose Visual from the Match menu to perform visual curve matching with theKGS Model solution.


2. As you move the mouse, the type curve also moves. AQTESOLV forWindows updates the value of Kr in the legend as the type curveposition changes. The values of Ss is fixed as you move the curve tothe left and right on the plot.


Choose Toolbox… from the Match menu to fine tune the match of the type curveto the data.

1. In the Tweak tab, select Ss from the Parameter list.

2. Check the Apply changes automatically option.


3. Move the button on the scroll bar to change the value of Ss. As youadjust the value, AQTESOLV for Windows updates the position of thetype curve on the screen.

4. Repeat these steps for Kr to fine tune the position of the type curve.

5. Click OK when you have finished adjusting the parameters.

Perform Automatic Matching with KGS Model

Choose Automatic... from the Match menu to perform automatic matching usingthe KGS Model type curve solution.

1. In the Parameters tab, select Inactive for the Estimation of Kz/Kr(the default for this solution).




The plot shown in the active window displays the values of transmissivity(Kr=4.034), storage coefficient (Ss=0.0003834) and hydraulic conductivityanisotropy ratio (Kz/Kr=1.0) determined by automatic estimation.

Save Data Set

Choose Save from the File menu to save your work in the KGS1.AQT data set.

Leaky Aquifer SolutionsChoose Solution... from the Match menu to choose a solution for analyzing apumping test in a leaky aquifer.

Solutions for Pumping Tests in Leaky Aquifers

1. Hantush-Jacob (1955) type curve solution (no storage in aquitard)

2. Hantush (1960) type curve solution (storage in aquitard, early time)

3. Moench (1985) type curve solution (large-diameter well, storage inaquitard)

4. Neuman-Witherspoon (1969) type curve solution (two-aquifer system,storage in aquitard)

No solutions are currently available for analyzing slug tests in a leaky aquifer.

Hantush-Jacob (1955) Solution for a Pumping Testin a Leaky AquiferHantush and Jacob (1955) derived an analytical solution for predicting water-levelchanges in response to pumping in a leaky confined aquifer assuming steady flow(no storage) in the aquitard(s):


sQ

T

e

ydy

y r B y

u

=− −∞

∫4

2 24

π

/

ur S

=2

4Tt

BTb

K=

′′

Hydrogeologists commonly refer to the integral expression in the drawdownequation as the Hantush well function for leaky aquifers, abbreviated as w(u,r/B).Therefore, we can write the Hantush drawdown equation in compact notation asfollows:

sQ

Tw u r B=

4π( , / )


Hantush (1961a,b) derived equations for the effects of partial penetration in a leakyaquifer. For a piezometer, the partial penetration correction is as follows:

sQ

Tw u r B

b

l d n

n l

b

n d

b

n z

b

w u r BKK

n rb

n

z

r

= +−

− ⋅ ⋅

+

=

∞

∑4

2 1

1

22

π ππ π π

π

( , / )( )

[sin( ) sin( )] cos( )

( , ( / ) )

For an observation well, the following partial penetration correction applies:

sQ

Tw u r B

b

l d l d n

n l

b

n d

b

n l

b

n d

bw u r B

K

K

n r

b

n

z

r

= +− ′ − ′

− ⋅

′ − ′ ⋅ +

=

∞

∑4

2 12

2 21

22

π ππ π

π π π

( , / )( )( )

[sin( ) sin( )]

[sin( ) sin( )] ( , ( / ) )

where w(u,r/B) is the Hantush well function for leaky aquifers.

AQTESOLV for Windows allows you to analyze both constant- and variable-ratepumping tests using the Hantush-Jacob solution. For tests with a variable dischargerate, the program uses the principle of superposition to compute drawdown in theaquifer. For more information concerning the application of the principle ofsuperposition in variable-rate pumping tests, refer to the "Theis (1935) Solution fora Pumping Test in a Confined Aquifer" on page 50.

Use the Hantush-Jacob r/B solution to estimate values of transmissivity (T), storagecoefficient (S), and r/B (or 1/B for a data set containing more than one pair ofpumping and observation wells) in a leaky aquifer with no storage in theaquitard(s). For partially penetrating wells, the Hantush-Jacob r/B solution alsoestimates the values of hydraulic conductivity anisotropy ratio (Kz/KrKz/Kr) andsaturated thickness (b).


aquiclude

aquitardK',S'=0

aquiferT,S,Kz/Kr

Q

b


after pumping


r1

r2

unpumped aquifer

b'

Assumptions






• aquifer is leaky




• confining bed(s) has infinite areal extent, uniform vertical hydraulicconductivity and uniform thickness

• confining bed(s) is overlain or underlain by an infinite constant-headplane source

• flow in the aquitard(s) is vertical

Data Requirements


• pumping rate(s)






Solution Options





Reference

Hantush, M.S. and C.E. Jacob, 1955. Non-steady radial flow in an infiniteleaky aquifer, Am. Geophys. Union Trans., vol. 36, pp. 95-100.

Hantush, M.S., 1961a. Drawdown around a partially penetrating well,Jour. of the Hyd. Div., Proc. of the Am. Soc. of Civil Eng., vol. 87, no.HY4, pp. 83-98.

Hantush, M.S., 1961b. Aquifer tests on partially penetrating wells, Jour. ofthe Hyd. Div., Proc. of the Am. Soc. of Civil Eng., vol. 87, no. HY5,pp. 171-194.

Tutorial

In this tutorial, you will use the Hantush-Jacob type curve solution to create andanalyze a constant-rate pumping test. This tutorial shows you how to use automaticcurve matching to match the Hantush-Jacob type curve to drawdown data measuredduring the pumping test.

Open a New Data Set




1. Select m (meters) for Length, min (minutes) for Time, L/sec (liters-per-second) for Pumping Rate and m/day (meters/day) for Hyd.Conductivity.

2. Click OK.


1. In the Title tab, enter Leaky Confined Pumping Test for the Title.

2. Click OK.


1. In the General tab, enter 7.0 for the value of Saturated Thickness.

2. Click OK.



1. In the Rates tab, enter values of 0.0 and 9.12 for time and rate,respectively, where time is in minutes and rate is in liters-per-second.

2. Click OK.


1. In the General tab, enter H-30 for the Observation Well Name.

2. Enter a value of 30.0 for the X-Coordinate location of the well.

3. In the Observations tab, click the Import button to importobservation well measurements from a delimited text file using theObservation Data Import Wizard. In Step 1 of the ImportWizard, enter H30.DAT for the name of the import file. The fileH30.DAT contains time and displacement data arranged in twocolumns separated by a tab delimiter. Click Next.




7. Click OK.


Save Data Set


1. Enter HANTUSH1.AQT for the file name.




Choose Hantush-Jacob Solution

Change the aquifer model and solution by choosing Solution... from the Matchmenu to choose a solution for analyzing a pumping test in a leaky aquifer.

1. Choose the Leaky Hantush-Jacob (1955) solution.

2. Click OK.


After you have selected the Hantush-Jacob solution for a pumping test in a leakyaquifer, AQTESOLV for Windows updates the window by plotting the data ondouble logarithmic axes, superimposing a Hantush-Jacob type curve on the plot, anddisplaying values of transmissivity (T), storage coefficient (S), leakage parameter(r/B), hydraulic conductivity anisotropy ratio (Kz/KrKz/Kr) and saturated thickness(b) in the legend.

To analyze a pumping test using the Hantush r/B type curve method, one plotsdrawdown as a function of time on double logarithmic axes. By matching a familyof type curves drawn by plotting w(u,r/B) as a function of 1/u and r/B, one canestimate the values of transmissivity and storage coefficient of the aquifer by visualanalysis.

Perform Visual Matching with Hantush-Jacob

Choose Visual from the Match menu to perform visual curve matching with theHantush-Jacob solution.




4. You can select different values of the r/B parameter from the Curvelist on the toolbar. Change the value of r/B until you find a type curvethat fits the data. Continue moving the curve until you obtain asuitable match.

Perform Automatic Matching with Hantush-Jacob

Choose Automatic... from the Match menu to perform automatic matching usingthe Hantush-Jacob type curve solution.




The plot shown in the active window displays the values of transmissivity(T=415.6), storage coefficient (S=0.0001562) and dimensionless leakage parameter(r/B=0.03229) determined by automatic estimation.

Save Data Set

Choose Save from the File menu to save your work in the HANTUSH1.AQT dataset.


Hantush (1960) Solution for a Pumping Test in aLeaky AquiferHantush (1960) derived an analytical solution for predicting water-leveldisplacements in response to pumping in a leaky confined aquifer assuming storagein the aquitard(s). The solution in AQTESOLV for Windows assumes for smallvalues of time, i.e., when t < b′S′/10K′ and t < b″S″/10K″.

sQ

T

e

yerfc

u

y y udy

y

u

=−

−∞

∫4πβ( )

ur S

=2

4Tt

β =′ ′

′+

′′ ′′′′

r K S

b TS

K S

b TS4


Refer to "Hantush-Jacob (1955) Solution for a Pumping Test in a Leaky Aquifer" onpage 103 for partial penetration correction equations for this solution.

AQTESOLV for Windows allows you to analyze both constant- and variable-ratepumping tests using the Hantush solution. For tests with a variable discharge rate,the program uses the principle of superposition to compute drawdown in theaquifer. For more information concerning the application of the principle ofsuperposition in variable-rate pumping tests, refer to the "Theis (1935) Solution fora Pumping Test in a Confined Aquifer" on page 50.

Use the Hantush solution to estimate values of transmissivity, storage coefficient,and βbeta (or β/rbeta/r for a data set containing more than one pair of pumping andobservation wells) in a leaky aquifer with storage in the aquitard(s) for small valuesof time. For partially penetrating wells, the Hantush solution also estimates thevalues of hydraulic conductivity anisotropy ratio (Kz/KrKz/Kr) and saturatedthickness (b).


aquiclude

aquitardK',S'

aquiferT,S,Kz/Kr

Q

b


after pumping


r1

r2

unpumped aquifer

b'

Assumptions










• confining bed(s) has infinite areal extent, uniform vertical hydraulicconductivity and storage coefficient, and uniform thickness



Data Requirements


• pumping rate(s)






Solution Options





Reference

Hantush, M.S., 1960. Modification of the theory of leaky aquifers, Jour. ofGeophys. Res., vol. 65, no. 11, pp. 3713-3725.

Tutorial

In this tutorial, you will use the Hantush solution to analyze the constant ratepumping test data set created and saved in the tutorial for the Hantush-Jacob leakyaquifer solution. In this tutorial, you will add an observation well to the data setand use automatic curve matching to match the Hantush type curve to drawdowndata measured in two observation wells during a constant rate test.

Open Data Set

Choose Open... from the File menu to open a data set stored on disk. You willopen the data set created and saved in the tutorial for the Hantush-Jacob (1955)solution.

1. Enter HANTUSH1.AQT for the name of the data set.



Choose Error Log from the View menu to display an Error Log report in theactive window.

Add Observation Well to Data Set

Choose Obs. Well>Add... from the Edit menu to add an observation well and editobservation well data.

1. In the General tab, enter H-90 for the Observation Well Name.


3. In the Observations tab, click the Import button to importobservation well measurements from a delimited text file using theObservation Data Import Wizard. In Step 1 of the ImportWizard, enter H90.DAT for the name of the import file. The fileH90.DAT contains time and displacement data arranged in twocolumns separated by a tab delimiter. Click Next.

4. In Step 2 of the Import Wizard, enter data describing the structure ofthe import file. The Import Wizard automatically determines that


the import file contains 2 columns of data. Enter 1 for the ElapsedTime column and 2 for the Displacement column. Click Next.



7. Click OK.


Save Data Set


1. Enter HANTUSH2.AQT for the file name.




Choose Hantush Solution


1. Choose the Leaky Hantush (1960) solution.

2. Click OK.

After you have selected the Hantush solution for a pumping test in a leaky aquifer,AQTESOLV for Windows updates the window by plotting the data on doublelogarithmic axes, superimposing two Hantush type curves on the plot, anddisplaying values of transmissivity (T), storage coefficient (S) and leakageparameter (beta/r) in the legend.

AQTESOLV for Windows displays two type curves, one for each observation well,because the leakage parameter (beta) in the Hantush solution is a function of theradial distance, r, between the pumping and observation wells. The parameterdisplayed (beta/r) is independent of r.

Perform Automatic Matching with Hantush

Choose Automatic... from the Match menu to perform automatic matching usingthe Hantush type curve solution.


2. As the automatic estimation procedure completes iterations, a progresswindow displays the changes in the residual sum of squares (RSS)criterion and the values of the aquifer properties. After the automaticestimation procedure finishes, AQTESOLV for Windows displays a


message box containing residual summary statistics. Click OK toclose the message box.


The plot shown in the active window displays the values of transmissivity(T=348.2), storage coefficient (S=0.0001658) and leakage parameter(beta/r=0.0009434) determined by automatic estimation.

Save Data Set

Choose Save from the File menu to save your work in the HANTUSH2.AQT dataset.

Moench (1985) Solution for a Pumping Test in aLeaky AquiferMoench (1985) derived an analytical solution for predicting water-leveldisplacements in response to pumping in a leaky confined aquifer assuming storagein the aquitard(s) and wellbore skin. The solution also assumes that an aquitard isoverlain or underlain by either a constant head boundary (Case 1) or a no-flowboundary (Case 2).

The Laplace transform solution for dimensionless drawdown in the pumped well isas follows:

hK x xS K x

p pW K x xS K x xK xwD

w

D w

=+

+ +2 0 1

0 1 1

[ ( ) ( )]

[ ( ) ( )] ( )

The following equation is the Laplace transform solution for dimensionlessdrawdown in an observation well:

hK r x

p pW K x xS K x xK xD

D

D w

=+ +2 0

0 1 1

( )

[ ( ) ( )] ( )

x p q D= +( ) /1 2

q m m Case

q m m Case

D

D

=

=

γ

γ

2

2

1

2

coth( ) ( )

tanh( ) ( )

mp

=( ) /σ

γ

1 2

γ =′′

rK

Kbbw

1 2/

σ =′ ′S b

S bs

s

rr

rDw

=


bSr2

rW

s2w

2c

D ππ

=



Use the Moench solution to estimate values of transmissivity, storage coefficient,r/B, βbeta and rwwell radius (or 1/B and β/rbeta/r for a data set containing morethan one pair of pumping and observation wells) in a leaky aquifer with storage inthe aquitard(s). If a data set contains more than one pumping well, AQTESOLVfor Windows estimates the well radius for the first pumping well contained in thedata set.

aquiclude

aquitardK',Ss'

aquiferK,Ss

Q

b


after pumping


r1

r2

unpumped aquifer(case 1) or

aquiclude (case 2)

b'2rc

2rw

Assumptions










• confining bed(s) has infinite areal extent, uniform vertical hydraulicconductivity and storage coefficient, and uniform thickness



Data Requirements


• pumping rate(s)



Solution Options





Reference

Moench, A.F., 1985. Transient flow to a large-diameter well in an aquiferwith storative semiconfining layers, Water Resources Research, vol.21, no. 8, pp. 1121-1131.

Tutorial

In this tutorial, you will use the Moench solution to analyze the constant ratepumping test data set created and saved in the tutorial for the Hantush leaky aquifersolution. In this tutorial, you will use automatic curve matching to match theMoench type curve to drawdown data measured in two observation wells during aconstant rate test.

Open Data Set

Choose Open... from the File menu to open a data set stored on disk. You willopen the data set created and saved in the tutorial for the Hantush (1960) solution.

1. Enter HANTUSH2.AQT for the name of the data set.



Choose Error Log from the View menu to display an Error Log report in theactive window.

Add Large-Diameter Well Data to Data Set



1. In the Construction tab, enter 0.00001 for both Wellbore Radiusand Casing Radius.

2. Click OK.

To analyze pumping tests using large-diameter well solutions, you must enter valuesfor the wellbore radius and casing radius of the pumping well(s). If the values ofeither of these two variables is 0.0, AQTESOLV for Windows assumes the pumpingwell radius is infinitesimal; if you enter 0.0 for either value, AQTESOLV forWindows will not allow you to select any of the large-diameter well solutionscontained in the program.


Save Data Set


1. Enter MOENCHL1.AQT for the file name.






1. Choose the Leaky Moench (1985) Case 1 solution.

2. Click OK.

After you have selected the Moench solution for a pumping test in a leaky aquifer,AQTESOLV for Windows updates the window by plotting the data on doublelogarithmic axes, superimposing two Moench type curves on the plot, anddisplaying values of transmissivity (T), storage coefficient (S) and leakageparameters (1/B and beta/r), wellbore skin (Sw) and wellbore radius (Rw) in thelegend.

AQTESOLV for Windows displays two type curves, one for each observation well,because the leakage parameters (r/B and beta) in the Moench solution are a functionof the radial distance, r, between the pumping and observation wells. Theparameters displayed (1/B and beta/r) are independent of r.




2. Enter a value of 0.00001 for Rw and set Estimation to Inactive.

3. Click OK.



Choose Automatic... from the Match menu to perform automatic matching usingthe Moench type curve solution.




The plot shown in the active window displays the values of transmissivity(T=347.5), storage coefficient (S=0.0001704) and leakage parameters(1/B=0.001683 and beta/r=0.0008894) determined by automatic estimation.

Save Data Set

Choose Save from the File menu to save your work in the MOENCHL1.AQTdata set.

Neuman-Witherspoon (1969) Solution for aPumping Test in a Leaky AquiferNeuman and Witherspoon (1969) derived an analytical solution for the problem offlow to a well in a confined infinite radial system consisting of two aquifersseparated by an aquitard. The well completely penetrates only one of the aquifers.The solution considers storage in the aquitard and drawdown in the unpumpedaquifer.

The following equation predicts drawdown in the pumped aquifer:

[ ] [ ] [ ] [ ] ∫∞

− ω−+ω+−π

=0

2010ty

ydy

)y(J)y(G1)y(J)y(G1)e1(T4

Qs 1D

where:

211

4111D1D )4/()B/r(tt β=

'ji

'jij bT/KrB/r =

sii'sj

'jiij SK/SKb4/r=β

)y(F/)y(M)y(G =

[ ]

[ ])y(F)y(N21

)y(

)y(F)y(N2

1)y(

22

21

−=ω

+=ω


2

211122

ysin

y)B/r)(B/r(2)y(M)y(F

+=

ycotyB

r

B

ry

)4(

)B/r(

)4(

)B/r()y(M

2

21

2

11

22

21

421

211

411

−

−

β

−β

=

ycotyBr

Br

y)4()B/r(

)4()B/r(

)y(N2

21

2

11

22

21

421

211

411

+

−

β

+β

=


AQTESOLV for Windows allows you to analyze both constant- and variable-ratepumping tests using the Neuman-Witherspoon solution. For tests with a variabledischarge rate, the program uses the principle of superposition to computedrawdown in the aquifer. For more information concerning the application of theprinciple of superposition in variable-rate pumping tests, refer to the "Theis (1935)Solution for a Pumping Test in a Confined Aquifer" on page 50.

Use the Neuman-Witherspoon solution to estimate values of transmissivity, storagecoefficient, r/B, βbeta and rwwell radius (or 1/B and β/rbeta/r for a data setcontaining more than one pair of pumping and observation wells) in a leaky aquiferwith storage in the aquitard(s).

aquiclude

aquitardK',S'

aquiferT,S,Kz/Kr

Q

b


after pumping


r1

r2

unpumped aquifer

b'

Assumptions


• aquifers are homogeneous, isotropic and of uniform thickness









• confining bed has infinite areal extent, uniform vertical hydraulicconductivity and storage coefficient, and uniform thickness

• flow in the aquitard is vertical

Data Requirements


• pumping rate(s)


Solution Options




Reference

Neuman, S.P. and P.A. Witherspoon, 1969. Theory of flow in a confinedtwo aquifer system, Water Resources Research, vol. 5, no. 4, pp. 803-816.


AQTESOLV for Windows provides a suite of tools for visual curve matching withthe Neuman-Witherspoon solution.

1. Choose Visual from the Match menu to perform visual curvematching.

2. Select values of r/B and βbeta from the Family and Curve lists on thetoolbar.

3. Choose Toolbox… from the Match menu and click the Options tabto select visual curve matching options. Use Match early data(Type A) to match the properties of the pumped aquifer (T and S).Match late data (Type B) lets you match the unpumped aquiferproperties (T' and S'). Check Active type curves to use activeinstead of static type curves.


4. Choose Toolbox… from the Match menu and click the Tweak tab.Check Apply changes automatically to move the type curve whileyou adjust individual parameters.

Tutorial

In this tutorial, you will perform sensitivity analysis with the Neuman-Witherspoonsolution to evaluate the effect(s) of unpumped aquifer properties on drawdown inthe pumped aquifer using the constant rate pumping test data set created and savedin the tutorial for the Moench leaky aquifer solution.

Open Data Set

Choose Open... from the File menu to open a data set stored on disk. You willopen the data set created and saved in the tutorial for the Moench (1985) solution.

1. Enter MOENCHL1.AQT for the name of the data set.




Choose Neuman-Witherspoon Solution


1. Choose the Leaky Neuman-Witherspoon (1969) solution.

2. Click OK.

After you have selected the Neuman-Witherspoon solution for a pumping test in aleaky aquifer, AQTESOLV for Windows updates the window by plotting the dataon double logarithmic axes, superimposing two Neuman-Witherspoon type curveson the plot, and displaying in the legend values of transmissivity (T) and storagecoefficient (S) for the pumped aquifer, leakage parameters (1/B and βbeta/r), andtransmissivity (T') and storage coefficient (S') for the unpumped aquifer.

AQTESOLV for Windows displays two type curves, one for each observation well,because the leakage parameters (r/B and βbeta) in the Neuman-Witherspoonsolution are each a function of the radial distance, r, between the pumping andobservation wells. The parameters displayed (1/B and βbeta/r) is independent of r.

Change Format of X Axis

Choose Format… from the View menu and click the X Axis tab to format the xaxis.

1. Change the Maximum value for the axis to 100000.

2. Click OK.

Perform Sensitivity Analysis with Neuman-Witherspoon

Choose Toolbox… from the Match menu and click the Tweak tab to performsensitivity analysis using the Neuman-Witherspoon solution.

1. From the Parameter list, choose T' (transmissivity in the unpumpedaquifer) as the parameter that you want to tweak.


2. Click the arrow buttons or the scroll bar to tweak the value of theparameter. Check Apply changes automatically to update theplot while you change the parameter.

3. For increasing values of T', drawdown in the pumped aquifer asshown by the type curve approaches a constant value at large values oftime. You can experiment with other parameters to see their effect onthe solution.

4. Click OK.

Save Data Set

Choose Save As... from the File menu to save your work in a new data set.

1. Enter NEUMANL1.AQT for the file name.


Fractured Aquifer SolutionsChoose Solution... from the Match menu to choose a solution for analyzingpumping tests in fractured aquifers.

Solutions for Pumping Tests in Fractured Aquifers

1. Moench (1984) type curve solution for a double-porosity fissuredaquifer with slab-shaped matrix blocks

2. Moench (1984) type curve solution for a double-porosity fissuredaquifer with spherical shaped matrix blocks

3. Gringarten-Witherspoon (1972) type curve solution for a fracturedaquifer with a plane vertical fracture

4. Gringarten-Ramey (1974) type curve solution for a fractured aquiferwith a plane horizontal fracture

No solutions are currently available in AQTESOLV for Windows for analyzing slugtests in a fractured aquifer.

Moench (1984) Solution for a Pumping Test in aFractured Aquifer with Slab-Shaped BlocksMoench (1984) derived an analytical solution for predicting water-leveldisplacements in response to pumping in a fractured aquifer assuming a double-porosity model with slab-shaped matrix blocks with fracture skin and wellbore skin.


hK x xS K x


w

D w

=+

+ +2 0 1

0 1 1

[ ( ) ( )]

[ ( ) ( )] ( )

The follow equation is the Laplace transform solution for dimensionless drawdownin an observation well:


hK r x


D

D w

=+ +2 0

0 1 1

( )

[ ( ) ( )] ( )

x p q D= +( ) /1 2

qm m

S m mDf

=+γ 2

1

tanh( )

tanh( )

mp

=( ) /σ

γ

1 2

γ =′

′

r

b

K

Kw

1 2/

σ =′S

Ss

s

rr

rDw

=

SK b

K bfs

s

=′

′

Wr

r S HDc

w s

=π

π

2

22




aquiclude

aquiclude

aquiferK,Ss,K',Ss',Sf

Q

H


after pumping


r1

r2

2rc

2rw,Sw

Assumptions




• pumping and observation wells are fully penetrating

• fractured aquifer represented by double porosity system consisting oflow-permeability, primary porosity blocks and high-permeability,secondary porosity fissures

• matrix consists of slab-shaped blocks



Data Requirements


• pumping rate(s)




• thickness of slab-shaped blocks

Solution Options






Reference

Moench, A.F., 1984. Double-porosity models for a fissured groundwaterreservoir with fracture skin, Water Resources Research, vol. 20, no. 7,pp. 831-846.


AQTESOLV for Windows provides a suite of tools for visual curve matching withthe Moench solution for fractured aquifers.


2. Select values of Sw from the Family and Curve lists on the toolbar.

3. Choose Toolbox… from the Match menu and click the Options tabto select visual curve matching options. Use Match early data(Type A) to match the properties of the fractures (K and Ss). Matchlate data (Type B) lets you match the matrix properties (K' and Ss').Check Active type curves to use active instead of static type curves.


Tutorial

In this tutorial, you will use the Moench type curve solution for fractured aquifers tocreate and analyze a constant-rate pumping test. This tutorial shows you how to useautomatic curve matching to match the Moench type curve to drawdown datameasured during a pumping test.

Open a New Data Set




1. Select m (meters) for Length, min (minutes) for Time, L/sec (liters-per-second) for Pumping Rate and m/sec (meters/second) for Hyd.Conductivity.

2. Click OK.


1. In the Title tab, enter Nevada Test Site for the Title.

2. Click OK.




2. In the Double Porosity tab, enter 80.0 for the Thickness of SlabBlocks.

3. Click OK.


1. In the General tab, enter UE-25b#1 for the Pumping Well Name.

2. In the Construction tab, enter 0.11 for the Wellbore Radius.

3. Enter 0.11 for the Casing Radius.

4. In the Rates tab, enter values of 0.0 and 35.8 for time and rate,respectively, where time is in minutes and rate is in liters-per-second.

5. Click OK.


1. In the General tab, enter UE-25a#1 for the Observation WellName.


3. In the Observations tab, click Import to import observation wellmeasurements from a delimited text file using the Observation DataImport Wizard. In Step 1 of the Import Wizard, enterUE25A1.DAT for the name of the import file. The file UE25A1.DATcontains time and displacement data arranged in two columnsseparated by a tab delimiter. Click Next.



6. After AQTESOLV for Windows has finished importing the data, amessage box displays the number of observations imported from thefile. Click the OK button to close the message box.

7. Click Select All to select all of the observations in the spreadsheet.

8. Click Math to transform the selected data.

9. Select Weights for the Data, Replace for the Operation and 10.0 forthe Constant to replace all measurement weights.

10. Click OK. Click Yes to confirm the transformation.

11. Click OK.

Choose Obs. Well>Add... from the Edit menu to add observation data for thepumping well.

1. In the General tab, enter UE-25b#1 for the Observation WellName.

2. In the Observations tab, click Import to import observation wellmeasurements from a delimited text file using the Observation Data


Import Wizard. In Step 1 of the Import Wizard, enterUE25B1.DAT for the name of the import file. The file UE25B1.DATcontains time and displacement data arranged in two columnsseparated by a tab delimiter. Click Next.



5. After AQTESOLV for Windows has finished importing the data, amessage box displays the number of observations imported from thefile. Click the OK button to close the message box.

6. Click OK.


Save Data Set


1. Enter MOENCHF1.AQT for the file name.





Change the aquifer model and solution by choosing Solution... from the Matchmenu to choose a solution for analyzing a pumping test in a fractured aquifer.

1. Choose the Fractured Moench (1984) w/ slab-shaped blockssolution.

2. Click OK.

After you have selected the Moench solution for a pumping test in a fracturedaquifer, AQTESOLV for Windows updates the window by plotting the data ondouble logarithmic axes, superimposing Moench type curves on the plot, anddisplaying values of fracture hydraulic conductivity (K), fracture specific storage(Ss), matrix hydraulic conductivity (K'), matrix specific storage (Ss'), wellbore skin(Sw) and fracture skin (Sf) in the legend.

Due to the large number of parameters in the Moench fractured aquifer solution, itis not practical to develop type curves for traditional visual analysis. Therefore,AQTESOLV for Windows provides you with the ability to match the Moenchsolution to your data by manually changing values of the six parameters in thesolution until you achieve a satisfactory match.



Choose Composite from the View menu to display a composite plot ofdisplacement vs. time/radius squared in the active window. The window displays aplot of the observation well data on semi-log axes.



1. Enter a value of 0.00005 for K.

2. Enter a value of 1.0E-6 for Ss.

3. Enter a value of 1.0E-6 for K'.

4. Enter a value of 0.0005 for Ss'.


6. Enter a value of 1.0 for Sf and set Estimation to Inactive.

7. Click OK.


Choose Automatic... from the Match menu to perform automatic matching usingthe Moench type curve solution.




The plot shown in the active window displays the values of fracture hydraulicconductivity (K=1.083E-05), fracture specific storage (Ss=1.794E-06), matrixhydraulic conductivity (K'=2.235E-06) and matrix specific storage (Ss'=0.0004165)determined by automatic estimation.

Save Data Set

Choose Save from the File menu to save your work in the MOENCHF1.AQTdata set.

Moench (1984) Solution for a Pumping Test in aFractured Aquifer with Spherical Shaped BlocksMoench (1984) derived an analytical solution for predicting water-leveldisplacements in response to pumping in a fractured aquifer assuming a double-porosity model with spherical shaped matrix blocks with fracture skin and wellboreskin.



hK x xS K x


w

D w

=+

+ +2 0 1

0 1 1

[ ( ) ( )]

[ ( ) ( )] ( )

The following equation is the Laplace transform solution for dimensionlessdrawdown in an observation well:

hK r x


D

D w

=+ +2 0

0 1 1

( )

[ ( ) ( )] ( )

x p q D= +( ) /1 2

qm m

S m mDf

=−

+ −3 1

1 1

2γ [ coth( ) ]

[ coth( ) ]

mp

=( ) /σ

γ

1 2

γ =′

′

r

b

K

Kw

1 2/

σ =′S

Ss

s

rr

rDw

=

SK b

K bfs

s

=′

′

Wr

r S HDc

w s

=π

π

2

22




aquiclude

aquiclude

aquiferK,Ss,K',Ss',Sf

Q

H

s1 s2



r1

r2

2rc

2rw,Sw

Assumptions





• fractured aquifer represented by double porosity system consisting oflow-permeability, primary porosity blocks and high-permeability,secondary porosity fissures

• matrix consists of spherical blocks



Data Requirements


• pumping rate(s)




• diameter of spherical shaped blocks

Solution Options






Reference

Moench, A.F., 1984. Double-porosity models for a fissured groundwaterreservoir with fracture skin, Water Resources Research, vol. 20, no. 7,pp. 831-846.







Tutorial

Perform the tutorial for the Moench (1984) solution for apumping test in a fractured aquifer with slab-shaped matrixblocks (see "Visual Curve Matching






Tutorial" on page 124) to learn how to use this solution.


Gringarten-Witherspoon (1972) Solution for aPumping Test in a Fractured Aquifer with a PlaneVertical FractureGringarten and Witherspoon (1972) and Gringarten, Ramey and Raghavan (1974)presented an analytical solution for flow to a well in a confined infinite radialsystem intersecting a single uniform-flux plane vertical fracture. The solutionassumes the well fully penetrates the aquifer and bisects the fracture.

The following equation predicts drawdown in the aquifer:

ττ

τ+

+τ

−ππ

= τ−

∫d

e2

x1erf

2

x1erf

2TT4

Qs y

x2DD

T

T

4

yt

0

DD

yx

where:

2f

xD Sx

tTt =

fD x

xx =

fD x

yy =

In this solution, the vertical fracture parallels the x axis of the coordinate systemand has a length of Lf (=2xf).

AQTESOLV for Windows allows you to analyze both constant- and variable-ratepumping tests using the Gringarten-Witherspoon solution. For tests with a variabledischarge rate, the program uses the principle of superposition to computedrawdown in the aquifer. For more information concerning the application of theprinciple of superposition in variable-rate pumping tests, refer to the "Theis (1935)Solution for a Pumping Test in a Confined Aquifer" on page 50.



aquiclude

aquiclude

aquiferKx,Ss,Ky/Kx

Q

b

s1



r1

xfverticalfracture

Assumptions





• fractured aquifer represented by anisotropic system with a single planevertical fracture




Data Requirements


• pumping rate(s)



• length of vertical fracture

Solution Options





Reference

Gringarten, A.C. and P.A. Witherspoon, 1972. A method of analyzingpump test data from fractured aquifers, Int. Soc. Rock Mechanics andInt. Assoc. Eng. Geol., Proc. Symp. Rock Mechanics, Stuttgart, vol. 3-B, pp. 1-9.

Tutorial

In this tutorial, you will use automatic curve matching and the Gringarten-Witherspoon type curve solution for fractured aquifers to match drawdown datameasured during a constant-rate pumping test.

Open a New Data Set





2. Click OK.


1. In the Title tab, enter Vertical Fracture with Uniform Flux for theTitle.

2. Click OK.



2. In the Single Fracture tab, enter 2.0 for the Length of theVertical Fracture.

3. Click OK.


1. In the Rates tab, enter values of 0.0 and 3.14159e-6 for time andrate, respectively, where time is in minutes and rate is in cubic feet perminute.

2. Click OK.


1. In the General tab, enter r'=0.2 for the Observation Well Name.

2. Enter values of 0.2 for the X-Coordinate and 0.0 for the Y-Coordinate locations of the well.

3. In the Observations tab, enter the following measurements from thekeyborad (set all weights equal to 1.0):


Time Displacement0.002 0.1584980.008 0.3170310.02 0.501290.08 0.9992570.2 1.539350.8 2.655862 3.507528 4.8598320 5.7691880 7.152200 8.06761800 9.453592000 10.36988000 11.756120000 12.672480000 14.0588200000 14.9751800000 16.3615




Save Data Set


1. Enter GRINV1.AQT for the file name.




Choose Gringarten-Witherspoon Solution


1. Choose the Fractured Gringarten-Witherspoon (1972) w/ verticalfracture solution.

2. Click OK.

After you have selected the Gringarten-Witherspoon solution for a pumping test in afractured aquifer, AQTESOLV for Windows updates the window by superimposinga Gringarten-Witherspoon type curve on the plot and displaying values of hydraulic


conductivity (Kx), specific storage (Ss), anisotropy ration (Ky/Kx) and fracturelength (Lf) in the legend.

Perform Automatic Matching with Gringarten-Witherspoon

Choose Automatic... from the Match menu to perform automatic matching usingthe Gringarten-Witherspoon type curve solution.

1. In the Estimation tab, change the Maximum number of iterations to100.

2. In the Parameters tab, set Estimation of Ky/Kx to Inactive.




The plot shown in the active window displays the values of hydraulic conductivity(Kx=2.5E-7), specific storage (Ss=2.5E-7), anisotropy ratio (Ky/Kx=1) and fracturelength (Lf=2) determined by automatic estimation.

Change View to Linear Flow Plot

Choose Linear Flow from the View menu to display a linear flow plot in theactive window.

1. Early-time data exhibiting a unit slope on this plot are indicative oflinear flow conditions to a single fracture with infinite conductivity oruniform flux along the fracture.

2. Choose Visual from the Match menu to match a line with unit slopeto the early-time data.

3. Click a point over the early-time data where you want to draw a linewith unit slope.

Save Data Set

Choose Save from the File menu to save your work in the GRINV1.AQT data set.

Gringarten-Ramey (1974) Solution for a PumpingTest in a Fractured Aquifer with a Plane HorizontalFractureGringarten and Ramey (1974) derived an analytical solution for flow to a well in aconfined infinite radial system intersecting a single plane horizontal fracture. Thesolution assumes uniform flux along the fracture.

The following equation predicts drawdown in a piezometer:

∫ ττ

⋅π

=Dt

0Dzr

dZP

H

2

KK4

Qs


where:

2fs

rD rS

tKt =

∫ υυ

τυ

= τυ

−τ

−1

0

4D0

4

r

de2

rIeP

22D

H

zncos

H

zncose21Z f

1n

H

n2D

22

ππ+= ∑∞

=

τπ−

zrf

D K/Kr

HH =

fD r

rr =

The Gringarten-Ramey solution only supports piezometers, not observation wells.

AQTESOLV for Windows allows you to analyze both constant- and variable-ratepumping tests using the Gringarten-Ramey solution. For tests with a variabledischarge rate, the program uses the principle of superposition to computedrawdown in the aquifer. For more information concerning the application of theprinciple of superposition in variable-rate pumping tests, refer to the "Theis (1935)Solution for a Pumping Test in a Confined Aquifer" on page 50.


aquiclude

aquiclude

aquiferKr,Kz,Ss

Q

H

spotentiometric surface

after pumping


r

zrf

zf

Assumptions






• fractured aquifer represented by anisotropic system with a single planehorizontal fracture




Data Requirements


• pumping rate(s)

• piezometer measurements (time and displacement)


• radius of horizontal fracture

Solution Options




Reference

Gringarten, A.C. and H.J. Ramey, 1974. Unsteady state pressuredistributions created by a well with a single horizontal fracture, partialpenetration or restricted entry, Soc. Petrol. Engrs. J., pp. 413-426.

Tutorial

In this tutorial, you will use automatic curve matching and the Gringarten-Rameytype curve solution for fractured aquifers to match drawdown data measured in thepumped well during a constant-rate pumping test.

Open a New Data Set





2. Click OK.



1. In the Title tab, enter Horizontal Fracture with Uniform Flux forthe Title.

2. Click OK.



2. In the Single Fracture tab, enter 1.0 for the Radius of theHorizontal Fracture and 0.5 for the Depth of the HorizontalFracture.

3. Click OK.


1. In the General tab, enter values of 0.0 for the X-Coordinate and 0.0for the Y-Coordinate locations of the well.

2. In the Construction tab, enter 0.001 and 0.001 for the CasingRadius and Wellbore Radius, respectively. For this solution,which assumes an infinitesimal well radius, we enter small values forthe casing and wellbore radius to calculate displacement in thepumped well.

3. In the Rates tab, enter values of 0.0 and 3.14159e-6 for time and rate,respectively, where time is in minutes and rate is in cubic feet perminute.

4. Click OK.

Choose Obs. Well>Edit... from the Edit menu to edit observation data for thepumped well.

1. In the General tab, enter the same coordinate values as the pumpedwell, i.e., 0.0 for the X-Coordinate and 0.0 for the Y-Coordinate.

2. In the Construction tab, select the Piezometer option and enter apiezometer depth z of 0.5.

3. In the Observations tab, click the Import button to importobservation well measurements from a delimited text file using theObservation Data Import Wizard. In Step 1 of the ImportWizard, enter GRINH1.DAT for the name of the import file. Thefile GRINH1.DAT contains time and displacement data arranged intwo columns separated by a tab delimiter. Click Next.





7. Click OK.


Save Data Set


1. Enter GRINH1.AQT for the file name.




Choose Gringarten-Ramey Solution


1. Choose the Fractured Gringarten-Ramey (1974) w/ horizontalfracture solution.

2. Click OK.

After you have selected the Gringarten-Ramey solution for a pumping test in afractured aquifer, AQTESOLV for Windows updates the window by superimposinga Gringarten-Ramey type curve on the plot and displaying values of hydraulicconductivity (Kr), specific storage (Ss), anisotropy ration (Kz/Kr) and fractureradius (Rf) in the legend.

Perform Automatic Matching with Gringarten-Ramey

Choose Automatic... from the Match menu to perform automatic matching usingthe Gringarten-Ramey type curve solution.

1. In the Estimation tab, change the Maximum number of iterations to100.

2. In the Parameters tab, change the Minimum and Maximumconstraints for Ss to 1.0e-10 and 1.0e-4, respectively.

3. Set Estimation of Kz/Kr to Inactive.





The plot shown in the active window displays the values of hydraulic conductivity(Kr=2.499E-7), specific storage (Ss=2.499E-7), anisotropy ratio (Kz/Kr=1) andfracture radius (Rf=1) determined by automatic estimation.

Save Data Set

Choose Save from the File menu to save your work in the GRINH1.AQT data set.


List of Symbolsa = constant defining variation in thickness of wedge - shaped aquifer [Lb = thickness of aquifer [L]b = thickness of aquifer at pumping well [L]b = thickness of fracture skin [L]b' = thickness of aquitard overlying aquifer in leaky system or one - half thickness of blocks in fissured system [L]b" = thickness of aquitard underlying aquifer [L]B = leakage factor [L ]B(r , t) = linear head - loss coefficient [T / L ]B (r , t) = linear aquifer - loss coefficient [T / L ]B = linear well - loss coefficient [T / L ]C = nonlinear well - loss coefficient [T / L ]d = vertical distance between top of perforations in pumping well and initial position of

-1

0

s

-1

e2

1 w2

22

5

D

]

2

water table divided by initial saturated thickness of aquifer [L]H = static height of water in well measured from base of well to static water level [L]H = initial displacement in well due to slug injection or extraction [L]J = Bessel function of first kind, zero orderJ = Bessel function of first kind, first orderK = hydraulic conductivity of fractures in fissured system [L / T]K = modified Bessel function of second kind, zero orderK = modified Bessel function of second kind, first orderK = radial (horizontal) hydraulic conductivity of aquifer [L / T]K = hydraulic conductivity of fracture skin [L / T]K = vertical hydraulic conductivity of aquifer [L / T]K' = hydraulic conductivity of aquitard overlying aqui

0

0

1

0

1

r

s

z

fer in leaky system or block system in fissured system [L / T]K" = hydraulic conductivity of aquitard underlying aquifer [L / T]l = vertical distance between bottom of perforations in pumping well and initial position of water table divided by initial saturated thickness of aquifer [L]L = length of well screen [L]p = Laplace transform variableP = order of nonlinear well - losses [dimensionless]Q = pumping rate [Lr = radial distance [L]r = well casing radius [L]r = equivalent radius over which head loss occurs [L]r = well radius [L]

D

3

c

e

w

/ ]T


s = displacement [L]s = displacement at time t [L]s = initial displacement in well [L]S = coefficient of storage of aquifer [dimensionless]S = fracture skin [dimensionless]S = specific storage of aquifer or fractures in fissured system [L ]S = specific storage of aquitard in leaky system or blocks in fissured system [L ]S = wellbore skin [dimensionless]S = specific yield of aquifer [dimensionless]S' = coefficient of storage of aquitard overlying aquifer [dimensionless]S" = coefficient of storage of aquitard underlying aquifer [dimensionless]t = time since pumping began [T]t = dimensionless time with respect to S equal to Tt / Sr [T]t = dimensionless time

t

0

f-1

s-1

w

y

s s2

y

s

′

with respect to S equal to Tt / S r [T]T = transmissivity [L

= x - coordinate location of pumping well [L]= variable of integration

y = y- coordinate location of pumping well [L]Y = Bessel function of second kind, zero orderY = Bessel function of the second kind, first orderz = vertical distance above bottom of aquifer divided by initial saturated thickness of aquifer [L]z = vertical distance from bottom of aquifer to bottom of observation well perforations divided by initial saturated thicknessof aquifer [L]z = vertical distance from bottom of aquifer to top of observation well perforations divided by initial saturated thickness of aquifer [L]

y y2

2

0

0

1

D

1D

2D

/ ]Txy

0

AQTESOLV for Windows User's Guide Estimating Aquifer Coefficients •• 143

Estimating Aquifer Coefficients

OverviewThe Match menu provides two methods for estimating the hydraulic properties ofaquifers from pumping tests and slug tests. Each method matches analyticalsolutions to data measured during an aquifer test.

• Visual matching is analogous to traditional graphical methods thatrely on manually fitting type curves or straight lines to determineaquifer parameters.

• Automatic matching uses nonlinear least-squares parameterestimation to automatically fit analytical solutions to aquifer test data.

Whichever method you choose, AQTESOLV for Windows allows you to visualizethe results of your analysis by plotting the solution and data. In addition, theautomatic curve matching technique provides statistical measures of the "fit" of thesolution to the data.

Automatic Curve MatchingClick on the toolbar toperform automatic curvematching

Choose Automatic... from the Match menu to open a dialog for estimatinghydraulic properties using automatic curve matching. The automatic parameterestimation procedure systematically adjusts the values of hydraulic properties toachieve the best statistical match between a solution (type curve) and the test data.

The automatic curve matching feature in AQTESOLV for Windows uses anonlinear least squares procedure to match a type curve or straight-line solution toyour data. The iterative procedure minimizes the “residuals” or errors between thecomputed and the observed drawdown or displacement.

Performing Automatic Estimation

1. Choose Automatic… from the Match menu.

2. Click Estimate to start automatic estimation.

3. A window appears that displays the progress of automaticestimation. Click Abort to halt the iterations.

4. When automatic estimation is complete, a message appears withconvergence information and residual statistics.

144 •• Estimating Aquifer Coefficients AQTESOLV for Windows User's Guide

TIPS

1. Prior to attempting automatic curve matching, perform visualcurve matching to improve the initial estimates of the aquiferproperties.

2. Generally, you should maintain the tolerances for RSS andparameter change at small values (e.g., 1x10-101.0E-10); however,for certain solutions, changing the maximum number of iterationsis helpful. For example, if automatic curve matching convergesslowly, try increasing the maximum number of iterations.

TIPS FOR NEUMAN (1974) SOLUTION

1. Perform visual curve matching with Quick Neuman to determineinitial estimates of hydraulic properties.

2. Perform automatic curve matching with Quick Neuman to refinethe parameter estimates.

3. In most cases, the parameter estimates determined using QuickNeuman are sufficiently accurate; however, if desired, you canfurther refine the parameter estimates by changing the solutionmethod to Neuman (1974) and performing automatic estimation.

Estimation Tab (Match>Automatic)Choose Automatic… from the Match menu and click the Estimation tab to setoptions controlling parameter estimation.

Iterations

1. Enter the Maximum number of iterations to perform usingautomatic curve matching.

2. The automatic curve matching procedure terminates when themaximum number of iterations is reached (or when convergencecriteria are met).

Convergence Criteria

1. Enter the RSS (residual sum of squares) convergence criterion.Automatic curve matching terminates when the residual sum ofsquares reaches this tolerance value.

2. Enter the Parameter Change (in percent) convergencecriterion. Automatic curve matching terminates when themaximum percent change in parameter values reaches thistolerance value.

3. The automatic curve matching procedure terminates when eitherconvergence criterion is met (or when the maximum number ofiterations is reached).

Display Options

1. Check the Intermediate updates box if you want AQTESOLVfor Windows to update the type curve position after eachautomatic curve matching iteration.


2. Check the Activity indicator box if you want AQTESOLV forWindows to display a flashing green lamp while automatic curvematching is in progress.

Parameters Tab (Match>Automatic)Choose Automatic… from the Match menu and click the Parameters tab toenter values, minimum and maximum (lower and upper) bounds, andactive/inactive status for aquifer parameters (see "Parameters Tab(Match>Toolbox)" on page 150).

Options Tab (Match>Automatic)Choose Automatic… from the Match menu and click the Options tab toconfigure options controlling partial penetration and multiple well calculations (see"Options Tab (Match>Toolbox)" on page 151).

How Automatic Curve Matching WorksAQTESOLV for Windows performs nonlinear weighted least-squares parameterestimation (automatic curve matching) using the Gauss-Newton linearizationmethod. To improve the convergence of the method from poor initial guesses forthe unknown parameters, AQTESOLV for Windows includes the Marquardtcorrection factor (Marquardt, 1963).

In the Gauss-Newton method of parameter estimation, the parameter correctionsnecessary to minimize the difference between observed and estimated values of theresponse variable can be expressed as a Taylor series expanded about the currentestimated value as follows:

y yy

bb

y

bb

y

bbi = + + +$

!( )

!( )

∂∂

∂∂

∂∂

∆ ∆ ∆2

22

3

33

2 3K

where:

yy

bbb

i

i

=== −

==

ith observed value of response variableestmate of the ith value of response variableparameter correction, b b

updated estimate of the unknown parametercurrent estimate of the unknown parameter

1 0

$$ $

$

$

∆1

0

The previous equation can be linearized by truncating the Taylor series after thefirst derivative as follows:

y yyb

bi i≈ +$∂∂

∆

Thus, for p unknown parameters, the general linearized equation for computingparameter corrections is written as follows:

y yy

bbi i

i

kk

k

p

≈ +=

∑$∂∂

∆1


The previous equation is written for each observed value of the response variable.The partial derivatives of the response variable with respect to the unknownparameters are known as sensitivity coefficients. The resulting system of linearizedequations is solved iteratively until convergence is obtained. The objective functionfor this minimization problem is the sum of the squared residuals given by thefollowing expression:

RSS y yi ii

n

= −=∑ ( $ )2

1

where n is the total number of observed values of the response variable. In matrixform, the Gauss-Newton method computes parameter correction as follows:

∆ ∆B X X X YT T= −( ) 1

where:

∆

∆

BXXX X

Y

T

T

= ×= ×= ×

= ×= × −

p 1 vector of parameter correctionsn p matrix of sensitivity coefficientsp n transpose of X

p p variance - covariance matrixn 1 vector of residuals (y yi i$ )

To improve the conditioning of the variance-covariance matrix, AQTESOLV forWindows adds the Marquardt correction factor to the previous equation:

∆ ∆B X X I X YT T= + ⋅ −( )λ 1

where:

λ ==

Marquardt correction factoridentity matrixI

The Marquardt correction factor is added when parameter corrections computed bythe Gauss-Newton method fail to reduce the residual sum of squares (RSS).Iterations performed with the Marquardt correction factor start with a sufficientlysmall value of λlambda; larger values of λlambda are added until the RSS isreduced. The parameter estimation algorithm terminates when the RSS isminimized.

Weighted least-squares estimation is accomplished as follows:

∆ ∆B X WX X W YT T= −( ) 1

where:

W = ×= ×

n n nonsingular symmetric matrix obtained from n n diagonal matrix of weights

Tω ωω

Thus, in this implementation of the weighted least-squares algorithm, a largerweight assigned to a measurement results in greater influence by that measurementin the parameter estimation procedure.


Visual Curve MatchingClick on the toolbar toperform visual curvematching

Choose Visual from the Match menu to perform visual curve matching. Byselecting this option, you can interactively match pumping test and slug testsolutions to your data or perform diagnostic analyses to evaluate specific flowconditions and regimes.

With displacement vs. time or composite plots, use the Visual option tomatch pumping test and slug test solutions to aquifer test data.

With diagnostic plots (radial flow, linear flow, bilinear flow or sphericalflow), use the Visual option to identify periods of specific flow conditions such asradial flow, wellbore storage, fracture flow or spherical flow.

AQTESOLV for Windows also provides an option for performing visual curvematching with derivative vs. time plots.

Visual Matching with Aquifer Test SolutionsMatching type curve solutions

1. Choose Visual from the Match menu.

2. Click and hold the left mouse button down within the plot area.

3. Move the mouse to match the type curve to your data. As youmove the type curve, AQTESOLV for Windows automaticallyupdates the plot legend to reflect changes in parameter values.

4. Release the left mouse button when you have finished matchingthe type curve.

Matching straight line solutions

1. Choose Visual from the Match menu.

2. Move the mouse to a point located on the new line you wish tomatch to your data.

3. Click and hold down the left mouse button to anchor the new lineat this point.

4. Move the mouse to match a new straight line to your data. As youmove the mouse, AQTESOLV for Windows drags a straight linebetween the anchor point and the position of the mouse.

5. Release the left mouse button when you have finished matching anew straight line. AQTESOLV for Windows automaticallyupdates the plot legend to reflect changes in parameter values.

Visual Matching with Diagnostic PlotsData exhibiting a unit slope on certain diagnostic plots are indicative of particularflow conditions such as wellbore storage, fracture flow and spherical flow.

Radial flow plots (log-log axes)

1. Early-time data exhibiting a unit slope are indicative ofwellbore storage.


2. Choose Visual from the Match menu to match a line with unitslope to the early-time data.

3. Click a point on the plot where you want to draw the line with afixed unit slope.

Linear flow plots (log-log axes)

1. Early-time data exhibiting a unit slope are indicative of linearflow conditions to a single fracture with infiniteconductivity or uniform flux along the fracture.



Bilinear flow plots (log-log axes)

1. Early-time data exhibiting a unit slope are indicative ofbilinear flow conditions to a single fracture with finiteconductivity.



Spherical flow plots (log-log axes)

1. Early-time data exhibiting a unit slope are indicative ofspherical flow conditions.



Visual Matching with Derivative PlotsPerform visual curve matching with derivative plots using the visual curvematching tools feature.

Derivative vs. time plots

1. Choose Toolbox… from the Match menu and click the Tweaktab.

2. Select an aquifer parameter to adjust from the Parameter list.

3. Change the value of the selected aquifer parameter using thescroll bar control.

4. Click the Apply button to update type curve plots.

5. Check the Apply changes automatically box to update typecurve plots automatically for each change.


Active Type CurvesClick on the toolbar toperform visual curvematching with active typecurves

AQTESOLV for Windows lets you perform visual curve matching with static oractive type curves.

The Active Type Curves feature is an enhanced method of performing visualcurve matching introduced by AQTESOLV for Windows. With active type curves,AQTESOLV for Windows automatically refreshes the complete type curve as youperform visual curve matching.

Select Active Type Curves when matching complicated solutions involving earlyand late responses or pumping tests with variable rates.

Active type curves

1. Choose Toolbox… from the Match menu and click theOptions tab to check the Active type curves box.

2. The Active Curves button on the toolbar toggles the active typecurves feature and simultaneously invokes visual curve matching.

Matching Early/Late DataClick or on the toolbarto perform visual curvematching to early data (TypeA) or late data (Type B)

Certain aquifer test solutions involve aquifer parameters that only affect early andlate data. AQTESOLV for Windows lets you choose the range of data to matchduring visual curve matching.

The Active Type Curves feature is an enhanced method of performing visualcurve matching introduced by AQTESOLV for Windows. With active type curves,AQTESOLV for Windows automatically refreshes the complete type curve as youperform visual curve matching.

For example, the Neuman (1974) solution for a pumping test in an unconfinedaquifer involves matching Type A curves to early data and Type B curves to latedata. The final match of the Type A curve determines the values of T, S and βbetaand the Type B curve determines T, Sy and βbeta.

Match early data

1. Choose Toolbox… from the Match menu and click theOptions tab to select the Match early data (Type A) option.

2. The Match Early Data button on the toolbar toggles the matchearly data (Type A) option and simultaneously invokes visualcurve matching.

Match late data

1. Choose Toolbox… from the Match menu and click theOptions tab to select the Match late data (Type B) option.

2. The Match Late Data button on the toolbar toggles the matchlate data (Type B) option and simultaneously invokes visual curvematching.

Solutions that allow you to perform visual matching to early and late data includethe following:

1. Neuman (1974) pumping test solution for unconfined aquifers,

2. Quick Neuman pumping test solution for unconfined aquifers,


3. Neuman-Witherspoon (1969) pumping test solution for leaky aquifers,

4. Moench (1984) pumping test solution for fractured aquifers with slab-shaped blocks, and

5. Moench (1984) pumping test solution for fractured aquifers withspherical blocks.

Matching Type Curve FamiliesIf type curve families are available for the active solution, you can select the aquiferparameter for the type curve family and its value from Family and Curve lists onthe toolbar.

Selecting New Type Curve From Family

1. Select an aquifer parameter for a type curve family from thoseavailable in the Family list on the toolbar.

2. Select a value for the aquifer parameter from the Curve list onthe toolbar.

3. To change the values shown in the Curve list, chooseOptions… from the View menu and click the Family tab.

4. The controls for the Family and Curve lists appear inactivewhen type curve families are not available for the active solution.

Toolbox for Curve MatchingClick on the toolbar toactivate curve matchingtools and options

Choose Toolbox… from the Match menu to view a suite of curve matching toolsand options. The toolbox allows you to tweak individual aquifer parameters,perform sensitivity analysis, edit parameters and select visual curvematching/solution options.

Tweak Tab (Match>Toolbox)Choose Toolbox… from the Match menu and click the Tweak tab to adjust thevalues of individual aquifer parameters. This tool provides a useful option forvisual curve matching and also for performing sensitivity analysis.

Tweak Parameters

1. Select an aquifer parameter to adjust from the Parameter list.

2. Change the value of the selected aquifer parameter using thescroll bar control.

3. Click the Apply button to update type curve plots.

4. Check the Apply changes automatically box to update typecurve plots automatically for each change.

Parameters Tab (Match>Toolbox)Choose Toolbox… from the Match menu and click the Parameters tab to entervalues, minimum and maximum (lower and upper) bounds, and active/inactivestatus for aquifer parameters.


Parameter Column

1. The Parameter column lists the aquifer parameters estimated forthe active solution.

2. Units for each parameter (if any) are shown with the parametersymbol.

Value Column

1. The Value column contains current estimates of the aquiferparameters in the solution.

2. Enter new values to change the starting guesses used by theautomatic curve matching procedure for each aquifer parameter.

Minimum Column

1. The Minimum column contains the minimum (lower) boundsused to constrain the aquifer parameters during automatic curvematching.

2. Enter new values to change the feasibility ranges for each aquiferparameter. The automatic curve matching procedure constrainsthe estimated value of each aquifer parameter to the feasibilityrange defined by the Minimum and Maximum bounds.

Maximum Column

1. The Maximum column contains the maximum (upper) boundsused to constrain the aquifer parameters during automatic curvematching.

2. Enter new values to change the feasibility ranges for each aquiferparameter. The automatic curve matching procedure constrainsthe estimated value of each aquifer parameter to the feasibilityrange defined by the Minimum and Maximum bounds.

Estimation Column

1. The Estimation column identifies the estimation status (active orinactive) for each aquifer parameter.

2. Choose whether the aquifer parameters are free to change (active)or not (inactive) during automatic curve matching.

Restoring a Set of Parameter Values

1. Click Automatic to set parameter estimates to values determinedmost recently from automatic curve matching.

2. Click Visual to set parameter values to their visual curvematching estimates.

3. Click Current to reset the parameters to their current values.

Options Tab (Match>Toolbox)Choose Toolbox… from the Match menu and click the Options tab to configurevisual matching and solution options.

Visual Matching


1. Check the Active type curves box to perform visual curvematching with active type curves.

2. Select the Match early data (Type A) option to perform visualmatching to early data.

3. Select the Match late data (Type B) option to perform visualmatching to late data.

4. The Match Early Data and Match Late Data buttons on thetoolbar toggle the options for matching early (Type A) or late(Type B) data and simultaneously invoke visual curve matching.

Solution

1. Check the Partial penetration box if you want AQTESOLV forWindows to include partial penetration in the calculations for theactive solution.

This option will appear inactive (grayed out) if all wells in thedata set are fully penetrating or if the active solution does notsupport partial penetration.

2. Check the Multiple wells box if you want AQTESOLV forWindows to include multiple pumping wells (including imagewells) in the calculations for the active solution.

This option will appear inactive (grayed out) if the data set onlyincludes one pumping well or if the active solution does notsupport multiple pumping wells.

3. Select the Normal convergence option for faster computationsor the High convergence option for higher accuracy inresearch applications.

These options will appear inactive (grayed out) if the activesolution method only has one convergence setting.

AQTESOLV for Windows User's Guide Obtaining Output •• 153

Obtaining Output

OverviewAQTESOLV for Windows has many options for obtaining output from the program.First, you can print plots and reports on output devices connected to your computer.Second, you can export data from the program to files for use by other software.Finally, you can copy plots and reports to the clipboard.

Printing OptionsThe File menu provides options for obtaining printer output from AQTESOLV forWindows. The options allow you to print plots and reports, preview the printedappearance of plots and reports prior to printing, and configure a printer connectedto your computer.

PrintClick on the toolbar toopen the Print dialog box

Choose Print... from the File menu to open a dialog box for printing the plot orreport in the active window. Click the Setup... button to select a specific printer.

Print PreviewClick on the toolbar forPrint Preview

Choose Print Preview from the File menu to preview the appearance of a plot orreport prior to printing. While previewing, click the Print... button to print theplot or report or click the Close button to end print preview without printing.

Print SetupChoose Print Setup... from the File menu to open a dialog box for choosing thespecific printer connected to your computer, selecting paper size and orientation,and setting printer options.

Page SetupChoose Page Setup... from the File menu to open a dialog box for configuringthe printing of report headers and footers.

154 •• Obtaining Output AQTESOLV for Windows User's Guide

Margins

Enter values (in inches) for the margins of printed pages of reports andplots.

Headers and Footers

Select these options to show headers and footers displayed on theprinted pages of reports.

Font Rotation

Select this option to display the y-axis plot labels with a rotated font.This option is disabled if the current default printer connected toyour system does not support font rotation.

Troubleshooting

Y-Axis Label Printed Horizontally

If you encounter difficulties printing the y-axis label of a plot, perform each of thefollowing steps in succession to remedy the problem.

1. Check the settings in the Print Setup... menu. Make sure you areusing the correct driver for your printer.

2. If available, select the option to print graphics in raster mode in thePrint Setup... menu.

3. If available, select the option to print True Type fonts as graphics inthe Print Setup... menu.

4. Override font rotation for the y-axis label in the Page Setup... menu.

Plot Legend Exceeds Page Size

If the legend beneath a plot exceeds the page size, choose Plot/Legend... from theFormat menu and perform one or more of the following remedies to decrease thesize of the legend.

1. Click the Font... button to select a smaller font size.

2. In the group of Printer Options, deactivate one or more of the textblocks displayed in the legend (e.g., title, project info, aquifer dataor well data).

Plot or Report Output Is Compressed

If the output for a plot or report appears compressed on the output device, attemptthe following remedies.

1. If available, select the option to print graphics in raster mode in thePrint Setup... menu.

2. If available, select the option to print True Type fonts as graphics inthe Print Setup... menu.

AQTESOLV for Windows User's Guide Obtaining Output •• 155

Export OptionsChoose Export… from the File menu to select options for exporting data. Theseoptions allow you to create files that you can use in other Windows applications.

Export Plot Data1. Choose Export... from the File menu.

2. Select X-Y Plot Data and click OK to export data displayed in theactive view to a file.

3. Enter a file name for the exported data and click OK.

Export Type Curve1. Choose Export... from the File menu.

2. Select Type Curve and click OK to export type curve data displayedin the active view to a file.

3. Enter a file name for the exported type curve and click OK.

Export Windows Metafile1. Choose Export... from the File menu.

2. Select Windows Metafile or Enhanced Metafile and click OK toexport the active plot or report to a file in Windows metafile format.

3. Enter a file name for the metafile and click OK.

Export Grid File1. Choose Export... from the File menu.

2. Select Grid File and click OK to launch the Grid Wizard forpreparing a grid file in Surfer for Windows format.

3. Follow the steps in the Grid Wizard to prepare the grid file andoptionally create and display a contour plot using Surfer for Windows(see "Contour" on page 44).

Clipboard Functions

CopyChoose Copy from the Edit menu to copy the current view (plot or report) to theclipboard in Windows metafile format. Use the Paste command in anotherWindows application to insert AQTESOLV for Windows plots and reports intodifferent documents.

AQTESOLV for Windows User's Guide References •• 157

References

Bouwer, H., 1989. The Bouwer and Rice slug test--an update, Ground Water, vol. 27, no. 3, pp. 304-309.

Bouwer, H. and R.C. Rice, 1976. A slug test method for determining hydraulic conductivity of unconfinedaquifers with completely or partially penetrating wells, Water Resources Research, vol. 12, no. 3, pp.423-428.

Birsoy, Y.K. and W.K. Summers, 1980. Determination of aquifer parameters from step tests and intermittentpumping data, Ground Water, vol. 18, pp. 137-146.

Cooper, H.H. and C.E. Jacob, 1946. A generalized graphical method for evaluating formation constants andsummarizing well field history, Am. Geophys. Union Trans., vol. 27, pp. 526-534.

Cooper, H.H., J.D. Bredehoeft and S.S. Papadopulos, 1967. Response of a finite-diameter well to aninstantaneous charge of water, Water Resources Research, vol. 3, no. 1, pp. 263-269.

Gringarten, A.C. and H.J. Ramey, 1974. Unsteady state pressure distributions created by a well with a singlehorizontal fracture, partial penetration or restricted entry, Soc. Petrol. Engrs. J., pp. 413-426.

Gringarten, A.C. and P.A. Witherspoon, 1972. A method of analyzing pump test data from fractured aquifers,Int. Soc. Rock Mechanics and Int. Assoc. Eng. Geol., Proc. Symp. Rock Mechanics, Stuttgart, vol. 3-B, pp. 1-9.

Hantush, M.S., 1960. Modification of the theory of leaky aquifers, Jour. of Geophys. Res., vol. 65, no. 11, pp.3713-3725.

Hantush, M.S., 1961a. Drawdown around a partially penetrating well, Jour. of the Hyd. Div., Proc. of the Am.Soc. of Civil Eng., vol. 87, no. HY4, pp. 83-98.

Hantush, M.S., 1961b. Aquifer tests on partially penetrating wells, Jour. of the Hyd. Div., Proc. of the Am.Soc. of Civil Eng., vol. 87, no. HY5, pp. 171-194.

Hantush, M.S., 1962. Flow of ground water in sands of nonuniform thickness; 3. Flow to wells, Jour.Geophys. Res., vol. 67, no. 4, pp. 1527-1534.

Hantush, M.S. and C.E. Jacob, 1955. Non-steady radial flow in an infinite leaky aquifer, Am. Geophys. UnionTrans., vol. 36, pp. 95-100.

Hvorslev, M.J., 1951. Time Lag and Soil Permeability in Ground-Water Observations, Bull. No. 36,Waterways Exper. Sta. Corps of Engrs, U.S. Army, Vicksburg, Mississippi, pp. 1-50.

158 •• References AQTESOLV for Windows User's Guide

Hyder, Z, J.J. Butler, Jr., C.D. McElwee and W. Liu, 1994. Slug tests in partially penetrating wells, WaterResources Research, vol. 30, no. 11, pp. 2945-2957.

Jacob, C.E., 1947. Drawdown test to determine effective radius of artesian well, Trans. Amer. Soc. of CivilEngrs., vol. 112, paper 2321, pp. 1047-1064.

Kruseman, G.P. and N.A. DeRidder, 1990. Analysis and Evaluation of Pumping Test Data (2nd ed.),Publication 47, Intern. Inst. for Land Reclamation and Improvement, Wageningen, The Netherlands,370p.

Marquardt, D.W., 1963. An algorithm for least-squares estimation of nonlinear parameters, Journ. Soc.Indust. Appl. Math., vol. 11, no. 2, pp. 431-441.

Moench, A.F., 1984. Double-porosity models for a fissured groundwater reservoir with fracture skin, WaterResources Research, vol. 20, no. 7, pp. 831-846.

Moench, A.F., 1985. Transient flow to a large-diameter well in an aquifer with storative semiconfining layers,Water Resources Research, vol. 21, no. 8, pp. 1121-1131.

Moench, A.F., 1993. Computation of type curves for flow to partially penetrating wells in water-tableaquifers, Ground Water, vol. 31, no. 6, pp. 966-971.

Moench, A.F., 1996. Flow to a well in a water-table aquifer: an improved Laplace transform solution,Ground Water, vol. 34, no. 4, pp. 593-596.

Moench, A.F., 1997. Flow to a well of finite diameter in a homogeneous, anisotropic water table aquifer,Water Resources Research, vol. 33, no. 6, pp. 1397-1407.

Murdoch, L.C., 1994. Transient analyses of an interceptor trench, Water Resources Research, vol. 30, no. 11,pp. 3023-3031.

Neuman, S.P., 1974. Effect of partial penetration on flow in unconfined aquifers considering delayed gravityresponse, Water Resources Research, vol. 10, no. 2, pp. 303-312.

Neuman, S.P. and P.A. Witherspoon, 1969. Theory of flow in a confined two aquifer system, Water ResourcesResearch, vol. 5, no. 4, pp. 803-816.

Papadopulos, I.S. and H.H. Cooper, 1967. Drawdown in a well of large diameter, Water Resources Research,vol. 3, pp. 241-244.

Ramey, H.J., 1982. Well-loss function and the skin effect: A review. In: Narasimhan, T.N. (ed.) Recenttrends in hydrogeology, Geol. Soc. Am., special paper 189, pp. 265-271.

Rorabaugh, M.J., 1953. Graphical and theoretical analysis of step-drawdown test of artesian well, Proc. Amer.Soc. Civil Engrs., vol. 79, separate no. 362, 23 pp.

Spane, F.A., Jr., and S.K. Wurstner, 1993. DERIV: A computer program for calculating pressure derivativesfor use in hydraulic test analysis, Ground Water, vol. 31, no. 5, pp. 814-822.

Streltsova, T.D., 1974. Drawdown in compressible unconfined aquifer, Jour. of the Hyd. Div., Proc. of theAm. Soc. of Civil Eng., vol. 100, no. HY11, pp. 1601-1616.

Streltsova, T.D., 1988. Well Testing in Heterogeneous Formations, John Wiley & Sons, New York, 413p.

AQTESOLV for Windows User's Guide References •• 159

Theis, C.V., 1935. The relation between the lowering of the piezometric surface and the rate and duration ofdischarge of a well using groundwater storage, Am. Geophys. Union Trans., vol. 16, pp. 519-524.

Zlotnik, V., 1994. Interpretation of slug and packer tests in anisotropic aquifers, Ground Water, vol. 32, no. 5,pp. 761-766.

AQTESOLV for Windows User's Guide Glossary of Terms •• 161

Glossary of Terms

AquicludeA saturated geologic unit that is incapable of transmitting significant quantities ofwater under ordinary hydraulic gradients.

AquiferA saturated permeable geologic unit that can transmit significant quantities of waterunder ordinary hydraulic gradients.

AquitardA saturated geologic unit that transmits water in quantities insufficient foreconomic use.

Casing RadiusRadius of unperforated portion of well casing.

Client NameA user-supplied character string (up to 30 characters) storing the name of the clientwhich sponsored the aquifer test. Used for reports and plots.

Coefficient of PermeabilitySee Hydraulic Conductivity.

Company NameA user-supplied character string (up to 30 characters) storing the name of thecompany which conducted the aquifer test. Used for reports and plots.

Confined AquiferAn aquifer with upper and lower boundaries consisting of aquicludes.

162 •• Glossary of Terms AQTESOLV for Windows User's Guide

Date of TestA user-supplied character string (up to 30 characters) storing the date of an aquifertest. Used for reports and plots.

Discrete Fractured AquiferAn aquifer consisting of low-permeability, primary porosity matrix and discretehigh-permeability, secondary porosity fissures (e.g., a single vertical or horizontalplane fracture).

DisplacementChange in water level relative to static condition.

Double-Porosity Fractured AquiferAn aquifer represented by a double porosity system consisting of low-permeability,primary porosity blocks and high-permeability, secondary porosity fissures.

DrawdownChange in water level relative to static condition due to pumping or slug withdrawalduring an aquifer test.

Fracture SkinA thin, low-permeability material coating the surface of fractures (e.g., mineraldeposit) that restricts flow of water.

Fractured AquiferSee Discrete Fractured Aquifer or Double-Porosity Fractured Aquifer.

Hydraulic ConductivityThe volume of water moving through a unit area of aquifer perpendicular to thedirection of flow in unit time under a unit hydraulic gradient.

Leaky AquiferAn aquifer with upper and lower boundaries of one aquitard and one aquiclude ortwo aquitards.

Location of TestA user-supplied character string (up to 30 characters) storing the location of theaquifer test. Used for reports and plots.

AQTESOLV for Windows User's Guide Glossary of Terms •• 163

Measurement WeightUse weights to assign the relative weight of each measurement for use duringautomatic curve matching. In typical cases, assign weights of 1.0 or 0.0 to includeor exclude measurements during automatic curve matching.

Observation Well NameA user-supplied character string (up to 30 characters) storing the name of theobservation well used in the aquifer test. Used for reports and plots.

PermeabilitySee Hydraulic Conductivity.

PiezometerAn open-ended pipe installed in an aquifer to measure hydraulic head at a specificdepth.

PorosityThe ratio of void volume to total volume in an unconsolidated material.

Project NumberA user-supplied character string (up to 30 characters) storing the company'snumber or ID of the aquifer test project. Used for reports and plots.

ResidualThe difference between simulated and observed displacement.

Residual DisplacementWater-level displacement measured from static condition in an observation wellafter pumping has stopped during the recovery phase of a pumping test.

Saturated ThicknessVertical distance measured from the top of an aquifer (confining layer or watertable) to the base of the aquifer.

Semiconfined AquiferSee Leaky Aquifer.

Semiconfined AquiferSee Leaky Aquifer.

164 •• Glossary of Terms AQTESOLV for Windows User's Guide

Specific StorageThe volume of water released from storage by a unit volume of confined aquifer perunit decline in hydraulic head.

Specific YieldThe volume of water released from storage per unit surface area of an unconfinedaquifer per unit decline of the water table.

Storage CoefficientSee Storativity.

StorativityThe volume of water released from storage per unit surface area of a confinedaquifer per unit decline in hydraulic head.

Test Well NameA user-supplied character string (up to 30 characters) storing the name of the testwell used in an aquifer test.

TransmissivityTransmissivity is the rate of flow under a unit hydraulic gradient through a cross-section of aquifer having a unit width and full saturated thickness. Also expressedas the product of hydraulic conductivity times saturated thickness.

Unconfined AquiferAn aquifer with an unrestricted (free) upper boundary and an impermeable lowerboundary (aquiclude).

Water Table AquiferSee Unconfined Aquifer.

Wellbore RadiusRadius of well boring (adjacent to well intake or screen).

Wellbore SkinA thin, low-permeability deposit on surface of wellbore (e.g., drilling mud) thatrestricts flow of water.

aqtesolv for windows user's guide

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