Version 4.

5
Users Guide

Glenn M. Duffield, Developer of AQTESOLV

HydroSOLVE, Inc.
2303 Horseferry Court
Reston, VA 20191
USA
Copyright 2004-2007 Glenn M. Duffield,
HydroSOLVE, Inc. All Rights Reserved.

Table Of Contents
TABLE OF CONTENTS ....................................................................................... 1
INTRODUCTION .................................................................................................. 8
Welcome........................................................................................................................ 8
What's New in AQTESOLV............................................................................................ 8
New Features in Version 4.5............................................................................................................8
New Features in Version 4...............................................................................................................9
New Features in Earlier Versions...................................................................................................12

Features....................................................................................................................... 12
Unique Features in AQTESOLV* ...................................................................................................12
Unique Solution Methods in AQTESOLV*......................................................................................14
Summary of Solution Methods .......................................................................................................15

Using Help ................................................................................................................... 16

Using the Help System...................................................................................................................16
Context-Sensitive Help...................................................................................................................16
Getting Started ...............................................................................................................................17
More Help On The Web .................................................................................................................17

QUICK START ................................................................................................... 18

How To Use AQTESOLV............................................................................................. 18
How to Analyze an Aquifer Test ..............................................................................................18
Pumping Test Design and Prediction......................................................................................20
Field Applications ....................................................................................................................20

Examples ..................................................................................................................... 21
Overview (Examples) ..............................................................................................................21
Pumping Test Examples ............................................................................................................21
Slug Test Examples ...................................................................................................................23
Constant-Head Test Examples ..................................................................................................23
Mounding Examples...................................................................................................................23

Pumping Tests ........................................................................................................................24

Pumping Test Example: Constant Rate (Gridley) ....................................................................24
Pumping Test Example: Recovery ..............................................................................................33
Pumping Test Example: Variable Rate .......................................................................................43
Pumping Test Example: Wellbore Storage (Saudi Arabia).....................................................48
Pumping Test Example: Wellbore Storage and Skin (Lynden)..............................................59
Pumping Test Example: Step-Drawdown (Saudi Arabia) .......................................................69
Pumping Test Example: Multiple Observation Wells (Sioux Flats) .......................................74
Pumping Test Example: Constant-Rate Test in a Leaky Confined Aquifer (Dalem)..........83
Pumping Test Example: Leaky (Texas Hill)...............................................................................90
Pumping Test: Unconfined (Saratoga) .......................................................................................99
Pumping Test Example: Unconfined (Cape Cod) ...................................................................108

Pumping Test Example: Double Porosity (Nevada) ...............................................................116

Pumping Test Example: Test Design (Forward Solution) .....................................................123
Pumping Test Example: Horizontal Well ..................................................................................127

Slug Tests..............................................................................................................................133
Slug Test Example: Unconfined.................................................................................................133
Slug Test Example: Translation Method ..................................................................................140
Slug Test: Double Straight-Line Effect (Dallas) .....................................................................146
Slug Test Example: High-K Aquifer ..........................................................................................150
Slug Test Example: Multiwell Test (Lincoln County, KS)......................................................154

Constant-Head Tests ............................................................................................................160

Constant-Head Test Example: Flow and Recovery (Grand Junction) ................................160

Mounding...............................................................................................................................168
Mounding Example: Rectangular Recharge Area ...................................................................168

More Examples .....................................................................................................................172

MENUS............................................................................................................. 173
File Menu ................................................................................................................... 173
Edit Menu................................................................................................................... 173
View Menu ................................................................................................................. 173
Match Menu ............................................................................................................... 175
Tools Menu ................................................................................................................ 175
Windows Menu .......................................................................................................... 175
Help Menu ................................................................................................................. 176
Toolbar....................................................................................................................... 176
Keyboard Shortcuts ................................................................................................... 177

ENTERING, EDITING AND IMPORTING DATA .............................................. 179

Overview (Data Sets)................................................................................................. 179
Data Entry Wizards.................................................................................................... 181
Pumping Test Wizard ............................................................................................................181
Constant-Head Test Wizard ..................................................................................................182
Slug Test Wizard ...................................................................................................................182
Forward Solution Wizard .......................................................................................................183
AQTESOLV for DOS Import Wizard .....................................................................................184

Editing Data ............................................................................................................... 185

Editing Test Data...................................................................................................................185

Importing Data ........................................................................................................... 186

Overview (Importing Data) ....................................................................................................186
Observation Data Import Wizard ...........................................................................................186
Pumping Rate Data Import Wizard .......................................................................................187

VIEWING DATA ............................................................................................... 188

2

Plots........................................................................................................................... 188
Overview (Plots) ....................................................................................................................188
Data Plots ..............................................................................................................................189
Displacement-Time Plot ..............................................................................................................189
Composite Plot ..............................................................................................................................191
Residual Drawdown Plot..............................................................................................................192
Agarwal...........................................................................................................................................195
Distance Drawdown Plot .............................................................................................................197
Derivative-Time Plot ....................................................................................................................199
Discharge-Time Plot.....................................................................................................................200

Diagnostic Flow Plots ............................................................................................................202

Radial Flow Plot.............................................................................................................................202
Linear Flow Plot.............................................................................................................................204
Bilinear Flow Plot ..........................................................................................................................206
Spherical Flow Plot .......................................................................................................................207

Residual Plots........................................................................................................................208
Residual-Time Plot .......................................................................................................................208
Residual-Simulated Plot ..............................................................................................................209
Normal Probability Plot................................................................................................................210

Customizing Plots..................................................................................................................212
Customizing Plots .........................................................................................................................212
Linear Axes ....................................................................................................................................212
Log-Linear Axes ............................................................................................................................213
Linear-Log Axes ............................................................................................................................214
Log Axes.........................................................................................................................................215
Format ............................................................................................................................................216
Options ...........................................................................................................................................224

Reports ...................................................................................................................... 233

Overview (Reports) ...............................................................................................................233
Diagnostics ............................................................................................................................233
Report....................................................................................................................................233
Error Log................................................................................................................................234
Customizing Reports .............................................................................................................234

MATCHING DATA............................................................................................ 235

Solutions .................................................................................................................... 235
Overview (Solutions) .............................................................................................................235
Pumping Tests ......................................................................................................................236
Overview (Pumping Test Solutions) .........................................................................................236
Constant-Rate Solutions .............................................................................................................237
Variable-Rate Solutions...............................................................................................................238
Recovery Solutions (Pumping Tests)........................................................................................239
Single-Well Solutions...................................................................................................................239
Wellbore Storage Solutions ........................................................................................................240
Single Fracture Solutions ............................................................................................................241

Double-Porosity Solutions...........................................................................................................241
Step-Drawdown Test Solutions..................................................................................................242
Well Loss Equation ............................................................................................................243
Linear Well Loss.................................................................................................................244
Nonlinear Well Loss...........................................................................................................244
Well Efficiency....................................................................................................................244
Solutions for Step Test Analysis ......................................................................................245
Horizontal Well Solutions ............................................................................................................246
Multiaquifer Solutions ..................................................................................................................246
Bounded Aquifer Solutions .........................................................................................................246
Nonuniform Aquifer Solutions ....................................................................................................246
Delayed OW Response Solutions...............................................................................................247
Diagnostic Flow Plots ...................................................................................................................248
Confined Aquifers.............................................................................................................................249
Theis (1935)/Hantush (1961) Solution for a Pumping Test in a Confined Aquifer......249
Theis (1935) Solution for a Recovery Test in a Confined Aquifer...................................253
Theis (1935) Solution for a Step-Drawdown Test in a Confined Aquifer.......................255
Cooper-Jacob (1946) Solution for a Pumping Test in a Confined Aquifer.....................258
Moench-Prickett (1972) Solution for a Pumping Test in a Confined/Unconfined Aquifer262
Butler (1988) Solution for a Pumping Test in a Confined Aquifer ..................................265
Papadopulos-Cooper (1967) Solution for a Pumping Test in a Confined Aquifer ........269
Dougherty-Babu (1984) Solution for a Pumping Test in a Confined Aquifer................273
Dougherty-Babu (1984) Solution for a Step-Drawdown Test in a Confined Aquifer ..278
Hantush (1962) Solution for a Pumping Test in a Wedge-Shaped Confined Aquifer..281
Murdoch (1994) Solution for a Pumping Test in a Confined Aquifer..............................284
Daviau et al. (1985) Solution for a Pumping Test in a Confined Aquifer ......................287
Barker (1988) Solution for a Pumping Test in a Confined Aquifer .................................290
Leaky Aquifers .................................................................................................................................292
Hantush-Jacob (1955)/Hantush (1964) Solution for a Pumping Test in a Leaky Aquifer292
Hantush-Jacob (1955) Solution for a Step-Drawdown Test in a Leaky Aquifer...........297
Hantush (1960) Solution for a Pumping Test in a Leaky Aquifer....................................300
Cooley-Case (1973) Solution for a Pumping Test in a Confined Aquifer Overlain by a
Water-Table Aquitard ..............................................................................................................305
Neuman-Witherspoon (1969) Solution for a Pumping Test in a Leaky Aquifer ...........309
Moench (1985) Solution for a Pumping Test in a Leaky Aquifer.....................................313
Unconfined Aquifers.........................................................................................................................319
Theis (1935) Solution for a Pumping Test in an Unconfined Aquifer .............................319
Cooper-Jacob (1946) Solution for a Pumping Test in an Unconfined Aquifer ..............321
Neuman (1974) Solution for a Pumping Test in an Unconfined Aquifer........................324
Moench (1997) Solution for a Pumping Test in an Unconfined Aquifer .........................328
Tartakovsky-Neuman (2007) Solution for a Pumping Test in an Unconfined Aquifer 334
Fractured Aquifers............................................................................................................................339
Moench (1984) Solution for a Pumping Test in a Fractured Aquifer ..............................339
Gringarten-Witherspoon (1972) Solution for a Pumping Test in a Fractured Aquifer 344
Gringarten-Ramey-Raghavan (1974) Solution for a Pumping Test in a Fractured
Aquifer ........................................................................................................................................347
Gringarten-Ramey (1974) Solution for a Pumping Test in a Fractured Aquifer...........351

Barker (1988) Solution for a Pumping Test in a Fractured Aquifer................................354

Slug Tests..............................................................................................................................360
Overview (Slug Test Solutions) .................................................................................................360
Overdamped Slug Test Solutions ..............................................................................................360
Underdamped Slug Test Solutions ............................................................................................363
Multiwell Slug Test Solutions .....................................................................................................364
Slug Test Solutions for Wells Screened Across Water Table................................................365
Nonlinear Slug Test Solutions ....................................................................................................366
Guidelines for Slug Test Analysis ..............................................................................................366
Overdamped Slug Tests ....................................................................................................366
Underdamped Slug Tests ..................................................................................................366
Confined Aquifers.............................................................................................................................367
Hvorslev (1951) Solution for a Slug Test in a Confined Aquifer .....................................367
Bouwer-Rice (1976) Solution for a Slug Test in a Confined Aquifer ..............................369
Cooper-Bredehoeft-Papadopulos (1967) Solution for a Slug Test in a Confined Aquifer372
Dougherty-Babu (1984) Solution for a Slug Test in a Confined Aquifer .......................374
Hyder et al. (1994) Solution for a Slug Test in a Confined Aquifer (KGS Model)........379
Butler (1998) Solution for a Slug Test in a Confined Aquifer ..........................................383
Butler-Zhan (2004) Solution for a Slug Test in a Confined Aquifer ...............................387
Peres-Onur-Reynolds (1989) Solution for a Slug Test in a Confined Aquifer...............394
McElwee-Zenner (1998) Solution for a Slug Test in a Confined Aquifer .......................397
Unconfined Aquifers.........................................................................................................................402
Bouwer-Rice (1976) Solution for a Slug Test in an Unconfined Aquifer........................402
Hvorslev (1951) Solution for a Slug Test in an Unconfined Aquifer...............................404
Dagan (1978) Solution for a Slug Test in an Unconfined Aquifer...................................406
Hyder et al. (1994) Solution for a Slug Test in an Unconfined Aquifer (KGS Model) .409
Springer-Gelhar (1991) Solution for a Slug Test in an Unconfined Aquifer..................413
Fractured Aquifers............................................................................................................................418
Barker-Black (1983) Solution for a Slug Test in a Fractured Aquifer ............................418

Constant-Head Tests ............................................................................................................421

Overview (Constant-Head Test Solutions) ..............................................................................421
Recovery Solutions (Constant-Head Tests).............................................................................421
Confined Aquifers.............................................................................................................................423
Jacob-Lohman (1952) Solution for a Constant-Head Test in a Confined Aquifer ........423
Hurst-Clark-Brauer (1969) Solution for a Constant-Head Test in a Confined Aquifer426
Dougherty-Babu (1984) Solution for a Constant-Head Test in a Confined Aquifer ....430
Barker (1988) Solution for a Constant-Head Test in a Confined Aquifer ......................434
Leaky Aquifers .................................................................................................................................435
Hantush (1959) Solution for a Constant-Head Test in a Leaky Aquifer ........................435
Moench (1985) Solution for a Constant-Head Test in a Leaky Aquifer .........................438
Fractured Aquifers............................................................................................................................444
Barker (1988) Solution for a Constant-Head Test in a Fractured Aquifer.....................444
Ozkan-Raghavan (1991) Solution for a Constant-Head Test in a Fractured Aquifer ..449

Curve Matching.......................................................................................................... 454

Overview (Curve Matching)...................................................................................................454
Curve Matching Tips for Pumping Tests ...............................................................................455

Curve Matching Tips for Slug Tests ......................................................................................455

Curve Matching Tips for Constant-Head Tests .....................................................................455
Diagnostic Methods...............................................................................................................457
Derivative Analysis.......................................................................................................................457
Check Slope...................................................................................................................................467

Visual Curve Matching ..........................................................................................................468

Overview (Visual Curve Matching)............................................................................................468
Active Type Curves ......................................................................................................................469
Matching Type Curve Families ...................................................................................................469
Matching Early/Late Data ...........................................................................................................470
Parameter Tweaking ....................................................................................................................471

Automatic Curve Matching ....................................................................................................472

Overview (Automatic Curve Matching) ....................................................................................472
How Automatic Curve Matching Works ....................................................................................472
Parameter Statistics.....................................................................................................................475
Confidence Interval ............................................................................................................475
Significance Test................................................................................................................475
Residual Statistics ........................................................................................................................476
Tips for Automatic Curve Matching...........................................................................................476
Starting Guesses................................................................................................................476
Windows and Weights .......................................................................................................477
Conditioning .......................................................................................................................477

OBTAINING OUTPUT ...................................................................................... 479

Printing....................................................................................................................... 479
Overview (Printing)................................................................................................................479
Print .......................................................................................................................................479
Print Preview .........................................................................................................................480
Print Setup.............................................................................................................................480
Page Setup............................................................................................................................480
Batch Print .............................................................................................................................481
Tips for Printing .....................................................................................................................483

Contouring ................................................................................................................. 484

Overview (Contouring) ..........................................................................................................484
Contour..................................................................................................................................484
Grid Wizard............................................................................................................................484

Exporting and Sharing Data....................................................................................... 486

Overview (Exporting and Sharing Data)................................................................................486
Export ....................................................................................................................................486
Send Mail...............................................................................................................................487

TOOLS ............................................................................................................. 488

Overview (Tools)........................................................................................................ 488
Mounding ................................................................................................................... 488

ModelCad .................................................................................................................. 488

TWODAN................................................................................................................... 488
WinSitu ...................................................................................................................... 489

SUPPORT ........................................................................................................ 490

Q & A ......................................................................................................................... 490
Aquifer Data .................................................................................................................................490
Well Data .....................................................................................................................................490
Importing Data .............................................................................................................................490
Recovery Tests ............................................................................................................................491
Curve Matching ............................................................................................................................493
Plots, Reports and Printing ..........................................................................................................493
Contouring ...................................................................................................................................494
Error Messages............................................................................................................................494
Miscellaneous ..............................................................................................................................495

Technical Support...................................................................................................... 495

Software Registration...................................................................................................................495
Web Resources............................................................................................................................495
Telephone Support.......................................................................................................................495
Special Services Available ...........................................................................................................496

REFERENCES ................................................................................................. 497

References ................................................................................................................ 497
General ........................................................................................................................................497
Pumping Tests .............................................................................................................................498
Constant-Head Tests ...................................................................................................................500
Slug Tests ....................................................................................................................................501
Mounding .....................................................................................................................................502
Derivative Analysis.......................................................................................................................503
Numerical Methods ......................................................................................................................503

Additional Sources..................................................................................................... 503

APPENDICES................................................................................................... 504
Conversions............................................................................................................... 504
Hydraulic Conductivity ............................................................................................... 506
Anisotropy Ratio ........................................................................................................ 507
Porosity...................................................................................................................... 507
Specific Yield ............................................................................................................. 508
Storativity ................................................................................................................... 509
Specific Capacity ....................................................................................................... 510

INDEX............................................................................................................... 514

Introduction
Welcome

AQTESOLV is the world's leading software for the analysis of aquifer tests
(pumping tests, constant-head tests and slug tests).
AQTESOLV--AQuifer TEst SOLVer (listen)
Software Developer: Glenn M. Duffield
HydroSOLVE, Inc.
2303 Horseferry Court
Reston, VA 20191-2739
USA
www.aqtesolv.com
Software Development
Training
Consulting
AQTESOLV for Windows HTML Help (2007.6.16)
Copyright 2004-2007 Glenn M. Duffield, HydroSOLVE, Inc. All Rights Reserved.
Duffield, G.M., 2007. AQTESOLV for Windows Version 4.5 User's Guide, HydroSOLVE,
Inc., Reston, VA.

What's New in AQTESOLV

New Features in Version 4.5
1. New Solution for Water-Table Aquifers

AQTESOLV now includes a pumping test solution by Tartakovsky and

Neuman (2007) that accounts for three-dimensional saturated and
unsaturated flow in an unconfined aquifer.

2. New Solution for Step-Drawdown Tests

Analyze data from a step-drawdown test in a confined aquifer using

the Jacob-Rorabaugh well-loss equation combined with the DoughertyBabu (1984) solution.

Instead of assuming a line source like the Theis (1935) solution, the
Dougherty-Babu solution accounts for wellbore storage.

Bear (1979, p. 375) discusses how the formation loss term in the well-loss

equation may be represented by any appropriate pumping test solution for

a given aquifer type.

New Features in Version 4

1. Constant-Head Tests

Analyze constant-head tests in confined, leaky and fractured aquifers.

Solution methods include options for wellbore skin and fracture skin.

Analyze recovery data for constant-head tests using either the exact
method of Ehlig-Economides (1982) or the approximate method of Uraiet
and Raghavan (1980).

2. Solutions for Nonuniform Aquifers

Use a solution by Moench and Prickett (1972) to analyze data from

pumping tests in an aquifer undergoing conversion from confined to
unconfined conditions.

Use a solution by Butler (1988) to analyze data from pumping tests in

nonuniform aquifers.

3. Generalized Radial Flow Model

Analyze pumping tests and constant-head tests using the generalized

radial flow (GRF) solution of Barker (1988).

Solution methods available for confined and double-porosity fractured

aquifers.

4. Solution for a Water-Table Aquitard

Use a solution by Cooley and Case (1973) to analyze data from pumping
tests in a confined aquifer overlain by a water-table aquitard.

5. New Solution for Underdamped Slug Tests

A new solution by Butler and Zhan (2004) simulates multi-well slug tests
in a confined aquifer with fully and partially penetrating wells, inertial
effects in the test and observation wells, and frictional loss.

6. Dagan's Slug Test Solution for Wells Screened Across Water Table

Use this solution by Dagan (1978) for the evaluation of slug tests in
wells screened across the water table.

Butler (1998) recommends this method for the analysis of wells screened
across the water table.

7. Slug Tests in Fractured Aquifers

Analyze a slug test in a double-porosity fractured aquifer with slabshaped blocks using a solution by Barker and Black (1985).
9

8. Dougherty-Babu Slug Test Solution

Analyze a slug test in a partially well in a confined aquifer with wellbore

skin and delayed observation well response using the Dougherty-Babu
(1984) solution.

Simulate single- or multi-well tests.

9. Horizontal Wells

A solution by Daviau et al. (1985) allows you to analyze pumping tests

with horizontal wells in confined aquifers.

10. Step-Drawdown Test in a Leaky Aquifer

Analyze data from a step-drawdown test in a leaky aquifer using the

Jacob-Rorabaugh well-loss equation combined with the Hantush-Jacob
(1955) solution.

Bear (1979, p. 375) discusses how the formation loss term in the well-loss
equation may be represented by any appropriate pumping test solution for
a given aquifer type.

11. New Single-Fracture Solution

Evaluate data from pumping tests and constant-head tests using a

solution by Gringarten et al. (1974) for an infinite-conductivity vertical
fracture in a confined aquifer.

This new solution supplements the uniform-flux vertical fracture solution

by Gringarten and Witherspoon (1972) released in AQTESOLV v3.0.

12. Aquifer Boundaries With Automatic Image Well Generation

Automatically generate image wells to analyze pumping tests in

bounded aquifers including single boundaries, two intersecting boundaries,
infinite strip aquifers (two parallel boundaries), semi-infinite strip aquifers
(three boundaries) and closed rectangular reservoirs (four boundaries).

An intuitive interface lets you easily enter boundary geometry and

select any combination of no-flow and constant-head boundaries.

Easily toggle boundaries on and off during analyses.

13. Distance-Drawdown Analysis

Use distance-drawdown plots to display pumping test data

Perform distance-drawdown visual curve matching with any pumping

test solution.

14. Agarwal's Method for Recovery Data Analysis

Use Agarwal plots to analyze recovery data from pumping tests and
constant-head tests.

10

Agarwal's straightforward method allows you to match standard

drawdown solutions (e.g., Theis 1935; Cooper-Jacob 1946; Neuman
1974; etc.) to recovery data.

15. Delayed Observation Well Response

AQTESOLV includes solutions that accounts for delayed response in an

observation well during a pumping test (Black and Kipp 1977; Moench
1997).

16. Solution Expert

The new Solution Expertinterface for selecting solution methods puts

essential solution method information at your fingertips.

Use intelligent filters to query the software for solutions that match your
test configuration. For example, you can search for all solutions that
include wellbore storage, wellbore skin effect and partial penetration.

Click the Help button for any selected solution and go directly to a
detailed help topic associated with the method (e.g., Theis 1935).

17. New Diagnostic Tool

AQTESOLV v4.0 introduces a new diagnostic tool for interactively

testing the slope of data from pumping tests and constant-head tests.

This diagnostic tool assists in the selection of appropriate solution

methods by helping to identify key features such as wellbore storage,
linear flow, boundary effects and flow dimension.

The new interactive tool supplements the diagnostic flow plots feature
introduced in AQTESOLV v3.0.

18. Groundwater Mounding in Water-Table Aquifers

Predict transient water-table rise beneath circular and rectangular

recharge areas using solutions by Hantush (1967).

Prepare contour maps of groundwater mounds using Surfer.

19. Batch Printing

Select a group of AQTESOLV data sets and apply consistent formatting

when printing plots and reports.

Batch printing is a very useful feature, for example, if you've conducted a

large number of tests at a site and you need to print your results for a
project report.

20. New Interface Features

A unified interface simplifies well data entry for pumping tests, constanthead tests and slug tests.

New plots added for distance-drawdown and Agarwal analysis.

11

An interactive slope checking tool helps you perform diagnostic analysis.

21. Revised Help System

A new and improved HTML help system increases your productivity with
new topics, an expanded index and greater cross-referencing.

The program provides even more context-sensitive help.

New Features in Earlier Versions

For a summary of features introduced in previous versions, please visit the
AQTESOLV web site.

Features
Unique Features in AQTESOLV*
1. Solution for Unconfined Aquifer with 3D Saturated/Unsaturated Flow
Only AQTESOLV includes a solution by Tartakovsky and Neuman (2007) for a
pumping test in an unconfined aquifer with three-dimensional flow in the
saturated and unsaturated zones.
2. Constant-Head Tests
Only AQTESOLV has solutions for constant-head tests in confined, leaky and
fractured aquifers.
3. Solutions for Nonuniform Aquifers
Only AQTESOLV includes solutions by Moench and Prickett (1972) for a
pumping test in an aquifer undergoing conversion from confined to
unconfined conditions and Butler (1988) for a pumping test in a
heterogeneous aquifer.
4. Generalized Radial Flow Model
AQTESOLV is the only software to feature the generalized radial flow (GRF)
solution by Barker (1988) which allows you to evaluate pumping tests and
constant-head tests for integer and non-integer flow dimensions.
5. Solution for a Water-Table Aquitard
Only AQTESOLV includes a solution by Cooley and Case (1973) for a pumping
test in a confined aquifer overlain by a water-table aquitard.
6. Underdamped Slug Tests with Partially Penetrating Wells
Only AQTESOLV provides solutions for slug tests with underdamped response
in partially penetrating wells.
7. Horizontal Wells
Only AQTESOLV provides a solution for analyzing flow to a uniform-flux or
infinite-conductivity horizontal well.

12

8. Single-Fracture Solutions
AQTESOLV is the only software for aquifer test analysis that includes solutions
for vertical and horizontal fractures. Single fracture solutions are available
for both pumping tests and constant-head tests.
9. Step-Drawdown Test in Leaky Aquifer
AQTESOLV is the first aquifer test software to provide a solution for a stepdrawdown test in a leaky aquifer.
10. Confined Two-Aquifer System
Only AQTESOLV lets you use the Neuman-Witherspoon (1969) solution to
analyze drawdown in the pumped aquifer, an aquitard and an unpumped
source aquifer.
11. Automatic Image Well Generation
AQTESOLV is the only software the provides automatic image well generation
for bounded aquifers with one to four boundaries and any combination of
no-flow and constant-head conditions.
12. Delayed Observation Well Response
Only AQTESOLV provides solutions for pumping tests in confined and
fractured aquifers with delayed response in observation wells.
13. Dagan's Slug Test Method for Wells Screened Across Water Table
Only AQTESOLV includes the Dagan (1978) solution for slug tests. This
solution is recommended by Butler (1998) for well screened across the
water table.
14. Slug Tests in Fractured Aquifers
Only AQTESOLV includes the solution by Barker and Black (1985) for a slug
test in a double-porosity fractured aquifer with slab-shaped blocks.
15. Diagnostic Flow Plots
Diagnostic flow plots (radial, linear, bilinear and spherical) are a unique
feature of AQTESOLV. Use these plots to diagnose wellbore storage, linear
flow, and boundary effects.
16. Active Type Curves
AQTESOLV v3.0 introduced a unique curve matching technique called active
type curves that radically alters the way you perform visual curve matching
with variable-rate pumping test solutions and underdamped (oscillatory)
slug test solutions.
17. Distance-Drawdown Analysis
AQTESOLV is the only software that lets you perform distance-drawdown
analysis using any of its pumping test solutions.

13

18. Agarwal Method for Recovery Data

AQTESOLV is the first program to introduce the Agarwal method for analyzing
recovery data from pumping tests and constant-head tests.
19. Groundwater Mounding
Only AQTESOLV has solutions for predicting the transient rise of the water
table beneath circular and rectangular recharge areas using solutions by
Hantush (1967).

Unique Solution Methods in AQTESOLV*

1. Moench-Prickett (1972) solution for a pumping test in a confined aquifer
undergoing conversion to water-table conditions.
2. Butler (1988) solution for a pumping test in a nonuniform aquifer.
3. Dougherty-Babu (1984) solution for a pumping test in a confined aquifer with
partially penetrating wells, wellbore storage and wellbore skin.
4. Hantush (1962) solution for a pumping test in a confined wedge-shaped
aquifer.
5. Murdoch (1994) solution for a pumping test in a confined aquifer with an
interceptor trench.
6. Daviau et al. (1985) solution for a pumping test in a confined aquifer with a
uniform-flux or infinite-conductivity horizontal well.
7. Barker (1988) generalized radial flow solution for a pumping test in a singleporosity confined aquifer with wellbore skin and nonintegral flow dimension.
8. Cooley-Case (1973) solution for a pumping test in a leaky confined aquifer
overlain by a water-table aquitard.
9. Neuman-Witherspoon (1969) solution for a pumping test in a leaky confined
two-aquifer system.
10. Tartakovsky-Neuman (2007) solution for a pumping test in an unconfined
aquifer with 3D flow in the saturated and unsaturated zones.
11. Gringarten-Witherspoon (1972) solution for a pumping test in a fractured
aquifer with a uniform-flux vertical fracture.
12. Gringarten-Ramey-Raghavan (1974) solution for a pumping test in a
fractured aquifer with an infinite-conductivity vertical fracture.
13. Gringarten-Ramey (1974) solution for a pumping test in a fractured aquifer
with a horizontal fracture.
14. Barker (1988) generalized radial flow solution for a pumping test in a doubleporosity fractured aquifer with slab shaped or spherical blocks, fracture skin,
wellbore storage, wellbore skin and nonintegral flow dimension.
15. Dougherty-Babu (1984) solution for a slug test in a confined aquifer with

14

partially penetrating wells and wellbore skin.

16. Butler (1998) solution for a slug test in a confined aquifer with partially
penetrating well and underdamped (oscillatory) response.
17. Butler-Zhan (2004) solution for a slug test in a confined aquifer with partially
penetrating wells and underdamped (oscillatory) response.
18. Springer-Gelhar (1991) solution for a slug test in an unconfined aquifer with
partially penetrating well and underdamped (oscillatory) response.
19. Dagan (1978) solution for a slug test in an unconfined aquifer with a well
screened across the water table.
20. Barker-Black (1985) solution for a slug test in a double-porosity fractured
aquifer with slab-shaped blocks.
21. Jacob-Lohman (1952) solution for a constant-head test in a confined aquifer.
22. Hurst-Clark-Brauer (1969) solution for a constant-head test in a confined
aquifer with wellbore skin.
23. Dougherty-Babu (1984) solution for a constant-head test in a confined aquifer
with partially penetrating wells and wellbore skin.
24. Barker (1988) solution for a constant-head test in a single-porosity confined
aquifer with wellbore skin and nonintegral flow dimension.
25. Hantush (1959) solution for a constant-head test in a leaky aquifer.
26. Moench (1985) solution for a constant-head test in a leaky aquifer with
wellbore skin and storage in the aquitard(s).
27. Barker (1988) generalized radial flow solution for a constant-head test in a
double-porosity fractured aquifer with slab shaped or spherical blocks,
fracture skin, wellbore skin and nonintegral flow dimension.
28. Ozkan-Raghavan (1991) solution for a constant-head test in a fractured
aquifer with a uniform-flux or infinite-conductivity vertical fracture.

Summary of Solution Methods

Pumping Test Solution Methods
Solution Category
Methods Available
Constant-Rate Tests
35
Variable-Rate Tests
34
Recovery Tests
33
Step-Drawdown Tests
3
Wellbore Storage
12
Confined Aquifers
14
Leaky Aquifers
9
Unconfined Aquifers
5
Fractured Aquifers
7
Bounded Aquifers
23

15

Constant-Head Test Solution Methods

Solution Category
Methods Available
Constant-Head Tests
11
Recovery Tests
10
Wellbore Skin
6
Confined Aquifers
5
Leaky Aquifers
2
Fractured Aquifers
4

Slug Test Methods

Solution Category
Methods Available
Slug Tests
18
Partial Penetration
15
Underdamped
5
Confined Aquifers
11
Unconfined Aquifers
6
Fractured Aquifers
1

*Compared to AquiferTestPro v3.5 and AquiferWin32 v3.0. Please notify

HydroSOLVE, Inc. of any changes to this information.

Using Help
Using the Help System
This help system includes several types of navigation components. Click on the
examples below to see how they work:
o

Expanding Hotspot

When you click on an expanding hotspot, details appear below it.

Click on the hotspot again to hide the details.

defined term (Click on a defined term to display its definition. Click the term
again to hide the definition)

Context-Sensitive Help
AQTESOLV provides context-sensitive help and tips throughout its menus and
windows.

Use What's This help to learn about a menu option or toolbar button.

Click Help or press F1 in dialog windows to view context-sensitive help.

Display tooltips by hovering the mouse over toolbar buttons and edit
windows.

Activate Quick Tips to display helpful prompts at key stages in the program.

16

Getting Started
You'll find step-by-step examples in the Quick Start chapter to lead you through the
process of analyzing many different types of aquifer tests using AQTESOLV.

More Help On The Web

Visit the AQTESOLV web site for additional help resources including the Knowledge
Base, examples and tutorials.

17

Quick Start
How To Use AQTESOLV

How to Analyze an Aquifer Test

Follow these steps to analyze an aquifer test (pumping test, slug test or constanthead test) with AQTESOLV:
Develop a Conceptual Model
The first step in the analysis of an aquifer test is the development of a conceptual
model. The conceptual model translates the elements of the real groundwater flow
system into a simpler model suitable for mathematical analysis.
In developing a conceptual model for an aquifer test, one should address the
following questions:

What is the basic configuration for the aquifer under consideration (e.g.,
confined, leaky confined, unconfined or fractured)? What is the thickness of
the aquifer? Is the aquifer isotropic?

What are the well construction details (e.g., casing radius, screen radius,
borehole radius, depth to top of screen and screen length)?

For a pumping test, what is the rate history (i.e., constant or variable)? What
was the duration of pumping?

For a slug test, what was the initial displacement in the test well? What was
the static water column height in the well? Is the filter pack, if present, more
permeable than the aquifer?

Is the aquifer infinite-acting? Are there recharge or no-flow boundaries that

may influence hydraulic response during the test?

Are there external sources or sinks that affect hydraulic response such as
pumping or injection wells, precipitation or infiltration basins?

Are there nearby bodies of water with fluctuating water levels that influence
water levels in the aquifer (e.g., tidal fluctuations)?

Do barometric pressure changes influence water levels in the aquifer?

Enter Data
After developing a conceptual model, enter data from the test into AQTESOLV.
Create a new data set and select an appropriate data entry wizard for a pumping
test, slug test or constant-head test.
When you have completed the steps in the data entry wizard, AQTESOLV displays an
Error Log that shows any missing data or errors detected in your data set. To correct
18

any reported errors, choose options from the Edit menu.

You are not restricted to using one of the wizards for data entry. You also may
choose options from the Edit menu to modify or add to a data set.
Evaluate Diagnostic Flow Plots
After entering data into AQTESOLV, use diagnostic flow plots and derivative analysis
to identify features such as wellbore storage, radial flow in an infinite-acting aquifer,
linear flow to a single fracture, boundary effects and delayed gravity response.
Diagnostic flow plots apply to the analysis of pumping tests. Radial flow plots are
especially useful for identifying wellbore storage, radial flow in an infinite-acting
aquifer and boundary effects. Use linear flow plots to identify periods of linear flow
during a pumping test such as early-time flow to a vertical fracture.
Derivative plots help to detect many hydraulic response features of pumping tests
such as wellbore storage, delayed gravity response, double-porosity effects and
radial flow in an infinite-acting aquifer.
Estimate Aquifer Properties (Curve Matching)
To estimate aquifer properties from your test data, first choose a solution and then
perform curve matching.
When choosing a solution method, use the Solution Expert to match methods to the
conditions of your test (e.g., wellbore storage, linear flow, etc.).
Use visual curve matching to estimate aquifer properties in the traditional way by
fitting a straight line or type curve to your test data. AQTESOLV provides special
tools to enhance the visual curve matching process such as active type curves,
parameter tweaking and combined drawdown and derivative plots.
AQTESOLV also provides automatic curve matching to estimate aquifer properties
from your test data using nonlinear least squares fitting procedure. Prior to
performing automatic estimation, use visual curve matching to obtain preliminary
estimates of aquifer properties.
Test Fit of Model (Diagnostic Checking)
Use residual plots to perform diagnostic checking on the model residuals after you
have performed model estimation (curve matching).
The residual-time and residual-simulated plots help you to identify model bias, i.e.,
correlation between the model errors and time or simulated value. Ideally, the
residuals should exhibit a random pattern on these plots with no clustering of
positive or negative residuals.
Use the normal probability plot to find out if the model residuals are normally
distributed.

19

Pumping Test Design and Prediction

To design a pumping test or forecast drawdown due to pumping using AQTESOLV,
enter the following information into the Forward Solution Wizard:
1. Units of measurement,
2. Aquifer data such as thickness and anisotropy,
3. Well data including locations, construction details and discharge rate(s), and
4. Aquifer properties (transmissivity and storativity).
After completing the wizard, choose a pumping test solution and use data plots and
contouring to view the model predictions.

Field Applications
Enter response data into AQTESOLV to monitor the progress of a field test.
1. Perform curve matching during a test to obtain preliminary estimates of
aquifer properties.
2. Examine data plots in the field to determine (a) the appropriate time for
terminating a pumping test or (b) the need for additional slug testing before
leaving a field site.

20

Examples

Overview (Examples)
Follow the examples in this chapter for pumping tests, slug tests, constant-head
tests and groundwater mounding to help you learn to use the many features in
AQTESOLV.
in one of the examples, it indicates that the example (or
When you see
a section of it) presents features found only in the Pro version of AQTESOLV.

Pumping Test Examples

1. Constant-rate test in a nonleaky confined aquifer near Gridley, OH
Keywords: Pumping Test Wizard; Import Wizard; diagnostic flow plots;
radial flow plot; derivative plot; visual curve matching; automatic curve
matching; prediction; contouring; Cooper-Jacob solution; Theis solution
2. Constant-rate test with recovery in a nonleaky confined aquifer
Keywords: Pumping Test Wizard; Import Wizard; diagnostic flow plots;
radial flow plot; derivative plot; Agarwal plot; residual drawdown plot; visual
curve matching; automatic curve matching; active type curves; Theis residual
drawdown solution; Theis solution
3. Variable-rate test with recovery in a nonleaky confined aquifer
Keywords: Pumping Test Wizard; Import Wizard; visual curve matching;
automatic curve matching; active type curves; Agarwal plot; Theis solution
4. Constant-rate test in pumped well (single-well test) with wellbore storage in a
nonleaky confined aquifer, Saudi Arabia
Keywords: Pumping Test Wizard; Import Wizard; single-well test; wellbore
storage; diagnostic flow plots; radial flow plot; derivative plot; visual curve
matching; automatic curve matching; parameter tweaking; active type
curves; recharge boundary; Cooper-Jacob solution; Papadopulos-Cooper
solution; Moench solution
5. Constant-rate test in pumped well (single-well test) with wellbore storage and
skin in a nonleaky confined aquifer, Lynden, WA
Keywords: Pumping Test Wizard; Import Wizard; single-well test; wellbore
storage; wellbore skin; diagnostic flow plots; radial flow plot; derivative plot;
visual curve matching; parameter tweaking; Cooper-Jacob solution;
Papadopulos-Cooper solution; Dougherty-Babu solution
6. Step-drawdown test in a confined aquifer, Saudi Arabia
Keywords: Pumping Test Wizard; Import Wizard, step-drawdown test;
automatic curve matching; wellbore skin; effective well radius; Theis step-

21

drawdown solution
7. Constant-rate test with multiple observation wells in a nonleaky confined
aquifer near Sioux Flats
Keywords: Pumping Test Wizard; Import Wizard; CSV file with missing
values; adding wells; diagnostic flow plots; radial flow plot; derivative plot;
composite plot; visual curve matching; automatic curve matching; distance
drawdown; Theis solution
8. Constant-rate test in a leaky confined aquifer near Dalem, The Netherlands
Keywords: Pumping Test Wizard; Import Wizard; diagnostic flow plots;
radial flow plot; derivative plot; automatic curve matching; Hantush-Jacob
solution; Hantush solution
9. Constant-rate test with multiple observation wells in a leaky confined aquifer
Keywords: Pumping Test Wizard; Import Wizard; CSV file; adding wells;
diagnostic flow plots; radial flow plot; derivative plot; composite plot; visual
curve matching; automatic curve matching; distance drawdown; CooperJacob solution; Hantush-Jacob solution
10. Constant-rate test in an unconfined aquifer with delayed gravity response
near Saratoga, NY
Keywords: Pumping Test Wizard; Import Wizard; delayed gravity response;
partial penetration; diagnostic flow plots; radial flow plot; derivative plot;
visual curve matching; automatic curve matching; Cooper-Jacob solution;
Neuman solution; Moench solution
11. Constant-rate test in an unconfined aquifer with noninstantaneous drainage at
the water table at Cape Cod, MA
Keywords: Pumping Test Wizard; Import Wizard; noninstantaneous
drainage; partial penetration; diagnostic flow plots; radial flow plot; derivative
plot; visual curve matching; automatic curve matching; Cooper-Jacob
solution; Neuman solution; Tartakovsky-Neuman solution
12. Constant-rate test in a double-porosity (fractured) aquifer at Nevada Test Site
Keywords: Pumping Test Wizard; Import Wizard; double porosity; adding
wells; diagnostic flow plots; radial flow plot; derivative plot; composite plot;
automatic curve matching; Moench solution
13. Pumping test design (forward solution)
Keywords: Forward Solution Wizard; prediction; test design; distance
drawdown;
vertical fracture; sensitivity analysis; Gringarten-Witherspoon solution
14. Constant-rate test in a horizontal well in a confined aquifer
Keywords: Pumping Test Wizard; Import Wizard; horizontal well; diagnostic

22

flow plots; derivative plot; automatic curve matching; Daviau et al. solution;
sensitivity analysis

Slug Test Examples

1. Single-well slug test in an unconfined aquifer
Keywords: Slug Test Wizard; Import Wizard; transforming depth-to-water
measurements to displacement; normalized head; recommended head range;
visual curve matching; automatic curve matching; sensitivity analysis;
screening data with Cooper et al. solution; Bouwer-Rice solution; KGS Model;
Peres et al. approximate deconvolution
2. Single-well slug test in an unconfined aquifer with noninstantaneous initiation
Keywords: Slug Test Wizard; Import Wizard; translation method;
normalized head; recommended head range; visual curve matching; BouwerRice solution
3. Single-well slug test in well screened across water table with drainage from
filter pack (double straight-line effect)
Keywords: Slug Test Wizard; Import Wizard; well screened across water
table; normalized head; drainage from filter pack; double straight-line effect;
visual curve matching; Bouwer-Rice solution
4. Single-well slug test in a high hydraulic conductivity, confined aquifer
Keywords: Slug Test Wizard; Import Wizard; inertial effect; underdamped;
correction for frictional well loss; normalized head; visual curve matching;
automatic curve matching; active type curves; Butler solution
5. Multi-well slug test in a confined aquifer in Lincoln County, Kansas
Keywords: Slug Test Wizard; Import Wizard; adding wells; normalized
head; automatic curve matching; screening data with Cooper et al. solution;
KGS Model

Constant-Head Test Examples

1. Constant-head test including flow and recovery near Grand Junction, CO
Keywords: Constant-Head Test Wizard; Import Wizard; importing rates;
importing recovery data; discharge plot; residual drawdown plot; Agarwal
plot; visual curve matching; automatic curve matching; Jacob-Lohman
solution; Hantush solution; exact recovery solution

Mounding Examples
1. Groundwater mounding beneath a rectangular recharge area
Keywords: mounding tools; contouring; report file; Hantush solution

23

Pumping Tests

Pumping Test Example: Constant Rate (Gridley)

Walton (1962) presented data from a pumping test conducted on July 2, 1953 near
Gridley, Illinois. The test well (Well 3) fully penetrated an 18-ft thick sand and gravel
aquifer under nonleaky artesian conditions. Pumping continued for eight hours at a
constant rate of 220 gallons-per-minute (gpm). Hydraulic response was monitored in
an observation well (Well 1) at a distance of 824 ft from the pumped well. Time and
drawdown measurements were recorded in minutes and feet, respectively.
This example will introduce you to the following tasks and features in AQTESOLV:

Creating a new data set with the Pumping Test Wizard

Importing data with the Observation Data Import Wizard

Saving a data set

Inspecting diagnostic plots (radial flow and derivative)

Estimating aquifer properties using Cooper-Jacob (1946) and Theis (1935)

solutions (visual and automatic)

Predicting future response over time and distance (distance-drawdown and

contour plots)

While following the steps in this example, click Help or press F1 to obtain
context sensitive help in the AQTESOLV application.
Create a New Data Set with Pumping Test Wizard
The first step in analyzing data from a pumping test is to create a new AQTESOLV
data set. In this example, we will use the Pumping Test Wizard to assist us with data
entry.
1. Create a new data set by choosing New from the File menu.
2. In the New Data Set dialog, select Pumping Test Wizard from the list.
Click OK.
3. Choose Multiwell test for the type of pumping test. Click OK.

24

4. The Pumping Test Wizard prompts you for data required to analyze a
pumping test. Click Next to begin the wizard.
5. For units of measurement, choose ft for length, min for time, gal/min for
pumping rate and gal/day/sq. ft for hydraulic conductivity. Click Next.
6. For project information, enter Gridley, Illinois for the location and July 2,
1953 for the test date. Click Next.
7. For aquifer data, enter 18 for the aquifer thickness. Enter 1 for the anisotropy
ratio (i.e., assume hydraulic conductivity is isotropic). Click Next.
8. For pumping well data, enter Well 3 for the well name. Enter coordinates of
X=0 and Y=0. Click Next.
9. For pumping well construction, select the option for vertical, full
penetration. Click Next.
10. For pumping well radius data, assume 0.5 for casing radius and 0.5 for well
radius. Click Next.
11. For pumping rates, enter 0 for time and 220 for rate in the first row of the
spreadsheet. Click Next.
12. For observation well data, enter Well 1 for the well name. Enter 824 and 0
for the X and Y coordinates, respectively. Click Next.
13. For observation well construction, select the option for vertical, full
penetration. Click Next.
14. For observations, click Import to launch the Observation Data Import Wizard
for importing data from a file.
We will import a text file consisting of 22 time-drawdown readings arranged
in two columns. The first column is elapsed time since the start of the test.
The second column contains drawdown measurements.
In Step 1 of the wizard, click Browse. Select the import file Gridley.txt in
the AQTESOLV installation folder and click Open. Click Next.
In Step 2 of the wizard, enter 2 for the number of columns, 1 for the
starting row in the file, 1 for the column containing elapsed time and 2 for
the column containing displacement. Click Next.
In Step 3 of the wizard, click Finish. Inspect the import file summary and
click OK.
Click Next to proceed with the Pumping Test Wizard.
15. You have completed the Pumping Test Wizard. Click Finish.
After completing the Pumping Test Wizard, AQTESOLV automatically displays an
Error Log to let you know if the data set contains any errors. If the Error Log
identifies any mistakes, choose options from the Edit menu to correct them.

25

Save Data Set

At this point, it's a good idea to save your work.
Save the data set by choosing Save As from the File menu. Choose a folder and
enter Gridley Well No. 1 for the name of the file. Click Save. AQTESOLV saves the
file with an .aqt extension.
Inspect Diagnostic Plots
Before performing curve matching to estimate aquifer properties, you may use
diagnostic features in AQTESOLV to evaluate aquifer and flow conditions.
Diagnostic flow plots help you select an appropriate solution method for your
pumping test data.
1. Choose Radial Flow from the View menu to display a radial flow plot on
log-linear axes.
View Radial Flow Plot
At late time on this graph, data plotting as a straight line indicate radial flow
conditions in an infinite-acting confined aquifer.

26

Derivative analysis is another useful diagnostic tool for evaluating aquifer conditions.
1. Choose Displacement-Time from the View menu to display a plot of the test
data. On semi-log axes, this plot is identical to the radial flow plot above.
2. Choose Wells from the Edit menu. Select Well 1 from the list and click
Modify.
In the Symbols tab, remove the check from Use data symbols properties
and select cross for the derivative symbol.
In the Curves tab, remove the check from Use type curve properties.
Click Color for the derivative curve properties, change the color to red, and
click OK.
Click OK and then Close.
3. Select Options from the View menu. In the Plots tab, check Derivative
curves. In the Derivative tab, select the option for Bourdet and enter
a differentiation interval of 0.3. Click OK.

27

View Derivative Plot

The form of the derivative plot is characteristic of radial flow in an infinite
confined aquifer. At late time, the derivative becomes essentially constant
when the data plot as a straight line.

Estimate Aquifer Properties

The radial flow and derivative plots that we have examined for this test confirm the
assumption of radial flow in an infinite-acting confined aquifer. To start our analysis,
we can use the Cooper-Jacob (1946) solution to obtain preliminary estimates of
aquifer properties.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. Remove the check from Solution is inactive. Click the + next to Confined
Aquifers to expand the list of available solutions for confined aquifers. Select
Cooper-Jacob (1946) and click OK.

28

3. Choose Displacement-Time from the View menu.

4. Choose Options from the View menu. In the Plots tab, remove the
check from Derivative curve(s) and check Valid time for CooperJacob approximation. Click OK.
The dashed vertical line shown on the plot is a guide indicating the time
when the Cooper-Jacob solution becomes valid. Match the solution to data
plotting to the right of the vertical line.
5. Choose Visual from the Match menu to perform visual curve matching with
the Cooper-Jacob solution.
To perform visual matching, move the mouse to a point where you wish to
begin drawing a new line with the Cooper-Jacob solution.
Click and hold down the left mouse button to anchor the new line at this
point.
Continue to hold the mouse button down and move the mouse to match a
new straight line to your data. As you move the mouse, AQTESOLV draws a
straight line between the anchor point and the position of the mouse.
Release the left mouse button when you have finished matching a new
straight line. AQTESOLV automatically updates the plot legend to reflect
changes in parameter values.
6. Repeat the previous step as needed to achieve a satisfactory match.
View Visual Match With Cooper-Jacob
Note that very few data points near the end of the test meet the validity
criterion (u 0.01) for the Cooper-Jacob solution. You can change the validity
criterion to a less stringent value if desired.

29

Having completed our preliminary analysis with Cooper-Jacob, let's continue by

matching the data with the Theis (1935) solution for a confined aquifer.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. From the list of solutions for Confined Aquifers, select Theis (1935) and
click OK.
3. Choose Log Axes from the View menu to change the axes to a log-log
format.
4. Select Options from the View menu. In the Plots tab, check Derivative
curves. Click OK.
The plot displays two curves. The blue curve is the drawdown predicted by
the Theis solution (i.e., the trace of the Theis type curve projected on the
data plot). The red curve is the derivative curve predicted by the Theis
solution.
5. Choose Visual from the Match menu to perform visual curve matching with
the Theis solution.
Click and hold the left mouse button down over a point within the plot area.

30

Continue to hold the mouse button down and move the mouse to match the
curves to the drawdown and derivative data. As you move the type curve,
AQTESOLV automatically updates the plot legend to reflect changes in
parameter values.
Release the left mouse button when you have finished matching the curves.
6. Walton (1962) reported values of T = 10,100 gal/day/ft and S = 0.00002 for
this test.
View Visual Match With Theis

7. Choose Automatic from the Match menu and click Estimate to perform
automatic curve matching.
During the iterative estimation procedure, AQTESOLV displays a progress
window and updates the curves displayed on the plot in the background.
8. When estimation has finished, click OK and then Close. Click OK to view the
new position of the type curve. The new values of T and S are close to the
estimates from visual curve matching.
9. Use residual-time, residual-simulated and normal probability plots to evaluate
the fit of the curve by examining residuals. The diagnostics report also
presents residual statistics for curve fitting.
31

10. Choose Save from the File menu to save your work.
Prediction
AQTESOLV provides tools for predicting response in the aquifer under future
conditions. Using the aquifer properties determined from curve matching analysis,
you may forecast drawdown over time or distance.
You may use the displacement-time plot to predict drawdown with time for the
observation well(s) in your data set.
1. Choose Displacement-time from the View menu to display a plot of
drawdown versus time.
2. Choose Log-Linear Axes from the View menu to display the plot on semi-log
axes.
3. Choose Format from the View menu and click the X Axis tab. Remove the
check from Auto and enter 10000 for the maximum value. Click OK.
Forecast drawdown over distance on a distance-drawdown plot.
1. Choose Distance drawdown from the View menu to display a plot of
drawdown versus distance.
2. Choose Options from the View menu and click the Distance tab. Enter
43200 min (30 days) for the time used in distance-drawdown calculations.
Click OK.
3. Choose Format from the View menu and click the Y Axis tab. Remove the
check from Auto and enter 50 ft for the maximum value. Click OK.
4. If observation wells in your data set do not contain a measurement at the
time specified for a distance-drawdown plot, AQTESOLV automatically
interpolates/extrapolates a data point for you.
If you have Surfer installed on your computer, you may use the Grid Wizard to
generate a contour plot of drawdown.
1. Choose Contour from the View menu.
2. In Step 1 of the Grid Wizard, enter the name of a Grid file to store data for
the contour plot. Select X-Y (Plan) for the grid orientation. Click Next.
3. In Step 2 of the Grid Wizard, enter -1000 and 1000 for the minimum and
maximum dimensions in the X and Y directions. Enter 51 for the number of
grid lines for both directions. For the depths, enter 0 and 18 (i.e., compute
the average drawdown over the full thickness of the aquifer). Enter 43200
for the time. Click Next.
4. In Step 3 of the Grid Wizard, check Display grid file with Surfer and
select Contour. Click Finish to display the contour plot with Surfer. Use
options in Surfer to customize the appearance of the plot.

32

Pumping Test Example: Recovery

This example guides you through the analysis of drawdown and recovery data from a
pumping test in a nonleaky confined aquifer (USBR 1995). The test well was pumped
at a constant rate of 162.9 ft3/min for 800 minutes. Drawdown was measured in an
observation well located 100 ft from the test well. Recovery was monitored for 800
minutes after pumping stopped.
This example will introduce you to the following tasks and features in AQTESOLV:

Creating a new data set for a recovery test with the Pumping Test Wizard

Importing data from a text file

Saving a data set

Inspecting diagnostic plots (radial flow and derivative)

Estimating aquifer properties using Theis (1935) type curve and Theis (1935)
residual drawdown solutions (visual and automatic)

Matching recovery data using Agarwal's method

While following the steps in this example, click Help or press F1 to context
sensitive help in the AQTESOLV application.
Create a New Data Set with Pumping Test Wizard
The first step in analyzing data from a pumping test is to create a new AQTESOLV
data set. In this example, you will use the Pumping Test Wizard to assist with data
entry.
1. Create a new data set by choosing New from the File menu.
2. In the New Data Set dialog, select Pumping Test Wizard from the list.
Click OK.
3. Choose Multiwell test for the type of pumping test. Click OK.
4. The Pumping Test Wizard prompts you for data required to analyze a
pumping test. Click Next to begin the wizard.
5. For units of measurement, choose ft for length, min for time,
consistent for pumping rate and consistent for hydraulic conductivity.

33

Click Next.
Consistent units for pumping rate and hydraulic conductivity are based on
the units of length and time selected for the data set. In this example,
consistent units are ft3/min for Q and ft/min for K.
6. For project information, enter Las Vegas for the location. Click Next.
7. For aquifer data, assume 100 for the aquifer thickness. Enter 1 for the
anisotropy ratio (i.e., assume hydraulic conductivity is isotropic). Click Next.
8. For pumping well data, enter Test Well for the well name. Enter coordinates
of X=0 and Y=0. Click Next.
9. For pumping well construction, select the option for vertical, full
penetration. Click Next.
10. For pumping well radius data, assume 0.5 for casing radius and 0.5 for well
radius. Click Next.
11. For pumping rates, click Insert Row. In the first row of the
spreadsheet, enter 0 for time and 162.9 for rate. In the second row,
enter 800 for time and 0 for rate. Click Next.

The first period is the constant-rate pumping phase of the test; the second
period is the recovery phase. Whenever you analyze recovery data, you need
to enter the pumping history prior to recovery as well as the time when
recovery begins.

34

12. For observation well data, enter Obs. Well for the well name. Enter 100 and
0 for the X and Y coordinates, respectively. Click Next.
13. For observation well construction, select the option for vertical, full
penetration. Click Next.
14. For observations, click Import to launch the Observation Data Import Wizard
for importing data from a file.
You will import a text file consisting of time-drawdown readings arranged in
two columns. The first column is elapsed time since the start of the test. The
second column contains drawdown measurements.
In Step 1 of the wizard, click Browse. Select the import file USBR
Recovery.txt in the AQTESOLV installation folder and click Open. Click
Next.
In Step 2 of the wizard, use the defaults determined by the Import Wizard.
Click Next.
In Step 3 of the wizard, accept the defaults and click Finish. Inspect the
import file summary and click OK.
Click Next to proceed with the Pumping Test Wizard.
15. You have completed the Pumping Test Wizard. Click Finish.
After completing the Pumping Test Wizard, AQTESOLV automatically displays an
Error Log to let you know if the data set contains any errors. If the Error Log
identifies any mistakes, choose options from the Edit menu to correct them.
Save Data Set
At this point, it's a good idea to save your work.
Save the data set by choosing Save As from the File menu. Choose a folder and
enter USBR Recovery for the name of the file. Click Save. The default extension for
an AQTESOLV data set is .aqt.
Inspect Diagnostic Plots
Before performing curve matching to estimate aquifer properties, you may use
diagnostic features in AQTESOLV to evaluate aquifer and flow conditions.
Diagnostic flow plots help you select an appropriate solution method for your
pumping test data.
1. Choose Radial Flow from the View menu to display a radial flow plot on
log-linear axes.
View Radial Flow Plot
During the first 800 minutes of the test (prior to the peak), the data
approach a straight line with time indicating radial flow conditions in an

35

infinite-acting confined aquifer. Data from the recovery phase of this test
display a declining trend on the plot after 800 minutes.

Derivative analysis is another useful diagnostic tool for evaluating aquifer conditions.
1. Choose Displacement-Time from the View menu to display a plot of the test
data. On semi-log axes, this plot is identical to the radial flow plot above.
2. Choose Log Axes from the View menu to plot the data on log-log axes.
3. Choose Wells from the Edit menu. Select Obs. Well from the list and click
Modify.
In the Symbols tab, remove the check from Use data symbols properties
and select cross for the derivative symbol.
In the Curves tab, remove the check from Use type curve properties.
Click Color for the derivative curve properties, change the color to red, and
click OK.
Click OK and then Close.

36

4. Select Options from the View menu. In the Plots tab, check Derivative
curves. In the Derivative tab, select the option for Spane and enter
0.3 for the differentiation interval. Click OK.
View Derivative Plot
During the first 800 minutes of the test (prior to the peak in the drawdown
data), the derivative approaches a constant value with time which is
characteristic of radial flow in an infinite confined aquifer.

Match Solution to Recovery Data

The radial flow and derivative plots that we have examined for this test confirm the
assumption of radial flow in an infinite-acting confined aquifer. You could begin the
analysis of this test by analyzing either the drawdown or the recovery data, but in
this example, you will start with the recovery phase of the test.
Begin your analysis using the familiar Theis (1935) residual drawdown method which
matches a straight line to the recovery data on a residual drawdown plot.
1. Choose Solution from the Match menu to select a method for analyzing the

37

data.
2. Remove the check from Solution is inactive. Click the + next to Confined
Aquifers to expand the list of available solutions for confined aquifers. Select
Theis (1935) residual drawdown/recovery and click OK.
3. Choose Residual Drawdown from the View menu.
The graph on log-linear axes shows residual drawdown, s', plotted as a
function of t/t' where t is time since pumping began and t' is time since
pumping stopped. Early recovery data (large t/t') plot to the right; as
recovery continues (decreasing s'), t/t' approaches unity.
4. Choose Visual from the Match menu to perform visual curve matching
with the Theis residual drawdown solution.
Match the straight line to late-time recovery data (t/t' approaching unity) to
achieve a valid match with the Theis residual drawdown solution.
To perform visual matching, move the mouse to a point where you wish to
begin drawing a new line.
Click and hold down the left mouse button to anchor the new line at this
point.
Continue to hold the mouse button down and move the mouse to match a
new straight line to your data. As you move the mouse, AQTESOLV draws a
straight line between the anchor point and the position of the mouse.
Release the left mouse button when you have finished matching a new
straight line. AQTESOLV automatically updates the plot legend to reflect
changes in parameter values.
5. Repeat the previous step as needed to achieve a satisfactory match.
View Visual Match With Theis Residual Drawdown

38

6. Curve matching with straight-line methods relies on your judgment to

position the line over the appropriate range of data; therefore, visual curve
matching is generally more efficient than automatic curve matching.
Now you will use Agarwal's method to analyze the same recovery data with the Theis
(1935) solution. Agarwal's procedure is used routinely in the petroleum industry for
recovery test analysis.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. From the list of solutions for Confined Aquifers, select Theis (1935) and
click OK.
3. Choose Agarwal from the View menu.
The Agarwal method plots recovery as a function of Agarwal equivalent time.
Through a simple transformation of the time scale, Agarwal's method enables
you to analyze recovery data with type curves developed for drawdown
analysis.
4. Choose Log Axes from the View menu.
The plot displays two curves. The blue curve is the recovery predicted by the
39

Theis solution using the Agarwal method (i.e., the trace of the Theis type
curve projected on the data plot). The red curve is the derivative curve
predicted by the Theis solution.
5. Choose Visual from the Match menu to perform visual curve matching with
the Theis solution using Agarwal's method for recovery data.
Click and hold the left mouse button down over a point within the plot area.
Continue to hold the mouse button down and move the mouse to match the
curves to the recovery and derivative data. As you move the type curve,
AQTESOLV automatically updates the plot legend to reflect changes in
parameter values.
Release the left mouse button when you have finished matching the curves.
6. Repeat the previous step as need to match the recovery data.
View Agarwal Match

Match Solution to Drawdown and Recovery Data

40

You are not limited to analyzing recovery data separately from drawdown data as we
did in the previous section. Now you will use the Theis (1935) solution to analyze
drawdown and recovery together.
You may use any pumping test solution in AQTESOLV (with the exception of
straight-line methods) to combine the analysis of drawdown and recovery
data.
1. Choose Displacement-Time from the View menu to display a plot of
drawdown/residual drawdown versus time.
2. Choose Log Axes from the View menu to display the plot on log-log axes.
3. Choose Automatic from the Match menu and click Estimate to perform
automatic curve matching.
During the iterative estimation procedure, AQTESOLV displays a progress
window and updates the curves displayed on the plot in the background.
4. When estimation has finished, click OK and then Close. Click OK to view the
new position of the type curve.
The estimated values of T and S are close to the values determined from
visual curve matching.
View Automatic Match for Drawdown and Recovery Data

41

5. Use residual-time, residual-simulated and normal probability plots to evaluate

the fit of the curve by examining residuals. The diagnostics report also
presents residual statistics for curve fitting.
6. Choose Active Curves from the Match menu to perform visual curve
matching with Active Type Curves.
Use Active Type Curves when matching pumping test data with variable
rates (including recovery). Visual curve matching with the active curves
option in AQTESOLV is a major improvement over static (traditional) curves
that assume a constant pumping rate. Active type curves are enabled when
you see a check next to the Active Curves option in the Match menu.
Click and hold the left mouse button down over a point within the plot area.
Continue to hold the mouse button down and move the mouse to match the
curves to the drawdown and derivative data. As you move the type curve,
AQTESOLV automatically updates the plot legend to reflect changes in
parameter values.
Release the left mouse button when you have finished matching the curves.

42

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

Pumping Test Example: Variable Rate

This example guides you through the analysis of drawdown and recovery data from a
hypothetical variable-rate pumping test in a nonleaky confined aquifer (modified
from Kruseman and De Ridder 1990). The rate in the fully penetrating test well
changed in a stepwise fashion over a period of 150 minutes.
Step
1
2
3
4

Elapsed Time
(min)
0
30
80
150

Duration
(min)
30
50
50
-

Rate
(m3/day)
500
700
600
0

Drawdown was measured in an observation well located 5 m from the test well.
Recovery was monitored after pumping stopped at 150 minutes.
This example will introduce you to the following tasks and features in AQTESOLV:

Creating a new data set for a recovery test with the Pumping Test Wizard

Importing data from a text file

Saving a data set

Estimating aquifer properties using Theis (1935) solution (visual and

automatic)

Matching data with active type curves

While following the steps in this example, click Help or press F1 to context
sensitive help in the AQTESOLV application.
Create a New Data Set with Pumping Test Wizard
The first step in analyzing data from a pumping test is to create a new AQTESOLV
data set. In this example, you will use the Pumping Test Wizard to assist with data
entry.
1. Create a new data set by choosing New from the File menu.
2. In the New Data Set dialog, select Pumping Test Wizard from the list.
Click OK.

43

3. Choose Multiwell test for the type of pumping test. Click OK.
4. The Pumping Test Wizard prompts you for data required to analyze a
pumping test. Click Next to begin the wizard.
5. For units of measurement, choose m for length, min for time, m3/day for
pumping rate and m/day for hydraulic conductivity. Click Next.
6. For project information, enter Variable-Rate Test for the title. Click Next.
7. For aquifer data, assume 50 for the aquifer thickness. Enter 1 for the
anisotropy ratio (i.e., assume hydraulic conductivity is isotropic). Click Next.
8. For pumping well data, enter PW for the well name. Enter coordinates of X=0
and Y=0. Click Next.
9. For pumping well construction, select the option for vertical, full
penetration. Click Next.
10. For pumping well radius data, assume 0.25 for casing radius and 0.25 for
well radius. Click Next.
11. For pumping rates, click Add Rows. Enter 3 for the number of rows to
add and click OK. Enter the rates for the test as shown below. Click
Next.
Enter the time for pumping periods as time since the start of the test. To
enter recovery, enter the time when pumping stopped and a rate of zero.

12. For observation well data, enter OW for the well name. Enter 5 and 0 for the

44

X and Y coordinates, respectively. Click Next.

13. For observation well construction, select the option for vertical, full
penetration. Click Next.
14. For observations, click Import to launch the Observation Data Import Wizard
for importing data from a file.
You will import a text file consisting of time-drawdown readings arranged in
two columns. The first column is elapsed time since the start of the test. The
second column contains drawdown and recovery measurements.
In Step 1 of the wizard, click Browse. Select the import file Variable
Rate.txt in the AQTESOLV installation folder and click Open. Click Next.
In Step 2 of the wizard, use the defaults determined by the Import Wizard.
Click Next.
In Step 3 of the wizard, accept the defaults and click Finish. Inspect the
import file summary and click OK.
Click Next to proceed with the Pumping Test Wizard.
15. You have completed the Pumping Test Wizard. Click Finish.
After completing the Pumping Test Wizard, AQTESOLV automatically displays an
Error Log to let you know if the data set contains any errors. If the Error Log
identifies any mistakes, choose options from the Edit menu to correct them.
Save Data Set
At this point, it's a good idea to save your work.
Save the data set by choosing Save As from the File menu. Choose a folder and
enter Variable Rate for the name of the file. Click Save. The default extension for
an AQTESOLV data set is .aqt.
Match Solution to Drawdown and Recovery Data
Use the Theis (1935) solution to analyze drawdown and recovery together.
You may use any pumping test solution in AQTESOLV (with the exception of
straight-line methods) to combine the analysis of drawdown and recovery
data.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. Remove the check from Solution is inactive. Click the + next to Confined
Aquifers to expand the list of available solutions for confined aquifers. Select
Theis (1935) and click OK.
3. Choose Displacement-Time from the View menu to display a plot of
drawdown/residual drawdown versus time.

45

4. Choose Log Axes from the View menu to display the plot on log-log axes.
5. Choose Automatic from the Match menu and click Estimate to perform
automatic curve matching.
During the iterative estimation procedure, AQTESOLV displays a progress
window and updates the curves displayed on the plot in the background.
6. When estimation has finished, click OK and then Close. Click OK to view the
new position of the type curve.
View Automatic Match for Drawdown and Recovery Data

7. Use residual-time, residual-simulated and normal probability plots to evaluate

the fit of the curve by examining residuals. The diagnostics report also
presents residual statistics for curve fitting.
8. Choose Active Curves from the Match menu to perform visual curve
matching with Active Type Curves.
Use Active Type Curves when matching pumping test data with variable
rates (including recovery). Visual curve matching with the active curves
option in AQTESOLV is a major improvement over static (traditional) curves

46

that assume a constant pumping rate. Active type curves are enabled when
you see a check next to the Active Curves option in the Match menu.
Click and hold the left mouse button down over a point within the plot area.
Continue to hold the mouse button down and move the mouse to match the
curve to the drawdown data. As you adjust the curve, AQTESOLV
automatically updates the plot legend to reflect changes in parameter
values.
Release the left mouse button when you have finished matching the curves.
9. Choose Save from the File menu to save your work.
Match Solution to Recovery Data
Now you will use Agarwal's method to analyze the recovery data with the Theis
(1935) solution. Agarwal's procedure is used routinely in the petroleum industry for
recovery test analysis.
1. Choose Agarwal from the View menu.
The Agarwal method plots recovery as a function of Agarwal equivalent time.
Through a simple transformation of the time scale, Agarwal's method enables
you to analyze recovery data from a variable-rate test with type curves
developed for constant-rate drawdown analysis.
2. Choose Log Axes from the View menu.
3. Choose Visual from the Match menu to perform visual curve matching with
the Theis solution using Agarwal's method for recovery data.
Click and hold the left mouse button down over a point within the plot area.
Continue to hold the mouse button down and move the mouse to match the
curve to the recovery data. As you move the type curve, AQTESOLV
automatically updates the plot legend to reflect changes in parameter
values.
Release the left mouse button when you have finished matching the curves.
4. Repeat the previous step as need to match the recovery data.
View Match with Agarwal Method

47

Pumping Test Example: Wellbore Storage

(Saudi Arabia)
In this example, you will analyze data from a single-well pumping test described by
Sen (1995). The 3-m diameter test well fully penetrates an aquifer consisting of fineand coarse-grained Quaternary deposits in wadi Uoranah in the eastern provinces of
Saudi Arabia. The aquifer is reportedly overlain by a thin layer of silt. Pumping
continued for more than 200 minutes at a constant rate of 0.478 m3/min. Time and
drawdown measurements were recorded in minutes and meters, respectively.
This example will introduce you to the following tasks and features in AQTESOLV:

Creating a new data set with the Pumping Test Wizard

Importing data with the Observation Data Import Wizard

Saving a data set

48

Inspecting diagnostic plots (radial flow and derivative)

Estimating aquifer properties using the Cooper-Jacob (1946) and

Papadopulos-Cooper (1967) solutions (visual and automatic)

While following the steps in this example, click Help or press F1 to obtain
context sensitive help in the AQTESOLV application.
Create a New Data Set with Pumping Test Wizard
The first step in analyzing data from a single-well pumping test is to create a new
AQTESOLV data set. In this example, we will use the Pumping Test Wizard to assist
us with data entry.
1. Create a new data set by choosing New from the File menu.
2. In the New Data Set dialog, select Pumping Test Wizard from the list.
Click OK.
3. Choose Single-well test for the type of pumping test. Click OK.
4. The Pumping Test Wizard prompts you for data required to analyze a
single-well pumping test. Click Next to begin the wizard.
5. For units of measurement, choose m for length, min for time,
consistent for pumping rate and m/day for hydraulic conductivity.
Click Next.
Consistent units for pumping rate are based on the units of length and time
selected for the data set. In this example, consistent units are m3/min for Q.
6. For project information, enter Saudi Arabia for the location. Click Next.
7. For aquifer data, assume 100 for the aquifer thickness. Enter 1 for the
anisotropy ratio (i.e., assume hydraulic conductivity is isotropic). Click Next.
8. For pumping well data, enter PW for the well name. Enter coordinates of X=0
and Y=0. Click Next.
9. For pumping well construction, select the option for vertical, full
penetration. Click Next.
10. For pumping well radius data, enter 1.5 for casing radius and 1.5 for well
radius. Click Next.
11. For pumping rates, enter 0 for time and 0.478 for rate in the first row of the
spreadsheet. Click Next.
12. For observations, click Import to launch the Observation Data Import Wizard
for importing data from a file.

49

We will import a text file consisting of 39 time-drawdown readings arranged

in two columns. The first column is elapsed time since the start of the test.
The second column contains drawdown measurements.
In Step 1 of the wizard, click Browse. Select the import file Uoranah.txt in
the AQTESOLV installation folder and click Open. Click Next.
In Step 2 of the wizard, accept the default entries and click Next.
In Step 3 of the wizard, click Finish. Inspect the import file summary and
click OK.
Click Next to proceed with the Pumping Test Wizard.
13. You have completed the Pumping Test Wizard. Click Finish.
After completing the Pumping Test Wizard, AQTESOLV automatically displays an
Error Log to let you know if the data set contains any errors. If the Error Log
identifies any mistakes, choose options from the Edit menu to correct them.
Save Data Set
At this point, it's a good idea to save your work.
Save the data set by choosing Save As from the File menu. Choose a folder, enter
Uoranah for the name of the file and click Save. AQTESOLV saves the file with an
.aqt extension.
Inspect Diagnostic Plots
Before performing curve matching to estimate aquifer properties, you may use
diagnostic features in AQTESOLV to evaluate aquifer and flow conditions.
Diagnostic flow plots help you select an appropriate solution method for your
pumping test data.
1. Choose Radial Flow from the View menu to display a radial flow plot on
log-linear axes.
View Semi-Log Radial Flow Plot
At late time, the data begin to flatten suggesting the influence of a recharge
boundary or leakage. Prior to the recharge effect, data plotting as a straight
line indicates radial flow conditions in an infinite-acting aquifer.

50

2. Choose Log Axes from the View menu to display the radial flow plot on loglog axes.
3. Choose Visual from the Match menu. Click the mouse over the second
data point on the plot to display a line with unit slope over the early-time
data.
View Log-Log Radial Flow Plot
Early-time data with unit slope on a radial flow plot with log-log axes is
characteristic of wellbore storage.

51

Derivative analysis is another useful diagnostic tool for evaluating aquifer conditions.
1. Choose Displacement-Time from the View menu to display a plot of the test
data. On semi-log axes, this plot is identical to the radial flow plot above.
2. Choose Wells from the Edit menu. Select PW from the list and click Modify.
In the Symbols tab, remove the check from Use data symbols properties
and select cross for the derivative symbol.
In the Curves tab, remove the check from Use type curve properties.
Click Color for the derivative curve properties, change the color to red, and
click OK.
Click OK and then Close.
3. Select Options from the View menu. In the Plots tab, check Derivative
curves. In the Derivative tab, select the option for Smoothing and
enter a factor of 2. Click OK.
View Derivative Plot
52

The peak on the derivative plot is characteristic of wellbore storage. At

intermediate to late time, the derivative approaches a constant value when
the aquifer is infinite acting. At the end of the test, the derivative approaches
zero suggesting the influence of recharge or leakage.

Estimate Aquifer Properties

The radial flow and derivative plots that we have examined for this test suggest a
confined or semi-confined aquifer. Although the data exhibit wellbore storage, we
can use the Cooper-Jacob (1946) solution, which neglects storage in the wellbore, to
obtain preliminary estimates of aquifer properties.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. Remove the check from Solution is inactive. Click the + next to Confined
Aquifers to expand the list of available solutions for confined aquifers. Select
Cooper-Jacob (1946) and click OK.
3. Choose Displacement-Time from the View menu.
53

4. Choose Visual from the Match menu to perform visual curve matching with
the Cooper-Jacob solution. Match the line to late-time data after the wellbore
storage effect has dissipated but before the onset of the recharge effect.
To perform visual matching, move the mouse to a point where you wish to
begin drawing a new line with the Cooper-Jacob solution.
Click and hold down the left mouse button to anchor the new line at this
point.
Continue to hold the mouse button down and move the mouse to match a
new straight line to your data. As you move the mouse, AQTESOLV draws a
straight line between the anchor point and the position of the mouse.
Release the left mouse button when you have finished matching a new
straight line. AQTESOLV automatically updates the plot legend to reflect
changes in parameter values.
5. Repeat the previous step as needed to achieve a satisfactory match to the
late-time data. Your estimate of T should be on the order of 500 m2/day.
Because Cooper-Jacob assumes a line source for the pumped well, the
estimate of S is less reliable.
View Visual Match with Cooper-Jacob

54

Having completed our preliminary analysis with Cooper-Jacob, let's account for
wellbore storage by matching the Papadopulos-Cooper (1967) solution to the data.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. From the list of solutions for Confined Aquifers, select PapadopulosCooper (1967) and click OK.
3. Choose Log Axes from the View menu to view the data on log-log axes.
4. Choose Toolbox from the Match menu. In the Tweak tab, select r(c)
from the list of parameters. Use the scroll bar to adjust the value of
casing radius to match the early-time data. You can limit the range of casing
radius values by editing the minimum and maximum values for r(c) in the
Parameters tab. After you have aligned the curve with the early-time data,
click OK.
View Tweaked Casing Radius
Adjust the casing radius value to match early-time data affected by wellbore
storage. In many cases, the effective casing radius turns out to be less than
the nominal value because of equipment in the well such as discharge tubing
55

and transducer cable.

5. Choose Active Curves from the Match menu to initiate visual curve matching
with Active Type Curves.
Click and hold the left mouse button down over a point within the plot area.
Continue to hold the mouse button down and move the mouse to match the
curves to the drawdown and derivative data. As you move the type curve,
AQTESOLV automatically updates parameter values in the plot legend.
Release the left mouse button when you have finished matching the curves.
6. Repeat the previous step as necessary to match the data.
7. Choose Wells from the Edit menu. Select PW from the list and click
Modify. In the Observations tab, scroll to the bottom of the
spreadsheet. Change the weight for the last three observations to 0. By
changing the weights to zero, these observations, which reflect the influence
of recharge or leakage, will be ignored during automatic curve matching. Click
OK and Close.
You may use observation weights to control which measurements are
56

included in automatic curve matching. To exclude a measurement, enter a

weight of zero.
8. Choose Automatic from the Match menu. In the Parameters tab, select
Active for the estimation status of r(c) and Inactive for r(w). In the
equations for the Papadopulos-Cooper solution, the values of S and r(w) are
correlated (i.e., appear together); hence we are unable to estimate both
parameters simultaneously in a single-well test. Click Estimate to perform
automatic curve matching.
During the iterative estimation procedure, AQTESOLV displays a progress
window and updates the curves displayed on the plot in the background.
9. When estimation has finished, click OK and then Close. Click OK to view the
new position of the type curve.
View Automatic Match with Papadopulos-Cooper

10. Use residual-time, residual-simulated and normal probability plots to evaluate

the fit of the curve by examining residuals. The diagnostics report also
presents residual statistics for curve fitting.
11. Choose Save from the File menu to save your work.

57

Evaluate Sources of Recharge

No specific information is available to define potential sources of recharge at the site
such as aquifer boundaries. Nevertheless, we can use AQTESOLV to simulate a
stream boundary.
1. Choose Aquifer Data from the Edit menu. In the Boundaries tab, check
Enable Boundaries. Assume a single linear boundary and select ConstantHead for condition along boundary B-C. For the remaining boundaries, A-B,
C-D and D-A, choose None for the boundary condition.
Next, enter two points along the boundary B-C. To place the boundary 1800
m from the pumped well, enter 1800 and 100 for the coordinates of point B
and 1800 and -100 for point C.
Click Apply to view the effect of the constant-head boundary on the
simulated drawdown curve. You can change the distance to the boundary to
evaluate different boundary locations.
Remove the check from Enable Boundaries and click OK.
View Effect of Constant-Head Boundary at 1800 m

58

Pumping Test Example: Wellbore Storage and

Skin (Lynden)
In this example, you will analyze data from a single-well pumping test conducted in a
500-ft deep confined aquifer near Lynden, Washington. The six-inch diameter test
well was constructed in an eight-inch borehole. The well is screened over the lower
10 feet of the sand and gravel comprising the 40-ft thick aquifer. Pumping continued
for more than two weeks at a constant rate of 50 gallons-per-minute (gpm). Time
and drawdown measurements were recorded in minutes and feet, respectively. Data
for this example provided courtesy of Associated Earth Sciences, Inc.
This example will introduce you to the following tasks and features in AQTESOLV:

Creating a new data set with the Pumping Test Wizard

Importing data with the Observation Data Import Wizard

Saving a data set

Inspecting diagnostic plots (radial flow and derivative)

Visual estimation of aquifer properties using the Cooper-Jacob (1946) and

Dougherty-Babu (1984) solutions (parameter tweaking)

While following the steps in this example, click Help or press F1 to obtain
context sensitive help in the AQTESOLV application.
Create a New Data Set with Pumping Test Wizard
The first step in analyzing data from a single-well pumping test is to create a new
AQTESOLV data set. In this example, we will use the Pumping Test Wizard to assist
us with data entry.
1. Create a new data set by choosing New from the File menu.
2. In the New Data Set dialog, select Pumping Test Wizard from the list.
Click OK.
3. Choose Single-well test for the type of pumping test. Click OK.
4. The Pumping Test Wizard prompts you for data required to analyze a
single-well pumping test. Click Next to begin the wizard.
5. For units of measurement, choose ft for length, min for time, gal/min for
pumping rate and ft/day for hydraulic conductivity. Click Next.
59

6. For project information, enter Lynden, WA for the location. Click Next.
7. For aquifer data, assume 40 for the aquifer thickness. Enter 1 for the
anisotropy ratio (i.e., assume hydraulic conductivity is isotropic). Click Next.
8. For pumping well data, enter PW-3 for the well name. Enter coordinates of
X=0 and Y=0. Click Next.
9. For pumping well construction, select the option for vertical, partial
penetration. Enter 30 for depth to top of screen and 10 for screen length.
Click Next.
10. For pumping well radius data, enter 0.333 for casing radius and 0.25 for well
radius. Click Next.
11. For pumping rates, enter 0 for time and 50 for rate in the first row of the
spreadsheet. Click Next.
12. For observations, click Import to launch the Observation Data Import Wizard
for importing data from a file.
We will import a text file consisting of 92 time-drawdown readings arranged
in two columns. The first column is elapsed time since the start of the test.
The second column contains drawdown measurements.
In Step 1 of the wizard, click Browse. Select the import file PW-3.txt in the
AQTESOLV installation folder and click Open. Click Next.
In Step 2 of the wizard, accept the default entries and click Next.
In Step 3 of the wizard, click Finish. Inspect the import file summary and
click OK.
Click Next to proceed with the Pumping Test Wizard.
13. You have completed the Pumping Test Wizard. Click Finish.
After completing the Pumping Test Wizard, AQTESOLV automatically displays an
Error Log to let you know if the data set contains any errors. If the Error Log
identifies any mistakes, choose options from the Edit menu to correct them.
Save Data Set
At this point, it's a good idea to save your work.
Save the data set by choosing Save As from the File menu. Choose a folder, enter
PW-3 for the name of the file and click Save. AQTESOLV saves the file with an .aqt
extension.
Inspect Diagnostic Plots
Before performing curve matching to estimate aquifer properties, you may use
diagnostic features in AQTESOLV to evaluate aquifer and flow conditions.
Diagnostic flow plots help you select an appropriate solution method for your
60

pumping test data.

1. Choose Radial Flow from the View menu to display a radial flow plot on
log-linear axes.
View Semi-Log Radial Flow Plot
Late-time data plotting as a straight line indicate radial flow conditions in an
infinite-acting aquifer.

2. Choose Log Axes from the View menu to display the radial flow plot on loglog axes.
3. Choose Visual from the Match menu. Click the mouse over the second
data point on the plot to display a line with unit slope over the early-time
data.
View Log-Log Radial Flow Plot
Early-time data with unit slope on a radial flow plot with log-log axes is
characteristic of wellbore storage.
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Derivative analysis is another useful diagnostic tool for evaluating aquifer conditions.
1. Choose Displacement-Time from the View menu to display a plot of the test
data.
2. Choose Log Axes from the View menu to display the data on log-log axes.
3. Choose Wells from the Edit menu. Select PW-3 from the list and click
Modify.
In the Symbols tab, remove the check from Use data symbols properties
and select cross for the derivative symbol.
In the Curves tab, remove the check from Use type curve properties.
Click Color for the derivative curve properties, change the color to red, and
click OK.
Click OK and then Close.
4. Select Options from the View menu. In the Plots tab, check Derivative

62

curves. In the Derivative tab, select the option for Bourdet and enter a
differentiation interval of 0.4. Click OK.
View Derivative Plot
The peak on the derivative plot is characteristic of wellbore storage. At
intermediate to late time, the derivative approaches a constant value when
the aquifer is infinite acting.

Estimate Aquifer Properties

The radial flow and derivative plots that we have examined for this test suggest a
confined aquifer. Although the data exhibit wellbore storage, we can use the CooperJacob (1946) solution, which neglects both wellbore storage and partial penetration,
to obtain preliminary estimates of transmissivity.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. Remove the check from Solution is inactive. Click the + next to Confined

63

Aquifers to expand the list of available solutions for confined aquifers. Select
Cooper-Jacob (1946) and click OK.
3. Choose Displacement-Time from the View menu.
4. Choose Visual from the Match menu to perform visual curve matching with
the Cooper-Jacob solution. Match the line to late-time data after the wellbore
storage effect has dissipated.
To perform visual matching, move the mouse to a point where you wish to
begin drawing a new line with the Cooper-Jacob solution.
Click and hold down the left mouse button to anchor the new line at this
point.
Continue to hold the mouse button down and move the mouse to match a
new straight line to your data. As you move the mouse, AQTESOLV draws a
straight line between the anchor point and the position of the mouse.
Release the left mouse button when you have finished matching a new
straight line. AQTESOLV automatically updates the plot legend to reflect
changes in parameter values.
5. Repeat the previous step as needed to achieve a satisfactory match to
the late-time data. Your estimate of T should be on the order of 250
ft2/day.
View Visual Match with Cooper-Jacob
The low value of S that you obtain with the Cooper-Jacob solution is an
indication of partial penetration effect and possibly wellbore skin effect at the
pumped well.

64

Having completed our preliminary analysis with Cooper-Jacob, let's account

for wellbore storage, wellbore skin and partial penetration by matching the
Dougherty-Babu (1984) solution to the data.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. From the list of solutions for Confined Aquifers, select Dougherty-Babu
(1984) and click OK.
3. Choose Log-Linear Axes from the View menu to view the data on log-linear
axes.
4. Choose Toolbox from the Match menu. In the Tweak tab, select S from
the list of parameters. Use the scroll bar to adjust the value of storativity
to match the late-time data. You can set the range of storativity values by
editing the minimum and maximum values for S in the Parameters tab.
View Match with Tweaked S
The Dougherty-Babu solution accounts for partial penetration; however, the
implausibly low value of S determined from this analysis indicates wellbore
skin effect.
65

5. In the Parameters tab, enter 0.0002 for S as a plausible estimate of

storativity in a confined aquifer. In the Tweak tab, select Sw from the
list of parameters. Use the scroll bar to adjust the value of wellbore skin
factor to match the late-time data. You can set the range of wellbore skin
factor values by editing the minimum and maximum values for Sw in the
Parameters tab.
View Match with Tweaked Sw
It is not possible to estimate S and Sw simultaneously from a single-well
test. If an estimate of S is available independently from an observation well,
we may use it as a known value in the analysis of pumping well data;
otherwise, we may assume a value of S based on local hydrogeologic
conditions.

66

6. In the Tweak tab, select r(c) from the list of parameters. Use the scroll
bar to adjust the value of casing radius to match the early-time data.
You can limit the range of casing radius values by editing the minimum and
maximum values for r(c) in the Parameters tab. After you have aligned the
curve with the early-time data, click OK.
View Final Match with Dougherty-Babu
Adjust the casing radius value to match early-time data affected by wellbore
storage. In many cases, the effective casing radius turns out to be less than
the nominal value because of equipment in the well such as discharge tubing
and transducer cable.

67

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

Uncertainty Analysis
Let's examine the relationship between wellbore skin factor and partial penetration.
1. Choose Aquifer Data from the Edit menu and enter 50 for the aquifer
thickness.
2. Choose Wells from the Edit menu, select PW-3 from the list and click
Modify. In the Construction tab, enter 40 for the depth to the top of screen.
Click OK. Click Close.
3. Choose Toolbox from the Match menu. In the Tweak tab, select Sw
from the list of parameters. Use the scroll bar to adjust the value of
wellbore skin factor to match the late-time data. You can set the range of
wellbore skin factor values by editing the minimum and maximum values for
Sw in the Parameters tab.
View Match with Tweaked Sw
Partial penetration and wellbore skin can produce virtually identical effects in
a pumping well's drawdown response. In this case, decreasing the penetration
ratio, L/b, was equivalent to increasing the wellbore skin factor. In the

68

petroleum industry, the effect of partial penetration is known as pseudo-skin

effect because it produces a response that is similar to wellbore skin.

Pumping Test Example: Step-Drawdown (Saudi

Arabia)
Clark (1977) presented data from a step-drawdown test in a well completed in a
confined sandstone aquifer in Saudi Arabia. The test consisted of six steps, each
lasting 180 minutes. Pumping stopped after 1080 minutes and recovery was
monitored for an additional 1570 minutes. Time and drawdown measurements were
recorded in minutes and meters, respectively.
This example will introduce you to the following tasks and features in AQTESOLV:

Creating a new data set with the Pumping Test Wizard

Importing data with the Observation Data Import Wizard

Saving a data set

69

Estimating aquifer properties using the Theis (1935) step-drawdown solution

(visual and automatic)

While following the steps in this example, click Help or press F1 to obtain
context sensitive help in the AQTESOLV application.
Create a New Data Set with Pumping Test Wizard
The first step in analyzing data from a single-well pumping test is to create a new
AQTESOLV data set. In this example, we will use the Pumping Test Wizard to assist
us with data entry.
1. Create a new data set by choosing New from the File menu.
2. In the New Data Set dialog, select Pumping Test Wizard from the list.
Click OK.
3. Choose Single-well test for the type of pumping test. Click OK.
4. The Pumping Test Wizard prompts you for data required to analyze a
single-well pumping test. Click Next to begin the wizard.
5. For units of measurement, choose m for length, min for time, m3/day for
pumping rate and m/day for hydraulic conductivity. Click Next.
6. For project information, enter Saudi Arabia for the location. Click Next.
7. For aquifer data, assume 100 for the aquifer thickness. Enter 1 for the
anisotropy ratio (i.e., assume hydraulic conductivity is isotropic). Click Next.
8. For pumping well data, enter Test Well 1 for the well name. Enter
coordinates of X=0 and Y=0. Click Next.
9. For pumping well construction, select the option for vertical, full
penetration. Click Next.
10. For pumping well radius data, assume 0.25 for casing radius and 0.25 for
well radius. Click Next.
11. For pumping rates, click Add Rows, enter 6 for the number of rows and click
OK. Enter the seven time and rate readings shown below for the test. The last
step, with a rate of zero, represents the recovery period. Click Next.
Pumping
Period
1
2
3
4
5

Elapsed Time Since Start Rate

of Test
(m3/day)
(min)
0
1306
180
1693
360
2423
540
3261
720
4094
70

6
7

900
1080

5019
0

12. For observations, click Import to launch the Observation Data Import Wizard
for importing data from a file.
We will import a text file consisting of 201 time-drawdown readings arranged
in two columns. The first column is elapsed time since the start of the test.
The second column contains drawdown measurements.
In Step 1 of the wizard, click Browse. Select the import file Clark.txt in the
AQTESOLV installation folder and click Open. Click Next.
In Step 2 of the wizard, accept the default entries and click Next.
In Step 3 of the wizard, click Finish. Inspect the import file summary and
click OK.
Click Next to proceed with the Pumping Test Wizard.
13. You have completed the Pumping Test Wizard. Click Finish.
After completing the Pumping Test Wizard, AQTESOLV automatically displays an
Error Log to let you know if the data set contains any errors. If the Error Log
identifies any mistakes, choose options from the Edit menu to correct them.
Save Data Set
At this point, it's a good idea to save your work.
Save the data set by choosing Save As from the File menu. Choose a folder, enter
Clark for the name of the file and click Save. AQTESOLV saves the file with an .aqt
extension.
Estimate Aquifer Properties
To evaluate the data from this test, we will use the Theis (1935) step-drawdown test
solution.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. Remove the check from Solution is inactive. Click the + next to Confined
Aquifers to expand the list of available solutions for confined aquifers. Select
Theis (1935) step-drawdown test and click OK.
3. Choose Displacement-Time from the View menu to display the test data.
4. Choose Log Axes from the View menu to view the data on log-log axes.
5. Choose Wells from the Edit menu. Select Test Well 1 from the list and
click Modify. In the Observations tab, change the weight for the first
two observations to 0. By changing the weights to zero, these observations,
which reflect the influence of recharge or leakage, will be ignored during
automatic curve matching. Click OK and Close.

71

You may use observation weights to control which measurements are

included in automatic curve matching. To exclude a measurement, enter a
weight of zero.
6. Choose Automatic from the Match menu.
In the Estimation tab, enter 50 for the maximum number of iterations.
In the Parameters tab, select Inactive for the estimation status of Sw and P.
In the equations for the Theis step-drawdown test solution, the values of S
and Sw are correlated (i.e., appear together); hence we are unable to
estimate both parameters simultaneously in a single-well test. In this case,
we'll assume that nonlinear well loss is quadratic (i.e., P=2). Enter 1.e-5 and
0.1 for the minimum and maximum values of S.
Click Estimate to perform automatic curve matching.
During the iterative estimation procedure, AQTESOLV displays a progress
window and updates the curves displayed on the plot in the background.
7. When estimation has finished, click OK and then Close. Click OK to view the
new position of the type curve.
View Automatic Match with Theis

72

8. Use residual-time, residual-simulated and normal probability plots to evaluate

the fit of the curve by examining residuals. The diagnostics report also
presents residual statistics for curve fitting.
9. Choose Save from the File menu to save your work.
Estimate Wellbore Skin
It is not feasible to estimate both S and Sw from a single-well test due to parameter
correlation. If data from a step-drawdown test included an observation well,
however, we could estimate S because the wellbore skin parameter only affects
drawdown in the pumped well.
Clark (1977) also conducted a constant-rate test in Test Well 1 and estimated S from
drawdown data measured in a nearby observation well. Using his estimate of for S,
we can determine Sw from the step-drawdown test.
1. Choose Automatic from the Match menu.
In the Parameters tab, select Active for the estimation status of Sw and
Inactive for the estimation status of S and P. Enter for the value of S.
Click Estimate to perform automatic curve matching.
During the iterative estimation procedure, AQTESOLV displays a progress
73

window and updates the curves displayed on the plot in the background.
2. When estimation has finished, click OK and then Close. Click OK to view the
new position of the type curve.
View Automatic Match with Theis Including Skin

3. The estimated values of T and C remain the same when we assume the value
of S = because the new estimate of Sw changes the effective radius of the
well. We can use Sw (= -0.3902) to compute the effective well radius as
follows:
effective well radius = r(w)*exp(-Sw) = (0.25 m)*exp(0.3902) = 0.37 m

Pumping Test Example: Multiple Observation

Wells (Sioux Flats)
This example guides you through the analysis of drawdown from a pumping test in a
nonleaky confined aquifer near Sioux Flats, South Dakota (USBR 1995). The test well
was pumped at a constant rate of 2.7 ft3/sec for 2045 minutes. Drawdown was
measured in three observation wells located 100, 200 and 400 ft from the test well.
This example will introduce you to the following tasks and features in AQTESOLV:

74

Creating a new data set for a pumping test with the Pumping Test Wizard

Importing data from a CSV file using the Import Wizard

Adding observation wells to the data set

Saving a data set

Inspecting diagnostic plots (radial flow and derivative)

Estimating aquifer properties using Cooper-Jacob (1946) and Theis (1935)

solutions (visual and automatic)

Performing distance-drawdown analysis

While following the steps in this example, click Help or press F1 to context
sensitive help in the AQTESOLV application.
Create a New Data Set with Pumping Test Wizard
The first step in analyzing data from a pumping test is to create a new AQTESOLV
data set. In this example, you will use the Pumping Test Wizard to assist with data
entry.
1. Create a new data set by choosing New from the File menu.
2. In the New Data Set dialog, select Pumping Test Wizard from the list.
Click OK.
3. Choose Multiwell test for the type of pumping test. Click OK.
4. The Pumping Test Wizard prompts you for data required to analyze a
pumping test. Click Next to begin the wizard.
5. For units of measurement, choose ft for length, min for time, ft3/sec for
pumping rate and consistent for hydraulic conductivity. Click Next.
6. For project information, enter Sioux Flats for the location. Click Next.
7. For aquifer data, assume 50 for the aquifer thickness. Enter 1 for the
anisotropy ratio (i.e., assume hydraulic conductivity is isotropic). Click Next.
8. For pumping well data, enter Test Well for the well name. Enter coordinates

75

of X=0 and Y=0. Click Next.

9. For pumping well construction, select the option for vertical, full
penetration. Click Next.
10. For pumping well radius data, assume 0.5 for casing radius and 0.5 for well
radius. Click Next.
11. For pumping rates, enter 0 for time and 2.7 for rate. Click Next.
12. For observation well data, enter OW 1 for the well name. Enter 100 and 0 for
the X and Y coordinates, respectively. Click Next.
13. For observation well construction, select the option for vertical, full
penetration. Click Next.
14. For observations, click Import to launch the Observation Data Import Wizard
for importing data from a file.
You will import 28 observations from a text file consisting of time-drawdown
readings arranged in four columns. The first column is elapsed time since the
start of the test. The remaining columns contain drawdown measurements for
the three observation wells. This file contains missing values; thus, there are
fewer observations for each well than rows of data in the file.
In Step 1 of the wizard, click Browse. Select the import file Sioux Flats.csv
in the AQTESOLV installation folder and click Open. Click Next.
In Step 2 of the wizard, use the defaults determined by the Import Wizard.
Click Next.
In Step 3 of the wizard, accept the defaults and click Finish. Inspect the
import file summary and click OK.
Click Next to proceed with the Pumping Test Wizard.
15. You have completed the Pumping Test Wizard. Click Finish.
After completing the Pumping Test Wizard, AQTESOLV automatically displays an
Error Log to let you know if the data set contains any errors. If the Error Log
identifies any mistakes, choose options from the Edit menu to correct them.
Add Observation Wells
The Pumping Test Wizard helped you enter data for the pumping well and the first
observation well. Now you will add the two remaining observation wells to the data
set.
1. Choose Wells from the Edit menu and click New to add a new well. Select
the new well in the list and click Modify to edit the well.
2. In the General tab, enter OW 2 for the well name. Enter 200 and 0 for the X
and Y coordinates.
3. In the Observations tab, click Import to launch the Observation Data
76

Import Wizard for importing data from a file.

You will import 27 observations from the same text file used in the Pumping
Test Wizard. The first column is elapsed time since the start of the test. The
third column contains drawdown measurements for the second observation
well.
In Step 1 of the wizard, click Browse. Select the import file Sioux Flats.csv
in the AQTESOLV installation folder and click Open. Click Next.
In Step 2 of the wizard, enter 3 for the displacement column and keep the
other values determined by the Import Wizard. Click Next.
In Step 3 of the wizard, accept the defaults and click Finish. Inspect the
import file summary and click OK.
4. Click OK to finish editing OW 2.
5. Click New to add another well. Select the new well in the list and click
Modify to edit the well.
6. In the General tab, enter OW 3 for the well name. Enter 400 and 0 for the X
and Y coordinates.
7. In the Observations tab, click Import to launch the Observation Data
Import Wizard for importing data from a file.
You will import 24 observations from the same text file used for the first two
observation wells. The first column is elapsed time since the start of the test.
The fourth column contains drawdown measurements for the third
observation well.
In Step 1 of the wizard, click Browse. Select the import file Sioux Flats.csv
in the AQTESOLV installation folder and click Open. Click Next.
In Step 2 of the wizard, enter 4 for the displacement column and keep the
other values determined by the Import Wizard. Click Next.
In Step 3 of the wizard, accept the defaults and click Finish. Inspect the
import file summary and click OK.
8. Click OK to finish editing OW 3.
9. Click Close to leave the Wells window.
Save Data Set
At this point, it's a good idea to save your work.
Save the data set by choosing Save As from the File menu. Choose a folder and
enter Sioux Flats for the name of the file. Click Save. The default extension for an
AQTESOLV data set is .aqt.

77

Inspect Diagnostic Plots

Before performing curve matching to estimate aquifer properties, you may use
diagnostic features in AQTESOLV to evaluate aquifer and flow conditions.
Diagnostic flow plots help you select an appropriate solution method for your
pumping test data.
1. Choose Radial Flow from the View menu to display a radial flow plot on
log-linear axes.
View Radial Flow Plot
By the end of the test, the data for each well approach a straight line with
time indicating radial flow conditions in an infinite-acting confined aquifer.

Derivative analysis is another useful diagnostic tool for evaluating aquifer conditions.
1. Choose Composite from the View menu to display a plot of the test data
on log-linear axes.

78

A composite plot normalizes time by the radius squared (t/r2). For fully
penetrating wells in a homogeneous and isotropic nonleaky confined aquifer
(i.e., the assumptions for the Theis solution), the composite plot facilitates
visual curve matching because data from more than one observation well plot
along a single curve (Theis) or straight line (Cooper-Jacob).
2. Select Options from the View menu. In the Plots tab, check Derivative
curves. In the Derivative tab, select the option for Smoothing and
enter 2 for the smoothing factor. Click OK.
View Derivative Plot
As the test progresses, the derivative data approach a constant value, i.e,
the slope of the time drawdown data becomes constant, which is
characteristic of radial flow in an infinite confined aquifer.

Estimate Aquifer Properties

To start our analysis, we can use the Cooper-Jacob (1946) solution to obtain
preliminary estimates of aquifer properties.

79

1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. Remove the check from Solution is inactive. Click the + next to Confined
Aquifers to expand the list of available solutions for confined aquifers. Select
Cooper-Jacob (1946) and click OK.
3. Choose Composite from the View menu to display a composite plot of the
data.
4. Choose Log-Linear from the View menu to display the plot on log-linear axes.
5. Choose Options from the View menu. In the Plots tab, remove the
check from Derivative curve(s) and check Valid time for CooperJacob approximation. Click OK.
The dashed vertical line shown on the plot is a guide indicating the time
when the Cooper-Jacob solution becomes valid. Match the solution to data
plotting to the right of the vertical line.
6. Choose Visual from the Match menu to perform visual curve matching with
the Cooper-Jacob solution.
To perform visual matching, move the mouse to a point where you wish to
begin drawing a new line with the Cooper-Jacob solution.
Click and hold down the left mouse button to anchor the new line at this
point.
Continue to hold the mouse button down and move the mouse to match a
new straight line to your data. As you move the mouse, AQTESOLV draws a
straight line between the anchor point and the position of the mouse.
Release the left mouse button when you have finished matching a new
straight line. AQTESOLV automatically updates the plot legend to reflect
changes in parameter values.
7. Repeat the previous step as needed to achieve a satisfactory match.
View Visual Match With Cooper-Jacob
Note that very few data points near the end of the test meet the validity
criterion (u 0.01) for the Cooper-Jacob solution.

80

Now you will use the Theis (1935) solution to analyze the drawdown data in all three
observation wells simultaneously.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. Select Theis (1935) and click OK.
3. Choose Log Axes from the View menu to display the plot on log-log axes.
4. Choose Options from the View menu. In the Plots tab, check Derivative
curve(s). Click OK.
5. Choose Visual from the Match menu to perform visual curve matching.
Click and hold the left mouse button down over a point within the plot area.
Continue to hold the mouse button down and move the mouse to match the
curves to the drawdown and derivative data. As you move the curves,
AQTESOLV automatically updates the plot legend to reflect changes in
parameter values.

81

Release the left mouse button when you have finished matching the curves.
6. Repeat the previous step until you have achieved a satisfactory match. Try to
match both the drawdown and derivative data.
View Visual Match With Theis

7. Choose Automatic from the Match menu and click Estimate to perform
automatic curve matching.
During the iterative estimation procedure, AQTESOLV displays a progress
window and updates the curves displayed on the plot in the background.
8. When estimation has finished, click OK and then Close. Click OK to view the
new position of the type curve.
9. Use residual-time, residual-simulated and normal probability plots to evaluate
the fit of the curve by examining residuals. The diagnostics report also
presents residual statistics for curve fitting.
10. Choose Save from the File menu to save your work.

82

Perform Distance-Drawdown Analysis

In addition to time-drawdown analyses, you can use AQTESOLV to evaluate distancedrawdown data.
1. Choose Distance Drawdown from the View menu to plot drawdown versus
distance at a specified time.
2. Choose Options from the View menu. In the Distance tab, enter 2045 for
the time used in distance-drawdown calculations. Click OK.
3. The plot shows drawdown for the three observation wells at the end of the
test (2045 minutes). You may use automatic estimation to match the curve to
just the distance-drawdown data points.

Pumping Test Example: Constant-Rate Test in a

Leaky Confined Aquifer (Dalem)
Kruseman and De Ridder (1990) present data from a pumping test conducted in a
leaky confined aquifer near Dalem, The Netherlands. The aquifer is overlain by a
peat aquitard and underlain by a unit regarded as an aquiclude. The test well (M77)
was pumped for eight hours at a constant rate of 761 m3/day. Drawdown was
monitored in an observation well located 90 m from the pumped well. You will
analyze data that were corrected for tidal fluctuations and partial penetration. Time
and drawdown measurements were recorded in days and meters, respectively.
This example will introduce you to the following tasks and features in AQTESOLV:

Creating a new data set with the Pumping Test Wizard

Importing data with the Observation Data Import Wizard

Saving a data set

Inspecting diagnostic plots (radial flow and derivative)

Estimating aquifer properties using Hantush-Jacob (1955) and Hantush

(1960) solutions (visual and automatic)

While following the steps in this example, click Help or press F1 to obtain
context sensitive help in the AQTESOLV application.
Create a New Data Set with Pumping Test Wizard
The first step in analyzing data from a pumping test is to create a new AQTESOLV
83

data set. In this example, we will use the Pumping Test Wizard to assist us with data
entry.
1. Create a new data set by choosing New from the File menu.
2. In the New Data Set dialog, select Pumping Test Wizard from the list.
Click OK.
3. Choose Multiwell test for the type of pumping test. Click OK.
4. The Pumping Test Wizard prompts you for data required to analyze a
pumping test. Click Next to begin the wizard.
5. For units of measurement, choose m for length, day for time,
consistent for pumping rate and consistent for hydraulic conductivity.
Click Next.
Consistent units for pumping rate and hydraulic conductivity are based on
the units of length and time selected for the data set. In this example,
consistent units are m3/day for Q and m/day for K.
6. For project information, enter Dalem, The Netherlands for the location.
Click Next.
7. For aquifer data, assume 40 for the aquifer thickness. Enter 1 for the
anisotropy ratio (i.e., assume hydraulic conductivity is isotropic). Click Next.
8. For pumping well data, enter M77 for the well name. Enter coordinates of
X=0 and Y=0. Click Next.
9. For pumping well construction, select the option for vertical, full
penetration. Click Next.
10. For pumping well radius data, assume 0.1 for casing radius and 0.1 for well
radius. Click Next.
11. For pumping rates, enter 0 for time and 761 for rate in the first row of the
spreadsheet. Click Next.
12. For observation well data, enter r=90 for the well name. Enter 90 and 0 for
the X and Y coordinates, respectively. Click Next.
13. For observation well construction, select the option for vertical, full
penetration. Click Next.
14. For observations, click Import to launch the Observation Data Import Wizard
for importing data from a file.
We will import a text file consisting of 12 time-drawdown readings arranged
in two columns. The first column is elapsed time since the start of the test.
The second column contains drawdown measurements.
In Step 1 of the wizard, click Browse. Select the import file Dalem r=90
m.txt in the AQTESOLV installation folder and click Open. Click Next.

84

In Step 2 of the wizard, enter 2 for the number of columns, 9 for the
starting row in the file, 1 for the column containing elapsed time and 2 for
the column containing displacement. Click Next.
In Step 3 of the wizard, click Finish. Inspect the import file summary and
click OK.
Click Next to proceed with the Pumping Test Wizard.
15. You have completed the Pumping Test Wizard. Click Finish.
After completing the Pumping Test Wizard, AQTESOLV automatically displays an
Error Log to let you know if the data set contains any errors. If the Error Log
identifies any mistakes, choose options from the Edit menu to correct them.
Save Data Set
At this point, it's a good idea to save your work.
Save the data set by choosing Save As from the File menu. Choose a folder and
enter Dalem r=90 m for the name of the file. Click Save. AQTESOLV saves the file
with an .aqt extension.
Inspect Diagnostic Plots
Before performing curve matching to estimate aquifer properties, you may use
diagnostic features in AQTESOLV to evaluate aquifer and flow conditions.
Diagnostic flow plots help you select an appropriate solution method for your
pumping test data.
1. Choose Radial Flow from the View menu to display a radial flow plot on
log-linear axes.
View Radial Flow Plot
At late time on this graph, the data begin to flatten suggesting the possibility
of leakage or the presence of a recharge boundary.

85

Derivative analysis is another useful diagnostic tool for evaluating aquifer conditions.
1. Choose Displacement-Time from the View menu to display a plot of the test
data. On semi-log axes, this plot is identical to the radial flow plot above.
2. Choose Wells from the Edit menu. Select r=90 from the list and click
Modify.
In the Symbols tab, remove the check from Use data symbols properties
and select cross for the derivative symbol.
In the Curves tab, remove the check from Use type curve properties.
Click Color for the derivative curve properties, change the color to red, and
click OK.
Click OK and then Close.
3. Select Options from the View menu. In the Plots tab, check Derivative
curves. In the Derivative tab, select the option for Bourdet and enter
a differentiation interval of 0.2. Click OK.

86

View Derivative Plot

The derivative plot at intermediate time is fairly constant suggesting radial
flow conditions. At late time, the derivative begins to approach zero which is
indicative of a source of recharge (leakage or boundary).

Estimate Aquifer Properties

The diagnostic plots that you have examined for this test tend to confirm a leaky
confined aquifer model. To start the analysis, you will use the Hantush-Jacob (1955)
solution to obtain estimates of aquifer properties. The Hantush-Jacob solution
assumes no storage in the aquitard(s).
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. Remove the check from Solution is inactive. Click the + next to Leaky
Aquifers to expand the list of available solutions for leaky confined aquifers.
Select Hantush-Jacob (1955) w/o aquitard storage and click OK.
3. Choose Displacement-Time from the View menu.

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4. Choose Log Axes from the View menu to display the solution on log-log axes.
5. Choose Automatic from the Match menu and click Estimate to perform
automatic curve matching.
During the iterative estimation procedure, AQTESOLV displays a progress
window and updates the curves displayed on the plot in the background.
6. When estimation has finished, click OK and then Close. Click OK to view the
new position of the type curve.
View Automatic Match with Hantush-Jacob

7. Use residual-time, residual-simulated and normal probability plots to evaluate

the fit of the curve by examining residuals. The diagnostics report also
presents residual statistics for curve fitting. For this solution, the residual sum
of squares is and the residual standard deviation is 0.001458.
Now you will use the Hantush (1960) early-time solution to evaluate the data from
this test assuming storage in the aquitard.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. From the list of available solutions for leaky confined aquifers, select

88

Hantush (1960) early-time solution and click OK.

3. Choose Automatic from the Match menu and click Estimate to perform
automatic curve matching.
During the iterative estimation procedure, AQTESOLV displays a progress
window and updates the curves displayed on the plot in the background.
4. When estimation has finished, click OK and then Close. Click OK to view the
new position of the type curve.
View Automatic Match with Hantush

5. Choose Diagnostics from the View menu. For this solution, the residual
sum of squares is and the residual standard deviation is 0.001818.
Divide the value of each estimated parameter by its standard error to
determine its precision. A standard error smaller than the estimated
parameter indicates greater precision and less model uncertainty. In this
instance, the small precision of the estimates suggests greater uncertainty in
the fit of the Hantush model. This finding is consistent with the remark by
Kruseman and De Ridder (1990) that curve fitting with the Hantush method is
imprecise when is less than 0.5.
6. Choose Save from the File menu to save your work.

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Experiment with the Hantush (1960) solution and automatic curve matching
to see if you can improve the fit of the theoretical curve to the derivative
data. How does the model affect the estimated value of T?

Pumping Test Example: Leaky (Texas Hill)

This example guides you through the analysis of drawdown data from a multiobservation well pumping test in a leaky confined aquifer at a site designated as
Texas Hill (USBR 1995). The test well was pumped at a constant rate of 4488
gallons-per-minute (gpm) for 420 minutes. Drawdown was measured by hand in
three observation wells located 40, 80 and 160 ft north of the test well.
This example will introduce you to the following tasks and features in AQTESOLV:

Creating a new data set for a pumping test with the Pumping Test Wizard

Importing data from a CSV file using the Import Wizard

Adding observation wells to the data set

Saving a data set

Inspecting diagnostic plots (radial flow and derivative)

Estimating aquifer properties using Cooper-Jacob (1946) and Hantush-Jacob

(1955) solutions (visual and automatic)

Performing distance-drawdown analysis

While following the steps in this example, click Help or press F1 to context
sensitive help in the AQTESOLV application.
Create a New Data Set with Pumping Test Wizard
The first step in analyzing data from a pumping test is to create a new AQTESOLV
data set. In this example, you will use the Pumping Test Wizard to assist with data
entry.
1. Create a new data set by choosing New from the File menu.
2. In the New Data Set dialog, select Pumping Test Wizard from the list.
Click OK.

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3. Choose Multiwell test for the type of pumping test. Click OK.
4. The Pumping Test Wizard prompts you for data required to analyze a
pumping test. Click Next to begin the wizard.
5. For units of measurement, choose ft for length, min for time, gal/min for
pumping rate and consistent for hydraulic conductivity. Click Next.
6. For project information, enter Texas Hill for the location. Click Next.
7. For aquifer data, assume 50 for the aquifer thickness. Enter 1 for the
anisotropy ratio (i.e., assume hydraulic conductivity is isotropic). Click
Advanced and enter 20 for the aquitard thickness, b'. Click Next.
8. For pumping well data, enter Test Well for the well name. Enter coordinates
of X=0 and Y=0. Click Next.
9. For pumping well construction, select the option for vertical, full
penetration. Click Next.
10. For pumping well radius data, assume 0.5 for casing radius and 0.5 for well
radius. Click Next.
11. For pumping rates, enter 0 for time and 4488 for rate. Click Next.
12. For observation well data, enter OW 1 for the well name. Enter 0 and 40 for
the X and Y coordinates, respectively. Click Next.
13. For observation well construction, select the option for vertical, full
penetration. Click Next.
14. For observations, click Import to launch the Observation Data Import Wizard
for importing data from a file.
You will import 26 observations from a text file consisting of time-drawdown
readings arranged in four columns. The first column is elapsed time since the
start of the test. The remaining columns contain drawdown measurements for
the three observation wells. This file contains missing values; thus, there are
fewer observations for each well than rows of data in the file.
In Step 1 of the wizard, click Browse. Select the import file Texas Hill.csv in
the AQTESOLV installation folder and click Open. Click Next.
In Step 2 of the wizard, use the defaults determined by the Import Wizard.
Click Next.
In Step 3 of the wizard, accept the defaults and click Finish. Inspect the
import file summary and click OK.
Click Next to proceed with the Pumping Test Wizard.
15. You have completed the Pumping Test Wizard. Click Finish.
After completing the Pumping Test Wizard, AQTESOLV automatically displays an
Error Log to let you know if the data set contains any errors. If the Error Log
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identifies any mistakes, choose options from the Edit menu to correct them.
Add Observation Wells
The Pumping Test Wizard helped you enter data for the pumping well and the first
observation well. Now you will add the two remaining observation wells to the data
set.
1. Choose Wells from the Edit menu and click New to add a new well. Select
the new well in the list and click Modify to edit the well.
2. In the General tab, enter OW 2 for the well name. Enter 0 and 80 for the X
and Y coordinates.
3. In the Symbols tab, select cross for the data symbol.
4. In the Observations tab, click Import to launch the Observation Data
Import Wizard for importing data from a file.
You will import 26 observations from the same text file used in the Pumping
Test Wizard. The first column is elapsed time since the start of the test. The
third column contains drawdown measurements for the second observation
well.
In Step 1 of the wizard, click Browse. Select the import file Texas Hill.csv in
the AQTESOLV installation folder and click Open. Click Next.
In Step 2 of the wizard, enter 3 for the displacement column and keep the
other values determined by the Import Wizard. Click Next.
In Step 3 of the wizard, accept the defaults and click Finish. Inspect the
import file summary and click OK.
5. Click OK to finish editing OW 2.
6. Click New to add another well. Select the new well in the list and click
Modify to edit the well.
7. In the General tab, enter OW 3 for the well name. Enter 0 and 160 for the X
and Y coordinates.
8. In the Symbols tab, select diamond for the data symbol.
9. In the Observations tab, click Import to launch the Observation Data
Import Wizard for importing data from a file.
You will import 26 observations from the same text file used for the first two
observation wells. The first column is elapsed time since the start of the test.
The fourth column contains drawdown measurements for the third
observation well.
In Step 1 of the wizard, click Browse. Select the import file Texas Hill.csv in
the AQTESOLV installation folder and click Open. Click Next.

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In Step 2 of the wizard, enter 4 for the displacement column and keep the
other values determined by the Import Wizard. Click Next.
In Step 3 of the wizard, accept the defaults and click Finish. Inspect the
import file summary and click OK.
10. Click OK to finish editing OW 3.
11. Click Close to leave the Wells window.
Save Data Set
At this point, it's a good idea to save your work.
Save the data set by choosing Save As from the File menu. Choose a folder and
enter Texas Hill for the name of the file. Click Save. The default extension for an
AQTESOLV data set is .aqt.
Inspect Diagnostic Plots
Before performing curve matching to estimate aquifer properties, you may use
diagnostic features in AQTESOLV to evaluate aquifer and flow conditions.
Diagnostic flow plots help you select an appropriate solution method for your
pumping test data.
1. Choose Radial Flow from the View menu to display a radial flow plot on
log-linear axes.
View Radial Flow Plot
By the end of the test, the data for each well approach a horizontal line with
time indicating a source of recharge (leakage).

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Derivative analysis is another useful diagnostic tool for evaluating aquifer conditions.
1. Choose Composite from the View menu to display a plot of the test data
on log-linear axes.
A composite plot normalizes time by the radius squared (t/r2). For fully
penetrating wells in a homogeneous and isotropic leaky confined aquifer, the
composite plot facilitates visual curve matching because data from more than
one observation well plot along a single curve until the onset of leakage.
2. Choose Log Axes from the View menu to display the plot on log-log axes.
3. Select Options from the View menu. In the Plots tab, check Derivative
curves. In the Derivative tab, select the option for Bourdet and enter
0.4 for the differentiation interval. Click OK.
View Derivative Plot
As the test progresses, the derivatives approach zero, i.e, the slope of the
time drawdown data becomes horizontal, which is characteristic of recharge

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or leakage.

Estimate Aquifer Properties

To start our analysis, we can use the Cooper-Jacob (1946) solution for a confined
aquifer to obtain preliminary estimates of transmissivity and storativity.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. Remove the check from Solution is inactive. Click the + next to Confined
Aquifers to expand the list of available solutions for confined aquifers. Select
Cooper-Jacob (1946) and click OK.
3. Choose Composite from the View menu to display a composite plot of the
data.
4. Choose Options from the View menu. In the Plots tab, remove the
check from Derivative curve(s) and check Valid time for CooperJacob approximation. In the Valid Time tab, enter 0.05 for the critical
value of u. Click OK.
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The dashed vertical line shown on the plot is a guide indicating the time
when the Cooper-Jacob solution becomes valid. Match the solution to data
plotting to the right of the vertical line.
5. Choose Visual from the Match menu to perform visual curve matching with
the Cooper-Jacob solution.
To perform visual matching, move the mouse to a point where you wish to
begin drawing a new line with the Cooper-Jacob solution.
Click and hold down the left mouse button to anchor the new line at this
point.
Continue to hold the mouse button down and move the mouse to match a
new straight line to your data. As you move the mouse, AQTESOLV draws a
straight line between the anchor point and the position of the mouse.
Release the left mouse button when you have finished matching a new
straight line. AQTESOLV automatically updates the plot legend to reflect
changes in parameter values.
6. Repeat the previous step as needed to achieve a satisfactory match.
View Visual Match With Cooper-Jacob
Note that very few data points near the end of the test meet the validity
criterion (u 0.05) for the Cooper-Jacob solution.

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Now you will use the Hantush-Jacob (1955) solution for a leaky confined aquifer to
analyze the drawdown data in all three observation wells simultaneously.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. Click the + next to Leaky Confined Aquifers to expand the list of available
solutions for leaky confined aquifers. Select Hantush-Jacob
(1955)/Hantush (1964) and click OK.
3. Choose Log Axes from the View menu to display the plot on log-log axes.
4. Choose Options from the View menu. In the Plots tab, check Derivative
curve(s). Click OK.
5. Choose Automatic from the Match menu and click Estimate to perform
automatic curve matching.
During the iterative estimation procedure, AQTESOLV displays a progress
window and updates the curves displayed on the plot in the background.
6. When estimation has finished, click OK and then Close. Click OK to view the
new position of the type curve.

97

View Automatic Match With Hantush-Jacob

7. Use residual-time, residual-simulated and normal probability plots to evaluate

the fit of the curve by examining residuals. The diagnostics report also
presents residual statistics for curve fitting. The complete report shows
estimates of aquitard properties derived from the leakage parameter, r/B.
8. Choose Save from the File menu to save your work.
Perform Distance-Drawdown Analysis
In addition to time-drawdown analyses, you can use AQTESOLV to evaluate distancedrawdown data.
1. Choose Distance Drawdown from the View menu to plot drawdown versus
distance at a specified time.
2. Choose Options from the View menu. In the Distance tab, enter 420 for the
time used in distance-drawdown calculations. Click OK.
3. The plot shows drawdown for the three observation wells at the end of the
test (420 minutes). You may use automatic estimation to match the curve to
just the distance-drawdown data points.
View Distance-Drawdown Plot
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Pumping Test: Unconfined (Saratoga)

In this example, you will analyze data from a pumping test conducted near Saratoga,
New York (Greenkorn 1983). The test well (SA 1077) partially penetrated a 16-ft
thick water-table aquifer described as interbedded silty fine sand and coarse sand.
Pumping continued for nearly two days at a constant rate of 17.2 gallons-per-minute
(gpm). Hydraulic response was monitored in an observation well (SA 1072) at a
distance of 15.2 ft from the pumped well. Time and drawdown measurements were
recorded in days and feet, respectively.
This example will introduce you to the following tasks and features in AQTESOLV:

Creating a new data set with the Pumping Test Wizard

Importing data with the Observation Data Import Wizard

Saving a data set

Inspecting diagnostic plots (radial flow and derivative)

99

Estimating aquifer properties using Cooper-Jacob (1946), Neuman (1974) and

Moench (1997) solutions (visual and automatic)

While following the steps in this example, click Help or press F1 to obtain
context sensitive help in the AQTESOLV application.
Create a New Data Set with Pumping Test Wizard
The first step in analyzing data from a pumping test is to create a new AQTESOLV
data set. In this example, we will use the Pumping Test Wizard to assist us with data
entry.
1. Create a new data set by choosing New from the File menu.
2. In the New Data Set dialog, select Pumping Test Wizard from the list.
Click OK.
3. Choose Multiwell test for the type of pumping test. Click OK.
4. The Pumping Test Wizard prompts you for data required to analyze a
pumping test. Click Next to begin the wizard.
5. For units of measurement, choose ft for length, day for time, gal/min for
pumping rate and gal/day/sq. ft for hydraulic conductivity. Click Next.
6. For project information, enter Saratoga, NY for the location. Click Next.
7. For aquifer data, enter 16 for the aquifer thickness. Enter 1 for the anisotropy
ratio (i.e., assume hydraulic conductivity is isotropic). Click Next.
8. For pumping well data, enter SA 1077 for the well name. Enter coordinates
of X=0 and Y=0. Click Next.
9. For pumping well construction, select the option for vertical, partial
penetration. Enter 9 for the depth to the top of the well screen and 6 for the
screen length. Click Next.
10. For pumping well radius data, assume 0.333 for casing radius and 0.5 for
well radius. Click Next.
11. For pumping rates, enter 0 for time and 17.2 for rate in the first row of the
spreadsheet. Click Next.
12. For observation well data, enter SA 1072 for the well name. Enter 15.2 and
0 for the X and Y coordinates, respectively. Click Next.
13. For observation well construction, select the option for vertical, partial
penetration. Enter 11 for the depth to the top of the well screen and 3 for
the screen length. Click Next.
14. For radius data, enter 0.0 for the casing radius to disable delayed observation
100

well response.
15. For observations, click Import to launch the Observation Data Import Wizard
for importing data from a file.
We will import a text file consisting of 44 time-drawdown readings arranged
in two columns. The first column is elapsed time since the start of the test.
The second column contains drawdown measurements.
In Step 1 of the wizard, click Browse. Select the import file Saratoga SA
1072.txt in the AQTESOLV installation folder and click Open. Click Next.
In Step 2 of the wizard, accept the default entries and click Next.
In Step 3 of the wizard, click Finish. Inspect the import file summary and
click OK.
Click Next to proceed with the Pumping Test Wizard.
16. You have completed the Pumping Test Wizard. Click Finish.
After completing the Pumping Test Wizard, AQTESOLV automatically displays an
Error Log to let you know if the data set contains any errors. If the Error Log
identifies any mistakes, choose options from the Edit menu to correct them.
Save Data Set
At this point, it's a good idea to save your work.
Save the data set by choosing Save As from the File menu. Choose a folder, enter
Saratoga SA 1072 for the name of the file and click Save. AQTESOLV saves the file
with an .aqt extension.
Inspect Diagnostic Plots
Before performing curve matching to estimate aquifer properties, you may use
diagnostic features in AQTESOLV to evaluate aquifer and flow conditions.
Diagnostic flow plots help you select an appropriate solution method for your
pumping test data.
1. Choose Radial Flow from the View menu to display a radial flow plot on
log-linear axes.
View Radial Flow Plot
The response shown on the radial flow plot is characteristic of delayed
gravity response in an unconfined aquifer. At late time, data plotting as a
straight line indicate radial flow conditions in an infinite-acting aquifer.

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Derivative analysis is another useful diagnostic tool for evaluating aquifer conditions.
1. Choose Displacement-Time from the View menu to display a plot of the test
data. On semi-log axes, this plot is identical to the radial flow plot above.
2. Choose Wells from the Edit menu. Select SA 1072 from the list and click
Modify.
In the Symbols tab, remove the check from Use data symbols properties
and select cross for the derivative symbol.
In the Curves tab, remove the check from Use type curve properties.
Click Color for the derivative curve properties, change the color to red, and
click OK.
Click OK and then Close.
3. Select Options from the View menu. In the Plots tab, check Derivative
curves. In the Derivative tab, select the option for Bourdet and enter
a differentiation interval of 0.3. Click OK.

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View Derivative Plot

The form of the derivative plot is characteristic of radial flow in an unconfined
aquifer with delayed gravity response. At intermediate time, the derivative
approaches zero during the period of delayed gravity response.

Estimate Aquifer Properties

The radial flow and derivative plots that we have examined for this test confirm the
assumption of radial flow in an unconfined aquifer with delayed gravity response.
Although the wells in this example are partially penetrating, we can use the CooperJacob (1946) solution, which assumes fully penetrating wells, to obtain first-cut
estimates of aquifer properties.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. Remove the check from Solution is inactive. Click the + next to
Unconfined Aquifers to expand the list of available solutions for unconfined
aquifers. Select Cooper-Jacob (1946) and click OK.

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3. Choose Visual from the Match menu to perform visual curve matching with
the Cooper-Jacob solution.
Match the solution to the late-time data to estimate T and Sy. Note that the
Cooper-Jacob solution only determines one value for the storative properties
of the aquifer (labeled S); however, when you match the straight line to the
late-time data, you really are estimating Sy.
To perform visual matching, move the mouse to a point where you wish to
begin drawing a new line with the Cooper-Jacob solution.
Click and hold down the left mouse button to anchor the new line at this
point.
Continue to hold the mouse button down and move the mouse to match a
new straight line to your data. As you move the mouse, AQTESOLV draws a
straight line between the anchor point and the position of the mouse.
Release the left mouse button when you have finished matching a new
straight line. AQTESOLV automatically updates the plot legend to reflect
changes in parameter values.
4. Repeat the previous step as needed to achieve a satisfactory match to the
late-time data. The estimates of T and S should be close to 1.18x104
gal/day/ft and 0.15, respectively. Because you have matched the CooperJacob solution to late-time data, you will use 0.15 for your estimate of Sy.
Note: Because the Cooper-Jacob solution assumes fully penetrating wells,
your preliminary estimate of Sy at this stage of the analysis is only a firstorder approximation. To obtain a more refined estimate of Sy, you could use
the Theis (1935) solution which accounts for partially penetrating wells.
5. Choose Toolbox from the Match menu. In the Tweak tab, select S from the
list of parameters. Use the scroll bar to decrease S until the line matches the
early-time data. Your adjusted estimate of S should be near 0.005.
Having completed our preliminary analysis with Cooper-Jacob, let's continue by
matching the data with the Neuman (1974) solution for an unconfined aquifer with
delayed gravity response.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. From the list of solutions for Unconfined Aquifers, select Neuman (1974)
and click OK.
3. Choose Log Axes from the View menu to view the data on log-log axes.
4. Choose Toolbox from the Match menu. In the Parameters tab, enter , 0.005
and 0.15 for the values of T, S and Sy, respectively. Click OK.
5. Visual curve matching with the Neuman solution involves fitting Type A and
Type B curves to the data. For a given value of , match the Type A curve to
the early-time data to estimate T and S; match the Type B curve to the late104

time data to determine T and Sy.

Begin visual curve matching by selecting =0.1 from the list on the toolbar.

First, click

on the toolbar to match the Type A curve for =0.1.

Click and hold the left mouse button down over a point within the plot
area.
Continue to hold the mouse button down and move the mouse to match
the Type A curve to the early-time data. As you move curve, AQTESOLV
automatically updates parameter values in the plot legend.
Release the left mouse button when you have finished matching the
curve.

Next, click

on the toolbar to match the Type B curve for =0.1.

Click and hold the left mouse button down over a point within the plot
area.
Continue to hold the mouse button down and move the mouse to match
the Type B curve to the late-time data. As you move curve, AQTESOLV
automatically updates parameter values in the plot legend.
Release the left mouse button when you have finished matching the
curve.
6. Repeat the previous step for different values of until you obtain a
satisfactory match.
7. Choose Automatic from the Match menu and click Estimate to perform
automatic curve matching.
During the iterative estimation procedure, AQTESOLV displays a progress
window and updates the curves displayed on the plot in the background.
8. When estimation has finished, click OK and then Close. Click OK to view the
new position of the type curve.
View Automatic Match with Neuman Solution

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9. Use residual-time, residual-simulated and normal probability plots to evaluate

the fit of the curve by examining residuals. The diagnostics report also
presents residual statistics for curve fitting.
The foregoing analysis with the Neuman (1974) solution assumed a line
source for the pumped well. To investigate the effect of a finite-diameter well with
wellbore storage, let's match the Moench (1997) solution for an unconfined aquifer
with delayed gravity response.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. From the list of solutions for Unconfined Aquifers, select Moench (1997)
and click OK.
3. At intermediate and late time, the curves for the Neuman and Moench
solutions appear virtually the same; however, at early time, the curve for the
Moench solution shifts to the right as a consequence of the finite-diameter
pumped well with wellbore storage. As radial distance from the pumped well
increases, the difference between the two solutions becomes less pronounced.
4. Choose Automatic from the Match menu. In the Parameters tab, select
Inactive for the estimation status of Sw, r(w), r(c) and alpha. Click
Estimate to perform automatic curve matching.

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During the iterative estimation procedure, AQTESOLV displays a progress

window and updates the curves displayed on the plot in the background.
5. When estimation has finished, click OK and then Close. Click OK to view the
new position of the type curve.
View Automatic Match with Moench Solution

6. In terms of the residual sum of squares (RSS), the objective function

minimized by the automatic curve matching procedure, the curve fit with the
Moench solution (RSS = 0.003745 ft2) is superior to the Neuman solution
(RSS = 0.00436 ft2). How do the residual plots compare for the two
solutions?
Delayed Observation Well Response
The Moench (1997) solution for a double-porosity aquifer is one of the solutions
in AQTESOLV that includes delayed observation well response. To produce
delayed response, enter positive nonzero values for the casing radius and well radius
of the observation well.
View Effect of Delayed Response
In this example, the blue curve shows our curve match with no delayed response
while the red curve illustrates the effect of delayed response assuming casing radius

107

= well radius = 0.25 ft at the observation well. Delayed observation well response
affects the match at early time.

Pumping Test Example: Unconfined (Cape Cod)

In this example, you will analyze data from a pumping test conducted by the USGS
at Cape Cod, Massachusetts (Moench et al. 2001). The test well (F507-080) partially
penetrated a 170-ft (51.82-m) thick water-table aquifer described as a glacial
outwash deposit consisting of sand and gravel. A constant pumping rate of 320
gallons per minute (0.0202 m3/s) was maintained in the well for 72 hours.
Drawdown was monitored in an observation well (F377-037) at a distance of 85.1 ft
(25.94 m) from the pumped well. Time and drawdown measurements were recorded
in minutes and feet, respectively.
This example will introduce you to the following tasks and features in AQTESOLV:

Creating a new data set with the Pumping Test Wizard

Importing data with the Observation Data Import Wizard

Saving a data set

108

Inspecting diagnostic plots (radial flow and derivative)

Estimating aquifer properties using Cooper-Jacob (1946), Neuman (1974) and

Tartakovsky-Neuman (2007) solutions (visual and automatic)

While following the steps in this example, click Help or press F1 to obtain
context sensitive help in the AQTESOLV application.
Create a New Data Set with Pumping Test Wizard
The first step in analyzing data from a pumping test is to create a new AQTESOLV
data set. In this example, we will use the Pumping Test Wizard to assist us with data
entry.
1. Create a new data set by choosing New from the File menu.
2. In the New Data Set dialog, select Pumping Test Wizard from the list.
Click OK.
3. Choose Multiwell test for the type of pumping test. Click OK.
4. The Pumping Test Wizard prompts you for data required to analyze a
pumping test. Click Next to begin the wizard.
5. For units of measurement, choose ft for length, min for time, gal/min for
pumping rate and m/sec for hydraulic conductivity. Click Next.
6. For project information, enter Cape Cod, MA for the location. Click Next.
7. For aquifer data, enter 170 for the aquifer thickness. Enter 1 for the
anisotropy ratio (i.e., assume hydraulic conductivity is isotropic). Click Next.
8. For pumping well data, enter F507-080 for the well name. Enter coordinates
of X=0 and Y=0. Click Next.
9. For pumping well construction, select the option for vertical, partial
penetration. Enter 13.2 for the depth to the top of the well screen and 47
for the screen length. Click Next.
10. For pumping well radius data, assume 0.333 for casing radius and 0.333 for
well radius. Click Next.
11. For pumping rates, enter 0 for time and 320 for rate in the first row of the
spreadsheet. Click Next.
12. For observation well data, enter F377-037 for the well name. Enter 85.1 and
0 for the X and Y coordinates, respectively. Click Next.
13. For observation well construction, select the option for vertical, partial
penetration. Enter 13.3 for the depth to the top of the well screen and 2 for
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the screen length. Click Next.

14. For observations, click Import to launch the Observation Data Import Wizard
for importing data from a file.
We will import a text file consisting of 30 time-drawdown readings arranged
in two columns. The first column is elapsed time since the start of the test.
The second column contains drawdown measurements.
In Step 1 of the wizard, click Browse. Select the import file F377-037.txt in
the AQTESOLV installation folder and click Open. Click Next.
In Step 2 of the wizard, accept the default entries and click Next.
In Step 3 of the wizard, click Finish. Inspect the import file summary and
click OK.
Click Next to proceed with the Pumping Test Wizard.
15. You have completed the Pumping Test Wizard. Click Finish.
After completing the Pumping Test Wizard, AQTESOLV automatically displays an
Error Log to let you know if the data set contains any errors. If the Error Log
identifies any mistakes, choose options from the Edit menu to correct them.
Save Data Set
At this point, it's a good idea to save your work.
Save the data set by choosing Save As from the File menu. Choose a folder, enter
F377-037 for the name of the file and click Save. AQTESOLV saves the file with an
.aqt extension.
Inspect Diagnostic Plots
Before performing curve matching to estimate aquifer properties, you may use
diagnostic features in AQTESOLV to evaluate aquifer and flow conditions.
Diagnostic flow plots help you select an appropriate solution method for your
pumping test data.
1. Choose Radial Flow from the View menu to display a radial flow plot on
log-linear axes.
View Radial Flow Plot
The response shown on the radial flow plot shows some characteristics of the
Neuman (1974) model for an unconfined aquifer. At intermediate time, the
drawdown data only exhibit a moderate delayed gravity response. Late-time
data almost appear to plot as a straight line.

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Derivative analysis is another useful diagnostic tool for evaluating aquifer conditions.
1. Choose Displacement-Time from the View menu to display a plot of the test
data. On semi-log axes, this plot is identical to the radial flow plot above.
2. Choose Wells from the Edit menu. Select F377-037 from the list and click
Modify.
In the Symbols tab, remove the check from Use data symbols properties
and select cross for the derivative symbol.
In the Curves tab, remove the check from Use type curve properties.
Click Color for the derivative curve properties, change the color to red, and
click OK.
Click OK and then Close.
3. Select Options from the View menu. In the Plots tab, check Derivative
curves. In the Derivative tab, select the option for Smoothing and
enter a smoothing factor of 1. Click OK.

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View Derivative Plot

The form of the derivative plot is not entirely consistent with an unconfined
aquifer exhibiting instantaneous drainage at the water table (Neuman 1974
model). With the Neuman model, one expects a pronounced dip in the
derivative at intermediate time and a constant derivative at late time. Neither
of these characteristics is evident on the derivative plot which suggests that a
model with noninstantaneous drainage at the water table (e.g., TartakovskyNeuman 2007) may be appropriate for our analysis.

Estimate Aquifer Properties

Although the wells in this example are partially penetrating, we can use the CooperJacob (1946) solution, which assumes fully penetrating wells, to obtain first-cut
estimates of aquifer properties.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. Remove the check from Solution is inactive. Click the + next to
Unconfined Aquifers to expand the list of available solutions for unconfined

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aquifers. Select Cooper-Jacob (1946) and click OK.

3. Choose Visual from the Match menu to perform visual curve matching with
the Cooper-Jacob solution.
Match the solution to the late-time data to estimate T and Sy. Note that the
Cooper-Jacob solution only determines one value for the storative properties
of the aquifer (labeled S); however, when you match the straight line to the
late-time data, you really are estimating Sy.
To perform visual matching, move the mouse to a point where you wish to
begin drawing a new line with the Cooper-Jacob solution.
Click and hold down the left mouse button to anchor the new line at this
point.
Continue to hold the mouse button down and move the mouse to match a
new straight line to your data. As you move the mouse, AQTESOLV draws a
straight line between the anchor point and the position of the mouse.
Release the left mouse button when you have finished matching a new
straight line. AQTESOLV automatically updates the plot legend to reflect
changes in parameter values.
4. Repeat the previous step as needed to achieve a satisfactory match to
the late-time data. Your estimates of T and S should be around 0.06
m2/sec and 0.1, respectively. Because you have matched the Cooper-Jacob
solution to late-time data, you will use 0.1 for your estimate of Sy.
Note: Because the Cooper-Jacob solution assumes fully penetrating wells,
your preliminary estimate of Sy at this stage of the analysis is only a firstorder approximation. To obtain a more refined estimate of Sy, you could use
the Theis (1935) solution which accounts for partially penetrating wells.
5. Choose Toolbox from the Match menu. In the Tweak tab, select S from the
list of parameters. Use the scroll bar to decrease S until the line matches the
early-time data. Your adjusted estimate of S should be on the order of
0.0025.
Having completed our preliminary analysis with Cooper-Jacob, let's continue by
matching the data with the Neuman (1974) solution for an unconfined aquifer with
delayed gravity response (instantaneous drainage at the water table).
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. From the list of solutions for Unconfined Aquifers, select Neuman (1974)
and click OK.
3. Choose Log Axes from the View menu to view the data on log-log axes.
4. Choose Toolbox from the Match menu. In the Parameters tab, enter 0.06,
0.0025 and 0.1 for the values of T, S and Sy, respectively. Keep the default
value of 0.1 for . Click OK.
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5. Choose Automatic from the Match menu and click Estimate to perform
automatic curve matching.
During the iterative estimation procedure, AQTESOLV displays a progress
window and updates the curves displayed on the plot in the background.
6. When estimation has finished, click OK and then Close. Click OK to view the
new position of the type curve.
View Automatic Match with Neuman Solution

7. The Neuman (1974) solution matches the late-time data well, but gives a
poor fit to the data at intermediate time. Choose Aquifer Data from the Edit
menu to find the estimated value of the hydraulic conductivity anisotropy
ratio (Kz/Kr = 0.243).
The foregoing analysis with the Neuman (1974) solution assumed
instantaneous drainage at the water table. To investigate the effect of
noninstantaneous drainage from the unsaturated zone, let's match the TartakovskyNeuman (2007) solution for an unconfined aquifer with 3D flow in the saturated and
unsaturated zones.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
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2. From the list of solutions for Unconfined Aquifers, select TartakovskyNeuman (2007) and click OK.
3. Choose Automatic from the Match menu. In the Parameters tab, select
Active for the estimation status of Kz/Kr. Click Estimate to perform
automatic curve matching.
4. When estimation has finished, click OK and then Close. Click OK to view the
new position of the type curve.
View Automatic Match with Tartakovsky-Neuman Solution

5. Compared to the previous match obtained with the Neuman (1974)

model, the Tartakovsky-Neuman (2007) solution yields a lower estimate
of T and gives a superior fit to the drawdown data measured at intermediate
time.
Note that as the dimensionless Gardner parameter, D, becomes large, the
Tartakovsky-Neuman solution is essentially identical to the Neuman (1974)
model.

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Pumping Test Example: Double Porosity

(Nevada)
Moench (1984) presented data from a pumping test conducted at the Nevada Test
Site. The test well (UE-25b#1) fully penetrated a fractured aquifer consisting of
Tertiary volcanic rocks. Pumping continued for nearly three days at a constant rate of
35.8 liters-per-second (L/sec). Hydraulic response was monitored in an observation
well (UE-25a#1) at a distance of 110 m from the pumped well. Time and drawdown
measurements were recorded in minutes and meters, respectively.
This example will introduce you to the following tasks and features in AQTESOLV:

Creating a new data set with the Pumping Test Wizard

Importing data with the Observation Data Import Wizard

Saving a data set

Inspecting diagnostic plots (radial flow and derivative)

Estimating aquifer properties using the Moench (1984) solution (visual and
automatic)

While following the steps in this example, click Help or press F1 to obtain
context sensitive help in the AQTESOLV application.
Create a New Data Set with Pumping Test Wizard
The first step in analyzing data from a pumping test is to create a new AQTESOLV
data set. In this example, we will use the Pumping Test Wizard to assist us with data
entry.
1. Create a new data set by choosing New from the File menu.
2. In the New Data Set dialog, select Pumping Test Wizard from the list.
Click OK.
3. Choose Single-well test for the type of pumping test (we will use the wizard
to enter data for the pumping well and add data for the observation well
later). Click OK.
4. The Pumping Test Wizard prompts you for data required to analyze a
pumping test. Click Next to begin the wizard.
5. For units of measurement, choose m for length, min for time, L/sec for
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pumping rate and m/sec for hydraulic conductivity. Click Next.

6. For project information, enter Nevada Test Site for the location. Click Next.
7. For aquifer data, assume 400 for the aquifer thickness. Enter 1 for the
anisotropy ratio (i.e., assume hydraulic conductivity is isotropic).
Click Advanced. In the Double Porosity tab, enter 80 for the thickness of
slab blocks. Click OK.
Click Next.
8. For pumping well data, enter UE-25b#1 for the well name. Enter coordinates
of X=0 and Y=0. Click Next.
9. For pumping well construction, select the option for vertical, full
penetration. Click Next.
10. For pumping well radius data, assume 0.11 for casing radius and 0.11 for
well radius. Click Next.
11. For pumping rates, enter 0 for time and 35.8 for rate in the first row of the
spreadsheet. Click Next.
12. For observations, click Import to launch the Observation Data Import Wizard
for importing data from a file.
We will import a text file consisting of 29 time-drawdown readings arranged
in two columns. The first column is elapsed time since the start of the test.
The second column contains drawdown measurements.
In Step 1 of the wizard, click Browse. Select the import file UE25b#1.txt in
the AQTESOLV installation folder and click Open. Click Next.
In Step 2 of the wizard, enter 2 for the number of columns, 1 for the
starting row in the file, 1 for the column containing elapsed time and 2 for
the column containing displacement. Click Next.
In Step 3 of the wizard, click Finish. Inspect the import file summary and
click OK.
Click Next to proceed with the Pumping Test Wizard.
13. You have completed the Pumping Test Wizard. Click Finish.
After completing the Pumping Test Wizard, AQTESOLV automatically displays an
Error Log to let you know if the data set contains any errors. If the Error Log
identifies any mistakes, choose options from the Edit menu to correct them.
Add Observation Well
The Pumping Test Wizard helped you enter data for the pumped well. Now you will
add data for the observation well.
1. Choose Wells from the Edit menu and click New to add a new well. Select
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the new well in the list and click Modify to edit the well.
2. In the General tab, enter UE-25a#1 for the well name. Enter 110 and 0 for
the X and Y coordinates, respectively.
3. In the Construction tab, select the option for vertical, full penetration.
4. In the Radius tab, enter 0.0 for the casing radius to disable delayed
observation well response.
5. In the Observations tab, click Import to launch the Observation Data
Import Wizard for importing data from a file.
You will import 24 observations from a text file. The first column is elapsed
time since the start of the test. The second column contains drawdown
measurements for the observation well.
In Step 1 of the wizard, click Browse. Select the import file UE25a#1.txt in
the AQTESOLV installation folder and click Open. Click Next.
In Step 2 of the wizard, accept the default values determined by the
Import Wizard. Click Next.
In Step 3 of the wizard, accept the defaults and click Finish. Inspect the
import file summary and click OK.
6. Click OK to finish editing well UE-25a#1.
7. Click Close to leave the Wells window.
Save Data Set
At this point, it's a good idea to save your work.
Save the data set by choosing Save As from the File menu. Choose a folder and
enter NTS for the name of the file. Click Save. AQTESOLV saves the file with an .aqt
extension.
Inspect Diagnostic Plots
Before performing curve matching to estimate aquifer properties, you may use
diagnostic features in AQTESOLV to evaluate aquifer and flow conditions. Derivative
analysis is one useful diagnostic tool for evaluating aquifer conditions.
1. Choose Composite from the View menu to display a plot of the test
data.
A composite plot normalizes time by the radius squared (t/r2).
2. Choose Log Axes from the View menu to display the plot on log-log axes.
3. Choose Wells from the Edit menu. Select UE-25a#1 from the list and click
Modify.
In the Symbols tab, select cross for the data symbol.

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In the Curves tab, click Color for the type curve properties, change the
color to red, and click OK.
Click OK and then Close.
4. Select Options from the View menu. In the Plots tab, check Derivative
curves. In the Derivative tab, select the option for Bourdet and enter
a differentiation interval of 0.2. Click OK.
View Derivative Plot
The form of the derivative plot is characteristic of radial flow in a doubleporosity confined aquifer.
Estimate Aquifer Properties
The derivative plot that we have examined for this test suggests a double-porosity
fractured aquifer. Before performing automatic curve matching, it's a good idea to
obtain preliminary estimates of aquifer properties using visual curve matching with
simpler solutions. We will begin our analysis using the Theis (1935) solution for a
confined aquifer to estimate fracture properties from the early-time data.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. Remove the check from Solution is inactive. Click the + next to Confined
Aquifers to expand the list of available solutions for confined aquifers. Select
Theis (1935) and click OK.
3. Choose Displacement-Time from the View menu.
4. Select Options from the View menu. In the Plots tab, remove the check from
Derivative curves for now. Click OK.
5. Choose Log Axes from the View menu to display the plot on log-log
axes.
The plot displays two sets of curves. The blue and red curves are drawdown
predicted by the Theis solution for the pumped well (UE-25b#1) and the
observation well (UE-25a#1), respectively.
6. Choose Visual from the Match menu to perform visual curve matching with
the Theis solution.
Click and hold the left mouse button down over a point within the plot area.
Continue to hold the mouse button down and move the mouse to match the
curves to the drawdown and derivative data. As you move the type curve,
AQTESOLV automatically updates the plot legend to reflect changes in
parameter values.
Release the left mouse button when you have finished matching the curves.
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7. Repeat the previous step as needed to achieve an approximate match of the

Theis solution to the early-time data for both wells.
View Visual Match with Theis

Now we will use automatic curve matching to obtain estimates of aquifer properties
with the Moench (1984) solution.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. Remove the check from Solution is inactive. Click the + next to Fractured
Aquifers (Double Porosity) to expand the list of available solutions for
double-porosity aquifers. Select Moench (1984) w/slab-shaped blocks
and click OK.
3. Choose Composite from the View menu to display a plot of the test data.
4. Choose Log Axes from the View menu to display the plot on log-log axes.
5. Select Options from the View menu. In the Plots tab, check Derivative
curves. Click OK.
6. Choose Automatic from the Match menu.
In the Estimation tab, enter 75 for the maximum number of iterations.
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Click Advanced. Select Conservative for the Updating Method. Check the
option to Apply SVD (singular value decomposition). SVD helps to improve
convergence of the automatic parameter estimation procedure when starting
guesses are poor. For the Observation Data Weighting Method, choose
Inverse maximum displacement magnitude. This weighting scheme gives
more weight to the observation well data which have smaller magnitude
compared to the pumped well. Click OK.
In the Parameters tab, enter 1.0 for the value of Sf and change its status
to Active. Set the status of Sw, r(w) and r(c) as Inactive.
Click Estimate to perform automatic curve matching.
During the iterative estimation procedure, AQTESOLV displays a progress
window and updates the curves displayed on the plot.
7. When estimation has finished, click OK and then Close. Click OK to view the
new position of the type curve.
View Automatic Match with Moench

8. Use residual-time, residual-simulated and normal probability plots to evaluate

the fit of the curve by examining residuals. The diagnostics report also
presents residual statistics for curve fitting.

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

Delayed Observation Well Response
The Moench (1984) solution for a double-porosity aquifer is one of the solutions in
AQTESOLV that includes delayed observation well response. Let's examine the effect
of delayed response.
1. Choose Wells from the Edit menu, select UE-25a#1 in the list and click
Modify.
2. In the Radius tab, enter 0.05 for casing radius and 0.05 for well radius.
Click OK. Click Close.
View Effect of Delayed Response
The effect of delayed response shifts the early-time drawdown in the
observation well to the right. No effect is observed at the pumping well. To
eliminate delayed response completely, enter zero for the casing radius of the
observation well.

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Pumping Test Example: Test Design (Forward

Solution)
You can use the Forward Solution Wizard in AQTESOLV to design an aquifer test. In
this example, you will predict the drawdown response during a single-well test in a
fractured aquifer. A single vertical fracture bisects the pumped well which fully
penetrates the aquifer.
This example will introduce you to the following tasks and features in AQTESOLV:

Creating a new data set with the Forward Solution Wizard

Saving a data set

Predicting future response over time and distance using the Theis and
Gringarten-Witherspoon solutions (time- and distance-drawdown plots)

While following the steps in this example, click Help or press F1 to obtain
context sensitive help in the AQTESOLV application.
Create a New Data Set with Forward Solution Wizard
The first step in designing a pumping test is to create a new AQTESOLV data set. In
this example, we will use the Forward Solution Wizard to assist us with entering data
needed for prediction.
1. Create a new data set by choosing New from the File menu.
2. In the New Data Set dialog, select Forward Solution Wizard from the list.
Click OK.
3. Choose Single-well test for the type of pumping test. Click OK.
4. The Forward Solution Wizard prompts you for data required to design a
pumping test. Click Next to begin the wizard.
5. For units of measurement, choose ft for length, min for time, gal/min for
pumping rate and ft/day for hydraulic conductivity. Click Next.
6. For project information, enter Aquifer Test Design for the title. Click Next.
7. For aquifer data, enter 200 for aquifer thickness. Enter 1 for anisotropy ratio
(i.e., assume hydraulic conductivity is isotropic). Click Advanced. In the
Single Fracture tab, enter 100 for vertical fracture length (Pro Only). Click
OK. Click Next.
8. For pumping well data, enter PW for well name. Enter coordinates of X=0 and
Y=0. Click Next.
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9. For pumping well construction, select the option for vertical, full
penetration. Click Next.
10. For pumping well radius data, enter 0.25 for casing radius and 0.25 for well
radius. Click Next.
11. For pumping rates, enter 0 for time and 100 for rate in the first row of the
spreadsheet. Click Next.
12. For forward solution data, enter 0.01 and 1440 for the minimum and
maximum simulation time, respectively. Enter 100 and 0.001 for T and S,
respectively. Click Next.
13. You have completed the Forward Solution Wizard. Click Finish.
After completing the Forward Solution Wizard, AQTESOLV automatically displays
an Error Log to let you know if the data set contains any errors. If the Error Log
identifies any mistakes, choose options from the Edit menu to correct them.
Save Data Set
At this point, it's a good idea to save your work.
Save the data set by choosing Save As from the File menu. Choose a folder and
enter Forward Solution for the name of the file. Click Save. AQTESOLV saves the
file with an .aqt extension.
Prediction
Let us start by predicting the response with the Theis (1935) solution for a fully
penetrating vertical well in a confined aquifer.
1. Choose Displacement-Time from the View menu to display a plot of the test
data.
2. Choose Log Axes from the View menu to display the plot on log-log axes.
3. Choose Format from the View menu. In the Y Axis tab, remove the check
from Auto and enter 1000 for the maximum value. Click OK.
4. Choose Solution from the Match menu to select a method for analyzing the
data.
5. Remove the check from Solution is inactive. Click the + next to Confined
Aquifers to expand the list of available solutions for confined aquifers. Select
Theis (1935) and click OK.
6. The curve (blue line) indicates the predicted drawdown for the well.
7. Choose Distance Drawdown from the View menu. Enter 1440 for the
prediction time and click OK.
8. Choose Log Axes from the View menu to display the plot on log-log axes.
9. Choose Format from the View menu. In the Y Axis tab, remove the check
from Auto and enter 100 for the maximum value. Click OK.

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10. The plot shows simulated drawdown with increasing radial distance from the
pumped well.
Now we will use the Gringarten-Witherspoon (1972) solution to predict the
response with a vertical fracture.
1. Choose Displacement-Time from the View menu.
2. Choose Log Axes from the View menu.
3. Choose Format from the View menu. In the Y Axis tab, remove the check
from Auto and enter 1000 for the maximum value. Click OK.
4. Choose Solution from the Match menu to select a method for analyzing the
data.
5. Click the + next to Fractured Aquifers (Single Fracture) to expand the list
of available solutions for single fractures intersecting the pumped well. Select
Gringarten-Witherspoon (1972) uniform-flux vertical fracture and click
OK.
6. Note that the slope of the predicted drawdown at early time shows a
unit half-slope. This behavior is characteristic of linear flow to a
fracture.
View Predicted Displacement-Time Plot
Choose Check Slope from the Match menu to measure the slope on a plot.
Click and hold the left mouse button down to draw a line over a portion of the
plot where you want to measure the slope.

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7. Choose Distance Drawdown from the View menu. Enter 1440 for the
prediction time and click OK.
8. Choose Log Axes from the View menu to display the plot on log-log axes.
9. Choose Format from the View menu. In the Y Axis tab, remove the check
from Auto and enter 100 for the maximum value. Click OK.
10. The plot shows simulated drawdown along the x-coordinate axis starting
at the pumped well located at the center of the fracture.
View Predicted Distance Drawdown Plot
Press Ctrl-K to toggle coordinate tracking as you move the mouse over the
plot. This feature is useful for identifying the distance at which drawdown on
the plot attains a particular value.

Add Observation Well

So far, we have examined drawdown along the x-coordinate axis in our distancedrawdown analysis. Because flow near the vertical fracture is not radially symmetric,
we may add observation wells to the data set to predict drawdown in other
directions.
1. Choose Wells from the Edit menu and click New to add a new well. Select
the new well in the list and click Modify to edit the well.
2. In the General tab, enter OW for the well name. Enter 0 and 10 for the X
and Y coordinates, respectively (you could enter any value not equal to zero
for the y coordinate to predict drawdown along the y axis).

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3. In the Curves tab, click Color for the type curve properties, change the color
to red, and click OK.
4. Click OK to finish editing the well.
5. Click Close to leave the Wells window.
6. The updated plot now shows two curves. The blue and red curves show
drawdown along the x- and y-coordinate axes, respectively.
Note how the two curves merge with distance. When Kx = Ky and radial
distance is greater than or equal to about five times the fracture half-length
(250 ft in this case), flow around the vertical fracture is essentially radial (i.e.,
the drawdown contours are nearly circular in shape rather than elliptical).
7. Choose Toolbox from the Match menu.
In the Tweak tab, select Ky/Kx in the Parameter list and click the left arrow
on the scroll bar to decrease its value. As you decrease Ky/Kx, the curves
diverge on the distance-drawdown plot.
Click Cancel to discard your changes.
Use the parameter tweaking feature to perform a sensitivity analysis on
individual parameters.
8. You may add more wells to predict drawdown in other directions.

Pumping Test Example: Horizontal Well

In this example, you will analyze data from a hypothetical constant-rate test in a
horizontal well used for remediation. The time-drawdown data were developed from
published dimensionless type curve values for the horizontal well solution, so this
example also serves as a benchmark.
This example will introduce you to the following tasks and features in AQTESOLV:

Creating a new data set with the Pumping Test Wizard

Importing data with the Observation Data Import Wizard

Saving a data set

Inspecting diagnostic plots (derivative)

Estimating aquifer properties using the Daviau et al. (1985) solution

(automatic)

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Sensitivity analysis (hemiradial and linear flow regimes)

While following the steps in this example, click Help or press F1 to obtain
context sensitive help in the AQTESOLV application.
Create a New Data Set with Pumping Test Wizard
The first step in analyzing data from a single-well pumping test is to create a new
AQTESOLV data set. In this example, we will use the Pumping Test Wizard to assist
us with data entry.
1. Create a new data set by choosing New from the File menu.
2. In the New Data Set dialog, select Pumping Test Wizard from the list.
Click OK.
3. Choose Single-well test for the type of pumping test. Click OK.
4. The Pumping Test Wizard prompts you for data required to analyze a
single-well pumping test. Click Next to begin the wizard.
5. For units of measurement, choose m for length, sec for time, L/sec for
pumping rate and consistent for hydraulic conductivity. Click Next.
Consistent units are based on the units of length and time selected for the
data set. In this example, consistent units are m/sec for K (m2/sec for T).
6. For project information, enter Horizontal Well for the title. Click Next.
7. For aquifer data, assume 20 for the aquifer thickness. Enter 1 for the
anisotropy ratio (i.e., assume hydraulic conductivity is isotropic). Click Next.
8. For pumping well data, enter HW for the well name. Enter the coordinates for
the midpoint of the horizontal well at X=0 and Y=0. Click Next.
9. For pumping well construction, select the option for horizontal. Enter 10 for
zh (depth of well) and 400 for Lh (length of well). Click Next.
10. For pumping well radius data, enter 0.1 for casing radius and 0.1 for well
radius. Click Next.
11. For pumping rates, enter 0 for time and 1.5 for rate in the first row of the
spreadsheet. Click Next.
12. For observations, click Import to launch the Observation Data Import Wizard
for importing data from a file.
We will import a text file consisting of 14 time-drawdown readings arranged
in two columns. The first column is elapsed time since the start of the test.
The second column contains drawdown measurements.

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In Step 1 of the wizard, click Browse. Select the import file Horizontal
Well.txt in the AQTESOLV installation folder and click Open. Click Next.
In Step 2 of the wizard, accept the default entries and click Next.
In Step 3 of the wizard, click Finish. Inspect the import file summary and
click OK.
Click Next to proceed with the Pumping Test Wizard.
13. You have completed the Pumping Test Wizard. Click Finish.
After completing the Pumping Test Wizard, AQTESOLV automatically displays an
Error Log to let you know if the data set contains any errors. If the Error Log
identifies any mistakes, choose options from the Edit menu to correct them.
Save Data Set
At this point, it's a good idea to save your work.
Save the data set by choosing Save As from the File menu. Choose a folder, enter
Horizontal Well for the name of the file and click Save. AQTESOLV saves the file
with an .aqt extension.
Inspect Diagnostic Plots
Before performing curve matching to estimate aquifer properties, you may use
diagnostic features in AQTESOLV such as derivative analysis to evaluate aquifer and
flow conditions.
1. Choose Displacement-Time from the View menu to display a plot of the test
data.
2. Choose Wells from the Edit menu. Select HW from the list and click Modify.
In the Symbols tab, remove the check from Use data symbols properties
and select cross for the derivative symbol.
In the Curves tab, remove the check from Use type curve properties.
Click Color for the derivative curve properties, change the color to red, and
click OK.
Click OK and then Close.
3. Select Options from the View menu. In the Plots tab, check Derivative
curves. In the Derivative tab, select the option for Bourdet and enter
a factor of 0.2. Click OK.
View Derivative Plot
The plot shows derivative is approximately constant (i.e., horizontal) during
two periods, early and late. At early time, radial flow is directed toward the
horizontal axis of the well and continues until drawdown reaches the upper
and lower impermeable boundaries. At late time and sufficiently large

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distances, the well behaves approximately like a point source; hence,

assuming no lateral boundaries, flow is nearly radial in a horizontal plane
between the upper and lower boundaries.

Estimate Aquifer Properties

We will use the Daviau et al. (1985) solution for a horizontal well to obtain estimates
of aquifer properties.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. Remove the check from Solution is inactive. Click the + next to Confined
Aquifers to expand the list of available solutions for confined aquifers. Select
Daviau et al. (1985) infinite-conductivity horizontal well and click OK.
3. Choose Automatic from the Match menu. Click Estimate to perform
automatic curve matching.
During the iterative estimation procedure, AQTESOLV displays a progress
window and updates the curves displayed on the plot in the background.
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4. When estimation has finished, click OK and then Close. Click OK to view the
new position of the type curve.
View Automatic Match with Daviau et al. Solution

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

Sensitivity Analysis
Thus far, we have identified two radial flow regimes, at early and late time, that may
develop in response to discharge from a horizontal well. Under certain conditions,
two additional flow regimes may be evident as well.
A horizontal well located near either the upper or lower impermeable boundary of a
confined aquifer may result in a hemiradial flow regime that follows the initial
radial flow period. In the case of a well positioned on or very close to the boundary,
hemiradial flow develops immediately and the first period of radial flow is not
observed.
In the case of a thin aquifer and a long well, a linear flow regime may develop
before the late-time radial flow period. Drawdown data on a log-log plot display a
unit half-slope during the linear flow period.
Now we will perform a sensitivity analysis to identify hemiradial and linear flow
regimes.

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1. Choose Wells from the Edit menu. Select HW from the list and click
Modify. In the Construction tab, enter 0.5 for zh. Click OK.
View Contour Plot of Hemiradial Flow
With the well positioned close to the upper no-flow boundary, hemiradial flow
occurs at intermediate time between about 100 and 3000 seconds as shown
by the constant theoretical derivative curve (i.e., the red line). A brief period
of radial flow is present immediately prior to the hemiradial flow regime.

Hemiradial flow in the vicinity of horizontal well near top of confined aquifer
2. Choose Aquifer Data from the Edit menu. Enter 10 for the aquifer
thickness and click OK.
As you decrease the thickness of the aquifer, the theoretical drawdown curve
(i.e., the blue line) shows a linear flow regime at intermediate time with a
slope approaching 0.5 on the log-log plot. You can choose Check Slope from
the Match menu to test the slope of the theoretical drawdown curve on the
plot.

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Slug Tests

Slug Test Example: Unconfined

Batu (1998) presented data for a falling-head slug test in a sandy unconfined aquifer
having a saturated thickness of 32.57 ft. The initial displacement in the well was
1.48 ft. The following table provides well construction details for the test.
Well Radius,
rw (inches)
5.0

Casing Radius,
rc (inches)
2.0

Depth to Top of
Screen, d (ft)
0.47

Screen Length,
L (ft)
13.80

Radius values are measured from the center of the test well. The five-inch well
radius reported by Batu (1998) includes a sand filter pack installed in the well
annulus. The depth of the well screen, d, is measured from the static water table.
From these data, we calculate the static water column height in the well as 14.27 ft
(d + L). Elapsed time and depth-to-water measurements were recorded in seconds
and feet, respectively.
This example will introduce you to the following tasks and features in AQTESOLV:

Creating a new data set with the Slug Test Wizard for a single-well test

Importing data with the Observation Data Import Wizard

Saving a data set

Inspecting diagnostic plots (screening data with Cooper et al. solution)

Estimating aquifer properties with KGS Model and Bouwer-Rice solutions

(visual and automatic)

Performing a discrete sensitivity analysis to evaluate uncertainty in aquifer

thickness

Applying approximate deconvolution approach (Peres et al. solution)

While following the steps in this example, click Help or press F1 to context
sensitive help in the AQTESOLV application.

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Create a New Data Set with Slug Test Wizard

The first step in analyzing data from a slug test is to create a new AQTESOLV data
set. In this example, we will use the Slug Test Wizard to assist us with data entry.
1. Create a new data set by choosing New from the File menu.
2. In the New Data Set dialog, select Slug Test Wizard from the list. Click
OK.
3. The Slug Test Wizard prompts you for data required for a slug test. Click
Next.
4. For units of measurement, choose ft for length, sec for time and cm/sec for
hydraulic conductivity. Click Next.
5. For project information, enter Falling-Head Slug Test for the title. Click
Next.
6. For general test well data, enter 1.48 for the initial displacement, 14.27 for
static water column height and Well 1 for the well name. Enter coordinates of
X=0 and Y=0. Click Next.
7. For aquifer data, enter 32.57 for aquifer thickness. Assume hydraulic
conductivity is isotropic and enter 1 for anisotropy ratio. Click Next.
8. For screen data, enter 0.47 for depth to top of screen and 13.8 for screen
length. Assume the transducer measures the position of the water surface in
the well and enter 0 for transducer depth. Click Next.
9. For radius data, enter 0.167 for casing radius and 0.417 for well radius.
Assume no well skin and enter 0.417 for the skin radius. Click Next.
10. Corrections are not required for this test. The gravel pack correction only
applies to wells screened across the water table. Click Next.
11. For observations, click Import to launch the Observation Data Import
Wizard for importing data from a file.
We will import a text file consisting of 27 time and water-level readings
arranged in two columns. The first column is elapsed time in seconds since
the start of the test. The second column contains depth-to-water
measurements in feet.
To convert depth-to-water to displacement, we will use the wizard to
subtract 10 ft (the static depth-to-water recorded before the test) from all of
the measurements in the file. For these test data, the subtraction operation
results in negative displacements. To make them positive, we use the wizard
to multiply all of the displacement values by -1.
In Step 1 of the wizard, click Browse. Select the import file Falling Head.txt
in the AQTESOLV installation folder and click Open. Click Next.
In Step 2 of the wizard, enter 2 for the number of columns, 1 for the
starting row in the file, 1 for the column containing elapsed time and 2 for
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the column containing displacement. Click Next.

In Step 3 of the wizard, check the second box to subtract a constant
from the displacement values and enter 10 for the constant. Check the
fourth box to multiply displacement values by a constant and enter -1 for
the constant. Click Finish. Inspect the import file summary and click OK.
Click Next to proceed with the Slug Test Wizard.
12. You have completed the Slug Test Wizard. Click Finish.
After completing the Slug Test Wizard, AQTESOLV automatically displays an Error
Log to let you know if the data set contains any errors. If the Error Log identifies
any mistakes, choose options from the Edit menu to correct them.
Save Data Set
At this point, it's a good idea to save your work.
Save the data set by choosing Save As from the File menu. Choose a folder and
enter Falling Head for the name of the file. Click Save. AQTESOLV saves the file
with an .aqt extension.
Inspect Diagnostic Plots
Following the guidelines developed by Butler (1998) for a slug test in a well screened
below the water table, we will use the Cooper et al. (1967) method to screen our
data. An implausibly low storativity (S) value determined from the screening analysis
would suggest the presence of vertical flow.
1. Choose Displacement-Time from the View menu to display a plot of the test
data.
2. Choose Options from the View menu. In the Plots tab, check Normalized
head to display data as normalized head. Click OK.
3. Choose Log-Linear Axes from the View menu.
On these axes, the data show a sigmoidal shape that is typical of solutions
based on the fully transient overdamped slug test model, e.g., Hyder et al.
(1994).
4. Choose Linear-Log Axes from the View menu.
The data show a slightly concave upward appearance which also is
characteristic of slug test solutions based on the fully transient overdamped
model; however, a good portion of the data give the appearance of a straight
line that we may analyze with solutions based on the quasi-steady-state slug
test model, e.g., Bouwer-Rice (1976).
5. Choose Solution from the Match menu to use the Cooper et al. (1967)
method as a screening tool.
6. Remove the check from Solution is inactive. Click the + next to Confined
Aquifers to expand the list of available solutions for confined aquifers. Select
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Cooper-Bredehoeft-Papadopulos (1967) and click OK.

7. Choose Log-Linear Axes from the View menu.
8. Choose Automatic from the Match menu and click Estimate to perform
automatic curve matching with the Cooper et al. solution.
During the iterative estimation procedure, AQTESOLV displays a progress
window and updates the curve displayed on the plot in the background.
9. When estimation has finished, click OK and then Close. Click OK to view the
new position of the type curve.
10. The estimated values of transmissivity (T) and storativity (S) are 0.3028
cm2/sec and 0.0007837, respectively.
According to the Butler (1998) guidelines, a plausible value of S obtained
with the Cooper et al. method allows us to assume that flow is essentially
constrained to the screened interval of the well (i.e., Kr Kz). Thus, we can
estimate Kr using the well screen length (L) as follows:
Kr = T/L = (0.3028 cm2/sec)/(13.8 ft)*(ft/30.48 cm) = 7.20 cm/sec
Match Solutions
Now we will attempt to use slug test models for unconfined aquifers to see
if the water-table boundary has an effect on our results. We will begin by analyzing
this slug test with the Hyder et al. (1994) solution (KGS Model) for an unconfined
aquifer. The KGS Model is a fully transient solution for overdamped slug tests that
accounts for elastic storage in the aquifer.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. Click the + next to Unconfined Aquifers to expand the list of available
solutions for unconfined aquifers. Select KGS Model (1994) and click OK.
3. Choose Log-Linear Axes from the View menu.
4. Choose Automatic from the Match menu and click Estimate to perform
automatic curve matching with the KGS Model.
5. When estimation has finished, click OK and then Close. Click OK to view the
new position of the type curve. The estimated value of Ss appears realistic, so
we will assume no wellbore skin effect. Compared to the Cooper et al.
screening analysis, the value of Kr obtained with the KGS Model is somewhat
lower owing to the influence of the water-table boundary condition.
View Automatic Match

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Next let us analyze the test with the Bouwer-Rice (1976) solution for an unconfined
aquifer. The Bouwer-Rice solution is based on the quasi-steady-state slug test model
that ignores elastic storage in the aquifer.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. From the available solutions for Unconfined Aquifers, select Bouwer-Rice
(1976) and click OK.
With the Bouwer-Rice solution, the plot legend shows two parameters: K
(hydraulic conductivity) and y0 (intercept of the line on the y axis).
3. Choose Options from the View menu. In the Plots tab, check
Recommended head range to display the range of normalized head
recommended by Butler (1998) for matching the Bouwer-Rice solution. Click
OK.
4. Choose Visual from the Match menu to perform visual curve matching with
the Bouwer-Rice solution.
To perform visual matching, move the mouse to a point where you wish to
begin drawing a new line.

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Click and hold down the left mouse button to anchor the new line at this
point.
Continue to hold the mouse button down and move the mouse to match a
new straight line to your data. As you move the mouse, AQTESOLV draws a
straight line between the anchor point and the position of the mouse.
Release the left mouse button when you have finished matching a new
straight line. AQTESOLV automatically updates the plot legend to reflect
changes in parameter values.
5. Repeat the previous step as needed to estimate K by matching the straight
line to the data within the recommended head range. How does your estimate
of hydraulic conductivity change if you match the straight line to earlier data?
View Visual Match

6. Matching the Bouwer-Rice method to the earlier test data, Batu (1998)
estimated K = cm/sec.
7. One could attempt to use automatic estimation to match the Bouwer-Rice
solution to these data; however, visual matching is generally more effective
for matching straight-line solutions because you can apply your judgment to
fit the line to the appropriate range of data.
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8. Choose Save from the File menu to save your work.

Perform Sensitivity Analysis
In this example, the aquifer thickness is known (32.57 ft); for some slug tests,
however, the thickness of the aquifer may not be directly available from drilling or
geophysical evidence. In such instances, one approach for evaluating uncertainty is
to estimate a reasonable range for aquifer thickness and perform a discrete
sensitivity analysis to evaluate the effect of varying thickness on the estimate of
hydraulic conductivity.
1. Choose Aquifer Data from the Edit menu. In the General tab, change the
value of aquifer thickness to 40. Click OK.
Changing the aquifer thickness has little effect on the position of the straight
line; hence, increasing the thickness to 40 ft does not greatly influence the
estimate of hydraulic conductivity.
2. Repeat the previous step for thickness values of 20 and 50 ft.
Apply Approximate Deconvolution Approach
The close fit between the data from this test and the Cooper et al. solution in the
screening analysis suggests that we might be able to match these data using the
approximate deconvolution approach of Peres et al. (1989). The Peres et al. method
transforms the response data from a slug test into equivalent heads for a constantrate pumping test. Although the Peres et al. approach is normally applied to confined
conditions, we will demonstrate its use with the data from this example.
1. Choose Solution from the Match menu.
2. Click the + next to Confined Aquifers to expand the list of available
solutions for confined aquifers. Select Peres et al. (1989) deconvolution
and click OK.
3. The plot of the data on log-linear axes displays equivalent head (ratenormalized head) on the y axis.
After applying the Peres et al. deconvolution procedure, the values of
equivalent head on the y (vertical) axis of the plot have the peculiar units of
time.
4. Choose Visual from the Match menu to perform visual curve matching with
the Peres et al. solution. The curve matching procedure is the same as the
familiar Cooper-Jacob (1946) solution for a pumping test.
To perform visual matching, move the mouse to a point where you wish to
begin drawing a new line.
Click and hold down the left mouse button to anchor the new line at this
point.
Continue to hold the mouse button down and move the mouse to match a
new straight line to your data. As you move the mouse, AQTESOLV draws a

139

straight line between the anchor point and the position of the mouse.
Release the left mouse button when you have finished matching a new
straight line. AQTESOLV automatically updates the plot legend to reflect
changes in parameter values.
5. Repeat the previous step as needed to estimate T by matching the straight
line to the data near the end of the test. Your estimate of T should be close to
the value obtained with the Cooper et al. solution.

Slug Test Example: Translation Method

A slug test performed in an unconfined bedrock aquifer allows us to demonstrate the
use of the translation method of data analysis. Well BR2 partially penetrates an 83-ft
thick limestone aquifer that behaves as an equivalent porous medium. The following
table provides construction details for the test well.
Well Radius,
rw (ft)
0.245

Casing Radius,
rc (ft)
0.255

Depth to Top of
Screen, d (ft)
21

Screen Length,
L (ft)
42

In this test, a solid slug introduced in the well resulted in noninstantaneous test
initiation as shown in the figure below.

Data collection in well BR2 started just prior to the introduction of the solid slug. The
effect of noninstantaneous test initiation is evident from the rising limb of the
displacement data that begins shortly after one second and continuing through the
subsequent period of noisy data. The peak displacement shown on the graph is
1.615 ft. At 10 seconds, the data begin to stabilize; therefore, you will translate the
start of the test to coincide with the reading at 10 seconds before analyzing these
data.
According to Butler (1998), the translation method is appropriate when a plot of
log displacement vs. time is approximately linear (i.e., the data conform to the

140

exponential decay assumption of quasi-steady-state slug test models). As we shall

see, data for this example generally meet this requirement.
This example will introduce you to the following tasks and features in AQTESOLV:

Creating a new data set with the Slug Test Wizard for a single-well test

Importing data with the Observation Data Import Wizard

Applying the translation method to observation data

Saving a data set

Estimating aquifer properties with Bouwer-Rice solution (visual)

While following the steps in this example, click Help or press F1 to context
sensitive help in the AQTESOLV application.
Create a New Data Set with Slug Test Wizard
The first step in analyzing data from a slug test is to create a new AQTESOLV data
set. In this example, we will use the Slug Test Wizard to assist us with data entry.
1. Create a new data set by choosing New from the File menu.
2. In the New Data Set dialog, select Slug Test Wizard from the list. Click
OK.
3. The Slug Test Wizard prompts you for data required for a slug test. Click
Next.
4. For units of measurement, choose ft for length, sec for time and cm/sec for
hydraulic conductivity. Click Next.
5. For project information, enter March 3, 2003 for the date. Click Next.
6. For general test well data, assume 1.615 for the initial displacement. Enter
83 for static water column height and BR2 for the well name. Enter
coordinates of X=0 and Y=0. Click Next.
7. For aquifer data, enter 83 for aquifer thickness. Assume hydraulic
conductivity is isotropic and enter 1 for anisotropy ratio. Click Next.
8. For screen data, enter 21 for depth to top of screen and 62 for screen length.
Assume the transducer measures the position of the water surface in the well
and enter 0 for transducer depth. Click Next.

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9. For radius data, enter 0.255 for casing radius and 0.245 for well radius.
Assume no well skin and enter 0.245 for the skin radius. Click Next.
10. Corrections are not required for this test. Click Next.
11. For observations, click Import to launch the Observation Data Import Wizard
for importing data from a file.
We will import a text file from an In-Situ MiniTroll. Data in the file are
arranged in five columns. Column three contains elapsed time and column
five contains displacement. Elapsed time and displacement are recorded in
seconds and feet, respectively.
In Step 1 of the wizard, click Browse. Select the import file BR2.txt in the
AQTESOLV installation folder and click Open. Click Next.
In Step 2 of the wizard, enter 5 for the column containing displacement
and accept the remaining default values. Click Next.
In Step 3 of the wizard, accept the default values and click Finish. Inspect
the import file summary and click OK.
Click Next to proceed with the Slug Test Wizard.
12. You have completed the Slug Test Wizard. Click Finish.
After completing the Slug Test Wizard, AQTESOLV automatically displays an Error
Log to let you know if the data set contains any errors. If the Error Log identifies
any mistakes, choose options from the Edit menu to correct them.
Save Data Set
At this point, it's a good idea to save your work.
Save the data set by choosing Save As from the File menu. Choose a folder and
enter BR2 for the name of the file. Click Save. AQTESOLV saves the file with an .aqt
extension.
Apply Translation Method
1. Choose Displacement-Time from the View menu to display a plot of the test
data.
2. Choose Options from the View menu. In the Plots tab, remove the check
from Normalized head (if necessary). Click OK.
3. Choose Log-Linear Axes from the View menu.
4. Choose Format from the View menu. In the Graph tab, check Show
Graph Paper and select the option for Major ticks only. Click OK.
View Plot
We can see from the graph that the noisy data associated with
noninstantaneous test initiation become stabile after 10 seconds. Therefore,
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we will use the translation method to translate the start of the test to the
reading at 10 seconds.

5. Choose Wells from the Edit menu. Select BR2 from the list and click Modify.
We will apply the translation method to the data.
In the Observations tab, click Select All. Click Math and check Perform
transformation. Select Time for the data, - (subtract) for the operation and
enter 10 for the constant. Click OK and Yes to proceed with the math
operations.
After translating the start of the test, the observations spreadsheet shows
that the displacement at elapsed time t = 0 is now 0.885 ft (i.e., the
displacement reading originally measured at 10 seconds). Click the General
tab and enter 0.885 for the initial displacement.

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Click OK and Close to finish editing the well data.

6. Choose Save from the File menu to save your work.
Match Solution
After having translated the start of the test, we are ready to analyze the test with
the Bouwer-Rice (1976) solution for an unconfined aquifer.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. Remove the check from Solution is inactive. Click the + next to
Unconfined Aquifers to expand the list of available solutions for unconfined
aquifers. Select Bouwer-Rice (1976) and click OK.
With the Bouwer-Rice solution, the plot legend shows two parameters: K
(hydraulic conductivity) and y0 (intercept of the line on the y axis).
3. Choose Options from the View menu. In the Plots tab, check Normalized
head and Recommended head range. Click OK.
4. Choose Format from the View menu. In the X Axis tab, remove the check
from Auto and enter 0 and 100 for the min and max values, respectively. In
the Y Axis tab, remove the check from Auto and enter 0.01 for the min
value.
5. Choose Visual from the Match menu to perform visual curve matching with
144

the Bouwer-Rice solution.

Normally, we would attempt the match the straight line within the head
range recommended by Butler (1998) for the Bouwer-Rice solution; however,
because we have altered the initial displacement through the application of
the translation method, we will ignore the recommended range (shown as two
horizontal lines on the plot) in this analysis.
To perform visual matching, move the mouse to a point where you wish to
begin drawing a new line.
Click and hold down the left mouse button to anchor the new line at this
point.
Continue to hold the mouse button down and move the mouse to match a
new straight line to your data. As you move the mouse, AQTESOLV draws a
straight line between the anchor point and the position of the mouse.
Release the left mouse button when you have finished matching a new
straight line. AQTESOLV automatically updates the plot legend to reflect
changes in parameter values.
6. Repeat the previous step as needed to estimate K by matching the straight
line to the data.
View Visual Match

145

7. One could attempt to use automatic estimation to match the Bouwer-Rice

solution to these data; however, visual matching is generally more effective
for matching straight-line solutions because you can apply your judgment to
fit the line to the appropriate range of data.
8. Choose Save from the File menu to save your work.

Slug Test: Double Straight-Line Effect (Dallas)

In this example, we will analyze a slug test conducted in a fully penetrating well
screened across the water table that exhibits the "double straight-line effect"
(Bouwer 1989) due to drainage from the filter pack. The test was conducted in an
unconfined aquifer having an estimated saturated thickness of 8 ft. The initial
displacement in the well was 3.792 ft. The following table provides well construction
details for the test. Data for this example provided courtesy of G. Zemansky.
Well Radius,
rw (ft)
0.344

Casing Radius,
rc (ft)
0.0861

Depth to Top of
Screen, d (ft)
0.0

Screen Length,
L (ft)
8.0

Radius values are measured from the center of the test well. The well radius includes
a filter pack installed in the well annulus. Elapsed time and depth-to-water
measurements were recorded in minutes and feet, respectively.
This example will introduce you to the following tasks and features in AQTESOLV:
146

Creating a new data set with the Slug Test Wizard for a single-well test

Importing data with the Observation Data Import Wizard

Saving a data set

Displaying data

Estimating aquifer properties with Bouwer-Rice solution (visual)

While following the steps in this example, click Help or press F1 to context
sensitive help in the AQTESOLV application.
Create a New Data Set with Slug Test Wizard
The first step in analyzing data from a slug test is to create a new AQTESOLV data
set. In this example, we will use the Slug Test Wizard to assist us with data entry.
1. Create a new data set by choosing New from the File menu.
2. In the New Data Set dialog, select Slug Test Wizard from the list. Click
OK.
3. The Slug Test Wizard prompts you for data required for a slug test. Click
Next.
4. For units of measurement, choose ft for length, min for time and cm/sec for
hydraulic conductivity. Click Next.
5. For project information, enter Well Screened Across Water Table for the
title. Click Next.
6. For general test well data, enter 3.792 for the initial displacement, 8.0 for
static water column height and MW-2 for the well name. Enter coordinates of
X=0 and Y=0. Click Next.
7. For aquifer data, enter 8.0 for aquifer thickness. Assume hydraulic
conductivity is isotropic and enter 1 for anisotropy ratio. Click Next.
8. For screen data, enter 0.0 for depth to top of screen and 8.0 for screen
length. Assume the transducer measures the position of the water surface in
the well and enter 0 for transducer depth. Click Next.
9. For radius data, enter 0.0861 for casing radius and 0.344 for well radius.
Assume no well skin and enter 0.344 for the skin radius. Click Next.

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10. For correction data, check the option to Apply correction for effective
casing radius. Select Bouwer-Rice (1976) for the correction method and
enter 0.28 for the effective porosity of the filter pack. Click Next.
11. For observations, click Import to launch the Observation Data Import Wizard
for importing data from a file.
We will import a text file consisting of 144 time and water-level readings
arranged in two columns. The first column is elapsed time in minutes since
the start of the test. The second column contains depth-to-water
measurements in feet.
In Step 1 of the wizard, click Browse. Select the import file MW-2.txt in the
AQTESOLV installation folder and click Open. Click Next.
In Step 2 of the wizard, accept the default values and click Next.
In Step 3 of the wizard, accept the default values and click Finish. Inspect
the import file summary and click OK.
Click Next to proceed with the Slug Test Wizard.
12. You have completed the Slug Test Wizard. Click Finish.
After completing the Slug Test Wizard, AQTESOLV automatically displays an Error
Log to let you know if the data set contains any errors. If the Error Log identifies
any mistakes, choose options from the Edit menu to correct them.
Save Data Set
At this point, it's a good idea to save your work.
Save the data set by choosing Save As from the File menu. Choose a folder and
enter MW-2 for the name of the file. Click Save. AQTESOLV saves the file with an
.aqt extension.
Display Data
1. Choose Displacement-Time from the View menu to display a plot of the test
data.
2. Choose Options from the View menu. In the Plots tab, check Normalized
head to display data as normalized head. Click OK.
3. Choose Linear-Log Axes from the View menu.
The data display the classic "double straight-line" pattern (Bouwer 1989) that
is commonly associated with drainage from the filter pack when a slug test is
conducted in a well screened across the water table. Bouwer (1989)
recommends fitting the Bouwer-Rice (1976) solution to the second (later)
straight-line segment when this phenomenon occurs.
Match Solutions
Let us analyze this test with the Bouwer-Rice (1976) solution for an unconfined
148

aquifer. The Bouwer-Rice solution is based on the quasi-steady-state slug test model
that ignores elastic storage in the aquifer.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. From the available solutions for Unconfined Aquifers, select Bouwer-Rice
(1976) and click OK.
3. Choose Options from the View menu. In the Plots tab, check
Recommended head range to display the range of normalized head
recommended by Butler (1998) for matching the Bouwer-Rice solution. Click
OK.
4. Choose Visual from the Match menu to perform visual curve matching with
the Bouwer-Rice solution.
To perform visual matching, move the mouse to a point where you wish to
begin drawing a new line.
Click and hold down the left mouse button to anchor the new line at this
point.
Continue to hold the mouse button down and move the mouse to match a
new straight line to your data. As you move the mouse, AQTESOLV draws a
straight line between the anchor point and the position of the mouse.
Release the left mouse button when you have finished matching a new
straight line. AQTESOLV automatically updates the plot legend to reflect
changes in parameter values.
5. Repeat the previous step as needed to estimate K by matching the straight
line to data falling on the second (less steep) straight-line segment. In this
particular case, the recommended head range doesn't help much in fitting the
line because of the filter pack drainage. How does your estimate of hydraulic
conductivity change if you match the solution to the first (steeper) straightline segment in the data?
View Visual Match

149

6. One could attempt to use automatic estimation to match the Bouwer-Rice

solution to these data; however, visual matching is generally more effective
for matching straight-line solutions because you can apply your judgment to
fit the line to the appropriate range of data. Using automatic curve matching
to fit the solution to the entire set of data would be clearly inappropriate for
this example.
7. Choose Save from the File menu to save your work.

Slug Test Example: High-K Aquifer

Butler (2002) described a slug test in a high hydraulic conductivity (high-K) confined
aquifer having a saturated thickness of 10.6 m. The initial displacement in the well
was 0.094 m. The following table provides well construction details for the test.
Well Radius,
rw (m)
0.0127

Casing Radius,
rc (m)
0.0074

Depth to Top of
Screen, d (m)
4.92

Screen Length,
L (m)
0.61

Radius values are measured from the center of the test well. The depth of the well
screen, d, is measured from the top of the aquifer. The static water column height is
11.13 m. Elapsed time and displacement measurements were recorded in seconds
and m, respectively.

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This example will introduce you to the following tasks and features in AQTESOLV:

Creating a new data set with the Slug Test Wizard for a single-well test

Importing data with the Observation Data Import Wizard

Saving a data set

Displaying data

Estimating aquifer properties with Butler (1998) solution (visual and

automatic)

While following the steps in this example, click Help or press F1 to context
sensitive help in the program.
Create a New Data Set with Slug Test Wizard
The first step in analyzing data from a slug test is to create a new AQTESOLV data
set. In this example, we will use the Slug Test Wizard to assist us with data entry.
1. Create a new data set by choosing New from the File menu.
2. In the New Data Set dialog, select Slug Test Wizard from the list. Click
OK.
3. The Slug Test Wizard prompts you for data required for a slug test. Click
Next.
4. For units of measurement, choose m for length, sec for time and m/day for
hydraulic conductivity. Click Next.
5. For project information, enter DP43C - 0.61 m Screen for the title. Click
Next.
6. For general test well data, enter 0.094 for the initial displacement, 11.13 for
static water column height and DP43C for the well name. Enter coordinates
of X=0 and Y=0. Click Next.
7. For aquifer data, enter 10.6 for aquifer thickness. Assume hydraulic
conductivity is isotropic and enter 1 for anisotropy ratio. Click Next.
8. For screen data, enter 4.92 for depth to top of screen and 0.61 for screen
length. Assume the transducer measures the position of the water surface in
the well and enter 0 for transducer depth. Click Next.

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9. For radius data, enter 0.0074 for casing radius and 0.0127 for well radius.
Assume no well skin and enter 0.0127 for the skin radius. Click Next.
10. For corrections, check Apply correction for frictional (viscous) well loss
to correct for well loss in a small diameter well. Click Next.
11. For observations, click Import to launch the Observation Data Import Wizard
for importing data from a file.
We will import a text file consisting of 197 time and displacement readings
arranged in two columns. The first column is elapsed time in seconds since
the start of the test. The second column contains displacement in m.
In Step 1 of the wizard, click Browse. Select the import file DP43CT1.txt in
the AQTESOLV installation folder and click Open. Click Next.
In Step 2 of the wizard, enter 2 for the number of columns, 1 for the
starting row in the file, 1 for the column containing elapsed time and 2 for
the column containing displacement. Click Next.
In Step 3 of the wizard, click Finish. Inspect the import file summary and
click OK.
Click Next to proceed with the Slug Test Wizard.
12. You have completed the Slug Test Wizard. Click Finish.
After completing the Slug Test Wizard, AQTESOLV automatically displays an Error
Log to let you know if the data set contains any errors. If the Error Log identifies
any mistakes, choose options from the Edit menu to correct them.
Save Data Set
At this point, it's a good idea to save your work.
Save the data set by choosing Save As from the File menu. Choose a folder and
enter DP43CT1 for the name of the file. Click Save. AQTESOLV saves the file with
an .aqt extension.
Display Data
1. Choose Displacement-Time from the View menu to display a plot of the test
data.
2. Choose Options from the View menu. In the Plots tab, check Normalized
head to display data as normalized head. Click OK.
3. Choose Linear Axes from the View menu.
The data show an oscillatory pattern that is typical of an underdamped slug
tests in a high-K aquifer.
Estimate Aquifer Properties
We will begin by analyzing this slug test with the Butler (1998) solution for a
152

confined aquifer. The Butler solution is an undamped model that accounts for inertial
effects in the test well.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. Remove the check from Solution is inactive. Click the + next to Confined
Aquifers to expand the list of available solutions for unconfined aquifers.
Select Butler (1998) inertial and click OK.
3. Choose Options from the View menu. In the Plots tab, check Solution
critically damped when C(D)=2. Click OK.
4. Choose Active Curves from the Match menu to perform visual curve matching
with the active type curves feature.
To perform visual matching, move the mouse over the plot.
Click and hold down the left mouse button to anchor the new line at this
point.
Continue to hold the mouse button down and move the mouse up and
down or left and right to adjust the shape of the curve.
Release the left mouse button when you have finished matching the curve.
AQTESOLV automatically updates the plot legend to reflect changes in
parameter values.
5. Repeat the previous step as needed to refine the estimate K. As you adjust
the curve, Le (estimated effective water column length) should be close to L
(theoretical effective water column length). Butler (2002) estimated K = 88.2
m/day.
View Visual Match

153

6. Choose Automatic from the Match menu and click Estimate to perform
automatic curve matching with the Butler solution.
During the iterative estimation procedure, AQTESOLV displays a progress
window and updates the curve displayed on the plot in the background.
7. When estimation has finished, click OK and then Close. Click OK to view the
new position of the type curve.
Visual and automatic curve matching yield very similar results.
8. Choose Save from the File menu to save your work.

Slug Test Example: Multiwell Test (Lincoln

County, KS)
Butler (1998) presented data for a slug test in a semiconsolidated sand aquifer in
Lincoln County, Kansas. Transducers monitored water levels in the test well (Ln-2)
and an observation well (Ln-3) located at a radial distance of 6.45 m from Ln-2. Both
wells fully penetrated the 6.1-m thick aquifer. Inflatable packers were used during
the test to eliminate the effect of wellbore storage in Ln-3. The initial displacement in
Ln-2 was 2.798 m. The following table provides well construction details for the test.

154

Well

Well Radius,
rw (m)
0.102
0.071

Ln-2
Ln-3

Casing Radius,
rc (m)
0.051
0.025

Radius values are measured from the center of each well. Elapsed time and depthto-water measurements were recorded in seconds and meters, respectively.
This example will introduce you to the following tasks and features in AQTESOLV:

Creating a new data set with the Slug Test Wizard for a single-well test

Importing data with the Observation Data Import Wizard

Saving a data set

Displaying data

Estimating aquifer properties with KGS Model solution (visual and automatic)

While following the steps in this example, click Help or press F1 to context
sensitive help in the program.
Create a New Data Set with Slug Test Wizard
The first step in analyzing data from a slug test is to create a new AQTESOLV data
set. In this example, we will use the Slug Test Wizard to assist us with data entry for
the test well (we will add data for the observation well later).
1. Create a new data set by choosing New from the File menu.
2. In the New Data Set dialog, select Slug Test Wizard from the list. Click
OK.
3. The Slug Test Wizard prompts you for data required for a slug test. Click
Next.
4. For units of measurement, choose m for length, sec for time and m/day for
hydraulic conductivity. Click Next.
5. For project information, enter Multi-Well Slug Test for the title. Click Next.
6. For general test well data, enter 2.798 for the initial displacement, 10 for
static water column height and Ln-2 for the well name. Enter coordinates of
X=0 and Y=0. Click Next.
7. For aquifer data, enter 6.1 for aquifer thickness. Assume hydraulic
155

conductivity is isotropic and enter 1 for anisotropy ratio. Click Next.

8. For screen data, enter 0 for depth to top of screen and 6.1 for screen length.
Assume the transducer measures the position of the water surface in the well
and enter 0 for transducer depth. Click Next.
9. For radius data, enter 0.051 for casing radius and 0.102 for well radius.
Assume no well skin and enter 0.102 for the skin radius. Click Next.
10. Corrections are not required for this test. The gravel pack correction only
applies to wells screened across the water table. Click Next.
11. For observations, click Import to launch the Observation Data Import Wizard
for importing data from a file.
We will import a text file consisting of 81 time and water-level readings
arranged in two columns. The first column is elapsed time in seconds since
the start of the test. The second column contains depth-to-water
measurements in meters.
In Step 1 of the wizard, click Browse. Select the import file Ln-2.txt in the
AQTESOLV installation folder and click Open. Click Next.
In Step 2 of the wizard, accept the default values determined by the
Import Wizard. Click Next.
In Step 3 of the wizard, accept the defaults and click Finish. Inspect the
import file summary and click OK.
Click Next to proceed with the Slug Test Wizard.
12. You have completed the Slug Test Wizard. Click Finish.
After completing the Slug Test Wizard, AQTESOLV automatically displays an Error
Log to let you know if the data set contains any errors. If the Error Log identifies
any mistakes, choose options from the Edit menu to correct them.
Add Observation Well
The Slug Test Wizard helped you enter data for the test well. Now you will add
data for the observation well.
1. Choose Wells from the Edit menu and click New to add a new well. Select
the new well in the list and click Modify to edit the well.
2. In the General tab, enter Ln-3 for the well name. Enter 6.45 and 0 for the X
and Y coordinates, respectively.
3. In the Screen tab, enter 0 for depth to top of screen and 6.1 for screen
length.
4. In the Observations tab, click Import to launch the Observation Data
Import Wizard for importing data from a file.
You will import 81 observations from a text file. The first column is elapsed
156

time since the start of the test. The second column contains drawdown
measurements for the observation well.
In Step 1 of the wizard, click Browse. Select the import file Ln-3.txt in the
AQTESOLV installation folder and click Open. Click Next.
In Step 2 of the wizard, accept the default values determined by the
Import Wizard. Click Next.
In Step 3 of the wizard, accept the defaults and click Finish. Inspect the
import file summary and click OK.
5. Click OK to finish editing well Ln-3.
6. Click Close to leave the Wells window.
Save Data Set
At this point, it's a good idea to save your work.
Save the data set by choosing Save As from the File menu. Choose a folder and
enter Lincoln County for the name of the file. Click Save. AQTESOLV saves the file
with an .aqt extension.
Inspect Diagnostic Plots
Following the guidelines developed by Butler (1998) for a slug test in a fully
penetrating well in a confined aquifer, we use the Cooper et al. (1967) method to
screen the data in the test well. An implausibly low storativity (S) value determined
from the screening analysis would suggest the presence of wellbore skin in the well.
1. Choose Displacement-Time from the View menu to display a plot of the test
data.
2. Choose Options from the View menu. In the Plots tab, check Normalized
head to display data as normalized head. Click OK.
3. Choose Log-Linear Axes from the View menu.
On these axes, the test well data show a sigmoidal shape that is typical of
solutions based on the fully transient overdamped slug test model, e.g.,
Hyder et al. (1994).
4. Choose Solution from the Match menu to use the Cooper et al. (1967)
method as a screening tool for the test well (Ln-2) data.
5. Remove the check from Solution is inactive. Click the + next to Confined
Aquifers to expand the list of available solutions for confined aquifers. Select
Cooper-Bredehoeft-Papadopulos (1967) and click OK.
6. Choose Automatic from the Match menu and click Estimate to perform
automatic curve matching with the Cooper et al. solution to the data for
the test well.
During the iterative estimation procedure, AQTESOLV displays a progress
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window and updates the curve displayed on the plot in the background.
7. When estimation has finished, click OK and then Close. Click OK to view the
new position of the type curve.
8. The estimated value of storativity (S) appears plausible; therefore, we
assume that wellbore skin is not a factor at the test well.
Match Solution
We will analyze this slug test with the Hyder et al. (1994) solution (KGS Model) for a
confined aquifer. The KGS Model is a fully transient solution for multiwell slug tests
that accounts for elastic storage in the aquifer. For fully penetrating wells in a
confined aquifer without wellbore skin, the KGS Model is equivalent to the Cooper et
al (1967) and Dougherty-Babu (1984) solutions.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. From the available solutions for Confined Aquifers, select KGS Model
(1994) and click OK.
3. Choose Automatic from the Match menu and click Estimate to perform
automatic curve matching with the KGS Model.
During the iterative estimation procedure, AQTESOLV displays a progress
window and updates the curve displayed on the plot in the background.
4. When estimation has finished, click OK and then Close. Click OK to view the
new position of the type curve.
View Automatic Match

158

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

159

Constant-Head Tests

Constant-Head Test Example: Flow and

Recovery (Grand Junction)
Lohman (1972) presents data from a constant-head test conducted on September
22, 1948 near Grand Junction, Colorado. The Artesia Heights test well (Well 28) fully
penetrates an artesian aquifer and has a radius of 0.276 ft. A two-inch gate valve
capping the well regulated flow. After a shut-in period of several days, the static
head in the well just prior to the test was 92.33 ft above the discharge point (94.55
ft above the measuring point). With the valve open, the well was allowed to flow
freely for 114 minutes. At the end of the test, the gate valve was closed and head in
the well during recovery was monitored for an additional 41 minutes. Lohman (1972)
reported head values in feet above land surface. The measuring point was 0.5 ft
above land surface (Lohman 1965); hence, the static head above land surface was
95.05 ft.
Lohman (1965) describes Well 28 as tapping the Jurassic Entrada Sandstone which
serves as the most widely used and productive artesian aquifer in the Grand Junction
area. The Summerville and Morrison Formations overlying the Entrada are described
as relatively impermeable; however, the underlying Triassic Kayenta Formation may
not provide complete hydraulic separation between the Entrada and Wingate
Sandstones (an underlying artesian aquifer) in the area (Lohman 1965). Therefore,
our analysis will consider the possibility of leakage.
This example will introduce you to the following tasks and features in AQTESOLV:

Creating a new data set with the Constant-Head Test Wizard

Importing data with the Pumping Rate Data Import Wizard and the
Observation Data Import Wizard

Saving a data set

Estimating aquifer properties using Jacob-Lohman (1952) straight-line and

type curve solutions for a confined aquifer (visual and automatic)

Estimating aquifer properties from recovery data using Hantush (1959)

solution for a leaky aquifer (automatic)

While following the steps in this example, click Help or press F1 to obtain
context sensitive help in the AQTESOLV application.

160

Create a New Data Set with Constant-Head Test Wizard

The first step in analyzing data from a constant-head test is to create a new
AQTESOLV data set. In this example, we will use the Constant-Head Test Wizard to
assist us with data entry.
1. Create a new data set by choosing New from the File menu.
2. In the New Data Set dialog, select Constant-Head Test Wizard from the
list. Click OK.
3. The Constant-Head Test Wizard prompts you for data required for a
constant-head test. Click Next.
4. For units of measurement, choose ft for length, min for time, gal/min for
pumping rate and ft/day for hydraulic conductivity. Click Next.
5. For project information, enter Grand Junction, Colorado for the location
and September 22, 1948 for the test date. Click Next.
6. For aquifer data, assume 150 for the aquifer thickness. Enter 1 for the
anisotropy ratio (i.e., assume hydraulic conductivity is isotropic). Click Next.
7. For pumping well data, enter Well 28 for the well name. Enter coordinates of
X=0 and Y=0. Click Next.
8. For pumping well construction, select the option for vertical, full
penetration. Click Next.
9. For pumping well radius data, we will assume a negligible casing radius.
Enter 0.00001 for casing radius and 0.276 for well radius. Click Next.
Wellbore storage plays no role in a constant-head test when the well is
flowing and the head in the well is constant; however, depending on well
configuration, wellbore storage may affect recovery because the boundary
condition changes at the test well. For this particular test, the action of
closing the gate valve seals the well at the end of the flow test and head in
the well recovers without storage in the casing. A suitable packer
arrangement in a well could produce the same effect. To perform recovery
calculations without wellbore storage, enter a negligible value for casing
radius.
10. For pumping rates, click Import to launch the Pumping Rate Data Import
Wizard for importing data from a file.
We will import a text file consisting of 20 time-rate readings arranged in two
columns. The first column is elapsed time since the start of the test. The
second column contains flow rate measurements.
In Step 1 of the wizard, click Browse. Select the import file Grand Junction
Rates.txt in the AQTESOLV installation folder and click Open. Click Next.
In Step 2 of the wizard, accept the defaults determined by AQTESOLV (2
for the number of columns, 8 for the starting row in the file, 1 for the
column containing elapsed time and 2 for the column containing rates).
161

Click Next.
In Step 3 of the wizard, click Finish. Inspect the import file summary and
click OK.
Click Next to proceed with the Constant-Head Test Wizard.
11. For constant-head data, enter 92.33 for the head maintained in the test well.
Check the option to Compute multi-rate Agarwal equivalent time. Click
Next.
12. For observations, click Import to launch the Observation Data Import
Wizard for importing data from a file.
We will import a text file consisting of 21 time-head readings arranged in two
columns. The first column is elapsed time since the start of the recovery. The
second column contains measurements of head above land surface during
recovery.
To convert elapsed time since the start of recovery to elapsed time since the
start of the test, we will use the wizard to add 114 minutes (the duration of
the test) to each of the imported time values. To transform head during
recovery to displacement, we subtract 95.05 ft (the static head above land
surface recorded before the test) from all of the head measurements in the
file. The subtraction operation results in negative displacements. To make
them positive, multiply all of the displacement values by -1.
In Step 1 of the wizard, click Browse. Select the import file Grand Junction
Recovery.txt in the AQTESOLV installation folder and click Open. Click
Next.
In Step 2 of the wizard, accept the defaults determined by AQTESOLV (2
for the number of columns, 11 for the starting row in the file, 1 for the
column containing elapsed time and 2 for the column containing
displacement). Click Next.
In Step 3 of the wizard, check the first box to subtract a constant from
the time values and enter -114 for the constant. Check the second box to
subtract a constant from the displacement values and enter 94.55 for the
constant. Check the fourth box to multiply displacement values by a
constant and enter -1 for the constant. Click Finish. Inspect the import file
summary and click OK.
Click Next to proceed with the Constant-Head Test Wizard.
13. You have completed the Constant-Head Test Wizard. Click Finish.
After completing the Pumping Test Wizard, AQTESOLV automatically displays an
Error Log to let you know if the data set contains any errors. If the Error Log
identifies any mistakes, choose options from the Edit menu to correct them.

162

Save Data Set

At this point, it's a good idea to save your work.
Save the data set by choosing Save As from the File menu. Choose a folder and
enter Grand Junction for the name of the file. Click Save. AQTESOLV saves the file
with an .aqt extension.
Estimate Aquifer Properties from Flow Test
To start our analysis, we can use the Jacob-Lohman (1952) straight-line solution to
obtain preliminary estimates of aquifer properties.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. Remove the check from Solution is inactive. Click the + next to Confined
Aquifers to expand the list of available solutions for confined aquifers. Select
Jacob-Lohman (1952) straight-line method and click OK.
3. Choose Displacement-Time from the View menu. For the Jacob-Lohman
straight-line method, the data are plotted on linear-log axes.
For a constant-head test, the displacement-time plot shows displacement
normalized by discharge, s/Q(t), where s is the constant head maintained in
the test well and Q(t) is discharge at time t.
4. Choose Visual from the Match menu to perform visual curve matching with
the Jacob-Lohman straight-line solution.
To perform visual matching, move the mouse to a point where you wish to
begin drawing a new line with the Jacob-Lohman solution.
Click and hold down the left mouse button to anchor the new line at this
point.
Continue to hold the mouse button down and move the mouse to match a
new straight line to your data. As you move the mouse, AQTESOLV draws a
straight line between the anchor point and the position of the mouse.
Release the left mouse button when you have finished matching a new
straight line. AQTESOLV automatically updates the plot legend to reflect
changes in parameter values.
5. Repeat the previous step as needed to achieve a satisfactory match.
View Visual Match With Jacob-Lohman

163

Having completed our preliminary analysis with the Jacob-Lohman straight-line

solution, let's refine our match with the Jacob-Lohman (1952) type curve solution for
a confined aquifer.
1. Choose Solution from the Match menu to select a method for analyzing the
data.
2. From the list of solutions for Confined Aquifers, select Jacob-Lohman
(1952) and click OK.
3. Choose Log Axes from the View menu to change the axes to a log-log
format.
4. Choose Automatic from the Match menu. In the Parameters tab, select
Inactive for the estimation status of both r(w) and r(c). Click Estimate
to perform automatic curve matching.
During the iterative estimation procedure, AQTESOLV displays a progress
window and updates the curves displayed on the plot in the background.
5. When estimation has finished, click OK and then Close. Click OK to view the
new position of the type curve. The estimated values of T and S from
automatic matching are close to the visual estimates.
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6. Choose Discharge-Time from the View menu to inspect the discharge rate
simulated by the Jacob-Lohman solution versus the observed flow rate
measurements.
View Automatic Match on Discharge-Time Plot

7. Use residual-time, residual-simulated and normal probability plots to evaluate

the fit of the solution by examining residuals. The diagnostics report also
presents residual statistics for curve fitting.
8. Choose Save from the File menu to save your work.
Estimate Aquifer Properties from Recovery Data
AQTESOLV provides an exact method for evaluating recovery data from a constanthead test. We will begin our recovery analysis with the Jacob-Lohman (1952) type
curve solution.
1. Choose Residual Drawdown from the View menu to plot residual
drawdown data on linear-log axes.
Although we obtained a good curve fit with the Jacob-Lohman solution when
matching only the data from the flow test, the residual drawdown plot
suggests a source of recharge (e.g., leakage) because the data recover more
165

quickly than the predicted curve. In addition, a line through the trend of the
data intercepts the x axis at a value greater than 1.
2. Choose Agarwal from the View menu. The plot displays recovery as a
function of Agarwal equivalent time.
The Agarwal method is an approximate recovery data analysis procedure for
constant-head tests (Uraiet and Raghavan 1980). If leakage were a factor in
the response for this test, we would observe the data to flatten with
increasing recovery time; however, due to the short duration of recovery
measurements, the leakage effect is not apparent.
Now let's use the Hantush (1959) solution for a constant-head test in a
leaky aquifer to investigate the potential effect of leakage.
1. Choose Solution from the Match menu. Click the + next to Leaky Aquifers
to expand the list of available solutions for leaky aquifers. Select Hantush
(1959) constant head and click OK.
2. Choose Displacement-Time from the View menu to display the data from the
flow test.
3. Choose Automatic from the Match menu. In the Estimation tab, enter
50 for the maximum iterations. Click Advanced and change the lambda
updating method to Conservative. Click Estimate to perform automatic
curve matching.
When estimation has finished, click OK and then Close. Click OK to view the
new position of the type curve.
The residual sum of squares (RSS) for the leaky aquifer model indicates an
improved match compared to the confined aquifer model: RSS = 0.7744 for
the confined aquifer model versus RSS = 0.6685 for the leaky aquifer model.
4. Choose Residual Drawdown from the View menu.
View Residual Drawdown Plot for Leaky Aquifer Model
The residual drawdown curve predicted with the leaky aquifer model matches
the recovery data much more closely than the model for a confined aquifer. If
you attempt to use automatic curve matching to estimate the aquifer
properties from just the recovery data, T and S are perfectly correlated and
the fit is nonunique.

166

167

Mounding

Mounding Example: Rectangular Recharge Area

In this example, you will use AQTESOLV to predict transient rise of the water table
beneath a rectangular recharge area using a solution by Hantush (1967). The length
and width of the recharge basin are both 100 ft. The hydraulic conductivity of the
unconfined aquifer is 0.1 ft/day and the specific yield is 0.1. The initial saturated
thickness of the aquifer is 10 ft.
The procedure for applying the circular recharge area solution by Hantush (1967)
is essentially the same as given below.
This example will introduce you to the following tasks and features in AQTESOLV:

Creating an empty data set

Predicting the growth of a groundwater mound using the Hantush solution for
a rectangular recharge area

Saving a data set

While following the steps in this example, click Help or press F1 to obtain
context sensitive help in the AQTESOLV application.
Create an Empty Data Set
The first step in performing groundwater mounding simulations is to create a new
AQTESOLV data set. In this example, we will create an empty data set before using
the groundwater mounding tools in AQTESOLV.
1. Create a new data set by choosing New from the File menu.
2. In the New Data Set dialog, select Default from the list. Click OK.
After creating an empty data set, AQTESOLV automatically displays an Error Log to
let you know if the data set contains any errors. For the purpose of simulating a
groundwater mound, you may ignore any errors shown in the Error Log.
Prediction
Now we can use the Hantush (1967) solution to predict the transient growth of a
groundwater mound beneath a rectangular recharge area.
1. Choose Units from the Edit menu.
2. For units of measurement, choose ft for length, day for time, consistent for

168

pumping rate and consistent for hydraulic conductivity. Click OK.

3. Choose Mounding>Rectangular Recharge Area from the Tools menu to enter
mounding data.
4. For aquifer properties, enter 0.1 for hydraulic conductivity (K), 0.1 for
specific yield (Sy) and 10 for initial saturated thickness (h(0)).
5. For recharge area properties, enter 0.01 for recharge rate (w), 100 for
the simulation time (t), 100000 for time when recovery begins (t(0)), 0
for x coordinate (X), 0 for y coordinate (Y), 100 for length (l) and 100 for
width (a).
To simulate recharge without recovery, enter a value for t(0) greater than
the simulation time.

6. Click Contour to launch the Grid Wizard for preparing a contour plot
with Surfer.
Surfer is a popular standalone software package that integrates seamlessly
with AQTESOLV to generate contour plots. Install Surfer on your computer to
gain access to this feature.
7. In Step 1 of the Grid Wizard, enter the name of a Grid file to store data for
the contour plot. Click Browse if you would like to store the file in a specific
folder on your computer. Select X-Y (Plan) for the grid orientation. Click
Next.

169

8. In Step 2 of the Grid Wizard, enter -100 and 100 for the minimum and
maximum dimensions in the X and Y directions. Enter 51 for the number of
grid lines in both directions. For the depths, enter 0 and 10. Enter 100 for
the time to predict the growth of the mound. Click Next.
9. In Step 3 of the Grid Wizard, check Display grid file with Surfer and
select Contour. Click Finish to display the contour plot with Surfer. You may
use options in Surfer to customize the appearance of the plot.
View Contour Plot

170

10. Click Report to save a file containing groundwater mounding results in

text or HTML format.
You may open a text or HTML report in Microsoft Excel to generate a quick
chart of the results.
11. Click OK when you have finished using the mounding tool for a rectangular
recharge area.

171

Save Data Set

Save the data set by choosing Save As from the File menu. Choose a folder and
enter Mound for the name of the file. Click Save. AQTESOLV saves the file with an
.aqt extension.

More Examples
On the Web
Visit the examples section of the AQTESOLV web site to find more example data sets
and tutorials.

172

Menus
File Menu
Select options in the File menu to manage data set files, import and export data,
print plots and reports, send data sets as email and exit the application.
New
Open
Close
Save
Save As
Export
Print
Print Preview
Print Setup
Page Setup
Batch Print
Send Mail
MRU
Exit

Create a new data set

Open a file containing a data set
Close the active data set
Save the active data set
Save the active data set using a specified
file name
Export data
Print the plot or report in the active
window
Preview the plot or report before printing
Configure printer options
Format the page for printing
Batch print a group of data sets
Send the active data set as an email
attachment
Most recently used files
Close the AQTESOLV application

Edit Menu
Select options in the Edit menu to modify the active data set.
Undo
Redo
Copy
Units
Annotations
Aquifer Data
Wells
Test Type

Undo the last curve adjustment

Redo the previously undone curve
adjustment
Copy plot or report to Windows clipboard
Select measurement units
Edit title, project information and end
notes
Edit aquifer/aquitard data
Edit, add or delete wells
Change the test type

View Menu
The View menu provides options for displaying data, solutions and estimation
results. Two general types of views, plots and reports, are available for viewing
data and solutions, and evaluating estimation results. Other options in the View
menu allow you to customize the appearance of plots and reports.
173

Displacement-Time
Composite
Residual Drawdown
Agarwal
Residual-Time
Residual-Simulated
Normal Probability
Discharge-Time
Derivative-Time
Radial Flow
Linear Flow
Bilinear Flow
Spherical Flow
Diagnostics
Report
Error Log
Linear Axes
Log-Linear Axes
Linear-Log Axes
Log Axes
Format
Options
Zoom
Refresh
Contour
Toolbar
Status Bar

Display displacement vs. time plot in

active window
Display composite plot in active window
Display residual drawdown plot in active
window
Display Agarwal plot in active window
Display residual vs. time plot in active
window
Display residual vs. simulated plot in
active window
Display normal probability plot in active
window
Display discharge vs. time plot in active
window
Display derivative plot in active window
(Pro only)
Display radial flow plot in active window
(Pro only)
Display linear flow plot in active window
(Pro only)
Display bilinear flow plot in active window
(Pro only)
Display spherical flow plot in active
window (Pro only)
Display diagnostics report in active
window
Display complete report in active window
Display error log in active window
Display plot on linear x and y axes
Display plot on logarithmic x and linear y
axes
Display plot on linear x and logarithmic y
axes
Display plot on logarithmic x and y axes
Format plot or report in active window
Select options for plot or report in active
window
Select zoom factor for active window
Refresh contents displayed in active
window
Generate grid and contour plot
Toggle toolbar on/off
Toggle status bar on/off

You also may select plot and report options from the list on the toolbar.

174

Match Menu
Choose options from the Match menu to select an aquifer test solution, perform
visual or automatic curve matching, tweak parameters (sensitivity analysis) and edit
matching options.
Solution
Automatic
Visual
Toolbox
Check Slope
Active Curves
Forward Solution

Choose an aquifer test solution

Perform automatic curve matching
Perform visual curve matching
Open the curve matching toolbox
Test the slope of a range of data
Toggle active type curves on/off
Toggle forward solution (predictive
simulation) on/off

Tools Menu
The Tools menu provides options for running other Windows applications (e.g.,
ModelCad for Windows, TWODAN and WinSitu) and setting other preferences. Use
these applications in conjunction with AQTESOLV to increase your productivity.
Mounding
ModelCad
TWODAN
WinSitu
Customize

Compute transient water-table rise

beneath a circular or rectangular recharge
area using Hantush (1967) solution
Launch ModelCad for Windows application
Launch TWODAN application
Launch Win-Situ application
Customize tools and configure application
settings

Windows Menu
The Windows menu provides options for managing windows. AQTESOLV provides a
multi-document interface so you can work on more than one data set at the same
time. In addition, you can open more than one window (e.g., showing different plots)
for the same data set.
New Window
Cascade
Tile Horizontal
Tile Vertical
Arrange Icons

Open a new window for the active data

set
Cascade all windows in the application
frame
Tile all windows horizontally
Tile all windows vertically
Arrange window icons at the bottom of
the application frame

175

Help Menu
Choose options from the Help menu to access the program's help features and find
software support options.
Contents and Index
Search
What's This
Quick Tips
Tip of the Day
Examples
AQTESOLV on the Web
Check for Updates
Register
About AQTESOLV

Display contents of help system

Search the help system
Get context-sensitive help
Show/hide quick tips
Display Tip of the Day window
Show examples
Find more information at the AQTESOLV
web site
Check for software updates
Register your copy of AQTESOLV
Display program copyright and version
information

Toolbar
(View > Toolbar)
Choose Toolbar from the View menu to show/hide the toolbar.
The toolbar contains buttons for the following commands:
New
Open
Save
Print
Print Preview
Undo
Redo
Aquifer Data
Wells
View
Linear Axes
Log-Linear Axes
Linear-Log Axes
Log Axes
Show Derivative

176

Contour
Refresh
Match Automatic
Match Visual
Match Toolbox
Active Type Curves
Match Early Data
Match Late Data
Type Curve Family
Type Curve Value
About AQTESOLV
What's This Help

Move the mouse over a toolbar control and pause for a moment to reveal a
tooltip that shows the button's function.

Select plot and report options from the drop-down list of views on the toolbar.

Change type curve families and curve values from drop-down lists on the
toolbar.

Keyboard Shortcuts
AQTESOLV provides the following keyboard shortcuts to program features.
Ctrl-C
Ctrl-D
Ctrl-K
Ctrl-N
Ctrl-O
Ctrl-P
Ctrl-S
Ctrl-T
Ctrl-Y
Ctrl-Z
F1
Shift-F1

Copy
Superimpose derivative
Toggle cursor coordinate tracking on/off
New
Open
Print
Save
Toggle type curves on/off
Redo
Undo
Help
Context help

177

Press ESC while AQTESOLV is refreshing a type curve to disable the display of
type curves. Press Ctrl-T to resume type curve display.

178

Entering, Editing and Importing Data

Overview (Data Sets)
Begin a new analysis in AQTESOLV by creating a new data set. AQTESOLV stores a
complete record of each aquifer test analysis in an AQTESOLV data set which
contains the following:

aquifer test data (e.g., aquifer geometry data, well data, pumping data and
time-displacement data),

information concerning the solution method used to analyze the test data
(e.g., solution method and aquifer properties), and

formatting parameters for plots and reports.

Learn more about working with data sets:

How Do I Begin a New Analysis (Creating New Data Sets)?
1. Create a new data set by choosing File>New.
2. Use the Pumping Test Wizard, Constant-Head Test Wizard, Slug Test Wizard
to enter test data. These wizards also help you to import data logger files.
3. Use the Forward Solution Wizard to create a data set and predict the response
in a pumping test (test design).
4. Use the AQTESOLV for DOS Import Wizard to import a data set created with a
DOS version of AQTESOLV.
5. Instead of using a wizard to create a new data set, you also may select the
Default option when you choose File>New. Choose options from the Edit
menu to enter your test data.
How Do I Open an Old Analysis (Opening Data Sets)?
1. Open a file containing an AQTESOLV data set by choosing File>Open. The
default file name extension for an AQTESOLV data set is .aqt.
2. Select options from the Edit menu to modify the data set.
How Do I Change My Analysis (Editing Data Sets)?
1. Choose options from the Edit menu to modify a data set.
2. Select View>Format to edit the appearance of a plot or report.
3. Choose Match>Solution to select an aquifer test solution.
4. To change aquifer properties for the active solution, choose Match>Toolbox.
How Do I Save My Analysis (Saving Data Sets)?

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1. Save the active data set using the current file name by choosing File>Save.
2. To save the active data set with a new file name, choose File>Save As.
3. The file name extension for AQTESOLV data sets is .aqt.

By default, AQTESOLV data sets have an .aqt file name extension.

180

Data Entry Wizards

Pumping Test Wizard

The easiest way to enter data from a pumping test is to use the Pumping Test
Wizard.
Using the Pumping Test Wizard
1. Choose New from the File menu.
2. In the New Data Set dialog, select Pumping Test Wizard from the list to
help you create a new data set for a typical pumping test. Click OK.
3. Configure the wizard for a Multiwell Test or Single-Well Test. Click OK.
4. Click Help in the wizard to get context-sensitive help.
5. Follow the steps in the wizard to enter pumping test data including
measurement units, aquifer data, well locations and construction details,
pumping rates and water-level observations.
6. In the Pumping Rates step of the wizard, click Import to import time-rate
data from a file or enter rates directly into the spreadsheet.
7. In the Observations step of the wizard, click Import to import timedisplacement data from a data logger file or enter observations directly into
the spreadsheet.
8. Click Finish at the end of the wizard.

After completing the Pumping Test Wizard, modify a data set using options
in the Edit menu.

Avoid repetitive data entry and save time by using an existing data set as a
template for a new test.
For example, if you conduct multiple pumping tests in a single well, you can
use the data set for the first test as a template for the successive tests.

Choose File>Open to open an existing data set file. Choose options from the
Edit menu to modify test data. Choose File>Save As to save the modified data
set in a new file.

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Constant-Head Test Wizard

The easiest way to enter data from a constant-head test is to use the ConstantHead Test Wizard.
Using the Constant-Head Test Wizard
1. Choose New from the File menu.
2. In the New Data Set dialog, select Constant-Head Test Wizard from the
list to help you create a new data set for a typical constant-head test. Click
OK.
3. Click Help in the wizard to get context-sensitive help.
4. Follow the steps in the wizard to enter constant-head test data including
measurement units, aquifer data, well locations and construction details,
pumping rates and water-level observations.
5. In the Pumping Rates step of the wizard, click Import to import time-rate
data from a file or enter rates directly into the spreadsheet.
6. In the Observations step of the wizard, click Import to import timedisplacement data from a data logger file or enter observations directly into
the spreadsheet.
7. Click Finish at the end of the wizard.

After completing the Constant-Head Test Wizard, modify the data set using
options in the Edit menu.

Avoid repetitive data entry and save time by using an existing data set as a
template for a new test.
For example, if you conduct multiple tests in a single well, you can use the
data set for the first test as a template for the successive tests.

Choose File>Open to open an existing data set file. Choose options from the
Edit menu to modify test data. Choose File>Save As to save the modified data
set in a new file.

Slug Test Wizard

The easiest way to enter data from a slug test is to use the Slug Test Wizard.
Using the Slug Test Wizard
1. Choose New from the File menu.

182

2. In the New Data Set dialog, select Slug Test Wizard from the list to help
you create a new data set for a typical slug test. Click OK.
3. Click Help in the wizard to get context-sensitive help.
4. Follow the steps in the wizard to enter slug test data including measurement
units, aquifer data, well locations and construction details and water-level
observations.
5. In the Observations step of the wizard, click Import to import timedisplacement data from a data logger file or enter observations directly into
the spreadsheet.
6. Click Finish at the end of the wizard.

After completing the Slug Test Wizard, modify a data set using options in
the Edit menu.

Avoid repetitive data entry and save time by using an existing data set as a
template for a new test.
For example, if you conduct multiple slug tests in a single well, you can use
the data set for the first test as a template for the successive tests.

Choose File>Open to open an existing data set file. Choose options from the
Edit menu to modify test data. Choose File>Save As to save the modified data
set in a new file.

Forward Solution Wizard

Use the Forward Solution Wizard to perform predictive simulations for a pumping
test.
Using the Forward Solution Wizard
1. Choose New from the File menu.
2. In the New Data Set dialog, select Forward Solution Wizard from the list
to help you create a new data set for predictive simulation. Click OK.
3. Configure the wizard for a Multiwell Test or Single-Well Test. Click OK.
4. Click Help in the wizard to get context-sensitive help.
5. Follow the steps in the wizard to enter test data including measurement units,
aquifer data, well locations and construction details and pumping rates.

183

6. In the Pumping Rates step of the wizard, click Import to import time-rate
data from a file or enter rates directly into the spreadsheet.
7. In the Forward Solution Data step of the wizard, enter the range of time for
the simulation and estimates of transmissivity and storage coefficient for the
aquifer. You can change these estimates later by choosing Match>Toolbox.
8. Click Finish at the end of the wizard.

After completing the Forward Solution Wizard, modify a data set using
options in the Edit menu.

Choose Match>Forward Solution to perform predictive simulations with any

complete data set.

AQTESOLV for DOS Import Wizard

Choose New from the File menu and select Import AQTESOLV for DOS Wizard
from the New Data Set dialog to import an AQTESOLV for DOS data set.
Using the AQTESOLV for DOS Import Wizard
1. Click Browse to select a file containing an AQTESOLV for DOS data set to
import.
2. Click Finish to import the data set.

After importing an AQTESOLV for DOS data set, you should review the
imported data to ensure its completeness using options in the Edit menu.
Many new features and data options have been added to AQTESOLV since the
release of DOS versions of the software.

Check Convert all data sets with .DAT extension in this folder if you
want to convert all AQTESOLV for DOS data sets (with a .DAT extension) into
AQTESOLV for Windows data sets (with a .AQT extension) in the folder you
have selected.

184

Editing Data

Editing Test Data

Choose from the following options in the Edit menu to enter data into a new data set
or modify an existing one.
Units
Annotations
Aquifer Data
Wells

Select measurement units for the data set

Edit the title, project information and end
notes for the data set
Edit aquifer data
Edit well data

Avoid repetitive data entry and save time by using an existing data set as a
template for a new test.
For example, if you conduct repeated tests in a single well, you can use the
data set for the first test as a template for the successive tests.

Choose File>Open to open an existing data set file. Choose options from the
Edit menu to modify test data. Choose File>Save As to save the modified data
set in a new file.

Choose File>New, select Default to create an empty data set, and click OK.
Choose options from the Edit menu to enter test data. Choose File>Save As
to save the new data set.

185

Importing Data

Overview (Importing Data)

AQTESOLV provides easy-to-use wizards that import aquifer test data from
external files. When convenient, you also may copy and paste data from another
application (e.g., Excel) directly into AQTESOLV.
o

Import observation data from data logger files using the Observation Data
Import Wizard.
In some cases, you may find it easier to copy and paste observation data
directly from another application into AQTESOLV (e.g., if your data are stored
in a spreadsheet such as Excel).

Import files containing pumping rate data using the Pumping Rate Data
Import Wizard. You also may copy and paste pumping rate data into
AQTESOLV.

Before you import observation or rate data, choose File>New to create a new
data set. Select a data set wizard which will assist you with importing data.

To import observation or rate data into the active data set, choose Edit>Wells
to modify well data.

Observation Data Import Wizard

(Edit > Wells > [Modify >] Observations > Import)
Import time and displacement data for a well with the Observation Data Import
Wizard, a versatile and flexible tool for importing measurements from a file. The
wizard works seamlessly with many types of data loggers including In-Situ and
Solinst products.
Before you begin importing a data logger file, ascertain the following basic
information about the contents of the file:

Identify the structure of the file (number of data columns in the file and
order of the columns containing elapsed time and displacement data).

Note the static transducer reading prior to the start of the test (you may
need to subtract this value from each imported reading to convert values
from depth to water or water column height above the transducer to
displacement).

Using the Import Wizard

1. Choose Wells from the Edit menu, select a well from the list and click
Modify.
186

2. In the Observations tab, click Import.

3. Follow the steps in the wizard: open the import file, identify the file structure
and specify transformation and filter operations.

If no data set is open and the Edit menu is not available, create a new data
set or open an existing data set.

Pumping Rate Data Import Wizard

(Edit > Wells > [Modify >] Rates > Import)
Import time and displacement data for a well with the Pumping Rate Data Import
Wizard, a versatile and flexible tool for importing rate measurements from a file.
Using the Import Wizard
1. Choose Wells from the Edit menu, select a well from the list and click
Modify.
2. In the Rates tab, click Import.
3. Follow the steps in the wizard: open the import file, identify the file structure
and specify transformation and filter operations.

If no data set is open and the Edit menu is not available, create a new data
set or open an existing data set.

187

Viewing Data
Plots

Overview (Plots)
The View menu provides options for plotting data, solutions and estimation results.
Other options in the View menu allow you to customize the appearance of a plot.
Data Plots

Plots for viewing aquifer test (displacement) data and matching analytical
solutions include displacement-time, composite, residual drawdown and
derivative-time plots.

AQTESOLV also provides discharge-time plots to view the discharge rate

history from variable-rate pumping tests.

Diagnostic Flow Plots

The radial flow, linear flow, bilinear flow and spherical flow plots help you to
choose appropriate models for your data set.

Use diagnostic flow plots to identify behavior produced by wellbore storage,

fracture flow and double-porosity phenomena.

Derivative plots also provide an important diagnostic tool.

Residual Plots

Use the residual-time, residual-simulated and normal probability plots to

examine residuals (i.e., errors between simulated and observed values of
displacement) from visual or automatic curve matching.

Use residual plots to evaluate how well a solution (type curve) matches your
test data.

Customizing Plots

Format plots to customize axes, labels and curve styles.

Select plot options to edit items to display on plots, type curve families,
derivative options and more.

188

Data Plots

Displacement-Time Plot
(View > Displacement-Time)
Choose Displacement-Time from the View menu to plot values of displacement as
a function of time in the active window.
Example: Pumping Test in Unconfined Aquifer (with Derivative)

Example: Slug Test in Confined Aquifer (Multiwell)

189

The displacement-time plot allows you to analyze displacement data from one
or more observation wells.

Displacement-time plots show one type curve for each observation well.

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

Choose Options from the View menu and select Family of Type Curves to
superimpose a type curve family on the plot.

Choose Options from the View menu and select Derivative Curves to
display displacement and derivative data on a single plot.

Choose Options from the View menu and select Theis Type Curves to
superimpose the Theis solution on the plot.

Choose Options from the View menu and select Recommended Head
Ranges to display head ranges recommended by Butler (1998) for the
analysis of slug tests.

190

Composite Plot
(View > Composite)
Select Composite from the View menu to plot values of displacement as a function
of time divided by the square of radial distance (t/r2).
Example: Pumping Test in Confined Aquifer (with Derivative)

Example: Pumping Test in Double-Porosity Aquifer (with Derivative)

191

The composite plot allows you to analyze displacement data from one or more
observation wells.

For pumping test solutions containing only two parameters, composite plots
display a single type curve regardless of the number of observation wells
shown on the plot. For solutions involving three or more parameters,
composite plots show one type curve for each observation well.

Composite plots are only active for pumping tests.

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

Choose Options from the Visual menu and select Derivative Curves to
display displacement and derivative data on the plot.

Residual Drawdown Plot

(View > Residual Drawdown)

192

Choose Residual Drawdown from the View menu to plot values of residual
drawdown measured during the recovery phase of a pumping or constant-head test
as a function of adjusted or equivalent time, t/t', where t is the time since pumping
began and t' is the time since pumping stopped.
Example: Pumping Test in Confined Aquifer

Example: Constant-Head Test in Leaky Confined Aquifer

193

In the petroleum industry, the residual drawdown plot is known as a Horner plot.

A residual drawdown plot allows you to analyze recovery data from one or
more observation wells.

Residual drawdown plots show one type curve for each observation well.

You may view residual drawdown plots with any pumping test solution as long
as the data set includes only one pumping well and the observation data
include recovery measurements (i.e., readings recorded after pumping
stopped).

As recovery (the time since pumping stopped) progresses, the adjusted time
ratio, t/t', approaches unity. Assuming an infinite aquifer, the residual
drawdown approaches zero (the pre-pumping or static condition) as the time
of recovery increases; hence, the recovery data plot closer to the origin of the
residual drawdown plot where t/t' = 1. If the aquifer is bounded or the prepumping condition is not static, the residual drawdown will approach a
nonzero value as t/t' approaches 1.

Choose Visual or Toolbox>Tweak from the Match menu to match a solution

194

to the recovery data.

Choose Automatic from the Match menu to perform automatic estimation for
the recovery data.

Agarwal
(View > Agarwal)
Choose Agarwal from the View menu to plot recovery data as a function of Agarwal
equivalent time in the active window.
Example: Recovery Test in Confined Aquifer (with Derivative)

Through a simple transformation of the time variable, Agarwal (1980) devised a

procedure that uses solutions developed for drawdown analysis (e.g., the Theis type
curve) to analyze recovery data.

For a constant-rate test, Agarwal equivalent time, tequiv, is defined as

195

where t is the elapsed time since pumping began [T], t' is time since
pumping stopped [T] and tp is the total time of pumping [T].

For a multi-rate test consisting of n steps, Agarwal equivalent time is given

as follows

where t0 = 0, q is pumping rate [L3/T], q0 = 0 and n > 1.

Recovery, srecov, is defined as

where s' is residual drawdown in the well at times after pumping stopped [L]
and sp is the drawdown in the well at time tp [L].

The Agarwal method assumes that the total time of pumping is larger than
the time since pumping stopped (tp>t').

The Agarwal plot allows you to analyze recovery data from one or more wells.

Agarwal plots show one type curve for each well.

Use of the Agarwal method is limited to tests with one pumping well.

For constant-head tests, Uraiet and Raghavan (1980) proposed an approximate

method for the analysis of recovery data based on the Agarwal procedure. Their
procedure uses the last rate measured prior to recovery and computes Agarwal
equivalent time with the constant-rate formula; however, because rates are variable
during a constant-head test, AQTESOLV also provides an option to compute Agarwal
equivalent time using the multi-rate formula.

To apply the Agarwal recovery method, your observation data must have a
drawdown measurement at tp, the time when the pump was shut off, to allow
computation of srecov.

Choose Visual or Toolbox>Tweak from the Match menu to match a solution

to the recovery data.

Choose Automatic from the Match menu to perform automatic estimation for
the recovery data.

Choose View>Options and select Family of Type Curves to superimpose a

type curve family on the plot.

Choose View>Options and select Derivative Curves to display displacement

196

and derivative data on a single plot.

Choose View>Options and select Theis Type Curves to superimpose the

Theis solution on the plot.

Distance Drawdown Plot

(View > Distance Drawdown)
Choose Distance Drawdown from the View menu to plot values of displacement as
a function of observation well distance in the active window.
Example: Pumping Test in Confined Aquifer

Example: Pumping Test in Leaky Confined Aquifer

197

The distance-drawdown plot allows you to analyze displacement data from

one or more observation wells.

AQTESOLV automatically interpolates or extrapolates a value of drawdown

when a well does not contain an observation at the time specified for the
distance-drawdown plot.

Choose Match>Automatic to perform automatic curve matching.

Choose Match>Toolbox to perform visual curve matching using parameter

tweaking.

Choose View>Option>Distance to enter the time for distance-drawdown plots.

AQTESOLV draws a curve on a distance-drawdown plot for each observation

well in the data set. Each curve may vary according to well construction (e.g.,
partial penetration) and radial direction from the pumped well. For the
pumped well, the distance-drawdown curve is drawn along the x-coordinate
axis. For radially symmetric problems and observation wells having identical
construction, all curves will overlay each other.

198

Derivative-Time Plot
(View > Derivative-Time)
Choose Derivative-Time from the View menu to perform derivative analysis by
displaying the derivative of displacement data as a function of logarithmic time:

If a solution is active, AQTESOLV also plots the derivative curve for the solution.
Example: Pumping Test in Unconfined Aquifer with 3D Saturated/Unsaturated
Flow

A derivative-time plot allows you to view the derivative of displacement

measurements from one or more observation wells.

Derivative-time plots provide a useful diagnostic tool for detecting deviations

in the rate of displacement change. For example, interpretation of a
derivative-time plot can help in the identification of wellbore storage, aquifer
boundaries, leakage and delayed gravity response.
199

Choose Options from the View menu to superimpose derivative data on

displacement plots.

Choose Options from the View menu to select a method for calculating
derivatives from displacement data.

Discharge-Time Plot
(View > Discharge-Time)
Choose Discharge-Time from the View menu to view pumping well discharge rates
from a variable-rate pumping test or constant-head test.
Example: Variable-Rate History for Pumping Test

200

Example: Constant-Head Test in a Confined Aquifer

The discharge-time view option allows you to view constant or variable

pumping rates for one or more pumping wells.

Discharge-time plots are active for pumping tests and constant-head tests.

201

Diagnostic Flow Plots

Radial Flow Plot

(View > Radial Flow)
Choose Radial Flow from the View menu to plot displacement as a function of time.
Radial Flow Schematic in Plan View

Radial flow to a discharging well.

Radial flow plots are useful diagnostic tools for identifying radial (infiniteacting aquifer) flow behavior or wellbore storage.

On semi-logarithmic (log-linear) axes, late-time data exhibiting a straight

line on a radial flow plot are indicative of radial flow conditions in an
infinite-acting aquifer. This late-time behavior on a semi-log plot is the
basis for the Cooper-Jacob straight-line method of analysis.

On log-log axes, early-time data exhibiting a unit slope on a radial flow plot
are indicative of wellbore storage.

View one or more observation wells on radial flow plots.

Example: Wellbore Storage

202

Example: Infinite-Acting Aquifer

203

Choose Visual from the Match menu to match a line with unit slope to data
plotted on a radial flow plot with log-log axes.

Linear Flow Plot

(View > Linear Flow)
Choose Linear Flow from the View menu to plot displacement as a function of the
square root of time.
Linear Flow to a Vertical Fracture in Plan View

204

Linear flow to an infinite-conductivity vertical fracture.

Linear flow plots are useful diagnostic tools for identifying fracture flow
behavior.

On log-log axes, early-time data exhibiting a unit slope on a linear flow plot
are indicative of linear flow conditions to a single fracture with infinite
conductivity or uniform flux along the fracture.

On log-log axes, late-time data exhibiting a unit slope on a linear flow plot are
indicative of linear flow conditions to a well in a strip aquifer (e.g., a buried
valley setting).

View one or more observation wells on linear flow plots.

Example: Uniform-Flux Vertical Fracture

205

Choose Visual from the Match menu to match a line with unit slope to data
plotted on a linear flow plot with log-log axes.

Bilinear Flow Plot

(View > Bilinear Flow)
Choose Bilinear Flow from the View menu to plot displacement as a function of the
fourth root of time.

Bilinear flow plots are useful diagnostic tools for identifying fracture flow
behavior.

On log-log axes, early-time data exhibiting a unit slope on a bilinear flow plot

206

are indicative of bilinear flow conditions to a single fracture with finite

conductivity.

View one or more observation wells on bilinear flow plots.

Choose Visual from the Match menu to match a line with unit slope to data
plotted on a bilinear flow plot with log-log axes.

Spherical Flow Plot

(View > Spherical Flow)
Choose Spherical Flow from the View menu to plot displacement as a function of
the inverse square root of time.

Spherical flow plots are useful diagnostic tools for identifying spherical flow
behavior.

On log-log axes, data exhibiting a unit slope on a spherical flow plot are
indicative of spherical flow conditions.

View one or more observation wells on spherical flow plots.

Choose Visual from the Match menu to match a line with unit slope to data
plotted on a spherical flow plot with log-log axes.

207

Residual Plots

Residual-Time Plot
(View > Residual-Time)
Choose Residual-Time from the View menu to plot residuals as a function of time.
Example: Pumping Test in Confined Aquifer

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

When residual-time data are plotted linear axes, AQTESOLV fits a straight line
to the data indicating the degree to which the residuals are biased with
respect to time.

Residuals are computed for the current (visual or automatic) curve fit.

208

Residual-Simulated Plot
(View > Residual-Simulated)
Choose Residual-Simulated from the View menu to plot residuals as a function of
simulated displacement.
Example: Pumping Test in Confined Aquifer

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

When residual-simulated data are plotted on linear axes, AQTESOLV fits a

straight line to the data indicating the degree to which the residuals are
biased with respect to simulated displacement.

Residuals are computed for the current (visual or automatic) curve fit.

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Normal Probability Plot

(View > Normal Probability)
Choose Normal Probability from the View menu to plot residuals on normal
probability axes.
Example: Pumping Test in Confined Aquifer

A normal probability plot displays the standard normal deviates of the ranked
residuals (residuals sorted from smallest to largest) as a function of the
residual values.

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

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

After sorting the residual values for all observation wells, AQTESOLV plots the
standard normal deviates using the plot symbol for the first observation well.

Residuals are computed for the current (visual or automatic) curve fit.
210

211

Customizing Plots

Customizing Plots
Select options from the View menu to customize a plot in the active window.

Choose Linear Axes, Log-Linear Axes, Linear-Log Axes or Log Axes to change
the scales of the x and y axes.

Choose Format to customize axes, labels, legends, styles for curve families
and other plot features.

Choose Options to select items to display on plots such as type curve families,
derivative curves and recommended head ranges.

Linear Axes
(View > Linear Axes)
Choose Linear Axes from the View menu or click
with linear x and y axes.

on the toolbar to display a plot

Example: Slug Test

212

Right-click over a plot to select Linear axes.

Log-Linear Axes
(View > Log-Linear Axes)
Choose Log-Linear Axes from the View menu or click
a plot with logarithmic x and linear y axes.

on the toolbar to display

Example: Single-Well Pumping Test (with Derivative)

Example: Slug Test

213

Right-click over a plot to select Log-Linear axes.

Linear-Log Axes
(View > Linear-Log Axes)
Choose Linear-Log Axes from the View menu or click
a plot with linear x and logarithmic y axes.

on the toolbar to display

Example: Slug Test

214

Right-click over a plot to select Linear-Log axes.

Log Axes
(View > Log Axes)
Choose Log Axes from the View menu or click
with logarithmic x and y axes.

on the toolbar to display a plot

Example: Pumping Test (with Derivative)

215

Right-click over a plot to select Log axes.

Format
(View > Format)
Choose Format from the View menu to select options for formatting a plot or
report.
How to Format Plots
o

Graph Tab

216

Properties

Enter values controlling the Border thickness and Tickmark thickness of

the plot.

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

Click Color to change the color used for drawing the axis labels.

Options

Check Upper Left Origin to place the origin of the plot axes in the upper
left corner of the plot (i.e., flip the y axis).

Check Show Graph Paper to display horizontal and vertical lines at the
major tickmarks of the graph.

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

X and Y Axis Tabs

217

Range

Check Auto to use minimum and maximum axis values selected

automatically by the program for your data.

Remove the Auto check to edit minimum and maximum axis values.

Tickmarks

Edit values controlling major and minor tickmark intervals.

Edit the label spacing for labels placed on the major tickmarks.

Labels

Edit Text for the axis label. Choose one of the predefined axis labels or
enter a new label.

Choose a format for appending Units to the axis label.

For example, if the time units in your data set are days, you may label a
time axis as Time (days) or Time in days or Time. If the length units
are meters, you may label a drawdown axis as Drawdown (m) or
Drawdown in m or Drawdown.
Choose Edit>Units to select the units that appear in axis labels.

Legend Tab

218

Text Properties

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

Click Font to change the font used to display the selected text.
Decrease the font size if the legend does not fit on one printed page.

Click Color to change the color used for the selected text.

Printer Options

Choose a Style from the list to format the appearance of printed output.

Click Browse to select a Windows bitmap (.bmp) file containing a

company logo (or other graphic) that you would like to display on printed
output (not all styles include a logo).

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

Family Tab

219

Style

Choose a Style for the optional type curve family.

Thickness

Enter the Thickness of the optional type curve family.

Color

Click Color to change the color of the optional type curve family.

Font

Click Font to change the font used for labeling members of the optional
type curve family.

Theis Curve Tab

220

Style

Choose a Style for the optional Theis curve.

Thickness

Enter the Thickness of the optional Theis curve.

Color

Click Color to change the color of the optional Theis curve.

Fitted Tab

221

Style

Choose a Style for the optional fitted line on residual plots.

Thickness

Enter the Thickness of the optional fitted line.

Color

Click Color to change the color of the optional fitted line.

How to Format Reports

o

Text Tab

222

Text Properties

Click Font to change the font used to display the report text.

Click Color to change the color used for the report text.

Sections

Check items to display in the report.

Header/Footer Tab

Enter text for the headers and footers of a report.

223

Click Apply to make changes immediately.

Click Cancel to undo any changes.

Right-click over a plot or report to select Format.

Double-click over a report or outside the graph area of a plot to open the
Format dialog.

If a plot does not fit on one printed page, decrease the font size in the
Legend tab.

Options
(View > Options)
Choose Options from the View menu to select optional plot items and enter
parameters controlling the display of type curve families, derivatives, validity criteria,
step-test parameters, distance-drawdown data and settings for rendering curves.
o

Plots Tab

224

What To Display

Check options to display on plots (Data, Legend, Type Curve, Curve

Family, Theis Curve, Derivative Curve, Valid Time, Normalized Head and
Recommended Head Range).

You can toggle the Type Curves option from the keyboard by pressing
Ctrl-T.

The Curve Family option only applies to certain solutions having three or
more parameters. Click the Family Tab to set more options for type
curve families.

The Theis Curves option applies to selected solutions. Select this option
to superimpose a Theis reference curve on your plot.
For example, this option displays two bounding Theis curves for the
Neuman (1974) solution for unconfined aquifers. The first curve uses the
values of T and S and the second curve uses T and Sy.

Choose Derivative Curves to superimpose derivative curves on a plot.

When this option is active, you can simultaneously match a solution to
displacement and derivative data using visual curve matching (most
effective using Active Type Curves). Click the Derivative Tab to set more
options for derivative data and curves.

The Valid Time option applies to the Cooper-Jacob (1946) solution for
confined or unconfined aquifers. Selecting this option shows the time after
which the straight-line approximation solution becomes valid on
displacement vs. time and composite plots. Click the Valid Time Tab to
set the critical value of u used to compute the valid time.

The option to display Normalized Head applies to slug test solutions.

The Recommended Head Range option displays the head ranges

recommended by Butler (1998) for matching certain slug test solutions.

Solution Critically Damped When C(D) = 2 calculates and displays the

dimensionless damping factor, C(D), assuming the solution is critically
damped when C(D) = 2. The default value is 1 when this option is not
checked. This feature applies to slug test solutions for high-K aquifers
such as Butler (1998) and Springer-Gelhar (1991).

225

Family Tab

Type Curve Family Attributes

For a type curve family consisting of two curves, select the option to
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 a multiplier greater
than 1.

For a complete set of type curves, choose the option to Show Preset
Family of Curves.

Select Show Custom Family of Curves to display type curves from the
values shown in the list box. Use New and Delete to add or remove curve
values. Click Clear to remove all curves from the list. Reset restores
curve values.

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

Select View>Format to edit formatting options for type curve families.

226

Derivative Tab

Differentiation Method

Choose a method for calculating derivatives from time-displacement data

(differentiation methods include nearest neighbor, Bourdet, Spane and
smoothing).

The nearest neighbor option provides the least amount of smoothing

and works well for displacement data that show ideal response.

The Bourdet, Spane and smoothing methods allow you to "smooth" the
calculation of derivatives with "noisy" data. Enter the smallest
differentiation interval or smoothing factor to discern the derivative
pattern from the data.

The standard method of computing the derivative is d(H)/d(log(t)) for

pumping tests and slug tests where H is the head or displacement and t is
time. For slug tests, you may choose Compute slug test derivative as
d(log(H))/dt to show the deviation of the derivative from the steadystate model of slug-induced flow.

Choose Edit>Wells to edit derivative symbol and curve properties.

227

Valid Time Tab

Validity Criterion for Straight-Line Methods

Set the Critical Value of u used to compute the valid time displayed for
the Cooper-Jacob (1946) solution when you enable Show Valid Time in
the Plots tab.
A conservative critical value of u is 0.01.

Enter the Estimated Value of S (storativity) to compute the valid time

displayed with the Theis (1935) residual drawdown method for recovery
tests.

228

Step Test Tab

Step Test Prediction Time

Set the Step Test Prediction Time used in the well loss prediction
equation.

229

Distance Tab

Time for Distance-Drawdown Plots

Enter the Time used to display distance-drawdown plots.

AQTESOLV automatically interpolates or extrapolates a value of drawdown

when a well does not contain an observation at the time specified for
distance-drawdown analysis.

The Distance tab only appears when the active view is a distancedrawdown plot.

230

Settings Tab

Curve Resolution Levels

Choose a level for the Plotting Interval to set the overall resolution of
the type curve displayed on the plot.
Higher levels plot the type curve at finer intervals, but refresh more
slowly.

Change the resolution of the type curve for variable-rate pumping tests by
selecting a resolution level for Pumping Periods
Higher levels increase the resolution of the type curve within pumping
periods at the expense of the refresh rate.
This option has no effect on the appearance of type curves drawn for
constant-rate pumping tests or slug tests.

The Curve Resolution Levels only affect the appearance (smoothness)

of plotted type curves not the accuracy of the underlying solution methods
(well functions).

Click Apply to make changes immediately.

Click Cancel to undo any changes.

231

Right-click over a plot or report to select Options.

232

Reports

Overview (Reports)
The View menu provides options for viewing data, solutions and estimation results
in several report formats.
Report Options

The report option gives a complete summary of the data set with the solution
and estimation results.

Use the diagnostics report with its summary of residual statistics and other
diagnostics to help assess the fit of a model.

Refer to the error log for a list of errors (if any) detected in the active data
set.

Customizing Reports

Customize the appearance of reports using formatting options.

Diagnostics
(View > Diagnostics)
Choose Diagnostics from the View menu to display a report containing estimation
statistics for parameters (hydraulic properties) and residuals. Inspect the diagnostics
report after performing automatic curve matching.

Parameter statistics include standard errors, confidence intervals and

correlations.

Residual summary statistics include number of residuals, mean, standard

deviation, variance and sum of squares.

Report
(View > Report)
Choose Report from the View menu to display a complete report summarizing the
contents of the AQTESOLV data set and estimation results.
The Report also shows derived properties such as leakance coefficient (K'/b') and
hydraulic conductivity (K') of aquitards.

233

A printout of this report is a convenient summary of your aquifer test analysis

that you can insert in your project report.

Error Log
(View > Error Log)
Choose Error Log from the View menu to display a report identifying errors (if any)
detected in the active data set.

The Error Log is the default view when create a new data set.

Correct errors detected in the test data by choosing options from the Edit
menu.

When the Error Log shows no errors, choose options from the View menu to
display data.

Select this report if the Check Errors message appears on the status bar.

Customizing Reports
(View > Format)
Choose Format from the View menu to customize a report.

Select Format to customize report text, color, headers and footers.

234

Matching Data
Solutions

Overview (Solutions)
After entering data for an aquifer test and performing diagnostics, choose Solution
from the Match menu to select a solution method for curve matching.

Use diagnostic flow plots and derivative analysis to help identify appropriate
solution methods before choosing a solution.

Find solution methods that meet specific criteria with the Solution Expert.

235

Pumping Tests

Overview (Pumping Test Solutions)

AQTESOLV provides the following solutions for pumping tests in confined, leaky,
unconfined and fractured aquifers.
Confined
Confined
Confined
Confined
Confined
Confined
Confined
Confined
Confined
Confined
Confined
Confined
Confined
Confined
Leaky
Leaky
Leaky
Leaky
Leaky
Leaky
Leaky
Leaky
Leaky
Unconfined
Unconfined
Unconfined
Unconfined
Unconfined
Fractured
Fractured
Fractured
Fractured
Fractured
Fractured

Theis (1935)/Hantush (1961)

Theis (1935) residual drawdown/recovery
Theis (1935) step-drawdown test
Cooper-Jacob (1946)
Moench-Prickett (1972) unconfined
conversion
Butler (1988) nonuniform aquifer
Papadopulos-Cooper (1967)
Dougherty-Babu (1984)
Dougherty-Babu (1984) step-drawdown
test
Hantush (1962) wedge-shaped aquifer
Murdoch (1994) trench
Daviau et al. (1985) uniform-flux
horizontal well
Daviau et al. (1985) infinite-conductivity
horizontal well
Barker (1988)
Hantush-Jacob (1955)/Hantush (1964)
without aquitard storage
Hantush-Jacob (1955) step-drawdown
test
Hantush (1960) with aquitard storage
Hantush (1960) early-time solution
Cooley-Case (1973) water-table aquitard
Neuman-Witherspoon (1969) confined
two-aquifer system
Moench (1985) Case 1: constant head
Moench (1985) Case 2: no-flow
Moench (1985) Case 3: both
Theis (1935)
Cooper-Jacob (1946)
Neuman (1974)
Moench (1997)
Tartakovsky-Neuman (2007)
Moench (1984) slab-shaped blocks
Moench (1984) spherical blocks
Barker (1988) slab-shaped blocks
Barker (1988) spherical blocks
Gringarten-Witherspoon (1972) uniformflux vertical fracture
Gringarten et al. (1974) infiniteconductivity vertical fracture
236

Fractured

Gringarten-Ramey (1974) uniform-flux

horizontal fracture

Choose Match>Solution to select a pumping test solution.

Constant-Rate Solutions
All of the pumping test solutions in AQTESOLV let you simulate constant-rate
pumping tests.
Example: Constant-Rate Test in Confined Aquifer

Choose Match>Solution to select a pumping test solution.

237

Variable-Rate Solutions
All of the pumping test solutions in AQTESOLV let you simulate variable pumping
rates using the principle of superposition in time which treats variable discharge as a
sequence of steps with a constant rate in each step. The sequence of steps may
include one or more periods of recovery in which the pumping rate is zero (e.g.,
recovery tests or intermittent pumping).
Example: Variable Discharge History

Choose Match>Solution to select a pumping test solution.

Enter variable rates as a sequence of pumping periods.

238

Recovery Solutions (Pumping Tests)

You may use any of the pumping test solutions in AQTESOLV to analyze data from a
recovery test.
AQTESOLV applies the principle of superposition in time to simulate pumping tests
with recovery.
Example: Recovery Test in Confined Aquifer

Choose Match>Solution to select a pumping test solution.

Use displacement-time, composite, residual drawdown and Agarwal plots to

analyze recovery tests.

Single-Well Solutions
You may use any of the pumping test solutions in AQTESOLV for the analysis of
single-well tests; however, when response data are only available from the pumped
well, the effects of wellbore storage, wellbore skin, and partial penetration are often
important. You can use the Solution Expert to identify pumping test solutions that
include these and other special conditions that may affect your test.
For example, let's suppose that you are analyzing a pumping test in a confined
aquifer with drawdown data from the pumping well. You could choose either the
239

Theis (1935) or Cooper-Jacob (1946) solution to analyze the single-well test data;
however, because these line-source solutions ignore wellbore storage, it may be
difficult to match early-time data. To account for wellbore storage, you could try to
match the Papadopulos-Cooper (1967) solution for fully penetrating wells, or, for
greater generality, the Dougherty-Babu (1984) solution which also includes wellbore
skin for fully or partially penetrating wells.

Wellbore Storage Solutions

The following pumping test solutions account for the wellbore storage effect in
confined, leaky, unconfined and fractured aquifers.
Example: Pumping Test in Confined Aquifer

Confined
Confined
Confined
Confined
Leaky
Unconfined

Papadopulos-Cooper (1967)
Dougherty-Babu (1984)
Dougherty-Babu (1984) step-drawdown
test
Barker (1988)
Moench (1985)
Moench (1997)

240

Fractured
Fractured

Moench (1984)
Barker (1988)

Choose Match>Solution to select a pumping test solution. Check the

Wellbore storage filter to find solutions that include wellbore storage.

Wellbore storage often distorts early-time drawdown behavior in a pumped

well. Use diagnostic flow plots to help identify response data affected by
wellbore storage.

All of the wellbore storage solutions allow you to estimate the value of casing
radius for the pumped well. You may determine the effective casing radius for
the pumped well by either (1) adjusting this parameter or (2) specifying
values for nominal casing radius and downhole equipment radius and letting
AQTESOLV compute the effective casing radius.

Single Fracture Solutions

Flow to a pumping well intersected by a single fracture may exhibit a period of linear
flow at early time. Use diagnostic flow plots to help identify linear and bilinear flow.
The following pumping test solution methods simulate flow to a single fracture.
Vertical fracture
Vertical fracture
Horizontal fracture

Gringarten-Witherspoon (1972) uniform

flux
Gringarten et al. (1974) infinite
conductivity
Gringarten-Ramey (1974) uniform-flux

Choose Match>Solution to select a pumping test solution.

Select Edit>Aquifer Data to edit data for single-fracture solutions.

Double-Porosity Solutions
Double-porosity solutions represent a fractured aquifer by two overlapping media:
fractures and matrix. Flow to a pumping well occurs in fractures while water stored
in matrix blocks contributes flow to the fractures.
Slab and spherical models are commonly used to depict the geometry of fractures
and matrix in double-porosity, fractured aquifers. In the slab model, the aquifer
consists of horizontal slabs of matrix separated by horizontal fractures. In the
spherical geometry, a three-dimensional, orthogonal fracture system breaks the

241

aquifer into cubic blocks of matrix.

The following pumping test solution methods simulate flow to a well in a doubleporosity aquifer. The solutions differ by the geometry of the matrix blocks and
fractures.
Example: Pumping Test in a Fractured Aquifer

Slab-shaped blocks
Spherical blocks
Slab-shaped blocks
Spherical blocks

Moench (1984)
Moench (1984)
Barker (1988)
Barker (1988)

Choose Match>Solution to select a pumping test solution.

Select Edit>Aquifer Data to edit data for double-porosity solutions.

Step-Drawdown Test Solutions

242

A step-drawdown test is a single-well pumping test designed to investigate the

performance of a pumping well under variable discharge rate conditions. In a step
test, the discharge rate in the pumping well is increased from an initially low
constant rate through a sequence of pumping intervals of progressively higher
constant rates. In each step of the test, the drawdown in the pumping well is allowed
to stabilize. Each step is typically of equal duration, lasting from approximately 30
minutes to 2 hours (Kruseman and de Ridder 1990).

Illustration of aquifer loss and well loss components in a pumping well (Kruseman
and de Ridder 1990).

Well Loss Equation

Various researchers have investigated the performance of pumping wells to
determine well loss as a function of discharge rate. Jacob (1947) proposed the
following drawdown equation to account for linear and nonlinear head losses in the
pumping well:

where B is linear (laminar) head-loss coefficient and C is nonlinear (turbulent) wellloss coefficient. The first term in Jacob's drawdown equation represents linear head
loss and consists of aquifer loss (s1) and linear well loss (s2). The second term in the

243

equation is nonlinear well loss (s3).

Linear Well Loss

The linear head-loss coefficient, B, is a function of the effective radius of the well and
time. The effective well radius, rwe, is defined as the radial distance from the center
of the well at which the theoretical drawdown in the aquifer (i.e., aquifer loss) is
equal to the total linear head loss in the well (i.e., total drawdown in the well
neglecting turbulent loss). The linear head-loss coefficient consists of two
components:

where B1 is linear aquifer-loss coefficient and B2 is linear well-loss coefficient. The

linear aquifer-loss coefficient is a function of the nominal radius of the well and time.
The linear well-loss coefficient is assumed independent of time. When B2 > 0, we find
that rwe < rw. When B2 is < 0, rwe > rw.
Ramey (1982) defines the linear well-loss coefficient in terms of a wellbore skin
factor, Sw, as follows:

Assuming nonlinear (turbulent) well loss is negligible, the skin effect is the difference
between the total drawdown in the well and the theoretical drawdown (aquifer loss)
at the well screen. A positive skin (B2 > 0) indicates permeability reduction at the
wellbore (e.g., clogging). Negative skin (B2 < 0) suggests permeability enhancement
(e.g., stimulation).

Nonlinear Well Loss

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

where P is the order of nonlinear well losses. According to Rorabaugh (1953), the
value 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).

Well Efficiency
The efficiency of a pumping well, which expresses the ratio of aquifer loss to total
drawdown in the well, is computed as follows (Kruseman and de Ridder 1990):

When the linear and nonlinear well loss terms are zero, the well efficiency becomes
100%.

244

Solutions for Step Test Analysis

According to Bear (1979), any pumping test solution may be used to compute the
linear aquifer-loss coefficient, B1, in the well loss equation. For example, you can
calculate aquifer loss using the Theis (1935) well function for confined aquifers or the
Hantush-Jacob (1955) well function for leaky confined aquifers.
Choose from the following solutions for analyzing step-drawdown tests in confined
and leaky aquifers.
Example: Step-Drawdown Test in Confined Aquifer

Confined
Confined
Leaky

Theis (1935) step-drawdown test

Dougherty-Babu (1984) step-drawdown
test
Hantush-Jacob (1955) step-drawdown
test

Choose Match>Solution to select a pumping test solution. Check the Stepdrawdown tests filter to find solutions for analyzing a step-drawdown test.

245

Horizontal Well Solutions

AQTESOLV includes the Daviau et al. (1985) method for a pumping test in a uniformflux or infinite-conductivity horizontal well in a confined aquifer.

Choose Match>Solution to select a pumping test solution.

Multiaquifer Solutions
The following pumping test solution methods simulate flow in a multiaquifer system.
Confined Two-Aquifer System

Neuman-Witherspoon (1969)

Choose Match>Solution to select a pumping test solution.

Select Edit>Aquifer Data to edit aquifer and aquitard data.

Bounded Aquifer Solutions

Many of the pumping test solutions in AQTESOLV support aquifer boundaries. When
you enable boundaries, AQTESOLV automatically generates images wells to simulate
a number of configurations for no-flow and constant-head boundaries. Use the
Solution Expert to identify which solutions support bounded aquifers.

To apply the Vandenberg (1977) solution for a leaky strip aquifer, use the
Hantush-Jacob (1955) solution with aquifer boundaries.

Nonuniform Aquifer Solutions

The following pumping test solution methods simulate flow in a nonuniform aquifer.
Confined
Confined

Moench-Prickett (1972) unconfined

conversion
Butler (1988) nonuniform aquifer

Choose Match>Solution to select a pumping test solution.

246

Delayed OW Response Solutions

The following pumping test solutions account for the delayed observation well
response in confined, unconfined and fractured aquifers.
Example: Pumping Test in Unconfined Aquifer

Confined
Unconfined
Fractured

Dougherty-Babu (1984)
Moench (1997)
Moench (1984)

Choose Match>Solution to select a pumping test solution. Check the Delayed

OW response filter to find solutions that include the correction for delayed
response in an observation well.

Delayed observation well response may affect early-time drawdown.

To eliminate the correction for delayed response in an observation well, enter

a small casing radius value (e.g., 1.e-5).

247

Diagnostic Flow Plots

Use diagnostic flow plots (radial flow, linear flow, bilinear flow and spherical flow) to
improve the interpretation of pumping test data.
Use diagnostic flow plots to help identify the following conditions:
o

Wellbore Storage Effects

1. Use a radial flow plot with log-log axes to help identify wellbore storage
effect in the pumped well. Early-time data exhibiting a unit slope on this
plot are indicative of wellbore storage.
2. AQTESOLV includes wellbore storage solutions for pumping tests in
confined, leaky, unconfined and fractured aquifers.

Radial Flow in an Infinite-Acting Aquifer

1. Use a radial flow plot with log-linear axes to help identify radial flow in an
infinite-acting aquifer, i.e., late-time data plotting as a straight line. This
late-time behavior on a semi-log plot is the basis for the Cooper-Jacob
straight-line method of analysis.

Fracture Flow Conditions

1. Use a linear flow plot with log-log axes to help identify linear flow
conditions to a fracture. Early-time data exhibiting a unit slope on this plot
are indicative of linear flow to a single fracture with infinite conductivity or
uniform flux along the fracture.
2. Use a bilinear flow plot with log-log axes to diagnose bilinear flow
conditions to a fracture. Early-time data exhibiting a unit slope on this plot
are indicative of bilinear flow to a single fracture with finite conductivity.
3. AQTESOLV includes single fracture and double porosity solutions for
pumping tests in fractured aquifers.

Spherical Flow Conditions

1. Use a spherical flow plot with log-log axes to help identify spherical flow
conditions. Early-time data exhibiting a unit slope on this plot are
indicative of spherical flow.

248

Confined Aquifers

Theis (1935)/Hantush (1961) Solution for a

Pumping Test in a Confined Aquifer
(Match > Solution)
Theis (1935) derived a solution for unsteady flow to a fully penetrating well in a
confined aquifer. The solution assumes a line source for the pumped well and
therefore neglects wellbore storage.
Hantush (1961a, b) extended the Theis method to correct for partially penetrating
wells. When you choose the Theis solution in AQTESOLV, you may analyze data for
fully or partially penetrating wells.
AQTESOLV uses the principle of superposition in time to simulate variable-rate tests
including recovery with the Theis solution. Use this solution to analyze both pumping
and recovery data from constant- or variable-rate pumping tests.
You can use the Theis (1935) solution for residual drawdown to analyze a recovery
test using a straight-line matching procedure. For a well performance test, you may
choose the Theis (1935) solution for a step-drawdown test.
o

Illustration

Equations

249

where

Q is pumping rate [L3/T]

r is radial distance [L]

s is drawdown [L]

S is storativity [dimensionless]

t is time [T]

T is transmissivity [L2/T]

Hydrogeologists commonly refer to the exponential integral in the drawdown

equation as the Theis well function, abbreviated as w(u). Therefore, we can
write the Theis drawdown equation in compact notation as follows:

Hantush (1961a, b) derived equations for the effects of partial penetration in

a confined aquifer. For a piezometer, the partial penetration correction is as
follows:

For an observation well, the following partial penetration correction applies:

where

b is aquifer thickness [L]

d is depth to top of pumping well screen [L]

d' is depth to top of observation well screen [L]

250

l is depth to bottom of pumping well screen [L]

l' is depth to bottom of observation well screen [L]

Kz/Kr is vertical to horizontal hydraulic conductivity anisotropy

[dimensionless]

w(u,) is the Hantush-Jacob well function for leaky confined aquifers

z is depth to piezometer opening [L]

At large distances, the effect of partial penetration becomes negligible when

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous and of uniform thickness

pumping well is fully or partially penetrating

flow to pumping well is horizontal when pumping well is fully penetrating

aquifer is confined

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

diameter of pumping well is very small so that storage in the well can be
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

constant or variable pumping rate including recovery

multiple pumping wells

multiple observation wells

251

partially penetrating wells

boundaries

Estimated Parameters

T (transmissivity)

S (storativity)

Kz/Kr (hydraulic conductivity anisotropy ratio)

b (saturated thickness)

Partially penetrating wells are required to estimate Kz/Kr and b.

o

Curve Matching Tips

Use the Cooper-Jacob (1946) solution to obtain preliminary estimates of

aquifer properties.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use active type curves for more effective visual matching with variablerate pumping tests.

For partially penetrating wells, select values of Kz/Kr from the Family and
Curve drop-down lists on the toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

References

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.

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

252

Theis (1935) Solution for a Recovery Test in a

Confined Aquifer
(Match > Solution)
Applying the principle of superposition in time, Theis (1935) proposed a straight-line
solution for determining transmissivity and storativity from residual drawdown (i.e.,
the drawdown in a well after pumping stops) data collected during the recovery
phase of a pumping test. The solution assumes a line source for the pumped well and
therefore neglects wellbore storage.
If your observation data contain both pumping and recovery measurements, you
may use the Theis recovery method to analyze only the recovery data recorded after
the cessation of pumping.
o

Illustration

Equations
Theis (1935) proposed the following equation for analyzing recovery data:

where

Q is pumping rate [L3/T]

s' is residual drawdown [L]

253

S is storativity during pumping [dimensionless]

S' is storativity during recovery [dimensionless]

t is time since pumping began [T]

t' is time since pumping stopped [T]

T is transmissivity[L2/T]

By plotting s' as a function of log(t/t') on semi-logarithmic axes, one can

determine values of T and S/S' by drawing a straight line through the data.
Without the influence of boundary effects, the value of S/S' determined
from the intercept of the straight line with the log(t/t') axis should be close
to unity. A value of S/S' > 1.0 indicates the influence of recharge during the
test. Conversely, a value of S/S' < 1.0 suggests the presence of a barrier or
no-flow boundary.
o

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous, isotropic and of uniform thickness

pumping well is fully penetrating

flow to pumping well is horizontal

aquifer is confined

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

diameter of pumping well is very small so that storage in the well can be
neglected

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

Data Requirements

pumping and observation well locations

pumping rate(s)

observation well measurements (time and displacement)

Solution Options

constant or variable pumping rates

Estimated Parameters

T (transmissivity)

S/S' (ratio of storativity during pumping to storativity during recovery)

254

Curve Matching Tips

Choose Match>Visual to perform visual curve matching using the

procedure for straight-line solutions.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

References

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

Theis (1935) Solution for a Step-Drawdown

Test in a Confined Aquifer
(Match > Solution)
We modify the Theis (1935) solution for unsteady flow to a well in a confined aquifer
to simulate linear and nonlinear well losses using a general procedure for stepdrawdown tests.
o

Illustration

255

Equations
The Theis (1935) solution for a fully penetrating pumping well in a confined
aquifer, modified to include linear and nonlinear well losses in a stepdrawdown test, is expressed as follows:

where

CQP is nonlinear well loss [L]

Q is pumping rate [L3/T]

r is radial distance [L]

sw is drawdown in the pumped well [L]

S is storativity [dimensionless]

Sw is wellbore skin factor [dimensionless]

t is time [T]

T is transmissivity [L2/T]

AQTESOLV also lets you simulate partially penetrating wells with this solution.
The effective well radius employed in this solution to incorporate wellbore skin
(linear well loss) leads to correlation in the equations between S
(storativity) and Sw (wellbore skin factor). Therefore, you should estimate
either S or Sw for a single-well test.
o

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous and of uniform thickness

pumping well is fully or partially penetrating

flow to pumping well is horizontal when pumping well is fully penetrating

256

aquifer is confined

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

diameter of pumping well is very small so that storage in the well can be
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 rate including recovery

multiple pumping wells

multiple observation wells

partially penetrating wells

Estimated Parameters

T (transmissivity)

S (storativity)

Sw (wellbore skin factor)

C (nonlinear well loss coefficient)

P (nonlinear well loss exponent)

Curve Matching Tips

Use the Cooper-Jacob (1946) solution to obtain preliminary estimates of

aquifer properties.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use active type curves for more effective visual matching with variablerate pumping tests.

257

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

Due to correlation in the equations between S (storativity) and Sw

(wellbore skin factor), estimate either S or Sw for a single-well test.

References

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.

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

Cooper-Jacob (1946) Solution for a Pumping

Test in a Confined Aquifer
(Match > Solution)
Cooper and Jacob (1946) developed a method of analyzing pumping tests based on a
straight-line approximation of the Theis (1935) equation for unsteady flow to a fully
penetrating well in a confined aquifer. The solution assumes a line source for the
pumped well and therefore neglects wellbore storage.
Using the principle of superposition in time, the Cooper-Jacob solution can simulate
variable-rate tests. The Cooper-Jacob solution as implemented in AQTESOLV
encompasses the method of Birsoy and Summers (1980) for variable pumping.
If your observation data contain recovery measurements, you may use the
Cooper-Jacob method to analyze drawdown data up to the first recovery period. You
also may use this solution to analyze data from the first recovery period on an
Agarwal plot. For intermittent pumping (i.e., where the pump cycles on and off),
choose the Theis (1935) solution (or any other pumping test solution in AQTESOLV)
to analyze the entire set of observations (i.e., all drawdown and recovery data).
The Cooper-Jacob solution is not applicable to more than one pumping well;
therefore, if your data set contains multiple pumping wells, the Cooper-Jacob
solution uses only the first pumping well in the analysis of observation data.

258

Illustration

Equations
For large values of time, Cooper and Jacob (1946) proposed the following
equation for displacement in a confined aquifer in response to pumping:

where

Q is pumping rate [L3/T]

r is radial distance [L]

t is time [T]

s is drawdown [L]

S is storativity [dimensionless]

T is transmissivity [L2/T]

259

The Cooper-Jacob solution derives from the truncation of an infinite series

expression for the Theis well function. The following expression computes
the value of the Theis well function, abbreviated as w(u):

For small values of u (e.g., u 0.01), the Cooper-Jacob solution approximates

the Theis well function using only the first two terms of the expression for
w(u):

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

After rearranging and rewriting as decimal logarithms, the drawdown

equation reduces to the following relationship:

By drawing a straight line through the data on a plot of s versus log t, we can
determine T and S from the following equations:

where s is change in drawdown per log cycle time and t0 is the intercept of
the fitted line on the time axis.
o

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous, isotropic and of uniform thickness

pumping well is fully penetrating

flow to pumping well is horizontal

aquifer is confined

flow is unsteady

260

water is released instantaneously from storage with decline of hydraulic

head

diameter of pumping well is very small so that storage in the well can be
neglected

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

Data Requirements

pumping and observation well locations

pumping rate(s)

observation well measurements (time and displacement)

Solution Options

constant or variable pumping rates

multiple observation wells

Estimated Parameters

T (transmissivity)

S (storativity)

Curve Matching Tips

Choose Match>Visual to perform visual curve matching using the

procedure for straight-line solutions.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Choose View>Options to display the critical value of u on the plot. Change

the critical u value in the Valid Time tab.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

Use Agarwal plots to analyze recovery data.

You may use the Cooper-Jacob solution to analyze drawdown data from
the start of the test up to the first recovery period (a recovery period is
any period with a rate equals zero).

If your data set contains more than one recovery period, you may use the
Cooper-Jacob solution to analyze recovery data in the first recovery period
on an Agarwal plot.

If your data set contains more than one pumping well, the Cooper-Jacob
solution uses the first pumping well in the well data to analyze test data.

261

References

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

Birsoy, Y.K. and W.K. Summers, 1980. Determination of aquifer

parameters from step tests and intermittent pumping, Ground Water, vol.
18, no. 2, pp. 137-146.

Moench-Prickett (1972) Solution for a Pumping

Test in a Confined/Unconfined Aquifer
(Match > Solution)
Moench and Prickett (1972) derived a solution for unsteady flow to a fully
penetrating well in a confined aquifer undergoing conversion to water-table
conditions. The solution assumes a line source for the pumped well and therefore
neglects wellbore storage.
o

Illustration

262

Equations
Moench and Prickett (1972) derived an analytical solution for unsteady flow to
a fully penetrating well in a confined aquifer undergoing conversion to
water-table conditions.
when r < R,

when r > R,

when r = R, h = b

where

b is aquifer thickness [L]

h1 is the elevation of the water table when r < R [L]

263

h2 is the elevation of the potentiometric surface when r > R [L]

H is the elevation of the initial potentiometric surface above the base of

the aquifer [L]

Q is pumping rate [L3/T]

r is radial distance [L]

R is the radial distance to the point of conversion [L]

S is storativity in the confined zone when r > R [dimensionless]

Sy is the storativity in the unconfined zone when r < R [dimensionless]

t is time [T]

T is transmissivity [L2/T]

Drawdown, s, is computed from the above equations as follows:

s1 = H - h1 (r < R)
s2 = H - h2 (r > R)
sR = H - b (r = R)
When is greater than about 3, which implies H - b is small, the curve
generated by the Moench-Prickett solution is essentially the same as the
Theis solution using T and Sy. On the other hand when H - b is large and
is small, the Moench-Prickett solution is virtually identical to the Theis
solution using T and S.
o

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous, isotropic and of uniform thickness

pumping well is fully penetrating

pumping rate is constant

flow to pumping well is horizontal

aquifer is confined/unconfined

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

diameter of pumping well is very small so that storage in the well can be
neglected

264

Data Requirements

pumping and observation well locations

pumping rate

observation well measurements (time and displacement)

Solution Options

constant pumping rate

multiple observation wells

Estimated Parameters

T (transmissivity)

S (storativity)

Sy (specific yield)

H - b (initial head above top of aquifer)

Curve Matching Tips

Use the Cooper-Jacob (1946) solution to obtain preliminary estimates of

aquifer properties.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use active type curves for more effective visual matching.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

References

Moench, A.F. and T.A. Prickett, 1972. Radial flow in an infinite aquifer
undergoing conversion from artesian to water-table conditions, Water
Resources Research, vol. 8, no. 2, pp. 494-499.

Butler (1988) Solution for a Pumping Test in a

Confined Aquifer
(Match > Solution)
Butler (1988) derived a solution for unsteady flow to a fully penetrating well in a
heterogeneous, isotropic confined aquifer. The solution assumes the pumping well is

265

located at the center of a disk of radius R embedded within an infinite matrix.

Hydraulic properties of the disk and matrix are assumed uniform, but may differ
between the two zones. The solution assumes a line source for the pumped well and
therefore neglects wellbore storage.
The Butler solution can simulate variable-rate tests including recovery using the
principle of superposition in time. Use this solution to analyze both pumping and
recovery data from constant- or variable-rate pumping tests.
o

Illustration
Cross Section

Plan View
(disk of radius R embedded in infinite matrix)

266

Equations
Butler (1988) derived a solution for unsteady flow to a fully penetrating well
in a heterogeneous, isotropic confined aquifer. The solution assumes the
pumping well is located at the center of a disk of radius R embedded within
an infinite matrix. The Laplace transform solution is as follows:

where

Ii is modified Bessel function of first kind, order i

267

Ki is modified Bessel function of second kind, order i

p is Laplace transform variable

Q is pumping rate [L3/T]

r is radial distance [L]

R is radial distance to disk-matrix interface [L]

s1 is drawdown in the disk [L]

s2 is drawdown in the matrix [L]

S1 is storativity in the disk [dimensionless]

S2 is storativity in the matrix [dimensionless]

t is time [T]

T1 is transmissivity in the disk [L2/T]

T2 is transmissivity in the matrix [L2/T]

Assumptions

aquifer has infinite areal extent

aquifer is heterogeneous with a disk embedded in a matrix

pumping well is fully penetrating

flow to pumping well is horizontal

aquifer is confined

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

diameter of pumping well is very small so that storage in the well can be
neglected

Data Requirements

pumping and observation well locations

pumping rate(s)

observation well measurements (time and displacement)

Solution Options

constant or variable pumping rate including recovery

multiple observation wells

268

Estimated Parameters

T1 (transmissivity in disk)

S2 (storativity in disk)

T2 (transmissivity in matrix)

S2 (storativity in matrix)

R (radial distance to disk-matrix interface)

Curve Matching Tips

Use the Cooper-Jacob (1946) solution to obtain preliminary estimates of

aquifer properties.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use active type curves for more effective visual matching with variablerate pumping tests.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

References

Butler, J.J., Jr., 1988. Pumping tests in nonuniform aquifersthe radially

symmetric case, Journal of Hydrology, vol. 101, pp. 15-30.

Papadopulos-Cooper (1967) Solution for a

Pumping Test in a Confined Aquifer
(Match > Solution)
Papadopulos and Cooper (1967) derived a solution for unsteady flow to a fully
penetrating, finite-diameter well with wellbore storage in a homogeneous, isotropic
confined aquifer.
AQTESOLV uses the principle of superposition in time to simulate variable-rate tests
including recovery with the Papadopulos-Cooper solution. Use this solution to analyze
both pumping and recovery data from constant- or variable-rate pumping tests.
Wellbore storage has a distinct signature in the early-time response of a pumped
well. Use the radial flow and derivative-time plots to detect the wellbore storage
effect.

269

Illustration

Equations
Papadopulos and Cooper (1967) derived a solution for a finite-diameter
pumping well with wellbore storage in a confined aquifer as follows:

270

where

Ji is Bessel function of first kind, order i

Q is pumping rate [L3/T]

r is radial distance [L]

rc is casing radius [L]

rw is well radius [L]

s is drawdown [L]

S is storativity [dimensionless]

t is time [T]

T is transmissivity [L2/T]

Yi is Bessel function of second kind, order i

If you enter a radius for downhole equipment, AQTESOLV uses the effective
casing radius instead of the nominal casing radius in the equations for this
solution.
o

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous, isotropic and of uniform thickness

pumping well is fully penetrating

flow to pumping well is horizontal

aquifer is confined

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

Data Requirements

pumping and observation well locations

pumping rate(s)

271

observation well measurements (time and displacement)

casing radius and wellbore radius for pumping well(s)

downhole equipment radius (optional)

Solution Options

constant or variable pumping rate including recovery

multiple pumping wells

multiple observation wells

boundaries

Estimated Parameters

T (transmissivity)

S (storativity)

r(w) (well radius)

r(c) (nominal casing radius)

Curve Matching Tips

Use radial flow plots to help diagnose wellbore storage.

Match the Cooper-Jacob (1946) solution to late-time data to obtain

preliminary estimates of aquifer properties.

Match early-time data affected by wellbore storage by adjusting r(c) with

parameter tweaking.

If you estimate r(c) for the test well, the estimated value replaces the
nominal casing radius and AQTESOLV still performs the correction for
downhole equipment.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use active type curves for more effective visual matching with variablerate pumping tests.

Select values of S, r(w) and r(c) from the Family and Curve drop-down
lists on the toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

272

References

Papadopulos, I.S. and H.H. Cooper, 1967. Drawdown in a well of large

diameter, Water Resources Research, vol. 3, no. 1, pp. 241-244.

Dougherty-Babu (1984) Solution for a Pumping

Test in a Confined Aquifer
(Match > Solution)
Dougherty and Babu (1984) derived an analytical solution for unsteady flow to a fully
or partially penetrating, finite-diameter well with wellbore storage and wellbore skin
in a homogeneous, isotropic confined aquifer. Moench (1988) extended the method
to include anisotropy. The Dougherty-Babu solution also includes delayed response in
an observation well based on the work of Moench (1997).
AQTESOLV uses the principle of superposition in time to simulate variable-rate tests
including recovery with the Dougherty-Babu solution. Use this solution to analyze
both pumping and recovery data from constant- or variable-rate pumping tests.
Wellbore storage has a distinct signature in the early-time response of a pumped
well. Use the radial flow and derivative-time plots to detect the wellbore storage
effect.
o

Illustration

Equations
Dougherty and Babu (1984) derived an analytical solution for predicting
273

drawdown in response to pumping in a confined aquifer assuming partially

penetrating wells, wellbore storage and wellbore skin. The following
equations include a modification by Moench (1988) to include anisotropy.
The Laplace transform solution for dimensionless drawdown in the pumped
well is as follows:

The following equation is the Laplace transform solution for dimensionless

drawdown in a piezometer:

The equation for dimensionless drawdown in an observation well is:

274

where

b is aquifer thickness [L]

d is distance from water table to top of pumping well screen [L]

dD is d/b

K, Kr is radial hydraulic conductivity [L/T]

Kz is vertical hydraulic conductivity [L/T]

Ki is modified Bessel function of second kind, order i

l is distance from water table to bottom of pumping well screen [L]

lD is l/b

p is the Laplace transform variable

Q is pumping rate [L3/T]

r is radial distance [L]

rc is casing radius [L]

rw is well radius [L]

Ss is specific storage [1/L]

Sw is wellbore skin factor [dimensionless]

t is time [T]

z is elevation of piezometer above base of aquifer [L]

zD is z/b

z1 is elevation of bottom of observation well screen above base of aquifer

[L]

z1D is z1/b

z2 is elevation of top of observation well screen above base of aquifer [L]

275

z2D is z2/b

In the Laplace transform solution, Sw is limited to positive values; however,

using the effective well radius concept, we also may simulate a negative
skin (Hurst, Clark and Brauer 1969).
If you enter a radius for downhole equipment, AQTESOLV uses the effective
casing radius instead of the nominal casing radius in the equations for this
solution.
Refer to the Moench (1997) solution for the equations relating to delayed
response in an observation well.
o

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous and of uniform thickness

aquifer potentiometric surface is initially horizontal

pumping and observation wells are fully or partially penetrating

flow is unsteady

aquifer is confined

water is released instantaneously from storage with decline of hydraulic

head

Data Requirements

pumping and observation well locations

pumping rate(s)

observation well measurements (time and displacement)

casing radius and wellbore radius for pumping well(s)

downhole equipment radius (optional)

partial penetration depths

saturated thickness

hydraulic conductivity anisotropy ratio

Solution Options

constant or variable pumping rate including recovery

multiple pumping wells

multiple observation wells

partially penetrating wells

276

boundaries

Estimated Parameters

T (transmissivity)

S (storativity)

Kz/Kr (hydraulic conductivity anisotropy ratio)

Sw (dimensionless wellbore skin factor)

r(w) (well radius)

r(c) (nominal casing radius)

Curve Matching Tips

Use radial flow plots to help diagnose wellbore storage.

Match the Cooper-Jacob (1946) solution to late-time data to obtain

preliminary estimates of aquifer properties.

Match early-time data affected by wellbore storage by adjusting r(c) with

parameter tweaking.

If you estimate r(c) for the test well, the estimated value replaces the
nominal casing radius and AQTESOLV still performs the correction for
downhole equipment.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use active type curves for more effective visual matching with variablerate pumping tests.

Select values of Kz/Kr from the Family and Curve drop-down lists on the
toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

References

Dougherty, D.E and D.K. Babu, 1984. Flow to a partially penetrating well
in a double-porosity reservoir, Water Resources Research, vol. 20, no. 8,
pp. 1116-1122.

Moench, A.F., 1988. The response of partially penetrating wells to

pumpage from double-porosity aquifers, Proceedings of the International
Conference on Fluid Flow in Fractured Rocks, Atlanta, GA, May 16-18,
1988.

277

Dougherty-Babu (1984) Solution for a StepDrawdown Test in a Confined Aquifer

(Match > Solution)
We modify the Dougherty-Babu (1984) solution for unsteady flow to a well in a
confined aquifer to simulate linear and nonlinear well losses using a general
procedure for step-drawdown tests.
o

Illustration

Equations
Dougherty and Babu (1984) derived an analytical solution for predicting
drawdown in response to pumping in a confined aquifer assuming partially
penetrating wells, wellbore storage and wellbore skin.
For a step-drawdown test, we modify the equations for drawdown in the
pumped well in the Dougherty-Babu (1984) solution by adding a term for
nonlinear well loss:
CQP
where

C is nonlinear well loss coefficient [T2/L5]

P is nonlinear well exponent [-]

278

Q is pumping rate [L3/T]

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous and of uniform thickness

aquifer potentiometric surface is initially horizontal

pumping and observation wells are fully or partially penetrating

flow is unsteady

aquifer is confined

water is released instantaneously from storage with decline of hydraulic

head

Data Requirements

pumping and observation well locations

pumping rate(s)

observation well measurements (time and displacement)

casing radius and wellbore radius for pumping well(s)

downhole equipment radius (optional)

partial penetration depths

saturated thickness

hydraulic conductivity anisotropy ratio

Solution Options

constant or variable pumping rate including recovery

multiple pumping wells

multiple observation wells

partially penetrating wells

boundaries

Estimated Parameters

T (transmissivity)

S (storativity)

Kz/Kr (hydraulic conductivity anisotropy ratio)

Sw (dimensionless wellbore skin factor)

279

r(w) (well radius)

r(c) (nominal casing radius)

C (nonlinear well loss coefficient)

P (nonlinear well loss exponent)

Curve Matching Tips

Use radial flow plots to help diagnose wellbore storage.

Match the Cooper-Jacob (1946) solution to late-time data to obtain

preliminary estimates of aquifer properties.

Match early-time data affected by wellbore storage by adjusting r(c) with

parameter tweaking.

If you estimate r(c) for the test well, the estimated value replaces the
nominal casing radius and AQTESOLV still performs the correction for
downhole equipment.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use active type curves for more effective visual matching with variablerate pumping tests.

Select values of Kz/Kr from the Family and Curve drop-down lists on the
toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

References

Dougherty, D.E and D.K. Babu, 1984. Flow to a partially penetrating well
in a double-porosity reservoir, Water Resources Research, vol. 20, no. 8,
pp. 1116-1122.

Moench, A.F., 1988. The response of partially penetrating wells to

pumpage from double-porosity aquifers, Proceedings of the International
Conference on Fluid Flow in Fractured Rocks, Atlanta, GA, May 16-18,
1988.

Bear, J., 1979. Hydraulics of Groundwater, McGraw-Hill, New York, 569p.

280

Hantush (1962) Solution for a Pumping Test in

a Wedge-Shaped Confined Aquifer
(Match > Solution)
Hantush (1962) derived a solution for unsteady flow to a fully penetrating well in a
wedge-shaped confined aquifer. The solution assumes a line source for the pumped
well and therefore neglects wellbore storage.
AQTESOLV uses the principle of superposition in time to simulate variable-rate tests
including recovery with the Hantush wedge aquifer solution. Use this solution to
analyze both pumping and recovery data from constant- or variable-rate pumping
tests.
o

Illustration

Equations
Hantush (1962) derived an equation which predicts drawdown in a wedgeshaped confined aquifer in response to pumping:

281

where

b is aquifer thickness [L]

Q is pumping rate [L3/T]

r is radial distance [L]

s is drawdown [L]

S is storativity [dimensionless]

t is time [T]

T is transmissivity [T2/T]

x is coordinate direction [L]

x0 is x-coordinate of pumped well [L]

Ordinarily, the slope on the base of the confined aquifer varies exponentially
in the x direction and is constant in the y direction. The slope orientation
angle measures the orientation of the slope in relation to the x-coordinate
axis and is measured counterclockwise from the positive x-coordinate axis
to the vector oriented in the updip direction of the slope. The parameter a is
a constant defining the variation in thickness of the wedge-shaped aquifer.
The solution assumes that the change in aquifer thickness, b, as a function of
distance meets the following criterion:

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

Hydrogeologists commonly refer to the integral in the drawdown equation as

the Hantush well function.

282

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous, isotropic and of uniform thickness

pumping well is fully penetrating

flow to pumping well is horizontal

aquifer is leaky confined

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

diameter of pumping well is very small so that storage in the well can be
neglected

the thickness of the aquifer varies exponentially in the direction of flow

the rate of change in aquifer thickness in the direction of flow does not
exceed 0.20

the influence of pumping does not extend beyond the section of the
aquifer at which the tangents of the maximum angles of dip of the
confining beds are greater than 0.20

Data Requirements

pumping and observation well locations

pumping rate(s)

observation well measurements (time and displacement)

Solution Options

constant or variable pumping rate including recovery

multiple observation wells

Estimated Parameters

T (transmissivity)

S (storativity)

r/a (leakage parameter)

Kz/Kr (hydraulic conductivity anisotropy ratio)

b (saturated thickness)

283

Curve Matching Tips

Use the Cooper-Jacob (1946) solution to obtain preliminary estimates of

aquifer properties.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use active type curves for more effective visual matching with variablerate pumping tests.

For partially penetrating wells, select values of r/a from the Family and
Curve drop-down lists on the toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

References

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. 15271534.

Murdoch (1994) Solution for a Pumping Test in

a Confined Aquifer
(Match > Solution)
Murdoch (1994) presented an analytical solution for unsteady flow to an interceptor
trench based on the Gringarten and Witherspoon (1972) solution for flow to a
uniform-flux plane vertical fracture in an anisotropic confined aquifer. The trench is
represented by a fully penetrating vertical plane source oriented parallel to the x
axis. In the uniform-flux formulation of this solution, drawdown is variable and flux is
uniformly distributed along the length of the trench.
AQTESOLV uses the principle of superposition in time to simulate variable-rate tests
including recovery with the Murdoch solution. Use this solution to analyze both
pumping and recovery data from constant- or variable-rate pumping tests.
The early-time response of a pumped well intersecting an interceptor trench has a
distinct signature that you can diagnose with a linear flow plot.

284

Illustration

Equations
In the Gringarten-Witherspon (1972) solution for a vertical fracture in a
confined aquifer, the Murdoch (1994) solution for an interceptor trench
replaces the length of the fracture (Lf) with the length of the trench (Lt).

Assumptions

aquifer has infinite areal extent

aquifer has uniform thickness

aquifer potentiometric surface is initially horizontal

interceptor trench and observation wells are fully penetrating

confined aquifer represented by anisotropic system with a single

interceptor trench

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

Data Requirements

interceptor trench and observation well locations

pumping rate(s)

observation well measurements (time and displacement)

285

saturated thickness

length of trench

Solution Options

constant or variable pumping rate including recovery

multiple pumping wells

multiple observation wells

boundaries

Estimated Parameters

Kx (hydraulic conductivity in x direction)

Ss (specific storage)

Ky/Kx (hydraulic conductivity anisotropy ratio)

Lt (length of trench)

Curve Matching Tips

Use linear flow plots to help diagnose linear flow.

Use the Cooper-Jacob (1946) solution to obtain preliminary estimates of

aquifer properties.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use active type curves for more effective visual matching with variablerate pumping tests.

Select values of Ky/Kx from the Family and Curve drop-down lists on the
toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

References

Murdoch, L.C., 1994. Transient analyses of an interceptor trench, Water

Resources Research, vol. 30, no. 11, pp. 3023-3031.

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. 19.

286

Daviau et al. (1985) Solution for a Pumping

Test in a Confined Aquifer
(Match > Solution)
In the petroleum industry literature, Daviau et al. (1985) and Clonts and Ramey
(1986) appear to have developed independently an analytical solution for a uniformflux or infinite-conductivity horizontal well in an anisotropic confined aquifer. The
horizontal well is represented in the solution by a line source oriented parallel to the
x axis.
AQTESOLV uses the principle of superposition in time to simulate variable-rate tests
including recovery with the Daviau et al. solution. Use this solution to analyze both
pumping and recovery data from constant- or variable-rate pumping tests.
When you choose a solution, AQTESOLV provides two options for the Daviau et al.
solution: uniform-flux and infinite-conductivity horizontal wells.
o

Illustration

Equations
The following equation by Daviau et al. (1985) and Clonts and Ramey (1986)
predicts drawdown in a point (piezometer) in a confined aquifer with a
uniform-flux horizontal well:

287

where

b is aquifer thickness [L]

Kr is radial hydraulic conductivity [L/T]

Kz is vertical hydraulic conductivity [L/T]

L is length of the well [L]

Q is pumping rate [L3/T]

rw is well radius [L]

s is drawdown [L]

S is storativity [dimensionless]

t is time [T]

288

T is transmissivity [L2/T]

x, y and z are coordinate distances [L]

Drawdown in an observation well may be found by integrating the preceding

equations with respect to z.
Following the work of Daviau et al. (1985), Clonts and Ramey (1986) and
Ozkan et al. (1989), the wellbore pressure is computed with yD = rwD.
Clonts and Ramey (1986) and Ozkan et al. (1989), citing the work of
Gringarten, Ramey and Raghavan (1974), modify the uniform-flux solution
to predict the drawdown in an infinite-conductivity fracture by simply setting
xD = 0.732 to compute head in the horizontal well.
o

Assumptions

aquifer has infinite areal extent

aquifer has uniform thickness

aquifer potentiometric surface is initially horizontal

pumping well is horizontal

observation wells are fully or partially penetrating

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

diameter of pumping well is very small so that storage in the well can be
neglected

Data Requirements

pumping and observation well locations

pumping rate(s)

observation well measurements (time and displacement)

saturated thickness

length of horizontal well

Solution Options

constant or variable pumping rate including recovery

multiple pumping wells

multiple observation wells

289

Estimated Parameters

T (transmissivity)

S (storativity)

Kz/Kr (hydraulic conductivity anisotropy ratio)

Curve Matching Tips

Use the Cooper-Jacob (1946) solution to obtain preliminary estimates of

aquifer properties.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use active type curves for more effective visual matching with variablerate pumping tests.

Select values of Kz/Kr from the Family and Curve drop-down lists on the
toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

References

Daviau, F., Mouronval, G., Bourdarot, G. and P. Curutchet, 1985. Pressure

analysis for horizontal wells, SPE Paper 14251, presented at the 60th
Annual Technical Conference and Exhibition in Las Vegas, NV, Sept. 2225, 1985.

Clonts, M.D. and H.J. Ramey, Jr., 1986. Pressure transient analysis for
well with horizontal drainholes, SPE Paper 15116, presented at the 56th
California Regional Meeting, Oakland, CA, April 2-4, 1986.

Ozkan, E., Raghavan, R. and S.D. Joshi, 1989. Horizontal-well pressure

analysis, SPE Formation Evaluation (December 1989), pp. 567-575.

Barker (1988) Solution for a Pumping Test in a

Confined Aquifer
(Match > Solution)
Barker (1988) derived a generalized radial flow model for unsteady, n-dimensional
flow to a fully penetrating source in an isotropic, single- or double-porosity fractured
aquifer. The single-porosity form of the model describes flow in a confined aquifer.
For details, refer to the Barker (1998) solution for a fractured aquifer.

290

291

Leaky Aquifers

Hantush-Jacob (1955)/Hantush (1964)

Solution for a Pumping Test in a Leaky Aquifer
(Match > Solution)
Hantush and Jacob (1955) derived a solution for unsteady flow to a fully penetrating
well in a homogeneous, isotropic leaky confined aquifer. The solution assumes a line
source for the pumped well and therefore neglects wellbore storage.
Hantush (1964) extended the method to correct for partially penetrating wells and
anisotropy. When you choose the Hantush-Jacob solution in AQTESOLV, you may
analyze data for fully or partially penetrating wells.
The Hantush-Jacob solution can simulate variable-rate tests including recovery
through the application of the principle of superposition in time. Use this solution to
analyze both pumping and recovery data from constant- or variable-rate pumping
tests.
Walton (1962) developed a manual curve-fitting procedure based on the HantushJacob solution. To apply Walton's method in AQTESOLV, choose the Hantush-Jacob
solution.
For a well performance test, you may choose the Hantush-Jacob (1955) solution for
a step-drawdown test in a leaky confined aquifer.
Vandenberg (1977) presented a solution for evaluating drawdown a leaky confined
aquifer bounded by two parallel no-flow boundaries (i.e., a leaky strip aquifer). In
AQTESOLV, you may use the Hantush-Jacob solution in conjunction with aquifer
boundaries to evaluate the same leaky strip aquifer problem as the Vandenberg
method. Unlike Vandenberg's method, however, you may use AQTESOLV to evaluate
partially penetrating wells and observation wells may be located at any radial
distance from the pumped well.

292

Illustration

Equations
Hantush and Jacob (1955) derived an analytical solution for predicting waterlevel changes in response to pumping in a homogeneous, isotropic leaky
confined aquifer assuming steady flow (no storage) in the aquitard(s):

where

b' is aquitard thickness [L]

293

K' is vertical hydraulic conductivity in the aquitard [L/T]

Q is pumping rate [L3/T]

r is radial distance [L]

s is drawdown [L]

S is storativity [dimensionless]

t is time [T]

T is transmissivity [L2/T]

Hydrogeologists commonly refer to the integral expression in the drawdown

equation 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 as follows:

Hantush (1964) derived equations for the effects of partial penetration and
anisotropy in a leaky aquifer. The partial penetration correction for a
piezometer is as follows:

For an observation well, the following partial penetration correction applies:

where

b is aquifer thickness [L]

d is depth to top of pumping well screen [L]

d' is depth to top of observation well screen [L]

l is depth to bottom of pumping well screen [L]

l' is depth to bottom of observation well screen [L]

Kr is radial hydraulic conductivity [L/T]

Kz is vertical hydraulic conductivity [L/T]

z is depth to piezometer opening [L]

294

At large distances, the effect of partial penetration becomes negligible when

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous and of uniform thickness

pumping well is fully or partially penetrating

flow to pumping well is horizontal when pumping well is fully penetrating

aquifer is leaky confined

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

diameter of pumping well is very small so that storage in the well can be
neglected

confining bed(s) has infinite areal extent, uniform vertical hydraulic

conductivity and uniform thickness

confining bed(s) is overlain or underlain by an infinite constant-head plane

source

flow is vertical in the aquitard(s)

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

constant or variable pumping rate including recovery

multiple pumping wells

multiple observation wells

partially penetrating wells

boundaries
295

Estimated Parameters

T (transmissivity)

S (storativity)

r/B (leakage parameter)

Kz/Kr (hydraulic conductivity anisotropy ratio)

b (saturated thickness)

Partially penetrating wells are required to estimate Kz/Kr and b.

The Report also shows aquitard properties (K'/b' and K') computed from the
leakage parameter (r/B).
o

Curve Matching Tips

Use the Cooper-Jacob (1946) solution to obtain preliminary estimates of

aquifer properties.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use active type curves for more effective visual matching with variablerate pumping tests.

For partially penetrating wells, select values of r/B and Kz/Kr from the
Family and Curve drop-down lists on the toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

References

Hantush, M.S. and C.E. Jacob, 1955. Non-steady radial flow in an infinite
leaky 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. of

the Hyd. Div., Proc. of the Am. Soc. of Civil Eng., vol. 87, no. HY5, pp.
171-194.

Hantush, M.S., 1964. Hydraulics of wells, in: Advances in Hydroscience,

V.T. Chow (editor), Academic Press, New York, pp. 281-442.

296

Hantush-Jacob (1955) Solution for a StepDrawdown Test in a Leaky Aquifer

(Match > Solution)
We modify the Hantush-Jacob (1955) solution for unsteady flow to a well in a leaky
confined aquifer to simulate linear and nonlinear well losses using a general
procedure for step-drawdown tests.
o

Illustration

Equations
The Hantush-Jacob (1955) solution for a fully penetrating pumping well in a
leaky confined aquifer, modified to include linear and nonlinear well losses
in a step-drawdown test, is expressed as follows:

297

where

CQP is nonlinear well loss

Q is pumping rate [L3/T]

r is radial distance [L]

r/B is leakage factor [dimensionless]

sw is drawdown in the pumped well [L]

S is storativity [dimensionless]

Sw is wellbore skin factor [dimensionless]

T is transmissivity [T2/T]

t is time [T]

AQTESOLV also lets you simulate partially penetrating wells with this solution.
The effective well radius employed in this solution to incorporate wellbore skin
(linear well loss) leads to correlation in the equations between S
(storativity) and Sw (wellbore skin factor). Therefore, you should estimate
either S or Sw for a single-well test.
o

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous and of uniform thickness

pumping well is fully or partially penetrating

flow to pumping well is horizontal when pumping well is fully penetrating

aquifer is leaky confined

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

diameter of pumping well is very small so that storage in the well can be
neglected

confining bed(s) has infinite areal extent, uniform vertical hydraulic

conductivity and uniform thickness

confining bed(s) is overlain or underlain by an infinite constant-head plane

source

298

flow in the aquitard(s) is vertical

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 rate including recovery

multiple pumping wells

multiple observation wells

partially penetrating wells

Estimated Parameters

T (transmissivity)

S (storativity)

r/B (leakage parameter)

Sw (wellbore skin factor)

C (nonlinear well loss coefficient)

P (nonlinear well loss exponent)

The Report also shows aquitard properties (K'/b' and K') computed from the
leakage parameter (r/B).
o

Curve Matching Tips

Use the Cooper-Jacob (1946) solution to obtain preliminary estimates of

aquifer properties.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use active type curves for more effective visual matching with variablerate pumping tests.

Select values of r/B from the Family and Curve drop-down lists on the
toolbar.

299

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

Due to correlation in the equations between S (storativity) and Sw

(wellbore skin factor), estimate either S or Sw for a single-well test.

References

Hantush, M.S. and C.E. Jacob, 1955. Non-steady radial flow in an infinite
leaky 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. of

the Hyd. Div., Proc. of the Am. Soc. of Civil Eng., vol. 87, no. HY5, pp.
171-194.

Hantush, M.S., 1964. Hydraulics of wells, in: Advances in Hydroscience,

V.T. Chow (editor), Academic Press, New York, pp. 281-442.

Bear, J., 1979. Hydraulics of Groundwater, McGraw-Hill, New York, 569p.

Hantush (1960) Solution for a Pumping Test in

a Leaky Aquifer
(Match > Solution)
Hantush (1960) derived a solution for unsteady flow to a fully penetrating well in a
homogeneous, isotropic leaky confined aquifer. The solution assumes a line source
for the pumped well and therefore neglects wellbore storage.
Hantush (1960) also derived an approximate solution for drawdown at early time in
the pumped aquifer. Using the work by Hantush (1961a, b; Hantush 1964),
AQTESOLV extends the early-time solution to correct for partially penetrating wells
and anisotropy. When you choose the early-time form of the Hantush solution, you
may analyze data for fully or partially penetrating wells.
The Hantush solution can simulate variable-rate tests including recovery using the
principle of superposition in time. Use this solution to analyze both pumping and
recovery data from constant- or variable-rate pumping tests.
When you choose a solution, AQTESOLV provides two configurations for simulating a
leaky confined aquifer with aquitard storage using the Hantush (1960) solution.

The complete solution models fully penetrating wells for any value
300

of time.

The early-time solution simulates fully or partially penetrating wells for

small values of time (see equations for time restrictions).

Both solution options assume constant-head source aquifers supply leakage across
overlying and underlying aquitards (Hantush Case 1). The solution by Moench (1985)
lets you simulate Hantush Cases 2 and 3.
o

Illustration

Equations
Hantush (1960) derived a solution for unsteady flow to a fully penetrating
well in a homogeneous, isotropic leaky confined aquifer assuming aquitard
storage. The Laplace transform solution is as follows:

301

where

b' is thickness of first aquitard [L]

b" is thickness of second aquitard [L]

K' is vertical hydraulic conductivity of first aquitard [L/T]

K" is vertical hydraulic conductivity of second aquitard [L/T]

Ki is modified Bessel function of second kind, order i

p is Laplace transform variable

Q is pumping rate [L3/T]

r is radial distance [L]

s is drawdown [L]

S is storativity [dimensionless]

S' is storativity of first aquitard [dimensionless]

S" is storativity of second aquitard [dimensionless]

t is time [T]

T is transmissivity [L2/T]

Hantush (1960) also presented an asymptotic solution for drawdown in the

pumped aquifer at short values of time:
302

or

The solution assumes small values of time, i.e., when t < b'S'/10K' and t <
b"S"/10K".
The early-time approximate solution can be corrected for partial penetrating
wells and anisotropy using the approach of Hantush (1961a, b).
At large distances, the effect of partial penetration becomes negligible when

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous and of uniform thickness

pumping well is fully or partially penetrating

flow to pumping well is horizontal when pumping well is fully penetrating

aquifer is leaky confined

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

diameter of pumping well is very small so that storage in the well can be
neglected

confining bed(s) has infinite areal extent, uniform vertical hydraulic

conductivity, storage coefficient and thickness

confining bed(s) is overlain or underlain by an infinite constant-head plane

source

303

flow is vertical in the aquitard(s)

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

constant or variable pumping rate including recovery

multiple pumping wells

multiple observation wells

partially penetrating wells (early-time solution)

boundaries

Estimated Parameters

T (transmissivity)

S (storativity)

r/B' (leakage parameter, first aquitard)

' (leakage parameter, first aquitard)

r/B" (leakage parameter, second aquitard)

" (leakage parameter, second aquitard)

The Report also shows aquitard properties (K'/b' and K'; K"/b" and K")
computed from the leakage parameters (r/B' and r/B").
Early-Time Solution

T (transmissivity)

S (storativity)

(leakage parameter)

Kz/Kr (hydraulic conductivity anisotropy ratio)

b (saturated thickness)

304

Curve Matching Tips

Use the Cooper-Jacob (1946) solution to obtain preliminary estimates of

aquifer properties.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use active type curves for more effective visual matching with variablerate pumping tests.

Select values of r/B, and Kz/Kr from the Family and Curve drop-down
lists on the toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

For < 0.5, all of the type curves in the early-time solution have a similar
shape (Kruseman and de Ridder 1991); hence, it is often difficult to obtain
a unique match with the early-time solution when 0 0.5.

References

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., 1964. Hydraulics of wells, in: Advances in Hydroscience,

V.T. Chow (editor), Academic Press, New York, pp. 281-442.

Cooley-Case (1973) Solution for a Pumping

Test in a Confined Aquifer Overlain by a WaterTable Aquitard
(Match > Solution)
Cooley and Case (1973) derived a solution for unsteady flow to a fully penetrating
well in a homogeneous, isotropic leaky confined aquifer overlain by a water-table
aquitard. The solution assumes a line source for the pumped well and therefore
neglects wellbore storage.
The Cooley-Case solution can simulate variable-rate tests including recovery using
305

the principle of superposition in time. Use this solution to analyze both pumping and
recovery data from constant- or variable-rate pumping tests.
o

Illustration

Equations
Cooley and Case (1973) derived a solution for unsteady flow to a fully
penetrating well in a homogeneous, isotropic leaky confined aquifer overlain
by a water-table aquitard. The Laplace transform solution is as follows:

306

where

b' is thickness of the aquitard [L]

K' is vertical hydraulic conductivity of the aquitard [L/T]

Ki is modified Bessel function of second kind, order i

L is height of capillary fringe [L]

p is Laplace transform variable

Q is pumping rate [L3/T]

r is radial distance [L]

s is drawdown [L]

S is storativity [dimensionless]

S' is storativity of the aquitard [dimensionless]

Sy is specific yield of the aquitard [dimensionless]

t is time [T]

T is transmissivity [L2/T]

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous and of uniform thickness

pumping well is fully penetrating

flow to pumping well is horizontal

aquifer is leaky confined

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

diameter of pumping well is very small so that storage in the well can be
neglected

confining bed has infinite areal extent, uniform vertical hydraulic

307

conductivity, storage coefficient, specific yield and thickness

flow is vertical in the aquitard

Data Requirements

pumping and observation well locations

pumping rate(s)

observation well measurements (time and displacement)

Solution Options

constant or variable pumping rate including recovery

multiple pumping wells

multiple observation wells

boundaries

Estimated Parameters

T (transmissivity)

S (storativity)

r/B (leakage parameter)

(leakage parameter)

S'/Sy (storage ratio in aquitard)

L/b' (dimensionless height of capillary fringe)

The Report also shows aquitard properties (K'/b' and K') computed from the
leakage parameter (r/B).
o

Curve Matching Tips

Use the Cooper-Jacob (1946) solution to obtain preliminary estimates of

aquifer properties.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use active type curves for more effective visual matching with variablerate pumping tests.

Select values of r/B and from the Family and Curve drop-down lists on
the toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

308

reasonable starting values for the aquifer properties.

o

References

Cooley, R.L. and C.M. Case, 1973. Effect of a water table aquitard on
drawdown in an underlying pumped aquifer, Water Resources Research,
vol. 9, no. 2, pp. 434-447.

Neuman-Witherspoon (1969) Solution for a

Pumping Test in a Leaky Aquifer
(Match > Solution)
Neuman and Witherspoon (1969) derived a solution for unsteady flow to a fully
penetrating well in a confined two-aquifer system. The solution assumes a line
source for the pumped well and therefore neglects wellbore storage.
The Neuman-Witherspoon solution can simulate variable-rate tests including
recovery through the application of the principle of superposition in time. Use this
solution to analyze both pumping and recovery data from constant- or variable-rate
pumping tests.
You may analyze data from wells screened in the pumped aquifer, unpumped aquifer
or aquitard with the Neuman-Witherspoon solution. Wells in the aquifers are
assumed to be fully penetrating; wells in the aquitard may be partially penetrating.
o

Illustration

309

Equations
Neuman and Witherspoon (1969) derived the following equations for
drawdown in a confined two-aquifer system:

310

where

bi is thickness of aquifer i [L]

bj' is thickness of aquitard j [L]

J0 is Bessel function of first kind, zero order

Ki is horizontal hydraulic conductivity in aquifer i [L/T]

Kj' is vertical hydraulic conductivity in aquitard j [L/T]

Q is pumping rate [L3/T]

r is radial distance [L]

s1 is drawdown in the pumped aquifer [L]

s'1 is drawdown in the aquitard [L]

s2 is drawdown in the unpumped aquifer [L]

S, S1 is storativity in the pumped aquifer [dimensionless]

t is time [T]

T, T1 is transmissivity in the pumped aquifer [L2/T]

Expressions for drawdown in the aquitard for fully or partially penetrating

wells can be found by averaging the drawdown over the length of the well
screen.
o

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous, isotropic and of uniform thickness

pumping well is fully penetrating

311

flow to pumping well is horizontal

aquifer is leaky confined

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

diameter of pumping well is very small so that storage in the well can be
neglected

confining bed(s) has infinite areal extent, uniform vertical hydraulic

conductivity, storage coefficient and thickness

flow is vertical in the aquitard(s)l

Data Requirements

pumping and observation well locations

pumping rate(s)

observation well measurements (time and displacement)

partial penetration depths (optional; aquitard only)

aquitard thickness, b' (for partially penetrating wells)

Solution Options

constant or variable pumping rate including recovery

multiple pumping wells

multiple observation wells

boundaries

Estimated Parameters

T (transmissivity in pumped aquifer = T1)

S (storativity in pumped aquifer = S1)

r/B (leakage parameter = r/B11)

(leakage parameter = 11)

T2 (transmissivity in unpumped aquifer = T2)

S2 (storativity in unpumped aquifer = S2)

The Report also shows aquitard properties (K'/b' and K') computed from the
leakage parameter (r/B).

312

Curve Matching Tips

Use the Cooper-Jacob (1946) solution to obtain preliminary estimates of

aquifer properties.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use active type curves for more effective visual matching with variablerate pumping tests.

For partially penetrating wells, select values of r/B and from the Family
and Curve drop-down lists on the toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

References

Neuman, S.P. and P.A. Witherspoon, 1969. Theory of flow in a confined

two aquifer system, Water Resources Research, vol. 5, no. 4, pp. 803816.

Moench (1985) Solution for a Pumping Test in a

Leaky Aquifer
(Match > Solution)
Moench (1985) derived a solution for unsteady flow to a fully penetrating, finitediameter well with wellbore storage and wellbore skin in a homogeneous, isotropic
leaky confined aquifer.
AQTESOLV uses the principle of superposition in time to simulate variable-rate tests
including recovery with the Moench solution. Use this solution to analyze both
pumping and recovery data from constant- or variable-rate pumping tests.
Wellbore storage has a distinct signature in the early-time response of a pumped
well. Use the radial flow and derivative-time plots to detect the wellbore storage
effect.
When you choose a solution, AQTESOLV provides three configurations for simulating
a leaky confined aquifer with aquitard storage using the Moench (1985) solution.

Case 1 assumes constant-head source aquifers supply leakage across

overlying and underlying aquitards.

Case 2 replaces both constant-head boundaries in Case 1 with no-flow

313

boundaries.

Case 3 replaces the underlying constant-head boundary in Case 1 with a noflow boundary.

Illustration

Boundaries in illustration refer to Case 1.

o

Equations
Moench (1985) derived an analytical solution for predicting water-level
displacements in response to pumping in a leaky confined aquifer assuming
fully penetrating wells, wellbore storage and wellbore skin.
The Laplace transform solution for dimensionless drawdown in the pumped
well is as follows:

The follow equation is the Laplace transform solution for dimensionless

drawdown in an observation well:

314

where

b is aquifer thickness [L]

b' is thickness of first aquitard [L]

315

b" is thickness of second aquitard [L]

K is aquifer hydraulic conductivity [L/T]

K' is vertical hydraulic conductivity of first aquitard [L/T]

K" is vertical hydraulic conductivity of second aquitard [L/T]

Ki is modified Bessel function of second kind, order i

p is the Laplace transform variable

Q is pumping rate [L3/T]

r is radial distance [L]

rc is casing radius [L]

rw is well radius [L]

Ss is aquifer specific storage [1/L]

Ss' is specific storage of first aquitard [1/L]

Ss" is specific storage of second aquitard [1/L]

Sw is wellbore skin factor [dimensionless]

t is time [T]

In the Laplace transform solution, Sw is limited to positive values; however,

using the effective well radius concept, we also may simulate a negative
skin (Hurst, Clark and Brauer 1969).
If you enter a radius for downhole equipment, AQTESOLV uses the effective
casing radius instead of the nominal casing radius in the equations for this
solution.
AQTESOLV reports the aquitard properties in terms of the more familiar
parameters from the Hantush (1960) solution, which one can readily
compute from Moench's parameters as follows:

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous, isotropic and of uniform thickness

aquifer potentiometric surface is initially horizontal

pumping and observation wells are fully penetrating

316

flow to pumping well is horizontal

flow is unsteady

aquifer is leaky confined

water is released instantaneously from storage with decline of hydraulic

head

confining bed(s) has infinite areal extent, uniform vertical hydraulic

conductivity and storage coefficient, and uniform thickness

confining bed(s) is overlain or underlain by an infinite constant-head plane

source (case 1) or no-flow boundary (case 2)

vertical flow in the aquitard(s)

Data Requirements

pumping and observation well locations

pumping rate(s)

observation well measurements (time and displacement)

casing radius and wellbore radius for pumping well(s)

downhole equipment radius (optional)

saturated thickness

Solution Options

constant or variable pumping rate including recovery

multiple pumping wells

multiple observation wells

boundaries

Estimated Parameters

T (transmissivity)

S (storativity)

r/B' (dimensionless leakage parameter, aquitard 1)

' (dimensionless leakage parameter, aquitard 1)

r/B" (dimensionless leakage parameter, aquitard 2)

" (dimensionless leakage parameter, aquitard 2)

Sw (wellbore skin factor)

r(w) (well radius)

317

r(c) (nominal casing radius)

The Report also shows aquitard properties (K'/b' and K'; K"/b" and K")
computed from the leakage parameters (r/B' and r/B").
o

Curve Matching Tips

Use radial flow plots to help diagnose wellbore storage.

Match the Cooper-Jacob (1946) solution to late-time data to obtain

preliminary estimates of aquifer properties.

Match early-time data affected by wellbore storage by adjusting r(c) with

parameter tweaking.

If you estimate r(c) for the test well, the estimated value replaces the
nominal casing radius and AQTESOLV still performs the correction for
downhole equipment.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use active type curves for more effective visual matching with variablerate pumping tests.

Select values of r/B and from the Family and Curve drop-down lists on
the toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

References

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.

318

Unconfined Aquifers

Theis (1935) Solution for a Pumping Test in an

Unconfined Aquifer
(Match > Solution)
The Theis (1935) solution is applicable to unconfined aquifers through the correction
of drawdown data as follows (Kruseman and de Ridder 1990):
s' = s - s2/2b
where s' is corrected displacement [L], s is observed displacement [L] and b is
saturated aquifer thickness [L]. This correction attributed to C.E. Jacob only applies
to pumping tests in which water is extracted from an unconfined aquifer; the
correction is not appropriate for injection tests.
The corrected displacement (s') predicted by this equation reaches a maximum of
one-half the aquifer saturated thickness (0.5b) when the observed displacement is
equal to the aquifer saturated thickness (s = b). Of course, complete dewatering of
the aquifer (s = b) is not a realistic condition; however, in some cases, the
displacement predicted with this correction equation along a type curve may exceed
the saturated thickness of the aquifer.
For more information regarding this method or to apply the solution without the
dewatering correction, refer to the Theis (1935) solution for confined aquifers.
o

Illustration

319

Equations
Refer to the Theis (1935) solution for fully or partially penetrating wells in a
confined aquifer.

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 fully penetrating

aquifer is unconfined

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

diameter of pumping well is very small so that storage in the well can be
neglected

no delayed gravity response in aquifer

low velocity is proportional to tangent of the hydraulic gradient instead of

the sine (which is actually the case)

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

displacement is small relative to saturated thickness of aquifer

Data Requirements

pumping and observation well locations

pumping rate(s)

observation well measurements (time and displacement)

partial penetration depths (optional)

saturated thickness

hydraulic conductivity anisotropy ratio (for partially penetrating wells)

Solution Options

constant or variable pumping rate including recovery

multiple pumping wells

multiple observation wells

320

partially penetrating wells

Estimated Parameters

T (transmissivity)

S (storativity)

Kz/Kr (hydraulic conductivity anisotropy ratio)

b (saturated thickness)

Curve Matching Tips

Use the Cooper-Jacob (1946) solution to obtain preliminary estimates of

aquifer properties.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use active type curves for more effective visual matching with variablerate pumping tests.

For partially penetrating wells, select values of Kz/Kr from the Family and
Curve drop-down lists on the toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

References

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

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.

Cooper-Jacob (1946) Solution for a Pumping

Test in an Unconfined Aquifer
(Match > Solution)
The Cooper-Jacob(1946) solution is applicable to unconfined aquifers through the
correction of drawdown data as follows (Kruseman and de Ridder 1990):
s' = s - s2/2b
where s' is corrected displacement [L], s is observed displacement [L] and b is
321

saturated aquifer thickness [L]. This correction attributed to C.E. Jacob only applies
to pumping tests in which water is extracted from an unconfined aquifer; the
correction is not appropriate for injection tests.
The corrected displacement (s') predicted by this equation reaches a maximum of
one-half the aquifer saturated thickness (0.5b) when the observed displacement is
equal to the aquifer saturated thickness (s = b). Of course, complete dewatering of
the aquifer (s = b) is not a realistic condition; however, in some cases, the
displacement predicted with this correction equation along a type curve may exceed
the saturated thickness of the aquifer.
For more information regarding this method or to apply the solution without the
dewatering correction, refer to the Cooper-Jacob (1946) solution for a confined
aquifer.
o

Illustration

Equations
Refer to the Cooper-Jacob(1946) solution for fully penetrating wells in a
confined aquifer.

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous, isotropic and of uniform thickness

pumping well is fully penetrating

flow to pumping well is horizontal

322

aquifer is unconfined

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

diameter of pumping well is very small so that storage in the well can be
neglected

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

no delayed gravity response in aquifer

low velocity is proportional to tangent of the hydraulic gradient instead of

the sine (which is actually the case)

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

displacement is small relative to saturated thickness of aquifer

Data Requirements

pumping and observation well locations

pumping rate(s)

observation well measurements (time and displacement)

saturated thickness

Solution Options

constant or variable pumping rate including recovery

multiple observation wells

Estimated Parameters

T (transmissivity)

S (storativity)

Curve Matching Tips

Choose Match>Visual to perform visual curve matching using the

procedure for straight-line solutions.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Choose View>Options to display the critical value of u on the plot.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

323

Use Agarwal plots to analyze recovery data.

You may use the Cooper-Jacob solution to analyze drawdown data from
the start of the test up to the first recovery period (a recovery period is
any period with a rate equals zero).

If your data set contains more than one recovery period, you may use the
Cooper-Jacob solution to analyze recovery data in the first recovery
period.

If your data set contains more than one pumping well, AQTESOLV uses
the first pumping well in the well data to match test data with the
Cooper-Jacob solution.

For more tips and information, refer to the Cooper-Jacob (1946) solution for a
confined aquifer.
o

References

Cooper, H.H. and C.E. Jacob, 1946. A generalized graphical method for
evaluating 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 of

Pumping Test Data (2nd ed.), Publication 47, Intern. Inst. for Land
Reclamation and Improvement, Wageningen, The Netherlands, 370p.

Neuman (1974) Solution for a Pumping Test in

an Unconfined Aquifer
(Match > Solution)
Neuman (1972, 1974) derived an analytical solution for unsteady flow to a fully or
partially penetrating well in a homogeneous, anisotropic unconfined aquifer with
delayed gravity response. The Neuman model assumes instantaneous drainage at
the water table. The solution also assumes a line source for the pumped well and
therefore neglects wellbore storage.
AQTESOLV applies the principle of superposition in time to simulate variable-rate
tests including recovery. You may use the Neuman solution to analyze both pumping
and recovery data from constant- or variable-rate pumping tests.
AQTESOLV uses computational enhancements by Moench (1996) to calculate type
curves for the Neuman solution.

324

Illustration

Equations
Neuman (1974) derived an analytical solution for unsteady flow to a partially
penetrating well in an unconfined aquifer with delayed gravity response:

where

b is aquifer thickness [L]

325

Kr is radial hydraulic conductivity [L/T]

Kz is vertical hydraulic conductivity [L/T]

Q is pumping rate [L3/T]

r is radial distance [L]

s is drawdown [L]

S is storativity [dimensionless]

Sy is specific yield [dimensionless]

t is time [T]

T is transmissivity [L2/T]

The drawdown in a piezometer is found using the following equations:

The drawdown in a partially penetrating observation well is found using the

following equations:

The gamma terms are the roots of the following equations:

where

dD is dimensionless depth to top of pumping well screen (d/b)

J0 is Bessel function of first kind, zero order

lD is dimensionless depth to bottom of pumping well screen (l/b)

326

zD is dimensionless elevation of piezometer opening above base of aquifer

(z/b)

z1D is dimensionless elevation of bottom of observation well screen above

base of aquifer (z1/b)

z2D is dimensionless elevation of top of observation well screen above base

of aquifer (z2/b)

Subsequent work by Moench (1993, 1996) presented improved methods for

evaluating the Neuman solution.
o

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous and has uniform thickness

aquifer potentiometric surface is initially horizontal

pumping well is fully or partially penetrating

aquifer is unconfined with delayed gravity response

flow is unsteady

diameter of pumping well is very small so that storage in the well can be
neglected

Data Requirements

pumping and observation well locations

pumping rate(s)

observation well measurements (time and displacement)

aquifer saturated thickness

partial penetration depths (optional)

Solution Options

variable pumping rates

multiple pumping wells

multiple observation wells

partially penetrating wells

Estimated Parameters

T (transmissivity)

S (storativity)

327

Sy (specific yield)

or Kz/Kr (hydraulic conductivity anisotropy ratio)

AQTESOLV displays for tests with a single observation well or Kz/Kr for
multiple observation wells.
o

Curve Matching Tips

Use the Cooper-Jacob (1946) solution to obtain preliminary estimates of

aquifer properties. Determine T by matching a straight line to late-time
data. If the wells are fully penetrating, you also may estimate Sy from the
late-time match. Estimate S from early-time data.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use active type curves for more effective visual matching with variablerate pumping tests.

Select values of or Kz/Kr from the Family and Curve drop-down lists on
the toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

References

Neuman, S.P., 1974. Effect of partial penetration on flow in unconfined

aquifers considering delayed gravity response, Water Resources Research,
vol. 10, no. 2, pp. 303-312.

Neuman, S.P., 1972. Theory of flow in unconfined aquifers considering

delayed gravity response of the water table, Water Resources Research,
vol. 8, no. 4, pp. 1031-1045.

Moench, A.F., 1993. Computation of type curves for flow to partially

penetrating 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 improved

Laplace transform solution, Ground Water, vol. 34, no. 4, pp. 593-596.

Moench (1997) Solution for a Pumping Test in

an Unconfined Aquifer
(Match > Solution)
Moench (1997) derived an analytical solution for unsteady flow to a fully or partially

328

penetrating, finite-diameter well with wellbore storage and wellbore skin in a

homogeneous, anisotropic unconfined aquifer with delayed gravity response. The
Moench solution also includes a correction for delayed observation well response.
AQTESOLV uses the principle of superposition in time to simulate variable-rate tests
including recovery with the Moench solution. Use this solution to analyze both
pumping and recovery data from constant- or variable-rate pumping tests.
Wellbore storage has a distinct signature in the early-time response of a pumped
well. Use the radial flow and derivative-time plots to detect the wellbore storage
effect.
o

Illustration

Equations
Moench (1997) derived an analytical solution for predicting drawdown in
response to pumping in a homogeneous, anisotropic unconfined aquifer
assuming partially penetrating wells, wellbore storage, wellbore skin and
delayed gravity response. The solution also includes a correction for delayed
observation well response.
The Laplace transform solution for dimensionless drawdown in the pumped
well is as follows:

The following equation is the Laplace transform solution for dimensionless

drawdown in a piezometer:

329

The equation for dimensionless drawdown in an observation well is:

330

are the roots of

where

1 is an empirical constant (fitting parameter) for noninstantaneous

drainage [1/T]

b is aquifer thickness [L]

d is distance from water table to top of pumping well screen [L]

dD is d/b

K, Kr is radial hydraulic conductivity [L/T]

Kz is vertical hydraulic conductivity [L/T]

Ki is modified Bessel function of second kind, order i

l is distance from water table to bottom of pumping well screen [L]

lD is l/b

p is the Laplace transform variable

Q is pumping rate [L3/T]

r is radial distance [L]

rc is casing radius [L]

rw is well radius [L]

Ss is specific storage [1/L]

Sw is wellbore skin factor [dimensionless]

Sy is specific yield [dimensionless]

t is time [T]

z is elevation of piezometer above base of aquifer [L]

zD is z/b

331

z1 is elevation of bottom of observation well screen above base of aquifer

[L]

z1D is z1/b

z2 is elevation of top of observation well screen above base of aquifer [L]

z2D is z2/b

In the Laplace transform solution, Sw is limited to positive values; however,

using the effective well radius concept, we also may simulate a negative
skin (Hurst, Clark and Brauer 1969).
If you enter a radius for downhole equipment, AQTESOLV uses the effective
casing radius instead of the nominal casing radius in the equations for this
solution.
Moench (1997) also included a correction for delayed water-level response in
a fully or partially penetrating observation well based on the work of Black
and Kipp (1977):

where

rco is casing radius of observation well [L]

rwo is well radius of observation well [L]

The correction is based on the quasi-steady-state flow model of Hvorslev

(1951) for a slug test. AQTESOLV uses the standard definition of the shape
factor given by Butler (1998) which depends on the position of the well
screen in the aquifer. Note that delayed response diminishes as rco
approaches zero; therefore, to eliminate the correction for delayed
response, enter a small value for the casing radius of the observation well.
o

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous and of uniform thickness

aquifer potentiometric surface is initially horizontal

332

pumping and observation wells are fully or partially penetrating

flow is unsteady

aquifer is unconfined with delayed gravity response

Data Requirements

pumping and observation well locations

pumping rate(s)

observation well measurements (time and displacement)

casing radius and wellbore radius for pumping well(s)

downhole equipment radius (optional)

saturated thickness

partial penetration depths (optional)

Solution Options

constant or variable pumping rate including recovery

multiple pumping wells

multiple observation wells

partially penetrating wells

boundaries

Estimated Parameters

T (transmissivity)

S (storativity)

Sy (specific yield)

Sw (dimensionless wellbore skin factor)

r(w) (well radius)

r(c) (nominal casing radius)

1 (Moench's empirical constant for noninstantaneous drainage at the

water table)

Curve Matching Tips

Use radial flow plots to help diagnose wellbore storage.

Match the Cooper-Jacob (1946) solution to late-time data to obtain

333

preliminary estimates of aquifer properties.

Match early-time data affected by wellbore storage by adjusting r(c) with

parameter tweaking.

If you estimate r(c) for the test well, the estimated value replaces the
nominal casing radius and AQTESOLV still performs the correction for
downhole equipment.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use active type curves for more effective visual matching with variablerate pumping tests.

Select values of from the Family and Curve drop-down lists on the
toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

Enter a large value for 1 (the drainage parameter) to achieve

instantaneous drainage at the water table (Neuman's model).

References

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.

Tartakovsky-Neuman (2007) Solution for a

Pumping Test in an Unconfined Aquifer
(Match > Solution)
Tartakovsky and Neuman (2007) derived an analytical solution for unsteady flow to a
fully or partially penetrating well in a homogeneous, anisotropic unconfined aquifer
with delayed gravity response considering three-dimensional flow in the saturated
and unsaturated zones. Unlike the Neuman (1974) solution, the TartakovskyNeuman solution allows for noninstantaneous drainage at the water table. The
solution assumes a line source for the pumped well and therefore neglects wellbore
storage.
AQTESOLV applies the principle of superposition in time to simulate variable-rate
tests including recovery. You may use the Tartakovsky-Neuman solution to analyze
both pumping and recovery data from constant- or variable-rate pumping tests.
The Tartakovsky-Neuman solution includes a parameter (D) that characterizes the
properties of the unsaturated medium. As D approaches , the Tartakovsky-Neuman
334

solution becomes equivalent to the Neuman (1974) model.

o

Illustration

Equations
Tartakovsky and Neuman (2007) developed a Laplace transform solution for
unsteady flow to a partially penetrating well in an unconfined aquifer with
three-dimensional flow in the saturated and unsaturated zones:

335

where

b is aquifer thickness [L]

dD is dimensionless depth to top of pumping well screen (d/b)

J0 is Bessel function of first kind, zero order

Kr is radial hydraulic conductivity [L/T]

Kz is vertical hydraulic conductivity [L/T]

D is dimensionless Gardner parameter for the unsaturated zone (b)

lD is dimensionless depth to bottom of pumping well screen (l/b)

p is Laplace transform variable [T-1]

Q is pumping rate [L3/T]

r is radial distance [L]

s is drawdown [L]

S is storativity [dimensionless]

Sy is specific yield [dimensionless]

t is time [T]

T is transmissivity [L2/T]

y is variable of integration

zD is dimensionless elevation of piezometer opening above base of aquifer

(z/b)

Expressions for fully and partially penetrating observations wells are obtained
by vertically averaging the drawdown computed with the piezometer
equation over the length of the observation well screen.
As D approaches , the effect of the unsaturated zone dies out and the
336

solution behaves like the model of Neuman (1974).

o

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous and has uniform thickness

aquifer potentiometric surface is initially horizontal

pumping well is fully or partially penetrating

aquifer is unconfined with delayed gravity response

the unsaturated zone has infinite thickness

flow is unsteady

diameter of pumping well is very small so that storage in the well can be
neglected

Data Requirements

pumping and observation well locations

pumping rate(s)

observation well measurements (time and displacement)

aquifer saturated thickness

partial penetration depths (optional)

Solution Options

variable pumping rates

multiple pumping wells

multiple observation wells

partially penetrating wells

Estimated Parameters

T (transmissivity)

S (storativity)

Sy (specific yield)

Kz/Kr (hydraulic conductivity anisotropy ratio)

k(D) (dimensionless Gardner parameter)

Curve Matching Tips

Choose Match>Visual to perform visual curve matching using the

337

procedure for type curve solutions.

Use active type curves for more effective visual matching with variablerate pumping tests.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

Change convergence levels to optimize the speed and accuracy of

computations for the solution. The default setting is suitable for all cases.
The fastest level works well for fully penetrating wells or partially
penetrating wells with longer screens. Use higher convergence levels to
check the performance of lower settings.

References

Tartakovsky, G.D. and S.P. Neuman, 2007. Three-dimensional saturatedunsaturated flow with axial symmetry to a partially penetrating well in a
compressible unconfined aquifer, Water Resources Research, W01410,
doi:1029/2006WR005153.

Neuman, S.P., 1972. Theory of flow in unconfined aquifers considering

delayed gravity response of the water table, Water Resources Research,
vol. 8, no. 4, pp. 1031-1045.

Neuman, S.P., 1974. Effect of partial penetration on flow in unconfined

aquifers considering delayed gravity response, Water Resources Research,
vol. 10, no. 2, pp. 303-312.

338

Fractured Aquifers

Moench (1984) Solution for a Pumping Test in a

Fractured Aquifer
(Match > Solution)
Moench (1984) derived an analytical solution for unsteady flow to a fully penetrating,
finite-diameter well with wellbore storage and wellbore skin in an isotropic fractured
aquifer assuming a double-porosity model with slab or spherical matrix blocks and
fracture skin.
Moench (1988) extended the method to include partially penetrating wells and
anisotropy based on the solution by Dougherty and Babu (1984). When you choose
the Moench solution in AQTESOLV, you may analyze data for fully or partially
penetrating wells. The solution also includes delayed response in an observation well
based on the work of Moench (1997).
AQTESOLV uses the principle of superposition in time to simulate variable-rate tests
including recovery with the Moench solution. Use this solution to analyze both
pumping and recovery data from constant- or variable-rate pumping tests.
Wellbore storage has a distinct signature in the early-time response of a pumped
well. Use the radial flow and derivative-time plots to detect the wellbore storage
effect.
When you choose a solution, AQTESOLV provides two configurations for simulating a
double-porosity aquifer with the Moench solution: slab-shaped and spherical blocks.
o

Illustration

339

Equations
Moench (1984) derived an analytical solution for predicting water-level
displacements in response to pumping in a fractured aquifer assuming a
double-porosity model with slab-shaped matrix blocks with fracture skin and
wellbore skin.
The Laplace transform solution for dimensionless drawdown in the pumped
well is as follows:

The following equation is the Laplace transform solution for dimensionless

drawdown in an observation well:

For slab blocks:

For spherical blocks:

340

where

b is aquifer thickness [L]

b' is block thickness [L]

bs is fracture skin thickness [L]

K is aquifer hydraulic conductivity [L/T]

K' is matrix hydraulic conductivity [L/T]

Ks is fracture skin hydraulic conductivity [L/T]

Ki is modified Bessel function of second kind, order i

p is the Laplace transform variable

Q is pumping rate [L3/T]

r is radial distance [L]

rc is casing radius [L]

rw is well radius [L]

Sf is fracture skin factor [dimensionless]

Ss is fracture specific storage [1/L]

Ss' is matrix specific storage [1/L]

Sw is wellbore skin factor [dimensionless]

t is time [T]

Moench (1988) extended the method to include partial penetration and

anisotropy based on the work of Dougherty and Babu (1984). The
anisotropy ratio, Kz/Kr, refers to the hydraulic conductivity of the fracture
system.
341

In the Laplace transform solution, Sw is limited to positive values; however,

using the effective well radius concept, we also may simulate a negative
skin (Hurst, Clark and Brauer 1969).
If you enter a radius for downhole equipment, AQTESOLV uses the effective
casing radius instead of the nominal casing radius in the equations for this
solution.
Refer to the Moench (1997) solution for the equations relating to delayed
response in an observation well.
o

Assumptions

aquifer has infinite areal extent

aquifer has uniform thickness

pumping and observation wells are fully or partially penetrating

aquifer is confined with double porosity

matrix blocks are slab shaped or spherical

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

Data Requirements

pumping and observation well locations

pumping rate(s)

observation well measurements (time and displacement)

casing radius and wellbore radius for pumping well(s)

downhole equipment radius (optional)

saturated thickness

thickness of slab blocks or diameter of spherical blocks

Solution Options

constant or variable pumping rate including recovery

multiple pumping wells

multiple observation wells

boundaries

Estimated Parameters

K (fracture hydraulic conductivity)

342

Ss (fracture specific storage)

K' (matrix hydraulic conductivity)

Ss' (matrix specific storage)

Sw (wellbore skin factor)

Sf (fracture skin factor)

r(w) (well radius)

r(c) (nominal casing radius)

Curve Matching Tips

Use radial flow plots to help diagnose wellbore storage.

Match the Cooper-Jacob (1946) solution to late-time data to obtain

preliminary estimates of aquifer properties.

Match early-time data affected by wellbore storage by adjusting r(c) with

parameter tweaking.

If you estimate r(c) for the test well, the estimated value replaces the
nominal casing radius and AQTESOLV still performs the correction for
downhole equipment.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use active type curves for more effective visual matching with variablerate pumping tests.

Select values of Sf from the Family and Curve drop-down lists on the
toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

References

Moench, A.F., 1984. Double-porosity models for a fissured groundwater

reservoir with fracture skin, Water Resources Research, vol. 20, no. 7, pp.
831-846.

Moench, A.F., 1988. The response of partially penetrating wells to

pumpage from double-porosity aquifers, Proceedings of the International
Conference on Fluid Flow in Fractured Rocks, Atlanta, GA, May 16-18,
1988.

Dougherty, D.E and D.K. Babu, 1984. Flow to a partially penetrating well
in a double-porosity reservoir, Water Resources Research, vol. 20, no. 8,

343

pp. 1116-1122.

Gringarten-Witherspoon (1972) Solution for a

Pumping Test in a Fractured Aquifer
(Match > Solution)
Gringarten and Witherspoon (1972) and Gringarten, Ramey and Raghavan (1974)
presented an analytical solution for unsteady flow to a fully penetrating well
intersecting a single uniform-flux vertical fracture in an anisotropic confined aquifer.
The pumped well bisects the fracture which is represented in the solution by a fully
penetrating vertical plane source oriented parallel to the x axis. In contrast to the
infinite-conductivity solution for a vertical fracture, drawdown in the uniform-flux
formulation varies along the fracture.
AQTESOLV uses the principle of superposition in time to simulate variable-rate tests
including recovery with the Gringarten-Witherspoon solution. Use this solution to
analyze both pumping and recovery data from constant- or variable-rate pumping
tests.
The early-time response of a pumped well intersecting a vertical fracture has a
distinct signature that you can diagnose with a linear flow plot.
Due to anisotropy, use of a distance-drawdown plot with the GringartenWitherspoon solution is limited to wells located on the x-coordinate axis.
o

Illustration

344

Equations
The following equation by Gringarten and Witherspoon (1972) predicts
drawdown in a confined aquifer with a uniform-flux vertical fracture:

where

Q is pumping rate [L3/T]

s is drawdown [L]

S is storativity [dimensionless]

t is time [T]

Tx is transmissivity in x direction [L2/T]

Ty is transmissivity in y direction [L2/T]

x and y are coordinate distances [L]

xf is the half-length of the fracture in the x direction [L]

Assumptions

aquifer has infinite areal extent

aquifer has uniform thickness

aquifer potentiometric surface is initially horizontal

pumping and observation wells are fully penetrating

fractured aquifer represented by anisotropic system with a single plane

vertical fracture
345

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

diameter of pumping well is very small so that storage in the well can be
neglected

Data Requirements

pumping and observation well locations

pumping rate(s)

observation well measurements (time and displacement)

saturated thickness

length of vertical fracture

Solution Options

constant or variable pumping rate including recovery

multiple pumping wells

multiple observation wells

boundaries

Estimated Parameters

Kx (hydraulic conductivity in x direction)

Ss (specific storage)

Ky/Kx (hydraulic conductivity anisotropy ratio)

Lf (length of fracture)

Curve Matching Tips

Use linear flow plots to help diagnose fracture flow.

Use the Cooper-Jacob (1946) solution to obtain preliminary estimates of

aquifer properties.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use active type curves for more effective visual matching with variablerate pumping tests.

Select values of Ky/Kx from the Family and Curve drop-down lists on the
toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

346

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

References

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. 19.

Gringarten, A.C., Ramey, H.J., Jr. and R. Raghavan, 1974. Unsteady-state

pressure distributions created by a well with single infinite-conductivity
vertical fracture, Soc. Petrol. Engrs. J., pp. 347-360.

Gringarten-Ramey-Raghavan (1974) Solution

for a Pumping Test in a Fractured Aquifer
(Match > Solution)
Gringarten, Ramey and Raghavan (1974) presented an analytical solution for
unsteady flow to a fully penetrating well intersecting a single infinite-conductivity
vertical fracture in an anisotropic confined aquifer. The pumped well bisects the
fracture which is represented in the solution by a fully penetrating vertical plane
source oriented parallel to the x axis. In contrast to the uniform-flux solution for a
vertical fracture, drawdown in the infinite-conductivity formulation is uniform along
the fracture.
AQTESOLV uses the principle of superposition in time to simulate variable-rate tests
including recovery with the Gringarten et al. solution. Use this solution to analyze
both pumping and recovery data from constant- or variable-rate pumping tests.
The early-time response of a pumped well intersecting a vertical fracture has a
distinct signature that you can diagnose with a linear flow plot.
Due to anisotropy, use of a distance-drawdown plot with the Gringarten et al.
solution is limited to wells located on the x-coordinate axis.

347

Illustration

Equations
The following equation by Gringarten and Witherspoon (1972) predicts
drawdown in an anisotropic confined aquifer with a uniform-flux vertical
fracture:

where

348

Q is pumping rate [L3/T]

s is drawdown [L]

S is storativity [dimensionless]

t is time [T]

Tx is transmissivity in x direction [L2/T]

Ty is transmissivity in y direction [L2/T]

x and y are coordinate distances [L]

xf is the half-length of the fracture in the x direction [L]

Gringarten, Ramey and Raghavan (1974) found that the foregoing solution
could be used to predict the drawdown in an infinite-conductivity fracture by
simply using xD = 0.732 to compute drawdown in the pumped well.
o

Assumptions

aquifer has infinite areal extent

aquifer has uniform thickness

aquifer potentiometric surface is initially horizontal

pumping and observation wells are fully penetrating

fractured aquifer represented by anisotropic system with a single plane

vertical fracture

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

diameter of pumping well is very small so that storage in the well can be
neglected

Data Requirements

pumping and observation well locations

pumping rate(s)

observation well measurements (time and displacement)

saturated thickness

length of vertical fracture

Solution Options

constant or variable pumping rate including recovery

349

multiple pumping wells

multiple observation wells

boundaries

Estimated Parameters

Kx (hydraulic conductivity in x direction)

Ss (specific storage)

Ky/Kx (hydraulic conductivity anisotropy ratio)

Lf (length of fracture)

Curve Matching Tips

Use linear flow plots to help diagnose fracture flow.

Use the Cooper-Jacob (1946) solution to obtain preliminary estimates of

aquifer properties.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use active type curves for more effective visual matching with variablerate pumping tests.

Select values of Ky/Kx from the Family and Curve drop-down lists on the
toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

References

Gringarten, A.C., Ramey, H.J., Jr. and R. Raghavan, 1974. Unsteady-state

pressure distributions created by a well with single infinite-conductivity
vertical fracture, Soc. Petrol. Engrs. J., pp. 347-360.

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. 19.

350

Gringarten-Ramey (1974) Solution for a

Pumping Test in a Fractured Aquifer
(Match > Solution)
Gringarten and Ramey (1974) presented an analytical solution for unsteady flow to a
well intersecting a single uniform-flux horizontal fracture in an anisotropic confined
aquifer. The solution assumes the fracture is a planar, disc-shaped source with the
pumped well located at its center.
AQTESOLV uses the principle of superposition in time to simulate variable-rate tests
including recovery with the Gringarten-Ramey solution. Use this solution to analyze
both pumping and recovery data from constant- or variable-rate pumping tests.
The early-time response of a pumped well intersecting a horizontal fracture has a
distinct signature that you can diagnose with a linear flow plot.
o

Illustration

Equations
The following equation by Gringarten and Ramey (1974) predicts drawdown
at a fixed point (piezometer) in an anisotropic confined aquifer with a
uniform-flux horizontal fracture:

351

where

b is saturated thickness [L]

I0 is modified Bessel function of first kind, zero order

Kr radial hydraulic conductivity [L/T]

Kz is vertical hydraulic conductivity [L/T]

Q is pumping rate [L3/T]

r is radial distance [L]

rf is the radius of the fracture [L]

s is drawdown [L]

Ss is specific storage [1/L]

t is time [T]

z is the z coordinate [L]

Drawdown in an observation well may be found by integrating the preceding

equations with respect to z.
o

Assumptions

aquifer has infinite areal extent

352

aquifer has uniform thickness

aquifer potentiometric surface is initially horizontal

fractured aquifer represented by anisotropic system with a single plane

horizontal fracture

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

diameter of pumping well is very small so that storage in the well can be
neglected

Data Requirements

pumping and observation well locations

pumping rate(s)

observation well measurements (time and displacement)

saturated thickness

radius and depth of horizontal fracture

Solution Options

constant or variable pumping rate including recovery

multiple pumping wells

multiple observation wells

boundaries

Estimated Parameters

Kr (radial hydraulic conductivity)

Ss (specific storage)

Kz/Kr (hydraulic conductivity anisotropy ratio)

Rf (radius of fracture)

Curve Matching Tips

Use linear flow plots to help diagnose fracture flow.

Use the Cooper-Jacob (1946) solution to obtain preliminary estimates of

aquifer properties.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

353

Use active type curves for more effective visual matching with variablerate pumping tests.

Select values of Kz/Kr from the Family and Curve drop-down lists on the
toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

References

Gringarten, A.C. and H.J. Ramey, 1974. Unsteady state pressure

distributions created by a well with a single horizontal fracture, partial
penetration or restricted entry, Soc. Petrol. Engrs. J., pp. 413-426.

Barker (1988) Solution for a Pumping Test in a

Fractured Aquifer
(Match > Solution)
Barker (1988) derived a generalized radial flow model for unsteady, n-dimensional
flow to a fully penetrating source in an isotropic, single- or double-porosity fractured
aquifer. The source is an n-dimensional sphere (projected through three-dimensional
space) of finite radius (rw), storage capacity () and skin factor (Sw).
As described by Doe (1990), the spatial dimension (n) determines the change in
conduit area with distance from the source. In a two-dimensional system (n=2), the
source is a finite cylinder, the typical configuration for analyzing cylindrical flow to a
well.
AQTESOLV uses the principle of superposition in time to simulate variable-rate tests
including recovery with the Barker solution. Use this solution to analyze both
pumping and recovery data from constant- or variable-rate pumping tests.
Wellbore storage has a distinct signature in the early-time response of a pumped
well in a cylindrical system (n=2). Use the radial flow and derivative-time plots to
detect the wellbore storage effect.
The early-time response of a source in a linear system (n=1) has a distinct signature
that you can diagnose with a linear flow plot.
When you choose a solution, AQTESOLV provides three configurations for the Barker
generalized radial flow model:

single-porosity (confined/fractured aquifer)

double-porosity with slab-shaped blocks (fractured aquifer)

354

double-porosity with spherical blocks (fractured aquifer)

Illustration

Diagram illustrating two-dimensional, cylindrical flow system (n=2).

o

Equations
Barker (1988) derived a generalized radial flow model for unsteady, ndimensional flow to a fully penetrating source in an isotropic, single- or
double-porosity fractured aquifer.
The Laplace transform solution for drawdown in the pumped well (source) is
as follows:

The following equation is the Laplace transform solution for drawdown in an

observation well:

355

For single-porosity models, we have:

For double-porosity models, we use the functions of Moench (1984) for slab
and spherical blocks including fracture skin.

slab blocks:

spherical blocks:

where

b is extent of flow region [L]

356

b' is block thickness [L]

bs is fracture skin thickness [L]

K is aquifer/fracture hydraulic conductivity [L/T]

K' is matrix hydraulic conductivity [L/T]

Ks is fracture skin hydraulic conductivity [L/T]

Kv is modified Bessel function of second kind, order v

n is flow dimension [dimensionless]

p is the Laplace transform variable

Q is pumping rate [L3/T]

r is radial distance [L]

rc is casing radius [L]

rw is well radius [L]

Sf is fracture skin factor [dimensionless]

Ss is aquifer/fracture specific storage [1/L]

Ss' is matrix specific storage [1/L]

Sw is wellbore skin factor [dimensionless]

t is time [T]

The parameter b, the flow region extent, has a simple interpretation for
integral flow dimensions. For one-dimensional flow (n=1), it is the square
root of the conduit flow area (normal to the flow direction). For n=2 (twodimensional radial flow), b is the thickness of the aquifer. For spherical flow
(n=3), the parameter b, which is raised to the power of 3-n, has no
significance. For nonintegral flow dimensions, b has no simple interpretation
(Barker 1988).
In the Laplace transform solution, Sw is limited to positive values; however,
using the effective well radius concept, we also may simulate a negative
skin (Hurst, Clark and Brauer 1969).
If you enter a radius for downhole equipment, AQTESOLV uses the effective
casing radius instead of the nominal casing radius in the equations for this
solution.
o

Assumptions

aquifer has infinite extent

aquifer has uniform extent of flow region

pumping and observation wells are fully penetrating

357

aquifer is confined with single or double porosity

matrix blocks in double-porosity models are slab shaped or spherical

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

Data Requirements

pumping and observation well locations

pumping rate(s)

observation well measurements (time and displacement)

casing radius and wellbore radius for pumping well(s)

downhole equipment radius (optional)

extent of flow region

thickness of slab blocks or diameter of spherical blocks (double-porosity

models)

Solution Options

constant or variable pumping rate including recovery

multiple pumping wells

multiple observation wells

boundaries

Estimated Parameters

K (fracture hydraulic conductivity)

Ss (fracture specific storage)

K' (matrix hydraulic conductivity)

Ss' (matrix specific storage)

n (flow dimension)

b (extent of flow region)

Sf (fracture skin factor)

Sw (wellbore skin factor)

r(w) (well radius)

r(c) (nominal casing radius)

358

Curve Matching Tips

Use radial flow plots to help diagnose wellbore storage.

Use linear flow plots to help diagnose linear flow.

Match the Cooper-Jacob (1946) solution to late-time data to obtain

preliminary estimates of aquifer properties.

Match early-time data affected by wellbore storage by adjusting r(c) with

parameter tweaking.

If you estimate r(c) for the test well, the estimated value replaces the
nominal casing radius and AQTESOLV still performs the correction for
downhole equipment.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use active type curves for more effective visual matching with variablerate pumping tests.

Select values of n, Sf and Sw from the Family and Curve drop-down lists
on the toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

References

Barker, J.A., 1988. A generalized radial flow model for hydraulic tests in
fractured rock, Water Resources Research, vol. 24, no. 10, pp. 17961804.

Moench, A.F., 1984. Double-porosity models for a fissured groundwater

reservoir with fracture skin, Water Resources Research, vol. 20, no. 7, pp.
831-846.

359

Slug Tests

Overview (Slug Test Solutions)

AQTESOLV provides the following solutions for slug tests in confined, unconfined and
fractured aquifers.
Confined
Confined
Confined
Confined
Confined
Confined
Confined
Confined
Confined
Unconfined
Unconfined
Unconfined
Unconfined
Unconfined
Fractured

Bouwer-Rice (1976)
Hvorslev (1951)
Cooper-Bredehoeft-Papadopulos (1967)
Dougherty-Babu (1984)
KGS Model (1994)
Butler (1998) inertial
Butler-Zhan (2004) inertial
Peres et al. (1989) deconvolution
McElwee-Zenner (1998) nonlinear
Bouwer-Rice (1976)
Hvorslev (1951)
KGS Model (1994)
Springer-Gelhar (1991) inertial
Dagan (1978) with partially submerged
screen
Barker-Black (1983)

Choose Match>Solution to select a slug test solution.

Follow guidelines developed by Butler (1998) for applying slug test models.

Overdamped Slug Test Solutions

The familiar response of a slug test is overdamped, in contrast to an underdamped
response (i.e., an oscillatory response due to inertial effects) sometimes observed in
high-K aquifers.

360

Example: Overdamped Slug Test Response

361

The following slug test solutions simulate the overdamped case in confined,
unconfined and fractured aquifers.
Confined
Confined
Confined
Confined
Confined
Confined
Unconfined
Unconfined
Unconfined
Unconfined
Fractured

Bouwer-Rice (1976)
Hvorslev (1951)
Cooper-Bredehoeft-Papadopulos (1967)
Dougherty-Babu (1984)
KGS Model (1994)
Peres et al. (1989) deconvolution
Bouwer-Rice (1976)
Hvorslev (1951)
KGS Model (1994)
Dagan (1978)
Barker-Black (1983)

Choose Match>Solution to select a slug test solution.

362

Underdamped Slug Test Solutions

Slug tests in high hydraulic conductivity (high-K) aquifers sometimes exhibit
underdamped (oscillatory) response due to inertial effects in the well.
Example: Underdamped Slug Test Response

The following slug test solutions simulate oscillatory response in confined and
unconfined aquifers.
Confined
Confined
Confined
Unconfined

Butler (1998)
Butler-Zhan (2004)
McElwee-Zenner (1998) nonlinear
Springer-Gelhar (1991)

Choose Match>Solution to select a slug test solution.

The Butler-Zhan (2004) solution simulates inertial effects in the test well and
observation wells.

Butler et al. (2003) provide guidelines for performing and analyzing slug tests
in high-K aquifers.

363

Multiwell Slug Test Solutions

You may use any of the slug test solutions in AQTESOLV for the analysis of singlewell slug tests. In addition, AQTESOLV provides the following solutions for multiwell
slug tests in confined, unconfined and fractured aquifers.
Example: Multiwell Slug Test

Confined
Confined
Confined
Unconfined
Fractured

Dougherty-Babu (1984)
KGS Model (1994)
Butler-Zhan (2004) inertial
KGS Model (1994)
Barker-Black (1983)

Choose Match>Solution to select a slug test solution.

Use the Butler-Zhan (2004) solution for cases identified in the slug test
analysis guidelines by Butler (1998) that would require the solution by Chu

364

and Grader (1991), i.e., multiwell slug tests with wellbore storage effects in
observation well(s).

Slug Test Solutions for Wells Screened Across

Water Table
AQTESOLV includes the following slug test solutions for wells screened across the
water table.
Example: Well Screen Across Water Table

Unconfined
Unconfined

Bouwer-Rice (1976)
Dagan (1978)

Choose Match>Solution to select a slug test solution.

365

Nonlinear Slug Test Solutions

The following slug test models account for nonlinear mechanisms including timevarying water column length and turbulent flow in the well.
Confined

McElwee-Zenner (1998)

Choose Match>Solution to select a slug test solution.

A systematic lack of fit by standard linear theory for repeat tests with
different initial displacements is an indication that nonlinear effects may be
important (McElwee and Zenner 1998).

Guidelines for Slug Test Analysis

Overdamped Slug Tests
Butler (1998) developed the following sets of guidelines for overdamped slug tests in
confined and unconfined aquifers:
o

Single-well test in a fully penetrating well in an confined aquifer

Single-well test in a partially penetrating well in an confined aquifer

Single-well test in a well screened below water table in an unconfined aquifer

Single-well test in a well screened across water table in an unconfined aquifer

Underdamped Slug Tests

Butler (1998), Zurbuchen et al. (2002) and Butler et al. (2003) provide guidance for
the analysis of underdamped slug tests.
o

Slug tests in high-K aquifers

366

Confined Aquifers

Hvorslev (1951) Solution for a Slug Test in a

Confined Aquifer
(Match > Solution)
Hvorslev (1951) developed a semi-analytical method for the analysis of an
overdamped slug test in a fully or partially penetrating well in a homogeneous,
anisotropic confined aquifer. The Hvorslev method employs a quasi-steady-state
model that ignores elastic storage in the aquifer.
In cases of noninstantaneous test initiation, apply the translation method of Pandit
and Miner (1986) prior to analyzing the data.
o

Illustration

Equations
Hvorslev (1951) developed an empirical relationship describing the waterlevel response in a confined aquifer due to the instantaneous injection or
withdrawal of water from a well:

where

367

h is displacement at time t [L]

H0 is initial displacement [L]

K, Kr is radial hydraulic conductivity [L/T]

Kz is vertical hydraulic conductivity [L/T]

L is screen length [L]

rc is casing radius [L]

rce is effective casing radius (= rc in confined aquifers) [L]

rw is well radius [L]

rwe is equivalent well radius [L]

t is time [T]

The above equations assume that the well screen does not contact any
impermeable boundaries. When the well screen abuts a confining unit, the
two occurrences of the term 2rwe are replaced by rwe.
For a fully penetrating well, the argument in the logarithmic term of the
governing equation is replaced by 200 (Butler 1998).
Zlotnik (1994) proposed an equivalent well radius (rwe) for a partially
penetrating well in an anisotropic aquifer. Enter the anisotropy ratio in the
aquifer data for the slug test well; the well radius is unchanged when the
anisotropy ratio is set to unity (1.0).
o

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous and of uniform thickness

test well is fully or partially penetrating

aquifer is unconfined

flow to well is quasi-steady-state (storage is negligible)

volume of water, V, is injected into or discharged from the well

instantaneously

Data Requirements

test well measurements (time and displacement)

initial displacement

casing radius and well radius

depth to top of well screen and screen length

368

saturated thickness

porosity of gravel pack for well screened across water table (optional)

hydraulic conductivity anisotropy ratio (for partially penetrating wells)

Estimated Parameters

K (hydraulic conductivity)

y0 (intercept of line on y axis)

Curve Matching Tips

Follow guidelines developed by Butler (1998) for analyzing slug tests.

Choose Match>Visual to perform visual curve matching using the

procedure for straight-line solutions.

For this solution, visual curve matching is often more effective than
automatic matching because you are interested in matching the straight
line to a specific range of data that meet the assumptions of the solution.
To achieve the same effect with automatic curve matching, it would
require the judicious application of weights to ignore observations outside
the desired range.

Choose View>Options and select the Recommended Head Range option

in the Plots tab to superimpose on the plot the head range recommended
by Butler (1998) to obtain the most reliable matching results for solutions
(assuming a steady-state representation of flow for a slug test).

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 unconfined aquifers with completely or partially
penetrating wells, Water Resources Research, vol. 12, no. 3, pp. 423-428.

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.

Zlotnik, V., 1994. Interpretation of slug and packer tests in anisotropic

aquifers, Ground Water, vol. 32, no. 5, pp. 761-766.

Bouwer-Rice (1976) Solution for a Slug Test in

a Confined Aquifer
(Match > Solution)
Bouwer (1989) observed that the Bouwer-Rice (1976) model for a slug test in an
369

unconfined aquifer also could be applied to approximate conditions in confined

aquifers. This is due to the fact that the water-table boundary in an unconfined
aquifer has little effect on slug test response unless the top of the well screen is
positioned close to the boundary.
In cases of noninstantaneous test initiation, apply the translation method of Pandit
and Miner (1986) prior to analyzing the data.
o

Illustration

Equations
Refer to the equations for the Bouwer-Rice (1976) solution which Bouwer
(1989) proposed to use for both confined and unconfined aquifers.
Note that the correction for filter pack porosity only applies to wells screened
across the water table. For the confined variant of the Bouwer-Rice solution,
the filter pack correction is unnecessary.

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous and of uniform thickness

test well is fully or partially penetrating

aquifer is confined

flow to well is quasi-steady-state (storage is negligible)

volume of water, V, is injected into or discharged from the well

instantaneously

370

Data Requirements

test well measurements (time and displacement)

initial displacement

casing radius and well radius

depth to top of well screen and screen length

saturated thickness

hydraulic conductivity anisotropy ratio (for partially penetrating wells)

Estimated Parameters

K (hydraulic conductivity)

y0 (intercept of line on y axis)

Curve Matching Tips

Follow guidelines developed by Butler (1998) for analyzing slug tests.

Choose Match>Visual to perform visual curve matching using the

procedure for straight-line solutions.

For this solution, visual curve matching is often more effective than
automatic matching because you are interested in matching the straight
line to a specific range of data that meet the assumptions of the solution.
To achieve the same effect with automatic curve matching, it would
require the judicious application of weights to ignore observations outside
the desired range.

Choose View>Options and select the Recommended Head Range option

in the Plots tab to superimpose on the plot the head range recommended
by Butler (1998) to obtain the most reliable matching results for solutions
(assuming a steady-state representation of flow for a slug test).

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 unconfined aquifers with completely or partially
penetrating wells, Water Resources Research, vol. 12, no. 3, pp. 423-428.

371

Cooper-Bredehoeft-Papadopulos (1967)
Solution for a Slug Test in a Confined Aquifer
(Match > Solution)
Cooper, Bredehoeft and Papadopulos (1967) derived a fully transient solution for a
slug test in a fully penetrating well in a confined aquifer.
Butler (1998) suggests using the Cooper et al. solution as a screening tool for most
overdamped slug tests in confined and unconfined aquifers with the exception of
wells screened across the water table.
For fully penetrating wells in a confined aquifer, the Cooper et al. solution is identical
to the KGS Model. For partially penetrating wells in a confined aquifer, you may use
either the KGS Model or the Dougherty-Babu (1984) solution.
o

Illustration

Equations
The equations for the Laplace transform solution derived by Cooper,
Bredehoeft and Papadopulos (1967) is as follows:

372

where

is the Laplace transform of h, the head in the well [L]

H0 is the initial displacement in the well [L]

Ki is modified Bessel function of second kind, order i

p is the Laplace transform variable

rc is casing radius [L]

rw is well radius [L]

S is storativity [dimensionless]

t is time [T]

T is transmissivity [L2/T]

If you enter a radius for downhole equipment or select a casing radius

correction, AQTESOLV uses the effective casing radius instead of the
nominal casing radius in the equations for this solution.
o

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous, isotropic and of uniform thickness

test well is fully penetrating

flow to test well is horizontal

aquifer is confined

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

volume of water, V, is injected into or discharged from the well

instantaneously

Data Requirements

test well measurements (time and displacement)

initial displacement

casing radius and well radius

373

downhole equipment radius (optional)

saturated thickness

Estimated Parameters

T (transmissivity)

S (storativity)

Curve Matching Tips

Follow guidelines developed by Butler (1998) for analyzing slug tests.

Choose Match>Visual to perform visual curve matching using the

procedure for type-curve solutions.

Select values of S from the Family and Curve drop-down lists on the
toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

References

Cooper, H.H., J.D. Bredehoeft and S.S. Papadopulos, 1967. Response of a

finite-diameter well to an instantaneous charge of water, Water Resources
Research, vol. 3, no. 1, pp. 263-269.

Dougherty-Babu (1984) Solution for a Slug Test

in a Confined Aquifer
(Match > Solution)
Dougherty and Babu (1984) derived a fully transient analytical solution for an
overdamped slug test in a confined aquifer for fully and partially wells. The solution
simulates water-level response at the test and observation wells and includes
wellbore skin. Based on the work of Moench (1988), we can extend the method to
include anisotropy. The Dougherty-Babu solution also includes delayed response in
an observation well based on the work of Moench (1997).
For fully penetrating wells in a confined aquifer, the Dougherty-Babu solution is
equivalent to the Cooper et al. (1967) solution. For partially penetrating wells in a
confined aquifer without wellbore skin, the Dougherty-Babu solution and KGS Model
are identical.
The Dougherty-Babu solution allows you to analyze data from multiwell slug tests
assuming no wellbore storage in observation wells. Use the Butler-Zhan (2004)
solution if you need to simulate the wellbore storage effect in observation wells.

374

Illustration

Equations
Dougherty and Babu (1984) derived an analytical solution describing the
water-level response due to the instantaneous injection or withdrawal of
water from a fully or partially penetrating well in a homogeneous, isotropic
confined aquifer. Moench extended the method to include anisotropy. The
equation for the Laplace transform solution for head in the test well is as
follows:

The following equation is the Laplace transform solution for dimensionless

drawdown in a piezometer:

The equation for dimensionless drawdown in an observation well is:

375

where

b is aquifer thickness [L]

d is distance from water table to top of pumping well screen [L]

dD is d/b

H0 is initial displacement [L]

K, Kr is radial hydraulic conductivity [L/T]

Kz is vertical hydraulic conductivity [L/T]

376

Ki is modified Bessel function of second kind, order i

l is distance from water table to bottom of pumping well screen [L]

lD is l/b

p is the Laplace transform variable

Q is pumping rate [L3/T]

r is radial distance [L]

rc is casing radius [L]

rw is well radius [L]

Ss is specific storage [1/L]

Sw is wellbore skin factor [dimensionless]

t is time [T]

z is elevation of piezometer above base of aquifer [L]

zD is z/b

z1 is elevation of bottom of observation well screen above base of aquifer

[L]

z1D is z1/b

z2 is elevation of top of observation well screen above base of aquifer [L]

z2D is z2/b

In the Laplace transform solution, Sw is limited to positive values; however,

using the effective well radius concept, we also may simulate a negative
skin (Hurst, Clark and Brauer 1969).
If you enter a radius for downhole equipment, AQTESOLV uses the effective
casing radius instead of the nominal casing radius in the equations for this
solution.
o

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous and of uniform thickness

aquifer potentiometric surface is initially horizontal

test and observation wells are fully or partially penetrating

aquifer is confined

flow is unsteady

377

water is released instantaneously from storage with decline of hydraulic

head

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

instantaneously

Data Requirements

test well measurements (time and displacement)

initial displacement

casing radius and well radius

saturated thickness

well depth and screen length

Estimated Parameters

T (transmissivity)

S (storativity)

Kz/Kr (hydraulic conductivity anisotropy ratio)

Sw (dimensionless wellbore skin factor)

Curve Matching Tips

Follow guidelines developed by Butler (1998) for analyzing slug tests.

Choose Match>Visual to perform visual curve matching using the

procedure for type-curve solutions.

Select values of Ss, Kz/Kr and Sw from the Family and Curve drop-down
lists on the toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

References

Dougherty, D.E and D.K. Babu, 1984. Flow to a partially penetrating well
in a double-porosity reservoir, Water Resources Research, vol. 20, no. 8,
pp. 1116-1122.

Moench, A.F., 1988. The response of partially penetrating wells to

pumpage from double-porosity aquifers, Proceedings of the International
Conference on Fluid Flow in Fractured Rocks, Atlanta, GA, May 16-18,
1988.

378

Hyder et al. (1994) Solution for a Slug Test in a

Confined Aquifer (KGS Model)
(Match > Solution)
Hyder et al. (1994) developed a fully transient model, also known as the KGS
Model, for an overdamped slug test in a confined aquifer for fully and partially
penetrating wells. The solution simulates water-level response at the test and
observation wells and includes a skin zone of finite thickness enveloping the test
well.
For fully penetrating wells in a confined aquifer, the KGS Model is equivalent to the
Cooper et al. (1967) solution. For partially penetrating wells in a confined aquifer
without wellbore skin, the KGS Model and the Dougherty-Babu (1984) solution are
identical.
The KGS Model allows you to analyze data from multiwell slug tests assuming no
wellbore storage in observation wells. Use the Butler-Zhan (2004) solution if you
need to simulate the wellbore storage effect in observation wells.
When you choose a solution, AQTESOLV provides two configurations for simulating a
slug test with the KGS Model. One configuration omits the well skin and the other
includes it.
o

Illustration

Equations
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 withdrawal of water from a fully or partially penetrating well in a
homogeneous, anisotropic confined aquifer. The equation for the Laplace

379

transform solution for head in the test well is as follows:

380

where

the subscript i = 1, 2 refers to the aquifer and well skin, respectively

d is depth to top of well screen [L]

I is modified Bessel function of first kind, order i

Kr is radial hydraulic conductivity [L/T]

Kz is vertical hydraulic conductivity [L/T]

Ki is modified Bessel function of second kind, order i

L is screen length [L]

p is the Laplace transform variable

r is radial distance [L]

rc is casing radius [L]

rsk is well skin radius [L]

rw is well radius [L]

Ss is specific storage [1/L]

z is depth below top of aquifer [L]

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous and of uniform thickness

aquifer potentiometric surface is initially horizontal

test and observation wells are fully or partially penetrating

aquifer is confined

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

381

head

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

instantaneously

Data Requirements

test and observation well measurements (time and displacement)

initial displacement

casing radius, well radius and outer radius of well skin for test well

saturated thickness

well depth and screen length

Estimated Parameters

Kr (radial hydraulic conductivity in aquifer)

Ss (specific storage in aquifer)

Kz/Kr (anisotropy ratio in aquifer)

Kr' (radial hydraulic conductivity in skin)

Ss' (specific storage in skin)

Kz/Kr' (anisotropy ratio in skin)

Curve Matching Tips

Follow guidelines developed by Butler (1998) for analyzing slug tests.

Choose Match>Visual to perform visual curve matching using the

procedure for type-curve solutions.

Select values of Ss and Kz/Kr from the Family and Curve drop-down lists
on the toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

References

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

382

Butler (1998) Solution for a Slug Test in a

Confined Aquifer
(Match > Solution)
Butler (1998) extended the Hvorslev (1951) solution for a single-well slug test in a
homogeneous, anisotropic confined aquifer to include inertial effects in the test well.
The solution accounts for oscillatory water-level response sometimes observed in
aquifers of high hydraulic conductivity. Butler (2002) amended the method to
incorporate frictional well loss in small-diameter wells.
The Butler solution predicts the theoretical change in water level in the test well;
however, McElwee (2001) and Zurbuchen et al. (2002) have noted that transducer
readings vary with depth and thus may not accurately measure the water-level
position. Butler et al. (2003) recommend placing the transducer close to the static
water surface in the well to avoid this problem.
o

Illustration

Equations
The Butler (1998) solution accounts for underdamped (oscillatory) water-level
response sometimes observed in aquifers of high hydraulic conductivity:

383

where

g is gravitational acceleration [L/T2]

H0 is initial displacement [L]

Kr is radial hydraulic conductivity [L/T]

Kz is vertical hydraulic conductivity [L/T]

L is screen length [L]

Le is effective water column length [L]

rc is casing radius [L]

rw is well radius [L]

s is displacement [L]

t is time [T]

If you enter a radius for downhole equipment, AQTESOLV uses the effective
casing radius instead of the nominal casing radius in the equations for this
solution.

384

In the foregoing equations, the dimensionless damping factor, CD, is termed

critically damped when its value equals 1. Certain publications (e.g., Butler
1998) use an alternate convention in which the equations are critically
damped when CD equals 2. In cases where the well screen abuts an
impermeable boundary, the two occurrences of terms 2 are replaced by .
Butler (2002) modified the definition of CD to include frictional well loss:

where

is length of water column above top of well screen [L]

is kinematic viscosity [L2/T]

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous and of uniform thickness

test well is partially penetrating

aquifer is confined

flow is quasi-steady state

volume of water, V, is injected into or discharged from the well

instantaneously

Data Requirements

test well measurements (time and displacement)

initial displacement

static water column height

casing radius and well radius

depth to top of well screen and screen length

saturated thickness

hydraulic conductivity anisotropy ratio

kinematic viscosity of water (optional)

gravitational acceleration constant (optional)

385

Estimated Parameters

K (hydraulic conductivity)

Le (effective water column length in test well)

For reference, AQTESOLV also displays the parameter L (theoretical effective

water column length) determined from well geometry data. One normally
expects Le to be close to the value of L.
o

Curve Matching Tips

Choose Match>Visual to perform visual curve matching using the

procedure for type-curve solutions. Move the mouse up and down to
adjust the amplitude of the curve. Move the mouse left and right to adjust
the period.

Select values of Le from the Family and Curve drop-down lists on the
toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

When performing automatic curve matching, save time by setting weights

to zero for any observations that have recovered to static near the end of
the test.

Choose View>Options to change the critically damped value of

dimensionless damping factor, C(D) (i.e., 1 or 2).

References

Butler, J.J., Jr., 1998. The Design, Performance, and Analysis of Slug
Tests, Lewis Publishers, Boca Raton, 252p.

Butler, J.J., Jr., 2002. A simple correction for slug tests in small-diameter
wells, Ground Water, vol. 40, no. 3, pp. 303-307.

Butler, J.J., Jr., Garnett, E.J. and J.M. Healey, 2003. Analysis of slug tests
in formations of high hydraulic conductivity, Ground Water, vol. 41, no. 5,
pp. 620-630.

McElwee, C.D., Butler, J.J., Jr. and G.C. Bohling, 1992. Nonlinear analysis
of slug tests in highly permeable aquifers using a Hvorslev-type approach,
Kansas Geol. Survey Open-File Report 92-39.

Zlotnik, V.A. and V.L. McGuire, 1998. Multi-level slug tests in highly
permeable formations: 1. Modifications of the Springer-Gelhar (SG)
model, Jour. of Hydrol., no. 204, pp. 271-282.

Zurbuchen, B. R., V.A. Zlotnik and J.J. Butler, Jr., 2002. Dynamic
interpretation of slug tests in highly permeable aquifers, Water Resources
Research, vol. 38, no. 3., 1025, doi:10.1029/2001WRR000354.

386

Butler-Zhan (2004) Solution for a Slug Test in a

Confined Aquifer
(Match > Solution)
Butler and Zhan (2004) derived an analytical solution for a slug test in fully or
partially penetrating wells in a confined high-K aquifer that accounts for frictional
loss in small-diameter wells and inertial effects in the test and observation wells. The
Butler-Zhan solution allows you to analyze data from underdamped or overdamped
single- or multi-well slug tests.
McElwee (2001) and Zurbuchen et al. (2002) have noted that transducer readings
vary with depth in the well and thus may not accurately measure the water-level
position. Butler et al. (2003) recommend placing the transducer close to the static
water surface in the well to avoid this problem. If the transducer depth is below the
top of the well screen, AQTESOLV uses the Butler-Zhan solution to compute the head
in the well screen.
Use the Butler-Zhan solution when you need to simulate the wellbore storage effect
in observation wells. If wellbore storage is not present in the observation wells (e.g.,
through the use of a packer and transducer), you may choose the KGS Model for
multiwell tests.
In the guidelines by Butler (1998) for the analysis of multiwell slug tests, you may
substitute the more versatile Butler-Zhan solution for the Chu and Grader (1991)
method.
When you choose a solution, AQTESOLV provides two configurations for simulating
inertial effects in a slug test with the Butler-Zhan solution. Both configurations allow
you to analyze data from the test well and observation wells.

Test well includes the inertial effect in the test well only.

All wells includes inertial effects in both test and observation wells.

387

Illustration

Equations
Butler and Zhan (2004) derived an analytical solution for a single- or multiwell slug test in fully or partially penetrating wells in a confined high-K
aquifer that accounts for frictional loss in small-diameter wells and inertial
effects in the test and observation wells.
Assuming inertial effect in only the test well, the Laplace transform solutions
for dimensionless head in the well, screen and aquifer are as follows:

388

389

where

b is test well screen length [L]

B is aquifer thickness [L]

d is depth to top of test well screen [L]

g is gravitational acceleration constant [L/T2]

h(r,z,t) is displacement in aquifer [L]

hs(z,t) is displacement in test well screen [L]

H(t) is displacement in test well [L]

H0 is initial displacement in test well [L]

H'0 is initial water-level velocity due to test initiation [L]

Kr is radial hydraulic conductivity [L/T]

Kz is vertical hydraulic conductivity [L/T]

Ki is modified Bessel function of second kind, order i

is length of static water column above top of test well screen [L]

Le is effective water column length in test well [L]

p is the Laplace transform variable

Q0 is normalizing parameter, = H0 for a slug test [L]

r is radial distance from center of test well [L]

rc is test well casing radius [L]

rw is test well radius [L]

Ss is specific storage [1/L]

t is time [T]

390

is kinematic viscosity of water [L2/T]

z is vertical coordinate [L]

Ordinarily, AQTESOLV computes the water level change in the test well, H(t);
however, the program computes the head in the test well screen, hs(z,t) if
the transducer depth is below the top of the well screen.
Taking into account inertial effect in the observation well, the Laplace
transform solutions for dimensionless water level in the observation well,
head in the observation well screen and head in the aquifer are as follows:

391

where

bo is test well screen length [L]

do is depth to top of test well screen [L]

ho(r,z,t) is displacement in aquifer due to perturbation in observation well

[L]

hso(z,t) is displacement in observation well screen due to perturbation in

observation well [L]

is length of static water column above top of observation well screen

[L]

Leo is effective water column length in observation well [L]

ro is radial distance from center of observation well [L]

rco is observation well casing radius [L]

rwo is observation well radius [L]

Wo(t) is displacement in observation well [L]

If you enter a radius for downhole equipment, AQTESOLV uses the effective
casing radius instead of the nominal casing radius in the equations for this
solution.
o

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous and of uniform thickness

test well is fully or partially penetrating

aquifer is confined
392

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

volume of water, V, is injected into or discharged from the well

instantaneously

Data Requirements

test and observation well measurements (time and displacement)

initial displacement

static water column height

casing radius and well radius

depth to top of well screen and screen length

saturated thickness

hydraulic conductivity anisotropy ratio

kinematic viscosity of water (optional)

gravitational acceleration constant (optional)

Estimated Parameters

K (hydraulic conductivity)

Ss (specific storage)

Kz/Kr (anisotropy ratio)

Le (effective water column length in test well)

Le(o) (effective water column length in observation well)

For reference, AQTESOLV also displays the parameters L and L(o) (see
equations) determined from well geometry data. One normally expects Le
and Le(o) to be close to the values of L and L(o).
o

Curve Matching Tips

Use the Butler (1998) solution to obtain preliminary estimates of aquifer

properties.

Choose Match>Visual to perform visual curve matching using the

procedure for type-curve solutions.

Select values of Ss from the Family and Curve drop-down lists on the
toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis. When performing visual curve matching with this tool, first tweak

393

the values of Le and Le(o) to align the peaks of the curve(s) with the
data. Next, adjust the value of Kr to match the amplitude of the curve(s)
with the data.

Change the convergence level for this solution to enhance visual curve
matching.

Use the curve resolution settings to optimize performance for specific

tasks such as visual curve matching or printing report graphics.

When performing automatic curve matching, save time by setting weights

to zero for any observations that have recovered to static near the end of
the test.

Convergence Settings

Choose Match>Toolbox and click Options to select convergence levels for

this solution.

The default level (1) applies convergence settings given in a program by

Butler and Zhan.

Select a faster setting to enhance visual curve matching.

References

Butler, J.J., Jr. and X. Zhan, 2004. Hydraulic tests in highly permeable
aquifers, Water Resources Research, vol. 40, W12402,
doi:10.1029/2003WR002998.

Butler, J.J., Jr., Garnett, E.J. and J.M. Healey, 2003. Analysis of slug tests
in formations of high hydraulic conductivity, Ground Water, vol. 41, no. 5,
pp. 620-630.

McElwee, C.D., Butler, J.J., Jr. and G.C. Bohling, 1992. Nonlinear analysis
of slug tests in highly permeable aquifers using a Hvorslev-type approach,
Kansas Geol. Survey Open-File Report 92-39.

Zurbuchen, B. R., V.A. Zlotnik and J.J. Butler, Jr., 2002. Dynamic
interpretation of slug tests in highly permeable aquifers, Water Resources
Research, vol. 38, no. 3., 1025, doi:10.1029/2001WRR000354.

Peres-Onur-Reynolds (1989) Solution for a

Slug Test in a Confined Aquifer
(Match > Solution)
Peres, Onur and Reynolds (1989) derived a fully transient solution for a slug test in a
fully penetrating well in a confined aquifer. The Peres et al. method is based on an
exact equation for transforming slug test data into equivalent head data for a
constant-rate pumping test with wellbore storage and skin effect. Through the use of
an approximate deconvolution technique, the method further eliminates wellbore

394

storage from the transformed equivalent head data, thereby making it possible to
analyze the equivalent heads using the Cooper-Jacob solution for a constant-rate
pumping test.
The Peres et al. method can be advantageous in determining the hydraulic
conductivity of an aquifer when nonideal conditions exist near the well (e.g., wellbore
skin). To use the method effectively, Butler (1998) recommends taking
measurements at closely spaced intervals and running the slug test to complete
recovery.
o

Illustration

Equations
The equations for the approximate deconvolution solution derived by Peres,
Onur and Reynolds (1989) is as follows:

where

H0 is the initial displacement due to slug test in well [L]

395

H(t) is displacement due to slug test at time t [L]

s is equivalent drawdown for a constant-rate pumping test with wellbore

storage [T]

is equivalent drawdown for a constant-rate pumping test with wellbore

storage removed [T]

versus time, one can determine the

By matching a straight line to a plot of
transmissivity of the aquifer using modified versions of the familiar CooperJacob equations for a constant-rate pumping test as follows:

where

is change in

over one log cycle [T]

rc is effective casing radius corrected for downhole equipment [L]

rw is well radius [L]

S is storativity [dimensionless]

t is time [T]

t0 is intercept of line on time axis [T]

T is transmissivity [L2/T]

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous, isotropic and of uniform thickness

test well is fully penetrating

flow to test well is horizontal

aquifer is confined

flow is unsteady

396

water is released instantaneously from storage with decline of hydraulic

head

volume of water, V, is injected into or discharged from the well

instantaneously

Data Requirements

test well measurements (time and displacement)

initial displacement

casing radius and well radius

downhole equipment radius (optional)

saturated thickness

Estimated Parameters

T (transmissivity)

S (storativity)

Curve Matching Tips

Follow guidelines developed by Butler (1998) for analyzing slug tests.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

References

Peres, A.M., Onur, M. and A.C. Reynolds, 1989. A new analysis procedure
for determining aquifer properties from slug test data, Water Resources
Research, vol. 25, no. 7, pp. 1591-1602.

McElwee-Zenner (1998) Solution for a Slug

Test in a Confined Aquifer
(Match > Solution)
McElwee and Zenner (1998) developed a model for a single-well slug test in a
homogeneous confined aquifer that includes various nonlinear mechanisms including
time-dependent water column length and turbulent flow in the well. The solution
accounts for the complete range of water-level response from overdamped to
underdamped.
The McElwee-Zenner (1998) solution predicts the theoretical change in water level in
the test well; however, McElwee (2001) noted that transducer readings vary with
397

depth and thus may not accurately measure the water-level position. The McElweeZenner solution includes a correction for transducer depth. Alternatively, Butler et al.
(2003) recommend placing the transducer close to the static water surface in the
well to circumvent this problem.
o

Illustration

Equations
The McElwee-Zenner (1998) solution accounts for overdamped and
underdamped (oscillatory) water-level response from a slug test in a
confined aquifer:

where

a is acceleration of water column [L/T2]

A is a nonlinear parameter related to velocities in the well [dimensionless]

398

is a correction parameter related to the effective length of the water

column in the well [L]

Hvorslev form factor [dimensionless]

g is gravitational acceleration [L/T2]

h, h(t) is head (displacement) in well [L]

h(t)' is the apparent head in the well measured by transducer [L]

H0 is initial displacement [L]

Kr is radial hydraulic conductivity [L/T]

Kz is vertical hydraulic conductivity [L/T]

L is screen length [L]

rc is casing radius [L]

rw is well radius [L]

t is time [T]

v is water column velocity [L/T]

Z0 is the static height of the water column above the top of the well
screen [L]

Zs is transducer depth below static water surface [L]

The McElwee-Zenner solution uses the Hvorslev model to describe flow

between the well and the aquifer. The Hvorslev solution is a quasi-steadystate model that neglects storage in the aquifer. Like the Hvorslev model,
2rwe replaces each occurrence of rwe in the definition of F when the well
screen abuts an impermeable boundary.
If you enter a radius for downhole equipment, AQTESOLV uses the effective
casing radius instead of the nominal casing radius in the equations for this
solution.
McElwee and Zenner (1998) defined the following Reynolds number for flow in
the well:

where

r is packer or casing radius [L]

Re is Reynolds number [dimensionless]

v is velocity [L/T]

399

is kinematic viscosity [L2/T]

For turbulent flow, the parameter A relates frictional forces to the square of
velocities in the well. In the McElwee-Zenner model, flow is deemed
turbulent when Re 3400. Under turbulent conditions, A is assumed to equal
a constant when a packer is present (i.e., rp > 0). In the absence of a
packer, A is a function of the wetted length of borehole (static water column
length above the top of the well screen).
When Re < 3400, the McElwee-Zenner model assumes flow is laminar. The
value of A is set to zero and the model adds a term representing frictional
(viscous) loss in the well:

where

FL is frictional loss [L]

FL equals zero when flow is turbulent.

The McElwee-Zenner solution is solved using a finite-difference algorithm
(McElwee 2001).
o

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous and of uniform thickness

test well is partially penetrating

aquifer is confined

flow is quasi-steady state

volume of water, V, is injected into or discharged from the well

instantaneously

Data Requirements

test well measurements (time and displacement)

initial displacement

static water column height

casing radius and well radius

equipment radius and packer radius (optional)

depth to top of well screen and screen length

saturated thickness

400

hydraulic conductivity anisotropy ratio

kinematic viscosity of water (optional)

gravitational acceleration constant (optional)

Estimated Parameters

K (hydraulic conductivity)

(correction for water column length in test well)

A (nonlinear flow parameter)

v(0) (initial velocity in well)

Curve Matching Tips

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

When performing automatic curve matching, save time by using a match

window or setting weights to zero for any observations that have
recovered to static near the end of the test.

References

McElwee, C.D. and M. Zenner, 1998. A nonlinear model for analysis of

slug-test data, Water Resources Research, vol. 34, no. 1, pp. 55-66.

McElwee, C.D., 2001. Application of a nonlinear slug test model, Ground

Water, vol. 39, no. 5, pp. 737-744.

401

Unconfined Aquifers

Bouwer-Rice (1976) Solution for a Slug Test in

an Unconfined Aquifer
(Match > Solution)
Bouwer and Rice (1976) developed a semi-analytical method for the analysis of an
overdamped slug test in a fully or partially penetrating well in an unconfined aquifer.
The Bouwer-Rice method employs a quasi-steady-state model that ignores elastic
storage in the aquifer.
In cases of noninstantaneous test initiation, apply the translation method of Pandit
and Miner (1986) prior to analyzing the data.
If the test well is screened across the water table, you may apply an optional
correction for the effective porosity of the filter pack. When the test well is fully
submerged (i.e., screened below the water table) or the aquifer is confined, the
correction is unnecessary.
o

Illustration

Equations
Bouwer and Rice (1976) developed an empirical relationship describing the
water-level response in an unconfined aquifer due to the instantaneous
injection or withdrawal of water from a well:

402

where

h is displacement at time t [L]

H0 is initial displacement [L]

K, Kr is radial hydraulic conductivity [L/T]

Kz is vertical hydraulic conductivity [L/T]

L is screen length [L]

ne is filter pack effective porosity [dimensionless]

rc is nominal casing radius [L]

rce is effective casing radius (= rc when well screen is fully submerged) [L]

re is external radius [L]

rw is well radius [L]

rwe is equivalent well radius [L]

t is time [T]

The term ln(re/rwe) is an empirical quantity that accounts for well geometry
(Bouwer and Rice 1976).
Zlotnik (1994) proposed an equivalent well radius (rwe) for a partially
penetrating well in an anisotropic aquifer. Enter the anisotropy ratio in the
aquifer data for the slug test well; the well radius is unchanged when the
anisotropy ratio is set to unity (1.0).
o

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous and of uniform thickness

test well is fully or partially penetrating

aquifer is unconfined

flow to well is quasi-steady-state (storage is negligible)

volume of water, V, is injected into or discharged from the well

instantaneously

Data Requirements

test well measurements (time and displacement)

initial displacement

403

casing radius and well radius

depth to top of well screen and screen length

saturated thickness

porosity of gravel pack for well screened across water table (optional)

hydraulic conductivity anisotropy ratio (for partially penetrating wells)

Estimated Parameters

K (hydraulic conductivity)

y0 (intercept of line on y axis)

Curve Matching Tips

Follow guidelines developed by Butler (1998) for analyzing slug tests.

Choose Match>Visual to perform visual curve matching using the

procedure for straight-line solutions.

For this solution, visual curve matching is often more effective than
automatic matching because you are interested in matching the straight
line to a specific range of data that meet the assumptions of the solution.
To achieve the same effect with automatic curve matching, it would
require the judicious application of weights to ignore observations outside
the desired range.

Choose View>Options and select the Recommended Head Range option

in the Plots tab to superimpose on the plot the head range recommended
by Butler (1998) to obtain the most reliable matching results for solutions
(assuming a steady-state representation of flow for a slug test).

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 unconfined aquifers with completely or partially
penetrating wells, Water Resources Research, vol. 12, no. 3, pp. 423-428.

Zlotnik, V., 1994. Interpretation of slug and packer tests in anisotropic

aquifers, Ground Water, vol. 32, no. 5, pp. 761-766.

Hvorslev (1951) Solution for a Slug Test in an

Unconfined Aquifer
(Match > Solution)
For slug tests in an unconfined aquifer, the preferred quasi-steady-state method is
404

the Bouwer-Rice (1976) solution; however, Bouwer (1989) observed that the watertable boundary in an unconfined aquifer has little effect on slug test response unless
the top of the well screen is positioned close to the boundary. Thus, in many cases,
we may apply the Hvorslev (1951) solution for confined aquifers to approximate
unconfined conditions when the well screen is below the water table.
In cases of noninstantaneous test initiation, apply the translation method of Pandit
and Miner (1986) prior to analyzing the data.
o

Illustration

Equations
Refer to the equations for the Hvorslev (1951) solution for a confined aquifer.
For the unconfined variant of the Hvorslev solution, AQTESOLV applies the
correction for filter pack porosity for wells screened across the water table.
For the confined Hvorslev solution, the filter pack correction is unnecessary.

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous and of uniform thickness

test well is fully or partially penetrating

aquifer is confined

flow to well is quasi-steady-state (storage is negligible)

volume of water, V, is injected into or discharged from the well

instantaneously

405

Data Requirements

test well measurements (time and displacement)

initial displacement

casing radius and well radius

depth to top of well screen and screen length

saturated thickness

hydraulic conductivity anisotropy ratio (for partially penetrating wells)

Estimated Parameters

K (hydraulic conductivity)

y0 (intercept of line on y axis)

Curve Matching Tips

Follow guidelines developed by Butler (1998) for analyzing slug tests.

Choose Match>Visual to perform visual curve matching using the

procedure for straight-line solutions.

For this solution, visual curve matching is often more effective than
automatic matching because you are interested in matching the straight
line to a specific range of data that meet the assumptions of the solution.
To achieve the same effect with automatic curve matching, it would
require the judicious application of weights to ignore observations outside
the desired range.

Choose View>Options and select the Recommended Head Range option

in the Plots tab to superimpose on the plot the head range recommended
by Butler (1998) to obtain the most reliable matching results for solutions
(assuming a steady-state representation of flow for a slug test).

References

Bouwer, H., 1989. The Bouwer and Rice slug test--an update, Ground
Water, vol. 27, no. 3, pp. 304-309.

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.

Dagan (1978) Solution for a Slug Test in an

Unconfined Aquifer
(Match > Solution)

406

Dagan (1978) developed a semi-analytical method for an overdamped slug test in a

well screened across the water table in a homogeneous, anisotropic unconfined
aquifer. Like the Bouwer-Rice and Hvorslev models, the Dagan method employs a
quasi-steady-state model that ignores elastic storage in the aquifer.
In cases of noninstantaneous test initiation, apply the translation method of Pandit
and Miner (1986) prior to analyzing the data.
For wells screened across the water table, you may apply an optional correction for
the effective porosity of the filter pack.
o

Illustration

Equations
Dagan (1978) developed semi-analytical method to predict the water-level
response due to the instantaneous injection or withdrawal of water from a
well screened across the water table in an unconfined aquifer:

where

h is displacement at time t [L]

H0 is initial displacement [L]

K, Kr is radial hydraulic conductivity [L/T]

407

L is screen length [L]

ne is filter pack effective porosity [dimensionless]

P is dimensionless flow parameter

rc is casing radius [L]

rce is equivalent casing radius [L]

rw is well radius including filter pack [L]

t is time [T]

The term P is a shape factor that depends on well geometry and hydraulic
conductivity anisotropy. Values of P are available in Dagan (1978), Boast
and Kirkham (1971) and Butler (1998). AQTESOLV uses a table look-up
procedure to find appropriate values of P.
o

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous and of uniform thickness

test well is partially penetrating

aquifer is unconfined

flow to well is quasi-steady-state (storage is negligible)

volume of water, V, is injected into or discharged from the well

instantaneously

Data Requirements

test well measurements (time and displacement)

initial displacement

casing radius and well radius

depth to top of well screen and screen length

saturated thickness

porosity of gravel pack for well screened across water table (optional)

hydraulic conductivity anisotropy ratio

Estimated Parameters

K (hydraulic conductivity)

y0 (intercept of line on y axis)

Curve Matching Tips

408

Follow guidelines developed by Butler (1998) for analyzing slug tests.

Choose Match>Visual to perform visual curve matching using the

procedure for straight-line solutions.

For this solution, visual curve matching is often more effective than
automatic matching because you are interested in matching the straight
line to a specific range of data that meet the assumptions of the solution.
To achieve the same effect with automatic curve matching, it would
require the judicious application of weights to ignore observations outside
the desired range.

Choose View>Options and select the Recommended Head Range option

in the Plots tab to superimpose on the plot the head range recommended
by Butler (1998) to obtain the most reliable matching results for solutions
(assuming a steady-state representation of flow for a slug test).

References

Boast, C.W. and D. Kirkham, 1971. Auger hole seepage theory, Soil
Science of America Proceedings, vol. 35, no. 3, pp. 365-373.

Bouwer, H. and R.C. Rice, 1976. A slug test method for determining
hydraulic conductivity of unconfined aquifers with completely or partially
penetrating wells, Water Resources Research, vol. 12, no. 3, pp. 423-428.

Butler, J.J., Jr., 1998. The Design, Performance, and Analysis of Slug
Tests, Lewis Publishers, Boca Raton, 252p.

Dagan, G., 1978. A note on packer, slug, and recovery tests in unconfined
aquifers, Water Resources Research, vol. 14, no. 5. pp. 929-934.

Hyder et al. (1994) Solution for a Slug Test in

an Unconfined Aquifer (KGS Model)
(Match > Solution)
Hyder et al. (1994) developed a fully transient model, also known as the KGS
Model, for an overdamped slug test in an unconfined aquifer for fully and partially
penetrating wells. The solution simulates water-level response at the test and
observation wells and includes a skin zone of finite thickness enveloping the test
well. The KGS Model allows you to analyze data from multiwell slug tests.
When you choose a solution, AQTESOLV provides two configurations for simulating a
slug test with the KGS Model. One configuration omits the well skin and the other
includes it.

409

Illustration

Equations
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 withdrawal of water from a fully or partially penetrating well in
an unconfined aquifer. The equation for the Laplace transform solution for
head in the test well is as follows:

410

where

the subscript i = 1, 2 refers to the aquifer and well skin, respectively

d is depth to top of well screen [L]

Ii is modified Bessel function of first kind, order i

Kr is radial hydraulic conductivity [L/T]

Kz is vertical hydraulic conductivity [L/T]

Ki is modified Bessel function of second kind, order i

L is screen length [L]

411

p is the Laplace transform variable

r is radial distance [L]

rc is casing radius [L]

rsk is well skin radius [L]

rw is well radius [L]

Ss is specific storage [1/L]

z is depth below top of aquifer [L]

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous and of uniform thickness

aquifer potentiometric surface is initially horizontal

test and observation wells are fully or partially penetrating

aquifer is unconfined

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

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

instantaneously

Data Requirements

test and observation well measurements (time and displacement)

initial displacement

casing radius, well radius and outer radius of well skin for test well

saturated thickness

well depth and screen length

Estimated Parameters

Kr (radial hydraulic conductivity in aquifer)

Ss (specific storage in aquifer)

Kz/Kr (anisotropy ratio in aquifer)

Kr' (radial hydraulic conductivity in skin)

Ss' (specific storage in skin)

412

Kz/Kr' (anisotropy ratio in skin)

Curve Matching Tips

Follow guidelines developed by Butler (1998) for analyzing slug tests.

Choose Match>Visual to perform visual curve matching using the

procedure for type-curve solutions.

Select values of Ss and Kz/Kr from the Family and Curve drop-down lists
on the toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

References

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

Springer-Gelhar (1991) Solution for a Slug Test

in an Unconfined Aquifer
(Match > Solution)
Springer and Gelhar (1991) extended the Bouwer-Rice (1976) solution for a slug test
in a homogeneous, anisotropic unconfined aquifer to include inertial effects in the
test well. The solution accounts for oscillatory water-level response sometimes
observed in aquifers of high hydraulic conductivity. Based on the work of Butler
(2002), we also incorporate frictional well loss in small-diameter wells.
The Springer-Gelhar solution predicts the theoretical change in water level in the test
well; however, McElwee (2001) and Zurbuchen et al. (2002) have noted that
transducer readings vary with depth and thus may not accurately measure the
water-level position. Butler et al. (2003) recommend placing the transducer close to
the static water surface in the well to avoid this problem.

413

Illustration

Equations
The Springer-Gelhar (1991) solution accounts for underdamped (oscillatory)
water-level response sometimes observed in aquifers of high hydraulic
conductivity:

414

where

g is gravitational acceleration [L/T2]

H0 is initial displacement [L]

Kr is radial hydraulic conductivity [L/T]

Kz is vertical hydraulic conductivity [L/T]

L is screen length [L]

Le is effective water column length [L]

rc is casing radius [L]

rw is well radius [L]

s is displacement [L]

t is time [T]

The term ln(re/rw) is an empirical quantity that accounts for well geometry
(Bouwer and Rice 1976).
In the foregoing equations, the dimensionless damping factor, CD, is termed
critically damped when its value equals 1. Certain publications (e.g., Butler
1998) use an alternate convention in which the equations are critically
damped when CD equals 2.
Butler (2002) modified the definition of CD to include frictional well loss:

where

is length of water column above top of well screen [L]

is kinematic viscosity [L2/T]

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous and of uniform thickness

415

test well is fully or partially penetrating

aquifer is unconfined

flow is quasi-steady state

volume of water, V, is injected into or discharged from the well

instantaneously

Data Requirements

test well measurements (time and displacement)

initial displacement

static water column height

casing radius and well radius

depth to top of well screen and screen length

saturated thickness

hydraulic conductivity anisotropy ratio

kinematic viscosity of water (optional)

gravitational acceleration constant (optional)

Estimated Parameters

K (hydraulic conductivity)

Le (effective water column length in test well)

For reference, AQTESOLV also displays the parameter L (theoretical effective

water column length) determined from well geometry data. One normally
expects Le to be close to the value of L.
o

Curve Matching Tips

Choose Match>Visual to perform visual curve matching using the

procedure for type-curve solutions. Move the mouse up and down to
adjust the amplitude of the curve. Move the mouse left and right to adjust
the period.

Select values of Le from the Family and Curve drop-down lists on the
toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

When performing automatic curve matching, save time by setting weights

to zero for any observations that have recovered to static near the end of
the test.

Choose View>Options to change the critically damped value of

416

dimensionless damping factor, C(D) (i.e., 1 or 2).

o

References

Springer, R.K. and L.W. Gelhar, 1991. Characterization of large-scale

aquifer heterogeneity in glacial outwash by analysis of slug tests with
oscillatory response, Cape Cod, Massachusetts, U.S. Geol. Surv. Water
Res. Invest. Rep. 91-4034, pp. 36-40.

Bouwer, H. and R.C. Rice, 1976. A slug test method for determining
hydraulic conductivity of unconfined aquifers with completely or partially
penetrating wells, Water Resources Research, vol. 12, no. 3, pp. 423-428.

Butler, J.J., Jr., 1998. The Design, Performance, and Analysis of Slug
Tests, Lewis Publishers, Boca Raton, 252p.

Butler, J.J., Jr., 2002. A simple correction for slug tests in small-diameter
wells, Ground Water, vol. 40, no. 3, pp. 303-307.

Butler, J.J., Jr., Garnett, E.J. and J.M. Healey, 2003. Analysis of slug tests
in formations of high hydraulic conductivity, Ground Water, vol. 41, no. 5,
pp. 620-630.

McElwee, C.D., Butler, J.J., Jr. and G.C. Bohling, 1992. Nonlinear analysis
of slug tests in highly permeable aquifers using a Hvorslev-type approach,
Kansas Geol. Survey Open-File Report 92-39.

Zlotnik, V.A. and V.L. McGuire, 1998. Multi-level slug tests in highly
permeable formations: 1. Modifications of the Springer-Gelhar (SG)
model, Jour. of Hydrol., no. 204, pp. 271-282.

Zurbuchen, B. R., V.A. Zlotnik and J.J. Butler, Jr., 2002. Dynamic
interpretation of slug tests in highly permeable aquifers, Water Resources
Research, vol. 38, no. 3., 1025, doi:10.1029/2001WRR000354.

417

Fractured Aquifers

Barker-Black (1983) Solution for a Slug Test in

a Fractured Aquifer
(Match > Solution)
Barker and Black (1983) derived an analytical solution for a slug test in a well that
fully penetrates an isotropic fractured aquifer assuming a double-porosity model with
slab-shaped matrix blocks.
o

Illustration

Equations
Barker and Black (1983) derived an analytical solution for a slug test in a well
that fully penetrates an isotropic fractured aquifer assuming a doubleporosity model with slab-shaped matrix blocks.
The Laplace transform solution for drawdown as follows:

418

where

d is one-half thickness of slab blocks [L]

H0 is initial displacement [L]

K' is matrix hydraulic conductivity [L/T]

Ki is modified Bessel function of second kind, order i

n is the number of horizontal fractures in the aquifer

p is the Laplace transform variable

r is radial distance [L]

rc is casing radius [L]

rw is well radius [L]

S is fracture storativity [dimensionless]

Ss' is matrix specific storage [1/L]

t is time [T]

T is fissure transmissivity [L2/T]

AQTESOLV computes n = aquifer thickness / slab block thickness.

If you enter a radius for downhole equipment, AQTESOLV uses the effective
casing radius instead of the nominal casing radius in the equations for this
solution.
o

Assumptions

aquifer has infinite areal extent

aquifer has uniform thickness

419

test well is fully penetrating

flow to test well is horizontal

aquifer is confined with double porosity

matrix blocks are slab shaped

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

volume of water, V, is injected into or discharged from the well

instantaneously

Data Requirements

test and observation well locations

test and observation well measurements (time and displacement)

casing radius and wellbore radius for test well

saturated thickness

thickness of slab blocks

Estimated Parameters

T (fracture transmissivity)

S (fracture storativity)

K' (matrix hydraulic conductivity)

Ss' (matrix specific storage)

Curve Matching Tips

Follow guidelines developed by Butler (1998) for analyzing slug tests.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

References

Barker, J.A. and J.H. Black, 1983. Slug tests in fissured aquifers, Water
Resources Research, vol. 19, no. 6, pp. 1558-1564.

420

Constant-Head Tests

Overview (Constant-Head Test Solutions)

Constant-head tests are sometimes performed as an alternative to constant-rate
tests (pumping tests). During a constant-head test, the head or drawdown in the
test well is held at a constant level, and discharge (flow rate) is recorded at regular
intervals. One can determine aquifer properties by matching analytical solutions to
the discharge measurements from a constant-head test.
After a well is shut-in following a constant-head test, special analytical techniques
are required for evaluating recovery data because the boundary condition at the test
well changes from constant head to constant rate. When you choose a constant-head
solution, AQTESOLV also provides an exact method of analyzing the recovery data.
AQTESOLV provides the following solutions for constant-head tests in confined, leaky
and fractured aquifers.
Confined
Confined
Confined
Confined
Confined
Leaky
Leaky
Fractured
Fractured
Fractured
Fractured

Jacob-Lohman (1952)
Jacob-Lohman (1952) straight-line
method
Hurst-Clark-Brauer (1969)
Dougherty-Babu (1984)
Barker (1988)
Hantush (1959)
Moench (1985) Case 1: constant head
Barker (1988) slab-shaped blocks
Barker (1988) spherical blocks
Ozkan-Raghavan (1991) uniform-flux
vertical fracture
Ozkan-Raghavan (1991) infiniteconductivity vertical fracture

Choose Match>Solution to select a constant-head test solution.

Recovery Solutions (Constant-Head Tests)

AQTESOLV provides two procedures for analyzing recovery data from constant-head
tests depending on the type of plot: Agarwal or residual drawdown.
On an Agarwal plot, the objective is to match an equivalent constant-rate solution
using the approximate method of Uraiet and Raghavan (1980). The Agarwal plot is
valuable as a diagnostic tool because the recovery data plot with the same
recognizable patterns as constant-rate drawdown tests. For any given constant-head
solution, we can find its equivalent constant-rate solution using a general formula. In
many cases, however, the equivalent constant-rate and constant-head solutions are

421

available in the literature. For example, we would use the Jacob-Lohman (1952)
solution to analyze a constant-head test in a confined aquifer with a fully penetrating
well. The equivalent constant-rate solution for Agarwal recovery analysis is given by
Papadopulos-Cooper (1967).
On a residual drawdown plot, AQTESOLV computes recovery with an exact
solution derived by Ehlig-Economides and Ramey (1981) that rigorously accounts for
the change in boundary condition from constant head to constant rate. The exact
solution is general and incorporates conditions at the wellbore for different aquifer
configurations.

Use the Solution Expert to identify solutions for recovery analysis.

Use residual drawdown and Agarwal plots to analyze recovery data from
constant-head tests.

422

Confined Aquifers

Jacob-Lohman (1952) Solution for a ConstantHead Test in a Confined Aquifer

(Match > Solution)
Jacob and Lohman (1952) derived a solution for a constant-head test in a
homogeneous, isotropic confined aquifer assuming a fully penetrating well.
Jacob and Lohman (1952) also devised a straight-line method for determining
aquifer coefficients from a constant-head test (excluding recovery). The straight-line
method is valid for sufficiently large values of time.
When you choose a solution, AQTESOLV provides two options for the Jacob-Lohman
solution: type-curve and straight-line methods.
o

Illustration

Equations
Jacob and Lohman (1952) derived an analytical solution for a constant-head
test in a homogeneous, isotropic confined aquifer assuming a fully
penetrating well.
The Laplace transform solution for dimensionless discharge is as follows:

423

where

Hw is the constant head in the test well [L]

Ki is modified Bessel function of second kind, order i

p is the Laplace transform variable

Q is discharge rate [L3/T]

rw is well radius [L]

S is storativity [dimensionless]

t is time [T]

T is transmissivity [L2/T]

Ehlig-Economides and Ramey (1981) derived an exact solution for recovery

following a constant-head test. The calculations use the PapadopulosCooper (1967) constant-rate well function to simulate the recovery period.
View the exact recovery solution on a residual drawdown plot.
For constant-head tests, casing radius only plays a role during recovery. If
you enter a radius for downhole equipment, AQTESOLV uses the effective
casing radius instead of the nominal casing radius in the recovery equations
for this solution.
Jacob and Lohman (1952) also presented a straight-line method for
estimating T and S as follows:

The straight-line is matched to a data plot of Hw/Q versus t/rw2 on semi-log

axes.

424

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous, isotropic and of uniform thickness

aquifer potentiometric surface is initially horizontal

well is fully penetrating

flow is unsteady

aquifer is confined

water is released instantaneously from storage with decline of hydraulic

head

Data Requirements

test well location

constant head maintained in test well

observed pumping rate(s)

casing radius and well radius

downhole equipment radius (optional)

Solution Options

recovery

Estimated Parameters

T (transmissivity)

S (storativity)

r(w) (well radius)

r(c) (nominal casing radius)

Curve Matching Tips

Match the Jacob-Lohman (1952) straight-line solution to late-time data to

obtain preliminary estimates of aquifer properties.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

425

The exact recovery solution introduces the casing radius, r(c), into the
calculations; casing radius has no effect on the solution when the well is
flowing.

If you estimate r(c) for the test well, the estimated value replaces the
nominal casing radius and AQTESOLV still performs the correction for
downhole equipment.

Recovery
For constant-head tests, the analytical solution displayed with recovery data
depends on the type of plot: Agarwal or residual drawdown.
When viewing recovery data from a constant-head test on an Agarwal plot,
the goal is to match an equivalent constant-rate solution using the
approximate method of Uraiet and Raghavan (1980). In the case of the
Jacob-Lohman (1952) solution for a constant-head test, the equivalent
constant-rate solution is given by Papadopulos-Cooper (1967) assuming a
fully penetrating well in a confined aquifer.
On a residual drawdown plot, AQTESOLV computes recovery after a
constant-head test with an exact solution derived by Ehlig-Economides and
Ramey (1981). The exact recovery calculation makes use of the
Papadopulos-Cooper (1967) constant-rate solution.

References

Jacob, C.E. and S.W. Lohman, 1952. Nonsteady flow to a well of constant
drawdown in an extensive aquifer, Trans. Am. Geophys. Union, vol. 33,
pp. 559-569.

Papadopulos, I.S. and H.H. Cooper, 1967. Drawdown in a well of large

diameter, Water Resources Research, vol. 3, no. 1, pp. 241-244.

Hurst-Clark-Brauer (1969) Solution for a

Constant-Head Test in a Confined Aquifer
(Match > Solution)
Hurst, Clark and Brauer (1969) derived a solution for a constant-head test in a
homogeneous, isotropic confined aquifer assuming a fully penetrating well with
wellbore skin.

426

Illustration

Equations
Hurst, Clark and Brauer (1969) derived an analytical solution for a constanthead test in a homogeneous, isotropic confined aquifer assuming a fully
penetrating well with wellbore skin.
The Laplace transform solution for dimensionless discharge is as follows:

where

Hw is the constant head in the test well [L]

Ki is modified Bessel function of second kind, order i

p is the Laplace transform variable

Q is discharge rate [L3/T]

rw is well radius [L]

427

S is storativity [dimensionless]

Sw is wellbore skin factor [dimensionless]

t is time [T]

T is transmissivity [L2/T]

In the Laplace transform solution, Sw is limited to positive values; however,

using the effective well radius concept, we also may simulate a negative
skin (Hurst, Clark and Brauer 1969).
Ehlig-Economides and Ramey (1981) derived an exact solution for recovery
following a constant-head test. The calculations use the Dougherty-Babu
(1984) constant-rate well function to simulate the recovery period. View the
exact recovery solution on a residual drawdown plot.
For constant-head tests, casing radius only plays a role during recovery. If
you enter a radius for downhole equipment, AQTESOLV uses the effective
casing radius instead of the nominal casing radius in the recovery equations
for this solution.
o

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous, isotropic and of uniform thickness

aquifer potentiometric surface is initially horizontal

well is fully penetrating

flow is unsteady

aquifer is confined

water is released instantaneously from storage with decline of hydraulic

head

Data Requirements

test well location

constant head maintained in test well

observed pumping rate(s)

casing radius and well radius

downhole equipment radius (optional)

Solution Options

recovery

428

Estimated Parameters

T (transmissivity)

S (storativity)

Sw (dimensionless wellbore skin factor)

r(w) (well radius)

r(c) (nominal casing radius)

Curve Matching Tips

Match the Jacob-Lohman (1952) straight-line solution to late-time data to

obtain preliminary estimates of aquifer properties.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

The exact recovery solution introduces the casing radius, r(c), into the
calculations; casing radius has no effect on the solution when the well is
flowing.

If you estimate r(c) for the test well, the estimated value replaces the
nominal casing radius and AQTESOLV still performs the correction for
downhole equipment.

Recovery
For constant-head tests, the analytical solution displayed with recovery data
depends on the type of plot: Agarwal or residual drawdown.
When viewing recovery data from a constant-head test on an Agarwal plot,
the goal is to match an equivalent constant-rate solution using the
approximate method of Uraiet and Raghavan (1980). In the case of the
Hurst-Clark-Brauer (1969) solution for a constant-head test, the equivalent
constant-rate solution is given by Dougherty-Babu (1984) assuming a fully
penetrating well with wellbore skin in a confined aquifer.
On a residual drawdown plot, AQTESOLV computes recovery after a
constant-head test with an exact solution derived by Ehlig-Economides and
Ramey (1981). The exact recovery calculation makes use of the DoughertyBabu (1984) constant-rate solution.

References

Hurst, W., J.D. Clark and E.B. Brauer, 1969. The skin effect in producing
wells, Journal of Petroleum Technology, November 1969, pp. 1483-1489.

429

Dougherty, D.E and D.K. Babu, 1984. Flow to a partially penetrating well
in a double-porosity reservoir, Water Resources Research, vol. 20, no. 8,
pp. 1116-1122.

Dougherty-Babu (1984) Solution for a

Constant-Head Test in a Confined Aquifer
(Match > Solution)
Dougherty and Babu (1984) derived a Laplace transform solution for a constant-rate
test that we can modify to evaluate a constant-head test in a homogeneous,
anisotropic confined aquifer assuming a fully or partially penetrating well with
wellbore skin.
o

Illustration

Equations
Dougherty and Babu (1984) derived a Laplace transform solution for a
constant-rate test in a homogeneous, anisotropic confined aquifer assuming
a fully or partially penetrating well with wellbore skin.
We may use the Dougherty-Dabu (1984) constant-rate solution in a general
formula to compute dimensionless discharge for a constant-head test:

430

where

b is aquifer thickness [L]

d is distance from water table to top of pumping well screen [L]

dD is d/b

Hw is the constant head in the test well [L]

K is hydraulic conductivity [L/T]

Ki is modified Bessel function of second kind, order i

l is distance from water table to bottom of pumping well screen [L]

lD is l/b

p is the Laplace transform variable

Q is discharge rate [L3/T]

rw is well radius [L]

Ss is specific storage [1/L]

Sw is wellbore skin factor [dimensionless]

t is time [T]

In the Laplace transform solution, Sw is limited to positive values; however,

using the effective well radius concept, we also may simulate a negative
skin (Hurst, Clark and Brauer 1969).
Ehlig-Economides and Ramey (1981) derived an exact solution for recovery
431

following a constant-head test. The calculations use the Dougherty-Babu

(1984) constant-rate well function to simulate the recovery period. View the
exact recovery solution on a residual drawdown plot.
For constant-head tests, casing radius only plays a role during recovery. If
you enter a radius for downhole equipment, AQTESOLV uses the effective
casing radius instead of the nominal casing radius in the recovery equations
for this solution.
o

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous and of uniform thickness

aquifer potentiometric surface is initially horizontal

well is fully or partially penetrating

flow is unsteady

aquifer is confined

water is released instantaneously from storage with decline of hydraulic

head

Data Requirements

test well location

constant head maintained in test well

observed pumping rate(s)

casing radius and well radius

downhole equipment radius (optional)

partial penetration depths

saturated thickness

hydraulic conductivity anisotropy ratio

Solution Options

partially penetrating well

recovery

Estimated Parameters

T (transmissivity)

S (storativity)

Kz/Kr (hydraulic conductivity anisotropy ratio)

432

Sw (dimensionless wellbore skin factor)

r(w) (well radius)

r(c) (nominal casing radius)

Curve Matching Tips

Match the Jacob-Lohman (1952) straight-line solution to late-time data to

obtain preliminary estimates of aquifer properties.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Select values of Kz/Kr from the Family and Curve drop-down lists on the
toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

The exact recovery solution introduces the casing radius, r(c), into the
calculations; casing radius has no effect on the solution when the well is
flowing.

If you estimate r(c) for the test well, the estimated value replaces the
nominal casing radius and AQTESOLV still performs the correction for
downhole equipment.

Recovery
For constant-head tests, the analytical solution displayed with recovery data
depends on the type of plot: Agarwal or residual drawdown.
When viewing recovery data from a constant-head test on an Agarwal plot,
the goal is to match an equivalent constant-rate solution using the
approximate method of Uraiet and Raghavan (1980). In the case of the
Dougherty-Babu (1984) solution for a constant-head test, the equivalent
constant-rate solution is given by Dougherty-Babu (1984) assuming a fully
or partially penetrating well with wellbore skin in a confined aquifer.
On a residual drawdown plot, AQTESOLV computes recovery after a
constant-head test with an exact solution derived by Ehlig-Economides and
Ramey (1981). The exact recovery calculation makes use of the DoughertyBabu (1984) constant-rate solution.

References

Dougherty, D.E and D.K. Babu, 1984. Flow to a partially penetrating well
in a double-porosity reservoir, Water Resources Research, vol. 20, no. 8,
pp. 1116-1122.

Moench, A.F., 1988. The response of partially penetrating wells to

pumpage from double-porosity aquifers, Proceedings of the International
433

Conference on Fluid Flow in Fractured Rocks, Atlanta, GA, May 16-18,

1988.

Barker (1988) Solution for a Constant-Head

Test in a Confined Aquifer
(Match > Solution)
Barker (1988) derived generalized radial flow model for unsteady, n-dimensional
flow to a fully penetrating source in an isotropic, single- or double-porosity fractured
aquifer. The single-porosity form of the model describes flow in a confined aquifer.
For details, refer to the Barker (1998) solution for a fractured aquifer.

434

Leaky Aquifers

Hantush (1959) Solution for a Constant-Head

Test in a Leaky Aquifer
(Match > Solution)
Hantush (1959) derived a solution for a constant-head test in a homogeneous,
isotropic leaky confined aquifer assuming a fully penetrating well.
o

Illustration

Equations
Hantush (1959) derived an analytical solution for a constant-head test in a
homogeneous, isotropic leaky confined aquifer assuming a fully penetrating
well.
The Laplace transform solution for dimensionless discharge is as follows:

435

where

b' is aquitard thickness [L]

Hw is the constant head in the test well [L]

K' is aquitard vertical hydraulic conductivity [L/t]

Ki is modified Bessel function of second kind, order i

p is the Laplace transform variable

Q is discharge rate [L3/T]

rw is well radius [L]

S is storativity [dimensionless]

t is time [T]

T is transmissivity [L2/T]

Ehlig-Economides and Ramey (1981) derived an exact solution for recovery

following a constant-head test. The calculations use the Moench (1985)
constant-rate well function for a fully penetrating, finite-diameter well in a
leaky confined aquifer without aquitard storage to simulate the recovery
period. View the exact recovery solution on a residual drawdown plot.
For constant-head tests, casing radius only plays a role during recovery. If
you enter a radius for downhole equipment, AQTESOLV uses the effective
casing radius instead of the nominal casing radius in the recovery equations
for this solution.
o

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous, isotropic and of uniform thickness

aquifer potentiometric surface is initially horizontal

well is fully penetrating

flow is unsteady

436

aquifer is leaky confined

water is released instantaneously from storage with decline of hydraulic

head

confining bed(s) has infinite areal extent, uniform vertical hydraulic

conductivity and uniform thickness

confining bed(s) is overlain or underlain by an infinite constant-head plane

source

flow is vertical in the aquitard(s)

Data Requirements

test well location

constant head maintained in test well

observed pumping rate(s)

casing radius and well radius

downhole equipment radius (optional)

Solution Options

recovery

Estimated Parameters

T (transmissivity)

S (storativity)

r/B (leakage parameter)

r(w) (well radius)

r(c) (nominal casing radius)

The Report also shows aquitard properties (K'/b' and K') computed from the
leakage parameter (r/B).
o

Curve Matching Tips

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Select values of r/B from the Family and Curve drop-down lists on the
toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

437

The exact recovery solution introduces the casing radius, r(c), into the
calculations; casing radius has no effect on the solution when the well is
flowing.

If you estimate r(c) for the test well, the estimated value replaces the
nominal casing radius and AQTESOLV still performs the correction for
downhole equipment.

Recovery
For constant-head tests, the analytical solution displayed with recovery data
depends on the type of plot: Agarwal or residual drawdown.
On an Agarwal plot, the goal is to match an equivalent constant-rate
solution using the approximate method of Uraiet and Raghavan (1980). In
the case of the Hantush (1959) solution for a constant-head test, the
equivalent constant-rate solution is given by Moench (1985) assuming a
constant-head boundary and no storage in the aquitard.
On a residual drawdown plot, AQTESOLV computes recovery after a
constant-head test with an exact solution derived by Ehlig-Economides and
Ramey (1981). The exact recovery calculation makes use of the Moench
(1985) constant-rate solution.

References

Hantush, M.S., 1959. Nonsteady flow to flow wells in leaky aquifers,

Journal of Geophysical Research, vol. 64, no. 5, pp. 1043-1052.

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 (1985) Solution for a Constant-Head

Test in a Leaky Aquifer
(Match > Solution)
Moench (1985) derived a Laplace transform solution for a constant-rate test that we
can modify to evaluate a constant-head test in a homogeneous, isotropic confined
aquifer assuming a fully penetrating well with wellbore skin.

438

Illustration

Equations
Moench (1985) derived a Laplace transform solution for a constant-rate test
that we can modify to evaluate a constant-head test in a homogeneous,
isotropic confined aquifer assuming a fully penetrating well with wellbore
skin.
We may use the Moench (1985) constant-rate solution in a general formula to
compute dimensionless discharge for a constant-head test:

439

where

b is aquifer thickness [L]

b' is thickness of first aquitard [L]

b" is thickness of second aquitard [L]

Hw is constant head in test well [L]

K is aquifer hydraulic conductivity [L/T]

K' is vertical hydraulic conductivity of first aquitard [L/T]

K" is vertical hydraulic conductivity of second aquitard [L/T]

Ki is modified Bessel function of second kind, order i

p is the Laplace transform variable

Q is pumping rate [L3/T]

r is radial distance [L]

rc is casing radius [L]

440

rw is well radius [L]

Ss is aquifer specific storage [1/L]

Ss' is specific storage of first aquitard [1/L]

Ss" is specific storage of second aquitard [1/L]

Sw is wellbore skin factor [dimensionless]

t is time [T]

AQTESOLV reports the aquitard properties in terms of the more familiar

parameters from the Hantush (1960) solution, which one can readily
compute from Moench's parameters as follows:

Ehlig-Economides and Ramey (1981) derived an exact solution for recovery

following a constant-head test. The calculations use the Moench (1985)
constant-rate well function for a fully penetrating, finite-diameter well in a
leaky confined aquifer to simulate the recovery period. View the exact
recovery solution on a residual drawdown plot.
For constant-head tests, casing radius only plays a role during recovery. If
you enter a radius for downhole equipment, AQTESOLV uses the effective
casing radius instead of the nominal casing radius in the recovery equations
for this solution.
o

Assumptions

aquifer has infinite areal extent

aquifer is homogeneous, isotropic and of uniform thickness

aquifer potentiometric surface is initially horizontal

well is fully penetrating

flow is unsteady

aquifer is leaky confined

water is released instantaneously from storage with decline of hydraulic

head

confining bed(s) has infinite areal extent, uniform vertical hydraulic

conductivity and storage coefficient, and uniform thickness

confining bed(s) is overlain or underlain by an infinite constant-head plane

source

441

Data Requirements

test well location

constant head maintained in test well

observed pumping rate(s)

casing radius and well radius

downhole equipment radius (optional)

Solution Options

flow is vertical in the aquitard(s)

recovery

Estimated Parameters

T (transmissivity)

S (storativity)

r/B' (dimensionless leakage parameter, aquitard 1)

' (dimensionless leakage parameter, aquitard 1)

r/B" (dimensionless leakage parameter, aquitard 2)

" (dimensionless leakage parameter, aquitard 2)

Sw (wellbore skin factor)

r(w) (well radius)

r(c) (nominal casing radius)

The Report also shows aquitard properties (K'/b' and K'; K"/b" and K")
computed from the leakage parameter (r/B' and r/B").
o

Curve Matching Tips

Match the Jacob-Lohman (1952) straight-line solution to late-time data to

obtain preliminary estimates of aquifer properties.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Select values of r/B' and ' from the Family and Curve drop-down lists on
the toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

442

The exact recovery solution introduces the casing radius, r(c), into the
calculations; casing radius has no effect on the solution when the well is
flowing.

If you estimate r(c) for the test well, the estimated value replaces the
nominal casing radius and AQTESOLV still performs the correction for
downhole equipment.

Recovery
For constant-head tests, the analytical solution displayed with recovery data
depends on the type of plot: Agarwal or residual drawdown.
When viewing recovery data from a constant-head test on an Agarwal plot,
the goal is to match an equivalent constant-rate solution using the
approximate method of Uraiet and Raghavan (1980). In the case of the
Moench (1985) solution for a constant-head test, the equivalent constantrate solution is given by Moench (1985) assuming a fully penetrating well
with wellbore skin in a leaky confined aquifer.
On a residual drawdown plot, AQTESOLV computes recovery after a
constant-head test with an exact solution derived by Ehlig-Economides and
Ramey (1981). The exact recovery calculation makes use of the Moench
(1985) constant-rate solution.

References

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.

443

Fractured Aquifers

Barker (1988) Solution for a Constant-Head

Test in a Fractured Aquifer
(Match > Solution)
Barker (1988) derived a generalized radial flow model for unsteady, n-dimensional
flow to a fully penetrating source in an isotropic, single- or double-porosity fractured
aquifer. The source is an n-dimensional sphere (projected through three-dimensional
space) of finite radius (rw), storage capacity () and skin factor (Sw).
As described by Doe (1990), the spatial dimension (n) determines the change in
conduit area with distance from the source. In a two-dimensional system (n=2), the
source is a finite cylinder, the typical configuration for analyzing cylindrical flow to a
well.
AQTESOLV uses the principle of superposition in time to simulate variable-rate tests
including recovery with the Barker solution. Use this solution to analyze both
pumping and recovery data from constant- or variable-rate pumping tests.
When you choose a solution, AQTESOLV provides three configurations for the Barker
generalized radial flow model:

single-porosity (confined/fractured aquifer)

double-porosity with slab-shaped blocks (fractured aquifer)

double-porosity with spherical blocks (fractured aquifer)

444

Illustration

Equations
Barker (1988) derived a generalized radial flow model for unsteady, ndimensional flow to a fully penetrating source in an isotropic, single- or
double-porosity fractured aquifer.
The Laplace transform solution for discharge is as follows:

For single-porosity models, we have:

445

For double-porosity models, we use the functions of Moench (1984) for slab
and spherical blocks including fracture skin.

slab blocks:

spherical blocks:

where

b is extent of flow region [L]

b' is block thickness [L]

bs is fracture skin thickness [L]

Hw is head maintained in the well [L]

K is aquifer/fracture hydraulic conductivity [L/T]

K' is matrix hydraulic conductivity [L/T]

Ks is fracture skin hydraulic conductivity [L/T]

Kv is modified Bessel function of second kind, order v

446

n is flow dimension [dimensionless]

p is the Laplace transform variable

r is radial distance [L]

rw is well radius [L]

Sf is fracture skin factor [dimensionless]

Ss is aquifer/fracture specific storage [1/L]

Ss' is matrix specific storage [1/L]

Sw is wellbore skin factor [dimensionless]

t is time [T]

The parameter b, the flow region extent, has a simple interpretation for
integral flow dimensions. For one-dimensional flow (n=1), it is the square
root of the conduit flow area (normal to the flow direction). For n=2 (twodimensional radial flow), b is the thickness of the aquifer. For spherical flow
(n=3), the parameter b, which is raised to the power of 3-n, has no
significance. For nonintegral flow dimensions, b has no simple interpretation
(Barker 1988).
Ehlig-Economides and Ramey (1981) derived an exact solution for recovery
following a constant-head test. The calculations use the Barker (1988)
constant-rate solution to simulate the recovery period. View the exact
recovery solution on a residual drawdown plot.
For constant-head tests, casing radius only plays a role during recovery. If
you enter a radius for downhole equipment, AQTESOLV uses the effective
casing radius instead of the nominal casing radius in the recovery equations
for this solution.
o

Assumptions

aquifer has infinite extent

aquifer has uniform extent of flow region

pumping and observation wells are fully penetrating

aquifer is confined with single or double porosity

matrix blocks in double-porosity models are slab shaped or spherical

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

Data Requirements

test well location

447

constant head maintained in test well

observed pumping rate(s)

casing radius and well radius

downhole equipment radius (optional)

extent of flow region

thickness of slab blocks or diameter of spherical blocks (double-porosity

models)

Solution Options

recovery

Estimated Parameters

K (fracture hydraulic conductivity)

Ss (fracture specific storage)

K' (matrix hydraulic conductivity)

Ss' (matrix specific storage)

n (flow dimension)

b (extent of flow region)

Sf (fracture skin factor)

Sw (wellbore skin factor)

r(w) (well radius)

r(c) (nominal casing radius)

Curve Matching Tips

Match the Jacob-Lohman (1952) straight-line solution to late-time data to

obtain preliminary estimates of aquifer properties.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Select values of n, Sf and Sw from the Family and Curve drop-down lists
on the toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

The exact recovery solution introduces the casing radius, r(c), into the

448

calculations; casing radius has no effect on the solution when the well is
flowing.

If you estimate r(c) for the test well, the estimated value replaces the
nominal casing radius and AQTESOLV still performs the correction for
downhole equipment.

Recovery
For constant-head tests, the analytical solution displayed with recovery data
depends on the type of plot: Agarwal or residual drawdown.
When viewing recovery data from a constant-head test on an Agarwal plot,
the goal is to match an equivalent constant-rate solution using the
approximate method of Uraiet and Raghavan (1980). In the case of the
Barker (1988) solution for a constant-head test, the equivalent constantrate solution is given by Barker (1988) assuming a fully penetrating well
with wellbore skin in a fractured aquifer.
On a residual drawdown plot, AQTESOLV computes recovery after a
constant-head test with an exact solution derived by Ehlig-Economides and
Ramey (1981). The exact recovery calculation makes use of the Barker
(1988) constant-rate solution.

References

Barker, J.A., 1988. A generalized radial flow model for hydraulic tests in
fractured rock, Water Resources Research, vol. 24, no. 10, pp. 17961804.

Moench, A.F., 1984. Double-porosity models for a fissured groundwater

reservoir with fracture skin, Water Resources Research, vol. 20, no. 7, pp.
831-846.

Ozkan-Raghavan (1991) Solution for a

Constant-Head Test in a Fractured Aquifer
(Match > Solution)
Ozkan and Raghavan (1991) derived a Laplace transform solution for a constant-rate
test that we can modify for a constant-head test assuming a fully penetrating well
which intersects a single vertical fracture in an anisotropic confined aquifer. The test
well bisects the fracture which is represented in the solution by a fully penetrating
vertical plane source oriented parallel to the x axis.
When you choose a solution, AQTESOLV provides two options for the OzkanRaghavan solution: uniform-flux and infinite-conductivity vertical fracture models.

449

Illustration

Equations
Ozkan and Raghavan (1991) derived the following Laplace transform solution
for dimensionless head in a fully penetrating, uniform-flux vertical fracture
in a confined aquifer assuming constant-rate flow (y=0):

where

Ky/Kx is hydraulic conductivity anisotropy ratio [L2/T]

K0 is modified Bessel function of second kind, zero order

p is Laplace transform variable

Q is pumping rate [L3/T]

s is drawdown [L]

450

S is storativity [dimensionless]

t is time [T]

Tx is transmissivity in x direction [L2/T]

Ty is transmissivity in y direction [L2/T]

x and y are coordinate distances [L]

xf is half-length of fracture in x direction [L]

For a constant-head test, we use the constant-rate solution to compute the

Laplace transform of dimensionless discharge using a general relationship
given by van Everdingen and Hurst (1949).
Ehlig-Economides and Ramey (1981) derived an exact solution for recovery
following a constant-head test. The calculations use the Ozkan-Raghavan
(1991) constant-rate solution to simulate the recovery period. View the
exact recovery solution on a residual drawdown plot.
Gringarten, Ramey and Raghavan (1974) found that the uniform-flux solution
could be used to predict the drawdown in an infinite-conductivity fracture by
simply using xD = 0.732 to compute head in the test well.
o

Assumptions

aquifer has infinite areal extent

aquifer has uniform thickness

aquifer potentiometric surface is initially horizontal

test well is fully penetrating

fractured aquifer represented by anisotropic system with a single plane

vertical fracture

flow is unsteady

water is released instantaneously from storage with decline of hydraulic

head

diameter of pumping well is very small so that storage in the well can be
neglected

Data Requirements

test well location

constant head maintained in test well

observed pumping rate(s)

length of vertical fracture

451

Solution Options

recovery

Estimated Parameters

Kx (hydraulic conductivity in x direction)

Ss (specific storage)

Ky/Kx (hydraulic conductivity anisotropy ratio)

Lf (length of fracture)

Curve Matching Tips

Match the Jacob-Lohman (1952) straight-line solution to late-time data to

obtain preliminary estimates of aquifer properties.

Choose Match>Visual to perform visual curve matching using the

procedure for type curve solutions.

Use active type curves for more effective visual matching with variablerate pumping tests.

Select values of Ky/Kx from the Family and Curve drop-down lists on the
toolbar.

Use parameter tweaking to perform visual curve matching and sensitivity

analysis.

Perform visual curve matching prior to automatic estimation to obtain

reasonable starting values for the aquifer properties.

Recovery
For constant-head tests, the analytical solution displayed with recovery data
depends on the type of plot: Agarwal or residual drawdown.
When viewing recovery data from a constant-head test on an Agarwal plot,
the goal is to match an equivalent constant-rate solution using the
approximate method of Uraiet and Raghavan (1980). In the case of the
Ozkan-Raghavan (1991) solution for a constant-head test, the equivalent
constant-rate solution is given by Ozkan-Raghavan (1991) assuming a fully
penetrating vertical fracture in a confined aquifer.
On a residual drawdown plot, AQTESOLV computes recovery after a
constant-head test with an exact solution derived by Ehlig-Economides and
Ramey (1981). The exact calculation makes use of the Ozkan-Raghavan
(1991) constant-rate solution.

References

Ozkan, E. and R. Raghavan, 1991. New solutions for well-test analysis

problems: Part I-analytical considerations, SPE Formation Evaluation,
Sept. 1991, pp. 359-368.

452

Gringarten, A.C., Ramey, H.J., Jr. and R. Raghavan, 1974. Unsteady-state

pressure distributions created by a well with single infinite-conductivity
vertical fracture, Soc. Petrol. Engrs. J., pp. 347-360.

453

Curve Matching

Overview (Curve Matching)

Use the following strategy to perform more effective curve matching with AQTESOLV.
1. Develop a conceptual model for the system under study based on sitespecific hydrogeologic data. Enter these data into a new data set.
TIPS

To help you identify reasonable values for aquifer properties, use

representative data from the literature forhydraulic conductivity, porosity,
specific yieldandstorativity.

2. Use diagnostic flow plots and derivative analysis to help identify appropriate
solution methods for the data.
TIPS

Use diagnostic methods to identify wellbore storage effects, linear flow,

bilinear flow, infinite-acting radial flow and boundary effects.

3. Perform visual curve matching or parameter tweaking to obtain estimates of

aquifer properties.
TIPS

Usevisual curve matchingto obtain preliminary estimates of aquifer

properties prior to performingautomatic curve matching.

For pumping tests, use the Cooper-Jacob straight-line method to obtain

preliminary estimates of aquifer parameters before applying more
complicated solution methods.

Useactive type curvesto perform more effective visual curve matching for
a variety of analyses.

4. Perform automatic curve matching to refine aquifer property estimates using

a nonlinear least-squares fitting procedure.
TIPS

The efficiency ofautomatic curve matchingis often sensitive to initial

estimates of aquifer properties. Usevisual curve matchingto obtain
reasonable starting values prior to performing automatic curve matching.

5. Use parameter tweaking to perform sensitivity analysis for specified aquifer

properties.

454

Curve Matching Tips for Pumping Tests

Use the Cooper-Jacob (1946) straight-line method to obtain preliminary

estimates of aquifer properties before proceeding to more complicated type
curve solutions.

Obtain preliminary estimates of aquifer properties with visual curve matching

prior to performing automatic curve matching.

Use active type curves for more effective visual curve matching with variablerate tests.

Match recovery data with residual-drawdown and Agarwal plots.

Use derivative and diagnostic flow plots to evaluate special conditions such as
wellbore storage, radial flow, linear flow and more.

Superimpose the derivative on plots to match derivative and displacement

data simultaneously.

Apply the slope checking tool to evaluate conditions including wellbore

storage, linear flow and boundary effects.

Adjust curve resolution settings to optimize curve plotting performance.

Curve Matching Tips for Slug Tests

Use guidelines developed by Butler (1998, Chapter 12) to assist in the

analysis of slug tests.

When using straight-line methods (e.g., Bouwer-Rice, Hvorslev), use the

recommended head ranges (Butler 1998) for more effective visual curve
matching.

For straight-line methods (e.g., Bouwer-Rice, Hvorslev), where curve

matching relies on your judgement to position the line over the data, visual
curve matching is often preferable to automatic curve matching.

Obtain preliminary estimates of aquifer properties with visual curve matching

prior to performing automatic curve matching.

Control the range of data used in automatic curve matching by defining a

match window or by assigning observation weights.

Use active type curves to match underdamped slug test solutions.

For type curve solutions (e.g., Cooper et al., KGS Model), you can plot data
and curves on either linear-log or log-linear axes.

If you prefer, you may analyze slug tests using normalized head.

Curve Matching Tips for Constant-Head Tests

Use the Jacob-Lohman (1952) straight-line method to obtain preliminary

455

estimates of aquifer properties before proceeding to more complicated type

curve solutions.

Obtain preliminary estimates of aquifer properties with visual curve matching

prior to performing automatic curve matching.

Match recovery data with residual-drawdown and Agarwal plots.

Limit the number of parameters estimated with automatic curve matching to

avoid parameter correlation.

Superimpose the derivative on plots to match derivative and displacement

data simultaneously.

456

Diagnostic Methods

Derivative Analysis
Derivative analysis, a technique introduced in the petroleum industry (Bourdet et al.
1983; Bourdet et al. 1989), provides a valuable diagnostic tool for aquifer test
analysis. In performing derivative analysis, it is common practice to plot drawdown
and derivative data on the same graph.
Example: Pumping Test in Confined Aquifer

Example: Pumping Test in Leaky Confined Aquifer

457

458

Example: Pumping Test in Unconfined Aquifer

459

Example: Pumping Test in Double-Porosity Aquifer (Multiwell)

The following simple formula is used to compute the derivative:

where T is an appropriate time function (e.g., elapsed time or Agarwal equivalent

time). Essentially, this formula is a weighted average of slopes computed from data
points on either side of data point i. In the above formula, the two slopes are

and

An important aspect of performing derivative analysis is the selection of an

appropriate calculation method. AQTESOLV provides four methods for calculating
derivatives from observed data. The default Nearest Neighbor option,
recommended by Bourdet (2002) for preliminary analysis, often results in noisy
derivatives. To remove noise from the calculated derivatives, apply the Bourdet,

460

Spane or Smoothing options as needed.

o

Nearest Neighbor

The nearest neighbor option computes the derivative for data point i using
adjacent data points.

Bourdet (2002) recommends using the nearest neighbor option for

preliminary derivative analysis.

For noise-free, logarithmically spaced data, this method introduces the

least amount of smoothing; however, noise in the data often makes this
method impractical.

Bourdet

The Bourdet method implements the "preferred" method of Bourdet et

al. (1989).

This method of calculating the derivative at data point i uses data points
separated logarithmically in time by a differentiation interval "L" that
normally ranges between 0.1 and 0.5 log cycles of time (Horne 1995).

A smaller differentiation interval is preferred to reduce distortion of the

derivative data.

Spane

The Spane method implements the method of Spane and Wurstner

(1993).

The Spane method of calculating the derivative at data point i uses linear
regression to compute slopes from all data points falling within a
differentiation interval "L" that normally ranges between 0.1 and 0.5
log cycles of time.

A smaller differentiation interval is preferred to reduce distortion of the

derivative data.

Smoothing

The smoothing method of computing the derivative at data point i uses

linear regression to compute slopes from a fixed number of data points.

This method works well with data spaced geometrically in time (e.g.,
logarithmic spacing).

A smaller number of points (i.e., smaller smoothing factor) is preferred to

reduce distortion of the derivative data.

Example: Use of Smoothing

The following figures show the use of AQTESOLV's derivative options for a single-well
pumping test (data from the pumped well). Drawdown data are shown in blue and
derivative data are shown in red.

461

Bourdet (2002) recommends using the nearest neighbor option (below) at the
outset of derivative analysis. If the derivative appears too noisy, as it often does with
high frequency data, apply higher levels of smoothing to clarify the derivative signal.

For this data set, one may smooth the derivative data with either the Bourdet or
Spane option to obtain a clear view of the derivative signal (below). The
differentiation interval "L" for this example is 0.2; however, a smaller or larger value
may be required for some data sets. For this particular data set, the Smoothing
option is not very effective because the data are spaced linearly rather than
logarithmically in time.

462

463

On a plot with log-log axes, more smoothing may be necessary because of the
exaggeration of noise on a log scale. For this data set, the Bourdet option with L =
0.5 (below) produces a satisfactory plot of the derivative data.

464

In many cases, an effective strategy for speeding up computations and performing

derivative analysis is to filter the number of observations. For example, if 20 points
per log cycle time are retained from the original data, we can use the Bourdet
option with L = 0.5 to observe the same derivative response as the full data set.

465

Choose Options from the View menu to select the calculation method for the
derivatives.

Select the nearest neighbor method to view the derivative with no

smoothing.

To reduce noise in the computed derivative, choose the Bourdet, Spane or

smoothing method.

466

Choose Derivative-Time from the View menu to display the derivative as a

function of time. Perform visual curve matching using parameter tweaking.

Select Options from the View menu to superimpose the derivative on

displacement-time, composite or Agarwal plots. Choose Visual from the
Match menu to perform visual curve matching.

Choose Wells from the Edit menu to modify derivative symbol and curve
properties.

Find examples of derivative plots in the Quick Start chapter.

Check Slope
(Match > Check Slope)
Choose Check Slope from the Match menu to test the slope of pumping test or
constant-head test data on a semi-log or log-log plot.
Use this option to test the slope of data on plots with semi-log or log axes.
o

Checking the Slope

1. Click and hold the left mouse button down.
2. While holding the mouse button down, move the mouse to draw a line
over a range of data on the plot.
3. The slope of the line is displayed in the message pane of the status bar.

When wellbore storage is present, early-time data on a log-log displacementtime or radial flow plot have a unit slope.

Assuming a constant-rate test, the slope of data on a log-log displacementtime or radial flow plot approaches the flow dimension when n < 2 (Barker
1988).

For constant-rate conditions, a single no-flow boundary doubles the slope of

data on a semi-log displacement-time or radial flow plot.

Tracking is disabled when you perform slope checking.

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Visual Curve Matching

Overview (Visual Curve Matching)

AQTESOLV provides a suite of tools for interactive visual curve matching that you
may use to obtain estimates of aquifer properties.
Visual Curve Matching Procedures
Type Curve Methods
1. Choose Visual from the Match menu.
2. Click and hold the left mouse button down over a point within the plot area.
3. Move the mouse to match the type curve to your data. As you move the type
curve, AQTESOLV automatically updates the plot legend to reflect changes in
parameter values.
4. Release the left mouse button when you have finished matching the type
curve.
Examples of type curve methods include Theis (1935), Hantush-Jacob (1955)
and Neuman (1974) for pumping tests; Cooper et al. (1967), Hyder et al.
(1994) and Springer-Gelhar (1991) for slug tests; and Jacob-Lohman (1952),
Hantush (1959) and Barker (1988) for constant-head tests.
Straight-Line Methods
1. Choose Visual from the Match menu.
2. Move the mouse to a point located on the new line you wish to match to your
data.
3. Click and hold down the left mouse button to anchor the new line at this
point.
4. Move the mouse to match a new straight line to your data. As you move the
mouse, AQTESOLV draws a straight line between the anchor point and the
position of the mouse.
5. Release the left mouse button when you have finished matching a new
straight line. AQTESOLV automatically updates the plot legend to reflect
changes in parameter values.
Examples of straight-line methods include Cooper-Jacob (1946) and Theis
(1935) residual drawdown for pumping tests; Bouwer-Rice (1976) and
Hvorslev (1951) for slug tests; and Jacob-Lohman (1952) for constant-head
tests.

Use visual curve matching to obtain preliminary estimates of aquifer

468

properties prior to performing automatic curve matching.

For pumping tests, use the Cooper-Jacob straight-line method to obtain

preliminary estimates of aquifer parameters before applying more
complicated solution methods.

Use active type curves to perform more effective visual curve matching for
variable-rate pumping tests, recovery tests, multi-well pumping and slug
tests, and slug tests with oscillatory response.

Quickly select type curve families on the toolbar.

Adjust individual aquifer properties using parameter tweaking.

Active Type Curves

Choose Active Curves from the Match menu or click
on the toolbar to toggle the
active type curves feature and simultaneously initiate visual curve matching.
The Active Type Curves feature is an enhanced method of performing visual curve
matching introduced by AQTESOLV. With active type curves, the program
automatically refreshes the complete type curve as you perform visual curve
matching.

Apply Active Type Curves for effective visual curve matching in the following
situations:

pumping tests with variable pumping rates

pumping tests with early- and late-time response such as delayed gravity
response or double porosity effects (see Matching Early/Late Data)

slug tests with oscillatory response (i.e., solutions with inertial effects in
high-K aquifers)

Matching Type Curve Families

If type curve families are
available for the active solution,
you can select the aquifer
parameter for the type curve
family and its value from Family
and Curve lists on the toolbar.

469

Selecting New Type Curve From Curve Family

1. Select an aquifer parameter for a type curve family from those available in
the Family list on the toolbar.
2. Select a value for the aquifer parameter from the Curve list on the toolbar.
3. To change the values shown in the Curve list, choose Options from the View
menu and click the Family tab.
4. To format curve families, select Format from the View menu and click the
Family tab.
5. The controls for the Family and Curve lists on the toolbar appear inactive
when type curve families are not available for the active solution.

Matching Early/Late Data

Certain aquifer test solutions involve aquifer parameters that affect early- or latetime response.
For example, visual curve matching with the Neuman (1974) solution for a pumping
test in an unconfined aquifer involves matching Type A curves to early-time data
and Type B curves to late-time data. The final match of the Type A curve
determines the values of T, S and ; the Type B curve determines T, Sy and .
How To Match Early- or Late-Time Data
1. Click Match Early Data
on the toolbar to toggle the Type A option and
simultaneously initiate visual curve matching.
2. Click Match Late Data
on the toolbar to toggle the Type B option and
simultaneously initiate visual curve matching.
Solutions Using Early/Late Visual Matching
1. Neuman (1974) pumping test solution for unconfined aquifers
2. Neuman-Witherspoon (1969) pumping test solution for leaky aquifers
3. Moench (1984) pumping test solution for fractured aquifers with slab-shaped
blocks
4. Moench (1984) pumping test solution for fractured aquifers with spherical
blocks

Use active type curves in conjunction with Type A and Type B visual curve
matching.

470

You also may choose Match>Toolbox>Options to set the Type A and Type B
options.

Parameter Tweaking
(Match > Toolbox > Tweak)
Choose Toolbox from the Match menu and click the Tweak tab to adjust the values
of individual aquifer parameters. Use this tool for visual curve matching and
sensitivity analysis.
Tweaking Parameters
1. Select an aquifer parameter to adjust from the Parameter list.
2. Tweak the value of the selected aquifer parameter using the scroll bar
control.
3. Click Apply to refresh all plots.
4. Check Apply changes automatically so you don't have to click the Apply
button when you tweak a parameter value.

Click the Parameters tab to adjust the range (minimum and maximum) of the
parameter that you are tweaking. Enter a smaller range to make finer
tweaking adjustments.

471

Automatic Curve Matching

Overview (Automatic Curve Matching)

AQTESOLV's automatic curve matching feature uses a nonlinear least squares
procedure to match solutions (type curves and straight lines) to data from an aquifer
test. Through a sequence of iterations, the program systematically adjusts the values
of hydraulic properties to achieve the best statistical match between a solution and
your test data. Each iteration seeks to minimize the sum of squared residuals. By
defining convergence tolerances, you control when iterations terminate.

To control the iterative automatic curve matching procedure, you can define
the maximum number of iterations and convergence criteria.

To hold parameter values constant during automatic estimation, you may

declare a set of inactive parameters.

Choose a set of active wells to limit automatic curve matching to selected

observation wells.

Define a time window for automatic estimation to match a type curve or

straight line to a desired range of data.

Assign weights to individual observations or select a weighting method to

control automatic curve matching.

Use visual matching to improve starting guesses for the automatic curve
fitting procedure.

How Automatic Curve Matching Works

AQTESOLV performs nonlinear weighted least-squares parameter estimation
(automatic curve matching) using the Gauss-Newton linearization method. To
improve the convergence of the method from poor initial guesses for the unknown
parameters, AQTESOLV includes the Marquardt damping parameter (Marquardt
1963).
In the Gauss-Newton method of parameter estimation, the parameter corrections
necessary to minimize the difference between observed and estimated values of the
response variable can be expressed as a Taylor series expanded about the current
estimated value as follows:

where:

472

The previous equation can be linearized by truncating the Taylor series after the first
derivative as follows:

Thus, for p unknown parameters, the general linearized equation for computing
parameter corrections is written as follows:

The previous equation is written for each observed value of the response variable.
The partial derivatives of the response variable with respect to the unknown
parameters are known as sensitivity coefficients. When a parameter is insensitive,
its sensitivity coefficients will approach zero. You can choose a method for calculating
the sensitivity coefficients in the advanced options for automatic estimation.
The resulting system of linearized equations is solved iteratively until convergence is
obtained. The objective function for this minimization problem is the residual sum
squares (RSS) given by the following expression:

where n is the total number of observed values of the response variable. In matrix
form, the Gauss-Newton method computes parameter correction as follows:

where:

To improve the conditioning of the XTX variance-covariance matrix, AQTESOLV adds

the Marquardt damping parameter to the previous equation:
473

where:

AQTESOLV also uses scaling of the variance-covariance matrix to improve the

conditioning of the procedure (Bard 1970).
A well-conditioned variance-covariance matrix has a small condition number. Large
condition numbers can result from poor starting guesses and lead to slow
convergence, or even divergence, of the iterative parameter updating procedure; in
these situations, singular value decomposition, an advanced estimation option,
can improve convergence of the procedure.
AQTESOLV adds the Marquardt damping parameter when parameter corrections
computed by the Gauss-Newton method fail to reduce the RSS. Iterations performed
with the Marquardt damping parameter start with a sufficiently small value of
lambda; larger values of lambda are applied until the RSS is reduced. As iterations
continue and the objective function approaches a minimum, AQTESOLV reduces
lambda for faster convergence. You can control the lambda updating method in the
advanced options for automatic estimation. The parameter estimation algorithm
terminates when user-defined convergence criteria are met.
Weighted least-squares estimation is accomplished as follows:

where:

In this implementation of the weighted least-squares algorithm, a larger weight

assigned to a measurement results in greater influence by that measurement in the
parameter estimation procedure.
AQTESOLV determines variances of the estimated parameters as follows:

The standard errors of the estimated parameters are given by the square root of the
main diagonal elements of the

matrix.

Correlations between the individual parameters are determined from the following
equation:

474

where the variance and covariance terms are components of

Parameter Statistics
Confidence Interval
Using the results from automatic curve matching, one can construct an approximate
confidence interval under the assumptions that the model is linear in the
neighborhood of the minimum of the objective function and the errors are normally
distributed:

where

is the estimate of ith parameter

t(/2,n-p) is the probability points of the Student t distribution with level of
significance and n-p degrees of freedom
is the standard error of the ith estimated parameter

AQTESOLV uses the above formula to report 95% confidence interval for parameters.
When the degrees of freedom (n-p) is large, the 95% (1-) confidence interval may
be conveniently approximated as follows (Draper and Smith 1981):

Significance Test
One can perform an approximate test of whether the true value of a parameter is
equal to a specific value * by comparing the following quantity (t-ratio):

to a table of Student's t distribution with n-p degrees of freedom.

For example, if n-p is large and one wishes to test whether b is different from zero at
the = 0.05 level of significance, one would reject the null hypothesis (i.e., b = 0)
when the t-ratio 2, where 2 is the approximate critical t-value when the degrees of
475

freedom is large and = 0.05.

Residual Statistics
A residual, e, is the difference between an observed value and its estimated
(simulated) value:

The objective function that is minimized during automatic curve matching is the sum
of the squared residuals (RSS) given by the following expression:

where n is the total number of observations.

The residual variance and standard deviation are defined as follows:

where p is the number of estimated parameters.

Finally, we compute the residual mean using the following formula:

Automatic curve matching seeks to minimize the residual sum of squares, residual
variance and standard deviation and obtain a residual mean close to zero.

Tips for Automatic Curve Matching

Starting Guesses
Improve the performance of automatic parameter estimation by developing

476

reasonable preliminary estimates of aquifer properties from site-specific data and

literature values (e.g., hydraulic conductivity). Refine the starting guesses using
visual matching before proceeding to automatic curve matching.

Windows and Weights

You may control automatic curve matching using the match window and observation
weighting features in AQTESOLV.
A match window defines a range of time for automatic curve matching. With the
window active, AQTESOLV matches the solution to observations within the window;
observations outside the time range of the window are excluded from the fitting
procedure. For example, you could assign a match window to exclude recovery data
and match only pumping data.
Two weighting options are available in AQTESOLV.
1. You may assign weights to individual observations. A weight of zero excludes
the observation from automatic curve matching; a larger weight increases the
importance of the observation in the fitting process. For example, you could
assign a weight of zero to observations known to have large measurement
error.
2. Alternatively, you may select a weighting method that applies to all active
observations in all active wells. For example, the weighting schemes are
useful for multiwell tests when the response data differ markedly in
magnitude between observation wells.

Conditioning
Automatic parameter estimation performs better when the covariance matrix (XTX)
formulated for the nonlinear least-squares algorithm is well conditioned (i.e., has a
small condition number). Convergence difficulties often are the result of a covariance
matrix having a large condition number.
In many cases, you can reduce the condition number of the covariance matrix and
improve automatic estimation performance by employing the strategies outlined
below.
1. Determine if the model (solution) is appropriate. Trying to match an
inappropriate model can lead to convergence problems. A model with fewer
parameters may be more appropriate.
2. Use visual matching to improve the starting guesses of model parameters
(hydraulic properties) as much as possible. Even a crude visual match that
moves the solution curve over the data may be sufficient to overcome
difficulties associated with ill conditioning.
3. Match a subset of the solution parameters by fixing (holding constant) the
values of insensitive parameters. During automatic estimation, the values of
insensitive parameters tend to fluctuate greatly between iterations.
For example, if you matching the Neuman solution to pumping test data that
do not exhibit the expected late-time behavior of an unconfined aquifer with
delayed gravity response, you will not be able to match specific yield (Sy)

477

with any precision. In this case, you could fix the value of Sy at an
appropriate value (e.g., 0.1 or 0.2) and match the remaining hydraulic
properties in the solution with automatic estimation.
In some instances, the sensitivity of certain parameters may increase as the
objective function is minimized. After performing a sequence of iterations with
a set of fixed parameter values, you may choose to attempt additional
iterations with all parameters active to improve the fit of the solution.
As an alternative to manually holding parameters constant, you can employ
singular value decomposition to improve conditioning (see below).
4. Try a different updating method for the Marquardt lambda parameter. A more
conservative scheme may take more iterations to converge, but avoid
problems sometimes caused by overshoot (parameter corrections that are too
large) during the iterative automatic estimation procedure.
5. Apply SVD (singular value decomposition) to improve convergence from poor
starting guesses.
SVD dampens the corrections of parameters with small eigenvalues in the
parameter updating equations, thereby decreasing the condition number of
the covariance matrix. AQTESOLV performs this procedure when a
parameter's eigenvalue, i, meets the following test:
i |max|/CTOL
where CTOL is the condition number threshold criterion set in the advanced
options for automatic estimation.

478

Obtaining Output
Printing

Overview (Printing)
Choose options from the File menu to send the active plot or report to a printing
device connected to your computer.
Print
Print Preview
Print Setup
Page Setup
Batch Print

Print the plot or report in the active

window
Preview the plot or report before printing
Configure printer options
Format the page for printing
Batch print a group of data sets

To customize the appearance of a plot or report for printing, choose

View>Format.

You can change to font size for a plot legend to fit more information on one
page.

As an alternative to printing, you may copy a plot or report and paste it into
another Windows application.

Print
(File > Print)
Choose Print from the File menu or click
on the toolbar to open a dialog for
printing the plot or report in the active window.

Click Setup or Properties to configure the selected printer.

If the legend of a plot does not fit on one page, choose View>Format>Legend
tab to decrease the font size.

479

Print Preview
(File > Print Preview)
Choose Print Preview from the File menu or click
appearance of a plot or report prior to printing.

on the toolbar to preview the

While previewing, click Print to print the plot/report or Close to end print
preview without printing.

If the legend of a plot does not fit on one page, choose View>Format>Legend
tab to decrease the font size.

Print Setup
(File > Print Setup)
Choose Print Setup from the File menu to open a dialog for selecting and
configuring a printer connected to your computer.

Page Setup
(File > Page Setup)
Choose Page Setup from the File menu to configure page options for report
headers and footers and other page customization features.
o

Margins Tab
1. Enter values (in inches) for the margins of printed pages of plots and
reports.

Print Tab
1. Select options to customize the printing of plots and reports.
2. If the y-axis label is not rotated when you print a plot, check Force font
rotation of y-axis label on plots. If the font is still not rotated after
selecting this option, your printer does not support font rotation.

480

Batch Print
(File > Batch Print)
Choose Batch Print from the File menu to launch the Batch Print Wizard for
printing a group of AQTESOLV data sets at one time.
Batch Print Wizard
Step 1

1. In Step 1 of the wizard, click Browse to select a group of AQTESOLV data

sets to batch print.
2. Place a check next to each plot or report that you want to print from each
data set.
3. Click Next.

481

Step 2

1. In Step 2 of the wizard, choose a formatting option for the data sets that you
are batch printing. You may use (a) formats contained in the individual data
sets without changes or (b) formats from a "master" data set to reformat all
of the data sets.
2. You can use the active data set (the data set in the active window) to apply a
consistent set of formats to each printed plot or report.
3. Check Save each batch data set with formats from active data set if
you would like to save a copy of each batch data set with the consistent
formats. The formats in original files are not changed.
4. Click Finish.

If you would like to print a group of data sets with a consistent set of formats,
first open a "master" data set from the group. Make any formatting changes
in the master data set before selecting Batch Print (do not close the master
data set).

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Tips for Printing

Decrease the font size of the legend text to fit more information on one page
when printing a plot.

Use Print Preview to inspect the layout of a plot before printing.

Set page orientation (portrait or landscape) with Print Setup.

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Contouring

Overview (Contouring)
Use AQTESOLV to create contour plots of observed and simulated drawdown from an
aquifer test.

To create a contour plot of simulated drawdown, choose View>Contour to

launch the Grid Wizard. AQTESOLV provides a seamless link for automatically
generating contour plots with Surfer.

To export data for generating a contour plot of observed data, choose

File>Export and select the option to export well data. You may imported the
exported file into contouring packages such as Surfer.

Contour
(View > Contour)
Choose Contour from the View menu or click
on the toolbar to launch the Grid
Wizard which prepares a grid file for contouring and optionally creates a contour plot
using Surfer (version 6 or higher).

Right-click over a plot to select Grid/Contour.

For bounded aquifers, enter grid dimensions within the specified boundaries.

Grid Wizard
Use the Grid Wizard to prepare a grid file for contouring. If you have Surfer
(version 6 or higher) installed on your computer, AQTESOLV can automatically
display a contour plot for you.
Using the Grid Wizard
1. Choose Contour from the View menu or click
Grid Wizard.

on the toolbar to launch the

2. Follow the steps in the wizard: open the grid file, specify the grid dimensions
and display the contour plot.

You can use the Grid Wizard to create a grid file without having Surfer
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installed on your computer. Use grid files to prepare plots with contouring
applications such as Surfer, Tecplot and RockWorks.

The Grid Wizard requires that you enter values greater than zero for casing
radius and wellbore radius for each pumping well.

485

Exporting and Sharing Data

Overview (Exporting and Sharing Data)

Choose options from the File menu to export and share data.
Export
Send Mail

Export data to files

Send the active data set as an email
attachment

You can print a plot or report or you may copy it to the Windows clipboard
and paste it into another Windows application.

Use AQTESOLV to contour simulated drawdown with the automated link to

Surfer.

Export
(File > Export)
Choose Export from the File menu to export data in file formats suitable for use in
other programs.
X-Y Plot Data

Export data shown on a plot (e.g., time

and drawdown) into a tab-delimited text
file.

Well Data

Export well coordinates, observed

drawdown and simulated drawdown data
for a specified time into a text file.

Type Curve (dimensional)

Type Curve (dimensionless)

Windows Metafile

Data are exported as commaseparated values (CSV).

Four values are exported for each

observation well: X coordinate; Y
coordinate; observed drawdown;
simulated drawdown.

AQTESOLV automatically interpolates or

extrapolates observed drawdown for the
specified time as required.
Export type curve data (e.g., time and
simulated drawdown) into a tab-delimited
text file. Values are dimensional (e.g.,
seconds and meters).
Export dimensionless type curve data
(e.g., time and simulated drawdown) into
a tab-delimited text file.
Export a plot or report as a placeable

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Enhanced Windows Metafile

Windows metafile (.wmf).

Export a plot or report as an enhanced
Windows metafile (.emf).

You can import a Windows metafile created with AQTESOLV into other
applications such as Microsoft Office (Word, Excel, PowerPoint, etc.).

You also may use AQTESOLV to copy a plot or report to the clipboard and
paste it into another Windows application.

Send Mail
(File > Send Mail)
Choose Send Mail from the File menu to send the active data set as an email
attachment.

487

Tools
Overview (Tools)
The Tools menu provides options for performing special tasks such as groundwater
mounding calculations and running related Windows applications such as ModelCad
for Windows, TWODAN and WinSitu.

Mounding
(Tools > Mounding)
Choose Mounding from the Tools menu to select options for predicting the
transient water table rise beneath circular and rectangular recharge areas.

Open a new or existing data set to access this tool.

ModelCad
(Tools > ModelCad)
Choose ModelCad from the Tools menu to launch the ModelCad for Windows
application, if installed on your computer. ModelCad for Windows is a modeling
environment for groundwater flow and solute transport simulator such as
MODFLOW/MT3D.

To configure this application, select Tools>Customize.

Find out more about the ModelCad for Windows software at our web site.

TWODAN
(Tools > TWODAN)
Choose TWODAN from the Tools menu to launch the TWODAN application, if
installed on your computer. TWODAN is a two-dimensional analytic element
groundwater flow model.

488

To configure this application, select Tools>Customize.

Find out more about the TWODAN software at our web site.

WinSitu
(Tools > WinSitu)
Choose WinSitu from the Tools menu to launch the WinSitu application, if installed
on your computer. The WinSitu software works in concert with In-Situ data logger
products.

To configure this application, select Tools>Customize.

Find out more about the WinSitu software at the In-Situ web site.

Use the Observation Data Import Wizard to import In-Situ data logger files.

489

Support
Q&A
When looking for answers to questions, remember that you can click the Help button
in any data entry window to get context-sensitive help about that window.
The following are answers to questions that occasionally arise with regard to the use
of AQTESOLV.

Aquifer Data
I don't have any information on aquifer thickness. What should I enter into
AQTESOLV?
We have prepared some tips to help you estimate the thickness of an aquifer.

Well Data
How do I enter well depths?
Enter depths for partially penetrating wells measured from the top of the aquifer
(confined, leaky or fractured aquifers) or from the water table (unconfined aquifers).
Refer to well construction data for more information.
When should I correct for gravel pack porosity?
The optional correction for gravel pack porosity recommended by Bouwer and Rice
(1976) is only required for slug tests in wells screened across the water table.
What is the well skin radius?
The skin radius only applies to certain slug test solutions (e.g., KGS Model). Refer to
the well radius data for more information.
The total depth of my well extends into a confining unit or my well is open above the
water table. What screen length should I enter?
The total depth of the well should not exceed the thickness of the aquifer.
For a pumping test or constant-head test, refer to the well construction data.
For a slug test, refer to the well screen data.

Importing Data
What files can AQTESOLV import from In-Situ data loggers?
Remember that you must use the Win-Situ software to convert the native In-Situ
data logger file (.wsl or .bin) into a file type that AQTESOLV can import.
Using Win-Situ, export a file that is compatible with AQTESOLV:
1. text (.txt) files

490

2. comma-separated values (.csv) files

Why won't AQTESOLV import data from an In-Situ Level TROLL text file?
1. Download and install the latest version of the Win-Situ software from the InSitu we site.
2. Before exporting a text file from Win-Situ, choose General Settings from the
Preferences menu.
3. Select the Custom option for the Time Format.
4. Enter H:mm:ss in the Time input box.
Note the "H" is capitalized in the format string.
This custom format displays and records the time stamp with a 24-hour
(military) clock format.
5. Click the "check" button to save your changes to the settings.
6. Export a text file from Win-Situ and import it into AQTESOLV.

Recovery Tests
How do I enter recovery data from a pumping test?
Entering data for a recovery test is no different than a pumping test.
For a recovery test, the pumping well data must include all pumping rates leading up
to and including the time when pump was shut off. Thus, for the final pumping
period in the rate data, enter the elapsed time since the start of the test when the
pump was shut off and a rate of zero. In the following example, pumping stopped
after 800 minutes.

491

When you enter observation data for a recovery test, enter residual drawdown data
(not recovery). Each value of time during the recovery period should be greater than
the time when pumping stopped. In the following example, recovery starts after 800
minutes.

492

Curve Matching
Why doesn't a straight-line solution fit the trend of my test data when I perform
automatic curve matching?
Matching a straight-line solution (e.g., Cooper-Jacob, Theis residual drawdown,
Bouwer-Rice, Hvorslev and Jacob-Lohman) to test data requires your judgment to
define the appropriate range of data for matching the solution.
With automatic curve matching, you can define this range using a match window;
however, it is usually more efficient to perform visual curve matching with these
solutions.
Why can't I see the simulated displacement curve (type curve) when I choose a
solution?
The curve for the simulated displacement may be plotting outside the plot window.
You can format the plot to expand the axes or you can use visual curve matching to
reposition the curve.
Can I match data from multiple observation wells?
Yes. You may add more than one observation well to a data set. When you perform
visual or automatic curve matching, AQTESOLV matches one set of aquifer properties
to all of the observation wells in the data set.
Here is a strategy that you may follow in analyzing multiple observation wells:
1. Create a master data containing all of the observation wells from your test.
Perform curve matching using all of the wells.
2. Due to heterogeneity or horizontal anisotropy, you may find that matching
one set of aquifer properties to all of the wells produces a poor fit. In this
situation, you may delete observation wells from the master data set that
behave differently and save the wells that behave in similar fashion in a
separate data set.
3. You may analyze wells singly by deleting the other wells from the master data
set and saving them in individual data sets.

Plots, Reports and Printing

Why don't the data plotted on my graph match the observed data?
There are two cases where this may occur.
1. If you are using the Theis or Cooper-Jacob solution for a pumping test in an
unconfined aquifer, the drawdown data are adjusted using Jacob's correction
for partial dewatering of the aquifer.
2. If you are using the Cooper-Jacob solution for a pumping test in a confined or
unconfined aquifer and the pumping rate is variable, the program transforms
the time and drawdown to allow you to match a straight line.
How do I place the origin in the upper-left corner of a plot?

493

Choose Format from the View menu and click the Graph tab to change the origin of
the plot to the upper-left corner.
When I print a graph, why aren't the characters in the y-axis label rotated as they
appear on the screen?
Your printer may not support font rotation; however, on most newer printers, you
can force font rotation to remedy this issue.
How do I print the plot legend on a single page?
To fit more legend information on a page when you print a plot, change formatting
options such as the font size or the number of items displayed.
How do I display axis tick labels as 102 instead of 1.E2?
Choose Format from the View menu. In the Graph tab, check Use Base10 Label
Format on Log Axes.
Why don't I see any data when I select the option for an Agarwal plot?
To use an Agarwal plot to analyze data from a recovery test, make sure that your
observation well data include a drawdown value measured at time tp when the pump
was shut off.
Let us suppose that you pump a well for 1440 minutes and monitor recovery after
turning off the pump. Your observation data must include a drawdown measurement
at 1440 minutes (tp) if you intend to use the Agarwal method.

Contouring
Why does the Grid Wizard ask for a depth interval when I contour drawdown in plan
view?
If the solution that you are contouring supports partially penetrating wells, you can
contour drawdown in plan view over a specific depth interval in the aquifer.
For example, assume the thickness of the aquifer under study is 10 feet. To contour
the drawdown in observation wells screened between 9 and 10 feet, enter minimum
and maximum z values in the Grid Wizard of 9 and 10, respectively.

Error Messages
What should I do when I see "Check Errors" at the bottom of the AQTESOLV window?
When you see Check Errors on the status bar, you should view the Error Log to
identify and correct errors that AQTESOLV has detected in the data set.
What does the "Maximum displacement > initial displacement" warning in the Error
Log mean?
In a slug test, the initial displacement is generally the maximum displacement
measured during the test. If you get this warning, it indicates that a displacement
measured after the initial reading exceeds the initial displacement value. Inspect the
observation data to find the displacement measurement that is greater than the
initial displacement and correct if necessary. Otherwise you may ignore the warning.

494

Why do I get a warning about "Initial Displacement > saturated thickness" in the
Error Log?
This warning applies to a slug test in an unconfined aquifer. It alerts you to a
possible error in the case of the initial displacement due to slug removal exceeding
the saturated thickness of the aquifer.
For confined aquifers or slug injection, you may ignore this warning.
Why do I get a warning about "Maximum Displacement > saturated thickness" in the
Error Log?
This warning applies to a pumping test in an unconfined aquifer. It alerts you to a
possible error in the case of the maximum drawdown in the observation data
exceeding the saturated thickness of the aquifer.
For confined aquifers or injection tests, you may ignore this warning.
How do I correct errors shown in the Error Log?
Choose options from the Edit menu to modify the data set.

Miscellaneous
How do you pronounce AQTESOLV anyway?
Click here to find out!
Find answers to other support questions in the Knowledge Base at the AQTESOLV
web site.

Technical Support
Software Registration
Please use our on-line form to register your copy of AQTESOLV.

Web Resources
Visit the support section of our web site to join the AQTESOLV Users' Group, find
answers to technical questions in the Knowledge Base, and download helpful
examples and tutorials.

Telephone Support
For other questions, contact HydroSOLVE, Inc. by telephone, fax or e-mail. Please
have your serial number available.
Glenn M. Duffield, Developer
HydroSOLVE, Inc.
2303 Horseferry Court
Reston, VA 20191-2739
Tel: (703) 264-9024
Fax: (209) 254-8831
E-Mail: hydrosolve@aqtesolv.com
WWW: www.aqtesolv.com

495

Please be prepared to provide as full a description of your problem as possible.

To assist us in answering your question, it is very helpful to send a copy of your
AQTESOLV data set (.aqt file) as an e-mail attachment.

Special Services Available

If you or your company would like specialized instruction on the analysis of aquifer
tests using AQTESOLV, feel free to contact HydroSOLVE, Inc. or visit our web site for
information on short courses, seminars and professional consulting services.

496

References
References
General
Pumping Tests
Constant-Head Tests
Slug Tests
Mounding
Derivative Analysis
Numerical Methods

General
Batu, V., 1998. Aquifer Hydraulics: A Comprehensive Guide to Hydrogeologic Data
Analysis, John Wiley & Sons, Inc., New York, 727p.
Bear, J., 1979. Hydraulics of Groundwater, McGraw-Hill, New York, 569p.
Butler, J.J., Jr., 1998. The Design, Performance, and Analysis of Slug Tests, Lewis
Publishers, Boca Raton, Florida, 252p.
Draper, N. and H. Smith, 1981. Applied Regression Analysis (2nd ed.), John Wiley
and Sons, New York, 709p.
Driscoll, F.G., 1986. Groundwater and Wells (2nd ed.), Johnson Filtration Systems,
Inc., St. Paul, Minnesota, 1089p.
Ferris, J.G., D.B. Knowles, R.H. Brown and R.W. Stallman, 1962. Theory of aquifer
tests, U.S. Geol. Survey Water-Supply Paper 1536-E, 174p.
Fitts, C.R., 2002. Groundwater Science, Academic Press, New York, 450p.
Greenkorn, R.A., 1983. Flow Phenomena in Porous Media, Marcel Dekker, New York,
550p.
Hantush, M.S., 1964. Hydraulics of wells, in: Advances in Hydroscience, V.T. Chow
(editor), Academic Press, New York, pp. 281-442.
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.
Lohman, S.W., 1972. Ground-water hydraulics, U.S. Geological Survey Prof. Paper
708, 70p.
Morris, D.A. and A.I. Johnson, 1967. Summary of hydrologic and physical properties
of rock and soil materials as analyzed by the Hydrologic Laboratory of the U.S.
497

Geological Survey, U.S. Geol. Surv. Water-Supply Paper 1839-D, 42p.

Raghavan, R., 1993. Well Test Analysis, Prentice Hall, Englewood Cliffs, New Jersey,
558p.
Sen, Z., 1995. Applied Hydrogeology for Scientists and Engineers, Lewis Publishers,
Boca Raton, Florida, 464p.
Streltsova, T.D., 1988. Well Testing in Heterogeneous Formations, John Wiley &
Sons, New York, 413p.
Todd, D.K., 1980. Groundwater Hydrology, John Wiley & Sons, New York, 535p.
USBR, 1995. Ground Water Manual, U.S. Dept. of Interior, Bureau of Reclamation,
Washington, D.C., 661p.
Van Everdingen, A.F. and W. Hurst, 1949. The application of the Laplace
transformation to flow problems in reservoirs, Petroleum Transactions, AIME, vol.
186, pp. 305-324.
Walton, W.C., 1962. Selected analytical methods for well and aquifer evaluation,
Illinois State Water Survey Bulletin 49, Urbana, Illinois, 81p.

Pumping Tests
Agarwal, R.G., 1980. A new method to account for producing time effects when
drawdown type curves are used to analyze pressure buildup and other test data, SPE
Paper 9289 presented at the 55th SPE Annual Technical Conference and Exhibition,
Dallas, TX, Sept. 21-24, 1980.
Barker, J.A., 1988. A generalized radial flow model for hydraulic tests in fractured
rock, Water Resources Research, vol. 24, no. 10, pp. 1796-1804.
Birsoy, Y.K. and W.K. Summers, 1980. Determination of aquifer parameters from
step tests and intermittent pumping, Ground Water, vol. 18, no. 2, pp. 137-146.
Black, J.H. and K.L. Kipp, 1977. Observation well response time and its effect upon
aquifer test results, Journal of Hydrology, vol. 34, pp. 297-306.
Butler, J.J., Jr., 1988. Pumping tests in nonuniform aquifersthe radially symmetric
case, Journal of Hydrology, vol. 101, pp. 15-30.
Clark, L., 1977. The analysis and planning of step drawdown tests, Q. Jour. Eng.
Geol., vol. 10, pp. 125-143.
Clonts, M.D. and H.J. Ramey, Jr., 1986. Pressure transient analysis for well with
horizontal drainholes, SPE Paper 15116, presented at the 56th Califorinia Regional
Meeting, Oakland, CA, April 2-4, 1986.
Cooper, H.H. and C.E. Jacob, 1946. A generalized graphical method for evaluating
formation constants and summarizing well field history, Am. Geophys. Union Trans.,
vol. 27, pp. 526-534.
Daviau, F., Mouronval, G., Bourdarot, G. and P. Curutchet, 1985. Pressure analysis
for horizontal wells, SPE Paper 14251, presented at the 60th Annual Technical
Conference and Exhibition in Las Vegas, NV, Sept. 22-25, 1985.

498

Dougherty, D.E and D.K. Babu, 1984. Flow to a partially penetrating well in a doubleporosity reservoir, Water Resources Research, vol. 20, no. 8, pp. 1116-1122.
Gringarten, A.C. and H.J. Ramey, 1974. Unsteady state pressure distributions
created by a well with a single horizontal fracture, partial penetration or restricted
entry, Soc. Petrol. Engrs. J., pp. 413-426.
Gringarten, A.C., Ramey, H.J., Jr. and R. Raghavan, 1974. Unsteady-state pressure
distributions created by a well with single infinite-conductivity vertical fracture, Soc.
Petrol. Engrs. J., pp. 347-360.
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, J. Geophys. Research, 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. Union Trans., vol. 36, pp. 95-100.
Huntley, D., Nommensen, R. and D. Steffey, 1992. The use of specific capacity to
assess transmissivity in fractured-rock aquifers, Ground Water, vol. 30, no. 3, pp.
396-402.
Mace, R.E., 1997. Determination of transmissivity from specific-capacity tests in a
karst aquifer, Ground Water, vol. 35, no. 5, pp. 738-742.
Moench, A.F., 1984. Double-porosity models for a fissured groundwater reservoir
with fracture skin, Water Resources 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. 11211131.
Moench, A.F., 1988. The response of partially penetrating wells to pumpage from
double-porosity aquifers, Proceedings of the International Conference on Fluid Flow
in Fractured Rocks, Atlanta, GA, May 16-18, 1988.
Moench, A.F., 1993. Computation of type curves for flow to partially penetrating
wells in water-table aquifers, Ground Water, vol. 31, no. 6, pp. 966-971.
Moench, A.F., 1995. Combining the Neuman and Boulton models for flow to a well in
an unconfined aquifer, Ground Water, vol. 33, no. 3, pp. 378-384.
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.
499

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.
Moench, A.F., Garabedian, S.P. and D.R. LeBlanc, 2001. Estimation of hydraulic
parameters from an unconfined aquifer test conducted in a glacial outwash deposit,
Cape Cod, Massachusetts, U.S. Geological Survey Professional Paper 1629, 69p.
Moench, A.F. and T.A. Prickett, 1972. Radial flow in an infinite aquifer undergoing
conversion from artesian to water-table conditions, Water Resources Research, vol.
8, no. 2, pp. 494-499.
Murdoch, L.C., 1994. Transient analyses of an interceptor trench, Water Resources
Research, vol. 30, no. 11, pp. 3023-3031.
Neuman, S.P. and P.A. Witherspoon, 1969. Theory of flow in a confined two aquifer
system, Water Resources Research, vol. 5, no. 4, pp. 803-816.
Neuman, S.P., 1972. Theory of flow in unconfined aquifers considering delayed
gravity response of the water table, Water Resources Research, vol. 8, no. 4, pp.
1031-1045.
Neuman, S.P., 1974. Effect of partial penetration on flow in unconfined aquifers
considering delayed gravity response, Water Resources Research, vol. 10, no. 2, pp.
303-312.
Ozkan, E., Raghavan, R. and S.D. Joshi, 1989. Horizontal-well pressure analysis, SPE
Formation Evaluation (December 1989), pp. 567-575.
Papadopulos, I.S. and H.H. Cooper, 1967. Drawdown in a well of large diameter,
Water Resources Research, vol. 3, no. 1, pp. 241-244.
Razack, M. and D. Huntley, 1991. Assessing transmissivity from specific capacity
data in a large and heterogeneous alluvial aquifer, Ground Water, vol. 29, no. 6, pp.
856-851.
Rorabaugh, M.J., 1953. Graphical and theoretical analysis of step-drawdown test of
artesian wells, Proc. of the Am. Soc. Civil Eng., vol. 79, separate no. 362, 23p.
Tartakovsky, G.D. and S.P. Neuman, 2007. Three-dimensional saturated-unsaturated
flow with axial symmetry to a partially penetrating well in a compressible unconfined
aquifer, Water Resources Research, W01410, doi:1029/2006WR005153.
Theis, C.V., 1935. The relation between the lowering of the piezometric surface and
the rate and duration of discharge of a well using groundwater storage, Am.
Geophys. Union Trans., vol. 16, pp. 519-524.
Vandenberg, A., 1977. Type curves for analysis of pump tests in leaky strip aquifers,
J. Hydrology, vol. 33, pp. 15-26.

Constant-Head Tests
Barker, J.A., 1988. A generalized radial flow model for hydraulic tests in fractured
rock, Water Resources Research, vol. 24, no. 10, pp. 1796-1804.
Doe, T.W., 1991. Fractional dimension analysis of constant-pressure well tests, SPE
Paper 22702, presented at the 66th Annual Technical Conference and Exhibition,
500

Dallas, TX, Oct. 8-9, 1991.

Dougherty, D.E and D.K. Babu, 1984. Flow to a partially penetrating well in a doubleporosity reservoir, Water Resources Research, vol. 20, no. 8, pp. 1116-1122.
Ehlig-Economides, C.A. and H.J. Ramey, Jr., 1981. Pressure buildup for wells
produced at a constant pressure, SPE Journal, February 1981, pp. 105-114.
Hantush, M.S., 1959. Nonsteady flow to flow wells in leaky aquifers, Journal of
Geophysical Research, vol. 64, no. 5, pp. 1043-1052.
Hurst, W., J.D. Clark and E.B. Brauer, 1969. The skin effect in producing wells,
Journal of Petroleum Technology, November 1969, pp. 1483-1489.
Jacob, C.E. and S.W. Lohman, 1952. Nonsteady flow to a well of constant drawdown
in an extensive aquifer, Trans. Am. Geophys. Union, vol. 33, pp. 559-569.
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. 11211131.
Ozkan, E. and R. Raghavan, 1991. New solutions for well-test analysis problems:
Part I-analytical considerations, SPE Formation Evaluation, Sept. 1991, pp. 359-368.
Uraiet, A.A. and R. Raghavan, 1980. Pressure buildup analysis for a well produced at
constant bottomhole pressure, Journal of Petroleum Technology, Oct. 1980, pp.
1813-1824.

Slug Tests
Barker, J.A. and J.H. Black, 1983. Slug tests in fissured aquifers, Water Resources
Research, vol. 19, no. 6, pp. 1558-1564.
Boast, C.W. and D. Kirkham, 1971. Auger hole seepage theory, Soil Science of
America Proceedings, vol. 35, no. 3, pp. 365-373.
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 unconfined aquifers with completely or partially penetrating wells,
Water Resources Research, vol. 12, no. 3, pp. 423-428.
Butler, J.J., Jr., 2002. A simple correction for slug tests in small-diameter wells,
Ground Water, vol. 40, no. 3, pp. 303-307.
Butler, J.J., Jr., Garnett, E.J. and J.M. Healey, 2003. Analysis of slug tests in
formations of high hydraulic conductivity, Ground Water, vol. 41, no. 5, pp. 620-630.
Butler, J.J., Jr. and X. Zhan, 2004. Hydraulic tests in highly permeable aquifers,
Water Resources Research, vol. 40, W12402, doi:10.1029/2003WR002998.
Chu, L. and A.S. Grader, 1991. Transient-pressure analysis for interference slug test,
SPE Paper 23444, Society of Petroleum Engineers.
Cooper, H.H., J.D. Bredehoeft and S.S. Papadopulos, 1967. Response of a finite-

501

diameter well to an instantaneous charge of water, Water Resources Research, vol.

3, no. 1, pp. 263-269.
Dagan, G., 1978. A note on packer, slug, and recovery tests in unconfined aquifers,
Water Resources Research, vol. 14, no. 5. pp. 929-934.
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.
Hyder, Z, J.J. Butler, Jr., C.D. McElwee and W. Liu, 1994. Slug tests in partially
penetrating wells, Water Resources Research, vol. 30, no. 11, pp. 2945-2957.
McElwee, C.D., 2001. Application of a nonlinear slug test model, Ground Water, vol.
39, no. 5, pp. 737-744.
McElwee, C.D., Butler, J.J., Jr. and G.C. Bohling, 1992. Nonlinear analysis of slug
tests in highly permeable aquifers using a Hvorslev-type approach, Kansas Geol.
Survey Open-File Report 92-39.
McElwee, C.D. and M. Zenner, 1998. A nonlinear model for analysis of slug-test data,
Water Resources Research, vol. 34, no. 1, pp. 55-66.
Pandit, N.S. and R.F. Miner, 1986. Interpretation of slug test data, Ground Water,
vol. 24, no. 6, pp. 743-749.
Peres, A.M., Onur, M. and A.C. Reynolds, 1989. A new analysis procedure for
determining aquifer properties from slug test data, Water Resources Research, vol.
25, no. 7, pp. 1591-1602.
Ross, B., 1985. Theory of the oscillating slug test in deep wells in Memoirs 17th Int.
Congr. Hydrogeol. Rocks Low Permeability, vol. 17, no. 2, Int. Assoc.
Hydrogeologists, pp. 44-51.
Springer, R.K. and L.W. Gelhar, 1991. Characterization of large-scale aquifer
heterogeneity in glacial outwash by analysis of slug tests with oscillatory response,
Cape Cod, Massachusetts, U.S. Geol. Surv. Water Res. Invest. Rep. 91-4034, pp. 3640.
Zlotnik, V., 1994. Interpretation of slug and packer tests in anisotropic aquifers,
Ground Water, vol. 32, no. 5, pp. 761-766.
Zlotnik, V.A. and V.L. McGuire, 1998. Multi-level slug tests in highly permeable
formations: 1. Modifications of the Springer-Gelhar (SG) model, Jour. of Hydrol., no.
204, pp. 271-282.
Zurbuchen, B.R., V.A. Zlotnik and J.J. Butler, Jr., 2002. Dynamic interpretation of
slug tests in highly permeable aquifers, Water Resources Research, vol. 38, no. 3.,
1025, doi:10.1029/2001WRR000354.

Mounding
Hantush, M.S., 1967. Growth and decay of groundwater mounds in response to
uniform percolation, Water Resources Research, vol. 3, no. 1, pp. 227-234.

502

Derivative Analysis
Bourdet, D., Ayoub, J.A. and Y.M. Pirard, 1989. Use of pressure derivative in welltest interpretation, SPE Formation Evaluation, June 1989, pp. 293-302.
Bourdet, D., Whittle, T.M., Douglas, A.A. and Y.M. Pirard, 1983. A new set of type
curves simplifies well test analysis, World Oil, May 1983, pp. 95-106.
Spane, F.A., Jr., and S.K. Wurstner, 1993. DERIV: A computer program for
calculating pressure derivatives for use in hydraulic test analysis, Ground Water, vol.
31, no. 5, pp. 814-822.

Numerical Methods
Abramowitz, M. and I.A. Stegun, 1972. Handbook of Mathematical Functions, Dover
Publications, Inc., New York, 1046p.
Bard, Y., 1970. Nonlinear Parameter Estimation, Academic Press, New York, 341p.
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.
Nielsen, H.B., 1999. Damping Parameter in Marquardts Method, Report IMM-REP1999-05, IMM, DTU, Lyngby, Denmark, 31p.
Press, W.H., Teukolsky, S.A., Vetterling, W.T. and B.P. Flannery, 2002. Numerical
Recipes in C++: The Art of Scientific Computing, 2nd ed., Cambridge University
Press, New York, 1002p.

Additional Sources
You may find additional resources relating to aquifer testing on the web. The Aquifer
Test Forum, maintained by HydroSOLVE, Inc., includes a bookstore and reference
list.

503

Appendices
Conversions
Use the following tables to convert units of length, area, volume and volumetric flow
rate.
Length
To Convert
ft
ft
cm
m
mile
mile

Multiply By
0.3048
30.48
2.54
3.2808
5280
1.6093

To Obtain
m
cm
in
ft
ft
km

Multiply By
43560
0.092903

To Obtain
ft2
m2

Multiply By
7.4805
62.38
0.26417
0.03531
35.3145
1000
264.17
0.8327

To Obtain
U.S. gallons
pounds of water
U.S. gallons
ft3
ft3
liters
U.S. gallons
Imperial gallons

Multiply By
2.832x10-2
4.381x10-5
0.06309

To Obtain
m3/sec
liters/sec
liters/sec

Multiply By
9.870x10-13
0.092903

To Obtain
m2
m2

Multiply By
2.3067196
0.101974

To Obtain
ft of water @ 4C
m of water @ 4C

Area
To Convert
acres
ft2
Volume
To Convert
ft3
ft3
liters
liters
m3
m3
m3
U.S. gallons
Volumetric Flow Rate
To Convert
ft3/sec
gpd
gpm
Permeability
To Convert
darcy
ft2
Pressure
To Convert
psi
kPa
Abbreviations

504

cm = centimeter
ft = foot
gpd = U.S. gallons/day
gpm = U.S. gallons/minute
in = inch
km = kilometer
kPa = kilopascal
m = meter
min = minute
psi = pound-force/in2
sec = second
Examples
1. Convert 25 U.S. gallons to liters.
(25 U.S. gallons)(liters/0.26417 U.S. gallons) = 94.6 liters
2. Convert 2 inches to meters.
(2 in)(2.54 cm/in)(m/100 cm) = 0.051 m
3. Convert 1 ft/min to cm/sec.
(1 ft/min)(12 in/ft)(2.54 cm/in)(min/60 sec) = 0.51 cm/sec
4. Convert 100,000 gpd/ft to m2/sec.
(100,000 gal/day/ft)(ft3/7.4805 gal)(0.092903 ft2/m2)(day/86400 sec) =
0.0144 m2/sec
5. Convert 1 darcy (permeability) to m/sec (hydraulic conductivity).
The relationship between the permeability of a porous medium and hydraulic
conductivity is K = kg/ where K is hydraulic conductivity [L/T], k is
permeability [L2], is density of water [M/L3], g is gravitational acceleration
[L/T2], and is dynamic viscosity of water [M/LT].
If we assume = 998.8 kg/m3, g = 9.8 m/sec2 and = 0.00111 Nsec/m2 @
15 and 1 atm, the conversion is as follows:
(1 darcy)(9.870x10-13 m2/darcy)(998.8 kg/m3)(9.8 m/sec2)/(0.00111
Nsec/m2) = 8.70x10-6 m/sec
Note that dynamic viscosity and density are dependent on temperature and
pressure. If we assume = 1000 kg/m3 and = 0.001 Nsec/m2, we find
that 1 darcy = 9.67x10-6 m/sec.

505

Hydraulic Conductivity
Hydraulic conductivity is defined as a constant of proportionality relating the specific
discharge of a porous medium under a unit hydraulic gradient in Darcy's law:
= -Ki
where is specific discharge [L/T], K is hydraulic conductivity [L/T] and i is hydraulic
gradient [dimensionless].
The transmissivity of an aquifer is related to hydraulic conductivity as follows:
T = Kb
where T is transmissivity [L2/T] and b is aquifer thickness [L].
The following tables show representative values of hydraulic conductivity for various
unconsolidated sedimentary materials, sedimentary rocks and crystalline rocks (from
Domenico and Schwartz 1990):
Unconsolidated Sedimentary Materials
Material
Hydraulic Conductivity
(m/sec)
Gravel
3x10-4 to 3x10-2
Coarse sand
9x10-7 to 6x10-3
Medium sand
9x10-7 to 5x10-4
Fine sand
2x10-7 to 2x10-4
Silt, loess
1x10-9 to 2x10-5
Till
1x10-12 to 2x10-6
Clay
1x10-11 to 4.7x10-9
Unweathered marine clay
8x10-13 to 2x10-9

Sedimentary Rocks
Rock Type
Karst and reef limestone
Limestone, dolomite
Sandstone
Siltstone
Salt
Anhydrite
Shale

Hydraulic Conductivity
(m/sec)
1x10-6 to 2x10-2
1x10-9 to 6x10-6
3x10-10 to 6x10-6
1x10-11 to 1.4x10-8
1x10-12 to 1x10-10
4x10-13 to 2x10-8
1x10-13 to 2x10-9

Crystalline Rocks
Material

Hydraulic Conductivity
(m/sec)
Permeable basalt
4x10-7 to 2x10-2
Fractured igneous and metamorphic rock 8x10-9 to 3x10-4
Weathered granite
3.3x10-6 to 5.2x10-5
Weathered gabbro
5.5x10-7 to 3.8x10-6
506

Basalt
Unfractured igneous and metamorphic
rock

To Convert
m/sec
m/sec
m/sec

2x10-11 to 4.2x10-7
3x10-14 to 2x10-10

Multiply By
100
2.12x106
3.2808

To Obtain
cm/sec
gal/day/ft2
ft/sec

Anisotropy Ratio
An anisotropy ratio relates hydraulic conductivities in different directions. For
example, vertical-to-horizontal hydraulic conductivity anisotropy ratio is given by
Kz/Kr where Kz is vertical hydraulic conductivity and Kr is radial (horizontal) hydraulic
conductivity. Anisotropy in a horizontal plane is given by Ky/Kx where Kx and Ky are
horizontal hydraulic conductivities in the x and y directions, respectively.
Todd (1980) reports values of Kz/Kr ranging between 0.1 and 0.5 for alluvium and
possibly as low as 0.01 when clay layers are present.
The following table shows representative values of horizontal and vertical hydraulic
conductivities for selected rock types (from Domenico and Schwartz 1990):
Material
Anhydrite
Chalk
Limestone, dolomite
Sandstone
Shale
Salt

Horizontal Hydraulic
Conductivity
(m/sec)
10-14 to 10-12
10-10 to 10-8
10-9 to 10-7
5x10-13 to 10-10
10-14 to 10-12
10-14

Vertical Hydraulic
Conductivity
(m/sec)
10-15 to 10-13
5x10-11 to 5x10-9
5x10-10 to 5x10-8
2.5x10-13 to 5x10-11
10-15 to 10-13
10-14

Porosity
Porosity (n) is defined as the void space of a rock or unconsolidated material:
n = Vv/VT
where Vv is void volume and VT is total volume.
The following tables show representative porosity values for various unconsolidated
sedimentary materials, sedimentary rocks and crystalline rocks (from Morris and
Johnson 1967):
Unconsolidated Sedimentary Materials
Material
Porosity (%)
Gravel, coarse
24 - 37

507

Gravel, medium
Gravel, fine
Sand, coarse
Sand, medium
Sand, fine
Silt
Clay

24
25
31
29
26
34
34

44
39
46
49
53
61
57

Sedimentary Rocks
Rock Type
Sandstone
Siltstone
Claystone
Shale
Limestone
Dolomite

Porosity (%)
14 - 49
21 - 41
41 - 45
1 - 10
7 - 56
19 - 33

Crystalline Rocks
Rock Type
Basalt
Weathered granite
Weathered gabbro

Porosity (%)
3 - 35
34 - 57
42 - 45

Specific Yield
Specific yield (Sy) is defined as the volume of water released from storage by an
unconfined aquifer per unit surface area of aquifer per unit decline of the water
table.
Bear (1979) relates specific yield to total porosity (n) as follows:
n = Sy + Sr
where Sr is specific retention, the amount of water retained by capillary forces during
gravity drainage of an unconfined aquifer. Thus, specific yield, which is sometimes
called effective porosity, is less than the total porosity of an unconfined aquifer (Bear
1979).
The following table shows representative values of specific yield for various geologic
materials (from Morris and Johnson 1967):
Material
Gravel, coarse
Gravel, medium
Gravel, fine
Sand, coarse
Sand, medium
Sand, fine

Specific Yield (%)

21
24
28
30
32
33
508

Silt
Clay
Sandstone, fine grained
Sandstone, medium grained
Limestone
Dune sand
Loess
Peat
Schist
Siltstone
Till, predominantly silt
Till, predominantly sand
Till, predominantly gravel
Tuff

20
6
21
27
14
38
18
44
26
12
6
16
16
21

Storativity
The storativity (S) of a confined aquifer (or aquitard) is defined as the volume of
water released from storage per unit surface area of a confined aquifer (or aquitard)
per unit decline in hydraulic head. Storativity is also known by the terms coefficient
of storage and storage coefficient.
In a confined aquifer (or aquitard), storativity is defined as
S = Ssb
where Ss is specific storage and b is aquifer (or aquitard) thickness [L]. Specific
storage is the volume of water that a unit volume of aquifer (or aquitard) releases
from storage under a unit decline in head by the expansion of water and
compression of the soil or rock skeleton. Storativity generally ranges between
0.00005 and 0.005 in confined aquifers.
Specific storage is related to the compressibilities of the aquifer (or aquitard) and
water as follows:
Ss = g( + ne)
where is mass density of water [M/L3], g is gravitational acceleration (= 9.8
m/sec2) [L/T2], is aquifer (or aquitard) compressibility [T2L/M], ne is effective
porosity [dimensionless], and is compressibility of water (= 4.4x10-10 m sec2/kg or
[T2L/M].
In an unconfined aquifer (or aquitard), storativity is given by
S = Sy + Ssb
where Sy is specific yield. Because Ssb is typically small in comparison to Sy,
storativity in an unconfined aquifer is essentially equal to specific yield.
The following table shows representative values of specific storage for various
geologic materials (from Batu 1998):

509

Ss (ft-1)
7.8x10-4 to 6.2x10-3
3.9x10-4 to 7.8x10-4
2.8x10-4 to 3.9x10-4
1.5x10-4 to 3.1x10-4
3.9x10-5 to 6.2x10-5
1.5x10-5 to 3.1x10-5
1x10-6 to 2.1x10-5
< 1x10-6

Material
Plastic clay
Stiff clay
Medium hard clay
Loose sand
Dense sand
Dense sandy gravel
Rock, fissured
Rock, sound

To Convert
ft-1

Divide By
0.3048

To Obtain
m-1

Freeze and Cherry (1979) provided the following representative values of

compressibility for various aquifer materials:
Compressibility, (m2/N or Pa-1)
10-8 to 10-6
10-9 to 10-7
10-10 to 10-8
10-10 to 10-8
10-11 to 10-9

Material
Clay
Sand
Gravel
Jointed rock
Sound rock

Pa-1 = m2/N = m sec2/kg

Examples
1. Use compressibility data to estimate the storativity of a 35-ft thick confined
sand aquifer (assume = 1000 kg/m3 and ne = 0.3).
S = Ssb = g( + ne)b = (1000 kg/m3)(9.8 m/sec2) m2/N + (0.3) m2/N)](35
ft)(0.3048 m/ft) =
2. Use specific storage data to estimate storativity for the same aquifer given in
the preceding example.
S = Ssb = (35 ft) =

Specific Capacity
A specific capacity of a pumping well is defined as follows:

where

Q is pumping rate [L3/T]

sw is drawdown in pumped well at a specified time since pumping began [L]

510

For example, if a well in a confined aquifer is pumped at a rate of 77 gpm and the
drawdown at the end of 24 hours is 25.4 ft, one computes the specific capacity as
follows:
Q/sw = 77 gpm/25.4 ft = 3.03 gpm/ft of drawdown at 24 hours

Using appropriate conversions, we compute the specific capacity in units of meters

and days as follows:

(3.03 gal/min/ft)(m3/264.17 gal)(1440 min/day)(3.2808 ft/m) = 54.2 m3/day/m of

drawdown at 24 hours
Estimating Transmissivity from Specific Capacity
In lieu of aquifer testing results, you may estimate the transmissivity of an aquifer
from specific capacity data.
Based on the Cooper-Jacob (1946) formula for drawdown in a confined aquifer, we
can compute specific capacity using the following equation:

where

rw is radius of the pumped well [L]

S is storativity [dimensionless]

t is time since pumping began [T]

T is transmissivity [L2/T]

Using the above equation for specific capacity, Driscoll (1986) assumed the following
"typical" conditions

rw = 0.5 ft

S = 0.0001 (confined aquifer) or 0.075 (unconfined aquifer)

T = 30,000 gpd/ft

t = 1 day

the pumped well is 100% efficient

and proposed the following approximate relationships for estimating transmissivity

from specific capacity data in confined and unconfined aquifers:
511

Q/sw = T/2000 (confined aquifer)

Q/sw = T/1500 (unconfined aquifer)
where

Q is pumping rate [gpm]

sw is drawdown in pumped well [ft]

T is transmissivity [gpd/ft]

Given the limiting assumptions, these two relationships for predicting transmissivity
are only approximate.
Using the above example for specific capacity, estimate transmissivity as follows:
T = (2000)(3.03 gpm/ft) = 6060 gpd/ft = 75.3 m2/day
Various authors have used regression methods to develop equations relating specific
capacity and transmissivity. For example, Razack and Huntley (1991) reported the
following prediction equation for 215 wells in a large heterogeneous alluvial aquifer
in Morocco:

where

T is transmissivity [m2/day]

Q is pumping rate [m3/day]

sw is drawdown in pumped well [m]

For units of ft instead of m, change the coefficient from 15.3 to 33.6 in the foregoing
equation.
Let us estimate the value of T with the relationship developed by Razack and
Huntley:

T = (15.3)(54.2 m3/day/m)0.67 = 222.1 m2/day

Mace (1997) developed a similar regression equation for 71 wells completed in a
confined karst aquifer located in central Texas (the Edwards aquifer):

where
512

T is transmissivity [m2/day]

Q is pumping rate [m3/day]

sw is drawdown in pumped well [m]

Using the same example as above, let's estimate T with the Mace equation:

T = (0.76)(54.2 m3/day/m)1.08 = 56.7 m2/day

Huntley et al. (1992) devised another predictive equation for estimating
transmissivity from specific capacity data in fractured aquifers:

where

T is transmissivity [m2/day]

Q is pumping rate [m3/day]

sw is drawdown in pumped well [m]

513

Index
A
Active type curves ..................................................................................................................... 469
Agarwal....................................................................................................................................... 195
equivalent time ....................................................................................................................... 195
example............................................................................................................................... 33, 43
method .................................................................................................................................... 195
plot........................................................................................................................................... 195
Anisotropy ratio ......................................................................................................................... 507
about ....................................................................................................................................... 507
AQTESOLV for DOS import wizard.......................................................................................... 184
Arranging windows ................................................................................................................... 175
Automatic curve matching
about ....................................................................................................................................... 472
applying windows and weights ............................................................................................ 476
conditioning............................................................................................................................ 476
convergence ........................................................................................................................... 476
how it works ........................................................................................................................... 472
parameter statistics ............................................................................................................... 475
residual statistics................................................................................................................... 476
singular value decomposition .............................................................................................. 476
tips........................................................................................................................................... 476
Axes ............................................................................................................................................ 216
customizing ............................................................................................................................ 212
flip y axis................................................................................................................................. 216
labels ....................................................................................................................................... 216
linear........................................................................................................................................ 212
linear-log ................................................................................................................................. 214
log............................................................................................................................................ 215
log-linear ................................................................................................................................. 213
origin ....................................................................................................................................... 216
range ....................................................................................................................................... 216
tickmarks ................................................................................................................................ 216

B
Barker (1988) solution....................................................................................................... 354, 434
Barker-Black (1983) solution .................................................................................................... 418
Batch printing ............................................................................................................................ 481
Bilinear flow plot........................................................................................................................ 206
Birsoy-Summers (1980) solution ............................................................................................. 258
Bourdet ....................................................................................................................................... 457
Bouwer-Rice (1976) solution ............................................................................................ 369, 402
example................................................................................................................... 133, 140, 146
Butler (1988) solution................................................................................................................ 265
Butler (1998) solution................................................................................................................ 383
example................................................................................................................................... 150
Butler-Zhan (2004) solution ...................................................................................................... 387

C
Check slope................................................................................................................................ 467
Chu and Grader (1991) solution ............................................................................................... 387

514

Coefficient of permeability ....................................................................................................... 506

Coefficient of storage................................................................................................................ 509
Composite plot........................................................................................................................... 191
Compressibility.......................................................................................................................... 509
Confidence interval ........................................................................................................... 233, 475
Confined aquifer solutions
constant-head tests ............................................................................................................... 421
pumping tests......................................................................................................................... 236
slug tests ................................................................................................................................ 360
Confined two-aquifer system ................................................................................................... 246
Constant-head test solutions ................................................................................................... 421
about ....................................................................................................................................... 421
Barker...................................................................................................................................... 434
Dougherty-Babu ..................................................................................................................... 430
Hantush................................................................................................................................... 435
Hurst-Clark-Brauer................................................................................................................. 426
Jacob-Lohman........................................................................................................................ 423
Moench.................................................................................................................................... 438
Ozkan-Raghavan .................................................................................................................... 449
recovery .................................................................................................................................. 421
Constant-head test wizard........................................................................................................ 182
Constant-head tests .................................................................................................................. 421
curve matching tips ............................................................................................................... 455
example................................................................................................................................... 160
recovery solutions ................................................................................................................. 421
Constant-rate solutions ............................................................................................................ 237
Contour....................................................................................................................................... 484
about ....................................................................................................................................... 484
example..................................................................................................................................... 24
grid wizard .............................................................................................................................. 484
Conversion factors.................................................................................................................... 504
Cooley-Case (1973) solution .................................................................................................... 305
Cooper-Bredehoeft-Papadopulos (1967) solution ................................................................. 372
example........................................................................................................................... 133, 154
Cooper-Jacob (1946) solution .......................................................................................... 258, 321
example............................................................................................................................... 24, 74
valid time................................................................................................................................. 224
Copy/paste data into AQTESOLV ............................................................................................ 186
Correlation.................................................................................................................................. 233
Covariance matrix ..................................................................................................................... 472
Critical value of u....................................................................................................................... 224
Curve matching.......................................................................................................................... 454
about ....................................................................................................................................... 454
examples................................................................................................................................... 21
plotting resolution ................................................................................................................. 224
tips for constant-head tests.................................................................................................. 455
tips for pumping tests ........................................................................................................... 455
tips for slug tests ................................................................................................................... 455
tweak parameters................................................................................................................... 471
Curve resolution ........................................................................................................................ 224
Curves
fitted line ................................................................................................................................. 216
Theis reference curve............................................................................................................ 216
type curve families................................................................................................................. 216
Customize................................................................................................................................... 216
legend...................................................................................................................................... 216
515

plots......................................................................................................................................... 212
reports..................................................................................................................................... 234

D
Dagan (1978) solution ............................................................................................................... 406
Darcy's law ................................................................................................................................. 506
Data loggers ............................................................................................................................... 186
copy/paste data...................................................................................................................... 186
import data.............................................................................................................................. 186
importing files ........................................................................................................................ 186
In-Situ ...................................................................................................................................... 186
Solinst ..................................................................................................................................... 186
WinSitu.................................................................................................................................... 489
Data sets..................................................................................................................................... 179
about ....................................................................................................................................... 179
constant-head test wizard..................................................................................................... 182
editing ..................................................................................................................................... 185
examples................................................................................................................................... 21
forward solution wizard......................................................................................................... 183
pumping test wizard .............................................................................................................. 181
slug test wizard ...................................................................................................................... 182
Daviau et al. (1985) solution ..................................................................................................... 287
example................................................................................................................................... 127
Deconvolution............................................................................................................................ 394
example................................................................................................................................... 133
Delayed response...................................................................................................................... 247
example............................................................................................................................. 99, 116
Derivative analysis .................................................................................................................... 457
about ....................................................................................................................................... 457
computation............................................................................................................................ 457
noise........................................................................................................................................ 457
settings ................................................................................................................................... 224
smoothing............................................................................................................................... 457
superimpose curve ................................................................................................................ 224
Derivative-time plot ................................................................................................................... 199
Diagnostic flow plots ................................................................................................................ 248
about ....................................................................................................................................... 248
bilinear .................................................................................................................................... 206
example............................................................................................. 24, 33, 74, 83, 99, 108, 116
linear........................................................................................................................................ 204
radial........................................................................................................................................ 202
spherical ................................................................................................................................. 207
Diagnostics report..................................................................................................................... 233
Discharge-time plot ................................................................................................................... 200
Displacement-time plot ............................................................................................................. 189
curve family ............................................................................................................................ 224
derivative ................................................................................................................................ 224
normalized head..................................................................................................................... 224
recommended head range .................................................................................................... 224
valid time................................................................................................................................. 224
Distance drawdown................................................................................................................... 197
example............................................................................................................................. 74, 123
plot........................................................................................................................................... 197
time.......................................................................................................................................... 224
DOS data sets ............................................................................................................................ 184
Double straight-line effect
516

example................................................................................................................................... 146
Double-porosity aquifers
example................................................................................................................................... 116
solutions ................................................................................................................. 241, 360, 421
Dougherty-Babu (1984) solution ...................................................................... 273, 278, 374, 430
example..................................................................................................................................... 59

E
Edit .............................................................................................................................................. 173
menu........................................................................................................................................ 173
Effective porosity....................................................................................................................... 508
about ....................................................................................................................................... 508
Effective well radius
step-drawdown tests ............................................................................................................. 243
Efficiency.................................................................................................................................... 243
Equivalent time .......................................................................................................................... 195
Error log...................................................................................................................................... 234
correcting errors .................................................................................................................... 490
warnings ................................................................................................................................. 490
Examples ...................................................................................................................................... 21
about ......................................................................................................................................... 21
active type curves ................................................................................................ 33, 43, 48, 150
Agarwal ............................................................................................................................... 33, 43
Cape Cod ................................................................................................................................ 108
constant-head test ................................................................................................................. 160
Dalem ........................................................................................................................................ 83
deconvolution......................................................................................................................... 133
delayed gravity response................................................................................................ 99, 108
delayed response............................................................................................................. 99, 116
diagnostic flow plots ......................................................... 33, 48, 59, 74, 83, 99, 108, 116, 127
distance drawdown.................................................................................................................. 74
double straight-line................................................................................................................ 146
forward solution ..................................................................................................................... 123
Grand Junction ...................................................................................................................... 160
Gridley....................................................................................................................................... 24
horizontal well ........................................................................................................................ 127
importing data ..................24, 33, 43, 48, 59, 69, 74, 83, 99, 108, 116, 127, 140, 146, 150, 154
Lincoln County....................................................................................................................... 154
Lynden ...................................................................................................................................... 59
mounding................................................................................................................................ 168
multiwell.................................................................................................................... 74, 116, 154
NTS .......................................................................................................................................... 116
on the web .............................................................................................................................. 172
parameter tweaking ................................................................................................................. 59
prediction.......................................................................................................................... 24, 123
pumping test................................................................... 24, 33, 43, 48, 59, 74, 83, 99, 108, 116
recommended head range ............................................................................................ 133, 140
recovery ........................................................................................................................ 33, 43, 69
Saratoga.................................................................................................................................... 99
sensitivity analysis ................................................................................................ 123, 127, 133
Sioux Flats ................................................................................................................................ 74
slug test .................................................................................................. 133, 140, 146, 150, 154
step-drawdown test ................................................................................................................. 69
translation method................................................................................................................. 140
underdamped ......................................................................................................................... 150
variable rate ........................................................................................................................ 43, 69
517

wellbore skin ............................................................................................................................ 59

wellbore storage .................................................................................................. 48, 59, 99, 116
Excel files ................................................................................................................................... 186
Export ......................................................................................................................................... 486

F
Families ...................................................................................................................................... 469
FAQ ............................................................................................................................................. 490
Features........................................................................................................................................ 12
new .............................................................................................................................................. 8
unique ....................................................................................................................................... 12
File............................................................................................................................................... 173
batch printing ......................................................................................................................... 481
export ...................................................................................................................................... 486
menu........................................................................................................................................ 173
print ......................................................................................................................................... 479
print preview........................................................................................................................... 480
print setup............................................................................................................................... 480
send as email ......................................................................................................................... 487
Filter pack correction
example................................................................................................................................... 146
Fitted line.................................................................................................................................... 216
Flip y axis ................................................................................................................................... 216
Footers
format ...................................................................................................................................... 216
page setup .............................................................................................................................. 480
Format......................................................................................................................................... 216
axes ......................................................................................................................................... 216
fitted line ................................................................................................................................. 216
headers and footers............................................................................................................... 216
legend...................................................................................................................................... 216
page margins.......................................................................................................................... 480
plots......................................................................................................................................... 216
reports..................................................................................................................................... 216
Theis reference curve............................................................................................................ 216
type curve families................................................................................................................. 216
Forward solution
example................................................................................................................................... 123
wizard ...................................................................................................................................... 183
Fractured aquifer solutions
constant-head tests ............................................................................................................... 421
pumping tests......................................................................................................................... 236
slug tests ................................................................................................................................ 360
Fractured aquifers
double-porosity solutions..................................................................................... 241, 360, 421
single-fracture solutions ....................................................................................................... 241
Frequently asked questions ..................................................................................................... 490
Frictional loss
example................................................................................................................................... 150

G
Graph paper on plots ................................................................................................................ 216
Grid ............................................................................................................................................. 484
Grid wizard ................................................................................................................................. 484
Gringarten-Ramey (1974) solution........................................................................................... 351

518

Gringarten-Ramey-Raghavan (1974) solution ........................................................................ 347

Gringarten-Witherspoon (1972) solution ................................................................................ 344
example................................................................................................................................... 123
Guided tours ................................................................................................................................ 21
Guidelines for slug test analysis ............................................................................................. 366

H
Hantush (1959) solution............................................................................................................ 435
example................................................................................................................................... 160
Hantush (1960) solution............................................................................................................ 300
example..................................................................................................................................... 83
Hantush (1961) solution.................................................................................................... 249, 292
Hantush (1962) solution............................................................................................................ 281
Hantush (1967) mounding solution ......................................................................................... 488
example................................................................................................................................... 168
Hantush-Jacob (1955) solution ........................................................................................ 292, 297
example..................................................................................................................................... 83
Headers....................................................................................................................................... 216
format ...................................................................................................................................... 216
page setup .............................................................................................................................. 480
Help ............................................................................................................................................. 176
menu........................................................................................................................................ 176
Q&A ......................................................................................................................................... 490
technical support ................................................................................................................... 495
using.......................................................................................................................................... 16
Hemiradial flow .......................................................................................................................... 127
High-K aquifer slug tests .......................................................................................................... 363
Horizontal fracture
pumping test solution ........................................................................................................... 351
Horizontal well
example................................................................................................................................... 127
solutions ................................................................................................................................. 246
Horner plot ................................................................................................................................. 192
How to use AQTESOLV............................................................................................................... 18
analyzing a test ........................................................................................................................ 18
field analysis............................................................................................................................. 20
forward solution ....................................................................................................................... 20
prediction.................................................................................................................................. 20
test design ................................................................................................................................ 20
Hurst-Clark-Brauer (1969) solution.......................................................................................... 426
Hvorslev (1951) solution ................................................................................................... 367, 404
Hyder et al. (1994) solution............................................................................................... 379, 409
example........................................................................................................................... 133, 154
Hydraulic conductivity .............................................................................................................. 506
about ....................................................................................................................................... 506
anisotropy ratio ...................................................................................................................... 507
representative values ............................................................................................................ 506

I
Import.......................................................................................................................................... 186
AQTESOLV for DOS data set ................................................................................................ 184
copy/paste data...................................................................................................................... 186
example...............................................21, 24, 33, 43, 48, 59, 69, 74, 83, 99, 108, 116, 140, 154
Excel files................................................................................................................................ 186
observation data .................................................................................................................... 186

519

pumping rates ........................................................................................................................ 187

troubleshooting...................................................................................................................... 490
wizards ............................................................................................................................ 186, 187
Infinite conductivity
horizontal well ........................................................................................................................ 287
vertical fracture .............................................................................................................. 347, 449
In-Situ.......................................................................................................................................... 186
Intermittent pumping................................................................................................................. 238

J
Jacob-Lohman (1952) solution................................................................................................. 423
example................................................................................................................................... 160

K
Keyboard shortcuts................................................................................................................... 177
KGS Model.......................................................................................................................... 379, 409
Knowledge base ........................................................................................................................ 495

L
Leaky aquifer solutions
constant-head tests ............................................................................................................... 421
pumping tests......................................................................................................................... 236
Legend ........................................................................................................................................ 216
displaying ............................................................................................................................... 224
font size................................................................................................................................... 216
formatting ............................................................................................................................... 216
printing.................................................................................................................................... 216
Linear aquifer-loss coefficient ................................................................................................. 243
Linear axes ................................................................................................................................. 212
Linear flow plot .......................................................................................................................... 204
Linear well-loss coefficient....................................................................................................... 243
Linear-log axes .......................................................................................................................... 214
Log axes ..................................................................................................................................... 215
Log-linear axes .......................................................................................................................... 213

M
Margins ....................................................................................................................................... 480
Marquardt ................................................................................................................................... 472
algorithm................................................................................................................................. 472
Match .......................................................................................................................................... 175
active type curves .................................................................................................................. 469
check slope............................................................................................................................. 467
menu........................................................................................................................................ 175
parameter tweaking ............................................................................................................... 471
sensitivity analysis ................................................................................................................ 471
tweak ....................................................................................................................................... 471
type curve families................................................................................................................. 469
McElwee-Zenner (1998) solution.............................................................................................. 397
Metafiles ..................................................................................................................................... 486
ModelCad.................................................................................................................................... 488
MODFLOW.................................................................................................................................. 488
Moench (1984) solution............................................................................................................. 339
example................................................................................................................................... 116
Moench (1985) solution..................................................................................................... 313, 438
example..................................................................................................................................... 48
520

Moench (1996) solution............................................................................................................. 324

Moench (1997) solution............................................................................................................. 328
example..................................................................................................................................... 99
Moench-Prickett (1972) solution .............................................................................................. 262
Mounding.................................................................................................................................... 488
example................................................................................................................................... 168
MT3D ........................................................................................................................................... 488
Multiaquifer systems................................................................................................................. 246
Multiwell tests ............................................................................................................................ 364
pumping test example ..................................................................................................... 74, 116
slug test example................................................................................................................... 154
Murdoch (1994) solution ........................................................................................................... 284

N
Nearest neighbor ....................................................................................................................... 457
Neuman (1974) solution ............................................................................................................ 324
example............................................................................................................................. 99, 108
type A and B curves .............................................................................................................. 470
Neuman-Witherspoon (1969) solution..................................................................................... 309
Nonlinear slug tests .................................................................................................................. 366
Nonlinear well-loss coefficient................................................................................................. 243
Non-uniform aquifers ................................................................................................................ 246
Normal probability plot ............................................................................................................. 210
Normalized head
displaying ............................................................................................................................... 224

O
Observation data
importing................................................................................................................................. 186
Observation well
delayed response................................................................................................................... 247
Options ....................................................................................................................................... 224
curve resolution ..................................................................................................................... 224
distance drawdown................................................................................................................ 224
normalized head..................................................................................................................... 224
recommended head range .................................................................................................... 224
show data................................................................................................................................ 224
show legend ........................................................................................................................... 224
show type curve ..................................................................................................................... 224
step test .................................................................................................................................. 224
superimpose curve family..................................................................................................... 224
superimpose derivative......................................................................................................... 224
superimpose Theis reference curve .................................................................................... 224
valid time................................................................................................................................. 224
view ......................................................................................................................................... 224
Origin on plots ........................................................................................................................... 216
Overdamped slug tests............................................................................................................. 360
Ozkan-Raghavan (1991) solution ............................................................................................. 449

P
Page margins ............................................................................................................................. 480
Page setup.................................................................................................................................. 480
Papadopulos-Cooper (1967) solution...................................................................................... 269
example..................................................................................................................................... 48
Parameters

521

confidence interval ........................................................................................................ 233, 475

correlations............................................................................................................................. 233
curve matching ...................................................................................................................... 454
precision ................................................................................................................................. 233
standard errors .............................................................................................................. 233, 475
statistics.................................................................................................................................. 475
t-ratio ............................................................................................................................... 233, 475
tweaking.................................................................................................................................. 471
Partially submerged screen
slug test solutions ................................................................................................................. 365
Peres-Onur-Reynolds (1989) solution ..................................................................................... 394
example................................................................................................................................... 133
Plots ............................................................................................................................................ 188
about ....................................................................................................................................... 188
Agarwal ................................................................................................................................... 195
axes ......................................................................................................................................... 216
axis settings ........................................................................................................................... 212
bilinear flow ............................................................................................................................ 206
composite ............................................................................................................................... 191
contour.................................................................................................................................... 484
customizing ............................................................................................................................ 212
data.......................................................................................................................................... 188
derivative-time........................................................................................................................ 199
diagnostic ............................................................................................................................... 188
discharge-time ....................................................................................................................... 200
displacement-time ................................................................................................................. 189
distance drawdown................................................................................................................ 197
fitted line ................................................................................................................................. 216
format ...................................................................................................................................... 216
graph paper ............................................................................................................................ 216
legend...................................................................................................................................... 216
linear axes............................................................................................................................... 212
linear flow ............................................................................................................................... 204
linear-log axes ........................................................................................................................ 214
log axes................................................................................................................................... 215
log-linear axes ........................................................................................................................ 213
normal probability.................................................................................................................. 210
options .................................................................................................................................... 224
origin ....................................................................................................................................... 216
radial flow ............................................................................................................................... 202
residual ................................................................................................................................... 188
residual drawdown ................................................................................................................ 192
residual-simulated ................................................................................................................. 209
residual-time........................................................................................................................... 208
spherical flow ......................................................................................................................... 207
Theis reference curve.................................................................................................... 216, 224
tickmarks ................................................................................................................................ 216
type curve families................................................................................................................. 224
Porosity ...................................................................................................................................... 507
about ....................................................................................................................................... 507
representative values ............................................................................................................ 507
Precision..................................................................................................................................... 233
Print............................................................................................................................................. 479
Print preview .............................................................................................................................. 480
Print setup .................................................................................................................................. 480
Printing ....................................................................................................................................... 479
522

about ....................................................................................................................................... 479

batch........................................................................................................................................ 481
font rotation ............................................................................................................................ 480
page margins.......................................................................................................................... 480
page setup .............................................................................................................................. 480
print ......................................................................................................................................... 479
print preview........................................................................................................................... 480
print setup............................................................................................................................... 480
tips........................................................................................................................................... 483
troubleshooting...................................................................................................................... 490
Pumping rate data
importing................................................................................................................................. 187
Pumping test solutions............................................................................................................. 236
about ....................................................................................................................................... 236
Barker...................................................................................................................................... 354
bounded aquifer ..................................................................................................................... 246
Butler....................................................................................................................................... 265
constant rate........................................................................................................................... 237
Cooley-Case ........................................................................................................................... 305
Cooper-Jacob ................................................................................................................. 258, 321
Daviau ..................................................................................................................................... 287
double porosity ...................................................................................................................... 241
Dougherty-Babu ............................................................................................................. 273, 278
Gringarten-Ramey.................................................................................................................. 351
Gringarten-Ramey-Raghavan ............................................................................................... 347
Hantush................................................................................................................... 281, 292, 300
Hantush-Jacob ............................................................................................................... 292, 297
horizontal well ........................................................................................................................ 246
Moench.................................................................................................................... 313, 328, 339
Moench-Prickett ..................................................................................................................... 262
multiaquifer............................................................................................................................. 246
Murdoch .................................................................................................................................. 284
Neuman ................................................................................................................................... 324
Neuman-Witherspoon............................................................................................................ 309
non-uniform aquifers............................................................................................................. 246
Papadopulos-Cooper............................................................................................................. 269
recovery .................................................................................................................................. 239
single fracture ........................................................................................................................ 241
single well ............................................................................................................................... 239
step drawdown....................................................................................................................... 243
Tartakovsky-Neuman............................................................................................................. 334
Theis................................................................................................................ 249, 253, 255, 319
variable rate ............................................................................................................................ 238
Walton ..................................................................................................................................... 292
wellbore storage .................................................................................................................... 240
Pumping test wizard.................................................................................................................. 181
Pumping tests ............................................................................................................................ 236
bounded aquifer solutions.................................................................................................... 246
constant-rate solutions ......................................................................................................... 237
curve matching tips ............................................................................................................... 455
double-porosity solutions..................................................................................................... 241
horizontal well solutions ....................................................................................................... 246
multiaquifer solutions ........................................................................................................... 246
single-fracture solutions ....................................................................................................... 241
single-well test solutions ...................................................................................................... 239
step-drawdown solutions...................................................................................................... 243
523

using diagnostic flow plots................................................................................................... 248

variable-rate solutions........................................................................................................... 238
wellbore storage solutions ................................................................................................... 240

Q
Quick start .................................................................................................................................... 18

R
Radial flow plot .......................................................................................................................... 202
Recommended head range for slug tests............................................................................... 224
Recovery
Agarwal plot............................................................................................................................ 195
constant-head tests ............................................................................................................... 421
example............................................................................................................................. 33, 160
pumping tests......................................................................................................................... 239
residual drawdown plot......................................................................................................... 192
References ......................................................................................................................... 497, 503
Registration................................................................................................................................ 495
Reports ....................................................................................................................................... 233
about ....................................................................................................................................... 233
complete report...................................................................................................................... 233
customizing ............................................................................................................................ 234
diagnostics ............................................................................................................................. 233
error log .................................................................................................................................. 234
format ...................................................................................................................................... 216
Residual
statistics.................................................................................................................................. 476
sum of squares (RSS).................................................................................................... 472, 476
Residual drawdown plot ........................................................................................................... 192
Residual plots ............................................................................................................................ 188
normal probability.................................................................................................................. 210
residual-simulated ................................................................................................................. 209
residual-time........................................................................................................................... 208
Residual-simulated plot ............................................................................................................ 209
Residual-time plot...................................................................................................................... 208
Resolution of type curves......................................................................................................... 224
RSS ............................................................................................................................................. 476

S
Send mail.................................................................................................................................... 487
Sensitivity analysis ................................................................................................................... 471
example................................................................................................................... 123, 127, 133
Sensitivity coefficient................................................................................................................ 472
Shortcuts
keyboard ................................................................................................................................. 177
Single-fracture aquifers
solutions ................................................................................................................................. 241
Single-well tests......................................................................................................................... 239
Singular value decomposition (SVD) ...................................................................................... 472
Skin
fracture.................................................................................................................................... 313
Slope checker ............................................................................................................................ 467
Slug test solutions .................................................................................................................... 360
about ....................................................................................................................................... 360
Barker-Black ........................................................................................................................... 418

524

Bouwer-Rice ................................................................................................................... 369, 402

Butler....................................................................................................................................... 383
Butler-Zhan ............................................................................................................................. 387
Chu-Grader ............................................................................................................................. 387
Cooper-Bredehoeft-Papadopulos ........................................................................................ 372
Dagan ...................................................................................................................................... 406
deconvolution......................................................................................................................... 394
double porosity ...................................................................................................................... 418
Dougherty-Babu ..................................................................................................................... 374
high-K aquifers....................................................................................................................... 363
Hvorslev .......................................................................................................................... 367, 404
Hyder et al....................................................................................................................... 379, 409
KGS Model ...................................................................................................................... 379, 409
McElwee-Zenner..................................................................................................................... 397
multiwell.................................................................................................................................. 364
nonlinear ................................................................................................................................. 366
overdamped............................................................................................................................ 360
partially submerged screen .................................................................................................. 365
Peres-Onur-Reynolds ............................................................................................................ 394
Springer-Gelhar...................................................................................................................... 413
underdamped ......................................................................................................................... 363
wellbore skin .................................................................................................. 374, 379, 394, 409
Slug test wizard ......................................................................................................................... 182
Slug tests.................................................................................................................................... 360
curve matching tips ............................................................................................................... 455
guidelines for analysis .......................................................................................................... 366
high-K aquifers....................................................................................................................... 363
multiwell.................................................................................................................................. 364
nonlinear ................................................................................................................................. 366
overdamped............................................................................................................................ 360
partially submerged screen .................................................................................................. 365
underdamped ......................................................................................................................... 363
Smoothing .................................................................................................................................. 457
example................................................................................................................................... 457
Solinst......................................................................................................................................... 186
Solution methods
Barker.............................................................................................................................. 354, 434
Barker-Black ........................................................................................................................... 418
bounded aquifers................................................................................................................... 246
Bouwer-Rice ................................................................................................................... 369, 402
Butler............................................................................................................................... 265, 383
Butler-Zhan ............................................................................................................................. 387
Chu-Grader ............................................................................................................................. 387
constant rate........................................................................................................................... 237
constant-head tests ............................................................................................................... 421
Cooley-Case ........................................................................................................................... 305
Cooper-Bredehoeft-Papadopulos ........................................................................................ 372
Cooper-Jacob ................................................................................................................. 258, 321
Dagan ...................................................................................................................................... 406
Daviau ..................................................................................................................................... 287
double porosity ...................................................................................................................... 241
Dougherty-Babu ............................................................................................. 273, 278, 374, 430
Gringarten-Ramey.................................................................................................................. 351
Gringarten-Ramey-Raghavan ............................................................................................... 347
Gringarten-Witherspoon ....................................................................................................... 344
Hantush........................................................................................................... 281, 292, 300, 435
525

Hantush-Jacob ............................................................................................................... 292, 297

high-K aquifers....................................................................................................................... 363
horizontal well ........................................................................................................................ 246
Hurst-Clark-Brauer................................................................................................................. 426
Hvorslev .......................................................................................................................... 367, 404
Hyder et al....................................................................................................................... 379, 409
Jacob-Lohman........................................................................................................................ 423
KGS Model ...................................................................................................................... 379, 409
McElwee-Zenner..................................................................................................................... 397
Moench............................................................................................................ 313, 328, 339, 438
Moench-Prickett ..................................................................................................................... 262
Murdoch .................................................................................................................................. 284
Neuman ................................................................................................................................... 324
Neuman-Witherspoon............................................................................................................ 309
nonlinear slug tests ............................................................................................................... 366
non-uniform aquifers............................................................................................................. 246
overdamped............................................................................................................................ 360
Ozkan-Raghavan .................................................................................................................... 449
Papadopulos-Cooper............................................................................................................. 269
Peres-Onur-Reynolds ............................................................................................................ 394
pumping tests......................................................................................................................... 236
recovery .......................................................................................................................... 239, 421
single fracture ........................................................................................................................ 241
single well ............................................................................................................................... 239
slug tests ................................................................................................................................ 360
Springer-Gelhar...................................................................................................................... 413
step tests ................................................................................................................................ 243
Tartakovsky-Neuman............................................................................................................. 334
Theis................................................................................................................ 249, 253, 255, 319
underdamped ......................................................................................................................... 363
Vandenberg ............................................................................................................................ 292
variable rate ............................................................................................................................ 238
Walton ..................................................................................................................................... 292
wellbore storage .................................................................................................................... 240
Spane .......................................................................................................................................... 457
Specific capacity ....................................................................................................................... 510
Specific retention....................................................................................................................... 508
Specific storage ......................................................................................................................... 509
Specific yield.............................................................................................................................. 508
about ....................................................................................................................................... 508
representative values ............................................................................................................ 508
Spherical flow plot..................................................................................................................... 207
Springer-Gelhar (1991) solution............................................................................................... 413
Standard error.................................................................................................................... 233, 472
Statistics
parameter................................................................................................................................ 475
residual ................................................................................................................................... 476
Step-drawdown tests ................................................................................................................ 243
about ....................................................................................................................................... 243
effective well radius............................................................................................................... 243
example..................................................................................................................................... 69
prediction equation................................................................................................................ 243
prediction time ....................................................................................................................... 224
skin effect ............................................................................................................................... 243
solutions ................................................................................................................................. 243
well efficiency......................................................................................................................... 243
526

well loss .................................................................................................................................. 243

Storage coefficient .................................................................................................................... 509
Storativity ................................................................................................................................... 509
about ....................................................................................................................................... 509
representative values ............................................................................................................ 509
Strip aquifers.............................................................................................................................. 246
solutions ................................................................................................................................. 246
Support ....................................................................................................................................... 495
Surfer .......................................................................................................................................... 484

T
Tartakovsky-Neuman (2007) solution...................................................................................... 334
example................................................................................................................................... 108
Technical support...................................................................................................................... 495
knowledge base ..................................................................................................................... 495
web examples......................................................................................................................... 495
Theis (1935) solution......................................................................................... 249, 253, 255, 319
displaying reference curve ................................................................................................... 224
example............................................................................................................. 24, 33, 43, 69, 74
formatting reference curve ................................................................................................... 216
Tickmarks ................................................................................................................................... 216
Tile window ................................................................................................................................ 175
Time-drawdown plot.................................................................................................................. 189
Toolbar........................................................................................................................................ 176
Toolbox
tweak ....................................................................................................................................... 471
Tools ........................................................................................................................................... 175
about ....................................................................................................................................... 488
menu........................................................................................................................................ 175
ModelCad ................................................................................................................................ 488
mounding................................................................................................................................ 488
TWODAN ................................................................................................................................. 488
WinSitu.................................................................................................................................... 489
Tours............................................................................................................................................. 21
Transducer
import data.............................................................................................................................. 186
Translation method
example................................................................................................................................... 140
Transmissivity............................................................................................................................ 506
estimating from specific capacity ........................................................................................ 510
t-ratio................................................................................................................................... 233, 475
Trench
pumping test solution ........................................................................................................... 284
Troubleshooting
font rotation ............................................................................................................................ 480
Q&A ......................................................................................................................................... 490
Tutorials........................................................................................................................................ 21
Tweak parameters ..................................................................................................................... 471
example..................................................................................................................................... 59
TWODAN..................................................................................................................................... 488
Type A and B curves ................................................................................................................. 470
Type curve families ................................................................................................................... 469
about ....................................................................................................................................... 469
formatting ............................................................................................................................... 216
settings ................................................................................................................................... 224
Type curves................................................................................................................................ 224
527

active ....................................................................................................................................... 469

display toggle ......................................................................................................................... 177
displaying ............................................................................................................................... 224

U
Unconfined aquifer solutions
pumping tests......................................................................................................................... 236
slug tests ................................................................................................................................ 360
Underdamped slug tests........................................................................................................... 363
example................................................................................................................................... 150
solutions ................................................................................................................................. 363
Uniform flux
horizontal fracture ................................................................................................................. 351
horizontal well ........................................................................................................................ 287
vertical fracture .............................................................................................................. 344, 449
Units
conversion factors................................................................................................................. 504
Unpumped aquifer ..................................................................................................................... 309
Using help .................................................................................................................................... 16

V
Valid time.................................................................................................................................... 224
Vandenberg (1977) solution ............................................................................................. 246, 292
Variable rates ............................................................................................................................. 238
example..................................................................................................................................... 43
solutions ................................................................................................................................. 238
Vertical fracture
constant-head test solution .................................................................................................. 449
pumping test solution ................................................................................................... 344, 347
View............................................................................................................................................. 173
Agarwal ................................................................................................................................... 195
bilinear flow ............................................................................................................................ 206
complete report...................................................................................................................... 233
composite ............................................................................................................................... 191
contour.................................................................................................................................... 484
derivative-time........................................................................................................................ 199
diagnostics ............................................................................................................................. 233
discharge-time ....................................................................................................................... 200
displacement-time ................................................................................................................. 189
distance drawdown................................................................................................................ 197
error log .................................................................................................................................. 234
format ...................................................................................................................................... 216
linear axes............................................................................................................................... 212
linear flow ............................................................................................................................... 204
linear-log axes ........................................................................................................................ 214
log axes................................................................................................................................... 215
log-linear axes ........................................................................................................................ 213
menu........................................................................................................................................ 173
normal probability.................................................................................................................. 210
options .................................................................................................................................... 224
radial flow ............................................................................................................................... 202
residual drawdown ................................................................................................................ 192
residual-simulated ................................................................................................................. 209
residual-time........................................................................................................................... 208
spherical flow ......................................................................................................................... 207

528

toolbar ..................................................................................................................................... 176

Visual curve matching .............................................................................................................. 468
about ....................................................................................................................................... 468
active type curves .................................................................................................................. 469
check slope............................................................................................................................. 467
curve resolution ..................................................................................................................... 224
matching early or late data ................................................................................................... 470
sensitivity analysis ................................................................................................................ 471
straight-line methods ............................................................................................................ 468
tweak ....................................................................................................................................... 471
type A and B curves .............................................................................................................. 470
type curve methods ............................................................................................................... 468

W
Walton (1962) method ............................................................................................................... 292
Warnings .................................................................................................................................... 490
Wedge-shaped aquifers
pumping test solution ........................................................................................................... 281
Well efficiency............................................................................................................................ 243
Well loss ..................................................................................................................................... 243
Well performance tests ............................................................................................................. 243
Well screened across water table ............................................................................................ 365
Wellbore skin
example..................................................................................................................................... 59
Wellbore storage
example................................................................................................................. 48, 59, 99, 116
solutions ................................................................................................................................. 240
Windows ..................................................................................................................................... 175
menu........................................................................................................................................ 175
Windows metafile ...................................................................................................................... 486
export ...................................................................................................................................... 486
WinSitu ....................................................................................................................................... 489
Wizards
constant-head test ................................................................................................................. 182
forward solution ..................................................................................................................... 183
grid .......................................................................................................................................... 484
pumping test........................................................................................................................... 181
slug test .................................................................................................................................. 182

X
X' X covariance matrix .............................................................................................................. 472

529