Aquifer and well test analysis and simulation

Clarke's Groundwater Programs, the CG programs

Note that these programs were originally written in about 1988, they run under DOS, not Windows, and have become antiquated.

Introduction
Conceptual models
Analysis methods
General tutorials
References
Index
Contact details:
A simulation fitted to drawdown and recovery in an aquifer test
David Clarke
20 Musgrave St., Crystal Brook 5523, S. Australia
Email daveclarkecb@yahoo.com

Introduction

These programs will give you powerful, quick and flexible help in all your discharge test analysis work. They can be applied to: Note that these programs run under DOS using keyboard input. A mouse cannot be used within the programs.
These notes have been converted from a .doc file. There are probably errors from the conversion and errors due to the programs being continually updated. I'd appreciate being notified of errors that anyone finds.

There are many ways in which the programs might be used. Some examples are:
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In all cases output of various combinations of measured data and/or simulated data is an additional option. This can be on a plotter or it can go to disk files for further handling by third party software.

It should be stressed that these notes are concerned with using the CG set of programs for simulation and analysis of groundwater discharge test data. They are not designed, in themselves, as a course in hydrogeology, although it is hoped that they may provide a tool toward that end.


Units

A wide variety of units may be used, metres, feet, seconds, minutes, hours, days, litres per second, cubic metres per day, cubic feet per day, etc. It is possible to switch from one unit to another, for example you may choose to enter data as minutes and seconds with discharge rates as litres per second. You can then switch to times in days and flow rates in cubic metres per day for analysis.

One of the available consistent sets of units is recommended for analysis.

The well test data recorded on disk is independent of the set of units that you choose. The set of units is recorded as a part of the current configuration.
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Installation

The programs should be copied into a single directory of your hard disk before you use them; ideally named CG. Also, if you are to follow the tutorials, a data subdirectory will have to be made, and data files copied into it; this should ideally be attached to the directory containing the programs (eg. CG/CGXample).

Instructions, where?

The first section of these notes deal generally with the programs. There are also two sets of tutorials, one designed to familiarise you with using the programs in discharge test analysis, the other is for education in aquifer and well test analysis. More instruction is available from the help system, available (by pressing [F1]) while you are running the programs.

Getting started

The programs are menu driven and are designed to be as nearly self explanatory as possible. To run them, change into the directory into which you installed the programs, then type CG and press [Enter]. You will then be shown an introductory page which you should read. Pressing any key will get you to the primary menu.

You will come back to the primary menu after all the major operations; data entry, graphing, simulation, analysis, etc. As soon as you select one of these options from the primary menu, CG will call up an autonomous program and also will pass some information to that program.

As you use the CG programs you will see several menus which look very like the primary one. There are two ways of selecting an option from these menus: you may use the up or down arrow keys to move the highlighted bar to the option and then press [Enter], or you can press the 'hot key' (the numeral or letter key on the left margin). (Pressing the up arrow when at the top of the menu will get you to the bottom, and vice-versa.)

I suggest that you use the former method as you are getting to know the programs because you will be given a short explanation of each option as you scroll up or down the menu.


How the CG programs work

The primary purpose of the CG group of programs is the analysis of discharge test data, both from well tests and from aquifer tests. To do this you type the data that you record in the field into the editor program (CGEdit). You then store the whole data-set in a file.

Most of the other programs can then be used to examine or analyse this data file in one way or another. Some methods of analysis look at the whole data set, others look only at some aspect of the data, yet others look at several data sets simultaneously.

The sole purpose of two programs is to produce simulated data. These are written to files in the same way as the field data that you enter. The simulations can be very useful for comparison with field data and also for educational purposes.


Well storage effects

It is important to understand the distinction between well storage and aquifer storage. Well storage is the volume of water that comes from the well itself rather than from the aquifer. It is usually very important for the first few minutes of discharge, then becomes progressively less important. Its exact significance depends on a combination of the well diameter, the hydraulic properties of the well, and the hydraulic properties of the aquifer.

Inclusion of well storage effects is an option in the production of simulated well test data and compensation for well storage effects is an option in the analysis of well test data. However, these programs do not make any allowance for well storage effects in the simulation or analysis of aquifer test data.

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The reason is simple. The well test simulation and analysis is based on a 'well equation' which models the way in which water flows into a well, while the aquifer test methods deal with flow through an aquifer. In the well test case we have everything we need to compensate for well storage in the well equation and the diameter of the well. To compensate for well storage in a piezometer during an aquifer test we would require, in addition to the aquifer values, data on the hydraulic properties of the piezometer itself; this would mean opening another whole can of worms.


Well characteristics files

An option provided by the 'Well equation' program (CGWellEq) is the production of a Well Characteristics file output in the '.csv' format for easy importation into a spreadsheet.

This file will contain a table of values derived from the well equation that you have evaluated for a particular well (refer to the Well Equation below). All the data in the file will relate to a single duration of pumping that you specify when you create the file.

The first column of the file will contain a series of 20 discharge rate values. The second column will contain drawdown values for the corresponding discharge rate. The third column will contain specific capacity (Q/s) values. The remaining three columns will contain the value of the A term, B term, and C term of the well equation, again for the corresponding discharge rate. Each column will be separated by a comma so that the file may conveniently be 'imported' into a spreadsheet. (The commas are automatically recognised as deviders so that each value goes into a different column.)

An example file is given in table 1...

Table 1

Q,s,Q/s,A term,B term,C term
100.000000,0.72000000,138.888889,0.70000000,0.0,0.02000000
200.000000,1.51313708,132.175731,1.40000000,0.0,0.11313708
300.000000,2.41176915,124.390015,2.10000000,0.0,0.31176915
400.000000,3.44000000,116.279070,2.80000000,0.0,0.64000000
500.000000,4.61803399,108.271182,3.50000000,0.0,1.11803399
600.000000,5.96363261,100.609819,4.20000000,0.0,1.76363261
700.000000,7.49283628,93.4225670,4.90000000,0.0,2.59283628
800.000000,9.22038672,86.7642567,5.60000000,0.0,3.62038672
900.000000,11.1600000,80.6451613,6.30000000,0.0,4.86000000
1000.00000,13.3245553,75.0494089,7.00000000,0.0,6.32455532
1100.00000,15.7262320,69.9468252,7.70000000,0.0,8.02623199
1200.00000,18.3766127,65.3003915,8.40000000,0.0,9.97661265
1300.00000,21.2867633,61.0708157,9.10000000,0.0,12.1867633
1400.00000,24.4672970,57.2192344,9.80000000,0.0,14.6672970
1500.00000,27.9284251,53.7087214,10.5000000,0.0,17.4284251
1600.00000,31.6800000,50.5050505,11.2000000,0.0,20.4800000
1700.00000,35.7315505,47.5770006,11.9000000,0.0,23.8315505
1800.00000,40.0923117,44.8963885,12.6000000,0.0,27.4923117
1900.00000,44.7712504,42.4379481,13.3000000,0.0,31.4712504
2000.00000,49.7770876,40.1791285,14.0000000,0.0,35.7770876



Figure 1. Well losses related to total drawdown (data from the table above)
The units for this file and figure were discharge rates in m3/day and drawdowns in metres. All drawdowns were for one day's discharge. A file having the same specifications is produced in Tutorial E8, below.

The graphing of selected columns taken from a file such as this can provide useful insights into the functioning of the well.

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Figure 1 provides and example graph extracted from the above data. It compares the 'C term' drawdown, considered to be mainly due to turbulent well losses, with the total drawdown. Selected discharge rates associated with data points are marked.

The naming of the well characteristics file is automatic. The file name has the form 'WCHnnn.csv' where nnn represents a three figure number. The file name extension, 'csv' indicates that the file is written in comma delimited ASCII (the American Standard Code for Information Interchange) format. If there are no files with names matching WCHnnn.csv in the current data directory then if you create a file it will be named WCH001.csv. If WCH001.csv already exists then the new file will be WCH002.csv, etc., up to WCH999.csv.


CG data files

While the CG set of programs can read data from, and write data to, ASCII files, the standard form of data file is a special type which cannot be read using ASCII editors. The names of these files end in the file name extension 'CTD'. There will usually be an associated file having the same main name but the extension name 'CTN' and containing notes relating to both the particular discharge test and the CTD file. The notes files are written in ASCII. In these instructions the extension part of the name is usually not mentioned, but when you view the file names using DOS you will see the above extensions.

When you are analysing data from the data files it will be obvious that each plot on a graph must have a time value and a drawdown value. Much less obvious, but of great importance, is the fact that each point also has a discharge rate value. It is this that allows the CG programs to take into proper consideration the periods of recovery or of differing discharge rate.

Examine several files using CGEdit to familiarise yourself with their forms. A file that contains stepped rate data from a well test might be most instructive, try WOOL38B.

From the primary menu select CGEdit (Data entry and editing). You will be asked if you want to load a data file, reply with [Y]. You will now be given a file name and asked if you want to load it, if it is not WOOL38B then reply with [N]. Now select WOOL38B from the list displayed, using the arrow keys and then pressing [Enter].

Now display the data by selecting Data entry/editing from the CGEdit menu. You can scroll through the data using the [PgDn] and [PgUp] keys.


Data file directory

The programs, as distributed, include a set of example data files. I recommend that the CG programs be placed in one directory and all the example data files in a subdirectory attached to the one containing the programs. For example, the programs could be in directory CG and the example files in directory CG/CGXample.

Data files will be read from, and written to, the 'current data directory'. After you install the programs you must change the current data directory to match the name of the directory you want to store data in and retreive data from.

To change the current data directory select 'Change configuration' from the primary menu and then select 'Change path'. The program will give you a list of the subdirectories attached to the directory containing the CG programs. Type in a valid data file directory name if you wish to change it, otherwise press [Esc] to retain the existing name.

If you want to create a new subdirectory for well test data files then you will need to exit from the CG programs and use Windows Explorer to create a new directory.
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Producing files of simulated drawdown data

There are at least four methods of producing simulated drawdown data and then having that data written into a disk file:

In every case a notes file will be written, in addition to the data file, to record information on the particular simulation. The notes file will have the same name as the data file except that while the extension part of the data file name will be '.CTD' that of the notes file will be '.CTN'.

Simulations by program CGDD
This will produce a simulation according to your specifications. You will be required to enter aquifer type, boundaries (if any), discharge rates and durations. The program then calculates the simulation and allows you to specify a file name by which to save the data.
Simulations by program CGPDD
Similarly to CGDD, this program produces a simulation according to your specifications. Where it differs from CGDD is in producing a file of well test data rather than aquifer test data; ie. the time/drawdown values are produced by solution of the well equation. Simulation of well storage effects are optional.
Simulations by program CGAnal
This is primarily an analysis program rather than a simulation program, however one analysis method ('Manual generalised') operates by allowing you to produces simulations on the VDU screen and comparing them with the measured aquifer test data. It is the data of these simulations which can be written to disk file.

The data will be written to a file having a name in the form SIMnnn.CTD, where 'nnn' represents a three digit number. The system can best be explained by example. If there are no files of this type in the currently selected data directory and you cause a file to be written, it will be named SIM001.CTD. If file SIM001.CTD exists then the data will be written to file SIM002.CTD etc. The maximum is SIM999.

The command to write the file is given by pressing [F] (for 'file') whenever you are using the Manual generalised method and there is a simulation on the VDU screen.

Simulations produced by CGAnal and CGPAnal will have identical times and discharge rates to those of the measured data files.

Simulations by program CGPAnal
This too is primarily an analysis program, but, in common with CGAnal, simulations used for comparison with the measured data may be written to disk. The procedure is the same as for CGAnal.

The simulation will be written to disk whenever you press [F] while the simulation is on the screen.


Help

The help system built into the programs is designed to answer many of your questions. It is available most of the time, simply by pressing [F1]. When you call for Help from one of the menus you will find that it is 'context sensitive', it will give you information relating to whatever the highlighted bar is on. At other times you will be presented with a menu of topics, select one by highlighting it with the arrow keys, and then pressing [Enter].

A text search is also available from the Help menu, press [S] and type in the text that you are interested in. Pressing [A] will then find the next occurrence of the same text.

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The search always starts at the beginning of the help file. It is not case sensitive, ie. if you type 'unit' then any occurrence of 'Unit' will also be found. Try it.


Where is it?

The arrangement of the programs and functions is logical and you will get used to it quickly. Below is a table for quick reference; menu names are shown in capitals, and indenting from the left indicates the menu hierarchy.

A short explanation is given in parentheses where it seems to be warranted. Remember that more information is given from the menus and from the help system. Table 2

Menu hierarchy

PRIMARY MENU
Data entry and editing
DATA EDITING, MAIN MENU
Data entry/editing
DATA EDITING MENU
Right(move cursor to next field right)
Left(move cursor to next field left)
Next record(move cursor to next record)
Previous record(move cursor to previous record)
Back up 16 records(move cursor back 16 records)
Forward 16 records(move cursor on 16 records)
Edit this field(edit the field under the cursor)
Add new data to end (append data to the end of the file)
Add constant (add a numeric constant to one or more numbers in the current column)
Multiply by constant(as above, but multiply)
Insert one record(insert at cursor's position)
Delete record(s) (Delete one or more records from cursor's position toward end of file)
Back to main menu(Exit to next higher menu)
Special editing
SPECIAL EDITING MENU
Simulate full recovery(For step test data)
Randomise drawdowns (Add a 'field' error to simulated data)
Simulate confined
Simulate unconfined
Correct for background (Correct for changes observed in a piezometer monitoring background noise)
Change test description(Well diameters, etc.)
Merge with file(Join current data with file data)
Sort(into chronological order)
Correct for residual (Correct for preceding pumping)
Return to main menu
Aquifer test simulation
Well test simulation
Aquifer test analysis
CG ANALYSIS MENU
Transmissivity
Storage coefficient
Leakage coefficient
Theisfit
Leakyfit
Automatic generalised
Manual generalised
Slug test
Change maximums (Change the limits on the graph)
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Well test analysis
Data plotting
Calculate well efficiency
Well equation
HOT KEYS
Modification of A, B, C, D, t, Q, Un/confined, Isotropic/strip
Output of s vs. Q and Q/s vs. Q in delimited file
Multiple well fit
DeGlee analysis
File index
INDEX MENU
Browse or edit
BROWSE EDIT MENU
Previous record
Next record
Insert a record
Delete a record
Change field(Replace contents of field)
Find in priority field (Refer to notes on index, below)
Search in any field (Refer to notes on index, below)
Exit
Change field names
Change sort order
Exit
Change configuration
CG CONFIGURATION MENU
Change path (Change the DOS path for data files)
Units(Select different units)
Customise colours
Exit
Exit to DOS


Keeping track

If you have any need to keep your old discharge data files for future reference then you will probably want something a bit more informative than just a file name. Two features have been provided to help: the file index and the notes files system.

Notes files

CG discharge test data files all have the extension name '.CTD'. You can also keep notes in a short text file associated with the data file, this will have the extension name '.CTN'. (For example, in the CGXAMPLE directory is the example discharge test data file WOOL38B.CTD. This has an associated file WOOL38B.CTN which contains some notes relating to the data.)

You can write in the notes files via the main menu of program CGEdit; or you can, if you prefer, use an ASCII editor program. The only rules about how the notes files should be formatted are that the lines must not be longer than 76 characters and there must be no more than 18 lines in a file. If you are using CGEdit to write your notes files you need not worry about these rules, CGEdit will keep you within the limits. When you exit from viewing and/or editing the notes file you have the option of writing it, with any modifications that you might have made, to disk.

CGEdit also provides a scan feature. With this you can quickly scan through the notes files in a given directory. You cannot modify the notes files from the scan mode.
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The discharge test simulation programs will produce notes files whenever they write a simulation to disk. The note file will record the specifications that you used when you produced the simulation.

The help system will give you more information on the notes files.


File index

A simple indexing system is provided by CGMenu to allow you to cross reference your data files. On the distribution disk it consists of six fields: file name, directory (the name of the subdirectory in which the file is stored), date, project, well name, and well number. You can change the name of any, or all, of these fields.

The index is kept sorted. It can be sorted on any field, the sort specification is up to you; you will probably use different specifications for different purposes. You might be looking for file relating to a certain project at one time, or files from tests carried out on a particular date at another time.

The index is in capital (upper case) letters. You may enter data in either upper or lower case, but everything will be converted to upper case.

Note that this is a simple index. If you want something more powerful and elaborate you will probably be well advised to use a data base manager.

Two items in the Browse/edit menu of the file index system should have a little explanation.

The help system will give you more information of the index.

Check your results

The CG set of programs is large (over 13 000 lines of source code) and complex. Although I have removed all the errors that I can find, you can be sure that there will still be errors in it somewhere. Therefore you should check your results.

Particularly if the analysis that you are working on is an important one and your report is going to result in commitments being made involving major expenses, then you should very carefully check your results.

As stated elsewhere, most of the data handling and analysis operations are done using the consistent set of units based on metres and days. If your analysis was done in other units then one check that you could do is to change to the metre/day set and repeat the analysis, checking that the results are the same.

You should not rely entirely on the CG programs, run an independent check by some other method if the results are important.

If you should find any errors, then please inform me of them, so that I can correct them.


Entry of times

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Available time units are: seconds, minutes, hours, and days. You will probably have your own preference for the units that you use in analysis; I use days. There are advantages in using a set of consistent units in analysis.

Whatever your preference for the time unit used in analysis, you are free to enter field data in any units at all; you can change units after you have completed data entry (for that matter you can change time unit half-way through data entry if you like).

Suppose your reading times were something like the following: 30 seconds, 1 minute 20 seconds, . . ., 55 minutes, 1 hour, 1 hour 10 minutes, . . ., 26 hours, 28 hours, etc.

The easiest way to enter these times would be to start data entry using minutes, and change the time unit to hours after entering the 55 minute reading. You would enter the seconds as sexagesimal fractions, eg. 30 seconds would be entered as 0;30, 1 minute 20 seconds as 1;20. After switching to hours you would similarly enter 1 hour 10 minutes as 1;10.

Throughout this you could be entering discharge rates in cubic metres per day, litres per second, US gallons per hour, or one of several other units.


Conceptual models

Infinite isotropic aquifer
This is the model of Theis and Thiem, and is the simplest of all aquifer models. Both the pumped well and the piezometer are considered to have infinitesimal diameter, and therefore no storage. The aquifer is considered to be infinite in extent and identical in all directions, it is fully confined. Vertical flow within the aquifer is neglected.

The time-drawdown curve, when plotted as a semilogarithmic graph, shows a straight line following an initial downward curve.

Leaky aquifer
This is the model of Hantush. It is subject to the same conditions as the infinite isotropic aquifer except that there is leakage from an overlying semiconfining layer (aquitard). The aquitard is considered to have infinite storage.

At early times the drawdown curve is identical to that of the Theis curve, but at later times drawdowns become progressively less, finishing in a horizontal line if discharge continues for a sufficient period.

Unconfined aquifer
These programs use the 'Cooper-Jacob correction' to approximate the drawdown in an confined aquifer, given drawdowns measured in an unconfined aquifer having similar characteristics.

The equation is: (apology, html is not great for writing equations)


Equation 1
Sc = Su- Su2

2D


where:
Sc is the simulated confined drawdown,
Su is the measured unconfined drawdown, and
D is the saturated thickness of the unconfined aquifer.

The inverse of the Cooper-Jacob equation will convert drawdowns measured in (or simulated for) a confined aquifer to approximate values which would be expected in an unconfined aquifer having similar characteristics. The inverse of the Cooper-Jacob correction is:-
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Equation 2
Su = D(1-root(1- 2Sc

D
)


where: Su is the calculated unconfined drawdown,
Sc is the measured confined drawdown, and
D is the saturated thickness of the hypothetical unconfined aquifer.

Figure 2. Effect of a discharge boundary and a recharge boundary
When drawdown in an unconfined aquifer is small in comparison to aquifer depth, drawdown will be equal to that in a confined aquifer under similar circumstances. With increasing rates of discharge, drawdown in an unconfined aquifer will be larger than in a confined aquifer because part of the aquifer has been dewatered, leading to reduced transmissivity.

Bounded aquifer
In its simplest form a single boundary is taken as a vertical plane cutting across an aquifer. On the first side of the plane the aquifer is as specified, confined, leaky, etc.; on the other side of the boundary the aquifer effectively ceases to exist.

There are two primary types of boundaries, discharge and recharge. The discharge boundary is a line through which no water may pass. It corresponds to the edge of the aquifer or an impermeable dyke, etc. The recharge boundary is a line source of unlimited water, such as a stream which fully penetrates the aquifer.

On a semilogarithmic graph the effect of a discharge boundary is to double the slope of what otherwise would be the straight line section of the curve. The recharge boundary results in the curve becoming a horizontal line for later times, as the point is reached where all the water flowing to the well is coming from the boundary.

Figure 2 shows a comparison of (upper curve) recharge boundary, (middle curve) no boundary, and (lower curve) discharge boundary. The middle curve is the data of example file CONF0030, while the other data for the other two curves were produced by the 'Manual generalised solution' of the aquifer test analysis program (CGAnal). The values used for CONF0030 were: T=200 m2/day, S=0.0001, R=30 m, Q=300 m3/day for 1 day. The discharge boundary model included a discharging image well at a distance of 400 metres from the piezometer, while the recharge boundary model had a recharging image well at the same distance.

Figure 3. Single boundary, distances

When you specify an aquifer configuration containing a boundary the programs will ask for the distances that are needed to define the model.

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There are three distances that must be entered into the program in the single boundary case: distance from piezometer to pumped well, distance from pumped well to boundary, and distance from piezometer to boundary. Entries are checked and you are informed when you enter a value which leads to an impossible geometry. The program calculates the distance from the image well to the piezometer.

As illustrated in the Figure 3, the distance from the pumped well to the boundary (a) is equal to the distance from the boundary to the image well (a').

Partially bounded aquifer
For the purpose of these programs a partial boundary (or semi-boundary) is a line beyond which the transmissivity differs from that in the part of the aquifer containing the wells.

Figure 4 is a simulation showing the effects of a partial boundary on drawdown in a confined aquifer. Here, the upper curve is the case where there is no boundary, the lower curve is a full discharge boundary, while the middle curve is a partial boundary where the transmissivity on the side of the aquifer containing the wells has been taken to be twice that on the far side of the boundary. The Delta s slope for the partial boundary is approximately half way between those of the unbounded and fully bounded cases. (Delta s is defined as the drawdown per log [base 10] cycle.)

Figure 4. Effect of a 'partial' boundary
The parameters used for the unbounded simulation in Figure 3 were: T=200 m2/day, R=100 m, S=0.0001, Q=300 m3/day for 10 days. Both the bounded simulations had an image well distance of 1200 m, roughly equivalent to the boundary being 600 metres from the two wells. The partial boundary case had a value for T2 of 100 m2/day.

Strip aquifer
A strip aquifer consists of an aquifer bounded on two sides by parallel discharge boundaries. While late-time drawdown in a simple confined aquifer is proportional to a constant plus the logarithm of time, in a strip aquifer it is proportional to a constant plus the square-root of time.

The strip aquifer case requires the same three distances needed in the single boundary case and also the width of the aquifer, c in Figure 5.

In this case there are, of course, an infinite number of image wells. The image wells are created by 'reflections' of the pumped well, with the boundaries acting like mirrors. The program considers image wells further and further from the piezometer until the point is reached where their effect is negligible.

Figure 5. Strip aquifer, distances

The calculated drawdown for the piezometer is the total of that calculated for a Theis aquifer and the sum of the drawdowns due to all the image wells.

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Analysis methods

These programs deal with two distinct forms of discharge test analysis, aquifer analysis and well analysis. The former is concerned only with the properties of the aquifer, while the latter is concerned with the properties of the well (which are also affected by the properties of the aquifer).

As is the case in manual analysis of discharge test data, many of the methods provided here are applicable only to data from discharge tests where the discharge rate was held constant.

In general the aquifer analysis methods deal with data from piezometers while well analysis deals with data from the pumped well. There are many exceptions to this, however, eg. slug analysis is an aquifer test which uses data from the pumped well, and transmissivity can be derived from a multistage well test.

Two methods available in the aquifer analysis program, CGAnal, are capable of considering data from tests which include variations in discharge rate. These methods, the 'automatic' and 'manual generalised' methods, therefore can take into account recovery data. I strongly suggest that recovery data should be included when these methods are used, as it provides something of an extra perspective on aquifer performance.

Most other methods are applicable to data containing changes in discharge rate so long as they are used on the part of the data before the change occurred.


Evaluation of transmissivity

Several methods are available for evaluation of transmissivity (T): These are described in more detail below.
Calculation of transmissivity from the Delta s slope
The Delta s slope is taken as the slope of the line of best fit drawn through some portion of the drawdown data, as plotted on a semilogarithmic graph. Exactly where and when the method is used is very much a matter of expert judgement, and will be dependent upon the user's interpretation of the aquifer configuration. In the case of a Theis aquifer the line is drawn through the straight line portion of the drawdown data.

This method is used by the aquifer test analysis program, CGAnal. The calculation of Delta s will be independent of the type of graph being used to display the data.

Transmissivity is calculated from Delta s by the equation:


Equation 3
T = 0.183 Q
______
Delta s


where Q is the discharge rate and the units are compatible.

T derived from the coefficient B of the well equation
The well equation is described below (Evaluation of the well equation). Transmissivity may be derived from B by the equation:-

Equation 4
T = 0.183
_____
B


This method is used in the well test analysis program (CGPAnal). Note that when T is derived from recovery the value obtained is usually greater than that obtained from drawdown data.

Simultaneous calculation (with storativity) using Theisfit
This method is used by the aquifer test analysis program (CGAnal). It has been adapted from a Fortran program written by McElwee (1980).

The best fit Theis type curve is found for the specified section of the data. Changes in discharge rate before or during the chosen section are not allowed.

Simultaneous calculation (with storativity and leakage), Leakyfit
This method has been adapted from a Fortran program written by Cobb et. al. (1982), and is used by program CGAnal.

The best fit leaky-artesian (Hantush, 1955) type curve is found for the selected subset of the data. Changes in discharge rate are not permitted before or during the selected data. This solution will fail to converge in many cases where there is not a close match to a theoretical type curve.

Simultaneous calculation (with other parameters) using the 'Automatic generalised' or computer-aided-manual (Manual generalised) curve fitting routines
This option is described below, and is discussed in the tutorials.

Calculation using DeGlee analysis
This is a simultaneous solution for T and leakage coefficient for leaky aquifer data from a number of wells. It is described below and covered in the tutorials.
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Evaluation of storage coefficient

As far as evaluation from the data is concerned little distinction is made between storage coefficient (confined aquifers) and specific storage (unconfined aquifers). The word 'storativity' has been used to cover both terms.

Five methods are available in the aquifer test analysis program (CGAnal), and another from the 'Multiwell fit' accessible from the primary menu.

In all but the first of the above, storativity is evaluated by curve-fitting, similarly to the evaluation of transmissivity in those methods. Therefore only the first method will receive further discussion here, except to say that Leakyfit and the multiwell Leakyfit are designed for leaky aquifer analysis.
Evaluate storage
This option is simply labelled 'Storage coefficient' on the menu of CGAnal. The program will require you to specify a point on the discharge test graph to be used for the evaluation, this will provide a time and a drawdown. There must be no changes in discharge rate before the point that you specify, this will be checked by the program.

The storage coefficient (or specific storage or storativity) is evaluated by solving the two equations below for S.


Equation 5
u = root(R) S
_______
4 T t


Equation 6
S = Q W(u)
______
4 pi t


where:
u is a dimensionless number,
R is the distance from the pumped well to the piezometer (recorded in the discharge test data file),
T is transmissivity,
t is time,
Q is discharge rate (recorded in the discharge test data file),
W(u) is the well function of u (Theis 1935),
s is drawdown.

Of the above, only T, and S itself are unknown. You will be requested to enter the value of T and then S will be evaluated.

(The well function of u is evaluated using a polynomial approximation detailed in Clarke 1988. The solution of the above equations for S, by Newton's method, is described in the same publication.)

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It is possible that the equations are insoluble for the T that you provide, in this case you will be informed that the solution failed to converge.

Note that the assumption is made that the aquifer is a simple confined isotropic one. If this is not justified, eg. the effects of a boundary or leakage are apparent at the time of the selected drawdown figure, then the derived figure for S will be in error. I suggest that the point selected for use in the evaluation be carefully considered bearing this in mind.

Evaluation of leakage coefficient

Six methods are available, the first five below are reached through the menu of the aquifer test analysis program, the last two are accessed from the primary menu.

These are explained below.

Evaluate leakage
This procedure is rather similar to the 'Evaluate storage' procedure above, the differences being that the leaky artesian well function, W(u,Rb), is used rather than the well function, and successive bisection is used for the solution rather than Newton's method. (The leaky artesian well function is evaluated using a method adapted from Cobb et. al. 1982.) Values for both T and S are required before the solution can proceed as there is one more unknown here.

Leakyfit to the manual generalised solution
These are all curve fitting methods and operate for leakage in a similar way to the transmissivity solutions described above.

Multiwell leaky artesian aquifer solution
This is a curve fitting method which attempts to find the best simultaneous fit for a set of leaky artesian aquifer type curves and data from a number of piezometers. As in Theisfit and the single piezometer Leakyfit the discharge test must involve a single, constant discharge rate.

Automatic and manual generalised
Again, curve fitting methods, but not confined to data from a constant discharge rate test. A description of the use of these methods is given below.

DeGlee analysis
This is a solution for T and L given steady state drawdown data in a number of wells. A description of the method is given below and in the tutorial section.

Leakage, units

The DeGlee analysis (Kruseman and DeRidder, 1983) uses a symbol 'c' to give a value to the amount of the leakage, while Cobb et. al. use Leakage coefficient, L. (Cobb also use the inverse of the leakage coefficient. This has the advantage of increasing as the amount of the leakage increases, while the value of L decreases as the amount of leakage increases.) Alternately one might wish to know the vertical hydraulic conductivity and the thickness of the aquitard.

It may be useful to provide some equations relating these values to each other. (I have given more equations than are really needed. In my experience hydrogeologists are not always dazzling mathematicians. {Just as programmers are not always brilliant spellers!})

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In the equations below:
L is leakage coefficient,
b is thickness of aquitard,
c is a constant used by DeGlee,
K' is vertical hydraulic conductivity of the aquitard.


Equation 7
L = root( T b
___
K'
)


Equation 8
c = L2
__
T


Equation 9
c = b
__
K'


Evaluation of thickness of unconfined aquifer

Drawdown in an unconfined aquifer is not directly proportional to discharge rate, as in a confined aquifer. This is because transmissivity declines as the aquifer close to the well is dewatered.

On the assumption that the Cooper-Jacob approximation gives a good characterisation of unconfined drawdown it is theoretically possible to evaluate the aquifer thickness from the time-drawdown curve (using either the automatic or manual generalised methods of CGAnal). In practice I would expect that unknown and extraneous factors would be too great to make this a practicality.

Evaluation of boundary distance

The automatic or manual generalised methods of the aquifer test analysis program (CGAnal) are able to produce a figure for the distance of the image well in a bounded aquifer. This distance might then be used to infer the location of the boundary responsible for the image well.

It should be remembered that the derived image well distance is going to be dependent on the uncertainties in T and S, and that these are usually substantial.

Evaluation of strip aquifer width

The automatic or manual generalised methods of the aquifer test analysis program (CGAnal) are able to produce a figure for the width of a strip aquifer.

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The accuracy of this figure is going to be affected by several things: any errors in the derivation of S or T, any inconsistencies within the strip, any leakage through the boundaries of the strip, the exact location of the wells within the strip, etc. I suggest that little weight be given to the calculated strip width, but rather it might be considered to be an order-of-magnitude estimate. It should be useful to relate the calculated strip width to observations of surficial geology or geophysical results.

Automatic generalised solution

This is a method of fitting a type curve to a set of data. The type curve can be any one that you select. Unlike more conventional type curves it will take into consideration any changes in discharge rate that are recorded in the data file.

The user defines the aquifer model and then enters first guesses for the aquifer parameters. The solution then systematically searches for changes that can be made to the parameter values which will lead to a reduced root-mean-square error. It starts by attempting large changes and progressively moves toward smaller changes, finally, when all factors have been reduced to below 1.02 the procedure terminates. The factors for adjusting the parameter values start at two and are progressively reduced by replacing the old values with their square roots.

An example of the use of the Automatic generalised solution is given in the tutorials.

Strip aquifer

The shape of the drawdown curve for strip aquifer data is dependent, to some extent, on the location of both the pumped well and the piezometer within the strip. For simplicity, however, this analysis assumes that both wells are in the centre of the strip.

Manual generalised solution

This procedure allows you to adjust the values of the aquifer parameters and, at the same time, view the effects on a simulation. The normal aim is to improve the fit between the simulation and the data curve which is also displayed.

Several examples of the use of the Manual generalised solution are given in the tutorials.

Also see the comments on strip aquifer analysis under the 'Automatic generalised solution' above.

DeGlee analysis

Best fit DeGlee analysis for well Waik6. T=27m2/day, L=334m.

A modification to the CG Programs (2003/06/07) allows a data dump to a .csv file suitable for convenient importation into a spreadsheet. To dump, press S or L with the graph on the screen. The data will be written to a file named Deglee.csv.

This is a computer adaptation of the DeGlee analysis (Kruseman and DeRidder, 1983). The data required for the analysis are: the (constant) discharge rate, the distance from the discharging well to each of the piezometers, and the drawdown when the water levels in the piezometers reach steady state.

There are two options for data entry, either the data are entered via the keyboard, or the program reads the data from the discharge test data files. Note that the assumption is made that drawdown in the piezometers has reached steady state.

The method operates by first plotting the Hankle function (the Bessel function of the second kind and zero order). The next step is to plot R/Ro against s/so for each piezometer. (Where R is the distance between the particular piezometer and the pumped well, s is the steady state drawdown in the particular piezometer, and Ro and so are constants.)

Ro and so are now adjusted to produce the best possible fit between the data and the plotted Hankle function. This is first done automatically then the fine adjustment is performed manually.

Transmissivity is calculated from the equation:


Equation 10
T = Q
____
2 pi s0


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where Q is the discharge rate, the leakage coefficient is taken as being equal to Ro, and
'c' is given by Equation 8 above.

There is a tutorial on the use of the DeGlee analysis below.

Slug test analysis

As described by Bouwer (1978). This procedure calculates the hydraulic conductivity for an unconfined aquifer following a test in which recovery has been measured after either extraction of a slug of water or introduction of a slug of water. It requires the following data: Two other example files are also included, 'PuttSlug' and 'TrebSlug'. Notes on all three are available via program CGEdit.

In my opinion a slug test may be useful in getting a quick approximation of hydraulic conductivity/transmissivity, but is no substitute for a full discharge test.

Evaluation of the well equation

Well test analysis differs from aquifer test analysis in its aim. It will tell you something about the performance of the well and less about the aquifer parameters. However, transmissivity may be evaluated from a well test (difficult if your units are inconsistent), something can also be learned about the presence or absence of boundaries, and there may be differences between confined and unconfined responses.

Well test analysis deals only with time-drawdown-discharge rate data from the pumped well.

The primary well equation, as used here is:


Equation 11
s = AQ + BQ log(t) + CQD


where:
s is drawdown,
t is time,
A, B, C, and D are constants for the particular well,
The units should be consistent.

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A second form, which is applicable to strip aquifers, is also available; in this the logarithm of time is replaced by the square root of time.

These two forms of the well equation assume negligible storage within the pumped well. A correction for well storage effects is available in both the simulation (CGPDD) and analysis (CGPAnal) programs. The correction uses the figure that you provide for the radius of the well in the area where the water level is rising and falling to calculate the well storage. It is an iterative method which seems to give a good simulation of reality.

When you use the well test analysis program (CGPAnal) you will be asked whether you want a preliminary analysis, in most cases you will reply yes to this as it will normally provide a good first approximation faster than can be achieved manually.

If you decide not to use the preliminary analysis then you will be asked for initial estimates for the four coefficients, A, B, C, and D. The numbers that you give will depend greatly on the set of units that you are using. When proficiency with the program is gained you will be able to find a quick solution even when your initial estimates were very far from the mark, but at the learning stage this may cause difficulties.

Typical initial values are:
UnitsABC
Metres/days0.010.00110e-6
Metres/seconds50010010000
Feet/days0.00110e-410e-8
Feet/seconds301070
Some general notes on using CGPAnal are given here, I strongly suggest that you also try Tutorial G7.

The best approach in using CGPAnal is to first evaluate coefficient B, as all the other coefficients are, to some extent, interdependent. (To begin adjusting B, press [2].) If your data include a recovery period then I suggest that you evaluate B from that, if there is no recovery period then evaluate B from the slope of the first stage (see also the notes on evaluation of transmissivity).

Next, progressively evaluate coefficients A and C. Adjust A to obtain a good fit for the stage having the lowest discharge rate, then adjust C to produce a good fit for the stage having the highest discharge rate. Repeat this process until the fit is sufficient for your needs (probably two or three times).

If your test consists of at least three stages and the fit with the intermediate stages is not good enough you can adjust coefficient D (the exponent in the third term). An increased exponent will produce proportionally greater drawdown at higher discharge rates than at intermediate rates. (Coefficient C will automatically be adjusted as you change D, but you will need to modify both A and C to optimise the simulation.)

Educational tutorials

The use of the programs in well or aquifer test analysis is covered in the general tutorials. While those tutorials may be used for hydrogeological education, these are specifically designed for that purpose.

The CG programs can provide a dynamic and very interactive educational resource to help students visualise how time/drawdown type curves change according to the aquifer characteristics.

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You can:

Unless otherwise stated, the units for these tutorials are the consistent set based on metres and days. All example files are in the subdirectory CGXample.

Tutorial E1: Using various types of graphs

Select 'change configuration' from the primary menu and then select Units. Make sure that the units are the consistent set based on metres and days. They should be: metres, days, m3/day, m2/day, and m/day, and there should be a statement to the effect that they are consistent; if not then change them. Press [6] to leave 'Units' and then [4] to exit from the Change Configuration menu.

Back at the primary menu pick CGPlot (Data plotting). You will be asked if you want to load some specified file. The specified file will be the one that has most recently been written to, or read from disk. For this exercise you need file 'CONF0100'.

(The full file name is 'CONF0100.CTD' but you just need to concern yourself with the first part of the name, the CG programs will add the second part. The file contains data simulated for a discharge rate of 300 m3/day, a duration of one day, a transmissivity of 200 m2/day, a storage coefficient of 0.0001, and a piezometer 100 metres from the discharging well.)

If the given file name is not CONF0100 then answering with [N] will cause a list of data file names to be displayed, and among those will be the one you want. Use the arrow keys to highlight CONF0100 and then press [Enter] to load this file into memory.

This data file is simulated time/drawdown/discharge rate data for a simple confined (Theis) aquifer. (The standard assumptions have been made, the aquifer is presumed to be infinite in extent, isotropic, fully confined, and the well is considered to have no storage; ie. to have an infinitesimal radius. Unrealistic, but quite good enough for a great many real situations.) Ask CGPlot to provide a screen graph.

The first graph will be linear, the simplest of them all. Select this by pressing [L]. Answer [N] to 'Alter any drawdown or time limits', and either [Y] or [N] to 'Join data points'. Notice that the water level in the piezometer fell very quickly in the early stages of discharge, and progressively more slowly at later times. Also notice that while the rate of fall declined, the fall did continue until the end of the simulation; in theory it would continue for ever.

Pressing any key (except [S] or [L]) will clear the graph from the screen and cause the question 'Exit or Another graph?' to be displayed, answer with [A]. Tell CGPlot that you do want to load CONF0100. The next graph we will view will be double logarithmic, that is, one having logarithmic time and drawdown scales on the axes. Pick this by pressing [O]. The data of file CONF0100 will now be displayed as a log-log graph. This is the form of graph traditionally used for type-curve matching. You will notice that time increases from left to right and drawdown increases from bottom to top.

Next, after exiting from the log-log graph and reloading CONF0100, select a semilogarithmic graph. While the time scale is exactly the same as for the previous graph, this time the drawdown scale is linear; it also increases from top to bottom, more reminiscent of a falling water level in a piezometer. Perhaps the most important point to notice, however, is that after a short curved section all the data points fall on a straight line. This straight line can be used to calculate the transmissivity of the aquifer (the operation is described elsewhere).
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The last type of graph that you should have a quick look at here is the root time graph. With this data it has some resemblance to the linear graph, but you will notice that the scale along the x axis is not linear, and the early time data are not so crowded up on the left. This type of graph is useful in examining data from a strip aquifer, when the later time data points will fall on a straight line (described elsewhere).


Tutorial E2: Discharge and recharge boundaries

For the purpose of modelling, aquifer boundaries are usually considered to be vertical planes cutting across the landscape. The aquifer characteristics are different, often very different, on each side of the line.

A discharge boundary is a line beyond which the aquifer does not exist. It might be something like a granite 'wall' at the edge of an alluvial gravel aquifer in a valley bottom. It is called discharge because its effect is identical to that of a discharging image well.

A recharge boundary is a line where no decline in the piezometric surface can be produced, no matter how much water is withdrawn from the aquifer. An example is a river fully penetrating the aquifer. It is called recharge because its effect is identical to a recharging image well.

Two example data files are provided: DISBOUND simulates the effects of a discharge boundary while REBOUND simulates the effects of a recharge boundary. Both can be compared with CONF0030, where the aquifer characteristics are taken to be the same apart from the boundary. In both cases the boundary is 200 metres from the piezometer and the same distance from the discharging well.

If you have changed the units then bring them back to the consistent set based on metres and days, as described in Tutorial E1. File CONF0030 is an identical simulation to file CONF0100 of Tutorial E1 except that the piezometer is now 30 metres from the discharging well.

From the primary menu choose CGPlot (Data plotting) and load the three files CONF0030, DISBOUND, and REBOUND; and then display them on a similogarithmic graph. You will notice that the curve of CONF0030 is very much the same as that of CONF0100 (of Tutorial E1) while DISBOUND falls away below and REBOUND rises above. What is not so obvious is that the slope of the DISBOUND curve approaches exactly twice that of CONF0030 while that of REBOUND approaches zero (a horizontal line). (This is reasonable on consideration of the image well model; in the discharge boundary case the extraction is doubled so the slope is also doubled, in the recharge case the total extraction is zero, so the slope approaches zero.)


Tutorial E3: Distance/time/drawdown graph

Figure 6. Distance/time/drawdown
Five example files have been provided to give confined aquifer type curves. The files are named CONF0010, CONF0030, CONF0100, CONF0300, and CONF1000. They simulate drawdowns in a piezometer at distances of 10, 30, 100, 300, and 1000 metres respectively, from a discharging well. All of these files are for a discharge rate of 300 m3/day and a duration of one day. Transmissivity is 200 m2/day and storage coefficient is 0.0001. No recovery data are included.

To simultaneously view all of these files select CGPlot (Data plotting) from the primary menu. Answer [N] to the question 'Do you want to load file xxx alone' and then select the five files shown above by using the arrow keys and [Enter]. Press [F10] when all five file names are highlighted.

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Select a double logarithmic graph (press [O], the letter, at the prompt), leave the graph maximums and minimums at the default, and join data points. You will now be presented with the five type curves displayed on one graph. This display shows how the type curve for a simple confined aquifer will change with changing piezometer distance.

All of these data files were produced by CGDD, the aquifer test simulation program. Note that the 'piezometer' at 10 metres (file CONF0010, the upper curve) already has 0.4 metres drawdown at one minutes discharge. In practice this would, in most cases, be obscured by well storage effects in the pumped well and in the piezometer.

You can produce your own simulations along similar lines if you wish. Of course you are not restricted to a simple confined aquifer, you can add a boundary, leakage, strip aquifer effects, changes in discharge rates, periods of recovery, etc.


Tutorial E4: Modifying S and T, effect on type curve

Next we will produce a dynamic view of the effect of different storage coefficients and different transmissivities.

From the primary menu select CGAnal (Aquifer test analysis), load file CONF0100, and select a double logarithmic graph by pressing [O]. From the CGAnal menu select the Manual Generalised solution, specify a confined aquifer with no boundaries. Indicate that no aquifer parameters are known. As your 'first guesses' give T=200 m2/day and S=0.0001, exactly as used to produce the simulation.

A graph will now be displayed, it will show the data from the file, and over that the simulation produced according to your specifications. As the two will exactly coincide you will see only one set of data.

At this point we can change the value of transmissivity (T) for the simulation by pressing the up or down arrow keys, but before you do that press [C] then press the up arrow key until the number displayed as the 'Current adjustment' is about 2.14, then press [C] again.

The 'current adjustment' is the factor used to multiply by T every time you press the up arrow. It was set at a small number so that a user could adjust it to fit a type curve to file data, but that is not our present purpose. Now a press of the up or down arrow keys will change T by roughly a factor of 2. Try modifying T, then bring it back to its original value.

To switch to adjusting storage coefficient (S) press [2]. ([1] selects T, [2] selects S.) Again, before changing S press [C] and change the 'current adjustment' as you did for T. Now you can modify either or both T and S and observe the effect on the type curve.


Tutorial E5: Modifying S, T, and L

This exercise is very similar to Tutorial E4, except that here we have three variables instead of two.

Call up CGAnal, but load file LEAKY instead of CONF0100. (LEAKY is a simulation based on the same values as file CONF0030 with the addition of a leakage coefficient of 500.) Call the 'Manual generalised' solution as before, and give T=200, S=0.0001, and L=500. Now modify T, S, and L in a similar way to Tutorial E4. You might find it best to use a smaller adjustment for L than 2, as the effect of leakage is proportional to the square of the value of L. You will notice that increasing L decreases the amount of the actual leakage.


Tutorial E6: Modifying boundary distance

Similarly to Tutorials E4 and E5 we will use the 'Manual generalised' solution of CGAnal to modify the boundary distance and observe the effect on the type curve.

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From the primary menu choose CGAnal (Aquifer test analysis) and load file DISBOUND (the values used in producing this file are given in Tutorial E2). Select confined aquifer, boundary, discharge boundary. Give T=200, S=0.0001, and image well distance of 401 metres.

When the graph is on the screen, press 3 to select image well distance as the current parameter. Now use the up and down arrow keys to modify the image well distance and note the effect on the curve. You may like to increase the magnitude of the factor used to modify the image well distance, to increase the size of the changes.

You will find that increasing the image well distance moves the curved section of the graph to the right, toward greater times; while decreasing it has the opposite effect.

You might like to repeat this exercise with file ReBound (recharge boundary).


Tutorial E7: Strip aquifer response

The file STRIP contains a simulation of piezometer drawdown in a strip aquifer, it is based on similar values to CONF0030, confined aquifer, T=200 m2/day, S=0.0001, Q (discharge rate)=300 m3/day, and a piezometer 30 metres from the discharging well. In addition, there is now an aquifer bounded by two parallel discharge boundaries 500 metres apart, and both the discharge well and piezometer are 200 metres from one of these boundaries.
Figure 7. Strip aquifer response - straight line on log-log graph
From the primary menu call CGPlot (Data plotting) and load files CONF0030, DISBOUND, and STRIP, ask for a semilogarithmic graph. Notice that while the DISBOUND curve is below CONF0030, the STRIP curve is lower again. There is more drawdown in the strip aquifer than in the other two. Notice too that the STRIP curve shows no sign of approaching a straight line, it is continually steepening across the whole of the graph. In fact it would not matter how far we extended the simulation, the curve would steepen for ever.

Exit from this graph and plot all three files on a square root of time graph. This time you will see that while CONF0030 and DISBOUND both curve upward, the later data points of STRIP fall on a straight line, the most useful feature of the root-time graph.

The later time points of strip aquifer data plotted on a log-log graph also fall on a straight line, but this simulation is not really long enough to demonstrate that; however, the same simulation carried on to 1000 days does demonstrate it very effectively, as shown in Figure 7. (The scale of the drawdown in Figure 7 is not very realistic, but the point is made.)

Tutorial E7b: Well location within strip

The wells for the simulation which produced the file STRIP were positioned close to the centre-line of the strip aquifer. What if they were near one or other boundary?

From the beginning of discharge the cone of drawdown moves out in a circle around the pumped well. It ceases to be circular when it intercepts one or more boundaries. As the cone intercepts boundaries so it steepens inside the strip. The time at which boundary effects will start to show up will depend on the distances between the pumped well and the nearest boundary, and the piezometer and boundary. More precisely, it will depend on the distance between the piezometer and the closest image well (see the notes on bounded and strip aquifers above).

Figure 8: Effect of well location within a strip aquifer
Figure 8 gives drawdown curves for two configurations of wells within a strip aquifer. Data file STRIP3 simulates a situation where both wells are near the centre of the aquifer while in STRIP4 the wells are close to the edge of the strip. (You can examine the details of the simulations by reading the notes files associated with the data files.)

Also note in Figure 8 that the recovery data from the simulations (the upper, shorter lines), at least when plotted as the square of root t minus root t', quickly become indistinguishable from each other.

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It seems, from an examination of this and other simulations, that the drawdown line is displaced downward on the graph as the wells become closer to one boundary of the strip. The drawdown line is at its highest (actual drawdowns are minimised) when the wells are in the centre of the strip. Displacement of the line is due to the time of the onset of the effects of the first boundary.


Tutorial E8: Producing a well characteristic file

To obtain a better understanding of the characteristics of a pumped well it can be useful to plot a range of discharge rates (Q values) against the corresponding drawdowns (s values), for a fixed duration of pumping. Alternatively, Q/s might be plotted against Q. While the CG programs do not themselves provide these graphs, the well equation program, CGWellEq, can produce a file of these values in what is known as 'comma delimited ASCII' format. This file can then be very easily imported into a spreadsheet for graphing.

Figure 9. Discharge rate versus drawdown
For this exercise I suggest using times in minutes with all the other units based on metres and days.

To produce a simulated well test data file, run CGPDD (the pumped well simulation program). Request an isotropic confined aquifer and give values of A=0.007, B=0.0016, C=2e-7, and D=2.5. The discharge rates and durations should be Q=500, 800, and 1300 against t=100, 200, and 300, respectively. Give 0.1 metres for both well radii, and save the output to disk. Call CGWellEq (Well equation) from the primary menu. Accept the values given as they will be the same as those you used in your simulation and press [F]. Give 30 minutes as the time for the calculation of drawdowns and 2000 cubic metres per day as the maximum discharge rate. The data will now be written to a file called WCHnnn.ASC, in the current data directory (directory CGXample, unless you have changed it).

Refer to the notes on 'Well characteristics files' for information on the structure of the file that you have created, and for more information about its name.

Figure 9 shows discharge rate plotted against drawdown, and Figure 10 shows discharge rate plotted against specific capacity; both being produced from the output produced by this exercise.
Figure 10. Discharge rate versus specific capacity


General tutorials

This section gives some example sessions on analysis of aquifer test data and well test data.

Please do not just follow these instructions to the letter, it is by experimentation that you will best learn the strengths, and the limitations, of the CG programs.


Tutorial G1: Analysis of a confined aquifer test

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This is an analysis of a set of simulated confined aquifer data. It is a simple analysis of theoretically near perfect data. While there is, therefore, a certain lack of realism, it is a good place to start.

If you have not already done so, start the CG programs by changing into the correct directory, typing 'CG', and pressing [Enter].

While still at the primary menu, select 'Change configuration' and then 'Units'. Make sure that the units are the consistent set based on metres and days. They should be: metres, days, m3/day, m2/day, and m/day, and there should be a statement to the effect that they are consistent. If not please change them until they are. Leave the 'Units' area, but do not leave the Configuration menu yet.

The file that contains the data for this tutorial is in the subdirectory 'CGXAMPLE'. Select 'Change Path' and, if necessary, change the path to 'CGXAMPLE'; this only involves typing in the word and pressing [Enter]. Once the path is set at CGXAMPLE and has been accepted, leave the 'Change path' area and also leave the 'Configuration' area.

From the primary menu select 'Aquifer test analysis'. You will be asked whether you want to load a file. If the file name given is 'CONF0030' then answer [Y] for yes, otherwise answer with [N] and then select CONF0030 from the list that you are shown.

Next you should choose a semilogarithmic graph. (This graph is chosen in this case because the later time data will always fall on a straight line on this type of graph, given a confined aquifer and a sufficiently long and steady discharge rate.) You will now be shown some information on the data file, unimportant in this case; pressing any key will get you to the main menu of this program (named CGAnal).

For the first step we will make an estimate of the transmissivity, so choose transmissivity from the menu. You will be asked to set a marker at the right end. This marker will indicate the last reading to consider in the analysis; you should, in this case, set it right at the end of the graph by pressing the right arrow several times, then press [Enter] to anchor it. Notice that while you are moving these markers you are given a display of the time of the reading concerned, the reading number, and the discharge rate at that time. (For this 'test' the discharge rate is constant.)

You will now be informed that the right marker is set and asked to set a marker at the left end. The program will calculate the transmissivity by measuring the slope of the straight line part of the graph (usually referred to as 'Delta s'), for more information on this, refer to the help system. Move the left marker to the beginning of the straight line section by pressing right arrow twice and left arrow three times; this will place the marker at 0.0194 days. Pressing [Enter] will cause the transmissivity to be calculated for this slope, the value given should be about 202 m2/day. Press any key until you are asked 'Another T', press [N] and you will get back to the main menu of CGAnal.

In the second part of this tutorial we will use Theisfit (adapted from a Fortran program written by Carl D. McElwee) to simultaneously calculate both transmissivity and storage coefficient for the whole of the curve. Select Theisfit from the menu, move the first marker to the right hand end, anchor it by pressing [Enter] and then anchor the second marker at the left end by pressing [Enter] again. Theisfit will calculate the transmissivity (200 m2/day) and storage coefficient (0.0001) in eight iterations. Pressing any key will display a graph with the calculated type-curve overlying the original data. The original data will be hidden because of the high quality of the fit.

Why did the first estimate of T come out at 202 instead of 200? Because the apparently straight line was not yet absolutely straight. Try another determination of transmissivity, but use later time data.

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Tutorial G2: Analysis of a leaky aquifer test

Includes: The units to be used for this example are metres and days. If necessary select these units by choosing 'Change configuration' from the primary menu and 'Change units'.

The example files are in subdirectory CGXAMPLE, select this also from the 'Change configuration' menu.

For this tutorial and the next the data are drawdowns measured in a piezometer. Unlike Tutorial G1, the data used here were obtained in the field.

Start by calling program CGAnal (Aquifer test analysis), load file WA66LB, and select semilogarithmic graphs.

The first parameter to evaluate is transmissivity, because it can be handled without knowledge of any other parameters. Transmissivity, when evaluated alone by CGAnal, is calculated from the steepness of the 'Delta s' slope and the recorded discharge rate. Use the arrow keys to highlight a section of the data on the straight line part of the graph. Press [Enter] after setting the first marker (the right hand, or upper time limit marker), and again after setting the second marker. Transmissivity is now calculated and displayed, it should be in the vicinity of 35 m2/day.

Now that we have a preliminary value for transmissivity we can get a value for storage coefficient. CGAnal calculates storage by solving the Theis equation (using Newton's method), this requires that the transmissivity be known. Select 'Storage' from the menu and place a marker at some point on the drawdown curve before leakage becomes significant, ie. before the line of plots begins to curve upward. The program gives you the option of accepting the previously calculated value for transmissivity, do so; then the value for storage coefficient is calculated and displayed; it should be close to 0.00027.

The Leakage procedure of CGAnal evaluates Leakage by solution of Hantush's variant of the Theis equation, using successive bisection. For this to be done we need both transmissivity and storage. This time select a point on the graph well after leakage effects have become obvious, you might even select the last point of the discharge test. After you accept the previously calculated values for T and S you should find that L is calculated to be about 580 m.

We now have preliminary estimates for T, S, and L; these should be refined by consulting Leakyfit (on the CGAnal main menu) so that all can be solved simultaneously.

Leakyfit will first ask you how many pointers you want, reply with 10. You now set the first pointer at the right hand (high time) end of the data that you want included in your analysis, in this case all the data. Leakyfit places the other nine pointers in provisional positions on the curve and you can either accept all of the provisional positions, or you can adjust or accept the positions one at a time. (You might experiment a little here, you can move the pointers over other pointers if you want. The aim of you adjusting the pointers individually is to allow you to avoid any time/drawdown/discharge rate points which appear doubtful.)

When all the pointers are in their places Leakyfit will ask for estimates of aquifer thickness (enter 5 m) and T, S, and L; you can use the previously calculated values. Leakyfit will now produce a refined value for all three parameters. (Note that T, S, and L are independent of the value that you entered for aquifer thickness, it is used only in the calculation of K'.) Leakyfit should give you values of about T=30, S=0.00033, and L=396.
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Tutorial G3: Producing and graphing a simulation

In Tutorial G2 we found the best leaky aquifer model we could achieve for the data of file WA66LB. But how good a fit is this really? What would a theoretical type curve based on T=30, S=0.00033, and L=396 look like when compared with our field data? This tutorial will show you how to produce a simulation based on the parameter values produced in Tutorial G2 and then compare the graphs of the two on your VDU screen.

The units should again be the consistent set based on the metre and the day.

Starting at the primary menu; call CGEdit. Load file WA66LB. Make a note of the value for R (45.6 m), this is, of course, the distance between the pumped well and the piezometer. Select 'Data entry/editing'. Note that the first non zero discharge rate is 772 m3/day. Scroll down through the data using [PgDn] and note that the discharge rate is constant. Finally, note that the last time is 6.0 days. We now have all the information we need to produce a simulation, so exit ([F10] and [A]) back to the primary menu.

To produce the simulation, call CGDD (Aquifer test simulation) from the primary menu. Specify a leaky aquifer, no boundaries, and a series of times. Give the distance as 45.6 m (from R, above), T as 30, and S as 0.00033 (from our analysis in Tutorial G2). The discharge rate was constant for the whole of the test, so we answer that there was 1 step. The discharge rate was 772 m3/day and the finishing time was 6 days (both from the data of WA66LB). Select 'Leakage coef' and enter 396 m.

Program CGDD now calculates a series of time/drawdown/discharge rate values for the simulated aquifer test, and then asks if these data are to be saved to a disk file; answer with [y] for yes and give the file name as 'TEMP'. (This file is unimportant and you will probably want to delete it later.) We now have our simulation.

To view the data of the simulation call CGEdit (Data entry and editing) from the primary menu. Answer the question 'Load file from disk' with [y], and also answer 'Load TEMP' with [y]. (You may notice that R(w.l.) is set at 0.1 m, although you did not specify this. This value was set by CGDD, it is not important because it is not used in analysis of aquifer test data.) Select 'Data entry/editing' and have a look at the data using the [PgDn] key. Go back to the main CGEdit menu by pressing [F10], and look at the notes file (View/Edit notes); you will see all the specifications that you gave when you created the simulation. Exit from 'View/Edit notes' by pressing [Esc], and go back to the primary menu by pressing [A].

The last step is to view a graph of both simulated and field data. Select program CGPlot (Data plotting) from the primary menu. Answer [n] to the question 'Load TEMP alone?'. Highlight the file names 'TEMP' and 'WA66LB' using the arrow keys and [Enter], then press [F10]. Request a screen graph, semilogarithmic. Answer 'Alter limits?' with [n] and 'Join points?' also with [n].

CGPlot gives now gives you the two curves on one graph. It is easy to see which data belongs to which curve because of the labels at the top left of the graph.


Tutorial G4: Multiple wells in a leaky artesian aquifer

Before running this tutorial run Tutorial G2, the leaky artesian aquifer analysis, described above.

The units to be used for this example are metres and days. If necessary select these units by choosing 'Change configuration' from the primary menu and 'Units'.

The example files which are used for this tutorial, together with the corresponding distances between discharging well and piezometers are:

WA645LBWA667LBWA66LB WA66NLBWA6WA5B
R values852m620m45.6m 384m599m
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Select program CGLeaky from the primary menu. Now use the Enter key and the arrow keys to tell the program that you want it to use data from the five files: WA645LB, WA667LB, WA66LB, WA66NLB, and WA6WA5B.

CGLeaky now selects and displays about 20 drawdown values for each file. (Some explanation of the method used is given in the program notes which can be reached through the help facility, look for 'CGLeaky data selection'.) Similarly to the Leakyfit analysis of CGAnal, you will be asked for the thickness of the aquitard (5 m) and initial estimates for T, S, and L. Give the T, S, and L values that you obtained from running the leaky artesian aquifer tutorial, above (approximately T=30, S=0.00033, L=396).

CGLeaky will now go through an iterative algorithm to refine the aquifer parameters, in this case only about 3 iterations will be required. The final values, calculated from all five data files, should be approximately T=28 m2/day, S=0.00036, and L=329 m.


Tutorial G5; DeGlee analysis

As for Tutorial G4, the units to be used for this example are metres and days. If necessary select these units by choosing 'Change configuration' from the primary menu and 'Units'.

When using the DeGlee analysis for your own data you can edit the example input file Waik6.gtd (it is in ASCII) and rename it. You must follow its format.
Choose DeGlee analysis from the primary menu. I suggest either reading the input data from Ctd files or from Gtd file. If the former then you go on to select the files that were used for Tutorial G4: WA645LB, WA667LB, WA66LB, WA66NLB, WA6WA5B; if the latter then you should select Waik6.gtd. Or you can enter data via the keyboard; if you choose this method example data will be provided.

As soon as you have pressed [F10] to indicate that you have finished selecting files the program will search through all the named files for the maximum drawdown and the distance from pumped well to each piezometer.

An explanation of the operation of the DeGlee analysis has been given above.
A modification to the CG Programs (2003/06/07) allows a data dump to a .csv file suitable for convenient importation into a spreadsheet. To dump, press S or L with the graph on the screen. The data will be written to a file named Deglee.csv.

The program now automatically adjusts the s offset and r offset to improve the fit and to minimise the root-mean-square (rms) error. You will find that a rms value of about 6.84 will result, together with T=33.8 m2/day, c=4211 days, and L=377 metres. You should now move the set of point plots with the arrow keys to reduce the rms error further, something like rms=5.81 should be achievable. At this point of best fit, the aquifer parameters will be approximately T=28.3, c=3946, and L=334.

Note that the T and L values are very similar to those obtained in Tutorial G4.


Tutorial G6: Slug test analysis

As with the previous tutorials, the units here are metres and days, and we are interested in aquifer values rather than well values.

Call CGAnal (aquifer test analysis) from the primary menu, and then load file BOUWERSL (Bouwer's slug test). This file contains example data as published by Bouwer (1978). See the references in the help section of the main programs.

More information on slug tests is also given in the help section.

CGAnal will ask you to specify a graph type, which type you choose is immaterial as it will be over-ridden for slug test analysis.

Now select 'Slug test' from the main menu. CGAnal gives you a graph of data from the file BOUWERSL, with linear times on the X scale and logarithmic residual drawdowns on the Y scale. You must now pick a point for use in the analysis, Bouwer states that it should be on the straight line section of the graph.

The slug test analysis now needs some data on the well. First, the effective radius of the discharge well (including any gravel pack or developed zone, 0.12 m), and the radius of the section of the well in which the water level is rising (0.076 m); both of these are contained in file 'BOUWERSL'. You must enter: The thickness of the unconfined aquifer (80 m in Bouwer's example), the depth of well penetration into the aquifer (5.5 m), and the length of the screened section of the well (4.56 m).

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CGAnal should now give you a value of around 32 m/day for hydraulic conductivity and a transmissivity of 2575 m2/day for transmissivity. Bouwer gives K=31 m/day.

Two other example files of slug test data are also included, 'PuttSlug' and 'TrebSlug', derived values for these tests are given in the '.CTN' notes files associated with the data files (you can view these from the main menu of CGEdit).


Tutorial G7: Step test analysis

This tutorial deals with data collected from a pumped well and evaluation of the coefficients of the well equation by program CGPAnal. The well equation, as the name implies, relates to the characteristics of the well rather than the aquifer. However, so long as the units used in this procedure are consistent, the transmissivity of the aquifer is evaluated, as that is important in predicting the behaviour of the well.

The units are days and metres.

Figure 11. Stepped test analysis
Call CGPAnal, 'Well test analysis' on the primary menu and then load file WOOL38B. Ask for the aquifer to be treated as confined and isotropic, and request a linear graph. Accept the preliminary analysis option, which will calculate the values, A=0.0126, B=0.00168, and C=2.50E-6 (C=0.00000250) (D is assumed to equal 2). Answer [Y] to 'Use preliminary analysis?'.

Now the measured data, together with the type curve based on the above values, will be displayed. Your aim is to obtain the closest possible match between the two curves. (Press [F1] at any time for a help page.)

I recommend the following procedure.
Start with adjusting the coefficient 'B' by pressing [2] and then using the up and down arrow keys. (You press [1] to adjust A, [2] for B, [3] for C, and [4] for D).

There are two options which you should try at some stage. Pressing [d] (lower case) will decrease the range of the graph and spread the recovery data over a wide area of the VDU screen. Go in the other direction by pressing [i]. (If you get lost, press [F1]; on exit from the help screen the graph will be refreshed.) Pressing [c] will allow you to change the magnitude of the adjustment that is made whenever you press the up or down arrows.

After you have obtained the best possible fit for B, adjust A (select by pressing [1]) until you have a fair fit for the first drawdown stage. Now adjust C until you have a reasonable fit for the third drawdown stage. You will need to alternate between these two steps until you obtain a good fit overall, but you will not find it difficult.

Press [F1] to check the values of all the coefficients. When you have obtained a good fit you should find values similar to: A=0.0116, B=0.0015, C=3.1e-6, and D=2. Transmissivity will be about 124 m2/day.

You will find that it is impossible to simultaneously obtain a good fit for all three drawdown stages so long as D=2. After having done the best you can you should adjust C and D until no further improvement can be obtained. (Some modification of A will also be required. You will also find it very helpful to modify the size of the adjustments by pressing [C].) This should get you to something like: A=0.0129, B=0.0015, C=1e-10, and D=3.4.

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Finally, pressing [W] will cause the program to compensate for the effects of well storage. You will find that this will considerably improve the fit, especially if you have adjusted A, B, C, and D to obtain the best fit for the data from later times.


Tutorial G8; Projecting drawdowns with the well equation

This tutorial must follow Tutorial G7 if it is to work as described. I will assume that you exited from CGPAnal with the coefficients: A=0.0129, B:=0.0015, C=9.7e-11, and D=3.4.

Call the Well Equation option from the primary menu and you will see that the values you finished with in CGPAnal are loaded into the well equation. You will be informed that for Q=1293 m3/day and t=0.125 days (the discharge rate and finishing time for the third drawdown step) the calculated drawdown is 18.61 m. (This is slightly different to the drawdown at the end of the third step because this latter calculation is for a constant rate rather than for three steps.)

You will now be able to very quickly calculate that, given this particular well equation, a discharge rate of 1000 m3/day for a duration of 1 day will give 14.44 m drawdown, while 1000 m3/day for one year will give 18.28 m drawdown.

Tutorial G8b: T from drawdown or recovery?

In Tutorial G8 transmissivity was derived from the recovery data, it is more usually derived from drawdown data. T derived in the latter way often is considerably lower than when derived from recovery. Here we will obtain a value for T from the data of the first drawdown step.

Example file WOOL38C has been produced from WOOL38B and simply by deleting everything after the first stage. Call aquifer test analysis (CGAnal) from the primary menu, load file WOOL38C, request a semilogarithmic graph, and select Transmissivity.

As described above, this method calculates T from a line of best fit through the 'straight line' section of the drawdown curve. The data of this stage has not settled down to a straight line, this is probably mainly due to well storage effects. We will avoid the worst affected part of the data by using the later part of the stage.

Move the first marker along to the right hand end of the data and press [Enter] to anchor it. Then move the second marker to 0.01111 days and press [Enter] again. The line of best fit will now be calculated from the selected data and transmissivity will be calculated from that. You should obtain T approximately equal to 114 m2/day.

The 114 obtained from drawdown here is close to the 124 obtained from recovery in Tutorial G8, but you will find that in many cases the difference is larger, although apparently always in the same direction.


Tutorial G9: Simulation of step test data

In this tutorial we will produce a file of simulated discharge test data based on the analysis of Tutorial G7.

The units must again be the set based on metres and days as the simulation is going to be based on an analysis in those units.

First we must obtain the information that we need for the analysis. We have the values for the coefficients of the well equation from Tutorial G7: A=0.0129, B=0.0015, C=1e-10, and D=3.4. The remainder can be obtained from a look at the WOOL38B data file as that is the data on which the analysis was done.

From the primary menu, check that the data subdirectory is still CGXAMPLE (Change configuration), then call CGEdit (Data entry and editing) and load file WOOL38B. Make a note of the two figures for R(aq.) and R(w.l) displayed on the main menu page of CGEdit, both of these are 0.148 m.
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Now select Data entry/editing and then use the [PgDn] key to find the discharge rate and finishing time for each step, don't forget that the recovery period is considered to be another step (the forth in this case). The finishing time and corresponding discharge rate will be found to be as below:
StepFinish (days)Discharge rate (m3/day)
Step 10.04167485 m3/day
Step 20.08333816
Step 30.1251293
Step 40.1460

This is all that is needed for the simulation, so return to the primary menu by pressing [F10] and [A].

Call program CGPDD (by selecting Well test simulation). Request an isotropic aquifer simulation (press [I]), confined (press [Y]es). Type in the above values for A, B, C, and D, as requested. Answer that there are 4 pumping steps and give the times and discharge rates as above. Reply with 0.148 for the two radius questions, and reply in the affirmative when asked whether well storage should be considered.

A series of time/drawdown/discharge test values will now be calculated and displayed. Some explanation of these is worthwhile.

Reply with [Y] to the question 'Save the data', and give the name 'TEMP'.

Finally, view a graph of both files TEMP and WOOL38B by using program CGPlot as explained in the last part of Tutorial G3, with the difference that a linear graph might be better for these data.


Tutorial G10: Step test analysis, feet and second units

This exercise is identical to Tutorial G7, except that different units are used.

From the primary menu select Change configuration, then change all the units until you have a consistent set based on feet and seconds. (At this stage the program will confirm that your units are consistent.)

Now follow the steps as above until it is time to enter the first approximations for the coefficients. This time you might enter A=20, B=10, C=50, and D=2. On adjustment of A, B, and C, you should find that the best fit is about A=35, B=12, and C=66 (assuming D is left at 2). Transmissivity will be about 0.016 ft2/sec.

This tutorial could be followed by a similar exercise to that of Tutorial G8.


Tutorial G11: Aquifer analysis on difficult data

The units used in this tutorial will be the set based on metres and days.

The example file is an extreme case of data not generally considered amenable to analysis for aquifer values, it consists of drawdowns (and some recoveries) recorded in a piezometer during a step test. Even worse, the first stage and a part of the second stage was missed because the contractor started earlier than I was expecting.

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This tutorial illustrates the use of the CG programs in analysis of aquifer test data having major variations in discharge rates.

Figure 12. Aquifer test analysis on step test data
Figure 12 shows the measured data (file WAFFLB) and a simulation based on the aquifer parameters derived from this analysis (file WAFFLBS1).

Select subdirectory CGXAMPLE, call CGAnal (Aquifer test analysis) from the primary menu and load file WAFFLB. Request a linear graph, the Automatic Generalised solution, a confined aquifer, and no boundaries. Reply that no values are known (this feature allows you to enter one value that you might feel you know in some cases, say transmissivity, and have the others evaluated by the computer) and request 20 pointers (the more pointers the slower the solution).

Now, as in Tutorial G2, you mark the data that you are interested in. First, move the single marker to the right side of the screen, using the right arrow key; then press [Enter]. Now you can accept all the provisional pointers, one by one, except for the one on the left side, at 60 minutes. This was not a measured drawdown, but is required to mark the beginning of the second drawdown step. Move this pointer to some other part of the graph.

When you have fixed the location of the last pointer you will be requested to enter your initial guesses for transmissivity and storage coefficient. Try 50 and 0.0003.

The solution will now run for a short time, depending on the speed of your computer and should then report final values of about T=100 and S=0.00044. On pressing a key the calculated points will be shown against your selected points and the other data points.

Next select the Manual Generalised solution, confined aquifer, no boundaries, and enter T=100 and S=0.00044 (or similar). You can then experiment with modifying these values and watch the effect on the type curve.

Further experiments could be carried out on file WAWIBOC which contains data from a pumped well, and WABBLB which contains data collected from a piezometer during an aquifer test.


Tutorial G12: Strip aquifer

The Theis solution is valid only for an aquifer which is isotropic and infinite in extent. Very often, especially in 'hard rock' areas, these conditions are not met, even approximately and for short periods of discharge. (I use the term 'hard rock' here to mean consolidated rock which is probably dipping at some significant angle, and may well contain fracture zones or intrusions having a marked effect on its hydraulic properties.)

Data file CLRPU1 contains time-drawdown data from a piezometer in an area of steeply dipping and deeply weathered hard rock. This piezometer was 72.6 metres from a well which pumped at a steady rate of 562 cubic metres per day for a period of 0.21181 days (5 hours, 5 minutes). Files CLRPU1S1 and CLRPU1S2 contain simulations based on two analyses if the data of CLRPU1.

Set the units to the metre-day consistent set and make the current data file subdirectory CGXAMPLE using option 'Change Configuration' from the primary menu.

As the first step it would be advisable to examine file CLRPU1 on several graphs to confirm that we are dealing with data from a strip aquifer. Call the graphing program, CGPlot, from the primary menu, load file CLRPU1 and plot it on a semilogarithmic graph on screen, leave the recovery data unchanged. There are two things to note on this graph: the data shows a continuous downward curve to the end of discharge, and there is no straight line section before the commencement of the downward curve. This very early onset of strip aquifer behaviour indicates that the width of the strip must be similar to, or smaller than, the distance from the piezometer to the pumped well. Ignore the plotted recovery data for the present.
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Now plot the same data on a square root of time graph. This time note that the plots fall along something close to a straight line, again indicative of a strip aquifer. Replot the file on a square root of time graph, but this time with the recovery data plotted as the square of root t minus root t'. You will observe that the recovery data now also fall close to a straight line, more evidence of a strip aquifer.

For the analysis call the aquifer analysis program from the primary menu and load the data file CLRPU1. When asked how to treat recovery data reply [N] for 'No change'. Request a semilogarithmic graph.

From the aquifer test analysis menu select Transmissivity and highlight the first five points, 0.00091 to 0.00903 days. The program calculates the Delta s slope of the best fit line through these points and then determines the transmissivity value from that, the result should be 4396 m2/day. (The transmissivity value will be highly dependent on the data chosen for calculation because of the downward curve, for example, using the first four points, 0.00091 to 0.00694 days would yield a transmissivity of 4898.)

Storage should be calculated next, select it from the menu. Transmissivity was calculated for the early time data so storage should be calculated for data in this vicinity too. Select the point corresponding to t=0.00903 days, give the T value calculated above, 4396, and storage should be calculated as 0.00137.

We now have first approximations of T and S, so we can move on to obtaining a figure for the width of the strip. Pick 'Automatic generalised' from the menu, define the aquifer type as Confined and Strip, reply that no values are known and request 15 pointers. Place the first pointer right over at the end of recovery, press [Enter] and then accept all the provisional pointer positions by pressing [Enter] another fifteen times (or hold the key down for a short time). Give the T and S values already obtained, and as your guess for strip aquifer width give 73m (about the distance from the piezometer to the pumped well). The program will now cogitate for some time and should produce parameter values of T=3967, S=0.00237, strip width=255, and a root-mean-square error value of 0.00267. (A model based on these values was used to produce simulation CLRPU1S1.)

Note here that different results will be obtained if you give different first guesses or you mark different points, eg. an alternative result is T=1160, S=0.00393, strip width=365, giving an rms error of 0.00244 (this model was used to produce example data file CLRPU1S2). It also should be mentioned that the drawdown curve for strip aquifer data is somewhat dependent on the location of both the pumped well and the piezometer within the strip. For simplicity, however, this analysis assumes that both wells are in the centre of the strip.

Finally, it is worth running the 'Manual generalised' solution to view the quality of the fit. Try it with both the above sets of values, one at a time. Press [F1] and check the root-mean-square error, this will differ from the rms error that resulted from the automatic fit because that used only 15 data points, the manual fit uses all the data. Try plotting the measured values and the two simulations on screen at the same time too.


Tutorial G13: Data entry

Typing data from a discharge test, whether aquifer or well test, into CGEdit is fairly straight forward, but there are some short-cuts that will take time to pick up if they are not explained. This tutorial is meant to help you to quickly learn how to enter your data efficiently.

The data that will be entered is a subset of those which makes up data file CLRPU1.

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It is best to use a consistent set of units for analysis, but perhaps the data, as received, are not in the units that we want for analysis, again, make CGEdit do the conversion. For this exercise set the time unit to minutes, the length unit to metres, and the flow rate unit to litres per second.

TimeWater levelsDischarge rateRemarks
min;secmetreslitres/sec.
07.0010
1;197.0036.5 Flow rate started at zero time. Water level was unchanged at 1 minute 19 secs.
4;137.011
77.017
137.027
197.034
26;207.043
37;207.053
477.060
567.067
727.076
867.086
1177.102
1627.121
2087.138
2657.158
3007.170
305The pump was switched off.
305.77.1710First recovery reading.
306.57.170
307;207.168 Water level responding to end of discharge.
308;267.166
3107.163
3147.157
3207.150
3307.141
3427.133
3587.122
3907.107
4207.097Last recovery reading

Note that the times in the list are a mixture of whole minutes, decimal minutes, and minutes and seconds (with a semicolon as a divider).

Call 'Data entry and editing' (CGEdit) from the primary menu and reply that you do not wish to load a data file.

From the CGEdit menu call 'Data entry/editing'. Reply that the data is from a piezometer, not a pumped well. The distance from the pumped well is 72.6 metres and the diameter of the well in the water level area may be entered as 0.075 metres.

After this entry you will be in the main data entry area, and in 'Add to end' mode (ie. the program will be expecting you to add data to the end of the incipient file).

Initial conditions

The first record must give the initial conditions, which simply means the 'drawdown' and discharge rate at time zero. For all of the discharge test data files initial discharge rate must be zero. It follows, then, that initial drawdown must logically be zero too, but for data entry it is often more convenient to enter water levels rather than drawdowns. All the water levels can be converted to drawdowns in one operation at a later time.

Enter the first time as 0, the first 'drawdown' as 7.001, and the first discharge rate as 0. As the second record, enter time as '1;19' (meaning 1 minute and 19 seconds, most characters will serve as the divider if you would prefer something other than a semicolon) and drawdown as 7.003. You will find that you are not asked for a discharge rate, it will be copied from the previous record. The reason for this will become clear later. You will also notice that the time entry has been converted to decimal minutes.

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Change discharge rate

As this is the first of a series of records to be entered for the discharge stage you must now exit from 'Add to end' mode and go into the 'Data entry/editing' mode so that you can change the discharge rate. Do this by pressing [Esc] while in the time field. In 'Data entry/editing' mode a menu will be displayed on the left half of the screen. The discharge rate of the second record must be changed, so move the cursor to that point on the screen using the arrow keys. Press [F3] to change the discharge rate figure, type in 6.5, and press [Enter].

Add data

Figure 13. The full data set
Go back to adding data to the end now by pressing [F4]. Type in the readings given above until you get to 305 minutes. No water level was recorded at 305 minutes but the program expects one, enter an estimate of 7.171 metres. All the data of the drawdown period have now been entered. Type in the first recovery reading, 305.7 minutes and the 'drawdown' of 7.171 metres. Press [Esc], change the discharge rate to 0 ([F3], [0], [Enter]), and press [F4] to get back into 'Add to end' mode.

Type in the remaining recovery values, press [Esc] to get back to 'Data entry/editing' and [F10] to go to the CGEdit main menu.

Save the data

Press [5] at the main menu. Type in a name for the file in which the data will be saved, you could use 'CLRPU1B'; do not add an extension part to the file name, the program will add the extension '.CTD'.

Check the data

Return to the primary menu and select Data plotting. Load your file, CLRPU1B, and plot it on a linear graph with points connected by a line. If you have entered your data correctly there will be a single line starting on the left margin of the graph and going most of the way to the right, the only inflection will be a rather sharp curve at just over 300 minutes, where the pump was stopped.

If you have made any typographic errors they will probably be fairly obvious. Make a note of them, go back to CGEdit and correct them. Figure 13 shows the whole of the data file (CLRPU1), your data should look similar.

Convert water levels to drawdowns

Go back to CGEdit, load data file CLRPU1B, and select Data entry/edit mode. Place the cursor on the first 'drawdown' value, 7.001 metres at time zero. To convert all the water level values to drawdowns the standing water level (7.001 metres) must be subtracted from them all. Press [F7] (add a constant), enter -7.001 as the constant, and press [Enter]. Now press [PgDn] until you have come to the end of the data.

Exit back to the main menu, press [5], and save the data. Use the same file name, CLRPU1B.

Change the units

If you have not done so, exit from CGEdit.

From the primary menu select Change configuration and then change the time unit to days and the discharge rate unit to cubic metres per day. You are now ready for analysis.

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Index

References

Clarke, D.K., 1987. Microcomputer Programs for Groundwater Studies. Elsevier Sci. Pub., Sara Burgerhartstraat 25, P.O. Box 211, 1000 AE Amsterdam, The Netherlands.

Clarke, D.K., 1988. Groundwater Discharge Tests: Simulation and Analysis. Elsevier Sci. Pub., Sara Burgerhartstraat 25, P.O. Box 211, 1000 AE Amsterdam, The Netherlands.

Cobb, P.M., Mc Elwee, C.D., and Butt, M.A., 1982. An Automated Numerical Evaluation of Leaky Aquifer Pumping Test Data: An Application of Sensitivity Analysis. Kansas Geo. Survey.

Hantush, M.S., and Jacob, C.E., 1955. Non-steady radial flow in an infinite leaky aquifer: Transactions of the American Geophysical Union, v. 36, pp. 95-100.

Kruseman G.P. and DeRidder N.A., 1983. Analysis and evaluation of Pumping Test Data. Bulletin 11, Internal Inst. for Land Reclamation and Improvement, Wageningen, The Netherlands.

McElwee, C.D., 1980. The Theis equation: evaluation, sensitivity to storage and transmissivity, and automated fit of pump test data. Kansas Geol. Syv., Uni. of Kansas, Lawrence, Kansas 66044, U.S.A.

Muskat, M., 1937. The Flow of Homogeneous Fluids through Porous Media. McGraw Hill Book Co., New York.

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. Trans. Am. Geophs. Un. 16:pp519-524.

Index

Home
On this page...
Analysis methods
Automatic generalised solution
Bounded aquifer
CG data files
Change discharge rate
Check your results
Conceptual models
Data file directory
DeGlee analysis
Educational tutorials
Entry of times
Evaluation of boundary distance
Evaluation of leakage coefficient
Evaluation of storage coefficient
Evaluation of strip aquifer width
Evaluation of the well equation
Evaluation of thickness of unconfined aquifer
Evaluation of transmissivity
General tutorials
Getting started
Help
How the CG programs work
Infinite isotropic aquifer
Initial conditions
Installation
Instructions
Introduction
Keeping track
Leakage units
Leaky aquifer
Leaky aquifer
Manual generalised solution
Menu hierachy
Notes files
Partially bounded aquifer
Producing files of simulated drawdown data
References
Slug test analysis
Strip aquifer
Strip aquifer
Top
Tutorial E1: Using various types of graphs
Tutorial E2: Discharge and recharge boundaries
Tutorial E3: Distance/time/drawdown graph
Tutorial E5: Modifying S, T, and L
Tutorial E6: Modifying boundary distance
Tutorial E7: Strip aquifer response
Tutorial E8: Producing a well characteristic file
Tutorial G10: Step test analysis, feet and second units
Tutorial G11: Aquifer analysis on difficult data
Tutorial G12: Strip aquifer
Tutorial G13: Data entry
Tutorial G1: Analysis of a confined aquifer test
Tutorial G2: Analysis of a leaky aquifer test
Tutorial G3: Producing a simulation
Tutorial G4: Multiple wells_leaky aquifer
Tutorial G5_DeGlee analysis
Tutorial G6: Slug test analysis
Tutorial G7: Step test analysis
Tutorial G8; Projecting drawdowns
Tutorial G8b: T from drawdown or recovery
Tutorial G9: Simulation of step test data
Tutorieal E4: Modifying S and T, effect on type curve
Units
Well characteristic files
Well storage effects
Where is it