Microcomputer Programs for Groundwater Studies

261 Pages·1987·3.343 MB·iii-v, I\261

by  David Clarke (Eds.)

MICROCOMPUTIR
PROGRAMS
fOR GRoUNDWAIIR
BIUDIIB
DAVID CLARKE
20 Musgrave Street, Crystal Brook, S.A. 5523(Australia)
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Appreciation
I must thank my former boss, Michael Cobb, for the encouragement that he
give me in developing the programs that preceded these.
Peter Pavy drew the line drawings that I found too difficult. His draw-
ings are the professional looking ones. Thankyou Peter.
Thanks are also due to my employer, The South Australian Department of
Mines and Energy, for putting in a position where the writing of the
me
program, and then the book, became the obvious course of action.
I'm grateful to Carl McElwee, M. Cobb, and Munir A. Butt of the Kansas
(USA) Geological Survey for the Fortran program on which is based the
solution of the Leaky Well function in this work.
Paul van der Heijde of the International Groundwater Modelling Center
(Indiana, USA) offered very welcome encouragement in the earlier stages of
the writing.
Collin Hazel of the Queensland (Aust.) Water Resources Commission
produced the description that allowed the writing of program for the Modified
Sternberg Analysis in this book.
More than any other, I thank my wife, Denece, a patient and under-
standing computer widow, for her encouragement and help.
Disclaimer
While the programs in this book are given in the belief that they will
give correct results if' they are used as instructed, no responsibility is
assumed by the author or publisher for any errors, mistakes, misrepresent-
or
ations that may occur from the use of these programs, and no compensation can
be given fbr any damages or whatever their cause.
losses
%
Introduction 1.1
Introduction
The primary aims of' this book are to provide a selection of subroutines
and programs with as wide and as basic as possible an application to ground
water science, and to explain their uperation. Readers familiar with micro
computer programming may apply the programs given here to their ownwork,
perhaps incorporating them as subroutines into larger, more specialized
programs; and those unfamiliar with programming can use the programs as they
are listed. The programs in this book are in no way a substitute for
knowledge and experience in groundwater science. The aim is more to make
complex procedures readily available to the practising hydrogeologist.
Several procedures that are described in this book are not confined to
groundwater in their application, but have been found to have a number of
uses in groundwater.
This is a practical book, written to solve real-life problems, overheads
have therefore been kept to a minimum. The derivation of equations and
functions are not described here, equations are taken from other sources and
used here. For those readers Who want to check on derivations, references
are given.
The first programs to be described are functions usable as subroutines
in practical applications. These are then used to solve typical groundwater
problems. More functions and procedures are introduced, and applied in
generally more involved groundwater situations as the reader progresses into
the book. Aprogram to produce a disk file from discharge test data, and to
analyse those data, is given later, as well as a program to graph the data.
An analytical model of changes in the piezometric surface due to a number of
discharging or recharging wells is included.
Most of the programs can be used with any set of consistent units.
Where units are specified, they are metric (normally metres and days are the
primary units used, although in order to follow common practice, minutes are
used in discharge test analysis).
The programs are designed to be run with little prior instruction.
Prompts given by the computer should give sufficient information about what
is required for the user to get right through a particular program with no
more than an occasional reference to the written instructions.
1. THE USE OF MICROCOMPUTERS IN GROUNDWATER SCIENCE.
Any complicated mathematical task not only can, but should be done by a
computer if one is available because of the fallibility of humans in solving
arithmetic operations. As well as almost never making arithmetical errors,
computers are much qUicker in any arithmetical operation. (Programmers do
make errors, as many as anyone else, but once the errors in a program have
been found and removed, they will not recur.) I believe that a complex
mathematical operation should be done manually only so that the person using
it can fully understand it. Thenceforth it should be computerised.
I.2 In~roduction
The computer is a tool which has recently become available for our use.
It should be used in any situation where it offers the best available method
of achieving the desired result.
2. APPLICATION OF NUMERICAL/ANALYTICAL METHODS TO GROUNDWATER
PROBLEMS.
Geology in general, and hydrogeology especially, often involves applying
numerical values to naturally occurring systems. ego An age to a rock form
ation, a transmissivity to an aquifer. While in physics quantities may be
known to high degrees of accuracy, hydrogeology uses approximations and
generalizations. It is often not possible, or even desirable, to be totally
accurate. ego The age of which part of the formation? - The transmissivity
of which part of the aquifer, and in which direction? Answers will be
required for these questions at times, but usually an approximate answer for
the whole unit is all that is needed.
The moment one applies a mathematical equation (ie. a model) to a ground
water problem, even if that equation is as simple a Darcy's law (Bouwer,
1978), some simplifying assumptions must be made. Some common assumptions
are;
1/ The porous medium is homogeneous.
2/ The piezometers used to monitor the system give values that are
representative of a significant cross-section of the system rather than of
just one point.
3/ Vertical flow within the aquifer is negligible.
4/ The aquifer is fully confined.
5/ The aquifer is of infinite extent.
In reality these assumptions are very often not justified.
If unjllstified simplifying assumptions are applied to a complex real
world situation in order to obtain information on that system, then it
foll~s that the information so obtained will at best be approximate. Only
in an ideal (and therefore nonexistent) groundwater system will our methods
of mathematical analysis give completely accurate answers.
Hydrogeology is not, cannot be, an exact science. The skill of the
competent and experienced hydrogeologist rests largely in his/her ability to
make meaningful generalizations and approximations, and in knowing how far
these can be pushed before errors become so great as to invalidate any
conclusions that he/she may make.
These arguments must be borne in mind in using the programs in this
book. There seems to be a tendency among some people to take any numbers
produced by a computer to be absolutely correct. There is a saying in
computer science; "rubbish in - rubbish out". Youcannot expect the output
of your computer to be better than it's input. In many cases errors in data
will be magnified, and results will be less accurate than input.
If all this sounds pessimistic and defeatist, then it is time for a note
of optimism. Very often the bulk properties of an aquifer can be
approximated by average figures in such a way as to produce a reasonable
simulation of the behaviour of that aquifer under given conditions of
Introduction 1.3
recharge or discharge. I've seen discharge test results from many wells that
indicated an aquifer that behaved very similarly to an ideal infinite,
confined, homogeneous, isotropic aquifer, at least for the duration of the
test.
In summary, I would like to make two suggestions.
1/ Don't expect five figure accuracy when using these programs to
evaluate some aquifer parameter, often one figure, or even order of magnitude
values may be both useful and the best that can be expected.
2/ Perhaps mathematical rigour should take second place to seat of
the pants empiricism at times?
3. THE BASIC COMPUTER LANGUAGE AS USED IN THIS BOOK.
Basic is universally used as the first language of microcomputers. It's
greatest advantages over other languages are it's capability to interact with
the programmer, and it's ease of debugging. It's greatest disadvantage is
it's lack of any enforced structure. Anystructure in a Basic program is
present due to a conscious effort from the programmer.
There are a number of versions of Basic that have been implemented in
modern microcomputers. In most cases they vary only in which key words are
recognised. The form of Basic used here will suit most micros other than the
cheap, games orientated machines. Most of these programs could be readily
rewritten to run on a more limited Basic, but it was thought likely that
readers interested in serious use of microcomputers would have access to
machines with a good version of Basic.
~. GETTING STARTED.
I will assume that you knowhow to setup your computer, this book is not
the place for that sort of instruction. Nor is this the place for detailed
instructions on the use of the Basic interpreter, you may find that you will
have to refer to your Basic manual, especially if you decide to type the
programs in from the listings in the book.
1/ Load your Basic interpreter. In most cases this will involve
making sure that you have a disk with Basic on it in the computer, and then
typing "Basic", or perhaps "Gwbasic", then pressing the enter key.
2/ If you have the programs on disk, put that disk in the computer
and type 'Load"filename'" (the double quotes are required) where filename is
the name as it appears in this book. Your computer may require either
'/bas', or '.bas' to be appended to filename, inside the quotes.
3/ If you want to type in the program, do so now, following the
directions in your Basic manual. Before switching off the computer, take
care to save the program to disk; or at least save Whatever part of the
program that you type in in one session.
~I Type the word "run", and press enter. Now the program will take
control.
51 If you are using an IBM or compatible, you can at any time
temporarily delay the program execution by holding down the 'Ctrl' key, and
at the same time pressing 'Num Lock'. Other computers may have other methods
1.4 Introduction
of achieving the same result. Pressing any key will then resume execution of
the program, and the display and printout should not be affected.
6/ Again, if you are using an IBM or compatible, if you want to
stop the program and return to the Basic command level at any time, hold down
'Ctrl' and press 'Break'. This allows you to interact with the computer at
any time in a program, perhaps to check the contents of variables. Typing
'cont' and pressing the Enter key will resume program execution, but in this
case the display will be affected.
7/ All the programs in this book are designed to terminate at the
end of their particular function, or when instructed to by the operator. At
that time you will be returned to the Basic command level.
5. THE PROGRAMS ON DISK.
To avoid the tedious job of typing the programs in from the listings,
you may purchase them on a thirteen centimetre double sided floppy disk for
(Australian) $100 from the author at Clarke Computer Services, 20 Musgrave
St., Crystal Brook, S.A., Australia, 5523. The disk is in a format
compatible with an IBM PC. The programs will run on many other computers,
and it may be possible to have the disk put into a format compatible with
your computer, especially if it is either a MS DOS machine, or a CP/M
machine, however, this will incur an additional cost.
The programs detailed in this book total some 10 000 lines of code or
more. I have no doubt that, even after many, many, hours of testing and
improving, there are still some bugs to be found, and many improvements that
could be made. Therefore I intend to make the latest versions of the
programs available on a second disk for a price around (Aust.) $25. (This
being for those who have purchased the original. Others could, of course,
have both for $125.) The prices are subject to change without notice, and do
not include postage and packing.
If any errors are found in any of the programs after the time that this
book goes to print, those errors will be corrected in the programs on disk,
and details given in a file named "READ.ME" on the disk.
The programs on the distribution disk are in ASCII format for greater
compatibility. This will cause them to be relatively slow to load. After
loading each program into Basic from the distribution disk, save it to
another disk in your own computers condensed form. (This is the default mode
that your computer will use unless instructed otherwise.) Do not use the
distribution disk for general work, after copying the programs from it onto
another disk, put it away in a safe place. The programs will load from your
copies more quickly than from the distribution disk; unless you make copies
using a Dos command rather than with Basic.
6. REFERENCE
Bouwer, H., (1978). Groundwater Hydrology. McGraw-Hill Kogakusha, Ltd. 480
pp.
Functions 1.1
Chapter 1
Over the last sixty years several functions have been developed that
have proved to have wide and fundamental importance in groundwater science.
Functions like the Gausian Error Function have been found to have more
limited use. Computer programs yielding solutions to some of these are
described in this chapter. Although these programs do not solve any
practical problems alone, later chapters will show that they can be put to
use in a number of field applications.
1. THE WELL FUNCTION
Theis (1935) adapted an equation from heat flow theory to describe the
lowering of the piezometric surface on pumping from a well fully penetrating
a confined aquifer. His equation (used in a form suitable for giving answers
in field applications in the next chapter) includes an integral with the
solution:
2 3
u u
W(u) = -0.577216 -In u + u +--- (1.1)
2 21 3 31
The variables W(u) and u will be defined in chapter 2.
It is quite possible to evaluate this equation by programming it
directly into a microcomputer, but there are several disadvantages. The
larger the value of u, the more terms must be included. With u greater than
about 10 to 15, (quite common in real cases, as the distance from the
discharging well to the point of observation becomes large) some of these
terms are very large although the well function itself is very small. This
is a classic case where round-off error due to addition or subtraction can
arise, (see Appendix II). Also, when more than a few of the terms must be
considered, the method becomes slow.
There is a better method. Huntoon (1980) described the use of two
polynomial approximations which gave values sufficiently close to be quite
acceptable for most, if not all, field applications.
for 0<=u<=1
W(u) -In u + Co (1.2)
and for 1<=u< infinity
W(u) (1.3)
u
u e
1.2 Functions
where
C =-0.57721566,
co = 0.99999193,
1
C =-0.24991055,
2
C = 0.05519968,
3
C =-0.00976004,
4
C = 0.00107857,
5
C 0.250621,
6
C 2.334733,
7
C 1.681534,
8
C 3.330657,
9
-7
and the error in (1.2) is less than plus or minus 2x10 ,and in (1.3) is
-5 u
less than plus or minus 5x10 I(ue).
1.1. Program WELLFUNC
WELLFUNC uses these approximations to solve the Well Equation. Several
techniques have been employed to improve speed in this program. While not
strictly required here (execution passes through the body of the program once
only) maximum speed will later be needed when this program is used as a
subroutine of more involved procedures, and is called many times during
program execution. Note in the program listing later in this chapter that
numerical constants are not used within the equations, the exponentiation
function has been avoided, and at the same time the number of multiplications
have been kept to a minimum. (See Appendix B for an explanation).
This is probably a good time to make a few comments on programming style
(See also Appendix C). It is not enough that a program should do the job it
is designed to do, it should also be as clear and as easily understandable as
possible. It should be' clear, not only so that people new to it can
understand it, but clarity makes it much easier for the author himself (or
herself) to come back at some later date and modify it. Aprogram is more
easily understood if it is structured. This program has ten distinct parts.
11 The program name (in line 1). Followed by the date of the last
modification.
21 An initialization section (lines 10 to 90), including a
preliminary print statement. In this case it tells people what the program
does, and gives them some indication that something is happening while the
computer is loading the variables. (The faster computers will not show any
significant delay.)
31 Program control (lines 200 to 280). This part could be thought
of as being in overall command of the program, it controls the sequence of
the major program operations by calling various subroutines with clearly
defined functions. Program flow should be relatively easily understood by
studying the control 'section.
41 The part of the program that actually does the work of coming up
with the answer (lines 2500 to 2550). In this case there is only one part to
it, in more complex programs this section will call other subroutines as well
Functions 1.3
as itself being larger. It is not at all uncommon for this, the heart of the
program, to make up a small part of the total. The other parts of the
program could perhaps be thought of as worker bees, and this the queen bee.
The rest of the program exists to prepare the data and environment for the
queen; it feeds the queen, and takes away the products of the queen.
5/ Input section (lines 7000 to 7020). Very simple in this case,
and could have been included in program control, but in other cases well
worth an extra subroutine.
6/ Video output section (lines 7250 to 7270). Again, very simple
in this case.
7/ A section to load the values into the variables (lines 8600 to
8650).
8/ An error message informing the user that he or she has made an
invalid entry (lines 9000 to 9020). In a larger program, this could be
called from a number of places.
9/ The end statement (line 9999). For the sake of consistency, and
understandability, it is worth having a single end statement, and at the end
of the main body of the program is the most logical location. It is probably
also a good idea to have only one return statement from a subroutine.
Generally both of these practices have been followed in this book.
Note that by keeping line numbers below 10000, five figure line numbers
are avoided, with consequently less typing in the debugging stage.
The operation of this program, as far as the user is concerned, is very
simple. When the program is run the uer will be asked to enter a value of
u. (It is usual practice to represent the function input as u, and output as
W(u)). After typing the number and pressing the <RETURN> key, (which is
alternately labelled ENTER, NEW LINE, or END LINE on various computers) the
value of the function will be given. The user may then enter another value
of u, or terminate the program.
The program has been checked against published tables of values for the
-15
well function for values of u raning from 10 up to nine. In all tests
the values given by the program agreed exactly with the published figures,
which were of three or four significant figures.
1.2. Program verification
Some values are given below so that users may check the operation of the
program.
u W(u)
1E-15 33.96
1E-10 <'2.45
1E-4 8.633
1E-2 4.038
0.1 1.823
1 0.2194
5 1.148E-3
9 1.245E-5