Hydraulic Parameter Identification: Generalized Interpretation Method for Single and Multiple Pumping Tests

370 Pages·1999·10.301 MB·English

by  Prof. Dr. Luc C. Lebbe (auth.)

Hydraulic Parameter Identification
Generalized Interpretation Method for Single and Multiple Pumping Tests
Springer
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Paris
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Luc C. Lebbe
Hydraulic Parameter
Identification
Generalized Interpretation Method
for Single and Multiple Pumping Tests
With 112 Figures and 34 Tables
, Springer
Author
Prof. Dr. Luc C. Lebbe
Research Associate
Fund ofSdentiflc Research-Flanders
University of Gent
Geological Institute
Krijgslaan 2.81 (58)
B'9000 Gent
Belgium
B·rnait: [email protected]
ISBN-13: 978'3.642.64264-7 Springer. Verlag Berlin Heidelberg New York
Library of Congress Cataloging-in-Publication Data
Lebbe. Lue. 19~0-
Hydraulic parameter identification: generalited interpretation method for single
and multiple pumping tests I Luc Lebbe.
p. em. Includes bibliograpbical references.
ISBN'13: 9'78-3-642-64264"7 e-ISBN"31 978-3-642-60"7-0
001: ,0,'007/978-3-642-60117-<)
I. Groundwater tlow--Mathem.tical moods. 1. Hydrog«llogy--M" hematical models. I. Tide.
TC176.L43 1999
55'·49'OI·~1111--dc21 99-191140
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Preface
This book is intended for all hydrogeologists or geohydrologists, environmental and
mining engineers who want to tackle a hydrogeological problem in general. The identifi
cation of the hydraulic parameters is a crucial step in any hydrogeological study and is the
fIrst aim of the book. This identifIcation process is demonstrated by using a unique and
generalized interpretation method for single and multiple pumping tests. The identified
parameters are the water conducting and water storing parameters of the groundwater
reservoir. Therefore, the work starts with an overview of the different ways to define and
determine these hydraulic parameters. The related parameters that are frequently used in
this work are also described. This part is followed by a review of the successive "classi
cal" analytical models that were developed to derive the frequently applied interpretation
methods. The most important drawbacks of these methods are their large variety, the
fragmented analyses of the observed drawdowns and the different derived values for one
identifIed hydraulic parameter. In this book a unique and generalized interpretation
method is presented which overcomes all these drawbacks.
This generalized interpretation method is obtained by a combination of a numerical
method and a non-linear analysis. The numerical model is an axi-symmetric two-dimen
sional model. This method is preferred because it requires much less computer time than
the three-dimensional model. This is an important characteristic because during sensitivity
analyses and the non-linear regression a large number of runs are made. The applied
numerical model also allows the drawdown simulation with similar accuracies at distances
close to the pumped well, in the order of centimeters, and at larger distances from the
pumped well, in the order of meters to hectometers. By the non-linear regression method
one set of optimal values for the hydraulic parameters is obtained along with the joint
confidence region and a set of corresponding residuals, i.e. the differences between the
logarithms of the observed and the calculated drawdowns. If the spatial and the temporal
trends of the residuals are suffIciently small the applied schematization of the flow can be
accepted and the optimal values of the parameters are then representative for the actual
physical parameters. The joint confIdence region gives us an insight of the reliability with
which the hydraulic parameters can be derived from the observed drawdowns. This region
and a number of statistical parameters that characterize this region allow the evaluation of
the degree of mutual dependency of the derived parameters or in other words to make a
collinear diagnostic. If the interdependency of a number of the required parameters is too
high then the generalized interpretation method can help to design an additional test. This
could result in the performance of a double or even a multiple pumping test. The general
ized interpretation method also allows the interpretation of a multiple pumping test.
The applicability of the axi-symmetric numerical model is augmented by the
possibility to simulate the drawdown in a laterally anisotropic aquifer. In addition the
drawdown in a pumped well can be calculated as the sum of the well loss and the aquifer
loss. With a supplementary computer program the drawdown due to a mUltiple well fIeld
can be calculated in a multilayered isotropic or anisotropic groundwater reservoir without
or with lateral constant hydraulic head and/or impervious boundaries, or with a vertical
plane of discontinuous lateral conductivity change. In all these cases the subsidence due to
VIII Preface
pumping can also be estimated assuming that the changes of the specific elastic storage,
the vertical and horizontal conductivity are constant in each layer during the compaction
process and are independent of the drawdown. The latter possibility allows the planning
of the development and the management of the groundwater resources.
This book can, however, also be considered as an introduction to inverse modeling
and its continuous interaction with the consecutive steps in hydrogeological investigations.
The design, the performance and the interpretation of a pumping test can be regarded as
an example of these consecutive steps. Pumping tests are simple and well-defined
hydrogeological studies that can be performed under favourable conditions. They are
simple because in most cases their lateral influence is rather limited so that the lateral
heterogeneity can be ignored. In hydrogeological studies on a larger scale this is not the
case so that the number of parameters can grow to an unacceptable large number. In the
pumping tests, the discharge rates are generally accurately measured. In hydrogeological
investigations on a larger scale and over a longer period the discharge rates of the
pumping wells and of the rivers are less well known. The installation of the pumping and
observation wells for a pumping test allows the collection of detailed information on the
lateral and layered heterogeneity of the groundwater reservoir which can be used during
the design of the test.
The effect of the layered heterogeneity on the water conducting properties of the
groundwater reservoir can be studied by the execution of multiple pumping tests. By the
design of these pumping tests one can create and observe large horizontal gradients in the
pervious layers to, deduce their horizontal conductivities and large vertical gradient over
semi-pervious layers to deduce their vertical conductivities. In hydrogeological studies on
the other hand, it is much more difficult to observe such large gradients. In most cases
the hydraulic gradients are smaller in regional groundwater flow problems. Here, the
location of the large gradients can be seasonally dependent.
It is easier to remedy some measurement errors during pumping tests then during
most of the hydrogeological studies on a larger scale. For example, the well storage can
be eliminated by the installation of packers above the pressure transducers. This is
necessary in wells with a rather large diameter, installed in rocks with a small permeabil
ity with a relatively fast growing drawdown. So, the interpretation of the pumping test is
an inverse problem of the first (simplest) type where the hydraulic parameters are the
only unknowns. Experiences with this simplest type of inverse modeling is preferred to
start with. These experiences can help to tackle more complicated inverse problems as for
example hydrogeological investigations on a large scale where sink and/or source term,
initial and/or boundary conditions must be identified besides a rather high number of
physical parameters.
Until now several FORTRAN programs are available on the world wide web.
They allow: the simulation of pumping tests without or with an artificial created error
(forward problem), the optimisation of a given number of hydraulic parameters (inverse
problem of first type), the information of the required input data and the creation of input
files needed in the forward and the inverse problem and the drawing of graphs with
results of the forward or the inverse problem. These programs are described in the book.
Although sufficient examples of simulations are given in the book, these programs allow
the reader to develop his/her own exercises, problems and pumping tests.
Preface IX
Acknowledgments
I would like to thank the Fund of Scientific Research - Flanders, under the auspices of
which the scientific work and the development of the computer programs were carried
out. I also 'wish to thank Prof. Dr. W. De Breuck for the opportunities he gave me to
design, to perform and to interpret a considerable amount of pumping tests at the
Laboratory of Applied Geology and Hydrogeology, Ghent University. Some of these
pumping tests are selected and represented in the last chapter. The double pumping test in
the quaternary sediments was performed in the framework of a hydrogeological study
which was financed by the Ministry of the Flemish Community and the Water Company
(T.M.V.W). The double pumping test in a laterally anisotropic aquifer formed by
fractured rocks of Palaeozoic and Mesozoic age (Sect. 7.2) was made with the financial
support of the Belgian Geological Survey. The triple pumping test in the layered ground
water reservoir (Sect. 7.3) on one of the campuses of Ghent University was made as part
of my research program. The single pumping test to determine the conductivity of the
tertiary, silty clay (Sect. 7.4) was made on order of SIDMAR, N.V. Finally, the artificial
recharge test in the natural bare dune valley (Sect. 7.5) was performed in collaboration
with the Intermunicipal Water Company of the Veurne Region (I.W.V.A.). I am greatly
indebted to all these organizations and companies.
I also thank the colleagues and students of the Laboratory of Applied Geology and
Hydrogeology, with whom I had numerous enlightened discussion about the design, the
performance and the interpretations of the pumping tests. The help of Ing. Eric Beeuw
saert and Ing. Jacques Vandenheede is also acknowledged for their work in performing
the pumping tests, for the development of a data logger and the numerous discussions that
lead to the installation of packers above the pressure transducers to eliminate the well
bore storage. I am also indebted to Freddy De Leeuw, Marleen Lacroix and Martine
Bogaert for the meticulous drawing of some of the figures. I thank Marisa Boesman who
helped me overcome my computer problems. Last, but not least I thank Drs. M.
Mahauden, Drs. Y. Vermoortel, Dr. I Gaus and Drs. N. Van Meir for the discussions
and correction of some parts of the work. Any comments anyone would care to make will
be received with great interest.
Computer codes
The executable codes are available on http://allserv.rug.ac.be/-luclebbe. The FORTRAN
codes were compiled by Lahey Fortran 90 v4.5 (Lahey Computer Syst., Inc). With the
exception of inrmp code the other codes can be subdivided in three groups. The inrmp
code allows to make the input files interactively for the forward and the inverse problems.
The first group of codes treat the forward problems. They allow the calculation and the
representation of the drawdown or the subsidence due to pumping on a single well or due
to pumping on a multiple well field: This group consists of the codes sipurS, outpuS,
sidap7 and multpl. They are described in Sect. 4.7 and further developments are given
in Chapter 5. The code sipurS simulates the drawdown of a pumping tests and compares
the calculated with the observed drawdown. The code sidap7 allows to make observed
drawdown files of hypothetical pumping test of which the drawdowns are simulated and
x Preface
whether or not increased with an artificial error. The code outpu5 plots the simulated
drawdown in time-drawdown and distance-drawdown graphs either with or without the
observed data. This last code allows also to plot the drawdown contour lines in a cross
section. With the code outpu5 the evolution of the subsidence can also be plotted in time
subsidence and distance-subsidence graphs and by means of subsidence contour lines in
cross sections (see Sect. 5.7). Additional input data to simulate the drawdown for
pumping test with variable discharge rates, in laterally anisotropic aquifers and in
pumping wells are described in respectively the Sects. 5.1, 5.2 and 5.3. With an
additional code multpl the drawdowns can be calculated due to a multiple well field. The
results can be plotted by the code mulpl2. With this code it is also possible to simulate
the drawdown in groundwater reservoirs with lateral bounds and with lateral discontinu
ous conductivity change. These possibilities are given in Sect. 5.6 and 5.7.
The second group of codes allows to run and control the inverse numerical model
for the interpretation of single and multiple pumping tests. These codes are described in
Sect. 6.6. The code inpur5 allows to run the successive iterations of the inverse model
for the interpretation of a pumping test. The code solpu5 is mostly used for the step by
step interpretation of a multiple pumping test. Based on residuals and sensitivities of
several pumping tests, which are joined in one data file, the adjustments of the considered
hydraulic parameters are calculated. The code etabdi plots the residuals versus their
probability along with the best fitted normal distribution. The codes plprcr, susqln,
susql3, sumsqr and sumsq2 plot two- or three-dimensional cross-sections through the
approximate or exact joint confidence region. The last group of codes allows the approxi
mation of the drawdown confidence intervals based on the optimal values and some
statistical parameters characterizing the joint confidence region. Four different computer
program packages are described in Sect. 6.7.3.
The author has written, researched and tested the source codes to ensure their
accuracy and effectiveness. Neither the author nor the publisher give any warranty of any
kind, expressed or implied, with regard to the performance of the codes. No warranties,
expressed or implied, are given by the author or the publisher that the codes are free of
errors, or are consistent with any particular standard of merchantability, or that they meet the
reader's requirements for any particular application. In no event shall the author or the
publisher be liable for incidental or consequential damages in connection with or use of the
codes. Support for the codes on the Internet is available in this book. All graphs are in HP
GU2 codes (trademark of Hewlett-Packard Company).
Although this book and its programs are copyrighted, the reader is authorized to make
one machine-readable copy of each program for personal use. Distribution of the machine
readable programs (either as copied by the reader or as available on the Internet) is not
authorized. Programs will only give meaningful results for reasonable problems. The
programs represent a basic and general model that can be modified for efficient application to
specific field problems. The user is cautioned that in some cases the accuracy and the
efficiency of the models can be affected significantly by the selection of values for certain
user-defined options, for example, the use of a large initial time and a reduced number of
rings per layer as demonstrated in Sect. 4.6.1. Another example is a too simplified
conceptualization of the flow as shown in Sect. 6.5.
Contents
Chapter 1 / Introduction .................................................................................... .
1.1 Previous literature on pumping test interpretation ............................................. .
1.2 Proposed generalized interpretation method ..................................................... 2
1. 3 Additional aims of the book ........................................................................ 5
1.4 Arrangement of subject matter............................... ...... ............................ .... 6
Chapter 2 / Hydraulic Parameters .............. ......................................................... 9
2.1 Hydraulic parameters describing water conducting properties ................................ 9
2.1.1 Darcy's law .............................................................................. 9
2.1.2 Hydraulic head and fresh water head................................................ 10
2.1.3 Intrinsic permeability................... ................................................ 12
2. 1.4 Heterogeneity and anisotropy of geological formations
with respect to hydraulic conductivity ...................................................... 13
2.1.4.1 Heterogeneity ............................................................... 13
2.1.4.2 Anisotropy....... ............................................................ 14
2.1.5 Generalized law of Darcy..................................................... ......... 19
2.1.6 Hydraulic conductivity ellipsoid...................................................... 21
2.1.7 Classification of layers according to their water conductive properties ....... 24
2.1.8 Hydraulic parameters derived from hydraulic conductivity ...................... 25
2.1.8.1 Transmissivity .............................................................. 25
2.1.8.2 Hydraulic resistance ....................... ................................ 26
2.1.8.3 Leakage factor.......... .................................................... 26
2.1. 9 Methods to derive the hydraulic conductivity ..................................... 27
2.1.9.1 Direct methods .................... ......................................... 27
2.1. 9.2 Indirect methods ............................................................ 30
2.2 Hydraulic parameters describing water storing properties ............... ..................... 36
2.2.1 Conservation of mass in a completely saturated volume of material
fixed in space ................................................................................... 36
2.2.2 Specific elastic storage................................................................. 39
2.2.2.1 Compressibility of water......................... ......................... 40
2.2.2.2 Effective stress concept .............................................. ..... 41
2.2.2.3 Compressibility of matrix ................................................. 42
2.2.2.4 Movement of solids in deforming medium............................ 43
2.2.3 Hydraulic parameters derived from specific elastic storage... .................. 44
2.2.3.1 Elastic storage coefficient... ............................................. 44
2.2.3.2 Diffusivity ................................................................... 45
2.2.4 Methods to derive specific elastic storage................................ .......... 45
2.2.4.1 Direct methods. ............................................................ 45
2.2.4.2 Indirect methods............................................................ 46
2.2.5 Storage coefficient near the water table... .............. ............................ 46
2.2.6 Hydraulic parameters derived from storage coefficient near watertable ....... 49
2.2.7 Methods to derive storage coefficient near water table ........................... 49
2.2.7.1 Determination by pF-curves .............................................. 49
2.2.7.2 Determination by pumping tests ......................................... 50
2.2.7.3 Determination by inverse models of unsteady state flow............ 51