Groundwater Engineering lecture Note

Gambella Unversity
College of Engineering & Technology
Department of Water Resources & Irrigation Engineering

Groundwater Engineering lecture Note

Compiled by Doup Rew

GMU Page 0
Groundwater Engineering Lecture Note

Contents
CHAPTER ONE ........................................................................................................................ 7

GROUNDWATER EXPLORATION ....................................................................................... 7

1.1 Introduction ...................................................................................................................... 7

1.2 Groundwater sources ....................................................................................................... 7

1.3 Groundwater distribution ................................................................................................. 7

1.4 Ground Water Investigations ........................................................................................... 8

1.4.1 Laboratory Investigations ......................................................................................... 8

1.4.2 Field Investigations ................................................................................................... 8

1.5 Methods of Groundwater Exploration ............................................................................. 9

1.5.1. Subsurface methods ................................................................................................. 9

1.5.2. Surface methods ....................................................................................................... 9

1.6 Summary ........................................................................................................................ 18

CHAPTER TWO ..................................................................................................................... 20

GROUNDWATER OCCURENCE ......................................................................................... 20

2.1 Historical Background ................................................................................................... 21

2.2 History of Groundwater use ........................................................................................... 22

2.3 Occurrence of Groundwater ........................................................................................... 22

2.3.1 Groundwater zone ................................................................................................... 25

2.3.2 Saturated Zone ........................................................................................................ 27

2.3.3 Aquifers and their characteristics............................................................................ 27

2.3.4 Determination of groundwater flow parameters ..................................................... 29

CHAPTER THREE ................................................................................................................. 48

GROUNDWATER MOVEMENT .......................................................................................... 48

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3.1 Darcy’s law and groundwater movement ...................................................................... 49

3.2 Mathematical equation for groundwater flow problems ................................................ 52

3.2.1 Groundwater flow in confined aquifer between two water bodies: ........................ 55

3.2.2 Groundwater flow in an unconfined aquifer ........................................................... 57

3.3 Regional and local groundwater flow ............................................................................ 64

3.3.1 Elementary flow system .......................................................................................... 64

3.3.2 Regional flow system .............................................................................................. 66

3.3.3 Regional Groundwater Flow Analysis .................................................................... 68

3.3.4 Local Groundwater Flow ........................................................................................ 75

3.4 One, two and three-dimensional flow in different aquifers ........................................... 76

CHAPTER FOUR .................................................................................................................... 78

HYDRAULICS OF WELLS ................................................................................................... 78

4.1 General ........................................................................................................................... 78

4.2 Steady and unsteady states of flow in different aquifers ............................................... 79

4.3 Partially penetrating wells and multiple well systems ................................................... 92

4.4 Pumping data test, analysis and interpretation ............................................................... 93

4.5 Design of tube well (deep well) ..................................................................................... 94

4.6 Well construction methods ............................................................................................ 95

4.6.1 Boring Method ........................................................................................................ 95

4.6.2 Driving Method ....................................................................................................... 95

4.5.3 Jetting method ......................................................................................................... 96

4.6.3 Well construction based on drilling equipment ...................................................... 98

4.6.4 Cable Tool Drilling Method (percussion) ............................................................... 98

4.6.5 Hydraulic Rotary (or Rotary Direct Circulation) Drilling Method ....................... 101

4.6.6 Reverse Circulation Rotary Drilling method ........................................................ 103

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4.6.7. Down-hole Hammer Drilling method .................................................................. 105

4.7 Drilling of fluid ............................................................................................................ 109

4.7.1 Water base mud..................................................................................................... 109

4.7.2 Oil Base mud......................................................................................................... 110

4.7.3 Low solid Mud ...................................................................................................... 110

4.7.4 Air, Gas or Mist Flush system .............................................................................. 110

4.7.5 Low velocity Foam system ................................................................................... 111

4.7.6 Drilling Fluid requirements................................................................................... 111

4.7.7 Drilling Fluid Control program ............................................................................. 112

4.8 Screened casing and gravel wells ................................................................................ 112

4.9 Well development, maintenance, well failures and rehabilitation ............................... 115

4.9.1 Water Well Development ..................................................................................... 117

4.9.2 Methods of well development ............................................................................... 118

4.9.3 Well Testing for performance ............................................................................... 120

4.10 Measurement of groundwater level ........................................................................... 121

4.11 Groundwater balance and groundwater management ................................................ 123

4.11.1 Groundwater balance .......................................................................................... 123

4.11.2 Groundwater Resources Management ................................................................ 127

4.12 The rate of aquifer exploitation.................................................................................. 128

CHAPTER FIVE ................................................................................................................... 133

Groundwater Recharge .......................................................................................................... 133

5.1 Introduction .................................................................................................................. 133

5.2 Types of Groundwater recharge................................................................................... 133

5.3 Factors Affecting Recharge ......................................................................................... 136

5.4 Artificial Recharge Methods ........................................................................................ 137

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CHAPTER SIX ...................................................................................................................... 140

GROUNDWATER POLLUTION & REMEDIATIONS ...................................................... 140

6.1 Introductions ................................................................................................................ 140

6.2 Conjunctive use of groundwater and surface water ..................................................... 140

6.3 Importance of Groundwater ......................................................................................... 144

6.4 Major Sources of Groundwater Contamination ........................................................... 145

6.4.1 Agricultural Chemicals ......................................................................................... 145

6.4.2 Septic Waste.......................................................................................................... 145

6.4.3 Landfills ................................................................................................................ 145

6.4.5 Hazardous Waste Sites.......................................................................................... 146

6.4.6 Storage Tanks........................................................................................................ 146

6.4.7 Atmospheric Pollutants ......................................................................................... 146

6.4.8 Underground Pipes................................................................................................ 146

6.4.9 Road Salts ............................................................................................................. 147

6.5 Effects of Contaminated Groundwater ........................................................................ 147

6.6 Groundwater remediation ............................................................................................. 147

6.6.1 Introductions .............................................................................................................. 147

6.6.2 Physical remedy of Groundwater.......................................................................... 147

6.6.2 Air sparging or oil vapor extraction (SVE) ........................................................... 149

6.6.3 Dual phase vacuum extractions ............................................................................... 150

6.6.4 Chemicals treatment technologies ........................................................................ 151

6.6.5 Biological treatment technologies......................................................................... 154

6.6.6 Phyto-treatment ..................................................................................................... 157

CHAPTER SEVEN ............................................................................................................... 159

INTRODUCTION TO GROUNDWATER MODELING .................................................... 159

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7.1. Introduction ................................................................................................................. 159

7.2. Modeling Approach .................................................................................................... 160

7.3. Concept of Groundwater modeling ............................................................................. 161

7.3.1 Conceptual Model ..................................................................................................... 161

7.4 Types of Models .......................................................................................................... 166

7.5. Modeling Solutions ..................................................................................................... 167

7.5.1. Analytical Solutions ............................................................................................. 167

7.5.2. Numerical Solutions............................................................................................. 167

7.6 Groundwater modeling methods .................................................................................. 168

7.6.1 Finite difference method ....................................................................................... 168

7.6.2. Finite Element Method ........................................................................................ 171

7.7. Model Calibration ....................................................................................................... 174

7.8. Model Verification and Validation ............................................................................. 175

7.9. Sensitivity Analysis .................................................................................................... 175

7.10. Uncertainty Analysis ................................................................................................. 176

7.9 Common Mistakes in Modeling................................................................................... 176

7.10.1 Applications of mathematical models in groundwater flow problems ............... 177

7.10.2 Multiple scales in modeling groundwater systems ............................................. 180

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Course Objectives: This course is considered to aware students about the groundwater
resource and fundamental science of hydrogeology. In this course the distribution and
movement of water through geologic formations, i.e. soil, sediments, and rocks should
have to be addressed and covered very well. Mathematical models of fluid flow in porous
media and methods for solving these equations (e.g analytical, numerical, and statistical
approaches), addressing practical groundwater engineering problems (laboratory and
field determination of hydraulic parameters, characterizing the subsurface using aquifer
tests, transport and remediation of contaminants, and innovations in groundwater
management, and modeling) are the core of this course.
Learning outcomes: After successful studying of the course, students will be able to;

 Identify the properties of artesian wells and describe the conditions under which
they form;
 list and describe the properties of aquifers that control the movement and storage
of groundwater;
 Use Darcy's Law to explain the roles of aquifer properties and driving forces in
governing the rate of groundwater flow;
 Apply the concept of hydraulic head to draw flow lines on maps and cross
sections;
 Conduct experiments on pumping test for drawdown computations.

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CHAPTER ONE
GROUNDWATER EXPLORATION
1.1 Introduction
Groundwater is an invisible natural resource available in different proportions of various
rock types at various depths under the surface layer of the earth. In the historical past,
when there is no visible flow of water along the rivers, people used to dig small pits, in the
river alluvium, wait and collect the groundwater coming through seepage and use it for
their drinking purposes and for meeting the domestic needs. Similarly, the people of
mountainous regions, natural springs provided the sources of water supply. Springs are the
outcome of seepage from any groundwater system in hilly terrains or in limestone regions.
More than 60 percent of the global population thrives by using only the groundwater
resources. The groundwater which existed at shallow depths in the open wells has gone
deep due to over-exploitation. Exploring these water sources become a challenging task to
geo-scientists.
1.2 Groundwater sources
Groundwater is a renewable source of water, which gets replenished after the heavy
rainfall called as rainfall recharge. The level of water seen in an open well denotes the
uppermost surface of the zone of saturation of the porous media called as the water table.
After every recharge, the water table raises, denoting that the porous media has saturated
more with water. When we pump out water, the water level goes down. Continuous
pumping of water beyond the recharge will make the wells go dry and force to deepen the
well. The search of groundwater got increased, due to the non-availability of sources and
due to the declining water tables.
1.3 Groundwater distribution
Groundwater is not uniformly distributed everywhere. The occurrence of groundwater
varies from formation to formation. In a typical crystalline hard rock terrain, the
quantitative occurrence of groundwater depends on the weathered and fractured zones.
The occurrence of groundwater in a sedimentary terrain will be more promising.
Groundwater prospecting is a very thought provoking scientific exercise in most of the
places. There is a need to understand the methods of groundwater exploration, as it is a

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practical decision-making approach. This module highlights some of the general methods
of groundwater exploration.
1.4 Ground Water Investigations
The main aim of groundwater investigations are;
 Location of recharge, storage and discharge zones of ground water
 Understanding of the functioning ground water regime with respect to
environment.
 The lateral and vertical extent of aquifer system, like its storage and transmission
properties and also the chemistry of waters.
Thus, the studies also include determination of hydraulic boundary conditions the
direction of groundwater movement, input, output and determination of functional
response of the system to physical and chemical changes. The data obtained after detail
studies of these aspects help in:
 Understanding the occurrence and availability of groundwater,
 Selecting methods to be adopted in exploitation of groundwater, and
 Deciding management policies and effective conservation of groundwater
resources.
From the foregoing description it is clear that, the characteristics of ground water regime
are the function of complex physical framework governed by several factors and their
components. Since these factors vary spatially within short distances and also with respect
to time, an ideal ground water regime having uniform and isotropic characteristics seldom
occurs in nature.
1.4.1 Laboratory Investigations
The laboratory investigations include:
 Review of literature pertaining to drainage basin under study,
 Qualitative and quantitative interpretation of data with the help of topo-sheets and
aerial photographs, and preparation of a photo-hydrogeological map.
1.4.2 Field Investigations
Field investigations include verification of interpretation as well as information obtained
in laboratory by taking appropriate field traverses aid tentatively dividing the drainage
basin area into potential, moderately potential and non-potential categories.

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1.5 Methods of Groundwater Exploration
Groundwater exploration is a typical task of a hydro geologist or an engineer to identify
the location and its availability under the ground. Groundwater Exploration is attempted
through either by direct or indirect methods. Test drilling is the direct approach to find out
the resource. This is an expensive affair. Every individual cannot go for test drilling.
During the last two centuries, more techniques have been developed to explore the
groundwater. They are classified into surface and sub-surface methods.
1.5.1. Subsurface methods
The subsurface methods of groundwater exploration include both Test Drilling &
Borehole Geophysical Logging techniques. When compared to the surface methods, the
subsurface methods are very expensive. These are done for government level projects
where large scale investigations are carried out to ascertain the results of surface surveys.
The subsurface methods are very accurate methods as it provide the direct observations of
features in the form of bore-hole lithology as core samples and also geophysical
measurements of formation properties.
1.5.2. Surface methods
The surface methods are easy to operate and implement with minimum required facilities
like topo-sheets, maps, reports, some field measurements and interpretations of data in the
laboratories. The surface methods of groundwater exploration include the following:
1. Esoteric Methods
2. Geomorphologic methods
3. Geological Methods
4. Structural Methods
5. Soil and Micro-Biological Methods
6. Remote Sensing Techniques
7. Surface Geophysical Methods
1. Esoteric methods
These are the oldest water divining methods practiced by ancient people for several
centuries. They are also called as water-dowsing. People believed that the flow of
groundwater can induce some vital currents above the surface. When a wet plant twig is
moved above such zones, it tends to rotate the twig as well. Wet twigs of trees, husk-

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removed coconuts, watches and other materials have been used as dowsing materials. The
person handling the twig has some role of induction and hence it is not applicable to
everybody attempting to divine water. All these methods have been practiced since 17th
century. There is no scientific explanation available with reference to these approaches.
Probability of success is a mere coin-tossing experiment. These methods are called as
water divining.
# Water Witching
Water witching is a traditional method adopted by people to detect bore-well locations.
Using a forked stick to locate water source is known as water witching. Although this
method is lacking any scientific justification for the method, water witches diligently
practice the art wherever people can be persuaded of its potential value. Commonly, the
method consists of holding a forked stick in both hands and walking over the local area
until the butt end is attracted downward-ostensibly by subsurface water. It is amazing that
the idea of supernatural powers has such a continued fascination for people to use despite
its limitations.
2. Geomorphological Methods
Surface drainage is the subdued replica of topography controlled by the basement rocks.
Mostly, groundwater flow coincides with the surface drainages. The streams and water
courses may also be controlled by some underlying structures. Junctions of streams at the
down slopes are promising zones for groundwater. Landforms originate due to several
geological processes. Some of them are likely to contain relatively permeable strata.
River-borne modern alluvial terraces, floodplains, stratified valley-fill deposits in
abandoned channels, glacial outwash and moraine deposits are good landforms for
groundwater. Alluvial fans, beach ridges, partly drift-filled valleys, sand dunes, moist
depressions, and marshy environments are good localities.
i. Study of Land forms
Landforms are the likely indicators to show the relatively permeable strata. The locations
of modern alluvial terraces and floodplains, stratified valley-fill deposits, glacial outwash
plains, glacial deltas, kames, moraine complexes, eskers, alluvial fans and beach ridges are
good locations for groundwater occurrence. Partly drift-filled valleys marked by a chain of
elongate closed depressions, largely masked bedrock valleys cutting across modern

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valleys that are indicated by local non-slumping of weak shale strata in valley sides, sand
dunes assumed to overlie sandy glacio-fluvial sediments, nearby locations of lakes and
streams are very good indicators for groundwater prospecting.
ii. Topography and Drainage
Physiographic methods analyze the surface topography and drainages. The locations of
confluence and junctions of surface streams at the downstream points of small watersheds
are good locations for groundwater for confluence. Hydraulic gradients of groundwater
systems will always follow the topographic gradients and slopes. Such locations are also
suitable for water collection and storage for recharge.
iii. Drainage density of stream network
Drainage density is the ratio between the total length of all streams and the area of
watershed or river basin. The resultant drainage density is used to indicate the potentiality
of groundwater. If the drainage density is low, groundwater potentiality will be more. If it
is high, due to more streams, runoff will be more.
3. Geological Methods
Geological investigation begins with the collection, analysis, and hydrogeological
interpretation of existing topographic maps, aerial photographs, geologic maps and logs,
and other pertinent records. This should be supplemented, when possible by geologic field
reconnaissance and by evaluation of available hydrologic data on stream flow and springs,
well yields, groundwater recharge, discharge, and water quality levels. In some places, the
drainages may be fully controlled by the presence of minor and major structures like
joints, faults and lineaments. Such zones are good and potential zones for groundwater
exploration. These are the conduits for groundwater flow.
4. Structural methods
Contact points between permeable water-bearing strata overlying relatively impermeable
strata-usually along the sides of valleys that cut across the interface between different
strata are suitable locations for groundwater. Springs occurring on or near the base of
hillsides, valley slopes, and local scarps are indicators of groundwater occurrence over
hilly terrain. Dykes are good barriers for arresting the flow of groundwater. Location of
dykes and analyzing their dip and strike help in selecting the groundwater potential zones
in the upstream side.

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i. Well-inventory
Well-inventory is a method of analyzing the well-cuttings and inner surfaces of open dug
wells to know about the subsurface geology, structures, seepage zones, and fluctuations of
water levels, rate of recovery after pumping and the geo-environmental setting of the wells
in a region. This method helps to analyze the data collected from more number of the
wells of a region and come to a conclusion about the regional groundwater potential. The
groundwater flow paths could be easily identified through well-inventory. Promising
zones could be identified for further investigations though this method.
5. Soil and Micro-Biological Methods
Geo-botanical indicators are valuable tools in groundwater exploration. The anomalous
growth of vegetation and alignment of big trees on a straight line, growth of termite
mounds and location of age old, deep rooted heritage trees can indicate the presence of
groundwater at shallow depths. Presence of Halophytes, plants with a high tolerance for
soluble salts, and white efflorescence of salt at ground surface, indicates the presence of
shallow brackish or saline groundwater. Xerophytes, the well-known desert plants,
subsisting on minimal water, suggest a considerable depth to the water table. All these are
supplementary tools in detecting the locations of groundwater zones.
i. Moist depressions and seepages
Moist depressions, marshy environments, and seepages, string of alkali flats or lakes
(playas) along inactive drainage systems, salt precipitates (e.g., salt crusts), localized
anomalous-looking "burn out" patches in the soil, and vegetation associated with salt
migration and accumulation are good indicators for groundwater availability. Depression
springs, where land surface locally cuts the water table or the upper surface of the zone of
saturation, Contact springs containing a permeable water-bearing strata overlying at
impermeable strata-usually along the sides of valleys that cut across the interface between
different strata are good locations. The presence of artesian springs occurring on
undulating upland till plains, and artesian springs occurring on or near the base of
hillsides, valley slopes, and local scarps are very good indicators.
6. Geophysical methods
Exploring the ground water by geophysical method is termed Ground water geophysics.
Geophysical investigations are conducted on the surface of the earth to explore the ground

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water resources by observing some physical parameters like density, velocity,
conductivity, and resistivity, magnetic, electromagnetic & radioactive phenomena.
Geophysical methods comprise of measurement of signals from natural or induced
phenomena of physical properties of sub surface formation. Geophysical methods detect
the differences, or anomalies of physical properties within the earth's crust. Density,
magnetism, elasticity, and electrical resistivity are properties that are most commonly
measured. The purpose of exploration is to detect the indirect indicators and locate the
potential zones for exploitation. The main geophysical methods which are useful in
solving some of the problems of hydrogeology are the Gravity, Magnetic methods,
Electrical, and Seismic.
i. Gravity Method
The gravity method is a widely used geophysical method for finding out mineral resources
and groundwater in sedimentary terrain. Gravimeters are used in this method to measure
the differences in density on the earth's surface that may indicate the underlying geologic
structures. Because the method is expensive and because differences in water content in
subsurface strata seldom involve measurable differences in specific gravity at the surface,
the gravity method has little application to groundwater prospecting. Under special
geologic conditions, such as a large buried valley, the gross configuration of an aquifer
can be detected from gravity variations.
ii. Magnetic Method
The magnetic method enables detecting the magnetic fields of the earth which can be
measured and mapped. Magnetometers are the equipment used to measure the magnetic
fields and variations. Because magnetic contrasts are seldom associated with groundwater
occurrence, the method has little relevance for exploring groundwater.
Indirect information pertinent to the groundwater studies, such as the presence of dikes
that form aquifer boundaries or limits of a basaltic flow, could be obtained with this
method.
iii. Seismic Method
Seismic methods are of two kinds as seismic refraction and reflection methods. The
seismic refraction method involves the creation of a small shock at the earth's surface
either by the impact of a heavy instrument or by a small explosive charge and measuring

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the time required for the resulting sound, or shock, wave to travel known distances.
Seismic waves follow the same laws of propagation as light rays and may be reflected or
refracted at any interface where a velocity change occurs. Seismic reflection methods
provide information on geologic structure thousands of meters below the surface, whereas
seismic refraction methods-of interest in groundwater studies-go only about 100 meters
deep. The travel time of a seismic wave depends on the media through which it is passing
through. The velocities are greatest in solid igneous rocks and least in unconsolidated
materials. Based on these indications, it is possible to delineate the subsurface zones of
fractures, fissures, faults and lineaments.
iv. Electrical resistivity method
The purpose of electrical surveys is to determine the subsurface resistivity distribution by
making measurements on the ground surface. From these measurements, the true
resistivity of the subsurface can be estimated. The ground resistivity is related to various
geological parameters such as the mineral and fluid content, porosity and degree of water
saturation in the rock. Electrical resistivity surveys have been used for many decades in
hydrogeological, mining and geotechnical investigations. More recently, it has been used
for environmental surveys. Each electrical property is the basis for a geophysical method.
The resistivity measurements are normally made by injecting current into the ground
through two current electrodes and measuring the resulting voltage difference at two
potential electrodes (P1 and P2). From the current (I) and voltage (V) values, an apparent
resistivity (pa) value is calculated, using pa = k V / I, where k is the geometric factor
which depends on the arrangement of the four electrodes. The electrode arrangement in
these investigations is called as arrays. Some of the most common electrode arrays are
Wenner, Schlumberger, pole-pole, and pole-dipole and dipole-dipole array.
The resistivity values of common rocks and soil materials are given in this table.
RESISTIVITY (Ω –m) AQUIFER CHARACTERISTICS
< 20 chloride ion concentration of 250ppm in a fine sand & Limestone
50– 70 Porosity is the principal determinant of resistivity
20– 30 Pore fluid conductivity affected by both water quality and lithology
30– 70 Affected by both water quality and lithology

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< 10 Delineate sediments enriched with salt water
<1 Clay / sand saturated with salt water
15– 600 Sand and Gravel saturated with fresh water
<5 Saltwater or Clay with saltwater
< 10 Brackish aquifer
10– 20 Moderately fresh
20–160 Freshwater
0.2 – 0.8 Clay
0.6–5 Dry sand contaminated
0.3 – 0.8 Brine bearing sand
3–6 Red clay
< 19 Clay / clay mixed with kankar
64– 81 Weathered sandstone
57– 111 Weathered granite and other crystalline rocks
< 10 Saline coastal zone sand (Sedimentary)
10– 20 Clay with or without diffused water
20– 60 Freshwater zone
Crystalline rocks: Granite and other igneous rocks and crystalline schist of
200-10000 normal physical character, compact sand stones, quartzite, marbles
100-1000 Consolidated sedimentary rocks: Slates, shale, sand stone, limestone
Unconsolidated sedimentary rocks: Marls, clays, sands, alluvium and
0.5-100 surface soils
4-800 Oil bearing sands:
Igneous and metamorphic rocks typically have high resistivity values. The resistivity of
these rocks is greatly dependent on the degree of fracturing, and the percentage of the
fractures filled with ground water. Sedimentary rocks, which usually are more porous and
have higher water content, normally have lower resistivity values. Wet soils and fresh
ground water have even lower resistivity values. Clayey soil normally has a lower
resistivity value than sandy soil. However, note the overlap in the resistivity values of the
different classes of rocks and soils. This is because the resistivity of a particular rock or

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soil sample depends on a number of factors such as the porosity, the degree of water
saturation and the concentration of dissolved salts.
v. Electromagnetic Method
The term electromagnetism is defined as the production of a magnetic field by current
flowing in a conductor. The magnetic field will be concentrated in the core. This
arrangement is called a solenoid. The more turns we wrap on this core, the stronger the
electromagnet and the stronger the magnetic lines of force become. The magnetic field
that surrounds a current-carrying conductor is made up of concentric lines of force. The
strength of these circular lines of force gets progressively smaller the further away from
the conductor. If a stronger current is made to flow through the conductor, the magnetic
lines of force become stronger. The strength of the magnetic field is directly proportional
to the current that flows through the conductor. There are two methods as Passive and
Active methods. The Passive method uses the natural ground signals (e.g.,
magnetotellurics), natural sources like lightning, magnetosphere activities, etc. The Active
method uses a transmitter to induce ground current, using an artificial source.
7. Geophysical Logging Techniques
The term “logging” refers to making records of some measurements or observations.
Borehole geophysical logging is a procedure to collect and transmit specific information
about the geologic formations penetrated by a well by raising and lowering a set of probes
that contain water-tight instruments in the well. The data obtained is normally used to
determine the general lithology of formations, distribution of structures, vertical flow of
fluids, and the water-yielding capabilities of the formations. The geophysical logging of
boreholes came a long way since 1927, when Schlumberger brothers ran the first electric
log.
Basically, there are two types of logging techniques- first utilizing the natural source &
second utilizing stimulated controlled source. Geophysical logging technique utilizes the
measurement of certain physical parameters across different subsurface formations with
the help of sensing probe inside the bore hole providing a continuous record of these
parameters versus depth. These parameters are interpreted in terms of lithology, porosity,
moisture content & quality of formation fluids.

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Different physical properties like electrical conductivity, magnetic susceptibility,
radioactivity & velocity etc. are utilized. The primary purpose of well logging is the
identification of formations traversed by a bore hole & salinity of fluids. Well logging is
used for stratigraphic correlation, detection of bed boundaries, porous & permeable zones
for the water well design & construction and for sea water intrusion studies of coastal
aquifers.
i. Logging methods
The different types of well-logging methods are:
1. Electric logging - electrical resistivity & Self-Potential (SP).
2. Radioactive logging - gamma ray & neutron logs.
3. Induction logging.
4. Sonic logging.
5. Fluid logging - temperature, fluid resistivity, flow meter & tracer logging.
6. Caliper logging.
Electric well logging involves the continuous recording of electrical resistance / resistivity
& SP of the formations by a drill bore hole. In the SP log, the potential drop between
borehole electrode & a reference electrode @ the surface is recorded. The SP logs are
highly useful in deciphering saline water & clay dominated zones. The Resistivity logs are
used for ground water & mineral explorations.
ii. Photo geology
Photo geology is the art of making aerial photographs that are suitable for analyzing the
earth’s physiographic features like rock types, structures, mineralized zones, water
resources, types of vegetation, zones of cultivation and urbanization. The Photographs of
the earth taken from the aircraft or satellite can provide useful information regarding
groundwater conditions. The technology of remote sensing has developed rapidly in recent
years. Stereoscopic examination of black-and-white aerial photographs has gained steadily
in importance. Observable patterns, colors, and relief make it possible to distinguish
differences in geology, soils, soil moisture and land use. Thus, photo geology can
differentiate between rock and soil types and indicate their permeability and areal
distribution-and hence areas of groundwater recharge and discharge. Maps classifying an
area into good, fair, and poor groundwater yields can be prepared. Aerial photographs also

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reveal the fracture patterns in rocks, which can be further related to the porosity,
permeability, and ultimately the well yields. They are suitable for identifying the
formations that are potential zones for the occurrence of groundwater.
8. Remote Sensing techniques
Remote sensing is the science of acquiring information about the Earth's surface without
actually being in contact with it. This is done by sensing and recording reflected or
emitted energy and processing, analyzing, and applying that information. In much of
remote sensing, the process involves an interaction between incident radiation and the
targets of interest. Remote sensing shows an increasing role in the field of hydrology and
water resources development. Remote sensing provides multi-spectral, multi-temporal and
multi-sensor data of the earth’s surface which are suitable for mineral explorations, water
resources evaluation, and environmental monitoring.
Remote sensing techniques help in the demarcation of groundwater potential zones,
identification of groundwater recharge sites and, to analysis the future artificial recharge
sites.
Applications of remote sensing
Satellite data products are much varied depending upon the spectra considered. High
resolution satellite images are visually or digitally interpreted to identify the groundwater
potential zones. Thematic layers are prepared based on hydro geomorphic units, land-use/
land-cover/ lineaments, rock types, structures and many other features. The methodology
involves the delineation of hydro geomorphological units, which are influenced by the
hydro geological conditions. The hydrogeological conditions are controlled by the
lithology, geomorphology, and structures like lineaments, faults and fractures. The visual
interpretation of satellite data in conjunction with limited field verification of these
features focus on the priority zones. Most of them are reflected as hydro geomorphic units
provided by remote sensing units.
1.6 Summary
Several geological, hydrogeological and geophysical methods are employed to target the
groundwater potential zones. The interpretation of satellite images and aerial photographs
also help more in this process. Groundwater exploration is a very unique exercise. As it is
a hidden resource, various indirect methods are attempted to identify the points. The

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success in the groundwater targeting lies in experience of understanding the geological
conditions, structural conditions and hydrogeological conditions which favour the
occurrence of groundwater. The modern tools like remote sensing and aerial photography
also provide a lot of spatial data for a quick understanding of the domain for a better
decision-making.

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CHAPTER TWO
GROUNDWATER OCCURENCE
The study of groundwater occurrence is equally important as studying the surface water
resources since about 22% of the world’s fresh water resources exist in the form of
groundwater. Further, the subsurface water forms a critical input for the sustenance of life
and vegetation in arid zones. Because of its importance as significant source of water
supply, various aspects of groundwater dealing with the exploration, development and
utilization have been extensively studied by workers from different disciplines, such as
geology, geophysics, geochemistry, agricultural engineering, water resources engineering
and civil engineering etc.
Groundwater occurrence is one part of the complex dynamic hydrologic cycle. The
Saturated formations below the surface act as mediums for the transmission points as well
as groundwater reservoirs for the storage. Water infiltrates to these formations from the
surface and is transmitted slowly for varying distances until it returns to the surface by the
action of natural flow, vegetation, or actions of man (Todd, 1980).

Figure 2.1: Groundwater flow in the hydrologic cycle

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Table 2.1 Amount of water on earth according to the survey conducted within the
international geophysical year (Holy, 1982)
Water occurrence 103 Gm3 Amount of water Rate of exchange
% of water % of freshwater (Years)

World oceans 1300000 97 - 3000

Salt lakes/seas 100 0.008 - -
Polar ice 28500 2.14 77.6 8000
Atmospheric water 12 0.001 0.035 0.027(10 days)
Water in 1 0.000 0.003 -
organisms
Fresh lakes 123 0.009 0.335 -
Water courses 1 0.000 0.003 0.031 (11 days)
Unsaturated zone 65 0.005 0.18 1
Saturated zone 8000 0.60 21.8 500
Total fresh water 36700 2.77 100 -
Total water 1337000 100 - -

2.1 Historical Background

Old Greek and Roman philosophers have speculated about groundwater. They were
puzzled by springs and discharge of water in to rivers in dry seasons; long after rainy
season has passed. Greek Plato (427-347 BC) and other philosophers offered solution for
that groundwater originated from the cavern which was connected to the ocean. By wave
action, water of the sea and ocean was transported upward in to caverns and from there to
the springs and rivers. They assumed that groundwater purifies by filtration of salt of sea
and ocean water, in order to explain that springs and river waters are fresh.
True explanation of groundwater was put forward by the French scientist Perrault (1608-
1680) and Mariotte (1620-1684). They found that precipitation could infiltrate in to the
ground in appreciable quantities that could sustain springs and rivers. French water works
engineer Darcy (1803-1858) made a start with groundwater hydraulics. Modern trends of
hydrogeology concern the conceptual development of flow systems, hydrochemistry and

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groundwater contamination. In this regard Thiem (1906), Theis (1935), Jacob (1950)
developed radial flow in to wells. Scientists including Van Dam (1983) developed
equations of fresh water lenses and fresh-saline water interface. Apollo and Postman
(1996) have paid attention to the interrelationship between groundwater chemical
compositions associated with rock types. Stuyvesant (1999) researched on groundwater
classification in to different water types. Recent research has increased in the field of
groundwater tracing in fractured and karstic rock areas. Such chemical aspects are focused
based on the need to provide good quality water for drinking water supply and irrigation
purposes.
2.2 History of Groundwater use
Since early days of humanity people have used groundwater for domestic water supply
and irrigation. Both springs and water wells were utilized for this purpose. Well
construction was carried out in old civilization in china, Middle East and Egypt. 2500
years ago, Khanates were installed in Persia (Iran) and latter practiced in Afghanistan and
Egypt. Since 12th century, due to modern technology many African countries including
Ethiopia are utilizing groundwater from wells.
Hydrogeology is the study of occurrence, movement and chemistry of groundwater in its
geological environment.
Checklist
Q#1 what is ground water?
Q#2 what is the importance of ground water in hydrologic cycle?
Q#3 Give a comment on the water supply scheme of Arba Minch University with respect
to ground water abundance.
Q#4 what are the purpose for which ground water can be used.
2.3 Occurrence of Groundwater
Groundwater system is the zone in the earth’s crust where the open space in the rock is
completely filled with groundwater at a pressure greater than atmospheric. Groundwater
stretches out below the groundwater table. Groundwater table, which is the top most part
of groundwater, may be located near or even at land surface and not fixed meaning it
fluctuate seasonally.
Two zones can be distinguished in which water occurs in the ground:

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a) The unsaturated zone/ Zone of aeration
b) The saturated zone
For the hydro-geologist both zones are important links and storage devices in the
hydrologic cycle. For the engineer the importance of each zone depends on his field of
interest.
The process of water entering into the ground is called infiltration. Downward transport of
water in the unsaturated zone is called percolation, whereas the upward transport in the
unsaturated zone is called capillary rise. The flow of water through saturated porous media
is called groundwater flow. The out flow from groundwater to surface water is called
seepage.

Figure 2.2a: Schematic representation of subsurface water in the soil

The type of openings (voids or pores) in which groundwater occurs is an important
property of the subsurface formation. Three types are generally distinguished.
a) Pores: Openings between individual particles as in sand and gravel. Pores are
generally interconnected and allow capillary flow for which Darcy’s law can be
applied.

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b) Fractures, Crevices or joints: This meant fractures and crevices in hard rock which
have developed from breaking of the rock. The pores may vary from super capillary
size to capillary size. Only for the latter situation application of Darcy’s law is
possible. Water in these fractures is known as fissure or fault water.
c) Solution channels and caverns in limestone (karst water): This meant solution
channels and openings resulting from gas bubbles in lava. These large openings result
in a turbulent flow of groundwater which cannot be described with Darcy’s law.
Table 2.2 Variation of groundwater density based on temperature and total dissolved
solids (TDS) concentration.
Temperature (oC) Density (Kg/m3) TDS (mg/l) Density at 4oC(Kg/m3)
0 999.87 0 1000
4 1000 1000 1000.70
5 999.90 5000 1003.60
10 999.75 100000 1072
20 998.27

Density differences as a result of variation in TDS concentration are more pronounced

than variations resulting from changes in temperature. Groundwater is contained in rocks.
Rocks may be classified as consolidated and unconsolidated. Consolidated rocks include
granites, basalt, gneiss, sandstone, shale etc.
The porosity, n of the subsurface formation is that fraction of its volume which consists of
openings and pores: n=Vv/V; Where Vv is the pore volume or volume of voids and V is
the total volume of the soil.
When water is drained by gravity from saturated material, only a part of the total volumes
is released. This portion is known as Specific yield (Sy). The water not drained is called
specific retention (Sr) and the sum of Sy and Sr is equal to the porosity. In fine-grained
material the forces that retain water against the force of gravity are high due to the small
pore size. Hence, the specific retention of fine-grained material (silt or clay) is larger than
that of coarse material (sand or gravel). Specific yield (Sy) =Vw/V and specific retention
(Sr) =Vr/V and Vv=Vw+Vr as shown above n=Vv/V.

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While porosity gives a measure of the water storage capability of a formation, not all the
water held in the pores is available for extraction by pumping or draining by gravity. The
pores hold back some water by molecular attraction and surface tension. The actual
volume of water that can be extracted by the force of gravity from a unit volume of
aquifer material is known as the specific yield, Sy. The fraction of water held back in the
aquifer is known as specific retention; Sr. Details of these will be discussed in part 1.3.
2.3.1 Groundwater zone
Unsaturated Zone: This is also known as zone of aeration. In this zone the soil pores are
only partially saturated with water. The space between the land surface and the water table
marks the extent of this zone. Further, the zone of aeration has three sub zones: soil water
zone, capillary fringe and intermediate zone.
The soil water zone lies close to the ground surface in the major root band of the
vegetation from which the water is lost to the atmosphere by evapotranspiration. Capillary
fringe on the other hand hold water by capillary action. This zone extends from the water
table upwards to the capillary rise. The intermediate zone lies between the soil water zone
and the capillary fringe.
The thickness of the zone of aeration and its constituent sub-zones depend upon the soil
texture and moisture content and vary from region to region. The soil moisture in the zone
of aeration is of importance in agricultural practice and irrigation engineering. This part is
however concerned only with the saturated zone.

Figure 2.2b: Classification of subsurface water and variation in degree of saturation

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Important conditions in the unsaturated zone are the wilting point and the field capacity.
Field capacity is the moisture content in the soil a few days after irrigation or heavy
rainfall, when excess water in the unsaturated zone has percolated. Often the soil water
pressure is given as a pF value, which is the 10base logarithm of the pressure in
centimeters of water column h, i.e. pF = log10 (-h).
Field capacity is often taken (by definition) as the soil moisture situation corresponding to
an under-pressure of 100cm (pF 2) but also larger pF values are used (pF 2.3 or pF 2.7).
Wilting point corresponds to a minimum soil moisture content for which the plant is no
longer capable of taking up the soil moisture and dies. The corresponding under-pressure
is approximately -16 bar (pF 4.2). At the phreatic surface, where the soil is completely
saturated, the under-pressure is zero (pF=0) and the moisture content equals the porosity
(n).

Figure 1.3: Typical pF-curves or soil moisture characteristics

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2.3.2 Saturated Zone

Groundwater is the water which occurs in the saturated zone. All earth materials, from
soils to rocks have pore spaces although these pores are completely saturated with water
below the groundwater table or phreatic surface (GWT). From the groundwater utilization
aspect only such material through which water moves easily and hence can be extracted
with ease are significant.
Natural variations in permeability and ease of transmission of groundwater in different
saturated geological formations lead to the recognition of aquifer, Aquitard, Aquiclude
and Aquifuge.
a) Aquifer: This is a water-bearing layer for which the porosity and pore size are
sufficiently large that which not only stores water but yields it in sufficient quantity
due to its high permeability. Unconsolidated deposits of sand and gravel form good
aquifers (e.g. sand, gravel layers).
b) Aquitard: It is less permeable geological formation which may be capable of
transmitting water (e.g. sandy clay layer). It may transmit quantities of water that are
significant in terms of regional groundwater flow.
c) Aquiclude: is a geological formation which is essentially impermeable to the flow of
water. It may be considered as closed to water movement even though it may contain
large amount of groundwater due to its high porosity (e.g. clay).
d) Aquifuge: is a geological formation, which is neither porous nor permeable. There are
no interconnected openings and hence it cannot transmit water. Massive compact rock
without any fractures is an aquifuge.
2.3.3 Aquifers and their characteristics
For a description or mathematical treatment of groundwater flow the geological formation
can be schematized into an aquifer system, consisting of various layers with distinct
different hydraulic properties. The aquifers are simplified into one of the following types
(see Fig. 1.4).
a) Unconfined aquifer (also called phreatic or water table aquifer): Such type of
aquifer consists of a pervious layer underlain by a (semi-) impervious layer. This type
of aquifer is not completely saturated with water. The upper boundary is formed by a

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free water-table (phreatic surface) that is in direct contact with the atmosphere. In most
places it is the uppermost aquifer.
b) Confined aquifer: Such an aquifer consists of a completely saturated pervious layer
bounded by impervious layers. There is no direct contact with the atmosphere. The
water level in wells tapping these aquifers rises above the top of the pervious layer and
sometimes even above soil surface (artesian wells).
c) Semi-confined or Leaky aquifers: consists of a completely saturated pervious layer,
but the upper and/or lower boundaries are semi-pervious. They are overlain by
aquitard that may have inflow and outflow through them.
d) Perched aquifers: These are unconfined aquifers of isolated in nature. They are not
connected with other aquifers.

Figure 2.4: Different types of aquifer formations

The pressure of the water in an aquifer is measured with a piezometer, which is an open
ended pipe with a diameter of 3-10 cm. The height to which the water rises with respect to
a certain reference level (e.g. the impervious base, mean sea level, etc.) is called the
hydraulic head. Strictly speaking the hydraulic head measured with a piezometer applies

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for the location of the lower side of the pipe, but since aquifers are very pervious, this
value is approximately constant over the depth of the aquifer. For unconfined aquifers, the
hydraulic head may be taken equal to the height of the water table. Water moves from
locations where the hydraulic head is high to places where the hydraulic head is low. The
hydraulic head will be split into its gravitational and pressure components. Generally the
head can be written as h = z + p/γw whereby the z is the gravitational elevation head and
the p/γw the pressure head.

Figure 2.5a: Cross section showing hydraulic head (h)

2.3.4 Determination of groundwater flow parameters

The following are some of the groundwater flow parameters or aquifer properties which
are important in the storage and transmission of water in aquifers.
Porosity (n), Specific yield (Sy), Specific retention (Sr), Coefficient of permeability (K),
Transmissivity (T), Storage coefficient (S) etc.
1. Porosity (n)
The porosity, n is the ratio of volume of the open space in the rock or soil to the total
volume of soil or rock.

 Vv 
n    * 100 (2.1)
 VT 
Where:
Vv = the pore volume or volume of voids
VT = the total volume of the soil

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Porosity is also the measure of water holding capacity of the geological formation. The
greater the porosity means the larger is the water holding capacity. Porosity depends up on
the shape, size, and packing of soil particles. Porosity greater than 20% is considered
large; 5-20% medium and less than 5% is small.

Table 2.3 Variation of porosity based on the rock type

Type of rock Range of porosity Type of rock Range of porosity
Unconsolidated Consolidated
Gravel 0.2-0.4 Basalt 0.05-0.5
Sand 0.2-0.5 Lime stone 0.05-0.5
Silt 0.3-0.5 Sand stone 0.05-0.3
Clay 0.3-0.7 Shale 0.0-0.1

While porosity gives a measure of the water storage capability of a formation, not all the
water held in the pores is available for extraction by pumping or draining by gravity. The
pores hold back some water by molecular attraction and surface tension. The actual
volume of water that can be extracted by the force of gravity from a unit volume of
aquifer material is known as the specific yield, Sy. The fraction of water held back in the
aquifer is known as specific retention, Sr.
2. Specific yield (Sy)
When water is drained by gravity from saturated material, only a part of the total volumes
is released. The ratio of volume of water in the aquifer which can be extracted by the force
of gravity or by pumping wells to the total volume of saturated aquifer is called Specific
yield (Sy).
V 
S y   w  *100 (2.2)
 VT 
Where: Sy= Specific yield, Vw=the volume of extractible water, VT = the total volume of
the soil.

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2.5b. Specific yield of unconfined aquifer

All the water stored in the water bearing formations can’t be extracted by gravity drainage
or pumping; a portion of water remains held in the voids of the aquifer by molecular and
surface tension forces.
For unconfined aquifers the specific yield (Sy) is defined as the amount of water stored or
released in an aquifer column with a cross-sectional area of 1m2 as a result of a 1m
increase or decrease in hydraulic head.
Table 2.4 Common values for Sy
Type of Rock Range Mean
Medium gravel 0.17-0.44 0.24
Fine gravel 0.13-0.40 0.28
Medium sand 0.16-0.46 0.32
Fine sand 0.01-0.46 0.33
Silt 0.01-0.39 0.20
Clay 0.01-0.18 0.06
Tuff 0.02-0.47 0.21
Sandstone 0.02-0.30 0.21
sandstone (non-cemented) 0.12-0.30 0.27
Siltstone 0.01-0.28 0.12

3. Specific retention (Sr)

The water which is not drained or the ratio of volume of water that cannot be drained (Vr)
to the total volume (VT) of a saturated aquifer is called specific retention (Sr).

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V 
S r   r  *100 (2.3)
 VT 
In fine-grained material the forces that retain water against the force of gravity are high
due to the small pore size. Hence, the specific retention of fine-grained material (silt or
clay) is larger than that of coarse material (sand or gravel). The total volume of voids (Vv)
equals to the sum of volume of water drained out (Vw) and volume of water retained (Vr);
hat is Vv=Vw+Vr.
From the above expression we can get:
Vv V  V 
*100   w  *100   r  *100 ↔n= Sy + Sr (2.4)
VT  VT   VT 
Meaning sum of Sy and Sr is equal to the porosity. It should be noted that; it is not
necessarily the soil with a high porosity will have a high specific yield because of its
permeability.
4. Coefficient of permeability (k)
Coefficient of permeability is also called hydraulic conductivity reflects the combined
effects of the porous medium and fluid properties. It is an ease with which water can flow
through a soil mass or rock and usually it is the capacity of geological formation to
transmit water. Coefficient of permeability is primarily dependent on the soil property and
water contained in it. Unconsolidated rocks are permeable when the pore spaces between
grains are sufficiently large.
K=ki.kw (2.5)
Where:
K = Coefficient of permeability,
ki = Intrinsic permeability; depending on rock properties (such as grain size &
packing),
kW = Permeability depending on fluid properties (such as density and viscosity of
water)
Further for unconsolidated rocks, from an analogy of laminar flow through a conduit the
coefficient of permeability K can be expressed as:
K = C dm2 ( / ) = C dm2 (g / ) (2.6)
Where:

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dm = Mean pore size of the porous medium (m),
 = unit weight of the fluid (kg/m2s2),
 = density of the fluid (kg/m3),
g = acceleration due to gravity (m/s2),
 = dynamic viscosity of the fluid (kg/ms),
C = a shape factor which depends on the porosity, packing, shape of grains and grain-
size distribution of the porous medium. Thus for a given porous material K  1/ where 
= kinematic viscosity = / = f (temperature).
Eq (1.6) can be split into two components: intrinsic permeability (ki) and permeability due
to fluid properties (kw).  ki = C dm2 and kw = / = g/.

2 n3 
According to Kozeny-Carman’s formula K i  Cd m  
 (1  n)
2

5. Transmissivity (T) and Vertical Resistance (C):
Transmissivity is the product of horizontal coefficient of permeability and saturated
thickness of the aquifer. For an isotropic aquifer (Kx = Ky = K):
T = KB (2.7)
Where:
T = aquifer Transmissivity (m2 / day),
B = aquifer thickness (m).
The vertical resistance of an aquitard is defined as the ratio of the thickness of the
aquitard and its permeability in the vertical direction (kz):
C = D / KZ (2.8)
Where:
C = vertical resistance (days),
D = thickness of the aquitard (m).
Values for the transmissivity of aquifers and vertical resistances of an aquitard are usually
determined from pumping tests. There are different stratifications in aquifers may be
stratification with different permeability in each stratum. Two main kinds of stratifications
(flow situations in stratified aquifers) are possible in aquifers; horizontal and vertical
stratifications.

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a) Horizontal stratification
When the flow is parallel to the stratification as in (Fig. 1.6) equivalent permeability Ke of
the entire aquifer of thickness B = Bi is:
n

K B i i
Ke  i 1
n
(2.9)
B i 1
i

Transmissivity of an aquifer formation will therefore be given as follows:

n n
 T  K e  Bi   K i Bi
i 1 i 1

Figure 2.6: Flow parallel to stratification

b) Vertical Stratification
When the flow is horizontal and normal to the stratification as in (Fig.2.7) the equivalent
n
permeability Ke of the aquifer length L   Li is:
i 1

L i
Ke  i 1
(2.10)
n
 Li 
 
i 1  K i



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Figure 2.7 Flow normal to stratification

Note that in this case L is the length of seepage and the thickness of the aquifer does not
come into picture in calculating the equivalent permeability. Transmissivity of the aquifer,
T = Ke.B
6. Storage Coefficient (S)
The amount of water stored or released in an aquifer column with a cross sectional area of
1m2 for a 1m increase or drop in head is known as storage coefficient. Storage coefficient
of unconfined aquifer is equal to the specific yield.
In confined or semi-confined aquifers water is stored or released from the whole aquifer
column mainly as a result of elastic changes in porosity and groundwater density.
Common values for the storage coefficients for confined and semi-confined aquifers range
form 10-7 to 10-3.
The volume of water drained from an aquifer, Vw may be found from the following
equation.
Vw=SAh
Where A is horizontal area and h is fall in head
7. Specific Storage (Ss)
In a saturated porous medium that is confined between two transmissive layers of rocks,
water will be stored in the pores of the medium by a combination of two phenomena;
water compression and aquifer expansion. As water is forced in to the system at a rate
greater than it is being extracted, the water will compress and the matrix will expand to
accommodate the excess. In a unit of saturated porous matrix, the volume of water that
will be taken in to storage under a unit increase in head, or the volume that will be

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released under a unit decrease in head is called specific storage. It is also the storage
coefficient per unit saturated thickness of an aquifer.
For confined aquifer, the relation between the specific storage and the storage coefficient
is as follows:
S = Ss*b (2.11)
Where:
S = Storage coefficient (dimensionless),
b = aquifer thickness (m)
Specific Storage is also called elastic storage coefficient and is given by the following
expression.
Ss=g (+n) (2.12)
Where:
=fluid (water) density,
g=gravitational acceleration,
=aquifer compressibility,
n= porosity,
=water compressibility.
Elastic storage is the only storage occurring in semi-confined and confined aquifers.
2.3.5 Laboratory and field determination of hydraulic conductivity
Definition: If hydraulic conductivity is consistent throughout a formation, regardless of
position, the formation is homogeneous. If hydraulic conductivity within a formation is
dependent on location, the formation is heterogeneous. When hydraulic conductivity is
independent of the direction of measurement at a point within a formation, the formation
is isotropic at that point. If the hydraulic conductivity varies with the direction of
measurement at a point within a formation, the formation is anisotropic at that point.
Figure 1-8 is a graphical representation of homogeneity and isotropy.
Geologic material is very rarely homogeneous in all directions. A more probable condition
is that the properties, such as hydraulic conductivity, are approximately constant in one
direction. This condition results because of:
a) Effects of the shape of soil particles, and
b) Different materials incorporate the alluvium at different locations.

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As geologic strata are formed, individual particles usually rest with their flat sides down in
a process called imbrications. Consequently, flow is generally less restricted in the
horizontal direction than the vertical and Kx is greater than Kz for most situations.
Layered heterogeneity occurs when stratum of homogeneous, isotropic materials are
overlain upon each other. Layered conditions commonly occur in alluvial, lacustrine, and
marine deposits. At a large scale, there is a relationship between anisotropy and layered
heterogeneity. In the field it is not uncommon for sites with layered heterogeneity to have
large scale anisotropy values of 100:1 or greater. Discontinuous heterogeneity results from
geologic structures such as bedrock outcrop contacts, clay lenses, and buried oxbow
stream cutoffs. Trending heterogeneity commonly occurs in sedimentary formations of
deltaic, alluvial, and glacial origin.

Figure 2.8: Homogeneity and isotropy

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A. Laboratory Tests
Permeability could be determined by direct method in either the laboratory or the field.
Direct and indirect methods are also applied for the determination of Permeability.
Determination of fine grained soils permeability takes considerable time. Hence indirect
methods are applied for instance consolidation test and triaxial compression test.
Direct permeability tests
1. Constant head permeameters
Permeameters (see the fig. 1.9a, b) may be Constant head or Falling head.

Figure 3.9a: Constant head permeameter

The principle in this setup is that the hydraulic head causing flow is maintained constant;
the quantity of water flowing through a soil specimen of known cross sectional area and
length in a given time is measured by graduated cylinder. In highly impervious soils the
quantity of water that can be collected will be small and accurate measurements are
difficult to make. Therefore constant head permeameters are mainly applicable in
relatively pervious soils.
Q * dl
K For k >10-3 cm/sec Water should be
A * dh
collected after a steady state of flow is attained.

Figure 3.9b: Falling head permeameter

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2. Falling head permeameters
Falling head permeameter is used for relatively less permeable soils where the discharge is
small. The water level in the standpipe falls continuously as water flows through the soil
specimen. Observations should be taken after a steady state of flow has reached. If the
head of water level in the stand pipe above that in the constant head chamber falls from h 0
to h1, corresponding to elapsed time t0 and t1, the coefficient of permeability, k is
determined as follows.
a L h
K * ln 0
A t1  t 0 h1
Where:
a= Cross sectional area of stand pipe,
A= Cross sectional area of soil sample,
L= Length of the soil sample,
Derivation
 Kh  dh  KA  dh
Q  KiA    A  a  dt  
 L  dt  aL  h
Integrating both sides and applying the limits t0 and t1 for t, and h0 and h1 for h
tt
h 
h h
KA 1 dh 0 dh  KA 
1

 dt      t1  t 0   ln  0 
aL t0 h0
h h1 h  aL   h1 
Transposing terms we get:
a L h
K * ln 0
A t1  t 0 h1
B. Field Methods
The average permeability of a soil in the field may be different form values obtained in the
laboratory. Some of the field methods are:
- Pumping tests (We will see it under ch-3)
- Tracer test (fluorescence) (Remember your Hydrometry course)
- Double Ring Infiltrometer tests (Remember your basic Hydrology co
Example-1; the aquifer located in Gambella Region at a zone of 930sq.km is bounded by
confined aquifer of 22m thick. The average maximum and minimum piezometric level

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variation range between 5-12m.Taking storage coefficients of 0.001.Calculate the annual
rechargeable ground water storage from the area. Calculate the average well yield; assume
the pumping day of 250days and 40 pumping units
Solution
Annual rechargeable ground water storage =A x ∆h x Sc = 930x106x (12-5) x 0.001 =
6.51Mm3
Average well yield x pumping rate x numbers of wells = annual fluctuation of the aquifer
Average yield of the well = annual fluctuation of aquifers/(pumping unit* pumping rate
= 6.51Mm3/ (250x40) =6.51x106m3/1000 = 651m3/day=27.125m3/h = 7.5lt/sec
Example-2; In an unconfined aquifer covering 2 sq.km,the original water table was 12.3m
below ground level. The pumping of 1Mm3 of water from the area dropped the water table
to 15.1m below GL. Calculate specific yield and retention of the aquifer if porosity of
aquifer material is 23%.
Solution
Volume of water pumped out=Aquifer area x change in ware table x specific yield
Sy = 106/(2 x 106m2 x (15.1-12.3)m)=0.1786 or 17.86%
Sr = n-Sy=23-17.86= 5.13%
Example-3; unconfined aquifer with a storage coefficient of 0.13 has an area of 120m2.
The water table drops 5m during drought. How much water is lost from storage?
Solution: Vw=SxAxh=0.13*120*5 = 78m3
Example-4; the hydraulic conductivity (K) of silty sand is 1.36x10-5 cm/sec at 15 oC.
What is the intrinsic permeability (Ki) in cm2? At 15 oC, density of water is 0.9991 gm/cm3
and viscosity is 0.0114 poise and g=980 cm/sec2.
Solution: K = KiKw= C dm2 (g /)
K=1.36x10-5 cm/sec
g=0.9991 gm/cm3*980 cm/sec2=979.118 g/cm2sec2
µ=0.0114 poise=0.0114 g/cm. sec
Kw=g / =85887.544 cm/sec
Ki=K/ Kw=1.36x10-5 cm/sec/85887.544 cm/sec=1.58*10-5 cm2.

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Example-5; An artesian aquifer of 20m thick has a porosity of 20% and bulk modulus of
compression 108 N/m2.Estimate the storage coefficient of the aquifer. What fraction of this
is attributable to the expansibility of water?
Solution
S=Ssxb=ρxg (ᵅ+ᵝn) = 9.81x20(1/108 +0.2x1/2.1x109)=1.98X10-3
The fraction of storage attributable to the expansibility of water (Taking only the second
term within the brackets): Sw=0.0187x10-3=1.87x10-5/1.98x10-3 of S=1% of S
Example-6 The volume of a moist sand specimen was 72.5 cm3 and its weight is 152.0
gram. After oven dryness, at 105 oc for 24 g hours, the specimen weighed 145 gram and
its volume was 71.2 cm3.The oven dried sample was then immersed in a chamber
containing 500cm3 of water and left until it becomes saturated (the chamber is sealed to
prevent water evaporation).Finally the sample was, removed from the chamber and the
volume of water in the chamber was measured to be 483.5 cm3.compute
A. Over all porosity
B. Effective porosity.
Solution
Vt=72.5cm, Wt=152g, Wd=145g, Vd=71.2cm3

A). ; Vv = Vt-Vs;

solid/2.65=145/2.65 = 54.717cm3
Vv=72.5-54.717 = 17.783cm3
n=17.783/72.5 x100= 24.53%
B) neff= Vveff/ Vt=500-483/72.5 = 0.2275
Example-7; an undisturbed core sample is obtained from a sandy material at a height of
20 cm above a water table. The core is 10.186cm in height and 5 cm diameter (inside
measurement).The net weight of the sample is 419 gram before drying and 371 gram after
oven drying. Calculate the following aquifer properties in relation to water occurrence.
A. water content by weight
b. Volumetric water content
C. Porosity
D. Void ratio

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E. Saturation percentage and
F. Bulk density.
Solution

Given A) ω= = =12.94%

h=10.186cm B) θ=ωx ρb/ρw =12.94x1.805=24%

d=5cm C) n=vv/vt= , vs=371/2.65 =140cm3

Wd = 171g n= = 30%

D) e=n/1-n=0.3/0.7=0.4286
E) Sp=vw/vv=48/60=0.8
F) Vt=10.186x52/4 xП = 200cm3
Ρb=wd/vt=371/200 =1.855 g/cm3
Example-8; following data is obtained from the difficult rocky areas of eastern Gambella:
Area of the rocky = 1km2, Normal rainfall = 700mm, Water table fluctuation before and
after rain = 3.2, Specific yield of the rock = 2%;
Examine how far the drinking water needs of the local population can be met.
Solution
Ground water storage available annually= Area x Gw fluctuation x specific yield
=106x 3.2x 2%=64,000m3(replenished by normal rainfall)
Assume infiltration rate=10%, rainfall volume=106 x 0.7 x 0.1=70,000m3.Again assuming
a per capital consumption of 180lpd,
Annual drinking water supply required is =154 x 180 x 365=10,120,000lt or 10,120m3.
The annual drinking water supply required is 10,120m3 against availability of 64,000m3.
Thus there is enough replenish able ground water resource available in the area to meet
their demand.
Example-9; In a phreatic aquifer extending over 1km2 the water table was initially at 25m
below ground level. Sometime later after irrigation with a depth of 20cm of water, the
water table rose to a depth of 24m below ground level; Later 3 x 105m3 of water was
pumped out and the water table dropped to 26.2m below ground level. Determine
i) Specific yield of the aquifer
ii) Deficit in soil moisture (below field capacity) before irrigation.

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Solution
i) Volume of water pumped out=Area of aquifer x drop in ground water table x specific
yield
3x 105 =106 x 2.2 x sy=> Sy=0.136 or 13.6%
ii) Volume of irrigation water recharging the aquifer = Area of aquifer x rise in ground
water table x specific yield.
Assume an area of 1m2 of aquifer and recharge depth of y: Soil moisture deficit (below
field capacity) before irrigation =200-136=64mm.
Example-10; in an area of 100ha, the water table dropped by 4.5m.If the porosity is 30%
and the specific retention is 10% determine
i) The specific yield of aquifer
ii) Change in ground water storage
Solution
i) Porosity =Sy+ Sr => 30%=sy+10%; Sy=20%
ii) Change in ground water storage=Area of aquifer x drop in g.w.t x Sr =100x4.5x0.2
=90ha-m
Example-11; In a certain place in Ethiopia, the average thickness of the confined aquifer
is 30m and extends over an area of 800km2. The piezometric surface fluctuates annually
from 19m to 9m above the top of the aquifer. Assuming a storage coefficient of 0.0008,
what ground water storage can be expected annually?
Assuming an average well yield of 30m3/yr and about 200days of pumping in a year, how
many wells can be drilled in the area?
Solution
∆GWS=Aaq x∆piezo.surface xS = (800x106) (19-9) x 0.0008 = 6.4Mm3
Annual draft=30x24x200=0.144Mm3
Number of wells that can be drilled in the area= = 44.5 wells, say 44
Example-12; An aquifer has an average thickness of 60m and an aerial extent of 100ha.
Estimate the available ground water storage if the aquifer is unconfined and the fluctuation
in ground water is observed as 15m.If
a) The aquifer is unconfined and the fluctuation in GWT is observed as 15m,

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b) The aquifer is confined and the piezometric head is lowered by 50m, which drains
half the thickness of the aquifer.
Solution
a)
b)
(as confined) (as unconfined)
-4
=100ha (20(2x10 ) +30(0.16))=480.4 ha-m.
Example-13; A constant-head permeameter has a cross-sectional area of 78.5 cm2. The
sample is 23 cm long. At a head of 3.4 cm, the permeameter discharges 50 cm3 in 38 s.
(A) What is the hydraulic conductivity in centimeters per second and feet per day?
(B) What is the intrinsic permeability if the hydraulic conductivity was measured at
15°C?
(C) From the hydraulic conductivity value, name the type of soil.
Solution

A)

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Example-14; the hydraulic conductivity of a silty sand was measured in a laboratory
permeameter and found to be 3.75 3 10–5 cm/s at 25°C. What is the intrinsic permeability
in cm2? Refer to Appendix 14 for values of density and viscosity.
Solution

Example-15; An aquifer has a specific yield of 0.19. During a drought period, the
following average declines in the water table were noted:
Area Size (km2) Decline (m)
A 15 2.34
B 7.5 1.22
C 18.3 0.76
D 22.5 3.44
E 9.44 1.89
F 22.7 0.35
What was the total volume of water represented by the decline in the water table?
Solution
Vw=SAh

and

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Example-16; an aquifer has three different formations. Formation A has a thickness of 22

ft and a hydraulic conductivity of 17.0ft/d. Formation B has a thickness of 3.5 ft and a
conductivity of 99 ft/d. Formation C has a thickness of 26ft and a conductivity of 22 ft/d.
Assume that each formation is isotropic and homogeneous. Compute both the overall
horizontal and vertical conductivities.

A 17.0 22
B 99 3.5 and total
C 22 26

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Checklist:
1. Differentiate between various saturated geological formations such as aquifer,
aquitard, aquiclude and aquifuge.
2. What is the difference and similarity between unconfined aquifer, confined aquifer,
perched aquifers and semi-confined or leaky aquifers?
3. Discuss about some of the groundwater flow parameters (aquifer properties) which
are important in the storage and transmission of water in aquifers.
4. What is the difference between:
a. Transmissivity (T) and vertical resistance (C)?
b. Storage coefficient (S) specific storage (Ss)?
c. Falling head and constant head permeameters?

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CHAPTER THREE
GROUNDWATER MOVEMENT
Part of the rain falling over the land surface infiltrates into the soil and the remaining
flows down as surface runoff. From the point of view of water resources engineering, the
surface water forms a direct source which is utilized for a variety of purposes. However,
most of the water that infiltrates into the soil travels down to recharge the vast
groundwater stored at a depth within the earth. In fact, the groundwater reserve is
actually a huge source of fresh water and is many times that of surface water. Such large
water reserve remains mostly untapped though locally or regionally, the withdrawal may
be high.

Figure 3.1: Subsurface water movement

What happens to the water that is infiltrated at the surface of the unsaturated soil during
application of water from above? It moves downward due to gravity through inter
connected pores that are filled with water. With increasing water content, more pores fill,

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and the rate of downward movement of water increases. A measure of the average rate of
movement of water within soil (or permeable bed rock) is the hydraulic conductivity,
indicated as ‘K’, and has the unit of velocity. Though it is more or less constant for a
particular type of soil in the saturated zone, it is actually a function of the moisture content
in the unsaturated portion of the soil.
In literature, the term ‘groundwater flow’ is used generally to describe the flow of water in
the saturated portion of soil or fractured rock. No doubt it is important from the point of
extraction of water from the zone using wells, etc. But the unsaturated zone, too, is
important because of the following reasons:
The water in the unsaturated zone (the soil water) is the source of moisture for vegetation.
This zone is the link between the surface and subsurface hydrologic processes as rain
water infiltrates through this zone to recharge the groundwater.
Water evaporated or lost by transpiration from the unsaturated zone (mainly from the soil
water zone) recharges the atmospheric moisture.
The water that infiltrates through the unsaturated soil layers and move vertically
ultimately reaches the saturated zone and raises the water table. Since it increases the
quantity of water in the saturated zone, it is also termed as ‘recharge’ of the groundwater.
3.1 Darcy’s law and groundwater movement
The theory of groundwater movement originates from a study by the French water works
engineer Henry Darcy, first published in 1856. From many experiments with a setup (Fig.
2.2) he concluded that the groundwater discharge, Q is proportional to the difference in
hydraulic head, h and cross-sectional area A and inversely proportional to the length, l,
thus:
Q = A*V = -K*((h2-h1) / l)*A = KiA (3.1)
Where:
K = the proportionality constant, hydraulic conductivity, expressed in units of velocity;
(h2-h1) = -h; is the drop in the hydraulic grade line in a length of l of the porous
medium; q = the specific discharge.
Darcy’s law is a particular case of the general viscous fluid flow. It has been shown valid
for laminar flows only. For practical purposes, the limit of the validity of Darcy’s law can

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be taken as Reynolds number (Re) of a maximum value of ten. Practical experiences show
that Darcy's law can be applied to most cases of groundwater flow in porous medium.
Re= (*q*d)/ µ = (q*d)/ (3.2)
Where:  = Density of the flowing fluid, q = the specific discharge, also called the
discharge velocity through a unit area of 1m2, d = representative particle size, usually d =
d10 where d10 represents a size such that 10% of the aquifer material is of smaller size, µ=
Dynamic viscosity and  is kinematic viscosity of water.
It may be noted that the apparent velocity, q used in Darcy’s law is not the actual velocity
of flow through the pores. Owing to irregular pore geometry the actual velocity of flow
(Vact) varies from point to point and the bulk pore velocity which represents the actual
speed of travel of water in the porous media is expressed as:
Vact = q/ne 3.3)
Where: ne = the effective porosity which is smaller than the porosity n, as the pores that do
not contribute to the transport are excluded (dead end pores).
The actual velocity is important in water quality problems, to determine the transport of
contaminants. The bulk pore velocity (V) is the velocity that is obtained by tracking a
tracer added to the groundwater.

Figure 3.2. Setup showing tube experiment of Henry Darcy

For the analysis of groundwater flow in natural groundwater basins, Darcy’s law is usually
written in a somewhat different form. The basic form of Darcy’s law is usually written in

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the differential form and the water levels in the manometers are replaced by the so called
hydraulic heads. Instead of the flow through a cross-section of a sand column we will
consider the specific discharge or the flow rate per unit area of rock material. Darcy’s law
for the computation of the specific discharge is then as follows:
 h 
q  K   (3.4)
 l 
Where:
q = specific discharge or flow rate per unit area (m/day),
K = coefficient of permeability or hydraulic conductivity of rock (m/day),
h = hydraulic head (m),
l = distance measured in flow direction (m).
We may split up the specific discharge into its components in the Cartesian coordinates X,
Y and Z directions. For the three dimensions, the following equations are then valid for
flow in isotropic porous medium and Darcy's law will be written as:
 h   h   h 
qx  K x  , q y   K y  , q z   K z   (2.5)
 X   Y   Z 
Where:
qx, qy, qz = Specific discharge in the X, Y and Z direction (m/day).
Kx, Ky, Kz = Coefficient of permeability in the X, Y and Z direction (m/day).
Example 3.1: At a certain point in an unconfined aquifer of 3 km2 area, the water table
was at an elevation of 102.00 m. Due to natural recharge in a wet season, its level rose to
103.20 m. A volume of 1.5 Mm3 of water was then pumped out of the aquifer causing the
water table to reach a level of 101.20 m. By assuming the water table in the entire aquifer
to respond in a similar way, estimate (a) the specific yield of the aquifer and (b) the
volume of recharge during the wet season.
Solution:
Volume pumped out = area * drop in water table * Sy  V=SAh, S=Sy
 1.5*106 = 3*106 * (103.20 - 101.20) * Sy  Sy = 0.25
b) Recharge volume = V=SAh =0.25 (103.20-102.00)*3*106 = 0.9*106 m3
Example 3.2: A field test for permeability consists in observing the time required for a
tracer to travel between two observation wells. A tracer was found to take 10h to travel

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between two wells 50 m apart when the difference in the water surface elevation within
them was 0.5m. The mean particle pore size of the aquifer was 2mm and the porosity of
the medium 0.3. If  = 0.01cm2/s, estimate (a) the coefficient of permeability and intrinsic
permeability of the aquifer and (b) the Reynolds number of the flow.
Solution:
a) The tracer records the actual velocity of water
S 50 *100
Va    0.139cm / s
t 10 * 60 * 60
Discharge velocity, q = n*Va = 0.3*0.139 = 0.0417cm/s
h 0.50
Hydraulic gradient,   0.01
S 50
q 0.0417
Coefficient of permeability, K    4.17cm / s
h 0.01
S
K 4.17 * 0.01
Intrinsic permeability, K i    4.25 *10 5 cm 2
g 981
Since 9.87*10-9 cm-2 = 1 Darcy  Ki = 4306 darcys
0.0417 * 2 *10 2
qd
b) Taking d = 2 mm, Reynolds number, Re    0.834
 10
3.2 Mathematical equation for groundwater flow problems
Continuity equations: Darcy’s law is a powerful tool and can be used by itself to compute
groundwater flow in groundwater basins. Nevertheless, the relationship is often used in
combination with the law of conservation of mass and its mathematical equivalent: the
equation of continuity.

If the density of groundwater is constant, mass balance will be identical to water balance.
Water balance states that:
Total flow in - total flow out = change of water storage

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Figure 3.3 the elemental control volumes for deriving continuity equation
Volume of water inflowing in unit time, dt, in x, y, z directions is:
= Vxdydzdt + Vy dz dx dt + Vz dx dy dt (3.6)
Volume of water flowing out of the system in unit time, dt, in x, y, z directions is:

  v     v     v  
Vx  x dx dxdydz  Vy  y dy  dydxdzVz  z dy  dzdxdy (3.7)
 
The law of the conservation of mass states that the sum of the gains or losses of mass flow
in the X, Y, and Z directions is equal to the loss or gain in mass of the groundwater stored
in the elemental control volume Per time unit and realizing that the change of the
groundwater mass in the control volume is equal to its volume times the change in density
and porosity n, we then obtain:
Volume inflowing in unit time - Volume out flowing in unit time = Change in storage
vx Vy Vz
(   )dxdydz  SsdHdxdydz (3.8)
x y z
vx Vy Vz dH
(   )  Ss. (3.9)
x y z dt

From Darcy’s Law:

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H H H
Vx   Kx ; Vy   Ky ; Vz   Kz (3.10)
x y z
Let us consider the unsteady state flow, in which there is a change of the mass of
groundwater in the control volume resulting from changes in the porosity of the rock
material and changes in the density of groundwater itself. By introducing the concept of
specific storage the change in the mass of groundwater can also be expressed in terms of a
change in hydraulic head. From (Eq. 3.10) including the specific storage term and for  =
constant:
 H  H  H dH
( Kx ) ( Ky ) ( Kz )  Ss. (3.11)
x x y y z z dt
 H  H  H dH
( Kx ) ( Ky ) ( Kz )   Ss. (3.12)
x x y y z z dt

For homogeneous and Isotropic Formation Material:

 H  H  H  Ss dH
( ) ( ) ( ) . (3.13)
x x y y z z K dt

 2 H  2 H  2 H  Ss dH
   . (3.13)
x 2 y 2 Z 2 K dt

Where: Ss = Volume of groundwater stored or released in a unit control volume for a 1m

increase or decline of the head h (1/m).
For Steady Flow:
Also combining Eq. (314) with Darcy’s law equation:
dH
0 (3.15)
dt
For K being constant in the directions X, Y and Z (Kx = Ky = Kz = K):
  2h    2h    2h 
 2    2    2   0 (3.16)
 X   Y   Z 
For one-dimensional steady flow in confined aquifer:
 2H   H   H 
 2   0 ;    0 ; c
 x  x  x   x 

Which has the solution for H as H  cx  c

H V V
But from Darcy’s Law ;  H   xC
x K K

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This indicates h decreases linearly along the flow direction
Flow in aquifer systems: The Darcy and continuity equations have been introduced as a
basis for the computation of groundwater flow. To apply these equations to practical cases
we can follow an analytical approach where by the combined Darcy and continuity
equations (for example Eq.3.11 & 3.16) are solved taking into account realistic boundary
conditions. Another approach is the numerical treatment of the basic equations which
forms the platform for the building of mathematical groundwater models.
As an application of the Laplace’s equation a simple steady state one dimensional
confined porous media flow is given below.
3.2.1 Groundwater flow in confined aquifer between two water bodies:
This is an application of the Laplace equation, a simple situation of steady state one-
dimensional confined porous media flow.
Fig. 3.4 shows a very wide confined aquifer of depth H connecting two water bodies. A
section of the aquifer of unit width is considered. The piezometric head at the upstream
end is H0 and at a distance X from the upstream end is h.
The relevant Darcy equation is: qx = -Kx (h / X).

Figure 3.4 Confined groundwater flow between two water bodies.

For one-dimensional flow in the X-direction only the continuity equation for steady flow
simplifies to:

(3.17)


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Integrating twice  H = C1 X + C2 (3.18)
The boundary conditions are:
(i) At X= 0, H = H0 hence, C2 = H0
 H  HL 
(ii) At X = L, H = HL hence, C1   0 
 L 
Up on substitution of the boundary conditions C1 and C2

 H  HL 
H  H0   0 X (3.19)
 L 
This is the equation of the hydraulic grade line, which is shown to vary linearly from H0 to
HL.
By Darcy Law, the discharge per unit width of the aquifer is:
 h   H  HL 
q  K    K *  0  (3.20)
 X   L 
 H  HL   H  HL 
 q  K 0  , And the total discharge with a thickness, H is Q  KH  0 
 L   L 
Where KH= Transmissivity (m2/s)
q K  H  HL 
Average groundwater velocity, V    0 
ne ne  L 
L
dS dS dX nL ne L2
To compute travel time, V  t   t  e 
dt V 0 V q K (H 0  H L )

Example 3.3: In order to determine the groundwater discharge, velocity and travel time,
hypothetical aquifer parametric values are given below. H0=20 m, HL=19 m, B=10 m,
K=10 m/d, L= 1000 m, ne=0.2. Find Q, q, V, and t.
 H  HL 
Solution: q  K  0  =10*1/1000=0.01 m/day
 L 
Q=q*H=0.01*10=0.1 m3/day
q 0.01
V   0.05m / day
ne 0.2

ne L 0.2 *1000
t   20,000days
q 0.01

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3.2.2 Groundwater flow in an unconfined aquifer
In unconfined aquifers the free surface of the water table, known as phreatic surface, has
the boundary condition of constant pressure equal to atmospheric pressure. These
boundary conditions cause considerable difficulties in analytical solutions of steady
unconfined flow problems by using the Laplace equation.
Consider an unconfined aquifer is above a horizontal impermeable base;
o The porous medium is homogeneous (K = constant);
o The aquifer receives uniform recharge (w = constant) on the top; w is defined as
amount of water entering to aquifer per unit length and width per unit time.
o The aquifer is bounded by two rivers of constant stages h0 and hL.
Although flow is two-dimensional in the cross-section, vertical flow velocity is much
smaller than the horizontal flow so that the flow is assumed to be one-dimensional
horizontal flow (Dupuit's assumption).
A simplified approach based on the assumptions suggested by Dupuit (1863) which gives
reasonably good results in relatively easier manner is described below.
i.) The curvature of the free surface is very small so that the streamlines can be assumed to
be horizontal at all sections.
ii.) The hydraulic grade line is equal to the free surface slope and does not vary with
depth.
iii.) The flow in aquifers is horizontal and that in aquitard is vertical.
As shown in Fig. (3.5). Further, there is a recharge at a constant rate of W (m3/s) per unit
horizontal area due to infiltration from the top of the aquifer. The aquifer is of infinite
length and hence one dimensional method of analysis is adopted. For a unit width of
aquifer:

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Figure 2.5 Unconfined groundwater flows between two water bodies

The water balance of the control volume taking the reference level of an aquifer at the
bottom of the aquifer and the height equals to saturated thickness of the aquifer is:
 (hq x )
hq x  wx  hq x  x (3.21)
x
Substituting Darcy’s equation in eq. (3.21) and rearranging terms we get:
  h  w
h    0 (3.22)
x  x  K
Equation (2.22) is the non linear governing groundwater flow equation in unconfined
aquifer.
  2 h 2  2w
Rearranging we get,  2   0
 x  K
 
Integrating this equation twice w.r.t x gives,
 w
h 2    x 2  C1 x  C 2 (3.23)
K
Where C1 and C2 are constants of integration and must be determined from the boundary
conditions.
The boundary conditions are:
(iii) At X= 0, h = h0 hence, C2 = h02

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 h0 2  hL 2  w
(iv) At X = L, h = hL hence, C1    L
 K
 L 
Thus substituting C1 and C2 in Eq. (2.23) gives:
 h0 2  hL 2 wL 
h  h0  
2 2
 x  w x 2 (3.24)
 L K  K

This is not equation of a straight line.

The unit width discharge in the aquifer will be:

h K  h0  hL wL 
2 2

q x   Kh     wx , Which is not a constant through the aquifer.

x 2  L K 

It is obvious that the discharge qx varies with X. At the upstream water body, X = 0 and
discharge to this left river will be:
 wL K h0 2  hL 2  K  h0 2  hL 2  wL
q L     
 2

 2 (3.25)
 2 2 L   L 
The (-) sign do mean flow is in opposite x-direction.
Discharge to this right river when x-L will be:
 wL K h0 2  hL 2  K  h0 2  hL 2  wL
q R     
 2

 2 (3.26)
 2 2 L   L 
When h0= hL, discharge to two rivers will be the same.
 wL 
qL  qR    And the total discharge to the two rivers, q L  q R  wL which is equals
 2 
to the total aquifer recharge.
The water table is thus not a straight line as shown by Eq. (2.24). The value of h will in
general rise above h0, reaches a maximum at X = d and falls back to hL at X = L as shown
in Fig (2.5). The value of d is obtained by equating dh/dX = 0 and qx=0, and is given by:

K  h0  hL wL 
2 2

qx     wx  0
2 L K 

L K  h0  hL 
2 2

d   
2 2  wL  (3.27)


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The location X = d is called the water divide. In Fig. (2.5), the flow to the left of the divide
will be to the upstream water body and the flow to the right of the divide will be to the
downstream water body.
In the case where there is no recharge to the aquifer, w = 0, water table (2.24) reduces to:

 h0 2  hL 2 
h  h0   x
2 2

L  (3.28)
 
This has a parabolic shape. In this case, the flow occurs only from the left river to the right
river with unit width discharge as:

K  h0  hL  h  hL h0  hL
2 2

qx  K 0 , This is the well-known Dupuit formula derived

2  L 
 2 L

in 1863. It indicates that the unit width discharge is a constant and can be obtained using
Darcy's law with average aquifer thickness, (h0 + hL)/2, and average hydraulic gradient,
(h0 - hL)/L.

Example 2.4: Two rivers located 1000 m apart fully penetrate a phreatic aquifer. The
parameters of the aquifer are: K= 0.5 m/d, w=1.4*10-4 m/day, h0=20 m, hL=18 m.
a.) Derive a formula for calculating a unit width discharge.
b.) Determine the location of d and the maximum height (hmax.) of the water divide.
c.) What is the unit width discharge of the aquifer to the right river?
Solution:
a

h K  h0  hL wL  0.5  20 2  18 2 1.4 *10 4 *1000 

2 2

q x   Kh     wx      1.4 *10 4 x
x 2  L K  2  1000 0.5 
-4
q= -0.051+1.4*10 x
At qx=0, x=0.051/1.4*10-4=364.3 m, which is the location of water divide.

L K  h0  hL  1000 0.5  20 2  18 2 
2 2

b. d         364.3m
2 2  wL  2 2  1.4 *10 *1000 
 4

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 h0 2  hL 2 wL 
hmax
2
 h0  
2
 d  w d 2
 L K  K

 20 2  18 2 1.4 *10 4 *1000  1.4 *10 4 * 364.3 2

hmax  20 2      437.14
2
4  * 364.3
 1.4 *10 *1000 0.5  0.5

hmax=20.9 m
 wL K h0 2  hL 2 
c. q R     =-0.051+1.4*10-4x= 0.089 m/d

 2 2 L 
Example 2.5: Two parallel rivers A and B are separated by a landmass as shown in the
figure below. Estimate the seepage discharge from river A to River B per unit length of
the rivers.

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Solution:
The aquifer system is considered as a composite of aquifers 1 and 2 with a horizontal
impervious boundary at the interface. This leads to the assumptions:
a) Aquifer 2 is a confined aquifer with K2 = 10 m/day,
b) Aquifer 1 is an unconfined aquifer with K1 = 25m/day. Consider a unit width of the
aquifers.
For the confined aquifer 2:
Here, h1 = 35.0 m, h2 = 15m, L = 3000 m, K2 = 10 m/day and B = 10 m.
 H  HL 
From Eq. (2.20), q  K  0 
 L 
q2 = 0.667 m3/day/meter width
For the unconfined aquifer 1:
Here, h1 = (35 - 10) = 25 m, h2 = (15 - 10) = 5 m, L = 3000 m, K1= 25 m/day

K  h  hL  h  hL h0  hL
2 2

From Eq. (2.25), q x   0 K 0

 q1 = 2.5 m3/day/meter width
2 L  2 L

Total discharge from river A to river B = q1 + q2  q = 0.667 + 2.5 = 3.167m3/day/ unit

length of the rivers
Example 2.6: An unconfined aquifer (K = 5m/day) situated on the top of a horizontal
impervious layer connects two parallel water bodies M and N which are 1200 m apart.
The water surface elevations of M and N measured above the horizontal impervious bed
are 10.00 m and 8.00 m. If a uniform recharge at the rate of 0.002m3/day/ m2 of horizontal
area occurs on the ground surface, estimate:
a) The water table profile
b) The location and elevation of the water table divide
c) The seepage discharges into the lakes and
d) The recharge rate at which the water table divides coincides with the upstream edge of
the aquifer and the total seepage flow per unit width of the aquifer at this recharge rate.

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Solution:
Consider unit width of the aquifer referring to the figure below: h0 = 10.00 m, R=w =
0.002 m3/day/m2, h1= 8.00 m, L = 1200 m, K = 5 m/day.
 h 2  h2 2 wL 
a) The water table profile: By Eq. (2.24), h 2  h1   1
2
  x  w x 2 h =
 L K  K

0.0004X2 + 0.45X +100

L K  h0  hL 
2 2

b) Location of water table divide: From Eq. (2.27), d     d =

2 2  wL 

562.5 m
At x = a=d = 562.5m, h = hm = height of water table divide
hm2 = - 0.0004 (562.5)2 + 0.45 (562.5) +100 = 226.56
hm = 15.05m
c) Discharge per unit width of the aquifer: Form Eq. (2.25)

K  h0  hL wL 
2 2

qx     wx
2 L K 

K  h0  hL wL 
2 2

At x =0, q1      1.125m 3 / d / m
2 L K 

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The negative sign indicates that the discharge is in (-X) direction i.e, into the water body
M.
At X = L, q2 = qL and from Eq (2.25) q2 = wL + q1
Hence, q2 = discharge into water body N = 0.002*1200 + (-1.125) = 1.275 m3/day/meter
width
d) When the distance of the water table divide d= 0: From Eq. (2.27),

L K  h  hL 
 
2 2

d    0   w  K2 h0 2  hL 2
2 2  wL  L

 w = 5/12002(102 - 82) = 1.25*10-4m3/day/m2
Since d = 0, q1 = 0 and by Eq. (2.24) q2 = qL = w *L = 1.25*10-4 *1200 =
0.15m3/day/meter width
3.3 Regional and local groundwater flow
3.3.1 Elementary flow system
The simplest flow system consists of a rectangular spatially-bounded region with
impermeable sides and bottom and one infiltration/recharge area and one
exfiltration/discharge area which are separated by a mid-line and connected by a single
flow branch. In the steady state flow conditions the boundaries of the recharge and
discharge areas are fixed as well as the position of the mid-line. Under non-steady state
flow conditions due to variations in recharge or discharge the recharge- and discharge
areas will shrink or expand and the boundary line will shift on the topographic slope. The
position of the stream lines will shift than as well.
Groundwater flow system
A groundwater flow system is a subsystem of a hydrological (water) system. It is located
in a geographically distinct domain of the subsoil, which it fills with a pattern of flow lines
from one coherent infiltration- or recharge area by one or more flow branches to one or
more exfiltration/discharge areas. The groundwater flow system includes the water and the
part of a flow medium which it occupies, together with its biotic communities and all
associated natural and artificial physical, chemical, biological characteristics and
processes.
Infiltration- or recharge area

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Each spatially coherent infiltration/recharge area feeds one or more flow branches of a
single flow system. A common infiltration area is subdivided by groundwater divides if
more flow branches are fed from the same area. A composite infiltration/recharge area
may consist of a mosaic of different planar, linear or point recharge elements with
different infiltration/recharge rates, e.g.: leaky, infiltrating surface water systems,
precipitation-fed recharge through the unsaturated zone, artificial recharge by different
types of irrigation systems, recharge wells.
Exfiltration/discharge area
Each spatially coherent exfiltration/discharge area is fed by one or more flow branches
from one or more different flow systems e.g. recharge areas. A composite exfiltration/
discharge area may consist of a mosaic of different planar, linear or point-discharge
elements with different exfiltration/discharge rates, e.g.: draining surface water systems
(sea, lake, river, canal, ditch), springs, seepage zones, evaporating saline soils,
phreatophytic vegetation, groundwater abstraction schemes, etc.
Hierarchy of flow systems
In nature the available subsurface flow will contain a number of different flow systems of
different orders of magnitude and relative, nested hierarchical order. Local systems are
nested in sub-regional systems, sub-regional systems in turn are nested in regional
systems.
Theoretically three types of flow systems may occur in a basin: local, intermediate and
regional as shown in figure (2.6). This original terminology by Toth (local, sub regional
and regional) relates to the relative position of flow systems in space but is not indicative
of their actual size (extent and penetration depth). Thus a local flow system might be just
as well of large extent and penetrate deeply or be very small and shallow, depending upon
the topography and permeability- scales.
Local flow systems
In local systems flow lines connect a topographic high acting as a recharge/infiltration
area with the immediately adjacent topographic low and the corresponding
discharge/exfiltration area. In case of local flow systems the in- and exfiltration areas are
juxtaposed and flow takes place via phreatic groundwater, implying that no other flow
systems are positioned on top of the system.

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'Local" bears no relation with the size and scale of the systems. Hence, these flow systems
may vary from shallow small-sized rainwater lenses under minor topographic
culminations with seasonally varying shape and travel times in the order of weeks or
months to large systems with dimensions of many kilometers and travel times in the order
of hundreds or thousands of years, but in which the discharge areas are still juxtaposed to
the recharge area without smaller nested systems on top.
Sub-regional (intermediate) flow systems
A sub-regional flow system has its origin also in a topographic high acting as a
recharge/infiltration area but it has flow branches to several discharge/exfiltration areas
which are separated from each other and located at some distance from the recharge area.
A local flow branch originating in the outer zone of the recharge/infiltration area feeds the
directly adjacent local discharge/exfiltration area. One or more deeper and farther reaching
flow branches originating in the central part of the recharge/infiltration area feed one or
more distant discharge/exfiltration areas which crop out as "windows" between other
hierarchically nested, overlying local flow systems. Again the scale, size and depth of the
flow may differ widely.
3.3.2 Regional flow system
Regional flow systems are at the top of the hierarchical organization and thereby the
highest level of scale. All other flow systems are nested within the regional one. A
regional flow system originates in the main and highest topographical culmination and
may have local, intermediate and regional flow branches, which are fed successively from
the periphery, the middle parts and the core of the regional recharge/infiltration area. The
local flow branches end up in them discharge/exflltration areas in the topographic lows or
breaks in slope immediately adjacent to the regional topographic high. The intermediate
flow branches discharge into discharge/exfiltration windows in still lower topographic
depressions farther away. The regional flow branches finally are the deepest penetrating
and farthest reaching branches which end up as groundwater discharge/exfiltration
windows in the regionally lowest topographic locations. Note that in the example of figure
1.7 the configuration of the topography/hydraulic head is such that the particular regional
flow system in it has only one regional flow branch with a regional discharge window and

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one local flow branch but no intermediate flow branch, e.g. sub-regional discharge
window.
In many cases the exfiltrating groundwater flow branches are connected to and feed
seepage zones and or surface water networks, especially in humid climates. In
topographically closed basins and under semi-arid and arid conditions groundwater
discharge areas may end in and be responsible for saline soils, playa lakes, phreatophytic
vegetation, etc.
The higher the local topographic relief and the vertical permeability, the greater is the
importance of local systems. The flow lines of large, unconfined flow systems do not
cross major topographic features. Semi-stagnant bodies of groundwater can occur in zones
where branches of different flow systems converge or diverge. Motion of groundwater is
sluggish or nil under extended flat areas with little chance of the water being freshened.
Regional flow systems show often the following properties:
1. Groundwater discharge will tend to be concentrated in major valleys;
2. Recharge areas are invariably larger than discharge areas,
3. In hummocky terrain, numerous sub-basins are superposed on the regional system;
4. Buried aquifers tend to concentrate flow toward the principal discharge area, having a
limited effect on sub-basins, and not outcrop to produce artesian flow conditions;
5. Stratigraphic discontinuities can lead to distributions of recharge and discharge areas
that are difficult to anticipate and that-are largely independent of the water table
configuration.

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Figure 2.6: Theoretical Flow pattern and boundary of flow systems

3.3.3 Regional Groundwater Flow Analysis
Regional groundwater can be analyzed using the basic groundwater flow equations. We
will assume that the groundwater basin is composed of one or more aquifer systems. Local
groundwater flow problems such as the flow to canals or rivers, the flow to wells, or the
flow to a building pit will be discussed.

Some of the methods that one can use to analyze regional groundwater flow in these
systems are the following:
 Methods primarily based on groundwater head contour maps
 Methods focusing on the compilation of flow nets
 Methods based on the application of groundwater flow models
Groundwater head contour maps
Whatever method we follow for our analysis the compilation of groundwater head contour
maps is a crucial activity. Groundwater head contour maps are maps, which show the
projections of the equipotential planes of groundwater heads in the aquifers. These maps
are also referred to as isohypse maps.

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Figure 3.7 Regional Groundwater flow

Using groundwater head contour maps we can determine the direction of groundwater
flow. It is known that groundwater moves perpendicular to equipotential lines. Therefore
this flow is also perpendicular to the groundwater head contours on the contour maps. It is
also known that groundwater moves from locations with a high groundwater head to
locations with a lower head. On the basis of these criteria the flow directions can be
indicated.

A. Simple Computations with Contour Maps:

Fig. 2.8 shows a cross-section indicating an aquitard sandwiched between two aquifers.
The section shows the groundwater heads in the upper and the lower aquifer. To compute
the average flow for a surface area, A through the aquitard the average difference in
hydraulic head, (h) should be estimated by subtracting groundwater heads for the upper
and lower aquifer. The groundwater head contour maps for both aquifers can be used for
this purpose. The area, A can be scaled off from the contour map. Also, the resistance, C
can be evaluated from pumping tests. It is emphasized that we work with average
groundwater head differences for the area A, which implies that we compute an average

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flow. In particular if we select a large area, A then within the area itself there may be a
substantial variations in vertical flow.
The volume of groundwater stored or released in a confined or semi-confined aquifer can
be computed by:
Qgws = A*S*(h / t) (3.29)
Where:
Qgws = Stored or released flow in the aquifer (m3/day),
A = Surface area of the aquifer (m2),
S= Storage coefficient (dimensionless),
h = difference in hydraulic head (m),
t = discrete length of time (day).
The expression for the computation of volumes of groundwater stored or released in an
unconfined aquifer is:
Qv = A*Sy *(h / t) (3.30)
Where:
Sy = specific yield (dimensionless)

Figure 3.8: Vertical flow through an aquitard

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To compute the flow in the aquifer at a selected location we can consider two adjoining
groundwater head contour lines to calculate the hydraulic gradient (h/S). The width, w
of the aquifer can be scaled off from the map. Additionally the value of the
Transmissivity, T can be evaluated from pumping tests.
To formulate an expression for the computation of the flow through the aquitard we will
consider the Darcy’s law equation in the vertical (Z) direction. Taking the hydraulic
gradient in the vertical direction in a discrete form the equation can be written as:
qz = -Kz *(h/Z) (3.31)
Then, Z can be replaced by the thicknesses D of the aquitard.
qz = (-Kz / D)*h = -h / C (3.32)
This expresses the specific discharge through the aquitard which is defined for a surface
area of 1m2. The total flow through an aquitard can be calculated from:
Qz = -A*(h / C) (3.33)
Where:
Qz = total groundwater flow through the aquitard (m3/day)
A = surface area (m2), h = difference in hydraulic head (m)
C = vertical resistance of the aquitard (days)
B. Flow net Analysis:
Flow nets for aquifer systems can be prepared on the basis of groundwater head contour
maps. For this purpose groundwater flow lines or streamlines are drawn perpendicular to
the contour lines on these maps (Fig. 3.9). We will find that we end up with a map
showing a grid of squares or rectangles. Such a grid is referred to as a flow net. For each
of the aquifers in an aquifer system we can make a map showing a flow net composed of
groundwater head contour lines and flow lines.

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Figure 3.9 Flow net near a river and subsurface moisture zone before and after infiltration
Flow nets have a characteristic shape at the boundaries of an aquifer system. Figure 2.10
shows the flow nets at three common types of boundaries: a) Impermeable boundaries b)
Constant head boundaries and c) Groundwater table boundaries.

The following comments can be made:

a) Impermeable boundary: This could be the boundary with an impermeable geological
formation like un-fractured igneous rock. Since there can be no flow component across
the boundary flow lines can only run parallel to the boundary while the groundwater
head contour lines are perpendicular to this boundary.
b) Constant head boundary: This could be the boundary with open water such as a river, a
lake or the sea. If we assume that the open water level is constant then the boundary
can be considered as a groundwater head contour line. The flow lines are
perpendicular to this open water boundary.
c) Groundwater table boundary: This is a boundary, which may be influenced by
recharge or discharge or none of these phenomena at all. First consider the case of
recharge or discharge. The flow lines and the groundwater head contour lines one both
at an angle to the boundary. In case there is no recharge or discharge then the
groundwater table acts as an impermeable boundary: the flow lines are parallel to the
table and the groundwater head contour lines are perpendicular.

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Figure 3.10 Flow nets at boundaries

The flow lines are in fact the borderlines of so called stream tubes. Groundwater which is
flowing through an individual stream tube is not losing, neither gaining groundwater from
the neighboring tubes. By summation of the flow through individual stream tubes the total
flow through an aquifer or aquitard can be calculated. The computation of the groundwater
flow in this way is more precise than to estimate it from groundwater head contour maps
only. This is in particular true for complex groundwater contour patterns where the
contour lines are not straight and parallel.

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Figure 3.11 Flow net computations

Expressions for flow net computations can be formulated. Let us consider a flow net for
an aquifer and try to find an expression for the flow through a stream tube. Using the
Darcy equation the groundwater flow through the tube can be approximated by taking into
consideration the hydraulic gradient for a discrete distance, the width of the stream tube
and the depth of the aquifer as follows:
qs = K*h*Ws*(h / S) (3.34)
Where:
qs = flow through the stream tube (m3/day),
K = coefficient of permeability of the aquifer (m/day),
h = aquifer thickness (m),
Ws = width of the stream tube (m),
h = difference in hydraulic head (m),
S = discrete distance (m)
This expression can be further simplified and evaluated. First of all we can replace the
product K*h by the aquifer Transmissivity T. Secondly, we can also simplify the
expression by constructing the flow lines in the flow net in such a way that, the width of
the stream tube is equal to the distance between selected contour lines: Ws = S. Finally,

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if there are n stream tubes for the whole width of the aquifer then, for constant T, the total
flow through the aquifer is:
Q = T*Nf/Nd (3.35)
Fig. 3.11 presents a flow net, which demonstrates the flow net computation. The flow net
relates to an aquifer system consisting of a single fully confined aquifer bounded by
impermeable formations. To compute the total flow through the aquifer the distance in
hydraulic head (h) is determined by subtracting the groundwater heads of adjacent
groundwater head contour lines. The number of steam tubes n can be counted from the
flow net. The transmissivity, T can best be assessed from the evaluation of pumping tests.
If all the variables are known then equation (3.37) can be used to compute the total flow
through the aquifer.
C. Groundwater flow models:
Regional groundwater flow can be modeled with numerical models. Before 1980’s,
techniques based on physical models were quite extensively used to simulate regional
flow in groundwater systems. From 1980’s on wards numerical models replaced the
physically based models. Computerized numerical models are superior to calculation
methods based on simple computations and flow nets. However these latter techniques
remain useful as they give quick estimates on flow rates and provide inputs for the
numerical models. Groundwater flow rates and hydraulic heads can be computed at the
cells of a model grid that covers part of the groundwater system. These models are also
used for the optimization of transmissivity, storage coefficients, recharge rates, or other
flow parameters. These models are also used to simulate the effect of groundwater
abstractions or other human activities on groundwater system.
Some examples of groundwater flow models: MODFLOW, SIMGRO, MICROFEM,
3DFEMFAT, FEFLOW, SLAEM, WinFLOW etc.
3.3.4 Local Groundwater Flow
Regional groundwater flow occurs in groundwater basins, which usually occupy large
areas. Regional flow may be influenced by local groundwater flow phenomena. For
example, the construction of canals may influence the regional natural flow. Another
example concerns wells: pumping from wells may also affect the regional flow and this
can often be observed on groundwater head contour lines parallel to the canals on the

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maps. Around wells or well fields the contour lines may follow a circular or ellipsoidal
pattern.
Computations on local groundwater flow phenomena can also be done in the same way as
regional groundwater flows. Estimates on the local flow of groundwater can be obtained
using groundwater head contour maps, flow nets or numerical groundwater models.
Traditionally, however, these local flow problems were also solved by analytical methods.
In these methods the differential Darcy and Continuity equations are solved in a direct
way; either separately or combined. We had briefly discussed the analytical methods by
presenting cases of the flow between rivers or two water bodies and we will discuss the
flow to wells in chapter 4.
3.4 One, two and three-dimensional flow in different aquifers
For isotropic soils one can directly get solution for the Laplace’s equation by analytical
method, Experimental method or by graphical method. The solution of Laplace’s
equation gives two sets of curves called equipotential lines and flow lines, which are
perpendicular to each other.
Consider the continuity equation for a steady three dimensional flow through anisotropic
  2h    2h    2h 
soil we have: K x    K y  2   K z  2   0 3.36
 X  Y   Z 
2

Meaning the flow is considered in the x, y and z directions. This is not a Laplace equation
therefore it is very difficult to draw a flow net. For two dimensional flows, the flow
component in the z-direction is considered zero. This result in following equations
 2h    2h 
K x    K y  2   0 3.37
 X  Y 
2

This is not a Laplace equation therefore it is very difficult to draw a flow net. However
this equation can be converted in to the Laplace’s equation as follows.
Kx   2h    2h 
    2   0
 X   Y 
2
Ky

This can be transformed by making substitution as follows.

  2h    2h 
  
 X 2   Y 2   0
 t   

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This is the Laplace equation for the transformed coordinates Xt and Y.
For one dimensional flow, only the flow component in the x-direction is considered. This
  2h    2h 
result in K x     0
2 
3.38
 X   X 
2

Questions:
1. What is the law of Darcy? What are its limitations in groundwater flow?
2. Why it is essential for a water resources engineer to study about unsaturated zone?
3. Derive the governing three dimensional groundwater flow equation.
4. What is the hierarchy of flow system?
5. What are stream tubes, equipotential lines and flow nets?

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CHAPTER FOUR
HYDRAULICS OF WELLS
4.1 General
Wells form the most important mode of groundwater extraction from an aquifer. While
wells are used in a number of different applications, they find extensive use in water
supply and irrigation engineering practice.
Consider the water in an unconfined aquifer being pumped at a constant rate from a well.
Prior to the pumping, the water level in the well indicates the static water table. A
lowering of this water level takes place on pumping. If the aquifer is homogeneous and
isotropic and the water table is horizontal initially, due to the radial flow into the well
through the aquifer the water table assumes a conical shape called inverted cone of
depression. The dropped line in the water table elevation at any point from its previous
static level is called drawdown curve. The base of the cone where original water table lies
is called circle of influence and its radial extent radius of influence (Fig. 4.1). At constant
rate of pumping, the drawdown curve develops gradually with time due to the withdrawal
of water from storage.
This phase is called unsteady flow as the water level at a given location near the well
changes with time. On prolonged pumping, an equilibrium state is reached between the
rate of pumping and the rate of inflow of groundwater from the outer edges of the zone of
influence. The drawdown surface attains a constant position with respect to time when the
well is known to operate under steady-flow conditions. As soon as the pumping is
stopped, the depleted storage in the cone of depression is made good by groundwater
inflow into the zone of influence. There is a gradual accumulation of storage till the
original (static) level is reached. This stage is called recuperation or recovery and is an
unsteady phenomenon. Recuperation time depends upon the aquifer characteristics.
Changes similar to the above take place to a pumping well in a confined aquifer also, but
with the difference that, it is the piezometric surface instead of the water table that
undergoes drawdown with the development of the cone of depression. In confined aquifers
with considerable piezometric head, the recovery into the well takes places at a very rapid
rate.

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Figure 4.1a: Unconfined aquifer when wells are pumped at constant rate

Figure 4.1b: Confined aquifer when wells are pumped at constant rate

4.2 Steady and unsteady states of flow in different aquifers

Steady Flow into a Well: steady-state groundwater problems are relatively simpler.
Expressions for steady-state radial flow into a well under both confined and unconfined
aquifer conditions are presented below.

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A. Steady flow to a well in confined aquifer: Fig. 4.2 shows a well completely
penetrating a horizontal confined aquifer of thickness B. Consider the well to be
discharging a steady flow, Q. The original piezometric head (static head) was ho and the
drawdown due to pumping is indicated below. The piezometric head at the pumping well
is hw and the drawdown Sw.

Figure 4.2: Radial flow to a well operating in a confined aquifer

At a radial distance r from the well, if h is the piezometric head, the velocity of flow by
Darcy’s law is: qr = K (dh/dr). The cylindrical surface through which this velocity occurs
is 2πrb. Hence by equating the discharge entering this surface to the well discharge, Q =
(2πrb)*[K (dh/dr)].  (Q/2πKb)*(dr/r) = dh. Integrating between limits r1 and r2 with the
corresponding piezometric heads being h1 and h2, respectively:
(Q/2πKb)*ln(r2/r1) = h2 - h1

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2Kbh2  h1 
Q (4.1)
r 
ln  2 
 r1 
This is the equilibrium equation for the steady flow in a confined aquifer popularly known
as Theim’s equation.
If the drawdowns S1 and S2 at the observation wells are known, then by noting that
S1 = h0 - h1, S2 = h0 - h2 and Kb = T, Eq. (4.1) will read as:
2T S1  S 2 
Q (4.2)
r 
ln  2 
 r1 
Further, at the edge of the zone of influence, S= 0, r2 = R and h2 = h0 at the well wall r1 =
rw, h1 = hw and S1 = Sw. Eq (4.2) would then be
R
Q ln  
2TS w  rw 
Q K (4.3)
R 2bH  hw ) 
ln  
 rw 
Equation (4.2) or (4.3) can be used to estimate T, and hence K, from pumping tests. For
the use of the equilibrium equation, Eq. (4.2) or its alternative forms could be used and it
is necessary that the assumption of complete penetration of the well into the aquifer and
steady state of flow are satisfied.
Example 4.1: A 30 cm diameter well completely penetrates a confined aquifer of 15 m
thickness and pumped at a steady rate of 30 lps. Under steady state of pumping the
drawdown at the radial distance of 10 m and 40 m are 1.5 m and 1 m respectively.
Compute the radius of influence (R), permeability (k), and drawdown (Sw) at the well.
Solution:
2T ( S1  S 2 ) 2 *15 * K * (1.5  1)
Q   K  8.83 *10 4 m / s
r   
40
ln  2  ln 
 r1   10 

T=KB=8.83*10-4*15=1.32*10-2 m2/s

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2KB( S w  S 2 ) 2 *15 * 8.83 *10 4 * ( S w  1)
Q   S w  3.02m
 r2   40 
ln   ln  
 w
r  0.15 

2KB * S w 2 *15 * 8.83 *10 4 * (3.02)

Q   R  634m
R  R 
ln   ln  
 rw   0.15 
Example 4.2: A 30 cm diameter well completely penetrates a confined aquifer of
permeability 45 m/day. The length of the strainer is 20 m. Under steady state of pumping
the drawdown at the well was found to be 3.0 m and the radius of influence was 300 m.
calculate the discharge.
Solution:
In this problem, referring to Fig. 4.2, rw = 0.15 m, R = 300 m, Sw = 3.0 m, b = 20 m, K =
45 m/d (60*60*24) = 5.208 * 10-4m/s, T= Kb = 10.416*10-3 m2/s, By Eq. (4.3)
2TS w 2 *10.416 *10 3 * 3
 Q   0.02583m 3 / s  1550lpm
R  300 
ln   ln  
 rw   0.15 

Example 4.3: For the well in the example (4.1), calculate the discharge: a) if the well
diameter is 45cm and all other data remain the same, b) if the drawdown is increased to
4.5 m and all other data remain unchanged.
Solution:
2TS w  R 
a) Q  , as T and Sw are constants  ln 
r 
 , and putting R = 300 m,
R Q1
  w2 
ln   Q2  R
ln 


 rw  r
 w1



Q1 = 1550litres/minute, rw1 = 0.15m, rw2 = 0.225m.  Q2 = 0.02728

m3/s=1637litres/minute. Note that the discharge has increased by about 6% for 50%
increase in the well diameter.
b) Q = (2T*Sw)/ ln(R/rw), QSw for constant T, R and rw. Thus Q1/Q2 = Sw1/ Sw2  Q2
= 2352 liters/minute. Note that the discharge increases linearly with the drawdown when
other factors remain constant.
B. Steady flow to a well in an unconfined aquifer: Consider a steady flow from a well
completely penetrating an unconfined aquifer. In this case because of the presence of a

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curved free surface, the streamlines are not strictly radial straight lines. While a streamline
at the free surface will be curved, the one at the bottom of the aquifer will be a horizontal
line, both converging to the well. To obtain a simple solution Dupuit’s assumptions as
discussed in the previous section are made. In the present case these are:
a) For small inclinations of the free surface, the streamlines can be assumed to be
horizontal and the equipotential are thus vertical.
b) The hydraulic gradient is equal to the slope of the free surface and does not vary with
depth. This assumption is satisfactory in most of the flow regions except in the
immediate neighborhood of the well.
Consider the well of radius, rw penetrating completely extensive unconfined horizontal
aquifers as shown in Fig.4.3. Water is pumped out from the well at a constant discharge, Q
for a long time. According to Darcy’s law, at any radial distance r, the velocity of radial
flow into the well is: qr = K (dh/dr). Where h is the height of the water table above the
aquifer bed at that location. For steady flow, by continuity: -
 dh   Q  dr  , Integrating between limits r and r
Q  Aq r  2rh * K  or , hdh     1 2
 dr   2K  r 
where the water table depths are h1 and h2 respectively and on rearranging:
 Q  r 2 dr  h2 2  h1 2  r 
  Q ln  2 
h2
 hdh   
 2K  r1 r
 
 2  2K  r 
 1
 
h1

Q

K h2 2  h1 2  (4.4)
r 
ln  2 
 r1 

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Figure 4.3 Radial flows to a well in an unconfined aquifer

Eq. (4.4) is the equilibrium equation for a well in an unconfined aquifer. As at the edge of
the zone of influence of radius R, H = saturated thickness of the aquifer, Eq. (4.4) can be
written as:

Q

K H 2  hw 2  (4.5)
R
ln  
 rw 
Where:
hw = depth of water in the pumping well of radius rw.

Equations (4.4) and (4.5) can be used to estimate satisfactorily the discharge and
permeability of the aquifer by using field data. Calculations of the water-table profile by

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Eq. (4.4) however will not be accurate near the well because of Dupuit’s assumptions. The
water-table surface calculated by Eq. (4.4) which involved Dupuit’s assumption will be
lower than the actual surface. The departure will be appreciable in the immediate
neighborhood of the well (Fig. 4.3). In general, values of ‘R’ are in the ranges of 300 to
500m and can be assumed depending on the type of aquifer and operating conditions of a
well. Due to difficulty in obtaining the radius of influence accurately, usually Sichardt’s
formula is used to estimate it. R=3000*Sw*K, where R= radius of influence (m),
Sw=drawdown in the well, and K=Coefficient of permeability (m/s).
As the logarithm of R is used in the calculation of discharge, a small error in R will not
seriously affect the estimation of Q. It should be noted that it takes a relatively long time
of pumping to achieve a steady state in a well in an unconfined aquifer. The recovery after
the cessation of pumping is also slow compared to the response of an artesian well which
is relatively fast.
Approximate equations: If the drawdown at the pumping well Sw = (H - hw) is small
relative to H, then: H2 - hw2 = (H + hw)*(H - hw)  2hwSw, Noting that T = KH, Eq. (3.5)
can be written as:
2TS w
Q (4.6)
R
ln  
 rw 
Which is the same as Eq. (4.3). Similarly Eq. (4.4) can be written in terms of S1 = (H -h1)
and S2 = (H - h2) as:
2T S1  S 2 
Q (4.7)
r 
ln  2 
 r1 
Equation (3.6) and (4.7) are approximate equations to be used only when Eq. (4.4) or (3.5)
cannot be used for lack of data. Equation (3.6) over estimates the discharge by [1/2 (H/Sw
- 1)] % when compared to Eq. (4.5).
Example 4.4: A 30 cm well completely penetrates an unconfined aquifer of saturated
depth 40m. After a long period of pumping at a steady rate of 1500 lpm, the drawdown in
two observation wells 25 and 75m from the pumping well were found to be 3.5 and 2.0 m,

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respectively. Determine the Transmissivity of the aquifer. What is the drawdown at the
pumping well?
Solution:
a) Q = 1500*10-3/60 = 0.025m3/s, h2 = 40-2 = 38m, r2 = 75m, h1 = 40-3.5 = 36.5m, r1 =
r 
Q ln  2 
25m. Substituting these values in Eq. (3.4) and solving for K results in, K   r1 
 h2 2  h12  
K = 7.823*10-5 m/s  T = KH = 7.823*10-5*40 = 3.13*10-3 m2/s

c) At the pumping well, rw = 0.15m, and solving Eq. (3.4) for hW gives, hW = 28.49 m
and hence, drawdown at the well, Sw = 11.51m.

r   75 
Q ln  2  0.025 ln 
hw  h2 
2  rw 
 38 
2  0.15 
 28.49m
K  * 7.82 *10 5

Example 4.5: The following observation was made on a 30cm diameter well in an
unconfined aquifer. Rate of pumping was 1500lpm, Test wells are at a distance of 30m
and 60m with drawdowns of 1.5 m and 0.6 m. The depth of water table in the well before
pumping was 40m. Determine the radius of influence (R) and coefficient of permeability
(K), and Sw.
Solution:
h1=40m-1.5 m=38.5 m and h2=40 m-0.6 m=39.4 m

Q

K H 2  h1 2  and; Q  K H 2
 h1
2

R R
ln   ln  
 r1   r1 

Equating these two,


K H 2  h1 2   K H  h2
2 2
  40  38.5 2 40 2  39.4 2
2

R R R R
ln   ln   ln   ln  
 r1   r2   30   60 

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R
ln  
By collecting similar terms,   
30 117.75
 2.471
 R  47.64
ln  
 60 
2.471(lnR-ln60) =lnR-ln301.471 lnR=2.471*ln60-ln30R=96 m

R  96 
Q ln   0.025 ln  
K  r1    30   7.86 *10 5 m / s

 H  h1
2 2
 
 40  38.5 2
2

R  96 
Q ln   0.025 ln  
hw  H 2   rw   40 2   0.15   30.75m
K  * 7.86 *10 5
Sw=H-hw=9.25 m

C. Unsteady flow In a Confined Aquifer: When a well in a confined aquifer starts

discharging, the water from the aquifer is released resulting in the formation of a cone of
depression of the piezometric surface. This cone gradually expands with time till
equilibrium is attained. The flow configuration from the start of pumping till the
attainment of equilibrium is in unsteady regime.
Figure 4.5 Unsteady flow In a Confined Aquifer
In polar coordinates, to represent the radial flow into a well, takes the form
 2 h 1  h  S  h 
     (4.8)
r 2 r  r  T  t 
Making the same assumptions as used in the derivation of the equilibrium equation (4.8),
Theis (1935) obtained the solution of this equation as:

Q e u
4T u u
s  h0  h  du (4.9)

Where: S = h0 – h; drawdown at a point distance r from the pumping well, h0 = Initial

constant piezometric head, Q = constant rate of discharge, T = transmissibility of the
aquifer, u = a parameter = r2S/ (4Tt), S = Storage coefficient and t = time from start of

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pumping. The integral on the right-hand side is called the well function, W (u) and is
given by:

 e u  u2 u3 u4
W u     du  -0.5772 - lnu  u -  -  ... (4.10)
u 
u 2 * 2! 3 * 3! 4 * 4!

Table of W (u) are available in literature. Values of W (u) can be also easily calculated by
the series (Eq.4.10) to the required number of significant digits which rarely exceed 4. For
small values of u (u 0.01), only the first two terms of the series are adequate.

The solution of Eq. (4.9) to find the drawdown S for a given S, T, r, t and Q can be
obtained in a straight forward manner. However, the estimation of the aquifer constants S
and T from the drawdown v/s time data of a pumping well, which involve trial - and error
procedures, can be done either by a digital computer or by semi-graphical methods such as
the use of Type Curve, or by Chow’s method.

Q Q u2 u3 u4
s W (u )  [-0.5772 - lnu  u -  -  ...] (4.11)
4T 4T 2 * 2! 3 * 3! 4 * 4!
For small values of u (u 0.01), Jacob (1950) showed that the calculations can be
considerably simplified by considering only the first two terms of the series of W(u),
Eq.(4.10). This assumption leads Eq. (4.9) to be expressed as:
Q  r2S  Q  Tt 
s [-0.5772 - ln    * ln  2.25 2  (4.12)
4T  4Tt  4T  r S

If S1 and S2 are drawdown’s at times t1 and t2:

Q t 
s1  s 2  ln  2  (4.13)
4T  t 1 

If the drawdown S is plotted against time t on a semi-log paper, the plot will be a straight
line for large values of time. The slope of this line enables the storage coefficient S to be
determined. From Eq. (4.12) when S = 0,

2.25Tt 0 2.25Tt 0
2
1 S  (4.14)
r S r2

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In which t0 = time corresponding to zero drawdown obtained by extrapolating the straight-
line portion of the semi-log curve of S vs t. It is important to remember that the above
approximate method proposed by Jacob assumes u to be very small less than 0.01 to avoid
large errors.

Example 4.6: A 30-cm well penetrating confined aquifer is pumped at a rate of 1200lpm.
The drawdown at an observation well at a radial distance of 30m is as follows:
time from start (min) 1 2.5 5 10 20 50 100 200 500 1000
drawdown (m) 0.2 0.5 0.8 1.2 1.8 2.5 3.1 3.7 4.4 5.0
Calculate the aquifer parameters S and T.
Solution

Time-drawdown plot
1
0.00, 0.36
0
0 0.5 1 1.5 2 2.5 3 3.5
-1
Drawdown, S (m)

1.30, -1.80
-2
1.70, -2.50
-3 2.00, -3.10
2.30, -3.70
-4
2.70, -4.40
-5 3.00, -5.00

-6
Time since pumping started, t (min)

Figure 4.4 Time-drawdown plot

The drawdown is plotted against time on a semi-log plot as shown in the figure above. It is
seen that for t>10minutes the drawdown values describe a straight line. A best-fitting
straight line is drawn for data points with t>10minutes. From this line, when S=0, t =t 0 =
2.5min. = 150s, S1 = 3.1m at t1 = 100min, S2 = 5.0 m at t2 = 1000 min. Also, Q = 1200 lpm
= 0.02m3/s. Substituting these values in Eq. (4.13) and solving for T results in T =
1.929*10-3 m2/s. And from Eq. (3.14), S = 7.23*10-4.

Q t  0.02
T ln  2   ln(60000 / 6000)  1.929 *10 3 m 2 / s
4 ( s1  s 2 )  t 1  4 *1.9

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2.25Tt 0 2.25 *1.929 *10 3 *150
S   7.23 *10 -4 m
r2 0.15 2

Example 4.7: A well is located in a 25 m confined aquifer of permeability 30 m/day and

storage coefficient 0.005. If the well is being pumped at the rate of 1750lpm, calculate the
drawdown at a distance of a) 100m and b) 50m from the well after 20h of pumping.
Solution:
 r2S  100 2 * 0.005
a) T = KB = 30/86400*25 = 8.68*10-3m2/s, u     3
 0.02
 4Tt  4 * 8.68 *10 * 20 * 3600
Using Theis method and calculating W (u) to four significant digits, W (u) = 3.3548
 S100 = Q/ (4T)*W (u) = 0.897m.
Q 0.0292
s100  W(u)  * 3.3548  0.897m
4T 4 * 8.68 *10 3
 r2S  50 2 * 0.005

b) r = 50m  u   
 3
 0.005 u = 0.005<0.01,  W(u) =
 4Tt  4 * 8.68 *10 * 20 * 3600
-0.5772 - ln(0.005) + 0.005 = 4.726. 
Q 0.0292
s50  W(u)  * 4.726  1.264m S50 = 1.264m.
4T 4 * 8.68 *10 3

Well Loss: In a well pumping artesian well, the total drawdown at the well S w, can be
considered to be made up of three parts:

a) Head drop required to cause laminar porous media flow, called formation loss, SwL.
b) Drop of piezometric head required to sustain turbulent flow in the region nearest to the
well where the Reynolds number may be larger than unity, Swt; and
c) Head loss through the well screen and casing, Swc.

Of these three, SwL  Q and Swt and Swc  Q2, Thus:

Sw = BQ + CQ2 (4.15)

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Where B and C are constants for given well (Fig.3.5). While the first term BQ is the
formation loss the second term CQ2 is termed as well loss.
R
ln  
B  w
r
2T
The magnitude of a well loss has an important bearing on the pump efficiency.
Abnormally high value of well loss indicates clogging of well screens, etc. and requires
immediate remedial action. The coefficients B and C are determined by pumping test data
of drawdown for various discharges.

Figure 4.5 Definition sketch for well loss

Specific Capacity: the discharge per unit drawdown at the well (Q/Sw) is known as
specific capacity of a well and is a measure of the performance of the well. Its reciprocal is
called specific draw down. For a well in a confined aquifer under equilibrium conditions
and neglecting well losses, Q/Sw = 2T/ln(R/rw)  Q/Sw  T. However, for common case
of a well discharging at a constant rate Q under unsteady drawdown conditions, the
specific capacity is given by:

Q 1 (4.16)

Sw  1  R 
 ln 
r   CQ 
 2T  w 

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Where t = time after the start of pumping. The term CQ2 is to account for well loss. It can
be seen that the specific capacity depends upon T, S, t, rw and Q. Further, for a given well
it is not a constant but decreases with increases in Q and t.
4.3 Partially penetrating wells and multiple well systems
The discharge from a partially penetrating well depends up on the depth of penetration of
the well in the aquifer. The partially penetrating well may be gravity well or an artesian
well depending up on the type of aquifer.

Figure 4.8 Partially penetrating wells

Discharge from a partially penetrating artesian well, Qp is given by:

2KS w (4.17)
Qp 
 1  L  0.1 1  R 
 ln     ln  
 L  w
2 r b b  2b 

In a partially penetrating gravity well the Kozeny’s equation for discharge is given as
follows.
L  
1  7 w cos L  
r
Q p  Q 
(4.18)
 H  2L  2 H  

Where Q= Discharge for a fully penetrating well.

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If there are a number of pumping wells in a given field, the drawdown at any point is the
sum of the drawdowns due to each pumping well, for which the distance of the point from
each well and the discharge of each well should be known. Multiple well systems are used
for lowering the groundwater table in a given area to facilitate excavation for foundation
work or to meet the large demand for water supply system etc.

Observations indicate that when a number of wells are introduced within a feed contour,
the output increases, but the efficiency of each additional well decreases. The effect is due
to the so called interference among wells.
4.4 Pumping data test, analysis and interpretation
Pumped-well techniques (or pumping tests) are conducted to determine the hydraulic
properties of aquifers such as hydraulic conductivity (K), transmissivity (T), and storage
coefficient (S) or specific yield of unconfined aquifers. Pumping tests are performed by
pumping a well at a constant rate and observing the drawdown of the piezometric surface
or water table in observation wells at some distance from the pumped well.
Pumping tests can be performed by either of the following two commonly used methods:
a) Steady-state pumping tests
b) Unsteady or transient-state pumping tests
In steady-state pumping tests, pumping is continued until equilibrium condition is
approached for water levels, whereas in the transient pumping tests, water-level drops in
observation wells are measured in relation to time, which then yields not only T but also
S. Transient pumping tests are more common than steady-state pumping tests.
Eq. (4.1) or (4.19) can be used to estimate T, S & K using steady-state pumping tests for
wells fully penetrating a horizontal base of confined and approximate estimate of
unconfined aquifers.
2Kbs1  s 2 
Q (4.19)
r 
ln 2 
 r1 
Eqs. (4.12) and (4.19) can be used to estimate S & T using transient pumping tests in the
case of confined aquifers.

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Q  Tt 
s * ln  2.25 2  (4.20)
4T  r S
Always it is good to use the largest capacity pump available to conduct the actual
pumping. Steady-state pumping may have continued for days, or even weeks and months.
In some cases before equilibrium conditions are reached. Careful observation of all the
wells should, therefore be made before starting pumping at regular intervals throughout
the test and during recovery of the levels after pumping has ceased, until the initial
equilibrium levels are regained.
4.5 Design of tube well (deep well)
Water well is a drilled hole in most cases vertical, sunk in to the ground intercepting one
or more water bearing strata, for extracting groundwater for various water resources
purposes. The objectives of water well is to:
 Provide water of good quality
 Provide water in a sufficient quantity
 Provide water for a long time
 Provide water at a low cost
Construction methods are many and varied ranging from simple digging with hand tools
(hand augers) to high speed drilling with sophisticated equipment. Well construction, in
terms of operations, basically includes:
 Drilling operation
 Casing Installation
 Gravel packing and well screen Installation
 Grouting and well head construction
 Developing the well to insure sand free operation at maximum yield
 Installation of Pumps
There are different equipment and drilling methods available for drilling bore holes. The
diversity of equipment allow to determine what equipment and drilling method is best
suited for drilling bore holes for any water resources project purpose. Selection of drilling
equipment depends upon the hydrogeology of the formation, diameter and depth of the
pumping well, availability of fund, maintenance and spaces, production capacity, volume

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of work, operating crew and easy movement of the drilling rig or drilling machine. Some
of this equipment is:
 Hand operated drilling equipment may be most appropriate for bore holes up to 15
m deep & 200 mm diameter which are drilled into unconsolidated formations;
 Cable-tool drilling rigs may be most appropriate for bore holes up to 50 m deep &
200 mm diameter which are drilled in unconsolidated & semi-consolidated
formations;
 Small air flush rotary rigs may be most appropriate for bore holes up to 50 m deep
& 200 mm diameter which are drilled into consolidated formations;
 A large multipurpose rotary rig could be justified for all holes, if cost, manpower,
and back-up support are not constraints and speed is all important.
Tube wells become an option for groundwater supply when water levels are deeper than,
say 6-10 m. They have the advantage of being able to penetrate deep into the aquifer
unlike dug wells with less water level fall problem and they are protected against
pollution. However, they are more costly, have no storage capacity, and often located
outside the community who cannot be involved to any great extent during the construction
processes.
4.6 Well construction methods
Shallow tube wells are constructed by boring, driving and jetting methods, and the wells
constructed by these methods are designated as bored wells, driven wells, and jetted wells,
respectively.
4.6.1 Boring Method
In this method the hole is constructed by the use of a selected diameter hand or power
driven auger which is turned to bore the hole to the designed depth. Cuttings are removed
by pulling and emptying the auger. It can drill to 30 m or more in soft sand & formations
that are free of rocks.
4.6.2 Driving Method
In this method the hole is constructed by forcing a casing (well pipe) equipped with a
drive (well) point into the ground by a series of blows either manually or machine
delivered on the top of the casing. Driven wells should be installed only in soft formations
that are relatively free of cobbles or boulders. A special device called a cap or drive head

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protects the top of the pipe during driving operation. After each length of pipe is
hammered into the ground the top is removed and additional sections are attached and
drive as required.
4.5.3 Jetting method
A jetted well is a well which is constructed by means of boring equipment using water
jetted under high pressure to facilitate rapid boring. Jetting is pumping water down the
pipe and out through the well point where the force of the water losing the surrounding
soil materials.

Figure 4.10 driven and jetted wells

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Figure 4.11 Hand boring or power driven angers

Figure 4.12 Driven angers

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Figure 4.13 Jetting method

4.6.3 Well construction based on drilling equipment
Deep wells (tube wells) are constructed by drilling. The most commonly used drilling
methods are Cable tool, hydraulic rotary, reverse rotary and down-the-hole hammer
methods, and they are discussed as follows.
4.6.4 Cable Tool Drilling Method (percussion)
The cable tool method consists of repeatedly raising and dropping a chisel-edged bit to
break loose and pulverize material from the bottom of the hole. A small amount of water
is kept in the hole, so that the excavated material will be mixed with it to form slurry.
Periodically the percussion bit is removed, and a bailer is lowered to remove the slurry
containing the excavated material. The bailer or bucket consists of a tube with a check
valve at the bottom and a bail for attaching a cable or rope to the top. When it has been
raised and dropped a number of times to fill it with the slurry it is brought to the surface
for emptying. Bailing is repeated until the hole has been adequately cleaned, at which time
drilling is resumed; drilling and bailing are then alternated. If the hole is unstable, casing
is lowered and the driving of casing is alternated with the other two processes. In loose
granular material, such as sand, bailing alone may be sufficient to remove the material

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from the bottom of the hole and allow the casing to be sunk. A heavy bailer with a cutting
edge at its lower end, known as a "mud scow" is used for this purpose.
The percussion method is versatile, allowing all types of materials to be penetrated.
However, in very hard stone, progress is slow. While this method is frequently associated
with large, motorized, truck-mounted equipment, it can be successfully scaled down and
used with manpower, or small engines.
In cable tool or percussion drilling there are basically three major operations:
1st: Drilling of the hole by chiseling or crushing the rock, clay, or other material by the
impact of the drill bit,
2nd: Removing the cuttings with a bailer as cuttings accumulate in the hole; and
3rd: Driving or forcing the well casing down into the hole as the drilling proceeds.
Well casing is used in most percussion- type drilling operations. This casing is used to
help the well bore from collapsing and to prevent surface or subsurface leakage of water
or contaminants in to the well bore the well bore.
The cable tool bit (drill bit) is a shaped steel bar, generally 4 to 8 ft long. The drill bit is
suspended from a cable called the drill line, which is struck over a pulley at the top of a
near vertical mast erected over the hole. Sharper bits are used in hard rock drilling.
The major advantages of the cable-tool system as opposed to other drilling systems are
listed below.
1. Relatively cheap and ease to operate & maintain
2. Better cuttings of sample, easily make well drillers log, (a more accurate sample
for formation can be obtained)
3. Easy identification of water bearing strata.
4. Lesser amount of water is required during drilling operations
5. Minimum contamination of production zones
6. Water can be tested immediately, for quality & yield from each water bearing
stratum
7. Rate of groundwater can be measured
8. Better ability to seal off undesirable zone.
9. Capability of drilling any formation
10. The well driller need not be as skilled as his counterpart in rotary drilling.

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The major disadvantages of the cable tool method
1. Slower drilling rate in hard formations.
2. Limitation on depth
3. Lack of control over fluid flow from penetrated formations
4. The need to case the hole as drilling progress, i.e., lack of control over bore hole
stability, the need to use temporary drill casing in overburden drilling to line a hole
in soft formations.
5. Frequent drill-line failure
6. Difficulty in pulling casing from deep wells

Cable tool drilling rigs may be most appropriate for boreholes up to 50 m deep and 200
mm diameter which are drilled into unconsolidated and semi-consolidated formations.
Usually drilling is started with a large diameter & the diameter is reduced telescopically
after drilling certain depths.

Figure 4.14 Basic drilling tools for cable tool method

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Figure 4.15 Cable Tool Drilling Method

4.6.5 Hydraulic Rotary (or Rotary Direct Circulation) Drilling Method

This method uses a rotary bit to cut the rock and a circulating drilling fluid to flash rock
cuttings to the surface. The drilling fluid is usually heavy mud which is able to support the
walls of the well and prevent them from collapsing. Generally, the drilling of bore holes
by the hydraulic rotary method requires a drill bit, a system for rotating the bit, the means
for controlling bit pressure on the formation, and a medium for removing the material
displaced by the bit.
In the conventional fluid-rotary method of drilling, drilling is accomplished by rotating a
drill pipe and bit by means of a power drive. The drill bit cuts and breaks up the rock
material as it penetrates the formation. Drilling fluid is pumped down through the rotating
drill pipe and holes in the bit. This fluid swirls in the bottom of the hole, picking up
material broken by the bit, and then flows upwards in the well bore, carrying the cuttings
to the surface. The drill pipe and bit move progressively downward, deepening the hole as
the operation proceeds.
At the land surface, the drilling fluid flows into a settling pit where the cuttings settle to
the bottom. From the settling (or mud) pit the fluid overflows into a second pit from which

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it is picked up though the suction hose of the mud pump and re-circulated through the drill
pipe. In the rotary drilling method the well casing is not introduced into the hole until
drilling operations are completed, the walls of the hole being supported by the pressure
(weight) of the drilling fluid and/ or mud cake formed on the wall of the bore hole. Such
drilling is widely practiced in Ethiopia.
Advantages of direct Circulation drilling Method
1. Rapid drilling rate (relatively high penetration rates)
2. The avoidance of placement of a casing during drilling
3. The convenience of electric logging
4. Ability to drill and maintain borehole in a wide variety of formations to depths in
excess of those required for water wells
5. Ability to drill small diameter low cost borehole for formation sampling &
geophysical logging. This information leads to the final well design. In most cases
the pilot borehole is used for this purpose.
6. Low cost for well construction in soft unconsolidated alluvium particularly with
depth greater than 300m.
7. Large diameter holes can be drilled more economically by the rotary method.
Disadvantages includes:-
1. A more complex drilling system compared with the cable-tool
2. Relatively high equipment capital cost.
3. Higher bit cost particularly in hard formations
4. Engineering & control drilling-fluid properties (Reynolds number, density, gel
strength, velocities) critical to well logging, completion & development.
5. High noise levels that create operating problems in urban areas.
6. Greater daily operating cost
7. Relatively high makeup water requirements
8. Relatively High equipment transportation cost
9. High cost for drilling karstic formations
10. The need to remove mud cake during well development
11. Not suitable for boulder formation and requires more water, repair & maintenance.

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Figure 4.16: Hydraulic Rotary Direct Circulation Drilling equipment

4.6.6 Reverse Circulation Rotary Drilling method

A modification of direct circulation rotary method is known as reverse circulation rotary
method. In this system, the drilling fluid with cutting return inside the drill string & is
discharged into a settling tank or pit. Downward flow is in the annulus between the drill
string & borehole. The system components are similar to those of the direct rotary except
for rotation.
The reverse circulation rotary differ from direct rotary rigs in the following respects:
a. Rotary rigs have lower speed range & fewer number of speed

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b. The drill pipes used are larger in size & are flanged and jointed
c. The pump used is centrifugal
d. Air lift method is used in heavier rigs for drilling deeper depths.
As the diameter of the drill pipe is relatively small, the velocity of the drilling fluid in the
pipe is high. This results in two advantages:
1. There is no need for the rotary bits to crash the formation at the bottom of the hole
into pieces.
2. There is no need to use heavy drilling fluid for bringing the cuttings to the surface
& clear water can be used. Thus the problem of clogging of the aquifer around the
well by mud intrusion is greatly reduced.
It is probably the most rapid method of drilling and hence it has become increasingly
popular:
Reverse circulation rotary drilling has a number of advantages under some drilling
conditions. These include:
1. Lower capital cost than equivalent-capacity direct rotary equipment.
2. Good for drilling large diameter holes in soft, unconsolidated alluvial formations.
3. Formation sampling is more accurate than with direct rotary.
4. High return velocity lowers drilling fluid viscosity requirement.
5. Lower noise levels with insulated compressors
6. Lower transportation costs than equivalent-capacity direct rotary.
7. Simpler and less costly circulating system.
8. Lower bit costs than with direct rotary.
9. Lower development pumping time where water without additives is used as drilling
fluid.
10. The boring is done without a casing and hydrostatic pressure is used to support the
walls of the bore-hole during construction
Disadvantages include:
1. Drilling efficiency declines rapidly below 250 to 300 m.
2. Large water supply requirements. It requires five times the amount of water required
for direct rotary drilling.

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3. The system is not suitable for drilling large boulders, consolidated rock formations,
and karstic formations. When drilling long sections of clay and shale, drill fluid
additives must be used.
4. Difficult to use where the static water level is less than 5m.
5. Boreholes smaller than 18’’ cannot be drilled due to the eroding effect of the higher
velocity fluid down the annulus.
6. Maintaining borehole alignment is more difficult than with direct rotary because of the
relationship of the drill collar diameter & weight to the large diameter borehole.
7. Resistivity logs are not reliable where water without additives is used as the drilling
fluid. It is unsuitable for exploratory test drilling.

Figure 4.17: Reverse Circulation Rotary Drilling method

4.6.7. Down-hole Hammer Drilling method
In this method pneumatic hammer operated at the lower end of the drill pipe is used. It
combines the percussion effect of cable tool drilling & the rotary action of rotary drilling.
In hard rock, compressed air can be used to blow out cuttings. This method is often used
in conjunction with a special bit that has a hammer action as it is rotated. This method is

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called down-the–hole (DTH) -hammer drilling and is commonly used to bore through
crystalline rocks.
The action is rotary percussive and does not rely on heavy down pressure. In hard
formation the DTH hammer is most effective but becomes less so as the rock strength
reduces.
The action is rotary percussive and does not rely on heavy down pressure. In hard
formation the DTH hammer is most effective but becomes less so as the rock strength
reduces.
Factors affecting the drilling rate:
1. Formation characteristics-Strength, abrasiveness, drill ability, etc.
2. Mechanical factors like rotary speed, condition of bit, bit type & diameter.
3. Hydraulic factors- circulation rates, friction losses
4. Drilling fluid properties- density, viscosity, etc
5. Intangible factor- personnel efficiency and rig efficiency.
DTH hammer drilling is the technique of drilling where by hammering action at the
bottom of the well is incorporated to the conventional rotary action. With such drilling
method penetration of about five meters per hours in hard formation is possible.
Percussion and rotary methods of well drilling are usually uneconomical in water well
drilling in hard rock formations due to the slow penetration rate, high bit rate, and high
maintenance cost of the machinery. Air-operated DTH drilling method has proved to be
the best for the construction of water wells in hard rock areas.

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Figure 4.18: Down-hole Hammer Drilling method

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Figure 4.19: Percussion and rotary drilling methods

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4.7 Drilling of fluid
Drilling fluid can simply be defined as the combination of fluids and solids required in
certain drilling processes to facilitate the production and removal of cuttings from a
borehole.
The conveying of the drilled cuttings to the surface is still an essential requirement but in
addition, the drilling fluid must perform other functions such as:-
1. Cooling the drill bit
2. The maintenance of borehole stability in preventing caving and sloughing of
unconsolidated formation.
3. Lubrication of the mud pump, bit bearings, and the drilling string & thus
reducing the torque required to turn it.
Five drilling fluid systems are:-
1. Water base clay mud (e.g. bentonite)
2. Oil base mud
3. Low solids mud
4. Air, gas or moist flush system
5. Low velocity foam system
4.7.1 Water base mud
Drilling mud is a mixture of clay, water & chemicals pumped down the drill string & up
the annulus during drilling in order to lubricate the system carry away rock cuttings
maintain the required pressure at the bit end and provide an aid to formation evaluation
etc.
It consists of
1. A liquid phase
2. A suspended-particle(colloidal) phase, and
3. Cuttings entrained during drilling
The oldest and probably the most widely used drilling fluid for water well drilling is a
water-based mud. In this fluid the continuous liquid phase is fresh water. Bentonite or
other clay-like materials in suspension in the water are adjusted to give the required mud
viscosity gel-strength (the ability to form a semi-solid, jelly-like –colloidal solution when
the mud is at rest) and filtration property (the formation of a wall or filter cake to prevent

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water from the fluid invading the formation adjacent to the bore which may otherwise
cause instability). Other chemicals may be added to control and overcome specific
problems. Salt water may be used occasionally as the continuous phase to overborne
formation clay swelling problems but salt is undesirable in water well & thus is rarely
used.
4.7.2 Oil Base mud
These are drilling fluids in which oil is the continuous phase and water is the dispersed
phase. As with salt water-base muds, the oil base muds are used to prevent the hydration
of the native clays which may reduce permeability, it also has other advantages in oil well
drilling and completion. Because of the obvious contamination problem oil-based muds
have no application in water well drilling.
4.7.3 Low solid Mud
This is a drilling fluid in which the solids content is less than 10% by weight or a mud
weight of less than 2.6 parts per liter. For water well drilling the continuous liquid phase is
water & the solids are CMC (sodium carboxyl methyl cellulose), HEC (Hydroxyethyl
cellulose) & other polymers.
4.7.4 Air, Gas or Mist Flush system
Of these, air has the greatest application in water well drilling. This may be used for air
flush lifting of cuttings from rotary drilled holes or may be used to operate and flush
cuttings from DTH hammers.
Air flush drilling is generally very much faster than water or mud drilling and bit life is
extended considerably as a result of the very rapid removal of drilled cuttings from the
face of the bit. However, problems arise when water is encountered in the hole. It is
impossible to restart drilling below a pressure head of water in the hole which exceeds the
air pressure available at the bit. Finally, the very high up- hole velocity required to lift the
cuttings (a minimum of 900 m/min) means that large drill pipe, to reduce the annular area,
and / or very large compressors are needed to achieve the velocity.
Obviously the large pipe, with its extra weight, limits the drilling depth capacity of the
drill rig whilst the large compressors have high capital and running costs.

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4.7.5 Low velocity Foam system
This is an extreme low solids system in which a slow moving column of foam transports
the cutting up the hole with the particles suspended and separated in bubble clusters. Very
low water & air volumes are required. Generally the system improves in efficiency as the
annular area increases. It can often be used, to considerable advantage, instead of the
reverse circulation system.
The material used for foam flush drilling is a concentrated foaming agent with good
emulsion and foam stability, which gives small, tight, thin –walled bubbles. The foam
column has a cuttings carrying capacity far in excess of conventional water-based muds
and, with a very low hydrostatic head, provides bottom-hole conditions which allow
extremely good bit penetration. The low up-hole velocity (about 15 m/min) of the foam
flush drilling system reduces hole erosion and of course, significantly lowers compressed
air costs.
The addition of HEC based polymers & other additives to the foam, to give a “Modified
Stable Foam” (MSF), increases the foam bubble strength and thus the lifting capacity of
the foam column. The MSF can handle water which may be flowing into the hole, can
stabilize swelling & sloughing shale formations, limit the loss of fluid into porous
formations by the formation of a thin wall cake, reduce the tendency for “balling-up”
(when clay particles adhere to one another) and the formation of mud collars when drilling
in sticky clay and be highly successful in bridging fissures in “lost circulation” zone.
The principal limitation to foam flush drilling is in conditions where a high hydrostatic
head is necessary, foam densities are very low, ranging from 0.05 to 0.1kg/liter. Therefore,
high hydrostatic head is not possible; however, this is rarely a water well drilling
requirement.
The quantity of low solids or foam additives to prepare a drilling fluid is roughly one fifth
(by weight) of the quantity of bentonite which would have to be used to achieve similar
results. Thus the use of the low solids mud or the foam flush system can affect a
significant economy in the transport of the drilling fluid additives in the field.
4.7.6 Drilling Fluid requirements
1. The drilling mud must be thick enough to hold the hole from caving

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2. The drilling mud should be able to keep the cuttings in suspension where
circulation is stopped for extending the drill rod or any other reasons.
3. The mud should be thin enough for efficiency.
4.7.7 Drilling Fluid Control program
Material used by the driller to prepare the drilling fluid should be composed of fresh, non-
polluted water and suitable fluid or mud additives to meet the viscosity specification
required. All fluid additives used will have to comply with recognized industry standards
and practices, and they should be applied and used as prescribed by the manufacturer. It is
expressly understood that toxic and /or dangerous substances will not be added to the
drilling fluid.
Additionally, the driller is normally responsible for maintaining the quality of the drilling
fluid to assure
a) Protection of water bearing and potential water bearing formations exposed in the bore
hole, and
b) Good representative samples of the formation materials.
The drilling fluid properties required will depend on:-
i) The type and size of drilling equipment to be used, and
ii) Down hole conditions anticipated or encountered.
Sample for the measurement or testing of drilling fluid properties are those caught at the
rig pump suction with care taken to assure a true and representative sample.
Tests are to be conducted:
1) Every 15m of depth or
2) Every four circulating hours or
3) Whenever conditions appear to have change or problem arises.
The driller must maintain current records on the site at all times to show
i) Time, depth and results of all mud tests, and
ii) All materials added to the system-kind, amount, time and depth.
4.8 Screened casing and gravel wells
Casing serves two major functions:
(i) To support the sides of the hole against collapse;
(ii) To exclude contaminated surface water.

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The screen, which allows the water to enter the well while preventing entry of the aquifer
materials, may be a perforated section at the lower end of the casing or may be a separate
structure attached to the casing.
Depending on the drilling method used and the materials penetrated, the casing may be
sunk as an integral part of the drilling operation, as in the case of jetting; it may be placed
after the hole is completed; or it may be placed at some intermediate point, such as when
the water table is reached and the sides of the hole will collapse if not supported.
A number of different materials have been used successfully for well casing. These
include wrought iron pipe or tubing, tubing rolled from sheet metal, pipe made of plastic
such as polyvinylchloride (PVC) or glass reinforced plastic (GRP), asbestos-cement pipe,
concrete tile, clay tile, bamboo/coir casing (made of bamboo strips attached to steel hoops
and wrapped with coconut husk fiber cord and burlap), large diameter bamboo stems with
the node membranes removed and split palm trunks. The type of casing used will be
determined by:
I). What materials are available locally?
II). What skills are available locally?
III). The relative costs of labor and materials;
IV). The drilling method being employed;
V). The nature of the geologic formation; and
VI). Minimum acceptable life of the well.
Well screens should have as large a percentage of non-clogging slots as possible, be
resistant to corrosion, have sufficient strength to resist collapse, be easily developed and
prevent sand pumping (Driscoll, 1986). These characteristics are best met in commercial
continuous-slot (wire wrap) screens consisting of a triangular-shaped wire wrapped
around an array of rod. If these screens are available, conduct a sieve analysis on samples
on the water-bearing formation and select a slot size which will retain 40-60 percent of the
material.
While wire wrap screen should be used whenever possible, it may be exorbitantly
expensive and/or not available. Most wells therefore are constructed using PVC casing
and screen. Grey PVC pipe, which is available in most countries, is relatively cheap,
corrosion resistant, lightweight, easy to work with and chemically inert.

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Slot Design: Using a hack saw, cut slots in the plastic casing which are as long and close
together as possible. Slots should be spaced as close together as possible vertically and
should extend about 1/5th the circumference of the pipe; there should be 3 even rows of
slots extending up the pipe separated by 3 narrower rows of solid, uncut pipe (for
strength).
A gravel pack is coarse sand or fine gravel (2-6 mm diameter) that is placed between the
borehole wall and screen. Filter (gravel) packs are used to settle-out fine grained particles
that may otherwise enter the well and to increase the effective hydraulic diameter of the
well. A filter pack is like a well "lungs" passing water to the "heart of the well" (the
screen). A filter pack should be installed in all wells except those completed in rock,
coarse sand or gravel.
Finding Material: The best material is coarse silica sand and fine gravel material which
is usually found in river-beds or ocean beaches. Separate the desired size fraction by using
two screens which have slot sizes of 3 and 6 mm. Put the screens on the top and bottom of
a strong wooden frame with the coarse slot screen on top. Suspend the frame in the water
and scoop sand and gravel onto the top screen. After rinsing, suitable material will be
trapped between the two screens. Suitably sized, strong window screen may not be readily
available overseas, but can be easily flattened and brought with you in your suitcase.
Volume of gravel pack required: Calculate the volume of filter material necessary to fill
the well annulus to 2 meters above the top of the well screen - this allows for areas of
borehole washout to be filled without exposing the upper screen to formation stabilizer or
borehole fines. Whenever possible, however, do not place gravel within 3-6 m of ground
surface.
Example 4.9 Using the following data calculate the number of 50 kg bags of gravel for
gravel packing the whole of the annular space (i.e. from the bottom of the well to ground
surface)- No consideration should be made over wash away (b/s it is necessitating
additional filter pack)
 Borehole depth, L= 100m
 Borehole diameter, D= 450mm
 Well screen and plain pipes outside diameter, Ds=300mm
 Total length of screen and plain pipes in borehole=100.5m

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 Grain size of gravel pack material=2 to 4 mm
 Porosity of gravel pack material=36%
 Dry density of gravel pack material=2650kg/m3
Solution
Volume of gravel, V= Volume of annual space in borehole
V= 100(0.2252-0.152) = 8.836 m3
Mass of gravel= m = density x volume (1 –porosity in % /100 %/)
= 2650 x 8.83 x (1-0.36) = 14975.68kg
mass of gravel in kg
The number of 50 kg bags required will be = n =
50 kg
n= 1495.68/50=299.5
Say n = 300 bags for formation stabilizing and filter packing
It is good practice to have extra filter pack on the site, especially if the stability of the
borehole is in doubt.
After the filter pack is placed, there is still an irregularly shaped annular space around the
casing. In caving material such as sand or sand and gravel, the annular space is often
quickly filled by caving material. However, where the material overlying the water-
bearing formation is firm sand, clay, shale etc. and the borehole does not cave-in, the
annular space must be filled. A formation seal (cement grout) is placed into the annular
space to prevent the seepage of contaminated surface water down along the outside of the
casing into the well.
4.9 Well development, maintenance, well failures and rehabilitation
The well screen is the "heart of a well" and the filter pack acts as the "lungs" passing water
to the screen! However, after drilling a borehole and installing a casing and filter pack, it
is necessary to get the "heart pumping" and the "lungs breathing" since the drilling fluid
forms a thin layer of mud on the sand grains of the borehole wall and is forced into the
pore spaces and cracks in the aquifer. This plugging effect decreases the flow of water into
the well.
The term Well Development refers to the process of removing the finer particles from the
aquifer immediately around the well screen in order to make the aquifer more permeable
and thus to decrease the resistance to flow of water into the well. This means that the act

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of cleaning out the clay and silt introduced during the drilling process as well as the finer
part of the aquifer directly around the well screen prior to putting the well into service. In
order to develop a well, it is important that the openings in the well screen be chosen of
the proper size. This necessitates collecting material taken from the aquifer during the
process of drilling. One rule-of-thumb states that the openings should be of such a size
that the smallest 2/3 of the aquifer particles will pass through them.
If an aquifer consists of fine particles without much variation in size, it may not be
possible to increase the permeability around the screen adequately by the development
techniques described above. In this case the capacity of the well can be increased by
gravel packing, i.e. by introducing material around the screen which has a particle size
greater than that found in the aquifer. Use of a gravel pack allows larger screen openings
to be used, and hence gives greater percentage of inflow area. It also surrounds the screen
with a layer of material of higher permeability than the aquifer itself.
One way to introduce the gravel is initially to sink a temporary casing of a diameter
greater than that of the final casing and screen. The final casing and screen are lowered
inside the temporary casing and are held concentric by guides while the gravel is
introduced into the annular space between the casings. The temporary casing can then be
jacked out of the hole. Another method is to drill the hole somewhat larger than the casing
down to the water table. The casing is then lowered and the annular space between the
casing and the hole is filled with gravel. As sinking of the casing into the aquifer proceeds,
some of the gravel descends with the casing. During development, more of the gravel
descends to occupy the volume left by the sand passing through the screen into the well.
Gravel may also be introduced around the screen through several small holes drilled for
this purpose around a. small circle concentric with the well.
The size and gradation of the gravel used should be such that very little of the material of
the surrounding aquifer can flow into the voids between the gravel particles. If this
happens, the permeability of the gravel pack may be greatly reduced. The screen opening
size is selected as large as possible without allowing any of the gravel pack material to
enter the well.

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4.9.1 Water Well Development
A tube well is not completely ready for use just after construction. The tube well can
function effectively only after proper development.
Water well development is a process, whereby the mud cake or compacted borehole wall,
resulting from drilling activity, is broken down; the mud cake liquefied and drawn with
other fines into the well. This material is then removed by bailing or pumping. Well
development, therefore, stabilizes the walls of a well adjacent to the screen by a process
which removes fine particle from the formation immediately surrounding the well screen,
leaving coarser particles to contact and surround the screen.
Tube wells are developed to increases their specific capacity, prevent sanding and obtain
maximum economic well life. Development work is necessary step in completing all types
of wells. Most wells will not perform at maximum efficiency if they are not properly
developed.
After the well has been developed it is usually desirable to fill in and seal the annular
space between the outside of the casing and the hole. This operation known as grouting is
carried out to prevent any dirty surface water from flowing directly into the well and to
give the upper end of the casing firm support. A mixture of Portland cement and water
mixed to a fairly liquid consistency is the most commonly used grouting material. Clay-
water slurry is sometimes also used at greater depths where changes in moisture will not
cause shrinking and swelling of the clay.
The main objectives of well development are:-
1. To correct any damage to or clogging of the water bearing formation; i.e., to remove
mud or clay particles which may have blocked the water movement from the aquifer
into the well.
2. To increase the porosity and improve the permeability of the water bearing formation
in the vicinity of the well.
3. To stabilize the sand formation (gravel pack) around a screened well and the
formation immediately
4. To reduce drawdown in the well during production or pumping.
Development is necessary in all gravel packed wells and other screened wells except when
the screen is formed of fine wire mesh located in a highly permeable formation.

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The benefits which result from well development are:
1. Sand pumping during well operation will be eliminated to a greater extent
2. The life of the well will be prolonged
3. Operation and maintenance costs will be reduced.
4. The specific capacity of the well will be improved (maximum yield at available
minimum drawdown)
4.9.2 Methods of well development
The methods commonly employed for well development are bailing, surge block, over
pumping, backwashing, use of compressed air, hydro fracturing, jetting and use of
dispersing agents (chemicals).
Bailing (a length of pipe with a one-way valve in the bottom) the well is probably the
simplest method of development. Each time the bailer is raised and dropped water surges
into and out of the well. Fine material entering the well is trapped inside the bailer and
removed from the well. The amount of fine material in the bailer indicates how far the
process of development has proceeded. A special type of bailer known as a sand pump has
a piston inside it. This piston is attached to the bailer line in such a way that it travels
upward inside the bailer as the line goes from slack to taut. The motion of this piston has a
strong surging effect on the well and helps to draw sand into the bailer.
A surge block (closely fits the casing interior and is operated like a plunger beneath the
water level), which acts as a piston or plunger inside the casing, can be attached to a string
of pipe and made to travel up and down for the purpose of development. A surge block
may consist of two or more wooden disks fastened together with rubber between them
which makes contact with the inside of the casing.
Over pumping:- Wells may also be developed by pumping water out at a high rate to
create a large drawdown. Pumping is suddenly stopped and a large quantity of water
which has been accumulated is allowed to run down into the well to reverse the flow
through the aquifer around the screen. By this method, loose sand and fine materials are
removed by pumping the well at a higher rate than the well will experience in its service
period. Over pumping has the advantage that much of the fine material brought into the
borehole is pumped out immediately.

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Backwashing: - Development is accomplished by causing the water to alternately flow
into and out of the well. During inflow some small particles will be carried into the well
through the screen, but other small particles will bridge between particles too large to pass
through the screen. The reversal of flow will dislodge such particles and give them the
opportunity to pass through the screen during the next period of inflow. The fine material
entering the well is ultimately removed with the water. Removal of the fine material
during development, in addition to increasing the capacity of the well, saves the pump
which is later installed from abrasion. Sand and fine materials are loosened by reversing
the direction of flow through the screen. By changing the flow respectively the loose
material will be moved through the screen into the well.
Air development: - Compressed air may also be used to surge a well during development
operations. Air lift technique can be used for surging and pumping. The practice of
alternatively surging and pumping with air has grown with the great increase in the
number of rotary drilling rigs equipped with large air compressors.
Surging is used to loosen sand and fine material in the screen and filter zone. The surging
action is created by lifting the water near to the surface by injecting air into the well and
then shut off the air to allow the water to flow back through the well and formation.
Pumping water with air lift can be used for cleaning a well from sand and fine material.
Using the air lift means no water, as would be the case if a submersible or turbine pump is
used to clean the well
Water Jetting: - High velocity water jetting can be used to loosen sand and fine material
from the filter zone and the screen. Maximum development efficiency is achieved if water
jetting is combined with simultaneous pumping with air lift, as the loosened material is not
allowed to settle again.
Hydro fracturing: - High pressure pumps are used to overcome the pressure of overlying
rock and inject fluids into newly opened fractures. Pressure in the production zone usually
causes small, tight breaks in the rock to open up and spread radially. The newly opened
fractures provide effective interconnections between nearby water-bearing fractures and
the well bore.

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Dispersing agents: - Sometimes it is necessary to add a chemical agent to disperse the
clay particles in the mud cake or in the formation to avoid their sticking to sand grains,
and to speed up the development process.
Well development work must be done in a manner that does not cause undue settlement
and disturbance of the strata above the water bearing formation, not disturb the seal effect
around the well casing and there by reduces the sanitary protection otherwise afforded by
such a seal.
Development of the well shall be continued until water pumped from the well at the
maximum test pumping rate is clear and free of sand. The water shall be considered sand-
free when samples, taken during test pumping, contain more than 2ppm of sand by weight.
2-3 ppm tolerable for municipal and industrial water supply, 1ppm may be permissible
limit in a system that has many values and small orifices 20ppm for irrigation.
But it can be recognized that any kind of sand in the water can damage the pump.
Sand content testing-5 samples averages
 15 minute after the start of the test
 after 1/4th of total planned test time
 after 1/2nd of total planned test time
 after 3/4th of total planned test time
 near the end of the pumping test
Excessive sand pumping may result in the formation of cavities around the screen and
subsidence of the soil.
4.9.3 Well Testing for performance
Following the development of a new well, the well should be tested to provide information
on the potential yield of the borehole and drawdown.
Purpose of conducting a pump test of water well: - water well may be pump tested for
either of two main purposes:
1. The usual objective is to obtain information about the performance and efficiency
of the well being pumped. The result in such a case is usually reported in terms of
the yield, the observed drawdown, and the calculated specific yield. These data,
taken under controlled conditions, give a measure of the productive capacity of the

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completed well and provide information needed for selection of the pumping
equipment.
2. Another objective of well pumping test is to provide data for which the principal
factors of aquifer performance, transmissivity and storage coefficient, can be
calculated
In general, the data obtained from pumping test provide information necessary to
determine:-
a) Capacity of the well
b) Aquifer characteristics
c) Well efficiency
d) Pumping rates
e) Pump installation depth settings
f) Other factors which will be of value in the long term operation and maintenance of
the well
g) Well design and construction equipment.
4.10 Measurement of groundwater level
Measurement of groundwater level is done usually by using observation wells.
Observation wells enable to measure the drop in groundwater table or piezometric surface.
At least three observation wells at different locations are used in pumping tests.

Observation wells should ideally be spaced at increasing intervals from the pumping well
(10 to 100 m) depending on the depth and expected productivity of the aquifer. Loham
(1972) mentioned that a good arrangement consists of a pair of observation wells at
distances of one, two and four times the thickness of the aquifer from the pumped well.
Each pair consists of a shallow well reaching just into the aquifer and a deep well
extending to the bottom of the aquifer. For unconfined aquifers, observation wells should
be at a distance of at least 1.5 times the aquifer thickness from the pumped well to avoid
errors due to vertical-flow components in the vicinity of the well.

Ground-water-level measurements are used to determine hydraulic gradients, directions of

flow, rates of flow, locations of ground-water recharge and discharge, the amount of water
in storage, the change in storage over time, and aquifer hydraulic characteristics. Repeated

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measurements of water levels over time provide a history of water-level fluctuations that
aids interpretation of water-quality and water-quantity data. For example, seasonal
variations in recharge induced by pumping can cause changes in hydraulic gradients that
may correspond to changes in water quality and water quantity.

Figure 4.20: Water level measurement using graduated steel tape (single measurement)

Figure 4.21: Water level measurement using Divers (Continuous measurement)

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4.11 Groundwater balance and groundwater management
4.11.1 Groundwater balance
In the management of groundwater resources, man intervenes in the hydrologic cycle in
order to achieve beneficial goals. This intervention takes the form of modifications
imposed on the various components of the water balance.
Water and pollutants carried with it may enter an aquifer, or a considered portion of one,
in the following ways:
1. Groundwater inflow through aquifer boundaries and leakage from overlying or
underlying aquifers.
2. Natural replenishment (infiltration) from precipitation over the area.
3. Return flow from irrigation and septic tanks (or similar structures, including faulty
water supply or sewage networks)
4. Artificial recharge.
5. Seepage from influent streams and lakes
Water and pollutants carried with it may leave an aquifer in the following ways
1. Groundwater outflow through boundaries and leakage out of the considered
aquifer into underlying or overlying strata.
2. Pumping and drainage
3. Seepage into effluent streams and lakes
4. Spring discharge
5. Evapotranspiration
The difference between total inflow and total outflow of water and of pollutants during
any period is stored in the aquifer, causing a rise/fall in water levels and in the
concentration of pollutants, respectively.
1. Inflow and outflow through Aquifer Boundaries, Qlsi and Qlso
When a boundary of an aquifer (or a portion of one) is pervious, groundwater may enter
the aquifer through it from the outside (another aquifer or the remaining part of the
aquifer. The leakage (volume of water per unit area and per unit time) through a semi
permeable layer from an overlying (or underlying) aquifer may take place.
2. Precipitation (Natural Replenishment) Qprec

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Phreatic aquifers can be replenished from above by precipitation falling directly over the
ground surface overlying the aquifer, provided the ground surface is sufficiently pervious.
Confined aquifers are replenished by groundwater inflow from an adjacent phreatic
aquifer, which in turn, is replenished from precipitation. Part of the area may be
completely impervious and does not contribute to the natural replenishment of the aquifer
beneath it.
3. Irrigation and sewage losses (Return Flow) Qirr
Even in efficient irrigation practices, a certain portion of the water applied to an area is not
used up as consumptive use, but infiltrates, eventually reaching the water table. We shall
refer to this contribution to an aquifer’s replenishment as return flow from irrigation. The
water used for irrigation may be that pumped from underlying aquifer (hence the term
return flow), surface water or water imported from other regions.
River-Aquifer Interrelationships Qsurfin and Qsurfout
Rivers passing through a region under-lain by a phreatic aquifer (and in special cases even
by a confined aquifer) may either contribute water to the aquifer or serve as its drain.
When a stream cuts through an impervious layer, establishing a direct contact with and
underlying confined aquifer, the stream may be either an influent one or and effluent one,
depending on whether the piezometric heads in the aquifer are above or below the water
level in the stream.

Much of the low water flow in streams (base flow) is derived from groundwater whose
water table elevations in the vicinity of a stream are higher than the stream; such streams
are called effluent streams. On the other hand, when the water level in a stream is higher
than the water level in an adjacent (or underlying) aquifer, water will flow from the river
to the aquifer. The river is called an influent river.

The same stream can be an influent one along one stretch and an effluent one along
another or it can be both influent and effluent at the same point. The volume of water
contributed to an aquifer by stream flow (or drained into a stream from an aquifer), is part
of the regional water balance.

Springs Qspring

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It is a point (sometimes a small area) through which groundwater emerges from and
aquifer to the ground surface. The discharge of some springs is small and of no
significance in the groundwater balance, however, some are very large and dominate the
flow pattern in their vicinity. There are several types of springs a depression spring,
contact spring, a perched spring.
4. Evapo-transpiration (ET)
This is another mechanism by means of which groundwater may leave an aquifer.
Evaporation is the net transfer of water from the liquid phase to the vapor one.
Transpiration is the process by means of which plants remove moisture from the soil and
release it to the atmosphere as vapor.
ET, a combination of the above two processes, is the term used to describe the total water
removal from an area partly covered by vegetation by transpiration, evaporation from soil
(actually from the water present in the void space of unsaturated soil), from snow, from
open water surface (lakes, streams, and reservoirs). Unless the groundwater table is
within 1-1.5m from ground surfaces evaporation from groundwater is practically zero.
When the water table is near the ground surface, ET may contribute a significant factor in
the water balance.
We do have some evaporation from water in the unsaturated zone.
5. Pumping and Drainage, Qwell
Water can be withdrawn from an aquifer for beneficial usage by means of shallow dug
wells, tube deep wells, horizontal wells, and galleries. A well can pump water as long as
the water table at its location is higher than the elevation of the pump installed in it.
For water to enter a gallery, the water table should be above its bottom.
In regional water balance, we are often interested only in the total withdrawal by pump
age during the balance period.
A drainage system (open channels, or buried drains) is usually installed in order to control
the elevation of the (ground) water table say, to maintain water levels below the root zone.
Groundwater will then leave the aquifer through this system (say, to a nearby stream)
whenever the water table is higher than the drains.
The volume of water drained out of an aquifer in this way should not be left out of the
Water-balance.

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6. Change in Storage, Sbal
The difference between all inflows and outflows during a balance period accumulates in
the considered aquifer region. In a phreatic aquifer, water is stored in the void space. In a
confined aquifer, water is stored on account of water and solid matrix compressibility. In
the first case, increased storage is followed by a rise of the phreatic surface. In the
second case, increased storage is followed by a rise in the piezometric head.
7. Regional Groundwater Balance
We can now summarize the regional groundwater balance by the following equation.
[Groundwater inflow] - [Groundwater outflow] + [Natural replenishment] + [Return flow]
+ [Artificial recharge] + [Inflow from streams and lakes]-[spring discharge]-[Evapo-
transpiration]-[Pump age and drainage] = [Change in volume of water stored in aquifer]
Where all the terms are expressed as volume of water during the balance period it can be
rewritten as follows.

Figure 4.22: Water balance components

Potential inflows into the saturated part of the CCL are recharge from precipitation (Q prec),
losses from irrigation (Qirr), inflow from surface water (Qsurfin), lateral subsurface inflow
(Qlsi) and upward flow (Qup) which roughly equates to (positive) seepage. On the other
hand the outflow terms could include outflow to surface water (Qsurfout), capillary flow

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from groundwater table (Qcap), abstractions from wells (Qwell), lateral subsurface outflow
(Qlso) and downward flow (Qdown) which correlates with (negative) seepage. The total
inflows minus total outflows should be equal to change in storage.
V
Q prec  Qirr  Qsurfin  Qart  Qlsi  Qup  Qspring  Qsurfout  Qwell  Qcap  Qlso  Qdown 
t
4.11.2 Groundwater Resources Management
Identifying the relevant issues is a crucial step in groundwater resources management
planning; omitting or misjudging one or more of them may lead to unbalanced, inefficient
or even ineffective plans.

The issue of concern for groundwater resources management reflects the physical
conditions and the socio-economic development of the area considered. But in spite of the
uniqueness of each groundwater system in this respect, the problems observed world-wide
seem to boil down to a relatively small list of main issues.

They can be grouped roughly under three different headings: Groundwater quantity
management, groundwater quality management and groundwater-related environmental
protection. Table 8.1 lists and classifies the groundwater resources management issues that
will be commented in this chapter.
Table 4.1 Common groundwater resources management issues
Groundwater Groundwater Environmental
quantity quality protection
management management
Rate of aquifer exploitation X
Allocation of groundwater X (X)
Conjunctive management
of groundwater and surface X (X) (X)
water
Groundwater salinity X (X)
control X (X)
Groundwater pollution

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control (X) x
Conservation of water (X) x
types (X) x
Groundwater level control
Control of land subsidence

Groundwater resources management is not new field of activity: some issues have been
recognized long ago in some countries and have given rise to the development of water
resources management approaches and activities. Such activities stared to be undertaken
one after another in response to observed needs, sometimes without people being aware
that they were dealing with groundwater resources management and with decision
problems.

A wealth of professional creativity, however, has accumulated in the numerous

approaches to groundwater resources management developed over the years in several
parts of the world. Professionals engaged in groundwater resources management may
benefit greatly from the ideas developed and experiences gained elsewhere.
Therefore, a brief review of the mentioned issues and suggested or pioneered approaches
will follow.
4.12 The rate of aquifer exploitation
“How much groundwater to abstract from a certain aquifer?” is an old problem that has
puzzled many hydro geologists and water resources engineers? Pumping at too low rate
means usually a loss of potential benefits from groundwater; and excessive pumping, on
the other hand, will produce groundwater depletion and other undesired effects.
The problem has frequently given rise to misconceptions and confusion. One of the
misconceptions is that it would be a technical problem only, to be solved merely by
technical means (which is suggested by the somewhat confusing term ‘safe yield’).
However, a hydrologist cannot provide a quantitative answer unless it is specified whether
the resources should be exploited under a ‘mining policy’ or under a policy of sustainable
yield.
Mining depletes the storage and thus can only be practiced for a limited period of time. It
is often a dilemma to what extent it is wise and ethically justifiable to allow present-day

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groundwater users to enjoy the benefits of groundwater mining and to leave the associated
problems for a future generation.
The sustainable-yield approach is based on the capture of recharge and thus will not
exhaust the aquifer. It avoids difficult decisions regarding intergenerational allocation of
water. Optimal yield is not only a function of physical factors, but depends equally well on
a complex of economic, social and political factors.
A second misconception is that the optimal rate of aquifer exploitation often implicitly is
thought to be constant in time (‘stationary approach’). As will be shown below, a more
dynamic approach-allowing discharge to be time-dependent-may be attractive.
 Sustainable-yield policy
Sustainable yield represents a groundwater abstraction rate that allows on a long term the
inputs and outputs of water to be balanced over the domain of the aquifer, thus leading to
a stable state of the aquifer. Many conventional groundwater assessment and development
studies implicitly associate maximum sustainable yield (MSY) with optimal yield. In
relation to sustainable yield, a few remarks can be made:
a) The maximum sustainable yield is not necessarily equal to the aquifer’s recharge:
rather, sustainable yield is the ‘ groundwater capture’, which is the difference between
recharge and ‘natural’’ discharge; consequently, maximum sustainable yield (MSY) is
the maximum capture attainable, which is sometimes considerably less than the
average recharge;
b) After all natural groundwater discharge has stopped due to abstraction, the dynamic
equilibrium between recharge and pumping at full MSY rate can be maintained at
different levels of groundwater storage so there is no typical value of stationary
groundwater stock in response to pumping at MSY rate;
c) Even under an sustainable-yield policy it is possible that economic or environmental
factors are limiting optimal yield to a level below ‘maximum sustainable yield’,
d) Sustainable exploitation regimes in principle may have abstraction rates that are
variable in time.

 Mining policy

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Although by tradition there is often preference for a sustainable-yield policy (because it
does not threaten continuity), such an approach may be excessively conservative under
certain circumstances. Frequently, it seems to be more profitable to adopt a mining policy
for some limited period, before in a later stage a sustainable-yield policy is followed. This
is because the exploitation of ‘mining resources’ definitely produces a certain economic
profit and often also increases the ‘renewable resources’ , either by decreasing the natural
outflow, or by increasing the recharge.
 Is there really need for control?
Trying to control groundwater abstraction is only worth to be considered if uncontrolled
competitive groundwater abstraction would diverge substantially from a planned, socially
‘optimal’ abstraction regime. What makes competitive abstraction rates in principle
diverge from socially optimal raters? At least the following factors are important:
Lack of knowledge; technology and /or money
These factors have caused for a long time ‘underdevelopment’ of groundwater resources
in many aquifers of the world; people were not able to exploit them at rates that would be
indicated as optimal in planning studies.
The need for aquifer-wide groundwater storage management is especially large in areas
where the water resources are scarce and groundwater is highly profitable at the same
time. On the basis of several papers it can be concluded that the discrepancy between
competitive pumping and optimal control may be pronounced if any of the following
conditions are present: multi-pumper conditions, elastic demands for water, low social
rates of discount, high contrast between financial and social rates of discount, and limited
capacity of the groundwater reservoir.
1) Allocation problems
Considering groundwater as a resource to be abstracted and used, two different types of
allocation problems will be discussed below: allocation among users and spatial
allocation.
 Allocation of abstracted groundwater among users
Under conditions of relative scarcity of water, groundwater demands of different users or
sectors may be competitive or even conflicting. Uncontrolled development then may cause
excessive interference or harmful aquifer depletion, both leading to economic losses. The

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water resources management response to such circumstances is to allocate the available
resources among the users, either by licensing (granting water rights) or by other measures
such as taxation related to the type and intensity of water use.
Such an allocation needs a guiding principle; different approaches for such a guiding
principle are:
a) priority of the oldest rights (‘firs come, first served’)
b) Priority differences between sectors (domestic supply, agriculture, industry);
c) Priority differences between zones (e.g. surface water priority for water are
available);
d) Economic optimization (e.g. by linear programming)
Which principle to choose depends very much on existing water resources management
policy and plans, or on water resources management objectives adopted, and of course has
to be consistent with prevailing water rights?
 Allocation in space
Given a certain demand to be satisfied from a specific aquifer, different spatial patterns of
wells may be chosen. Some of these patterns are more favorable than other ones; hence
the problem is to find an optimal distribution in space of abstraction well. Depending on
the details of the problem and on the management objectives chosen, the analysis will
focus either on optimization (if the of decision-process is complex) or on simulation (if the
system’s behaviors is complex). An elegant approach is to combine optimization and
simulation in a spatially discrete model.
It a number of distinct aquifers is present, basically a similar approach can be followed,
but complexity increases. In the case that local groundwater and surface water resources
are insufficient to satisfy crucial water demands under acceptable conditions, inter basin
transfer of water becomes unavoidable. This is often the case in rapidly expanding
metropolitan zones.
1. Conjunctive management of groundwater and surface water
Groundwater and surface water tend to be strongly interrelated, in the sense that
groundwater may feed surface water bodies, and vice versa. Variations of flow, storage or
quality of water in one of the subsystems may directly affect the state of the other one.
These variations may have a natural cause (e.g. Weather conditions), but they can also be

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induced by water resources development or management activities. Artificial recharge,
base flow suppletion and surface water dams are typical examples of the latter category.
Furthermore, the availability of both surface water and groundwater in an area opens the
possibility of conjunctive use of groundwater and surface water.
 Base flow Separation
This is in fact the opposite of artificial recharge: groundwater is pumped from aquifers to
maintain a minimum base flow in streams during periods of drought. The activity is
usually related to the environment impacts of water
 Surface water storage dams
Although not always recognized, a surface water storage dam may have very important
consequences for the recharge of aquifers fed by the stream where the dam is constructed.
Water resources management officials should be aware of this interdependence, and
should care for an integrated analysis before any decision is taken on the physical works
or on the operation rules.
Storage dams and artificial recharge can be considered as alternatives: storage and use of
water via the recharge alternative is often more energy-consumptive, whereas surface
water reservoirs may be subject to higher losses of water due to evaporation.

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CHAPTER FIVE
Groundwater Recharge
5.1 Introduction
Groundwater recharge may be defined in a general sense as the downward flow of water
reaching the water table, forming an addition to the groundwater reservoir. Recharge may
occur naturally from precipitation, rivers, canals, lakes, as man induced phenomena
(irrigation, urban recharge). Recharge can be instantaneous, event, season, year, historical
or geologic time. A clear distinction must be made between the potential amount of water
available for recharge from the soil zone and the actual recharge.

5.2 Types of Groundwater recharge

Three types of recharge can be identified:
1. Direct recharge - water added to the groundwater reservoir in excess of soil moisture
deficits and evapotranspiration, by direct vertical percolation of precipitation through the
unsaturated zone.

2. Indirect recharge - percolation to the water table following runoff and localization in
joints, as ponding in low lying areas or through the beds of surface water sources such as
rivers, lakes and reservoirs.

3. Localized recharge– resulting from horizontal surface concentrations of water in the

absence of well-defined channels.

4. Natural Recharge
It is usually produced under one or more of the following conditions
i) Deep infiltration of precipitation
ii) Seepage from surface water (stream & lakes)
iii) Under flow from another basin (if hydraulically interrelated)
5. Incidental Recharge
Incidental or unplanned recharge occurs where water enters the ground as a result of a
human activity whose primary objective is unrelated to artificial recharge of groundwater.

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Incidental recharge includes water from Irrigation, cesspools, septic tanks, water mains,
sewers, landfills, waste-disposal facilities, canals, and reservoirs. The quantity of
incidental recharge normally for exceeds that deliberately accomplished by artificial
recharge projects. Because several of these sources introduce polluted water into the
underground degradation of the quality of groundwater can occur.
6. Artificial Recharge
It may be defined as man’s planned operations of transferring water from the ground
surface into aquifers. This is in contradiction to natural replenishment (or natural recharge)
whereby water from precipitation and surface runoff reaches the aquifer without man’s
intervention. Whereas natural replenishment is an uncontrolled (by man) input to the
groundwater system, artificial recharge is a controlled input.
The quantity, quality, location, and time of artificial recharge are decision variables, the
values of which are determined as part of the management policy of a considered
groundwater system.
Artificial recharge consists of storing surface water in an aquifer. Usually the main
purpose is to utilize the storage facility offered by the aquifer, thus enabling certain
volumes of surface water to be kept for use at other times (and increasing the permissible
abstraction from the aquifer). Other objectives sometimes aimed at by artificial recharge is
the improvement of the quality of the infiltrated water (decay of pathogen bacteria, mixing
with other waters, filtering), the use of the aquifer as a means to convey water to where it
is needed, or the control of the interface between fresh and saline groundwater. In order to
increase the natural supply of groundwater, people artificially recharge groundwater
basins. Artificial recharge may be defined as man’s planned operations of transferring
water from the ground surface into aquifers, or artificial recharge may be defined as
augmenting the natural movement of surface water into underground formation by some
method of construction, by spreading of water, or by artificially changing natural
conditions.
Objectives of Artificial Recharge
AR may be practiced in order to achieve various objectives. Among them, we may list the
following.

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1) Control of regional hydrological regime. By artificially recharging an aquifer, water
level, or piezometric heads, is raised. By manipulating these levels (obviously, taking
also the effect of pumping into account), we can control the rate and direction of flow
in an aquifer, control the movement of water bodies of inferior quality, (eg. Sea water
intrusion, control spring discharge, and control seepage to or out of adjacent water
bodies (rivers and lakes, etc.).
2) Storage of water; water can be stored in an aquifer, to be pumped at a later time.
Phreatic aquifer may serve as very large storage reservoirs. Water is stored in the void
later time by pumping long term storage in years with excess surface runoff, water
may be diverted from streams& lakes to be stored in aquifers for use in dryer years.
Short term storage may be used to make a more efficient use of the water supply lines.
Water may be delivered to a demand area at a constant rate throughout the year, to be
stored in the aquifer when supply exceeds demand and pumped by local wells to
supplement demand in excess of direct supply.
3) Control of water quality; as water is introduced into an aquifer and the indigenous
water of the aquifer moves, they mix as a result of hydrodynamic dispersion. Mixing is
also achieved by wells which pump simultaneously from the two kinds of water. We
can control the quality (in terms of dissolved matter) of pumped water by manipulating
pumping and artificial recharge, thus controlling the movement of the water bodies
introduced into the aquifer and the mixing that takes place in the aquifer and in the
pumping wells. The water used for artificial recharge ma be either water of a quality
higher than that of the indigenous water of the aquifer, or of an inferior quality. Due to
the very slow movement of water in the aquifer, a period of year, sometimes many
years, may elapse between the time water is introduced into an aquifer and the time it
is pumped. During that time phenomena such as chemical reactions among
constituents present in the water, interaction with the solid skeleton (adsorption and
ion exchange), and decay (eg. Radioactive), and filtering may take place. Thus the
aquifer acts to improve the quality of the injected water. Suspended line material in
surface water used for AR can be removed by the filtering that takes place as the water
percolates through the bottom of a spreading basin and the soil underlying it on its
downward way to the aquifer. Of special interest is the improvement of water quality

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(e.g. Removal and destruction of microorganisms) as the recharge water percolates
through the unsaturated zone.
In addition to these major objectives, we may also mention the following additional ones.
1. Supplementing the difference between the demand for groundwater and natural
replenishment of an aquifer.
2. Disposal of liquid waste into deep formation where it will stay, or move very slowly
(sometimes for thousands of years) to wards outlets.
3. Using the aquifer as a conduit or a water distribution system. By recharging and
pumping, water levels are raised and lowered, respectively. It is therefore, possible to
create a flow pattern within the aquifer from the area of recharge to that of withdrawal
by pumping, with the aquifer serving as a conduit. Wells distributed over an area may
withdraw water for local use, thus avoiding the need for a distribution system.
4. Maintenance of high water levels (or heads) to prevent land subsidence or other
undesirable phenomena which result from lowered water levels (eg. Damage to
foundations).
5. Conservation of water. For example, water used only for cooling can be re-circulated
by injecting the warm water back into the aquifer from which it is pumped.
In most cases, artificial recharge is implemented to achieve a number of goals and in
conjunction with the utilization of surface water.
5.3 Factors Affecting Recharge
 Topography and geology

 Precipitation (magnitude, intensity, duration, spatial distribution)

 Runoff and ponding of water

 Irrigation (nature of irrigation scheduling, losses from canals and water courses.

 Rivers (rivers flowing into and leaving out of the area under consideration, rivers
gaining water from or losing water to the aquifer, etc.).

 Soil zone (nature of the soil, depth, hydraulic parameters, variability of the soil
spatially and with depth, rooting depth of the soil, and cracking of soil on drying out
or swelling due to wetting)

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 Unsaturated zone between soil and aquifer (flow mechanism through unsaturated
zone, zones with different hydraulic conductivity, etc.)

Ability of aquifer to accept water and variation of aquifer condition with time
5.4 Artificial Recharge Methods
Artificial recharge can be implemented by several methods, the choice of method for each
particular case depends on the source of water, the quality of the water, the type of aquifer,
the topographical and geological conditions, type of soil, economic conditions, etc.
The most widely practiced methods can be described as types of water spreading releasing
water over the ground surface in order to increase the quality of water infiltration into the
ground and then percolating to the water table.
Although field studies of spreading have shown that many factors govern the rate at which
water will enter the soil, from a quantitative stand point, area of recharge and length of
time water is in contact with soil are most important. Spreading efficiency is measured in
terms of the recharge rate, expressed as the velocity of downward water movement over
the wetted area.
Spreading methods may be classified as basin, stream channel, ditch and furrow, flooding,
irrigation, and methods enhancing infiltration.
a) Methods for enhancing infiltration
In these methods, the objective is to increase infiltration by various agro techniques which
affect ground surface roughness, slope, vegetation cover, etc.
The purpose is to extend the time and area over which infiltration from surface runoff
takes place.
Both the slopes of the water shed and the drainage channel network can be treated to
achieve this purpose. For example, small check dams in natural channels will cause the
water to spread over a large area.
b) Basin Method
Here water is diverted to specially constructed ponds or basins, and allowed to infiltrate
through their pervious bottom.
Sometimes ditches, dug along around surface contours, are used instead of basins. Two
objectives are achieved by storage and purification methods. The latter is related to the

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filtering of fine materials, mainly in the settling basin, but also through the soil layer just
beneath the infiltration basins.
c) Stream Channel Method
Water spreading in a natural stream channel involves operations that will increase the time
and area over which water is recharged from a naturally losing channel.
This involves both u/s management of stream flow and channel modifications to enhance
infiltration u/s reservoirs enable erratic runoff to be regulated ideally to limit stream flows
to rates that do not exceed the absorptive capacity of d/s channels.
Improvement of stream channels may include widening, leveling, scarifying, or ditching
to increase infiltration.
d) Ditch and Furrow Method
In this method water is distributed to a series of ditches, or furrows, that are shallow, flat
bottomed, and closely spaced to obtain maximum water contact area.
e) Flooding Method
In relatively flat topography, water may be diverted to spread evenly over a large area. In
practice, canals and earth distributing gullies are usually needed to release the water at
intervals over the upper end of the flooding area. It is desirable to from a thin sheet of
water over the land, which moves at a minimum velocity to avoid disturbing the soil.
f) Irrigation Method
In irrigated areas water is sometimes deliberately spread by irrigating cropland with
excess water during dormant, winter, or non-irrigating seasons. The method requires no
additional cost for land preparation because the distribution system is already installed.
g) Pit Method
A pit excavated into a permeable formation serves as ideal facilities for groundwater
recharge. In areas where shallow subsurface strata, such as hard pans and clay layers,
restrict the downward passage of water, pits can effectively reach materials with higher
infiltration rates.
h) Recharge well Method
Recharge well may be defined as a well that admits water from the surface to freshwater
aquifers.

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Its flow is the reverse of a pumping well, but its construction may or may not be the same.
Well recharging is practical where deep, confined aquifers must be recharged, or where
economy of space, such as in urban areas, is an important consideration, where extended
impervious layers are present between the g/surface and an underlying phreatic aquifer,
and where existing pumping wells can be used for recharge, thus eliminating the need for
costly artificial recharge installation.
i) Induced Recharge
Direct methods of AR described above involve the conveyance of surface water to some
point where it enters the ground
Induced recharge is accomplished by withdrawing groundwater at a location adjacent to a
river or lake so that lowering of the groundwater level will induce water to eater the
ground form the surface source.
By induced recharge we can achieve two goals: recharge the aquifer by river water, to be
pumped for beneficial use, without constructing any recharge installations the aquifer
itself is used as a conduit, and filtration and purification of the river water as it travels
through the aquifer towards the abstraction installation.
Questions:
1. What is artificial recharge and what are the different types of artificial recharge
methods?

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CHAPTER SIX
GROUNDWATER POLLUTION & REMEDIATIONS
6.1 Introductions
Groundwater, as the name suggests, is water found underneath the surface of the earth.
The water from rainfall, lakes, rivers, and streams seeps through the porous ground to
reach the water table; a level where the ground beneath is saturated with water.
Groundwater is usually contained in an aquifer. An aquifer can be described as a
geological structure made of permeable components able to store large quantities of water.
Groundwater is found in almost all places but the depth of the water table varies
depending on the region, meteorological factors, and rate of exploitation. The amount of
groundwater also changes with the season. In the rainy season, the water levels increase
while in the dry season, the level of groundwater decrease.

6.2 Conjunctive use of groundwater and surface water

Groundwater and surface water have different properties regarding to flow variability,
storage, quality parameters, cost of exploitation and vulnerability for pollution.
Coordinated use of groundwater and surface water (conjunctive use) may take advantage
of the ‘stronger’ properties of either source of water at proper time and location.
Especially under conditions of scarcity this approach may have distinct advantages over
the isolated exploitation of each of the resources.
Conjunctive use of groundwater and surface water is a component of almost all water
resources management plans for larger regions of high and conflicting demands for ware.
1. Salinity control
Many aquifers contain both fresh groundwater and saline or brackish groundwater. The
fresh zones usually are recharged by rain or by streams. The saline or brackish waters are
most frequently of marine origin and may be either connate waters (‘deposited’
simultaneously with the aquifer rocks; sometimes migrated and/ or mixed with fresh
waters) or intruded saline waters.
Although all kinds of configuration may occur, the situation that fresh water overlies
saline or brackish groundwater is very common; physically, this is a rather ‘stable’
situation, in particular when the ‘interface’ is approximately horizontal. Saline

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groundwater on top of fresh groundwater, on the other hand, presents an unstable
situation, unless lithological conditions prevent downward migration of the heavier saline
water.
The purpose of groundwater salinity control is to prevent or minimize salination of the
fresh groundwater resources; in other words: to conserve the resource for future use. In
order to do so, it is important to analyze how the flow processes in the aquifer might
develop under different technical alternatives of groundwater development. Due to the
differences in density between fresh water and saline water, the interface between fresh
and saline groundwater is extremely sensitive for disturbances of the groundwater regime.
Salinization of a fresh part of an aquifer is partially irreversible (as a consequence of
dispersion processes), thus is difficult to cure. Hence, protective measures are required,
and such measures should be designed on the basis of simulation.
Usually, sophisticated models are available for the simulation of fresh-saline groundwater
problems.
 Salt water upcoming
It is a common phenomenon under wells that abstract fresh water, which overlies brackish
or saline groundwater. Declines of the fresh-water head under such wells motivate an
upward movement of the saline groundwater. It is a local phenomenon that may reduce the
useful life of wells. Hence, a time horizon of some tens of years is often convenient for the
analysis of local upcoming problems.
 Saline water intrusion
Saline water intrusion may occur in coastal areas. Whereas upcoming often is little more
than a certain redistribution of fresh and saline groundwater within the aquifer, saline
intrusion always increases the volumes of saline water stored underground and may finally
lead to salinization of the entire aquifer.
 Soil salination
Soil salinity may be interrelated with aquifer management in different ways: evaporation
via capillary rise from shallow groundwater may cause soil salination, and soils-in turn
may contribute to aquifer salinity.

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If the salts that are accumulating in soils are flushed down periodically by rain or by
irrigation water, then an influx of salt into the underlying aquifer will occur. The amounts
involved for irrigated lands in arid zones are of the order of 104kg per hectare.
2. Groundwater pollution control
 Well field protection
One of the most obvious options to protect a well field against pollution is to locate it at a
suitable site: in an aquifer zone of relatively low vulnerability regarding pollution (e.g.
covered by confining beds) and as far as possible or up gradient from sites that represent a
risk (e.g. a polluting industry).
Once in existence, well fields in many countries are protected against pollution by
establishing so-called groundwater protection zones. Inside these areas there is usually a
distinction between several zones: closer to the well field the control becomes more and
more strict. Table 4.3 shows characteristics of protection areas in a number of European
countries. The dimensions of the different more or less concentric protection zones are
based commonly on estimates of the time it would take for a contaminant to move from
the land surface or from the top of the aquifer to the wells.
Karstic aquifers pose a special problem: the size of protection zones based on the usual
travel time criteria would become easily too large to give it special protection.
 Aquifer protection
Protection of the entire aquifer against pollution has become a major concern during
recent years, after more and cases of severe contamination have been discovered in many
different countries.
The trend in groundwater management is shifting from the ‘defensive’ attitude (well field
protection) to wards control of the sources of contamination over the total exposed surface
of the aquifer. Intensive research is being carried out in many parts of the world to develop
a scientific base for this control. As far as the diffuse sources of pollution are concerned, it
becomes clear that control of land use and agricultural practices may contribute highly to
the conservation of groundwater quality. Strict regulations on the disposal of industrial
and hazardous domestic waste may greatly reduce point-source pollution.
4. Conservation of chemical water types

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Water quality management is not only concerned with salinity control and pollution
control. It may also focus on apparently ‘minor’ changes in water quality, if these changes
have important practical implications.
Many of these changes in water quality are closely interlinked with water quantity
processes. Declines of shallow phreatic levels may enrich groundwater in nutrients
(because of mineralization processes) and in Sulphates (because of the oxidation of
poyrite). Intensive pumping from deep aquifers may cause a reduction of natural outflow
of deep groundwater, and ‘shallow’ flow systems may replace largely the contribution of
the deeper flow systems to the seepage in groundwater exfiltration zone. Increases of
water levels in surface water bodies may cause or increase the mixing of shallow
groundwater with surface water which is often of a different chemical composition. And
irrigation will lead to subsurface accumulation of solutes which tend to change the
chemical characteristics of shallow groundwater.
Important practical consequences of changing chemistry of groundwater have been
reported in relation to phreatophytic ecosystems. Such ecosystems occur preferently in
groundwater exfiltration zones and are extremely vulnerable. They do not only violently
react to relatively small declines of the groundwater level; they may also degenerate in
response to changes in shallow groundwater chemistry.
5. Groundwater level control
Control of shallow groundwater levels is traditionally the domain of drainage engineers.
Drainage activities are usually carried out independently of groundwater development
activities, but it is clear that both types of groundwater engineering may interfere
considerably. That is why groundwater management needs to ensure that such activities
are carried out in a co-ordinated way.
The level that should be considered as the optimum groundwater level varies according to
soil type, land use and climate conditions.
In agriculture, there is considerable empirical knowledge in the relation between yields of
groundwater-fed crops and the depth to groundwater.
Ecologists have similar information on the relation between depth to groundwater and the
survival or modification of ecosystems.

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In the urban sector, in general, there are certain requirements on minimum depths
(sometimes also maximum depths) to groundwater to be maintained.
Thus, different sectors will come up with different requirements regarding the target
groundwater levels. This leads to spatial variation in drainage depth criteria, but sometime
also to incompatibilities.
The design of adequate drainage systems requires some kind of groundwater flow
analysis, which may range from the application of very simple to the use of numerical
groundwater models. Common technical means of groundwater level control are ditches,
drains and well-point systems.
It is perceived that ecological issues such as wetland conservation are gaining importance
in the planned control of groundwater level.
3. Control of land subsidence
Significant land subsidence may occur as a consequence of groundwater abstraction or
groundwater level control. This may be expected in particular when important drops of
hydraulic head are produced in zones where water-saturated peat, clay or silty layers occur
at relatively shallow depths (within some tens of meters from land surface).
Limiting land subsidence is in such cases an important constraint to water resources
development. Under particularly unfavorable conditions this may become so critical that
prevention of any further land subsidence becomes the main groundwater management
objective; an example is the situation of Venice, where further subsidence would cause the
city to drown in the Adriatic Sea.
Predication by simulation is also in subsidence prone cases the key to good management
approaches.
Not only is it important to assess the total expected land subsidence, the rate of subsidence
is also a crucial factor
6.3 Importance of Groundwater
Groundwater is an essential natural resource in most places. It makes up about 30% of the
world’s freshwater reserve. It is often clean and easily accessible. In the United States,
more than half of the population depends on groundwater as the primary source for their
drinking water. In most farming areas where irrigation is practiced, groundwater is often
used to irrigate the crops. In dry regions like Australia, groundwater provides a cheap

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water source because it is the most cost-effective to extract. In times of no rain, the
groundwater plays a vital role in the environment by releasing water into rivers, lakes, and
streams. As a result, groundwater prevents them from drying up. It also sustains the
ecosystem by providing water for the vegetation when rainwater has dried up.

6.4 Major Sources of Groundwater Contamination

For a long time, groundwater was known to be clean and free from contamination.
However, due to rapid industrialization and increased use of chemicals, numerous
contaminants often find their way into the groundwater. The significant sources of
contamination in groundwater are farming chemicals, septic waste, landfills, uncontrolled
hazardous waste, storage tanks, and atmospheric pollutants.

6.4.1 Agricultural Chemicals

Agricultural production has been scaled up in most developed nations. This large-scale
production of farm goods means increased use of farm chemicals such as pesticides,
herbicides, and fertilizers. These chemicals used on farms settle on the ground, and when
it rains, they mix with the rainwater and seep through the porous ground to reach the
underground water. That way, the chemicals pollute the groundwater.

6.4.2 Septic Waste

It is essential that septic waste is treated before it is disposed into the ground. Treatment
prevents harmful substances from getting into the ground and spreading to the water.
Additionally, the septic systems are structured to release the waste into the ground at an
extremely slow rate which is harmless to the environment. However, poorly designed
septic systems release viruses, bacteria, and household chemicals into the groundwater and
make it unfit for human consumption. Poorly maintained septic tanks also result in leaks
which cause groundwater contamination.

6.4.3 Landfills
As the human population grows, so does the garbage produced daily. This garbage is
collected and taken to particular locations known as landfills where it is buried. Landfills
are required to have a protective layer at the bottom to stop the waste from seeping into
the ground. Nonetheless, some landfills lack that protective layer, and in some cases, it is

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cracked. Such landfills result in leaks of contaminants such as household chemicals, car
battery acid, oil, and medical products into the groundwater.

6.4.5 Hazardous Waste Sites

There are numerous sites around the world where hazardous products such as radioactive
components, war chemicals, electronic waste, and similar products are disposed. The
numbers of these waste sites keep growing by the day. In many cases, hazardous products’
disposal sites are not adequately monitored. The lack of proper monitoring and
maintenance of such sites leads to leakage of dangerous substances into the groundwater.

6.4.6 Storage Tanks

Chemicals, oil, minerals, and other products are often kept in storage tanks above or below
ground. In the United States alone, it is estimated that more than 10 million storage
barrels containing different substances are stored underground. Over time, the storage
containers erode, and this may result in harmful substances leaking into the ground.
Subsequently, the contaminants move through the soil and reach the groundwater making
it unfit for human use.

6.4.7 Atmospheric Pollutants

Groundwater is maintained through the hydrological cycle which is the movement of
water above, below, and on the surface of the earth. As the water moves, it comes into
contact with pollutants in the atmosphere such as harmful gases. When it rains, the water
carries these contaminants into the ground and pollutes the groundwater.

6.4.8 Underground Pipes

As nations develop, they invent new methods of transporting different products using the
underground pipes. Products such as oil, farm chemicals, cooking gas, and drinking water
are mainly transported through underground pipes. In many instances, the underground
pipes burst and release their content into the ground. These incidents often lead to
groundwater contamination.

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6.4.9 Road Salts
Road salts are mainly used in places that have snowfall during winter. Road salts are
chemical products used to melt ice on the road. Once the ice melts it flows with the
chemicals through the ground and into the groundwater hence contaminating the water.

6.5 Effects of Contaminated Groundwater

Contaminated groundwater can lead to severe effects on the environment, animals, and
human beings. Firstly, groundwater is the primary source of drinking water for most
people and animals around the globe. Once the groundwater is contaminated with harmful
chemicals and bacteria, the humans and animals consume the harmful substances through
drinking water and subsequently suffer health problems such as amoeba, typhoid,
diarrhea, and even cancer. Secondly, the trees and vegetation that rely on groundwater are
likely to dry up after absorbing contaminated water. As a result, the loss of vegetation
leads to an imbalance in the ecosystem. Thirdly, contaminated groundwater may seep into
rivers and streams and lead to the loss of marine life which is detrimental to the
environment. Lastly, when groundwater is contaminated with reactive substances, it may
result in harmful chemical reactions that destroy the soil around the area. The
consequences of destroyed soil include poor plant development and bad soil quality.

6.6 Groundwater remediation

6.6.1 Introductions
Groundwater is the water locked beneath the ground surface that saturates the pore space
in the subsurface. Since last few decades it has come up as a sustainable source of water.
Due to various anthropogenic activities and illegal dumping or disposal of untreated
industrial effluents, this perennial source has been degraded up to the extent in some
regions that sincere and immediate remediation efforts are highly required to restore its
quality. Groundwater remediation is the process used to remove/reduce concentration of
contaminants up to the level that ground water can be safely used for various applications.
Remediation can be done by applying various physical, chemical and biological
techniques thereby making it safe for use.
6.6.2 Physical remedy of Groundwater
Pump treatment

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This involves removing contaminated groundwater from strategically placed wells,
treating the extracted water after it is on the surface to remove the contaminates using
mechanical, chemical, or biological methods, and discharging the treated water to the
subsurface, surface, or municipal sewer system.
Applications:
This method can be designed for removal of any contaminants or combination of
contaminants. Common contaminants are

 Volatile and semi volatile organic compounds (including Diesel range organics
(DRO) & Petroleum range organics (PRO)).
 Heavy metals like Lead, Chromium, etc.
 Pesticides
 pH

Figure 6.1 pump and treatment methods

Limitations:

 Its effectiveness depends on the geology of the aquifer and the type of
contaminant.
 It is slow, taking decades to centuries to remove all contaminated water
 It is very costly.
 It treats only ground water. Some contaminants stick to soil and rock and Non-
Aqueous Phase Liquids NAPLs cannot be removed.

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6.2.2 Air sparging or oil vapor extraction (SVE)
Air sparging is an in situ remedial technology which involves the injection of fresh air/
hot air directly into the subsurface saturated zone. As the bubbles rise in the ground
water, the contaminants are removed from the groundwater by physical contact with the
air and are carried up into the unsaturated zone (i.e., soil). As the contaminants move into
the soil, a SVE system is usually used to remove vapors.

Figure 6.2 Air sparging methods

Applications:

Air Sparging has been found to be effective in reducing concentrations of

 Volatile organic compounds found in petroleum products like gasoline, diesel, etc.
 BTEX components.
 Chlorinated solvents like PCE, TCE, DCE, etc.
Limitations:

 The main limitations for air sparging are controlling the distribution of the injected
air and off-site vapor migration.
 There is a potential of enhanced dissolved/free phase contaminant migration and
aquifer clogging, both physically and chemically, if it is not controlled.
 The site must be capable of supporting drilling operations in the locations where the
vapor extraction and air sparging wells are desired.
 Some lithologies are not conducive to this type of treatment. For example, a layer of
low permeability soil overlying the saturated zone may prevent the injected air from
being scavenged by the vapor extraction system installed above it.

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 Existing underground utilities may limit installation in some areas.
6.6.3 Dual phase vacuum extractions

Figure 6.3 dual phase extraction at travaini LRP

Dual-phase Vacuum extraction (DPVE), is an in- situ technology in which vacuum

applied to the subsurface with DPE systems creates vapor-phase pressure gradients
toward the vacuum well. In response to the imposed gradients the subsurface liquids
present and those liquids existing in a continuous phase (e.g., water and "free" petroleum
product)will flow toward the vacuum well. Extracted liquids and vapor are treated and
collected for disposal, or re-injected to the ground.
Applications:

 The DPE systems are more effective in removing separate-phase product/free

products from the subsurface.
 They are typically designed to maximize the effectiveness of soil vapor extraction
(SVE) by lowering the water table and therefore increasing air-phase permeability in
the vadose zone.

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Limitations:

 Site geology and contaminant characteristics influence the effectiveness of this

technology.
 Complementary technologies, such as pump- and-treat, may be combined with
DPE.
 DPE requires both water treatment and vapor treatment.
 Two-phase extraction requires an oil/water separator.

6.6.4 Chemicals treatment technologies

1) CHEMICAL PRECIPITATION
Chemical precipitation is a conventional technology which involves addition of chemical
precipitants, coagulants, and flocculants in pumped ground water stream in a stirred
reaction vessel to increase particle size through aggregation, either batch wise or with
steady flowfollowed by the separation of the precipitated solids from the cleaned water.
Applications:

 It can remove hardness, heavy metals, fats, oils and greases (FOG), suspended solids
and some organics from ground water. It can also be used to remove phosphorus,
fluoride, ferrocyanide and other inorganics.
 It is applicable to the following situations:
 mining-influenced water
 high or low volume of material
 solo technology or in conjunction with others
 multiple contaminants of concern
Limitations:

 High cost
 Not applicable for all cases
 Requires operation and maintenance (O&M)
 Requires power
 It may generate waste products.

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2) ION EXCHANGE
Ion exchange for ground water remediation is virtually always carried out by passing the
water downward under pressure through a fixed bed of resins or granular medium (either
cation exchange media or anion exchange media) or spherical beads bed where ions
cations and anions in the resins are exchanged by the cations and anions in contaminated
water. Ion exchange media most often used for remediation are zeolites (both natural and
synthetic) and synthetic resins. After the resin capacity has been exhausted, some can be
regenerated for re-use, while others are meant for single use.
Applications:

 Ion exchange can remove dissolved metals (chromium), radionuclides and other
inorganic chemicals from water.
 It can also be used to remove non-metallic compounds such as perchlorate, nitrate,
and ammonia.
Limitations:

 Oil and grease in the groundwater may clog the exchange resin.
 The acidity or alkalinity of the incoming water may limit ion exchange capability.
This can usually be controlled.
 Oxidants in groundwater may damage the ion exchange resin.
 Wastewater is generated during the regeneration step and requires additional
treatment and disposal.
 The process does not destroy the contaminants; it transfers them to a different
medium which must be treated or disposed of.
 If the system is designed as a single-use system, resin must either be disposed in a
landfill or incinerated.
3) CARBON ADSORPTION
Liquid phase carbon adsorption is a full-scale technology in which ground water is
pumped through one or more vessels containing activated carbon to which dissolved
organic contaminants are adsorbed. When the concentration of contaminants in the
effluent from the bed exceeds a certain level, the carbon can be regenerated in place or at

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an off- site facility.The most common activated carbon used for remediation is derived
from bituminous coal.
Applications:

 The target contaminant groups for carbon adsorption are hydrocarbons, SVOCs and
explosives.
 Liquid phase carbon adsorption is effective for removing contaminants at low
concentrations (less than 10 mg/L) from water at nearly any flow rate, and for
removing higher concentrations of contaminants from water at low flow rates
(typically 2 to 4 liters per minute or 0.5 to 1 gm).
 It is particularly effective for polishing water discharges from other remedial
technologies to attain regulatory compliance.
 This system can be deployed rapidly, and contaminant removal efficiencies are high.
Limitations:
The presence of multiple contaminants can impact process performance. Bench tests may
be conducted to estimate carbon usage for mixtures.
 Streams with high suspended solids (> 50 mg/L) and oil and grease (> 10 mg/L) may
cause fouling of the carbon and may require frequent treatment.
 It is costly if used as the primary treatment on waste streams with high contaminant
concentration levels.
 Type, pore size, and quality of the carbon, as well as the operating temperature, will
impact process performance.
 Carbon used for explosives- or metals- contaminated ground water is not regenerated.
 Highly Water-soluble compounds and small molecules are not adsorbed well.
 All spent carbon eventually needs to be properly disposed.
4) CHEMICAL OXIDATION
In the process called In Situ Chemical Oxidation or ISCO, oxidants such as air , ozone or
certain chemical oxidants chemicals such as hydrogen peroxide, permanganate and
persulfateare delivered in the subsurface in the form of liquids or gases to destroy the
organic contaminants or to neutralize contamination caused by petroleum and volatile
organic compounds (VOCs) in soil and groundwater . Chemical oxidation has proven to
be an effective technique for dense non-aqueous phase liquid or DNAPL when it is

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present.

Figure 6.4 Insitu chemical oxidation

Applications:

 Chemical oxidation is most often deployed at sites contaminated with petroleum-

based fuels, chlorinated and non-chlorinated solvents, polychlorinated biphenyls,
organic pesticides and other organic contaminants in ground water and saturated soil.
Limitations:

 Requirement for handling large quantities of hazardous oxidizing chemicals due to the
oxidant demand of the target organic chemicals and the unproductive oxidant
consumption of the formation.
 Some COCs are resistant to oxidation.

 There is a potential for process-induced detrimental effects. Further research and

development is ongoing to advance the science and engineering of in situ
chemical oxidation and to increase its overall cost effectiveness.
6.6.5 Biological treatment technologies

BIOVENTING
Bioventing is an in situ remediation technology that uses the supply of oxygen and
nutrients through direct air injection into residual contamination in soil (unsaturated
zone) and ground water to enhance the activity of indigenous bacteria and to simulate the
natural in situ biodegradation of hydrocarbons (adsorbed fuel residues & VOCs).

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Applications

Bioventing has proven to be very effective in remediating the releases of

 All aerobically biodegradable constituents
 Petroleum products including gasoline, jet fuels, kerosene, and diesel fuel.
 Mid-weight petroleum products (i.e., diesel fuel and jet fuel. Heavier products (e.g.,
lubricating oils) generally take longer to biodegrade than the lighter products.
 Nonchlorinated solvents, some pesticides, wood preservatives, and other organic
chemicals.

Figure 6.5 bioventing methods

Limitations
Factors that may limit the applicability and effectiveness of the process include:
1) Low permeability soils (reduce bioventing performance).
2) Air near the structure of concern has to be extracted in order to avoid vapor build up
in basements within the radius of influence of air injection wells.
3) Monitoring of off-gases at the soil surface may be required.
4) Aerobic biodegradation of many chlorinated compounds may not be effective.
5) Low soil moisture content, limits biodegradation.
BIOSLURPING

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Bio slurping, an in situ remediation technique is combination of the two remedial
approaches of bioventing and vacuum-enhanced free-product recovery technologies to
simultaneously recover free product without extracting large quantities of ground water
and bio-remediate vadose zone soils.
Vacuum-enhanced pumping involves the application of negative pressure to a well point
to increase the rate of flow of groundwater and soil gas into the wells. Bioventing of
vadose zone soils isachieved by drawing air into the soil due to withdrawing soil gas via
the recovery well.

Figure 6.6 bio-slurping

Applications
Bioslurping can be successfully used to remediate oils contaminated by petroleum
hydrocarbons.
 It is a cost-effective in situ remediation technology that simulataneously accomplishes
LNAPL Removal and soil remediation in the vadose zone.
 It is also applicable at sites with a deep ground water table (>30ft.).
Limitations:
 Bioslurping is less effective in tight (low- permeability) soils.
 Low soil moisture content may limit biodegradation and the effectiveness of
bioventing.
 Aerobic biodegradation of many chlorinated compounds may not be effective unless

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there is a co-metabolite present.
 Low temperatures slow down remediation.
 The off-gas from the bioslurper system requires treatment before discharge. However,
treatment of the off-gas may only be required shortly after the startup of the system as
fuel rates decrease.
 At some sites, bioslurper systems can extract large volumes of water that may need to
be treated prior to discharge depending on the concentration of contaminants in the
process water.
 Since the fuel, water and air are removed from the subsurface in one stream, mixing of
the phases occurs. These mixtures may require special oil/water separators or
treatment before the process water can be discharged.
 Bioslurping does not treat residual contamination in saturated soils.
 Liquid ring pumps (and other high-velocity pump systems) tend to form emulsions,
especially when diesel is part of recovered fluids and hence Biofouling of well
screens is possible due to active aeration of bioslurping wells.
6.6.6 Phyto-treatment
Phytoremediation is the application of plant- controlled interactions with groundwater
and organic and inorganic molecules at contaminated sites to remove pollutants like
metals, pesticides, explosives, and oil from soils, sludge, sediments, surface water, or
ground water. This process can be carried out in areas where the roots can tap the ground
water.

Plants remove harmful chemicals from the ground when their roots take in water and
nutrients from polluted soil, streams, and groundwater. Once inside the plant, chemicals
can be stored in the roots, stems, or leaves; changed into less harmful chemicals within
the plant; or changed into gases that are released into the air as the plant transpires
(breathes). If the chemicals are not taken into the plant by the roots, they can stick or sorb
to plant roots.
Examples:
 Chinese Ladder fernPterisvittata, also known as the brake fern, is a highly efficient
accumulator of arsenic.
 Genetically altered cottonwood trees are good absorbers of mercury from the

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contaminated soil in Danbury Connecticut.
 Transgenic Indian mustard plants to soak up dangerously high selenium deposits in
California.
 Thlaspicaerulescens (alpine pennycress, a small, weedy member of the broccoli and
cabbage family) can accumulate up to 30,000 ppm zinc and 1,500 ppm cadmium in its
shoots.

Figure 6.7 Phyto-treatment methods

Applications:
 Phytoremediation works best at sites contaminated with low to medium amount of
pollution.
 Heavy metals and metals like elements, such as arsenic, lead, uranium, selenium,
cadmium, and other toxins such as nutrients, hydrocarbons and chlorinated
hydrocarbons can be removed by Phytoremediation.
Limitations:
 This method is limited to remediation of ground water that is close enough to the
surface that if can be reached by plant roots.

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CHAPTER SEVEN
INTRODUCTION TO GROUNDWATER MODELING
7.1. Introduction
Groundwater modeling is a way to represent a system in another form to investigate the
response of the system under certain conditions, or to predict the behavior of the system in
the future. It is powerful tool for groundwater resources management, protection and
remediation. Decision makers use models to predict the behavior of a groundwater system
prior to implementation of a project or remediation scheme. Clearly, it is a simple and
cheap solution compared to project establishment in reality.

By definition, models simplify reality, and are, therefore, imperfect. The famous
statistician George Box insisted that all, “all models are wrong, but some are useful” (Box
and Draper 1987). Applicability of any model and its usage depends on the objectives of
that model. Though they are imperfect, models are very useful in hydrogeology. It is a
challenge to the modeler to represent the real word problem in a simplified form without
compromising the accuracy or making invalid assumptions. Modelers try to get the best
representation of reality by collecting as much data as possible and feeding the models
with new data. Groundwater models can be classified into three categories: physical,
analogue or mathematical. Solution of mathematical models can be either analytical or
numerical.

Analytical methods do not require much data, but their application is limited to simple
problems. Numerical solutions can handle more complicated problems than analytical
solutions. With the rapid development of computer processors and increasing speed,
numerical modeling has become more effective and easy to use.

The most commonly used numerical modeling approaches are the “finite difference”
method and the “finite element” method. Each method has its advantages and limitations.
Depending on the problem of concern and the objectives of modeling, the appropriate
modeling approach can be selected. Finite difference method can produce different results
to finite element method if the problem of concern is complicated.

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Modeling approach is not the only factor that affects the model’s results; other factors like
boundary conditions, initial condition, time and space discretization, and quality of data
influence the results.

This chapter outlines the stepwise methodology of groundwater modeling, differences

between modeling approaches and difficulties accompany groundwater modeling.
Common mistakes in groundwater modeling are also discussed.
7.2. Modeling Approach
Groundwater Models can be simple, like one-dimensional analytical solutions
(spreadsheet) models or very sophisticated three-dimensional models. It is always
recommended to start with a simple model, as long as the model concept satisfies
modeling objectives, and then the model complexity can be increased. Regardless of the
complexity of the model being used, the model development is the same.

The stepwise methodology of groundwater modeling is shown in bellow. The first step in
modeling is identification of model objectives. Data collection and processing is a key
issue in the modeling process. The most essential and fundamental step in modeling,
however is model conceptualization. Calibration, verification and sensitivity analysis can
be conducted after model completion and the first run. The following sections explain in
detail each step in groundwater modeling.

Figure 7.1 Stepwise methodology of groundwater modeling

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7.3. Concept of Groundwater modeling
Groundwater models are normally used to support a management decision regarding
groundwater quantity or quality. Depending on the objectives of modeling, the model
extent, approach and model type may vary.

Groundwater models can be interpretive, predictive or generic. Interpretive models are

used to study a certain case and to analyses groundwater flow or contaminant transport.
Predictive models are used to see the change in groundwater head or solute concentration
in the future. Generic models are used to analyses different scenarios of water resource
management or remediation schemes. Objectives of groundwater modeling can be listed
as:
Prediction of groundwater flow and groundwater head temporally and spatially.
 Investigating the effect of groundwater abstraction at a well on the flow regime and
predicting the resulting drawdown.
 Investigating the effect of human activities (e.g. wastewater discharge, agricultural
activities, landfills) on groundwater quality.
 Analysis of different management scenarios on groundwater systems, quantitatively
and qualitatively.

Depending on the objectives of study and the intended outcome, selection of model
approach and data requirements can be made to suit the area of study and the objectives.
For example, if the objective is a regional groundwater flow assessment, then a coarse
model may satisfy this objective, but if the area of study is small then a fine-grid model
with high data-density should be used.
7.3.1 Conceptual Model
A conceptual model is a descriptive representation of a groundwater system that
incorporates an interpretation of the geological and hydrological conditions. Information
about water balance is also included in the conceptual model. It is the most important part
of groundwater modeling and it is the next step in modeling after identification of
objectives.

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Building a conceptual model requires good information on geology, hydrology, boundary
conditions, and hydraulic parameters. A good conceptual model should describe reality in
a simple way that satisfies modeling objectives and management requirements.

It should summarize our understanding of water flow or contaminant transport in the case
of groundwater quality modeling. The key issues that the conceptual model should include
are:
 Aquifer geometry and model domain
 Boundary conditions
 Aquifer parameters like hydraulic conductivity, porosity, storativity, etc
 Groundwater recharge
 Sources and sinks identification
 Water balance
Once the conceptual model is built, the mathematical model can be set-up. The
mathematical model represents the conceptual model and the assumptions made in the
form of mathematical equations that can be solved either analytically or numerically.
A. Boundary Value Problem
Mathematical models are all based on the water balance principle. Combining the mass
balance equation and Darcy’s Law produces the governing equation for groundwater flow.
The general equation that governs three-dimensional groundwater steady-flow in
isotropic, homogeneous porous media is:

Where h is the groundwater head. This equation is also called the Laplace equation and it
has many applications in physics and hydromechanics. Solving Equation (1) requires
knowledge of boundary conditions to get a unique solution. For this reason, Equation (1)
is called a boundary value problem. So the boundary conditions delineate the area or the
domain where the boundary value problem is valid.
Box 1: Conceptual model: questions to answer
 Is there enough hydrogeological data to describe the geometry of the aquifer/s in
the area of study?

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 Should the model be one, two or three-dimensional?
 Is the aquifer/s homogeneous? Isotropic?
 What are the sources and sinks?
 What are the sources of contamination (if applicable)?
 Do the boundaries stay the same over time?

B. Boundary Conditions
Identification of boundary conditions is the first step in model conceptualization. Solving
of groundwater flow equations (partial differential equations) requires identification of
boundary conditions to provide a unique solution. Improper identification of boundary
conditions affects the solution and may result in a completely incorrect output. Boundary
conditions can be classified into three main types:
 Specified head (also called Dirichlet or type I boundary). It can be expressed in a
mathematical form as: h (x,y,z,t) = constant.
 Specified flow (also called a Neumann or type II boundary). In a mathematical
form it is: ∇h (x,y,z,t)=constant.
 Head-dependent flow (also called a Cauchy or type III boundary). Its mathematical
form is: ∇h (x,y,z,t)+a*h=constant (where “a” is a constant).

In addition to the above-mentioned types there are other sub-types of boundaries. These
will be explained later.

In groundwater flow problems, boundary conditions are not only mathematical constraint,
they also represent the sources and sinks within the system. Selection of boundary
conditions is critical to the development of an accurate model.

It is preferable to use physical boundaries when possible (e.g., impermeable boundaries,

lakes, rivers) as the model boundaries because they can be readily identified and
conceptualized. Care should be taken when identifying natural boundaries. For example
groundwater divides are hydraulic boundaries and can shift position as conditions change
in the field. If water table contours are used to set boundary conditions in a transient
model, in general it is better to specify flux rather than head. In transient simulation, if
transient effects (e.g. pumping) extend to the boundaries, a specified head acts as an

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infinite source of water while a specified flux limits the amount of water available. If the
groundwater system is heavily stressed, boundary conditions may change over time. For
this reason, boundary conditions should be continuously checked during simulation.

C. Examples of Different Boundaries

Reilly (2001) has surveyed different types of physical features and their equivalent
mathematical representations. Figure 2 shows different types of boundaries. These
different boundaries are briefly described as follows:

Constant head boundary: This is a special case of a specified head boundary, which
occurs where part of the boundary surface of an aquifer coincides with a surface of
essentially constant head. Constant head boundaries assume that the head is constant over
time. Lines ABC and EFG in Figure 2 are examples of constant head boundaries, where
part of the aquifer occurs underneath a reservoir.

Specified head boundary: This is a generalized form of constant head boundary. This
occurs when head can be specified as a function of time and location. Rivers and streams,
which are in hydraulic connection with an aquifer, are examples of specified head
boundary.

No flow boundary: This is a special case of a specified flux boundary. This occurs at a
line normal to streamline (i.e. normal to flow direction). This case normally occurs where
impermeable media exist. Line HI in Figure 2 represents a no-flow boundary. A water
divide can be used as a no-flow boundary but with caution, as position of the water divide
may move with time as a result of stresses on the aquifer.

Specified flux boundary: This is a generalized case of a no-flow boundary. This occurs
when flow across the boundary can be specified in time and location. An example of a
specified flux boundary is recharge across the water table in a phreatic aquifer. Line CD in
Figure 2 is a specified flux boundary.

Head-dependent flux boundary: This occurs when flux across a boundary depends on
head adjacent to that boundary. A semi-confined aquifer, where the water head depends on

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the flux through the semi-confining layer, is an example of this type of boundary. This can
be represented by lines ABC and EFG in Figure 2.

Free-surface boundary: The water table and the fresh-saline water interface in a coastal
aquifer are examples of free-surface boundaries. Line CD in Figure 2 represents a free-
surface boundary. Pressure head at free-surface boundary is always zero and the total head
equals elevation head.

Seepage face boundary: This occurs at the boundary between saturated flow and the
atmosphere. The face of a landfill dam, as shown by line DE in Figure 2 is an example of
a seepage face boundary.

Figure 7.2 Different types of boundaries.

Box 2: Boundary conditions comments
 Always use natural boundaries when possible.
 Boundary conditions always influence a steady state solution but may not
influence a transient solution.
 A steady state solution with all specified flux boundary conditions (including no
flow) without specified head or head-dependent internal boundaries may not
converge or may not give a unique solution.
 A specified head boundary acts as an infinite source or sink.
 A water divide should be used as a no-flow boundary with caution.

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7.4 Types of Models
There are different types of models to simulate groundwater movement and contaminant
transport. In general, models can be classified into three categories: physical, analogue and
mathematical models. The latter type can be classified further depending on the type of
solution.
1. Physical Models
Physical models (e.g. sand tanks) depend on building models in the laboratory to study
specific problems of groundwater flow or contaminant transport. These models can
demonstrate different hydrogeological phenomena like the cone of depression or artesian
flow. In addition to flow, contaminant movement can be investigated through physical
models. Though they are useful and easy to set-up, physical models cannot handle
complicated real problems.

2. Analogue Models
The equation which describes groundwater flow in isotropic homogenous porous media is
called the Laplace’s Equation (Equation (1)). This equation is very common in many
applications in physical mathematics like heat flow, and electricity. Therefore, comparison
between groundwater flow and other fields where the Laplace equation is valid is possible.

The most famous analogue model is the flow of electricity. The electric analogue is based
on the similarity between Ohm’s law of electric current flow and Darcy’s law of
groundwater movement. As electric current moves from high voltage to lower voltage, so
does the groundwater, which moves from high head to lower head.

Simple analogue models can easily be setup to study the movement of groundwater flow.
More detailed information on analogue models is available.

3. Mathematical Models
Mathematical models are based on the conceptualization of the groundwater system into a
set of equations. These equations are formulated based on boundary conditions, initial
conditions, and physical properties of the aquifer. Mathematical models allow an easy and
rapid manipulation of complex models. Once the mathematical model is set-up, the

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resulting equations can be solved either analytically, if the model is simple, or
numerically.
7.5. Modeling Solutions
As discussed in the preceding sections, the mathematical models can be solved either
analytically or numerically. Some approaches use a mixture of analytical and numerical
solutions. The following sections briefly discuss the main types of solutions used in
groundwater modeling.
7.5.1. Analytical Solutions
Analytical solutions are available only for simplified groundwater and contaminant
transport problems. They were developed before the use of numerical models. The
advantages of analytical solutions are that they are easy to apply and produce continuous
and accurate results for simple problems. Unlike numerical solutions, analytical solutions
give a continuous output at any point in the problem domain (Figure 3). However,
analytical solutions make many assumptions like isotropy and homogeneity of an aquifer,
which are not valid in general. Analytical solutions; therefore, cannot deal with complex
groundwater systems. Examples of analytical solutions are the Toth solution. More details
on analytical solutions of groundwater problems can be found in Bear.
7.5.2. Numerical Solutions
Because analytical solutions of partial differential equations (PDE) imply many
assumptions, simplifications and estimations that do not exist in reality, they cannot
handle complicated real problems. Numerical methods were developed to cope with the
complexity of groundwater systems.
Numerical models involve numerical solutions of a set of algebraic equations at discrete
head values at selected nodal points (Figure 3). The most widely used numerical methods
are finite difference and finite element methods. Other methods have been developed, such
as the boundary-element method.

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Numerical

Distance (x)

Figure 7.3. Analytical versus numerical solutions for a 1-D groundwater flow problem
7.6 Groundwater modeling methods
7.6.1 Finite difference method
Finite difference method (FDM) has been widely used in groundwater studies since the
early 1960s. FDM was studied by Newton, Gauss, Bessel and Laplace (Pinder and Gray
1977).
This method was first applied in petroleum engineering and then in other fields. The finite
difference method depends on the estimation of a function derivative by a finite difference
(Figure 4). The finite difference approximation is given by:

The accuracy of the method depends on grid size and uniformity. The approximation of
the derivative improves as grid spacing approaches zero; however, numerical dispersion
and truncation error increases. There are three different methods of finite difference
approximation: forward, backward and central difference, depending on the way the finite
difference is implemented. The central difference gives the best results as the truncation
error is of second order O (Δx)2

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Figure 7.4 Finite difference approximation.

The general governing equation for transient, heterogeneous, and anisotropic conditions is
given by:

( ) ( )

where Kx, Ky, and Kz are hydraulic conductivity in x, y and z directions, respectively. W is
the sink or source term and Ss is specific storage.
For simplicity, consider a one-dimensional case of Equation (3) and solve for h using the
finite difference method. This yields:

where hi, hi+1 are the head at node i, and node i+1 respectively (Figure 5). Irregular
spacing can be used to increase accuracy at selected areas of the grid, but this increases
associated error more than regular-spaced grids. As a rule of thumb for expanding a finite
difference grid, the maximum multiplication factor should not be higher than 1.5

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Figure 7.5 The finite difference method

Figure 7.5 Discretization of model domain into a finite difference grid.

The advantages of the finite difference method are that it is easy to implement, well
documented and produces reasonably good results. However, finite difference method has
some disadvantages. The main disadvantage is that it does not fit properly to an irregular
model boundary (Figure 6). In addition, the distribution of grids, their size, and whether
they are of equal size highly affects the accuracy and computation effort. Output accuracy
of the finite difference method is not good in the case of solute transport modelling. Mass

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balance is not guaranteed if conductivity or grid spacing varies. The most widely used
finite difference based groundwater model is MODFLOW.
Box 3: Considerations in selecting the size of the nodal spacing in grid or mesh design
 Variability of aquifer characteristics (e.g.. conductivity, storativity).
 Variability of hydraulic parameters (e.g. recharge, pumping).
 Curvature of the water table.
 Desired detail around sources and sinks (e.g., rivers).
 Vertical change in head (vertical grid resolution/layers).

7.6.2. Finite Element Method

The basis of the finite element method is solving integral equations over the model
domain. When finite element method is substituted in the partial differential equations, a
residual error occurs. The finite element method forces this residual to go to zero.

There are different approaches for the finite element method. These are: basis functions,
variation principle, Galerkin’s method, and weighted residuals. Detailed description of
each method can be found in Pinder and Gray (1970).

Finite element method discretizes the model domain into elements (Figure 7). These
elements can be triangular, rectangular, or prismatic blocks. Mesh design is very important
in the finite element method as it significantly affects the convergence and accuracy of the
solution.

Mesh design in the finite element method is an art more than a science, but there are
general rules for better mesh configuration. It is highly recommended to assign nodes at
important points like a source or sink, and to refine mesh at areas of interest where
variables change rapidly. It is better to keep the mesh configuration as simple as possible.
In the case of triangular mesh, a circle intersecting vertices should have its center in the
interior of the triangle.

The weighted residual method is being widely used in groundwater finite element
problems. The Russian engineer B. G. Galerkin introduced this method in 1915 (Pinder

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and Gray 1970). To illustrate the weighted residual approach, consider a groundwater or
solute transport problem. This problem over a domain B can be written as:
L(φ (x, y, z)) − F (x, y, z) = 0
Where L is a differential operator, φ(x,y,z) is the dependent variable (i.e. groundwater
head) and F(x,y,z) is a known function. Approximation function φ (x, y, z) . The later
approximation function is made up of a linear combination of a new function that satisfies
the boundary conditions of the main problem. It can be written as:

where Ni is an interpolation function, φi is the unknown nodal value of dependent variable

at node i, and m is the number of nodes. Because φ (x, y, z) is an approximation, there will
be a residual R(x,y,z) at each node. This residual is given by:
ˆ
R(x, y, z) = L((φ (x, y, z) − F (x, y, z) ≠ 0

The weighted residual method forces the residual in Equation (7) to go to zero. This
requires:
∫∫∫W (x, y, z) •R(x, y, z)dxdydz = 0

Where W (x,y,z) is a weighting function and B is the problem domain. The above
equation can be written in terms of approximation function as follows:

∫∫∫W (x, y, z)[L(φˆ(x, y, z)) − F (x, y, z)]dxdydz = 0

In case of a steady state, two-dimensional groundwater flow problem, Equation (9) can be
written as:

To solve Equation (10), the weighting function W (x,y,z) needs to be identified. There are
different methods of weighting residuals in addition to Galerkin’s approach. More details

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on weighting residuals methods can be found in Gray and Pinder (1970) and Reddy
(2006).
The main characteristics of the finite element method are: properties and source/sink are
assigned at nodes, nodes are located at flux boundaries, and it suites aquifer anisotropy
better than FDM. Advantages of this method include: a better mesh configuration, which
suites irregular model boundaries, anisotropy is well incorporated, the governing system
of equations is symmetric and irregular shapes can be used to represent elements.

Figure 7.6 Discritization of the model domain into a finite element mesh.
The finite element method has some disadvantages. The finite element mesh is not easy to
build and consumes time, especially in complicated problems. Also, there is less
documentation on the finite element method compared to finite difference method. Unlike
the finite difference method, mass balance in the finite element method can be achieved
for the entire domain but not for every element. The most wellknown finite element based
groundwater models are
Box 4: Finite element or finite difference?
Finite element Finite difference

Model boundary Incorporates irregular and Difficult to incorporate

curved boundaries irregular boundaries

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At vertices and flux
Nodes boundary Nodes located at centre of
cell

Mesh/grid building Difficult to generate an Easy to build a finite

efficient mesh difference grid

Anisotropy Easily incorporated Difficult to incorporate

Accuracy Acceptable accuracy More accurate especially in

solute transport modelling

Computation time Good and acceptable time Computation time can be

requirement long in 3D problems.

7.7. Model Calibration

After the first run of a model, model results may differ from field measurements. This is
expected because modelling is just a simplification of reality and approximations and
computational errors are inevitable.

The process of model calibration is aimed at fine-tuning the model results to match the
measurements in the field. In a groundwater flow models, the resulting groundwater head
is forced to match the head at measured points. This process requires changing model
parameters (i.e. hydraulic conductivity or groundwater recharge) to achieve the best
match. The calibration process is important to make the model predictive and it can also
be used for inverse modeling.

To illustrate the calibration process of a groundwater flow model, consider the

groundwater head measurements (hob)i at the observation point i. The simulated head at
the same point is (hsim)i. The root mean square error of the residual is given by:

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Calibration involves an optimization process to minimize the RMSE given in equation

above. To get a well-calibrated model, proper site characterization and ample data are
required. Otherwise, the calibrated model will only be valid for a set of conditions and not
for any condition. Calibration can be manually done or automatically. Software like PEST
(Doherty et. al. 1994) and UCODE can be used for automatic calibration.
Box 4: The calibrated model should satisfy:
 A good match between measured and modeled head.
 A good water mass balance.
 The groundwater gradient from the model is similar to the observed gradient in the
field.
 Similar behavior for any dataset.

7.8. Model Verification and Validation

The term “validation” is not completely true when used in groundwater modeling. Oreskes
et. al. (1994) asserted it is impossible to validate a numerical model because modeling is
only approximation of reality. Model verification and validation is the next step after
calibration. The objective of model validation is to check if the calibrated model works
well on any dataset. Because the calibration process involves changing different
parameters (i. e. hydraulic conductivity, recharge, pumping rate etc.) different sets of
values for these parameters may produce the same solution. Reilly and Harbaugh (2004)
concluded that good calibration did not lead to good prediction. The validation process
determines if the resulting model is applicable for any dataset. Modelers usually split the
available measurement data into two groups; one for calibration and the other for
validation.
7.9. Sensitivity Analysis
Sensitivity analysis is important for calibration, optimisation, risk assessment and data
collection. In regional groundwater models, there are a large number of uncertain
parameter. Coping with these uncertainties is time-consuming and requires considerable
effort. Sensitivity analysis indicates which parameter or parameters have greater influence

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on the output. Parameters with high influence on model output should get the most
attention in the calibration process and data collection. In addition, the design of sampling
location and sensitivity analysis can be used to solve optimization problems.
The most common method of sensitivity analysis is the use of finite difference
approximations to estimate the rate of change in model output as a result of change in a
certain parameter. The Parameter Estimation Package “PEST” uses this method (Doherty
et. al. 1994).
Some other more efficient methods of sensitivity analysis have been used. Automatic
differentiation has been used for sensitivity analysis in groundwater models and it
produces precise output compared to finite difference approximations.
7.10. Uncertainty Analysis
Uncertainty in groundwater modeling is inevitable for a number of reasons. One source of
uncertainty is the aquifer heterogeneity. Field data has uncertainty. Mathematical
modelling implies many assumptions and estimations, which increase the uncertainty of
the model output
There are different approaches to incorporate uncertainty in groundwater modeling. The
most famous approach is stochastic modeling using the Monte Carlo or Quasi Monte
Carlo method The problem with stochastic models is that they require a lot of
computations, and thus they are time consuming. Some modifications have been done on
stochastic models to make them more deterministic, which reduce computational and time
requirements. Latin Hypercube Sampling is a modified form of Monte Carlo Simulation,
which considerably reduces the time requirements.
7.9 Common Mistakes in Modeling
A major mistake in modeling is conceptualization. If the conceptual model is incorrect, the
model output will be incorrect regardless of data accuracy and modeling approach. A good
mathematical model will not resurrect an incorrect conceptual model.

In all models, it is necessary to identify a certain reference elevation for all head so that
the model algorithm can converge to a unique solution.

Boundary conditions should be treated with care, especially in a steady state simulation.
Sometimes boundary conditions change during simulation and become invalid. A model

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with hydraulic boundary conditions will be invalid if stresses inside or outside the model
domain cause the hydraulic boundaries to shift or change. Therefore, boundary conditions
should be monitored at all times to ensure they are valid.

Model parameterization is a common mistake in modeling. Theoretical values of hydraulic

properties or groundwater recharge should never substitute field data and field
investigation. Assumptions like isotropy and homogeneity should not be used without
support from field investigation.

Selection of the model code is important to obtain a good solution. Different codes involve
different mathematical settings that suit a certain problem. The selected code should
consider characteristics of the area of interest and the objectives of modeling.

Models can be well calibrated and match well with the measured values, but have an
incorrect mass balance. This can be a result of an improper conceptual model.
7.10.1 Applications of mathematical models in groundwater flow problems
A groundwater system has two basic hydraulic functions: in storing water it acts as a
reservoir, and in transmitting water from recharge to discharge areas it serves a conduit. A
groundwater system can be considered as a reservoir that integrates various inputs
(through mixing, among others) and dampens and delays the propagation of changes in
inputs. The water movement is dictated by hydraulic gradients and geology-dependent
hydraulic conductivity. In turn, these gradients are influenced by groundwater system
boundary conditions such as those resulting from human-induced stresses on the system,
climatic effects, and topography (land-surface and stream-related boundary conditions).
Groundwater systems are characterized by complex inflow-outflow-storage relations.
System outflows are influenced by the origin and pathways of the groundwater. These
relations are difficult to define directly from input and response data because of the
dampening effect of storage on inflow, the lag or delay between the time water enters and
exits the system, the variable rate and sometimes diffuse manner of recharge and
discharge, and the heterogeneity of the geology. Therefore, mathematical models, based
on a mechanistic description of the physical and chemical processes internal to the
groundwater system, are widely used in groundwater hydrology.

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The mathematical model for groundwater flow is derived by applying principles of mass
conservation (resulting in the continuity equation) and conservation of momentum
(resulting in the equation of motion). The applicable equation of motion in groundwater is
Darcy's law, which originated in the mid-nineteenth century as an empirical relationship.
Later, a mechanistic approach related this equation to the basic laws of fluid dynamics
(Bear, 1972). Variability of parameters in space and time and uncertainty in data are often
incorporated in these models.
Mathematical model consists of:
(i) Definition of a geometry of the considered domain and its boundary
(ii) Equations that express the balance of the considered quantities
(iii) Flux equations to the relevant state variables of the problems
(iv) Constitutive equations that define the behavior of the particular material (fluids
and solids) involved
(v) Initial and boundary conditions
Mathematical models of groundwater flow can be undertaken at the start or at the end of a
hydro-geological investigation. At the start for conceptualizing the main controls on
groundwater flow in the model area and for indicating the type and length of field data
that will be required to construct a model; and at the end for predicting future aquifer
response under different groundwater conditions. With a well-constructed model, the
ability to predict groundwater flow patterns for example the effects of different
groundwater abstraction patterns on the sensitive aquatic system, or the shape of well head
capture zones for protecting groundwater quality, or future aquifer response to changing
recharge amounts under changing climatic conditions, makes groundwater modeling
essential tool for managing local and regional groundwater resources.
The rate of groundwater movement can be expressed in terms of time required for
groundwater to move from a recharge area to a discharge zone. This time ranges from a
few days in zones adjacent to discharge areas in local systems, to thousands of years for
water that moves through deeper parts of the groundwater system. Large residence time in
groundwater basins gives relatively slow chemical processes a chance to influence the
composition of the water.

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The groundwater transport of dissolved chemicals and biota such as bacteria and viruses is
directly related to the flow of water in the subsurface. Many of the constituents occurring
in groundwater can interact physically and chemically with solid phases such as clay
particles, and with various dissolved chemicals. As a consequence, their displacement is
both a function of mechanical transport processes such as advection and dispersion, and of
physicochemical interactions such as adsorption-desorption, ion exchange, dissolution-
precipitation, reduction-oxidation, and radioactive decay. Biotransformation taking place
during the transport can alter the composition of the groundwater significantly.
In modelling the transport of dissolved chemicals, the principle of mass conservation is
applied to each of the chemical constituents present. The resulting equations include
physical and chemical interactions, as between the dissolved constituents and the solid
subsurface matrix, and among the various solutes themselves. These equations might
include the effects of biotic processes. To complete the mathematical formulation of a
solute transport problem, equations are added describing groundwater flow and chemical
interactions, as between the dissolved constituents and the solid subsurface matrix, and
among the various solutes themselves. In some cases equations of state are added to
describe the influence of temperature variations and the changing concentrations on the
fluid flow through the effect of these variations on density and viscosity
The solution of the equations describing a deterministic system is approached in three
ways. If the solution is continuous in both time and space, it is called an analytical
solution or model. For a solution that is discrete in either time or space, the term semi-
analytical model is used. A numerical model is discrete in both time and space and uses
approximations for the derivatives in the governing equations. Spatial and temporal
resolution in applying such models is a function of study objectives and availability of
data.
No universal model can solve all kinds of groundwater problems; different types of
models are appropriate for solving different types of problems. It is important to realize
that comprehensiveness and complexity in a simulation do not necessarily equate with
accuracy. An extensive discussion of the status of groundwater models is presented by
Bachmat et al. (1985).

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7.10.2 Multiple scales in modeling groundwater systems
A wide range of both spatial and temporal scales is involved in the study of groundwater
problems. Spatial scales range from less than a nanometer for studying such phenomena as
the interactions between water molecules and dissolved chemicals (Cusham, 1985), to
hundreds of kilometers, for the assessment and management of regional groundwater
systems (Toth, 1963). For temporal scales, two major categories can be distinguished:
steady-state, and transient state. Periodic fluctuations on a seasonal scale are frequent in
hydrogeology. Other processes display certain trends or occur rather randomly in nature.
Many processes exhibit a strong temporal effect immediately after their initiation but
become stable after a while, moving to a steady-state. Other processes fluctuate on a scale
that is often much smaller than necessary to include in the analysis of such systems. An
averaging approach is then taken, resulting in steady-state analysis. The steady-state is
also assumed when the analysis period is so short that temporal effects are not noticeable.
An important aspect of the scaling problem is related to the difference between the scale
on which processes are mathematically described, and the subsequent aggregation into
larger-scale formulations amenable to field analytical procedures. Small-scale descriptions
are aggregated into large-scale models by applying averaging procedures. Such averaging
applied to a statistical description of microscopic processes is commonly used to obtain
continuous hydrodynamic field equations on the macroscopic scale (e.g. Bear, 1979).
Although the resulting model requires less supporting field data than is required for a
problem of the same physical extent, a certain amount of information regarding the real
physical systems is lost. Also, in going to larger spatial and temporal scales, variations in
system characteristics that could be ignored on the smaller scale may become important.
Examples are the increasing importance of heterogeneities and anisotropy as related to the
geology of the system for larger spatial scales, and the effects of long-term recharge
variations on the water balance of a system for long time periods.
A major problem in this averaging process lies in evaluating the effects of assumptions
made on the microscopic scale and the effects on the level of uncertainty in the modelling
of a groundwater system. If such assumptions have to be incorporated in the macroscopic
description, their formulation may be problematic. Another problem that may arise as a
result of an averaging approach is that of defining the physical meaning of the resulting

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state variables and system parameters. Thus far, no systematic evaluation of the
consequences of this aggregation process in groundwater has been published, although an
extensive database is available to carry out such a study.
The processes of water movement and the transport of energy and dissolved constituents
through porous media are well understood and are mathematically described on a
macroscopic scale, using a representative equivalent volume (Bear, 1979). Such an
approach can also be applied to flow and transport in fractured rock (Wang and
Narasimhan, 1984). One way to make a system of fractures of varying size and orientation
accessible to quantitative analysis is through the concept of equivalent porous media.
Another approach often taken is based on applying stochastic principles to obtain
representative parameters. Such approaches can be used to extend the results of small-
scale studies to larger-scale problems.
The essential scaling problem is how to distinguish between the variables that can be
considered as constants or as being uniform across discrete intervals of pertinent
dimension (space, time), and the variables that cannot be so considered (Beck, 1985).
Problem decomposition in space or time is often applied to obtain optimal resolution in
relation to computational efficiency. An example of such spatial and temporal
decomposition is found in the modelling of infiltration into the soil and subsequent
percolation toward the saturated zone. A distinction has been made between spatial
discretization and connectiveness for local (Fig. 3.6) and for regional (Fig. 3.7) scales.
Runoff from precipitation is split into a surface component (lumped horizontal segment)
and infiltration (one- or two-dimensional, vertical). The infiltrated water percolates to the
groundwater where a two-dimensional horizontal or three-dimensional model is used. For
each of the sub models a different time step is used, from hourly for the surface runoff and
daily for the percolation, to weekly or monthly for the flow in the saturated zone.

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Figure 7.7 Typical dimensionalities used to represent surface, unsaturated, and saturated
zones in local-scale groundwater models (after Boutwell et al., 1985).

Figure 7.8 Typical dimensionalities used to represent surface, unsaturated, and saturated
zones in regional groundwater models
In groundwater models, a significant distinction exists between local and regional
discretization of the surface zone. This distinction reflects the difference in physiographic

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character between the subsurface and the surface, resulting in different approaches in
aggregating small-scale phenomena into large-scale models. Also, limitations in presently
existing data acquisition techniques influence the resolution used in modelling the surface
zone.
Note the difference in treatment of the vertical components in groundwater models. In the
regional models the flow in soils and between aquifers is mainly one-dimensional and
vertical, to reduce the computational load. In the local model, second-order effects may be
important enough to warrant the use of two-dimensional vertical simulation in the soil
zone. Consecutively
Another example can be found in simulating solute transport in fractured porous media
where the movement of the solute in the fractures can be two orders of magnitude greater
than in the porous matrix. A split-time approach increases the efficiency of the simulations
(DeAngelis et al., 1984).
With the increasing capacity and decreasing cost of computers, a trend prevails toward
using smaller time scales for the same types of problems, resulting in higher temporal
resolution. Some of the applications of Groundwater flow models are for the study of
regional flow in the aquifer system, regional changes in hydraulic head caused by the
aquifer system, change in head near the well field, dewatering the well system, injection
well, and surface groundwater interactions.

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