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5/22/2018 Lecture Groundwater Hydrology
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Groundwater Hydrology
Guchie Gulie (Lecturer)Arba Minch University,
Department of Water Resources
and Irrigation Engineering
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Contents
9Groundwater modeling9
8Artificial recharge of groundwater8
7Groundwater quality and its monitoring7
6Pumping test6
5Well hydraulics: steady and unsteady flow, multiplewell system
5
4Fundamentals of groundwater movement4
3Aquifers3
2Occurrence of groundwater2
1Groundwater in hydrologic cycle1
ChapterContentsS.N
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Groundwater in Hydrologic cycle
Water on earth circulates in a spacecalled the hydrosphere, which extendsabout 15km up in to the atmosphereand about 1km down into thelithosphere
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Hydrologic cycle
Inflow Outflow =change in storage
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5Animation of Hydrological processes in an area
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Usually groundwater constitutes part of thehydrologic cycle which lies under the surface
of the ground.
But Connate waters are those which have beenout of the water cycle for at least an appreciable
part of the geological period. They consist
essentially of fossil interstitial water that has
migrated from its original burial location bymeans of various phenomena. Being also
entrapped within particular groundwater
reservoirs, they are typically highly mineralized.
They may have been derived from oceanic orfresh water sources.
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Magmatic waters are those which are
derived from magmas through
hydrothermal phenomena.
Metamorphic waters are those which are orhave been associated with rocks during
their metamorphism.
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Sources of natural recharge to groundwater include:
precipitation,
stream flows, and lakes
Even sea-water can enter under ground along thecoasts where hydraulic gradient shapes downward
in an inland direction.
Other contributions, known as arti ficial recharge, occur from:
excess irrigation,seepage from canals, reservoirs andwater purposely applied to augmentgroundwater.
However, the ultimate source of groundwater
recharge is assumed to be precipitation
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Most natural discharge from groundwateroccurs as flow into surface water bodies, such
as streams, lakes, and oceans, and to thesurface as springs.
Groundwater near the surface may returndirectly to the atmosphere by evaporation fromthe soil surface and by transpiration fromvegetation.Pumpage from wells constitutes major artificialdischarge of groundwater.
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OCCURRENCE OF GROUNDWATER
Describing the occurrence ofgroundwater needs to review where and
how groundwater exists and itssubsurface distribution, both in verticaland aerial extents.
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The possibility of occurrence and movementof groundwater mainly depends upon two
main geological factories of the rock materials:
porosityCoefficient of permeabil ity
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Aquifer properties that affect
groundwater occurrence & movement
Basic hydrogeological parameters
Porosity
Hydraulic conductivity
compressibility
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Derived hydrogeological parameters
Transmissivity of aquifers
Coefficient of storage (storativity)
Specific yield of aquifers
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Porosity and void ratio Porosity refers the portions of soils and
rocks which are not occupied by solidmatter, but possibly by water and air. These
portions are normally called voids,interstices, pores or empty spaces.
Since these empty spaces serve as waterconduits or storages, they are very important
when groundwater problems are concerned.Open spaces are characterized by their sizes,shapes, irregularities and distributions,
which depend on their origin. Porosity maybe classified as primary or secondary.
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The storage available in an aquifer is
related to the void space that it
contains (total porosity). The totalporosity as percentage is expressed
as
( )100t
v
vv=
Porosity
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Where =total porosity
Vv= volume of void spaces in the sample
Vt = total volume of the sample
There is evident that porosity depends upon
the gradation and shape of soil particle
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Porosity depends on:
Sorting of grains (not only on grain size)
Degree of cementing
Degree of fracturing
Primary porosity, and
Secondary porosity
Types of porosity:
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Secondary porosity are those which develop after
the rocks were formed, and are found in all typesof rocks as joints, fractures, faults, solution
openings, etc.
Primary porosity are those which are originated by
the same geological processes which gave rise to
the various geological formations, and are found insedimentary, igneous and metamorphic rocks.
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Porosity
(Primary and secondary)
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Values of porosity
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Void ratio (e):
It is expressed as the ratio (in percentage) of
the volume of the voids to the volume of the
solid matter:e = (Vv / Vs) x 100
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Vertical profile of water distribution
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1.Soil water zone
2. Intermediate vadose water
zone
3.Capillary water zone
a) Vadose zone
b) Phreatic water zone (zone of saturation)
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Capillary zone (capillary fringe)
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Fu
= cosx 2 rFd = r2 h x g x
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= surface tension of water against air
(= 0.073kg/s2
at 200
c)
= contact angle water with tube (=0 for
water and in pure glass, cos 1)r = equivalent radius of tube (cm)
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= density of water (= 1000kg/m3)
g= acceleration due to gravity (=9.8/m/s2
)h = height of capil lary rise (cm)
Fu = Fd
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gr
gr
rh
gxhrrx
cos2
2cos
2cos
2
2
=
=
=
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215.0
,&,
cmrh
getwegofvaluesthengSubstituti
=
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Phreatic water zone
In this zone, groundwater fills all of the interstices.
Hence the porosity provides a direct measure of thewater contained per unit volume of the formation in
that zone. A portion of water can be removed from
the strata of this zone by drainage or pumping well.
The zone below the water table is generally calledphreatic water zone and the water in this zone is
termed as groundwater.
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Properties of formation materias Infiltrability
Coefficient of permeability Hydraulic conductivity
Compressibilty
Transmissivity
Coefficient of storage (Storativity)
Specific yield of aquifers Hydaulic resistance
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Types of Geologic formations (based on
water storing and transmitting capability)
i) Aquifers:
ii) Aquicludes
iii) Aquifuge
iV) Aquitard
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Geologic formations as Aquifers
I. Unconsolidated or loosely consolidated
sand and gravel deposits (Fluvial and
Aeolian deposits). These generally formthe best aquifers
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The fluvial deposits are the materials laiddown by physical processes in river channels
or on flood plains. These materials are also
known as alluvial deposits. Probably 90percent of all developed aquifers in the world
consists unconsolidated rocks, chiefly gravel
and sand, which are of alluvial origin. These
aquifers may be divided into four categories,
based on manner of occurrence, as:
Fluvial Deposits .
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1.Water courses,
2.Abandoned or buried valleys,
3.Plains, and
4. Intermountain valleys
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Materials that are transported and deposited
by wind are known as Aeolian deposits.
Aeolian deposits consist of sand or siltmaterials. Aeolian deposits of sil t are known
as leoss.
Aeolian deposits:
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II. Semi-consolidated and consolidated
conglomerate (the consolidated
equivalent of gravel) and sandstoneformations
Their water yielding capacity depends up onthe degree of cementation. Partially cemented
and fractured sandstones are the best type of
these formations.
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III. Carbonate formations like limestone,
marble, dolomite, etc
Carbonate rocks with primary porosity, such as
old unfractured limestone and dolomite, areusually important in petroleum mining rather
than as the significant sources of groundwater.
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But sometimes openings in limestone may rangefrom microscopic original pores to secondary large
solution caverns forming subterranean channels
sufficiently large enough to carry the entire flow of
a stream. The term lost river has been applied to astream that disappears completely underground in
a limestone terrain. Large springs are frequently
found in limestone areas.
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IV.Volcanic Rock
They are generally not porous, but whenthey are poured on the surface of the
earth by volcanic eruption and jointed
and fractured due cooling of the volcaniclava, they form satisfactory formations
that can hold and bear groundwater
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Volcanic rock can form highly permeable
aquifers; basalt flows, in particular, often
display such characteristics. The types of
openings contributing to the permeability
of basaltic aquifers include, in order ofimportance:
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1.Interstitial spaces in clinker lava at the
tops of flows,
2.Cavities between adjacent lava beds,
3.Shrinkage cracks,
4.Lava tubes,
5.Gas vesicles,
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6.Fissures resulting from faulting and
cracking after rocks have cooled, and
7.Holes left by the burning of trees
overwhelmed by lava.
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Types of Aquifers (Aquifer conditions)
1.Unconfined Aquifers
Perched Water1.Semi-confined /leaky aquifers
2.Confined aquifers
aquifers
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aquifers
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Artisian aquifers (flowing wells)
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Artisian aquifers (flowing wells)
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o
1
o
1
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Fundamentals of groundwater flow
p
Elevation, z = z
Pressure p = p
Velocity V = V
Density p = p
Volume of unit mass U = 1/p
Arbitrary standard state
Elevation z = o,Pressure p = po,Velocity V = o,
Density o, and
Volume of unit mass = 1/o
Energy contained in groundwater
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1) Potential Energy, W1:
W1 = mgz
2) Kinetic Energy, W2
2
2
2
mVW =
3) The work required to be done on the fluid in
raising the fluid pressure from p = po to p, w3
=p
po
VdpW3 == P
P
P
Po o
dp
mdpm
V
m
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Total Energy, WT:
WT = W1 + W2 + W3
+=mgzWT +2
2
mV
p
po
dpm
++= P
PT
o
dpmmVmgzW2
2
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The total water potential (total mechanical
energy per unit mass), , is given by:
m
WT=
oppVgz ++=2
2
The total hydraulic head (total mechanicalenergy per unit weight), H, is given by:
g
p
g
V
ZgH
++== 2
2
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Darcys Law:
Who was Henry Darcy?
Henry Darcy was born in Dijon,
in the Southern part of France,in 1803.
Darcy cont
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He enrolled at the Ecole Polytechnique in Paris
in 1821, and then continued in 1823 to study at
the Ecole des Ponts in Chaussees.
His studies led him to a position with the
Dept. of Bridges & Roads
One of his main early projects was the water
supply system (pressure pipes) for the city of
Dijon, bringing water by a covered aqueduct
from the Roster Spring, some 12.7 km from the
city, to a reservoir. He was also involved in
many other projects, as well as in city politics
Darcy cont.
Darcy cont
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During the period, he modified the Prony equation
for calculating the head loss in pipes, due to
friction. Later, this equation was further modified
by Julius Weisbach to become the well knownDarcy-Weisbach equation for head losses in
pipes.
Darcy cont.
His lifelong goal was to convert the water supply
system of the city of Dijon, which was using highly
polluted water from shallow wells and streams to a
centralized water distribution system that hedesigned.
Darcy cont
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In 1848 he became the Chief Engineer for the
Department of Cote-d`Or (around Dijon). However,
due to political pressure, he had to leave to become
the Chief Director for Water and Pavements in Paris.
But due to poor health, he resigned and returned to
Dijon in 1855, where he continued his research.
During 1855-1856, he devoted his research to study
the flow of water and the resulting head loss in sand
columns. This research led to what we refer to asDARCYs LAW. The motivation for this research:
filtration of the water for the fountains of the city of
Dijon.
Darcy cont.
Th d l i t l t
Darcy cont.
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Original modified
The sand column experimental setup:
Darcy cont
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Flow rate, Q, is proportional to head difference, cross-
sectional area and inversely proportional to the length
of the sand column. That is:
Darcy cont.
AL
h
KQ
AL
hQ
=
in which K is a coefficient of proportionality that
depends on the permeability of the sand, h is head
difference,A is cross-sectional area and L is lengthof sand column.
To visualize the flow phenomena in porous medium
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like soil, lets consider the flow between two parallelplates, one at rest and the other moving with constant
velocity (u):
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dy
dus
dy
du
s =
Where the proportionality constant, , is the dynamicviscosity of the fluid.
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s
x
y
PoP1 L
2R
U(y)
R y
Now, lets consider a fluid flow through a straightcylindrical tube of diameter 2R, laid horizontally:
Consider the coaxial fluid cylinder of length L and
radius y
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The pressure force acting on face-2
Fp1= P1y2The pressure force acting on face-1
Fpo=Poy2
The frictional resistance due to shear
stress, s, is:
F = 2 y Ls
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Fp1-Fpo= P1y2 - Poy2
=Py2
For flow of constant velocity, force of frictional
resistance due to shear stress is equal to the force
due to pressures, p1 and po. i.e:
p y2 = 2 y Ls
py = 2 Ls
L
py
s 2
=
=2
y
L
p
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But we know that:
=2
y
L
p
dy
du
2
y
L
p
dy
du
=
dy
dus =
( )224
)( yRL
pyU
=
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LpRu4
2
max =
The discharge can now be evaluated as thevolume of a paraboloid of revolution as:
Q = (base area x height)
Q =
22
421 R
L
pR
=
L
pRQ
8
4 = Poiseuilles equation
R2 umax
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If we assume that the soil column is composed of n number
of interconnected equal tubes, the total discharge QT can be
expressed as:
QT=nQ
L
pRnQT
8
4 =
ARnBut e =2
porosityeffectivewheree=
columnsoilofareationcrosstotalA sec
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columnsoilofareationcrosstotalA sec=
L
pARQ eT
8
2 =
From Darcys law,
AL
hKQ
T
=
Equating the two equations of Q, we get :
L
pReAL
hK A 8
2 =
h
pR
eK
=
8
2
8
2 gR
e=
gk=
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Thus the parameter k depends on the porosity of themedium, the pore-size distribution of the medium, the
shape, orientation and arrangement of the individual
grains of the medium.
That is, k depends on only the characteristics of the
porous medium and called coefficient of
permeability or just permeability. The term intrinsic
permeability is also used for k
But hydraulic conductivity, K, depends on both the
characteristic of the porous medium and thecharacteristic of the flowing fluid.
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Validity of Darcys Law
It is valid as long as the Re, that indicates the
magnitude of the inertial forces relative to theviscous drag, value does not exceed about 1 (but
sometimes as high as 10).
Darcys equation can be applied with in a certain
limit. It is valid only if the flow is laminar.
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The kinematics viscosity and permeability are given as:
= 1.12 cm2/sec and
k = 7.5 darcys (1 Darcy = 9.87x 10-9cm2).
Determine the value of the hydraulic conductivity of theaquifer .
Example
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x
z
Vx
3-D Flow in homogeneous and isotropic formation:
Consider a volume element of porous medium in the shape ofcubic parallelepiped inside a space defined by a set of
rectangular coordinates x, y, z, as shown in the figure blow
dzzvV zz
+
dyy
vV
y
y
+
dxx
vV xx
+
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Volume of water inflowing in unit time, dt, in x, y, z
directions:
Vx dy dz dt + Vy dz dx dt+ Vz dx dy dt
Volume of water out flowing in unit time, dt, in x, y, z
directions:
dtdydxdxz
vVzdtdxdzdy
y
vVdydtdzdx
x
VV z
y
yx
x
++
++
+=
=
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Volume
inflowing in
unit time dt
Volume out
flowing in unit
time dt
Change
in storage
moisture
storageinchangez
v
y
v
x
v zyx =++
From Darcys Law:
zHKV
yHKV
xHKV zzyyxx
=== ,,
For steady flow:
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y
02
2
2
2
2
2
=
+
+
zH
Ky
H
Kx
H
K zyx
0=
+
+
z
HK
zy
HK
yx
HK
x zyx
Horizontal f low through layered Layered
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Horizontal f low through layered Layered
formations
qx3
h1 h2
qx2
qx1K1
K2
K3
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IDKqx 111 =
IDKqx 222 =
IDKqx 333 =
Flow through each layer may be expressed as:
IDKDKDKqqqq xxxx )( 332211321 ++=++=
=
=3
1i
iiDKI
For homogeneous system this would be
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g y
expressed as:
qx = Kx I(D1+D2+D3)
Eliminating qx from both equations, we get an
expression for equivalent horizontal hydraulic
conductivity for layered formations as:
=
==3
1
3
1
i
i
i
ii
x
D
DK
K
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Vertical flow through layered soils
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21
1
1
1
211 hh
K
DVor
D
hhKV zz =
=
32
2
2
2
32
2 hhK
DVor
D
hhKV zz ==
43
3
3
3
433 hh
KDVor
DhhKV zz ==
If we add up, we get
433221
3
3
2
2
1
1 hhhhhhK
D
K
D
K
DVz ++=
++
41 hh =
For a homogeneous system,
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41
321 hhK
DDDV
z
z =
++
Eliminating (h1-h4), we get an expression for
equivalent vertical hydraulic conductivity of
layered formations as:
3
3
2
2
1
1
321
K
D
K
D
K
D
DDDKz
++
++=