Hydrogeology
ES-405 Hydrogeology 2-Credits
Hydrogeology & Geohydrology, Aquifer and their types including water-table,
confined, Leaky, and semi unconfined, Methods for reorganization and
management of aquifer system , Hydrological properties of rocks and their
measurements including porosity, permeability, intrinsic permeability,
hydraulic conductivity, specific capacity, specific storage etc. Effect of
geology in groundwater movement, Darcy law and its application, Recharge
and discharge areas of groundwater, Tube well drilling techniques, Designing
& development of tube well, Pumping test analysis to find the hydraulic
properties of different aquifers, Step draw down test, Refraction of flow
lines, Flow net analysis for isotropic and anisotropic media. Magnetic
resonance imaging techniques and their applications in hydrogeology.
Books Recommended
1. Lin, Y. F. F. (2014). Hydrogeology: Objectives, Methods, and Applications.
2. Gilli,É., Mangan, C., &Mudry, J. (2012). Hydrogeology: Objectives, Methods,
Applications. CRC Press.
3. Brassington, R. (2007). Field hydrogeology. John Wiley & Sons.
4. Kresic, N. (2006). Hydrogeology and groundwater modeling. CRC press.
5. Todd, D. K., & Mays, L. W. (2005). Groundwater hydrology edition. Wiley, New Jersey.
6. Fetter, C. W., & Fetter, C. W. (2001). Applied hydrogeology (Vol. 3, No. 3). Upper
Saddle River, NJ: Prentice Hall.Press.
Hydrogeology …………….?
Geohydrology………………?
Importance and Distribution of
Earth’s Water
Water is a vital natural resource and essential for
existence of life, all the economic and social activities are
dependent upon the water.
About 97.5% of Earth’s water is saline water and only
2.5% is fresh water. In 97.5% about 96.5% consist of oceans
and 1% consist of saline groundwater and saline lakes.
Whereas in 2.5% freshwater more than 68% water is locked up
in glaciers and ice caps and another 30% of freshwater is on
the ground. Only a little more than 1.2% of all freshwater is
surface water.
In case of surface freshwater, most of this water is
locked up in ground ice, and another 20.9% is found in lakes.
Rivers make up 0.49% of surface freshwater.
Importance and Distribution of
Earth’s Water
What is Groundwater?
Groundwater and its occurrence
Groundwater: is water located beneath the ground surface in
soil pore spaces and in the fractures of lithologic formations.
Groundwater can be found at nearly every point in the Earth's
shallow subsurface, to some degree; although aquifers do not
necessarily contain fresh water.
The Earth's crust can be divided into two regions:
The saturated zone (its study is called hydrogeology)
(phreatic), where all available spaces are filled with water
OR the subsurface zone in which all rock openings are filled
with water.
The unsaturated zone (its study is called geohydrology)
, where there are still pockets of air with some water that
can be replaced by water.
Factors affecting the flow of ground water:
Slope of the water table - the steeper the water table, the
faster ground water moves.
Porosity and Permeability - if rock pores are small and
poorly connected, water moves slowly; when openings are large
and well connected, the flow of water is more rapid.
Capillary fringe: a transition zone with
higher moisture content at the base of
the vadose zone just above the water
table. OR The capillary fringe is the
subsurface layer in which groundwater
seeps up from a water table by capillary
action to fill pores.
Water table: the upper surface of the zone of saturation.
Vadose zone: a subsurface zone in which rock openings are
generally unsaturated and filled partly with air and partly with
water; above the saturated zone. Above the water table
unsaturated region is called the vadose zone.
Aquifer, Aquitard and Aquifuge
Aquifer- Geologic unit that can store (porosity) and transmit (permeability)
significant quantities of water. OR
A formation, group of formations, or part of a formation that
contains sufficient saturated, permeable material to yield significant
quantities of water to wells.
When an aquifer is "capped" by a confining layer it cause the water to be
pressurized. This forces the water out of a well without pumping. This would
be called an artesian well.
e.g. Sandstone, Conglomerate, Well-jointed limestone, Sand and gravel,
Highly fractured volcanic rock.
All aquifers have two fundamental characteristics:
i. A capacity for groundwater storage (Porosity ) and;
ii. A capacity for groundwater flow (Permeability).
The amount of water a material can hold depends upon its
porosity. The size and degree of interconnection of those openings
(permeability) determine the materials’ ability to transmit fluid.
Aquitard - A confining bed that retards but does not prevent the flow of
water to or from an adjacent aquifer. Aquitard is slightly impervious layer
which can absorb some water and slowly transmit it. OR
A water-saturated sediment or rock whose permeability is so low it
cannot transmit any useful amount of water. OR
An aquitard is a zone within the earth that restricts the flow of
groundwater from one aquifer to another. OR
A water bearing layer of rock or sediment that transmits small
quantities of water in relation to aquifer.
e.g. sandy clay, unfractured crystalline rocks.
Aquiclude (impermeable layer) - A hydrogeologic unit which, although porous
and capable of storing water, does not transmit it at rates sufficient to
furnish an appreciable supply for a well. E.g clay
Aquiclude and aquitard are very similar and often used
interchangeably.
Aquifuge - An aquifuge is a geologic formation which doesn’t have
interconnected pores. It is neither porous nor permeable. Thus, it can
neither store water nor transmit it. Examples of aquifuge are rocks like
basalt, granite, etc. without fissures (long fine cracks).
Aquifers
— Aquifer: A formation, that contains sufficient
saturated, permeable material to yield significant
quantities of water to wells and springs.
Types of Aquifers
 •Unconfined aquifer(Water-table aquifer)
 — •Confined aquifer(Artesian aquifer)
 — Semi confined aquifer.
Unconfined Aquifer
•An aquifer that is close to the ground surface, with
continuous layers of materials of high intrinsic permeability
extending from the land surface to the base of the aquifer.
•Recharge from downward seepage through the
unsaturated zone, lateral ground water flow, or upward
seepage from underlying strata.
Confined Aquifer
•An aquifer that are overlain by a confining layer.
•Recharge occurs in recharge area, where the aquifer
crops out, or by slow downward leakage through a leaky
confining layer.
•Potentiometric surfaces the surface representative of the
level to which water will rise in a well cased to the aquifer
Artesian Wells
A well whose source of water is a confined
aquifer•
The water level in artesian wells is at some height
above the water • table due to the pressure of the
aquifer
Perched Aquifer
Perched Aquifer - aquifer in the vadose zone
because of a lens of impermeable material
- common in glacial outwash (clay from ponds),
volcanic deposits .
the top of a body of ground water separated
from the main water table beneath it by a zone
that is not saturated
PROPERTIES OF
AQUIFERS
Properties of aquifer
Porosity
Porosity: the percentage of rock or sediment
that consists of voids or openings.
porous: a rock that holds much water
Porosit
y
Effective Porosity
Effective porosity is the fraction of
the porosity that is available for
transporting water (excludes fraction
of pores too small to hold water, or
those that are not interconnected
- can be measured in the lab
directly by saturating a dried sample
of known volume and measuring
water uptake in a sealed chamber
over time
- for unconsolidated coarse-grained
sediments there is no significant
difference
Porosity of Sedimentary Rocks
•Primary porosity
•Pores between grains
••Secondary porosity
•Fractures
Permeability
permeability: the capacity of a rock to
transmit a fluid such as water or petroleum
through pores and fractures
permeable: a rock that allows water to
flow easily through it
impermeable: a rock that does not allow
water to flow through it easily
Specific Yield (Sy)
— •Specific Yield Sy the ratio of the
volume of water that drains from
a saturated geomaterial owing to
the attraction of gravity to the
total volume of the geomaterial
Specific Retention (Sr)
•Specific retention Sr the ratio of the
volume of water a geomaterial can
retain against gravity drainage to the
total volume of the geomaterial.
n = Sy+ Sr
Storativity
Storativity (S) or Storage coefficient
•The volume of water that a
permeable unit will absorb or expel
from storage per unit surface area per
unit change in head.
Storativity
Confined aquifer
S = B Ss
Unconfined aquifer
S = Sy+ h Ss
Artesian zone: The artesian zone is a complex
system of interconnected voids that can
discharge water to the surface (stream).
Artesian well: Water may rise to a level above
the top of a confined aquifer, producing an
artesian well. OR
A well in which water rises above the
aquifer is called artesian well.
30
Recharge and Discharge Area
Recharge Areas: Areas where water enters the
saturated zone are called recharge areas,
because the saturated zone is recharged with
groundwater beneath these areas.
Discharge Areas: Areas where groundwater
reaches the surface (lakes, streams, swamps
and springs) are called discharge areas,
because the water is discharged from the
saturated zone.
Generally, recharge areas are greater than
discharge areas.
Recharge and Discharge Area
Applied Hydrogeology
C.W. Fetter
Chapter: 3 (Properties of Aquifer)
When pumping rate in both wells is same
Shape of cone of depression…..?
Slope of cone of depression in both wells…?
DARCY’S LAW
The law of flow of water through soil was first studied by Darcy in 1856.
We can compute the discharge of aquifer.
The Darcy’s law is,
“The velocity is directly proportional to the change in head
and inversely proportional to the distance b/w the two heads.”
Depends upon hydraulic conductivity
Distance b/w source wells
Head difference
i.e. V is directly proportional to h2-h1 ( ∆h )
V is directly proportional to 1/ ∆l
V is directly proportional to ∆h / ∆l
-V =
He used and inclined cylinder filled with sand,
and inject some non-quantity of water at one end.
Two piezometers P1 and P2 are installed in the
cylinder at the two ends to measure the depth of
water table or the hydraulic head at each
piezometer. In order to install piezometers we
have to puncture the cylinder, which is under
pressure, if the sand has water in it then it will
rise in piezometers. Water moves through pores
of sand from left to right.
Height of first piezometer from datum plane is Z1
and height of second piezometer is Z2. Head of
first piezometer is h1 and of second is h2.
Where k is hydraulic conductivity of material which is
the property of material and also dependent of the
property of fluid. As we know that discharge velocity is :
V=Q/A comparing with Darcy's velocity
V=Q/A = -K dh/dl
Q= -K A dh/dl
Thus Q= -KiA where i=dh/dl
where i is the hydraulic gradient b/w two hydraulic heads.
DARCY’S LAW IN 2-D AND 3-D
Generally Darcy's law can be written in form of vector as:
V= -K dh/dl ( the negative sign shows that the
gradient is decreasing )
Darcy’s law can also be expressed in 3-D or in vector
form.
V=Vxi + Vyj + Vzk = i( -K dh/dx ) + j(-K
dh/dy ) + k(-K dh/dz )
We always consider groundwater in 2-D so we convert 3-D
equation in 2-D i.e. horizontal flow x-axis and vertical flow y-axis
by using Dupit Assumption, which states that:
There is no flow and head losses in z-direction(in isotropic
condition) or
∂h/ ∂z =0 and Vz=0.
Hence the equation reduces to
V=Vxi + Vyj = i( -K dh/dx ) + j(-K dh/dy )
Now if we our aquifer is isotropic then K1= K2 = K
V=Vxi + Vyj = -K (∂h/ ∂x i + ∂h/ ∂y j)
V=-K ∆h
If our aquifer is anisotropic then,
K1 is not equal to K2 so V is not equal to -K ∆h
ASSUMPTIONS OF DARCY’S LAW
The following assumptions are made in Darcy’s law.
The soil is saturated.
The flow through soil is laminar.
The flow is continuous and steady.
The total cross sectional area of soil mass is
considered.
VALIDITY OF DARCY’S LAW
1. Darcy’s law is valid if the flow through soils is laminar:
The flow of water through soils depends upon the dimension of
particles. In fine grained soils the dimensions of the interstices (voids)
are very small and flow is necessarily laminar.
In course- grained soil, the flow is also laminar. However, in very coarse
grained soils, such as gravels, the flow may be turbulent.
2. It is valid for flow in clays, slits and fine sands. In coarse sands,
gravels and boulders, the flow may be turbulent and Darcy’s law may not
be applicable.
3. For Darcy’s law to be valid, the relationship between velocity (v) and
hydraulic gradient (i) should be linear.
LAPLACE EQUATION
When subsurface aquifer is in steady state equation this
equation is used. It states that:
Head remains constant at a particular time of year and time
must be in years.
( Mass Balance Equation )
For a unit area V=Q
Replacing Q with V in above equation
( -kx ) + ( -ky ) + ( -kz ) = 0
Applying the Dupit Assumption no flow along the z-
axis
( -kx ) + ( -ky ) = 0
Assume the isotropic aquifer
= 0 ( steady state condition )
h = 0
FOR NON STEADY STATE CONDITION
OR TRANSIENT CONDITION
A is not equal to B so laplace equation can not be applied. For
example,some water will store in aquifer so the net result is not
zero, it is replaced by storavity.
pumpage>recharge
When heads are not constant,there is fluctuation and time must
be in years. There is continuous drawdown so laplace equation
failed for it.
A
B
Pumping Test: A pumping test is a field experiment in which a well is pumped at a controlled
rate and water-level response (drawdown) is measured in one or more surrounding
observation wells and optionally in the pumped well (control well) itself; response data from
pumping tests are used to estimate the hydraulic properties of aquifers, evaluate well
performance and identify aquifer boundaries. Aquifer test and aquifer performance test (APT)
are alternate designations for a pumping test. In petroleum engineering, a pumping test is
referred to as a drawdown test.
The principle of a pumping test involves applying a stress to an aquifer by extracting
groundwater from a pumping well and measuring the aquifer response to that stress by
monitoring drawdown as a function of time. These measurements are then incorporated into
an appropriate well flow equation to calculate the hydraulic parameters of the aquifer.
Pumping test are carried out to determine:
 How much water can be extracted from a well based on long term yield and well
efficiency.
 Hydraulic properties of aquifer.
 Spatial effect of pumping on aquifer.
 Determine the suitable depth of pump.
 Information of water quality and its variability with time.
Thiem calculated to find the hydraulic properties by pumping test analysis. His
equation was for confined and unconfined aquifer and he assumed constant pumping rate and
equilibrium condition (steady state flow).
Then Theis (1935) also developed the equation for confined aquifer with constant pumping
rate and equilibrium condition assumptions. When Thiem developed the equation he did not
use the master curve but Theis use Thiem relation and develop a master curve.
Derivation of the Thiem Equation for
Confined Radial Flow
Darcy's law describes the flow of water through a saturated porous medium and
can be written as follows
Q = -KA dh/dl
where ‘A’ is the cross-sectional area through which the water flows, ‘r’ is
distance along the ground-water flow path (in this case, radial distance). As
shown in figure, the area (A) through which flow occurs is
A = 2πrb
where ‘b’ is the thickness of the completely confined aquifer. Substituting
this expression for ‘A’ into Darcy's law gives:
Q = -2πrbK dh/dl
For steady flow, Q, the constant quantity of water pumped from the well, is
also the flow rate through any cylindrical shell around the well.
This equation can be solved by separating variables and integrating
both sides of the equation. Separation of variables gives:
There are two observation wells;
Head is h1 at a distance r1 from the pumping well
Head is h2 at a distance r2 from the pumping well
1.hydrogeology basics.pptx Hydrolic cycle
1.hydrogeology basics.pptx Hydrolic cycle

1.hydrogeology basics.pptx Hydrolic cycle

  • 1.
  • 2.
    ES-405 Hydrogeology 2-Credits Hydrogeology& Geohydrology, Aquifer and their types including water-table, confined, Leaky, and semi unconfined, Methods for reorganization and management of aquifer system , Hydrological properties of rocks and their measurements including porosity, permeability, intrinsic permeability, hydraulic conductivity, specific capacity, specific storage etc. Effect of geology in groundwater movement, Darcy law and its application, Recharge and discharge areas of groundwater, Tube well drilling techniques, Designing & development of tube well, Pumping test analysis to find the hydraulic properties of different aquifers, Step draw down test, Refraction of flow lines, Flow net analysis for isotropic and anisotropic media. Magnetic resonance imaging techniques and their applications in hydrogeology. Books Recommended 1. Lin, Y. F. F. (2014). Hydrogeology: Objectives, Methods, and Applications. 2. Gilli,É., Mangan, C., &Mudry, J. (2012). Hydrogeology: Objectives, Methods, Applications. CRC Press. 3. Brassington, R. (2007). Field hydrogeology. John Wiley & Sons. 4. Kresic, N. (2006). Hydrogeology and groundwater modeling. CRC press. 5. Todd, D. K., & Mays, L. W. (2005). Groundwater hydrology edition. Wiley, New Jersey. 6. Fetter, C. W., & Fetter, C. W. (2001). Applied hydrogeology (Vol. 3, No. 3). Upper Saddle River, NJ: Prentice Hall.Press.
  • 3.
  • 4.
    Importance and Distributionof Earth’s Water
  • 5.
    Water is avital natural resource and essential for existence of life, all the economic and social activities are dependent upon the water. About 97.5% of Earth’s water is saline water and only 2.5% is fresh water. In 97.5% about 96.5% consist of oceans and 1% consist of saline groundwater and saline lakes. Whereas in 2.5% freshwater more than 68% water is locked up in glaciers and ice caps and another 30% of freshwater is on the ground. Only a little more than 1.2% of all freshwater is surface water. In case of surface freshwater, most of this water is locked up in ground ice, and another 20.9% is found in lakes. Rivers make up 0.49% of surface freshwater. Importance and Distribution of Earth’s Water
  • 6.
  • 7.
    Groundwater and itsoccurrence Groundwater: is water located beneath the ground surface in soil pore spaces and in the fractures of lithologic formations. Groundwater can be found at nearly every point in the Earth's shallow subsurface, to some degree; although aquifers do not necessarily contain fresh water. The Earth's crust can be divided into two regions: The saturated zone (its study is called hydrogeology) (phreatic), where all available spaces are filled with water OR the subsurface zone in which all rock openings are filled with water. The unsaturated zone (its study is called geohydrology) , where there are still pockets of air with some water that can be replaced by water.
  • 8.
    Factors affecting theflow of ground water: Slope of the water table - the steeper the water table, the faster ground water moves. Porosity and Permeability - if rock pores are small and poorly connected, water moves slowly; when openings are large and well connected, the flow of water is more rapid. Capillary fringe: a transition zone with higher moisture content at the base of the vadose zone just above the water table. OR The capillary fringe is the subsurface layer in which groundwater seeps up from a water table by capillary action to fill pores. Water table: the upper surface of the zone of saturation. Vadose zone: a subsurface zone in which rock openings are generally unsaturated and filled partly with air and partly with water; above the saturated zone. Above the water table unsaturated region is called the vadose zone.
  • 9.
    Aquifer, Aquitard andAquifuge Aquifer- Geologic unit that can store (porosity) and transmit (permeability) significant quantities of water. OR A formation, group of formations, or part of a formation that contains sufficient saturated, permeable material to yield significant quantities of water to wells. When an aquifer is "capped" by a confining layer it cause the water to be pressurized. This forces the water out of a well without pumping. This would be called an artesian well. e.g. Sandstone, Conglomerate, Well-jointed limestone, Sand and gravel, Highly fractured volcanic rock. All aquifers have two fundamental characteristics: i. A capacity for groundwater storage (Porosity ) and; ii. A capacity for groundwater flow (Permeability). The amount of water a material can hold depends upon its porosity. The size and degree of interconnection of those openings (permeability) determine the materials’ ability to transmit fluid.
  • 10.
    Aquitard - Aconfining bed that retards but does not prevent the flow of water to or from an adjacent aquifer. Aquitard is slightly impervious layer which can absorb some water and slowly transmit it. OR A water-saturated sediment or rock whose permeability is so low it cannot transmit any useful amount of water. OR An aquitard is a zone within the earth that restricts the flow of groundwater from one aquifer to another. OR A water bearing layer of rock or sediment that transmits small quantities of water in relation to aquifer. e.g. sandy clay, unfractured crystalline rocks. Aquiclude (impermeable layer) - A hydrogeologic unit which, although porous and capable of storing water, does not transmit it at rates sufficient to furnish an appreciable supply for a well. E.g clay Aquiclude and aquitard are very similar and often used interchangeably. Aquifuge - An aquifuge is a geologic formation which doesn’t have interconnected pores. It is neither porous nor permeable. Thus, it can neither store water nor transmit it. Examples of aquifuge are rocks like basalt, granite, etc. without fissures (long fine cracks).
  • 11.
    Aquifers — Aquifer: Aformation, that contains sufficient saturated, permeable material to yield significant quantities of water to wells and springs. Types of Aquifers  •Unconfined aquifer(Water-table aquifer)  — •Confined aquifer(Artesian aquifer)  — Semi confined aquifer.
  • 12.
    Unconfined Aquifer •An aquiferthat is close to the ground surface, with continuous layers of materials of high intrinsic permeability extending from the land surface to the base of the aquifer. •Recharge from downward seepage through the unsaturated zone, lateral ground water flow, or upward seepage from underlying strata. Confined Aquifer •An aquifer that are overlain by a confining layer. •Recharge occurs in recharge area, where the aquifer crops out, or by slow downward leakage through a leaky confining layer. •Potentiometric surfaces the surface representative of the level to which water will rise in a well cased to the aquifer
  • 13.
    Artesian Wells A wellwhose source of water is a confined aquifer• The water level in artesian wells is at some height above the water • table due to the pressure of the aquifer
  • 15.
    Perched Aquifer Perched Aquifer- aquifer in the vadose zone because of a lens of impermeable material - common in glacial outwash (clay from ponds), volcanic deposits . the top of a body of ground water separated from the main water table beneath it by a zone that is not saturated
  • 17.
  • 18.
    Properties of aquifer Porosity Porosity:the percentage of rock or sediment that consists of voids or openings. porous: a rock that holds much water
  • 19.
  • 20.
    Effective Porosity Effective porosityis the fraction of the porosity that is available for transporting water (excludes fraction of pores too small to hold water, or those that are not interconnected - can be measured in the lab directly by saturating a dried sample of known volume and measuring water uptake in a sealed chamber over time - for unconsolidated coarse-grained sediments there is no significant difference
  • 21.
    Porosity of SedimentaryRocks •Primary porosity •Pores between grains ••Secondary porosity •Fractures
  • 22.
    Permeability permeability: the capacityof a rock to transmit a fluid such as water or petroleum through pores and fractures permeable: a rock that allows water to flow easily through it impermeable: a rock that does not allow water to flow through it easily
  • 23.
    Specific Yield (Sy) —•Specific Yield Sy the ratio of the volume of water that drains from a saturated geomaterial owing to the attraction of gravity to the total volume of the geomaterial
  • 24.
    Specific Retention (Sr) •Specificretention Sr the ratio of the volume of water a geomaterial can retain against gravity drainage to the total volume of the geomaterial. n = Sy+ Sr
  • 26.
    Storativity Storativity (S) orStorage coefficient •The volume of water that a permeable unit will absorb or expel from storage per unit surface area per unit change in head. Storativity Confined aquifer S = B Ss Unconfined aquifer S = Sy+ h Ss
  • 28.
    Artesian zone: Theartesian zone is a complex system of interconnected voids that can discharge water to the surface (stream). Artesian well: Water may rise to a level above the top of a confined aquifer, producing an artesian well. OR A well in which water rises above the aquifer is called artesian well.
  • 30.
    30 Recharge and DischargeArea Recharge Areas: Areas where water enters the saturated zone are called recharge areas, because the saturated zone is recharged with groundwater beneath these areas. Discharge Areas: Areas where groundwater reaches the surface (lakes, streams, swamps and springs) are called discharge areas, because the water is discharged from the saturated zone. Generally, recharge areas are greater than discharge areas.
  • 31.
  • 32.
  • 33.
    When pumping ratein both wells is same Shape of cone of depression…..? Slope of cone of depression in both wells…?
  • 38.
    DARCY’S LAW The lawof flow of water through soil was first studied by Darcy in 1856. We can compute the discharge of aquifer. The Darcy’s law is, “The velocity is directly proportional to the change in head and inversely proportional to the distance b/w the two heads.” Depends upon hydraulic conductivity Distance b/w source wells Head difference i.e. V is directly proportional to h2-h1 ( ∆h ) V is directly proportional to 1/ ∆l V is directly proportional to ∆h / ∆l -V =
  • 40.
    He used andinclined cylinder filled with sand, and inject some non-quantity of water at one end. Two piezometers P1 and P2 are installed in the cylinder at the two ends to measure the depth of water table or the hydraulic head at each piezometer. In order to install piezometers we have to puncture the cylinder, which is under pressure, if the sand has water in it then it will rise in piezometers. Water moves through pores of sand from left to right. Height of first piezometer from datum plane is Z1 and height of second piezometer is Z2. Head of first piezometer is h1 and of second is h2.
  • 41.
    Where k ishydraulic conductivity of material which is the property of material and also dependent of the property of fluid. As we know that discharge velocity is : V=Q/A comparing with Darcy's velocity V=Q/A = -K dh/dl Q= -K A dh/dl Thus Q= -KiA where i=dh/dl where i is the hydraulic gradient b/w two hydraulic heads.
  • 42.
    DARCY’S LAW IN2-D AND 3-D Generally Darcy's law can be written in form of vector as: V= -K dh/dl ( the negative sign shows that the gradient is decreasing ) Darcy’s law can also be expressed in 3-D or in vector form. V=Vxi + Vyj + Vzk = i( -K dh/dx ) + j(-K dh/dy ) + k(-K dh/dz )
  • 43.
    We always considergroundwater in 2-D so we convert 3-D equation in 2-D i.e. horizontal flow x-axis and vertical flow y-axis by using Dupit Assumption, which states that: There is no flow and head losses in z-direction(in isotropic condition) or ∂h/ ∂z =0 and Vz=0. Hence the equation reduces to V=Vxi + Vyj = i( -K dh/dx ) + j(-K dh/dy ) Now if we our aquifer is isotropic then K1= K2 = K V=Vxi + Vyj = -K (∂h/ ∂x i + ∂h/ ∂y j) V=-K ∆h If our aquifer is anisotropic then, K1 is not equal to K2 so V is not equal to -K ∆h
  • 44.
    ASSUMPTIONS OF DARCY’SLAW The following assumptions are made in Darcy’s law. The soil is saturated. The flow through soil is laminar. The flow is continuous and steady. The total cross sectional area of soil mass is considered.
  • 45.
    VALIDITY OF DARCY’SLAW 1. Darcy’s law is valid if the flow through soils is laminar: The flow of water through soils depends upon the dimension of particles. In fine grained soils the dimensions of the interstices (voids) are very small and flow is necessarily laminar. In course- grained soil, the flow is also laminar. However, in very coarse grained soils, such as gravels, the flow may be turbulent. 2. It is valid for flow in clays, slits and fine sands. In coarse sands, gravels and boulders, the flow may be turbulent and Darcy’s law may not be applicable. 3. For Darcy’s law to be valid, the relationship between velocity (v) and hydraulic gradient (i) should be linear.
  • 47.
    LAPLACE EQUATION When subsurfaceaquifer is in steady state equation this equation is used. It states that: Head remains constant at a particular time of year and time must be in years. ( Mass Balance Equation ) For a unit area V=Q Replacing Q with V in above equation ( -kx ) + ( -ky ) + ( -kz ) = 0
  • 48.
    Applying the DupitAssumption no flow along the z- axis ( -kx ) + ( -ky ) = 0 Assume the isotropic aquifer = 0 ( steady state condition ) h = 0
  • 49.
    FOR NON STEADYSTATE CONDITION OR TRANSIENT CONDITION A is not equal to B so laplace equation can not be applied. For example,some water will store in aquifer so the net result is not zero, it is replaced by storavity. pumpage>recharge When heads are not constant,there is fluctuation and time must be in years. There is continuous drawdown so laplace equation failed for it. A B
  • 50.
    Pumping Test: Apumping test is a field experiment in which a well is pumped at a controlled rate and water-level response (drawdown) is measured in one or more surrounding observation wells and optionally in the pumped well (control well) itself; response data from pumping tests are used to estimate the hydraulic properties of aquifers, evaluate well performance and identify aquifer boundaries. Aquifer test and aquifer performance test (APT) are alternate designations for a pumping test. In petroleum engineering, a pumping test is referred to as a drawdown test. The principle of a pumping test involves applying a stress to an aquifer by extracting groundwater from a pumping well and measuring the aquifer response to that stress by monitoring drawdown as a function of time. These measurements are then incorporated into an appropriate well flow equation to calculate the hydraulic parameters of the aquifer. Pumping test are carried out to determine:  How much water can be extracted from a well based on long term yield and well efficiency.  Hydraulic properties of aquifer.  Spatial effect of pumping on aquifer.  Determine the suitable depth of pump.  Information of water quality and its variability with time. Thiem calculated to find the hydraulic properties by pumping test analysis. His equation was for confined and unconfined aquifer and he assumed constant pumping rate and equilibrium condition (steady state flow). Then Theis (1935) also developed the equation for confined aquifer with constant pumping rate and equilibrium condition assumptions. When Thiem developed the equation he did not use the master curve but Theis use Thiem relation and develop a master curve.
  • 51.
    Derivation of theThiem Equation for Confined Radial Flow Darcy's law describes the flow of water through a saturated porous medium and can be written as follows Q = -KA dh/dl where ‘A’ is the cross-sectional area through which the water flows, ‘r’ is distance along the ground-water flow path (in this case, radial distance). As shown in figure, the area (A) through which flow occurs is A = 2πrb where ‘b’ is the thickness of the completely confined aquifer. Substituting this expression for ‘A’ into Darcy's law gives: Q = -2πrbK dh/dl For steady flow, Q, the constant quantity of water pumped from the well, is also the flow rate through any cylindrical shell around the well. This equation can be solved by separating variables and integrating both sides of the equation. Separation of variables gives:
  • 52.
    There are twoobservation wells; Head is h1 at a distance r1 from the pumping well Head is h2 at a distance r2 from the pumping well

Editor's Notes

  • #50 Pumping rate is constant in pumping test/constant pumping test. In step draw down pumping rate variable.