Aquifers , Analysis of Groundwater Flow to Wells, Steady flow in a well, OPEN WELLS, WELL LOSS

1. MINI PROJECT ON GROUND WATER
FLOW TO WELLS
HYDROLOGY AND FLOOD CONTROL (CE-1206)
Bachelor of Technology, 6th
end-semester evaluation
Submitted by
Sayan Dey
Scholar I’d: 17-11-077
Course Instructor: Dr. Briti Sundar Sill
Assistant Professor
Department of Civil Engineering
NATIONAL INSTITUTE OF TECHNOLOGY SILCHAR
June 2020

2. ACKNOWLEDGEMENT
At this moment I feel grateful and loyal to our guide Dr. B.S.SIL for his
enthusiastic suggestions and kind help towards me in achieving
success of my Mini project. His constant encouragement and
invaluable share of his valuable time with me made such a difficult
task so easy. I take this opportunity to express my heartfelt gratitude
to all those who helped us in various ways during this mini project.
I would like to use this opportunity to express my gratitude to all the
faculty members of the Civil Engineering Department who played a
vital role in bringing and bringing me to this level.
Sayan Dey
(17-1-1-078)
Department of Civil Engineering
NIT Silchar

3. TABLE OF CONTENTS
1. INTRODUCTION
1.1 General
2. GROUND WATER EXTRACTION FROM AQUIFERS
3. ANALYSIS OF GROUND WATER FLOW TO WELLS
3.1 steady Flow-
➢ Confined Flow
➢ Unconfined Flow
3.2 Unsteady Flow-
➢ Confined Flow
➢ Unconfined Flow
4. APPROXIMATE EQUATIONS
5. OPEN WELLS
6. WELL LOSS
7. CONCLUSION
REFERENCES

4. INTRODUCTION
A well is an excavation or structure created in the ground
by digging, driving, or drilling to access groundwater in
underground aquifers.
The well water is generally drawn out by a pump, or using any
containers like buckets.
Aquifer-An aquifer is an underground layer of, rock fractures or
unconsolidated materials like Gravel, sand, or silt which is completely
saturated i. e water is in it and surrounding it.
➢ Confined aquifer-confined aquifer is an aquifer which is
confined between two impermeable layers and thus won’t
allow water to pass.
Well digged through confined aquifer is called Artisan well
➢ Unconfined aquifer- unconfined aquifer are those in which
water seeps from ground surface and is in contact with the
atmosphere.
Well through unconfined aquifer is called Non Artisan well

6. GROUND WATER EXTRACTION
FROM AQUIFER
• Consider the water in an unconfined aquifer pumped at a
constant rate from a well.
• Prior to the pumping, the water table in the well indicates the
static water table.
• During pumping, the water table level will lower down.
• Effect of pumping in wells-
1. Water table drawdown
2. A cone of depression will be formed.

8. Definitions-
• Drawdown - The fall of the Water Table elevation from its
static level in a well due to pumping.
• Cone of depression - The formation of conical shape of water
table surrounding the well due to the pumping of water.
• Area of influence - The areal extent of the cone of depression is
called area of influence.
• Radius of influence - maximum horizontal extend of the cone.
• Unsteady flow - Due to withdraw of water at the constant rate
of pumping the drawdown curve develops gradually with time,
this is called unsteady flow.
• Steady flow - An equilibrium state is achieved between rate of
pumping and rate of water inflow after continuous pumping
and is assumed to be in steady state.
After the pumping is stopped the cone of depression is recovered by
groundwater inflow into the zone of influence and is called
recuperation or recovery.
In case of confined aquifer similar phenomenon occurs except the
piezometric head that undergoes drawdown instead of water table.

9. Analysis of Groundwater Flow
to Wells
It consists of-
• Steady Flow -
1. Confined flow
2. Unconfined flow
• Unsteady Flow -
1. Confined flow
2. Unconfined flow

10. Steady flow in a well
Confined Flow-
Consider a well penetrating a confined horizontal confined aquifer
with following parameters as shown in figure below
Where,
B=thickness of aquifer
Q=steady flow discharge
H=original piezometric head
hw = piezometric head at pumping
sw = drawdown

11. At a radial distance r with h as piezometric head the velocity of flow
according to the Darcy law-
𝑽𝒓 = 𝑲
𝒅𝒉
𝒅𝒓
Hence discharge through cylindrical surface with this velocity of 2πrB
is given by –
𝑸 = (𝑲
𝒅𝒉
𝒅𝒓
) (𝟐𝛑𝐫𝐁)
Integrating the above equation with limits between r1 and r2 with
corresponding piezometric head h1 and h2 we get final equation as –
𝑸 =
𝟐𝝅𝑲𝑩(𝒉𝟐−𝒉𝟏)
𝐥𝐧
𝒓𝟐
𝒓𝟏
(1)
If the drawdown s1 and s2 are known then
S1=H-h1
S2=H-h2
KB=T
So the equation becomes –
𝑸 =
𝟐𝝅𝑻(𝒔𝟏−𝒔𝟐)
𝐥𝐧
𝒓𝟐
𝒓𝟏

12. Boundary condition-
At the edge of the zone of influence
h2 = H
r2 = R
s2=0
At the pumping well
h1 = hw
r1 = rw
s1 = sw
Thus the equation would be-
𝑸 =
𝟐𝝅𝑻(𝒔𝒘)
𝐥𝐧
𝑹
𝒓𝒘

13. UNCONFINED FLOW-
Radial Flow to a Well in an Unconfined Aquifer
The above figure shows a well of radius rw completely penetrating
an extensive unconfined horizontal aquifer.
• For unconfined groundwater flow some of the Dupit’s assumptions
is considered and these are-
1. If the water table is only slightly inclined, Flow lines can be
considered horizontal and parallel to impervious layer

14. 2. Slopes of the water table and hydraulic gradient are equal and
doesn’t vary with depth
The velocity of radial flow into the well is given by according to the
Darcy law-
𝑽𝒓 = 𝑲
𝒅𝒉
𝒅𝒓
Where,
h is the height of the water table above the aquifer bed at that
location
The cylindrical surface through which this velocity occurs is 2πrh
Hence discharge through cylindrical surface with this velocity of 2πrh
is given by –
𝑸 = (𝑲
𝒅𝒉
𝒅𝒓
) (𝟐𝝅𝒓𝒉)
Integrating the above equation with limits between r1 and r2 with
corresponding piezometric head h1 and h2 we get final equation as –
𝑸 =
𝝅𝑲(𝒉𝟐
𝟐
−𝒉𝟏
𝟐
)
𝒍𝒏
𝒓𝟐
𝒓𝟏
This equation also known as Dupit’s Equation

15. Boundary condition –
At the edge of the zone of influence of radius R , H= thickness of
saturated aquifer ,hw=depth of water into the pumping well with
radius rw above equation simplifies to-
𝑄 =
𝜋𝐾(𝐻2
−ℎ𝑤
2
)
ln
𝑅
𝑟𝑤
(2)
However the water table surface calculated from the above equation
which assumes Dupit’s assumption is lower than the actual surface.

16. Approximate equations
If the drawdown at the pumping well sw= (H –hw) is small
relative to H, then
H2
-hw
2
= (H + hw) (H - hw) ≈ 2Hsw
Above equation can be written as –
𝑸 =
𝟐𝝅𝑻(𝒔𝒘)
𝐥𝐧
𝑹
𝒓𝒘
(4)
Similarly, Eq. 1 can be written in terms of drawdown if the drawdown
s1 and s2 at the observation wells are known-
𝑸 =
𝟐𝝅𝑻(𝒔𝟏−𝒔𝟐)
𝐥𝐧
𝒓𝟐
𝒓𝟏
(3)
IMPORTANT NOTE:
Eq. 3 and Eq. 4 are approximate equations to be used only when Eq.
1 or Eq. 2 cannot be used because lack of data.

17. UNSTEADY FLOW IN A CONFINED AQUIFER-
The steady state flow condition is very difficult to achieve under field
condition as flow through pumping is mostly unsteady
The three dimensional ground water flow equation for confined
aquifer can be expressed in polar coordinate
-
The solution of the above equation is given as
𝒔 =
𝑸
𝟒𝝅𝑻
𝐥𝐧 [
𝟐. 𝟐𝑻𝒕
𝒓𝟐
]
Where S, T = aquifer constants
Lf s1 and s2 are drawdowns at time t1 and t2
𝒔𝟐 − 𝒔𝟏 =
𝑸
𝟒𝝅𝑻
𝐥𝐧 [
𝒕𝟐
𝒕𝟏
]
The graph between drawdown s and time t in semi log plane will be a
straight line for larger values of time.
Storage coefficient S can be determined from the slope of the line
and is given as-
𝑺 =
𝟐. 𝟐𝟓𝑻𝒕𝟎
𝒓𝟐
In which 𝑡0 = time corresponds to zero drawdown obtained by
extending the semi log portion of the s vs t curve.

18. OPEN WELLS
Open wells generally known as Dug wells and are used as drinking
water supply in small areas. They are constructed in shallow depth
aquifers. They may be rectangular or circular based on types of rocks
with depth of about 10 m.
They water enter into the well through joints, cracks or hole at the
bottom of the well
When the water is pumped out of the well, the water table inside the
well is lowered. The difference between the water table elevation
and the water table inside the well is known as depression head.
Discharge into the well is directly proportional to the depression
head H and is expressed as
𝑸 = 𝑲𝟎𝑯
• Where 𝐾0 is proportionality constant depend upon the area of
the well and aquifer characteristics also called as storage
capacity
• The depression head beyond which removing of soil particle
occurs due to the high flow velocity, it is called critical
depression head
• A working head with factor of safety between 2.5-3 is
considered and its corresponding yield (head) is known as safe
yield
The yield of open well can be determined by recuperation test.

19. Recuperation test
In a time interval Δt and a small change Δh in the water level
Q . Δt=𝑲𝟎H .Δt= -A . Δh
Where A is area of the well
In differential form
𝒅𝒕 = −
𝑨
𝑲𝟎
𝒅𝒉
𝒉
Integrating for a time interval Tr and a drawdown from H1 to H2 we
get final equation as-
𝑲𝟎
𝑨
=
𝟏
𝑻𝒓
𝐥𝐧
𝑯𝟏
𝑯𝟐

20. Where,
𝐾0
𝐴
= Ks =specific capacity per unit well area of the aquifer
𝐻1 = drawdown at the start of the recuperation, t=0
𝐻2 = drawdown at a time , t = 𝑇𝑟
h = draw down at any time t
Δh= decrease in drawdown at time Δt
The yield Q from an open well under a depression head H is obtained
as –
𝑸 = 𝑲𝒔𝑨𝑯

21. WELL LOSS
In a pumping artisan well the total drawdown (sw) at the well consist
of three parts –
1. head loss required to cause laminar porous media flow called
formation loss(swL)
2. Drop of piezometric head required to sustain turbulent flow in
the region nearest to the well where Reynold no. may be
greater than unity (swt)
3. Head loss through the well screen and casins (swc)
𝒔𝒘𝑳 ∝ 𝑸
𝒔𝒘𝒕 𝒂𝒏𝒅 𝒔𝒘𝒄 ∝ 𝑸𝟐
Thus
𝒔𝒘 = 𝑪𝟏𝑸 + 𝑪𝟐𝑸𝟐
Where 𝐶1 and 𝐶2 are constants for the given well.
First term 𝐶1𝑄 is termed as formation loss and second term 𝐶2𝑄2
is
termed as well loss
Abnormally high value of well loss is a sign of clogging of well screens
and thus requires immediate attention.

23. CONCLUSION
Ground water wells are very useful in water supply or for irrigation
practice. Water can also be injected back into the aquifer through
the well. An aquifer is a body of rock that can store water. It can be
unconfined or confined. Artesian well is a water well that does not
require pumping. The safe yield of an aquifer is the maximum rate of
extraction of water that does not produce a long-term decline in the
average water table level. A cone of depression is formed in the
water level around a well from which water is being pumped. The
steady state flow condition is very difficult to achieve under field
condition as flow through pumping is mostly unsteady. Well loss is
the difference of water level after drawdown to the actual water
level in well. A significant high well losses shows clogging of well
screen.
REFERENCES:
1. ENGINEERING HYDROLOGY BY K SUBRAMANYA
2. WIKIPEDIA